noble metals, noble metal halides and nonmagnetic transition metals

Ref. p. 12] 1.1 Historical remarks 1

L a nd o l t - B ö r ns t e inNew Series III/23C1

1 Introduction

1.1 Historical remarks

The photoelectric effect has been discovered already in 1887 by Heinrich Hertz [1887H], when heobserved that sparking of a spark gap was enhanced by ultraviolet light. Subsequent work [1888H, 1899T,1900L, 1902L] revealed that electrons were emitted whose maximum kinetic energy was proportional tothe frequency of the incident light, and whose number was proportional to the light intensity. In 1905Albert Einstein [1905E] published the quantum theory of the photoelectric effect, for which he receivedthe Nobel Prize in 1921. Several reviews give an account of the early and the further history ofphotoelectron spectroscopy [32H, 77J, 78C1, 82S1, 82S2, 88M]. After more than 100 years since itsdiscovery, we may state that the photoelectric effect and the many photoelectron spectroscopies based onit represent one of the most productive areas in solid state and surface science, with considerable impactalso to today's technology.

Modern photoemission spectroscopy, now representing one of the most important tools to investigatethe electronic structures of atoms, molecules, solids and surfaces (including interfaces), started 20 to 30years ago. Several important experimental developments contributed (among others) to the rapid progressof that field: The field of X-ray photoelectron spectroscopy (XPS) was pioneered by Kai Siegbahn and hisgroup, mainly by the development of high-resolution, high-sensitivity electron spectrometers and intensesoft X-ray line-sources (for details see Table 1, Section 1.3) [67S, 69S]. This work was awarded with theNobel Prize in 1981 [82S1]. The field of ultraviolet photoelectron spectroscopy (UPS) was pushedforward mainly by three advances: First, the development of windowless high-intensity uv-lamps such asthe HeI and the HeII line-sources (for details see Table 1, Section 1.3). Second, the advent of high-resolution, high sensitivity, electrostatic electron energy analyzers which allowed angle-resolved UPSinvestigations in reasonable times [82P, 83H, 84C]. Third, the availability of synchrotron radiation from"dedicated" storage rings as tunable, intense sources of linearly and/or circularly polarized photons [83K].This instrumental progress allowed to develop experimental methods to measure both the energy and themomentum of the electrons, i.e. to map the electronic energy band structure along many k-space directions[82P, 83H, 84C, 92K, 95H1].

For the future we may predict further progress in the field of photoelectron and related spectroscopies.A new generation of dedicated sychrotron radiation sources is now available. These are based on magneticinsertion devices (wigglers, undulators) and improved monochromator concepts [97P1]. They supply uswith very intense, high-brilliance radiation of simultaneously high energy-resolution and tunablepolarization. These sources will allow measurements to be performed with photons in the energy range upto about 1 keV at high photon energy resolution (10...100 meV), high lateral resolution (10...100 nm) andspectroscopically relevant temporal resolution (pico- to nanoseconds). In conclusion, these sources willenable us to collect data like those presented in this volume at, however, much improved resolution andaccuracy. This statement refers to core-level spectroscopy as well as to symmetry-resolved mapping ofenergy bands.

We may summarize that after more than a century of photoemission studies [95B] the kinematics ofthe photoemission process is well understood. This refers to both one-photon photoemission [92K, 95H1]and two-photon photoemission [95F, 95S]. Provided good quality single-crystals as well as recipes toprepare surfaces with the desired stoichiometry and sufficient lateral order are available, the determinationof energies and energy bands is now almost routine using tunable photon sources. This business, however,is only the lower level of every spectroscopy. The higher and more sophisticated level concentrates onmeasurement and understanding of line shapes [98H, 98M, 99H, 99V, 00L, 00M] and peak intensities

2 1.2 Arrangement of data, 1.3 Definition of quantities [Ref. p. 12


[98M, 99M, 01P]. In the last few years photoelectron spectroscopy has progressed to a point [98H, 98P,99V, 00R], where these quantities are no longer exclusively determined by experimental resolutionconstraints, but also by the "intrinsic" quantities like photohole-lifetime [98H, 00C2, 00P, 01G, 01Z, 02G,02Z] and the lifetime of the excited electron [00C1, 00E, 00P, 02B]. Spoken more generally, the lineshape may give detailed information on the dynamics of the solid as a correlated many-particle system,including electron-electron [97P3, 00C1, 00E] and electron-phonon [99H, 99P, 99V, 00L, 00R]interactions. This development opens up a completely new field which recently got additional impetus bythe advent of two-photon photoelectron spectroscopies with time-resolution on the femtosecond scale[95H2, 96O, 97O, 97P2, 97P3, 97W, 98A, 98K, 00E, 00P]. Moreover, free-electron-lasers with high-intensity and high-brilliance specifications will be operating in the near future. We may thereforeanticipate further progress in photoelectron and related spectroscopies.

1.2 Arrangement of data

Each chapter has a separate introduction referring to special aspects of the materials under consideration.Within each chapter the organisation is as follows. First, general data (as far as available) are summarizedon crystal structure, electronic configuration, work functions, plasmon energies, core level bindingenergies, valence band critical point energies, and other relevant quantities. Then diagrams are collectedreproducing angle-integrated as well as angle-resolved valence-band and core level spectra, calculatedenergy bands and corresponding densities of states, and in particular experimental electron energydispersion curves E(k). When considered necessary, also optical spectra and results obtained with otherexperimental techniques are shown to supplement the electronic structure information.

Figures and tables within Chaps. 2.9, 2.10 and 2.11 are numbered consecutively through theirsubsections.

In the tables of this volume, experimental errors are given in parentheses referring to the last decimalplaces. For example 1.23(45) stands for 1.23 ± 0.45 and 9.9(11) stands for 9.9 ± 1.1.

1.3 Definition of quantities

Two features of photoemission spectroscopy (PES) and its time-reversed counterpart, inversephotoemission spectroscopy (IPES) are of particular interest: First, initial and final state energies ofradiative transitions are directly determined by the experiment. Other methods, e.g. light absorption orreflection, can in general only determine the energy difference between initial and final state. Second, theelectron momentum k may be determined in angle-resolved experiments using single-crystal samples.The schematics of PES and IPES are shown in Fig. 1. PES and IPES can supply information on theelectron energy eigenvalues E(k) and their dependence on the electron wave vector k. As is evident fromFig. 1, the combination of both techniques can investigate all energy bands below and above the Fermilevel at EF.

Ref. p. 12] 1.3 Definition of quantities 3


Fig. 1. Schematics of photoemission (top) and inverse photoemission(bottom). The angles of photon (α) and electron (θ) are defined with respectto the surface normal. The shaded region of the energy band structure isaccessible to the respective technique. Radiative transitions occur betweeninitial state | i⟩ and final state | f⟩.

It is not intended here to describe the techniques and theories of PES and IPES in detail, since manyexcellent reviewing articles and detailed monographs are available [70T, 72S, 77B, 77I, 78C1, 78C2,78C3, 78F, 79B, 79C, 80W, 83D, 83S, 83W, 84B, 84D, 85D, 86H, 86S, 87B, 87L, 88S, 95S]. Therefore,only a very brief overview of the methods will be given. The typical PES [82P, 83H, 84C, 92K, 95H1]experiment is illustrated in Fig. 1. Photons of energy ω impinge on the sample. If a photon is absorbed inan occupied state | i⟩, at energy Ei below the Fermi level EF (Ei = 0 at EF), an electron is excited into an

empty state | f⟩ at energy Ef. Energy conservation requires Ef − Ei = ω (The sign convention used in thisvolume is summarized in Fig. 2). If Ef > Evac, the energy of the vacuum level, the electron in the excitedstate may leave the sample. The emitted electrons are then analyzed with respect to their intensity, kineticenergy Ek, and other variables of interest like: direction and polarisation of incident light, emissiondirection of electrons with respect to incident photon direction and/or with respect to the crystal latticecoordinates, and (sometimes) the electron spin-polarization [85K, 86F, 94D]. PES gives thus informationon the occupied states below EF and empty states above Evac. Energy conservation states that ω = Ef − Ei

= Ek + φ − Ei, where φ = Evac − EF is the work function. If φ is known [79H] or measured (the width of the

experimental photoelectron distribution is given by ω − φ, compare Fig. 3) both Ei and Ef are uniquelydetermined. IPES [83D, 83W, 84D, 85D, 86H, 86S, 88S] is illustrated in Fig. 1 (bottom). The electron at

4 1.3 Definition of quantities [Ref. p. 12


Ei = Ek + φ impinges on the crystal, penetrates the surface and enters the previously empty state | i⟩ at Ei >Evac. By emission of a photon, the state at Ei is connected with state | f⟩ at Ef ≥ EF = 0. The emitted photon

of energy ω is registered in an energy-resolving detector [84D, 86H, 86D, 86S]. Again, Ei and Ef aredetermined by the kinematics of the experiment.

Fig. 2a. Sign convention for energies in case ofmetallic samples, where the position of EF is clearlyobserved in the photoelectron spectra. If not statedotherwise, the energy zero is at EF. In the literature onPES, the term "binding energy" is often used, with theconvention that | Ei | = Eb ≥ 0.

Fig. 2b. Sign convention for energies in case ofsemiconductors and/or insulators, where in general theupper valence band edge at EVBM (valence bandmaximum) is better defined in the experimental spectrathan the position of EF. If not stated otherwise, theenergy zero is at EVBM. In the literature on PES, theterm "binding energy" is often used, with theconvention that | Ei | = Eb ≥ 0.

Most PES experiments measure an electron distribution curve (EDC), i.e. the number I(Ek) of emitted

electrons, see Fig. 3. If ω is sufficiently large, emission out of core levels is observable. The area of thecorresponding peak (shaded in Fig. 3, and superimposed to a continuous background of inelasticallyscattered electrons) is proportional to the number of emitting atoms. Its energy Ei identifies the emittingelement and very often ("chemical shift") also the chemical environment. Emission from occupied valencestates in PES or into empty valence states in IPES yields information on the density of states. In general,however, even the angle-integrated EDC does not directly reflect the density of states D(Ei), as idealizedin Fig. 3. In the following we will discuss this point for PES in some detail. Angle-integrated PES of bulkstates can transparently be described by a three-step model [68S] (for more refined treatment we refer to[83H, 84C, 92K, 95H1]): photoexcitation of an electron, travelling of that electron to the surface, andescape through the surface into the vacuum. Beyond the low-energy cutoff at Evac travelling through thesolid and escape are described by smooth functions of E and will not give rise to structure in I(Ek).Therefore primarily the photoexcitation process determines the shape of the EDC. For bulk states, where



crystal momentum k is a quantum number conserved in the reduced zone scheme ("vertical transitions"in Fig. 1) we then find for the distribution of photoexcited electrons

I(Ek, ω) ≈ ∫∑i f,

d3k |⟨f | p | i⟩|2 · δ1 . δ2 (1)

where δ1 = δ{Ef(k) − Ei(k) − ω} and δ2 = δ{Ef(k) − φ − Ek}, and the k-space integral is to be extendedonly over occupied states | i⟩. The δ1-function assures energy conservation, while δ2 selects from all

transitions possible with photons of energy ω only those that are registered by the electron energyanalyser. If we take for the moment the transition matrix element Mfi = ⟨f | p | i⟩ to be constant, eq. (1)reduces to the so-called energy distribution of the joint density of states

I (Ek, ω) ≈ ∫∑i f,

d3k · δ1 . δ2 (2)

Fig. 3. Illustration of the fact that in angle-integratedPES the density of occupied states D(Ei) is oftenapproximately reflected in the emitted electron energydistribution curve I(Ek).

We will then expect that at low photon energies (typically ω < 20 eV) the angle-integrated EDC doesgenerally not reflect the density of occupied states, since only few final states for photoexcitation areavailable. However, at increasing ω, the number of accessible final states increases and the intensitymodulation through these | f⟩ states becomes less important. The EDC will then progressively become areplica of the initial density of states (DOS), as long as Mfi = constant. If Mfi is not constant, the EDCrepresents the initial DOS modulated by the matrix element varying in k-space. Similar considerations areapplicable to IPES.

The experimental method for mapping Ei(k) is angle-resolved PES, with vacuum-ultravioletexcitation radiation [82P, 83H, 84C]. While Ei and Ef are easily determined, a problem [82P, 83H, 84C,92K, 95H1] arises with k. Upon penetration of a single-crystal surface by an electron only k||, the wave-vector component parallel to the surface, is conserved and directly obtainable from the kinematicalparameters: k|| = sinθ (2m/ 2)l/2 Ek

l/2, where m is the free electron rest mass. The investigation of bulkstates E (k||, k⊥) requires additional information on k⊥ which is not conserved. In most PES experimentsreasonable assumptions were therefore made (e.g. "free-electron-like", i.e. parabolic final state bands[82P, 83H, 84C, 92K, 95H1]) to extract k⊥ from one EDC. However, several (albeit time-consuming andtedious) "absolute" methods may also be applied to determine the full wave-vector (k||, k⊥) experimentallyfrom at least two ECD's viewing the k-space from different directions. A detailed discussion of suchmethods has been presented in [82P, 83H, 84C, 92K, 95H1]. For a most elegant new strategy of bandmapping, which provides full control of the three-dimensional k-vector, see [00S, 01S].



Photoelectric cross sections at 1.5 keV for atomic levels are shown in subvolume a, see Fig. 3 ofsection 2.5 (see also Fig. 13 of section 2.8 in subvolume b). Data for other excitation energies can befound in [81G, 76S]. Calculated partial photoionization cross sections in the energy region 0...1500 eVare given for all elements Z = 1...103 in [85Y]. A list of line sources commonly used in laboratory PES isgiven in Table 1.

Table 1. Commonly used line sources for photoelectron spectroscopy [78C1].

Source Energy[eV]

Relativeintensity

Typical intensity atthe sample[photons s–1]

Linewidth[meV]

He I 21.22 100 1 ⋅ 1012 3Satellites 23.09, 23.75, 24.05 < 2 eachHe II 40.82 20a) 2 ⋅ 1011 17

48.38 2a)Satellites 51.0, 52.32, 53. 00 < 1a) eachNe I 16.85 100 8 ⋅ 1011

16.67Ne II 26.9 20a)

27.8 10a)30.5 3a)

Satellites 34.8, 37.5, 38.0 <2 eachAr I 11.83 100 6 ⋅ 1011

11.62 80...40a)Ar II 13.48 16a)

13.30 10a)Y Mζ 132.3 100 3 ⋅ 1011 450Mg Kα1, 2 1253.6 100 1 ⋅ 1012 680Satellites Kα3 1262.1 9

Kα4 1263.7 5Al Kα1, 2 1486.6 100 1 · 1012 830Satellites Kα3 1496.3 7

Kα4 1498.3 3

a) Relative intensities of the lines depend on the conditions of the discharge. Values given are therefore onlyapproximate.

Photoelectron spectroscopies and related or complementary techniques are looking through aparticular surface into the bulk of a solid material. Therefore unavoidably surface and bulk informationare superimposed in the experimental data. Although this volume concentrates on the electronic bulkproperties (for detailed information on the surface electronic and geometric properties see Landolt-Börnstein III/24a-d) careful inspection of the spectra as well as sufficient understanding of the literaturequoted in this volume require some understanding of the surface as well. To support the reader wereproduce the relevant bulk and surface Brillouin zones in Figs. 4 - 10.

For further details concerning unit cells, reciprocal lattices and first Brillouin zones see Landolt-BörnsteinIII/13c, p.451.



Fig. 4. fcc(100). (Bottom) Bulk Brillouin zone (BBZ)and (top) Surface Brillouin zone (SBZ) showing theprojection of the bulk onto the (001) surface. The bulkvectors are given by ΓX = [1,0,0] (2π/a), ΓL = [½, ½,½] (2π/a), ΓK = [¾, ¾, 0] (2π/a), ΓW = [1,½,0] (2π/a)where a is the lattice constant.

Fig. 6. fcc(111). (Bottom) BBZ and (top) SBZ showingthe projection of the bulk onto the (111) surface.

Fig. 5. fcc(110). (Bottom) BBZ and (top) SBZ showingthe projection of the bulk onto the (110) surface.



Fig. 7. bcc(100). (Bottom) BBZ and (top) SBZshowing the projection of the bulk onto the (001)surface. The bulk vectors are given by ΓH = [0,0,2](π/a), ΓN = [1,1,0] (π/a), ΓP = [1,1,1] (π/a) where a isthe lattice constant.

Fig. 8. bcc(110). (Bottom) BBZ and (top) SBZshowing the projection of the bulk onto the (110)surface.

←Fig. 9. bcc(111). (Bottom) BBZ and (top) SBZshowing the projection of the bulk onto the (111)surface.



Fig. 10. hcp(0001). (Bottom) BBZ and (top) SBZshowing the projection of the bulk onto the (0001)surface.

Fig. 11. hcp(1010). (Bottom) BBZ and (top) SBZshowing the projection of the bulk onto the (1010)surface.

10 1.4 Frequently used symbols


1.4 Frequently used symbols

Symbol Unit Property

a, b, c Å lattice parametersDOS eV−1atom−1, density of states

eV−1atom−1spin−1,atom−1Ry−1

e C elementary chargeE eV, Ry energy

Eb binding energy (Eb ≥ 0)EF Fermi energyEf final state energy (of radiative transition), (Ef ≥ 0)Eg energy gap, band gapEi initial state energy (of radiative transition), (Ei ≤ 0 in

PES, Ei > 0 in IPES), electron incidence energyEk kinetic (photoelectron) energyEvac vacuum energy levelEVBM energy of valence band maximum

∆E eV energy resolutionfi Phillips ionicityI arb. units, counts s−1 intensity in spectral distributionk Å−1 wavevector (of electrons)

k||, k⊥ wavevector components parallel and perpendicularto the surface

kF Fermi surface radiusNOS electrons atom−1 number of statesR reflectivityT K, °C temperatureZ atomic number

α cm−1 absorption coefficientα deg angle of incidence of photons in PES, photon

emission angle in IPESΓ center of Brillouin zoneΓe, Γh inverse life time of electrons, holes

ε2 imaginary part of dielectric constant

q deg angle of incidence of electrons in IPES, electronemission angle in PES

ν s−1 frequencyhν eV photon energyσ b cross sectionσ s−1 optical conductivityφ eV work function φ = Evac − EF

ω rad s−1 circular frequencyωp plasmon frequency

ω eV photon energy

1.5 List of abbreviations 11


1.5 List of abbreviations

APS appearance potential spectroscopyAPW augmented plane wave (method)arb arbitraryARIPES angle resolved IPESARUPS angle resolved ultraviolet photoemission spectroscopyASW augmented spherical wave (method)B, b bulkbcc body centered cubicBG backgroundBIS bremsstrahlung isochromat spectroscopyBZ Brillouin zoneCIS constant initial state (spectroscopy)DOS density of statesfcc face centered cubicFWHM full width at half maximumhcp hexagonal close packedIPES inverse photoemission spectroscopyKKR Kohn-Korringa-Rostoker (method)KKRZ KKR (method) modified by ZimanLAPW linearized augmented plane wave methodLCAO linear combination of atomic orbitalsLDA local density approximationLEED low energy electron diffractionLEER low-energy electron reflectionLMTO-ASA linearized muffin-tin orbital-atomic sphere approximationMTO (linear) muffin-tin-orbital (method)NOS number of statesPE(S) photoemission (spectroscopy)pol polarizedRAPW relativistic APWRS-LMTO-ASA real-space LMTO-ASA (method)RT room temperatureRy Rydberg (1Ry = 13.605 eV)S, s surfaceSEE secondary electron emissionUHV ultra high vacuumUPS ultraviolet photoemission spectroscopyUV ultravioletVBM valence band maximumw.r. with respectXPS X-ray photoelectron spectroscopy⊥, || perpendicular, parallel to a crystallographic axis

12 1.6 References for 1


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00L LaShell, S., Jensen, E., Balasubramanian, T.: Phys. Rev. B 61 (2000) 2371.00M Michalke, T., Gerlach, A., Berge, K., Matzdorf, R., Goldmann, A.: Phys. Rev. B 62 (2000)

10544.00P Petek, H., Nagano, H., Weida, M. J., Ogawa, S.: Chem. Phys. 251 (2000) 71.00R Reinert, F., Nicolay, G., Eltner, B., Schmidt, S., Hüfner, S., Probst, U., Bucher, E.: Phys. Rev.

Lett. 85 (2000) 3930.00S Strocov, V. N., Blaha, P., Starnberg, H. I., Rohlfing, M., Claessen, R., Debever, J.-M.,

Themlin, J.-M.: Phys. Rev. B 61 (2000) 4994.01G Gerlach, A., Berge, K., Goldmann, A., Campillo, I., Rubio, A., Pitarke, J. M., Echenique, P.

M.: Phys. Rev. B 64 (2001) 085423.01P Pforte, F., Michalke, T., Gerlach, A., Goldmann, A.: Phys. Rev. B 63 (2001) 115405.01S Strocov, V. N., Claessen, R., Nicolay, G., Hüfner, S., Kimura, A., Harasawa, A., Shin, S.,

Kakizaki, A., Starnberg, H. I., Nilsson, P. O.: Phys. Rev. B 63 (2001) 205108.01Z Zhukov, V. P., Aryasetiawan, F., Chulkov, E. V., Gurtubay, I. G., Echenique, P. M.: Phys. Rev.

B 64 (2001) 195122.02B Berge, K., Gerlach, A., Meister, G., Goldmann, A., Braun J.: Surf. Sci 498 (2002) 1.02G Gerlach, A., Berge, K., Michalke, T., Goldmann, A., Müller, R., Janowitz, C.: Surf. Sci. 497

(2002) 311.02Z Zhukov, V. P., Aryasetiawan, F., Chulkov, E. V., Echenique, P. M.: Phys. Rev. B 65 (2002)

115116.

Ref. p. 79] 2.9 Noble metals (Introduction)

L a nd o l t - Bö r ns t e inNew Ser ies III/23C1

15

2 Data

(Chap. 2.1-2.5 see subvolume 23A, 2.6-2.8 see subvolume 23B, 2.12 see subvolume 23C2)

2.9 Noble metals

2.9.1 Introduction

The noble metals have played a central role in the elucidation of the electronic structure of solids, inparticular in the development of angle-resolved photoemission and related experimental techniques, andthey provided a testing ground for our theoretical understanding of non simple elements involvingelectronic d-bands. Some of the reasons for this role are of experimental nature: sizable single crystals ofsufficient quality were available, recipes to prepare the low-index surfaces were known and these surfacesare relatively inert (as compared to other materials) with respect to the residual gas in ultrahigh vacuumenvironment. Moreover, the noble metals show clear and intense photoelectron structures which are notobscured by collective (e.g. plasmon) excitations. Also Cu, Ag and Au represent a series of isostructuraland isoelectronic elements which allow to study the influence of relativistic effects in considerable detail.Finally the interpretation of the electronic structure is not additionally complicated by magnetic effects.

In particular Cu has been a "drosophila" of photoemission techniques. Significant experimentalprogress has been demonstrated first at low-index copper surfaces. Quite early polarization dependentphotoemission results [71G, 76D, 78D1] implied the occurrence of direct, k-conserving transitions and nosignificant scattering for a large fraction of those excited electrons which leave the crystal. Systematicband mapping used copper single crystals [78E, 79K1, 79K2, 79T, 81H1] and presented directdeterminations of the energy-dependent inverse lifetimes Γe(Ef) of a bulk band [78E] and of the photoholelifetime Γh(Ei) [79T]. Later on a long and fruitful series of investigations started to explore the linewidthsof higher lying final bands, and their damping that makes final state gaps almost disappear and mimicsbands with a nearly-free-electron shape [79H2, 79N, 82G1, 83S]. Much of the pioneering work has beenreviewed in detail elsewhere [84C].

This chapter collects data mainly on energy positions of core levels and band dispersions and presentsrepresentative spectra demonstrating photon-energy dependence and variation with electron emissionangle along high-symmetry (mirror-plane) azimuths. For the interpretation of this material it might beuseful in some cases to use additional sources of information. Therefore we give here some (necessarilyincomplete) listing of references. Comprehensive information on light-polarization effects is found e.g. in[77H, 78S, 79R, 80E, 81B, 95H, 98G, 99M, 00M, 01P]. The influence of Γh(Ei) and Γe(Ef) on measuredlinewidths is discussed in great detail by [92S2, 93S1, 98M1, 00C3, 02B], experimental and calculatedwidths are collected in [91G, 94M2, 99P1, 00C3, 00E, 00P1, 01G, 01Z, 02B, 02G, 02Z]. See also [98H].The influence of experimental parameters like energy-resolution, angular resolution and finite sampletemperature is carefully discussed in [98M1], including many references to earlier work; see also [00K,00N]. The experimental determination of Fermi surfaces using photoemission techniques is a very recentdevelopment and is described in [94A, 95H, 95Q, 98A]. Two-photon photoemission studies, operatingeither in the energy domain or using time-resolved (pulse-probe) techniques down to the femtosecondscale, have started to explore the dynamics of excited ("hot") electrons [97O, 97P1, 97P2, 97W, 98K,98P, 00E, 00P1]. However, these results go beyond the scope of the present volume and are therefore notincorporated systematically in this book.

All data refer to room-temperature samples unless stated differently.

http://dx.crossref.org/10.1007/10714318_6

























































2.9 Noble metals (Cu) [Ref. p. 79


16

2.9.2 Cu (Copper) (Z = 29)

Lattice: fcc, a = 3.61 Å [63W].Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Ar)3d104s1

Work-function [78C2, 79H4]:φ (100) = 4.59 eVφ (110) = 4.48 eVφ (111) = 4.94 eVφ (poly) = 4.65 eV

Typical errors are ±0.15 eV.

Table 1. Cu. Core-level binding energies in eVrelative to EF [78C2, 92F, 95H]. Typical scatterbetween various sources is ± 0.1 eV.

Level n = 2 n = 3

ns1/2 1096.7 122.5np1/2 952.5 77.4np3/2 932.5 75.2

For core-hole lifetime broadenings see [92F].

Table 2. Cu. Occupied valence bands. Comparison of experimental and theoretical determination of thesymmetry points Γ and X in the BZ. Energy values are given in eV w.r. to EF . Experimental errors are± 0.03 eV if not explicitly given in parentheses. Symmetries are given in double (single) point groupnotation.

Symmetry ARUPS ARUPS ARUPS ARUPS ARUPS TheoryPoints [79T] [78D2, 79D] [79K2] [84C] [84E]

Γ8+(12) –2.80 –2.75 –2.85 –2.79 –2.85(10)1) –2.73

Γ7+(25) –3.50 –3.56 –3.65 –3.42 –3.40(10)1) –3.34

Γ8+(25) –3.50 –3.56 –3.65 –3.60 –3.70(10)1) –3.54

Γ6+(1) –8.60 – – – – –8.75

X7+(5) –2.00 –2.05 –2.05 –1.95 –2.032,3) –2.01

X6+(5) – –2.15 – –2.12 – –2.16

X7+(2) –2.30 –2.35 – –2.30 –2.353) –2.33

X7+(3) –4.80 –4.80 –4.50 –4.78 – –4.63

X6+(1) –5.15 –5.20 –5.20 –5.14 – –5.14

1) [89W1]. 2) [83W]. 3) [79H1].

For a detailed comparison of differently calculated Γ and X points see [79K2]. For d-hole lifetimes at Γ,L and X see [99P2, 00C2, 00P1, 01G, 01Z, 02Z]. See also [01S1] for a band-mapping experiment withabsolute determination of wavevectors.

























Ref. p. 79] 2.9 Noble metals (Cu)


17

Table 3. Cu. Occupied valence bands. Comparison of theoretical and experimental energies at K and L.For details see legend to Table 2.

Symmetry Theory [84E] Experimental (ARUPS)Points

K5(2) –2.26 –2.15 1,4) , –2.13 6)

K5(4) –2.66 –2.50 4) , –2.66 6)

K5(3) –3.06 –2.95 4) , –3.3 2)

K5(1) –4.24 –4.5 1,2) , –4.40 6)

K5(1) –4.59 –4.60 4) , –4.68 6)

L6– (2') –0.39 –0.9(1) 3), –0.85 5)

L4+,5+(3) –2.21–2.25 (10) 3,4)

L6+(3) –2.32L6+(3) –3.41

–3.7 (1) 3,4)

L4+,5+ –3.62L6+(1) –5.04 –5.15 (10) 6)

1) [78D2]. 2) [79D]. 3) [79K2]. 4) [79T]. 5) [82L]. 6) [84C].

Table 4. Cu. Unoccupied bands of the bulk BZ. Energies of symmetry points are given in eV relative toEF. Symmetries are given in double (single) group notation.

Symmetry points Theory Theory*) Theory *) Experimental[63B] [75J] [84E]

Γ(2') 23.3 24.2 23.8 23.7(5) 1) *)

Γ(15) 24.6 26.4 25.8 26.5(5) 1) *)

Γ(25') 28.3 – 28.5 28.5(5) 1)*)

L(1) 3.94 4.1 3.8 4.1 2)

L(2') 21.4 22.2 21.521.9 3)*)

L(3') 25.7 23.3 22.7

X6– (4') 2.03 2.02 2.21 2.3(3) 4)

X6+(1) 7.29 7.5 6.74 7.4(4) 5), 7.5(5) 6) , 7.9(2)7)

X6–(5') 13.6213.4 13.8 13.5(5) 3)*), 13.6 8)

X7–(5') 13.81X7+(3) 18.5 18.6 18.1 18.1(5) 3)*), 18.6 8)

X6+(1) 20.2 21.7 20.1 19.7(5) 4)

*) Data taken from a figure. See also [01S1].1) [82J]. 2) [82L]. 3) [84C]. 4) [88A]. 5) [83D]. 6) [84Z]. 7) [79K2]. 8) [79D].

Fermi surface radii (in units of 2π/a): kF [100] = 0.827, kF[110] = 0.743 [82C]. For Fermi surfaces see alsoLandolt–Börnstein, New Series, Group III,Vol. 13c (1984), p. 116. For information on the surfaceelectronic properties see Landolt–Börnstein Vol. III/24b and Vol. III/24d.























18

Figures for 2.9.2

102

10

1

10−1

10 −2

10−3

10−4

0 200 400 600 800 1000 1200 1400

Cu

3d

3s

2p3p

2s3s

3d4s

Photon energy [eV]hω

Cros

s sec

tion

[M

b]σ

Fig. 1. Cu. Atomic subshellphotoionization cross sections forphoton energies from 0 to 1500 eV[85Y].

1000 900 800 700 600 500 400 300 200 100 0

Cu

Cu(2p )3/2

Cu(2p )1/2

Cu(LMM)MgKα

Cu(3s)Cu(3p)

CuVB

(×4)

Binding energy [eV]Eb

[eV]Eb

IIn

tens

ity

()/

EE

bb

I

Cu(LMM) L VV335.0

3

L M V414.2

3 23

406.8L M V395.0

2 23L VV315.0

2

L M M486

3 23 23

479

500 450 400 350 300

Fig. 2. Cu. Overview XPS spectrum.The insert shows a blow-up of theCu(LMM) Auger-electron spectrum[79W1]. Data taken withunmonochromatized MgKα radiation.Eb w.r. to EF.

Cu


IIn

tens

ity

2p1/2

2p3/2

19.8

975 965 955 945 935 925

Fig. 3. Cu. XPS data showing theregion of the spin-orbit-split 2p core-levels taken with unmonochromatizedMgKα radiation [79W1]. Eb w.r. toEF.






19

3.8

3.4

3.0

2.6

2.2

1.890 85 80 75 70 65

Cu

IIn

tens

ity

[arb

.uni

ts]


Fig. 4. Cu. XPS spectrum of the spin-orbit-split 3p corelevels, taken with unmonochromatized MgKα radiation(hν = 1254 eV) [73H]. Eb w.r. to EF.

Cu

IIn

tens

ity

[arb

.uni

ts]

0 2 4

1.0

0.8

0.6

0.4

0.2

0

Initial state energy [eV]E i

−2−4−6−8−10

EF

Fig. 5. Cu. XPS spectrum of the valence band obtainedwith monochromatized (0.5 eV) AlKα radiation (hν =1487 eV) [73H].

IIn

tens

ity


0 = EF−2−4−6

Cu

He (48.4 eV)

He (40.8 eV)

He I

II

II

Fig. 6. Cu. Photoelectron spectra obtained frompolycrystalline samples at different photon energies hν.Energy resolution ∆E = 80 meV at hν = 40.8 eV and 30meV at 21.2 eV [77B]. For further experimental datataken at hν between 9 eV and 26 eV and a comparisonto theoretical photoemission energy distributions see[75J].

Cu

Energy [eV]E E− F

IIn

tens

ityDO

S

EF0 = 2 4 6 8 10

0

0

Fig. 7. Cu. Top: Experimental bremsstrahlungisochromat spectrum (photon energy hν = 1486.7 eV,total resolution 0.7 eV). Bottom: Calculated density-of-states. Dashed without broadening, solid line includingbroadening to simulate instrumental and lifetime widths[84S].








20

Energy [eV]E

DOS

[sta

tes /

eV

atom

]⋅

DOS

[sta

tes /

eV

atom

]⋅

3

2

1

0

−10 −5 0 5 10 15

0

0.1

0.2

0.3

Cu

Fig. 8. Cu. Comparison of experimentally determineddensities-of-states (solid lines) with theoreticalcalculations (dashed lines). The left-hand vertical scalerefers to the occupied valence states, while the right-hand scale refers to the empty conduction states [82D].

Cu

Energy [eV]E

IIn

tens

ity

DOS

EF10 20 30 40 50 60 70

BIS

DOS

Fig. 9. Cu. Bremsstrahlung-isochromat spectrum takenat hν = 1486.7 eV (full circles) and calculated density-of-states (thin line: unbroadened, thick line: broadenedto take experimental resolution and life-time width intoaccount). The correspondence of structures in themeasured spectrum with features in the broadened DOSis indicated. [85S]. See also [92F].


Refle

ctiv

ityR

Cu

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 10. Cu. Experimental normal-indicence reflectivitydata [81W] obtained from different experiments. Fordetails and tables of the "most recommended", data see[81W]. See also [85P, 01S2]. For surface opticalproperties see [00M, 00P1].


Cu

0 5 10 15 20 25 30

20

15

10

5

Diel

ectri

c con

stan

tε2

10 2ε

Fig. 11. Cu. Experimental ε2 spectra [81W] obtainedfrom different experiments. For details and tables of the"most recommended" data see [81W]. See also [85P,01S2].
















21

Wavevector k

Ener

gy[R

y]E

EF

Σ

-0.039

-0.539

-0.939

Cu

Γ Γ∆ Z Q ΛX W L K

1’

1’1

1

1 1

1

11

1

22

2

3

3

33

3

3

34

44

2’2’

2’

5

5

3

3

3

1

1

1

1

1

11

1

2 2

1

25’

12

Fig. 12. Cu. Energy bands along high-symmetry directions of the bulkBrillouin zone using Chodorow's potential for d-electrons and Slater'sAPW method [63B]. See also [75J, 78M] for results of a selfconsistentnonrelativistic KKR calculation. Symmetries given in single group notation.

Wavevector k

Ener

gy[R

y]E

EF

Σ

Cu


1’

1 1

11

1 1

1

1

1

1

1

1

2 2

2

3

3

3

33

3

33

3

3

4

4

4’

4

4

2’

2’

2’

2’

2’

2’

5

5

5’

5

33

3

3’

1 1 1

1

1

11

1

1

1

2

2

1

2.061

1.061

0.061

-0.939

+

3

1

1

43

1

2’15

25’

25’

12

Fig. 13. Cu. Energy bands, showing the continuation of Fig. 12 to higherenergies above EF [63B]. Dashed bands obtained by numerically lessaccurate interpolation. See also [75J, 78M] for results of a selfconsistentnonrelativistic KKR calculation. Symmetries given in single group notation.









22

Wavevector k

Ener

gy[e

V]E

EF

Cu

Γ ΓX XW L K,U

28

24

20

16

12

8

4

0

− 4

− 8

Fig. 14. Cu. Band structure calculatedby a second-principles method using acombined interpolation scheme[81L2].

EF

Cu

Energy [eV]E- EF

5

4

3

2

1

0-10 -5 0 5 10 15 20 25

1.0

0.5

0

L(8)X(8)

W(8)X(7)L(7)X(6)

X(9)

(×4)

DOS

[ele

ctro

ns/a

tom

eV]

⋅

DOS

[ele

ctro

ns/a

tom

eV]

⋅

Fig. 15. Cu. Density-of-stateshistogram calculated with thecombined interpolation scheme andthe band structure of Fig. 14. High-symmetry ciritical-point locations areindicated [81L2].

Diel

ectri

c con

stan

tε2


7

6

5

4

3

2

1

0 4 8 12 16 20 24 28

Cu

Fig. 16. Cu. Calculated ε2 spectrum (solid line) incomparison with experimental data (dots). Thecalculations were performed using a combinedinterpolation scheme and include spin-orbit effects andmomentum matrix elements [81L2]. See also [01S2].







23

Wavevector k

Ener

gy[e

V]E

EF

Σ

Cu

Γ Γ∆ Z Q ΛX W L K55

S X

4

2

0

−2

−6

−8

−10

6

78+

7 6

7

6

6+

8+7 +

5

6-

7+

6+

7+

7 +

6+

76767

6+

6-6

4+56

4+5 6

6+

6+

6

6+

8+

7+

8+

5

6-

7 +

6+

7 +

7+

6+

4 +5+ +

4 +5+ +

3+4

Fig. 17. Cu. Relativistic band structure along high-symmetry directions.The calculation rests on Kohn-Sham-type relativistic one-particleequations with a local exchange-correlation potential [84E]. For anextended-LAPW-based complex band structure calculation see [95K].For metastable bcc Cu see [02T]. Symmetries given in double groupnotation.

Wavevector k

Ener

gy[e

V]E

EF

Σ

Cu


1’

1

1

1

1

1

1

1

1

22

2

2

2

3

3

3

3

3

4

4’

4

2’

2’

2’

2’

5

5

5’

3

3

3

1

1

11

1

1

2

2

2

12’

2’

2’

5

15

25’

25’5 5

S X

1

2 2

3’2’

1

2’

331

3

3

1

31

1

13

1

1

3

25’

15

2’

1212

25’

1

1

31

1

3

1

4

1

33

1

1

1

1

44

5’

3

1

1

1

13

1 1

3 4’

2

31

24311

24

20

16

12

8

4

0

−4

−8

Fig. 18. Cu. Scalar-relativistic energy bands. The calculation uses a setof energy parameters optimized for the energy region above EF and isbased on Kohn-Sham-type relativistic one-particle equations with alocal exchange-correlation potential [84E]. Symmetries given in singlegroup notation.







24

−2

− 4

− 6

− 8

−10

KX Σ Γ

1.5 2.0 2.5

5

2

2

4

1

1

1

1

3

3

1

12

25’

Cu (110)

Wavevector [2 /a]k πT

Initi

al st

ate

ener

gy[e

V]E i

0EF=

Fig. 19. Cu(110). Experimentally determined valencebands along the ΓKX line of the bulk Brillouin zone.The full curves correspond to the band structurecalculation of [63B], see also Fig. 12. The height of thedata points gives the experimental uncertainty [79T].

Cu

Wavevector k

EF = 0

−1

−2

−3

−4

−5

−6

L Λ Γ ∆ X

7 18 h [eV] = 14ω

Initi

al st

ate

ener

gy[e

V]E i

Fig. 21. Cu. Temperature dependent energy bands alongthe ΓL and ΓX direction of the bulk Brillouin zone.Experiments: filled circles at 25°C, empty circles at400°C from normal emission photoelectron spectra.Initial states are calculated at 25°C (solid lines) and400°C (dot-dashed). Final state bands (dashed at 25°C,dotted at 400°C) are shifted down in energy by thephoton energy ω as indicated. Shifts from 25°C to400°C are exaggerated by a factor of 2.5 to show theeffects more clearly [79K1].

Wavevector k

Cu

Γ ΓL KX

−1

−2

−3

− 4

−5

− 6

−7

−8

−9

Initi

al st

ate

ener

gy[e

V]E i

dHvA dHvA

6(3)

6-(2’)

4,5(3)

6(3)

6(1) 4,5(3)4 ,5+ +

4 ,5+ +

6 (3)+

6 (3)+

6 (1)+

6(1) 6(1)

6+

8+

7+

8+ (12)

(25’)7(2’)

6(5)

7(2)

6(1)

7+

7+

6+

(1)

7+

7+

6 +

7(5)

(5)

(2)

(3)

(1)

5(1)

5(1)

5(1)

8 (12)+

8 (25’)+

5(2)

5(4)

5(3)

6+(1)

0EF=

Fig. 20. Cu. Compilation ofexperimental data for the occupiedvalence band structure [84C].Different symbols reflect resultsobtained using different experimentaltechniques and/or by different researchteams, for details see [84C]. The solidlines represent the calculated bands of[84E], compare also Fig. 17. Bandsymmetries are given in double(single) group notation. See also[01S1]. For d-hole lifetimes at X, Land Γ see [99P2, 00C2, 00P1, 01G,01Z, 02Z]. For a quasiparticlecalculation treating self-energy effectssee also [02M].

















25

EF=0−2−4−6−8Initial state energy [eV]E i

400

300

200

100

0

Line

wid

th (

FWHM

) [m

eV]

Ag CuFig. 22. Cu, Ag. Experimental upperlimits for the lifetime width Γh of d-holes derived from photoelectronlinewidths of several bulk bandtransitions. The solid-line parabolastarting at EF results from calculationbased on the free-electron-gas model.Data taken from [01G, 02G]. For moreelaborated calculations taking the fullelectronic structure into account see[00C2, 01Z, 02Z].

Wavevector k

Ener

gy[e

V]E

EF = 0

25

20

15

10

5

L Λ Γ ∆ X S K Σ Γ

Cu

8-(15)6-(15)

4,5(3)4-,5-(3’)

6(1)6(3)

6-(2’)

6-(3’)

6-(5’)

7-(5’)

7-(2’)

(1)6

6 (1)+

6(1)

6(1)

6(1)

6-(4’) 5(1)

5(1)

5(1)

5(1)

5(4)

5(3)6 (1)+

6(5)

7(2’)

7(5)

7 (3)+

6 (1)+

Fig. 23. Cu. Compilation ofexperimental data for the unoccupiedbands above EF [84C]. Differentsymbols reflect results obtained usingdifferent experimental techniquesand/or by different research teams, fordetails see [84C]. The solid linesrepresent the calculated bands of[84E], see also Fig. 18. Bandsymmetries are given in double(single) group notation. For energybands along ΓX up to Ef = 37 eV see[89W1]. See also [01S1].













26

Wavevector k

Ener

gy[e

V]E

EFΣ Γ

Γ

25

20

15

10

5

= 0

W X K

W Z X S K

Cu

(1)

(1)

(1)

(1)

(1)

(1) (1)

(1)

(1)(1)

(4)

(4)

(4)

(4)

(3)(3)

(3)

b

6- (15)

7-(2’)

8-(15’)

Fig. 24. Cu. Compilation of experimental data for theunoccupied bands above EF [86G1]. Different symbolsrefer to results obtained by absolute photoemissiontechniques (open circles [84C]), inverse photoemission(solid squares and vertical arrows [86J]), secondaryelectron spectroscopy (triangles [84Z]), low-energyelectron reflection (diamonds [82J]) and de Haas-vanAlphen effect (open square [84C]). Solid lines arecalculated bands [84E]. Band symmetries are given indouble (single) group notation. See also [01S1].

Ener

gy[e

V]E

EF

Γ

= 0

XK

Cu(110)

2.0 2.5 3.0 3.5 4.0 4.5

70

60

50

40

30

20

10

K

Wavevector [Å ]k −1

Fig. 25. Cu(110). Final state band along the ΓKXdirection of the bulk Brillouin zone determinedexperimentally from angle-resolved photoelectronspectra. The bridging of a gap at the X-point is clearlyrevealed. For comparison a "nearly-free-electron"parabola is indicated by the dashed line [85B]. See also[01S1].


0 = EF−2−4−6−8

Cu

IIn

tens

ity[1

0co

unts

/cha

nnel

]4

6

4

2

0

4

2

0

1

0

(111)

(001)

(110)

Fig. 26. Cu. Normal-emissionphotoelectron spectra taken from thethree low-index surfaces at a photonenergy hν = 21.2 eV. The three spectraare normalized to the same measuringtime and indicate the drastic differencein relative intensities resulting from"gap emission" [95H] in Cu(110) andbulk direct transitions in Cu(111) andCu(001) [79C1].















27I

Inte

nsity

IIn

tens

ity

Initial state energy [eV]E i Initial state energy [eV]E i

0 = EF 0 = EF−2 −2−4 −4−6 −6−8 −8

Cu(100)θ θ35°

30°

25°

20°

15°

10°

5°

75°

70°

65°

60°

55°

50°

45°

40°

S1

= =

0°

Fig. 27. Cu(100) Angle-resolved photoelectron spectrataken at different polar angles θ along the ΓXWK bulkmirror plane. Photon energy hν = 21.2 eV, sampletemperature T = 50K [93M1]. For further data, taken atroom temperature, see [79H1]. The sharp peaks (label

S1) observed next to EF between θ = 50° and 75° resultfrom a d-like surface state [79H1]. For data taken withlinear-polarized photons at θ = 40° see [83G]. For bulktransitions observed on a stepped Cu(610) surface see[98M2].

IIn

tens

ity


0 = EF−2−4−6−8

Cu(100)θ 35°

30°

25°

20°

15°

10°

5°

=

0°

Fig. 28. Cu(100). Angle-resolved photoelectron spectrataken at different polar angles θ along the ΓXUL bulkmirror plane. Photon energy hν = 21.2 eV, sampletemperature T = 50 K [93M1]. For further data taken atroom temperature see [79H1]. For data taken withlinear-polarized photons at hν = 40° see [83G].











28I

Inte

nsity


0 = EF−2−4−6−8

Cu(100)

unpol.

unpol.

E II XULΓ

E II XWKΓ

E XULΓ

E XWKΓ

T

T

a

b

c

d

e

f

Fig. 29. Cu(100). Two examples showing angle-resolved photoelectron spectra taken with 90%-linearlypolarized HeI radiation (hν = 21.2 eV): (a)-(c)measured at polar angle θ = 20° along the ΓXUL bulkmirror plane and photon incidence angle α = 20°.Results are displayed for p-polarized (a), s-polarized (c)and unpolarized (b) light. In (d)-(f) analogous resultsare given for the ΓXWK plane, with θ = 20° and α =60° [83W].

IIn

tens

ity


0 = EF−2−4−6−8

Cu(100)

θ35°

35°

30°

25°

21°

16°

12°

8°

=

0°

IIn

tens

ity


0 = EF−2−4−6−8

θ

70°

65°

60°

55°

50°

45°

40°

S

S

=

4°

80°

×4

Fig. 30. Cu(100). Angle-resolved photoelectron spectra taken at different polar angles θ along the ΓXWK bulk mirrorplane. Photon energy hν = 40.8 eV [83W]. Peak S is a d-like surface state.





29

Wavevector k Wavevector k

Ener

gy[R

y]E

EF

∆

∆∆

∆

∆

∆

∆

∆

∆

∆

∆

∆

X

X

X

X

X

X

XX

X

X

X

XX

Γ

Γ

ΓΓ

Cu(100)2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

0.70.60.50.40.30.20.1

0−0.1

1

1

1

1

1

1

1

1

1

2

2

2

2’

3

3

5

5

55

5’

4’

0.24

0.200.16

0.120.08

0.040

upper

lower0.012

0.0080.004

0

0.040.02

0

× 0.1Pm

f i

2 /2[R

y]P

mf i

2 /2[R

y]P

mf i

2 /2[R

y]

Fig. 31. Cu(100). Band structure (left) and momentummatrix elements |Pfi|

2 along the [100] direction of theBrillouin zone. The calculation is based on thecombined interpolation scheme [79S] and refers tobulk→bulk band transitions. The full (dashed) curves inthe panels on the right show the variations of |Pfi|

2 with

k⊥ for transitions from the initial-state bands indicatedto final states to the third (fourth) upper band of ∆1-symmetry. For ∆1 initial states Pfi || [100], for ∆5 initialstates Pfi ⊥ [100]. From [79S]. For a critical discussionsee [80S].

IIn

tens

ity


0 = EF−2−4−5 −3 −1

Cu(100)

h [eV]ν17

16

15

14

13

12

11

10

9

8

Fig. 32. Cu(100). Normal-emission photoelectronspectra taken with mixed s/p-polarization at differentphoton energies hν [79K2].

IIn

tens

ity


0 = EF−4−8

Cu(100)

h [eV]ν40

35

32

30

2825

22

Fig. 33. Cu(100). Normal-emission photoelectronspectra taken with s-polarized light at different photonenergies hν [89W1].








30I

Inte

nsity


−4.0 −3.0 −2.0−4.5 −3.5 −2.5

Cu(100)

Fig. 34. Cu(100). Photoelectronspectrum taken at T = 35K in normalemission at a photon energy hν = 40.8eV. An almost constant backgroundhas been subtracted already. Solidlines indicate the decomposition intothree Lorentzians, and their sum[94M2]. For data taken at hν = 48.4eV see [79C1].

IIn

tens

ity


Cu(100) Γ ΓΓ8+

7 +8+

T = 485 K

T = 275 K

T = 70 K

− 6 −5 −4 −3 −2 −1 0 = EF

Fig. 35. Cu(100). Temperature dependence of normal-emission photoelectron spectra taken at hν = 40.8eV.The spectra result from direct transitions at Γ and showthe corresponding splitting of the d-bands [01G]. Seealso [93G, 93M1].

IIn

tens

ity


Cu(100)

T = 973 K

T = 793 K

T = 77 K

T = 295 K

− 6−8 −4 −2 0 = EF

Fig. 36. Cu(100). Temperature-dependent spectra fornormal-emission photo-electrons taken at hν = 66 eV.Note that inelastic background has been subtracted fromthe experimental data [86W1, 87W].










31I

Inte

nsity

IIn

tens

ity

Energy [eV]E Energy [eV]E

Cu(100)

θθ

30°29°

==

0 = EF 0 = EF

28°

27°

25°

23°

18°

13°

0°

26°

24°

21°

16°

11°

6°

0°

1 12 23 34 45 5

Fig. 37. Cu(100). The left panel shows experimentally observed inverse photoelectron spectra (hν = 9.7 eV) atdifferent polar angles θ along the ΓXWK plane, the right-hand panel shows theoretical spectra calculated on thebasis of a one-step theory [84A]. For surface states see also [85G].

IIn

tens

ity

IIn

tens

ity


Cu(100)

0 = EF 0 = EF−5 −4 −3 −2 −1 1 2 3 4

Ei [eV]

13.00

12.75

12.50

12.25

12.00

11.75

11.50

11.00

10.75

10.50

10.25

10.00

9.759.509.25

h [eV]ν

12.00

11.75

11.50

11.25

11.00

10.75

10.50

10.25

10.00

9.75

9.50

9.25

9.00

11.25

Fig. 38. Cu(100). Photoemission (left) and inverse photoemission (right) spectra showing the s,p-like ∆1 bandcrossing the Fermi level for parallel momentum k|| = 0. Photon energies hν and electron incidence energies Ei aregiven as parameters [92H2]. For a discussion of linewidths see [93S1] and [93S2, 94M1, 02B].










32

For Fig. 39 see next page

IIn

tens

ity

IIn

tens

ity

IIn

tens

ity


Cu(100)

θθ

=

0 = EF0 = EF5 510 1015 1520 2025 25

Energy [eV]E0 = EF 5 10 15 20 25

S2S3

B2

B4

B1

-30°

-35°

-40°

-45°

-50°

-55°

-60°

-65°α α= 0° = 35°S2

S3

B2

S1

B4

B1

α = 75°

-65°

-55°

-50°

-45°

-40°

-35°

-30°

-25°

-20°

-10°

= 0°

θ = 0°

S2S3

B3

S1

B1

-55°

-50°

-45°

-40°

-35°

-30°

-25°

-20°

-10°

Fig. 40. Cu(100). Inverse photoemission spectra taken at hν = 9.6 eV and at various polar angles θ of the electrons inthe ΓXUL bulk mirror plane for three photon take-off angles α = 0°, α = 35°, and α = 75°. Transitions into bulk andsurface states are labeled B and S, resp. Data from [92S1], see also [86D, 89F].






33I

Inte

nsity

Energy [eV]E

Cu(100)

0 = EF−2 2 4 6

0

X

1 2

4’

Fig. 39. Cu(100). Normal-incidence inversephotoemission spectrum taken at an electron initialenergy Ei = 14.5 eV. Peaks labeled 1,2 are due to imagepotential surface states [92H2].

IIn

tens

ity

Energy [eV]E

Cu(100)

0 = EF

α = 20°−

0°

15°

35°

55°

75°

2 4 6 8

Fig. 41. Cu(100). Inverse photoelectron spectra taken athν = 9.6eV. Electron incidence angle θ = –60° andphoton detection along the ΓXUL bulk mirror plane.The photon take-off angle α is given as a parameter.The spectra are normalized to equal amplitude at Ef =5.7 eV and demonstrate the importance of light-polarization effects [92S1], see also [89F].

Ener

gy[e

V]E

0 = EF

2

4

6

8

1.5 1.0 0.5 0 0.5 1.0 1.5 2.0

Wavevector [Å ]kII1−

X MΓΓ ΓXUL XWK

Cu(100)

Fig. 42. Cu(100). E(k||) diagram forinverse photoemission spectroscopyalong the ΓXUL and ΓXWK bulkmirror planes at a photon energy ofhν = 9.6 eV [90S]. Calculated bulkband transitions are shown by opensymbols without error bars and locateemission peaks expected on the basisof a combined interpolation-schemecalculation [90S]. Experimental peakpositions resulting from bulk states aregenerally shown as solid symbolswith error bars. The size of thesymbols indicates the intensity of thetransition. The band gaps of theprojected bulk band structure areshown as grey shaded areas.Experimentally observed transitionsinto surface states are marked as opensymbols with error bars. Thedispersion of the surface states isindicated by solid line parabolas[90S]; see also [86J, 90L]. Symbolsmarked with large squares indicatedata points which have been studied asa function of temperature in [90S].












34I

Inte

nsity


0 = EF−2−4−6 −5 −3 −1

Cu(100)

Cu(110)

θ

θ

=

=

0°

80°

75°70°65°60°55°50°45°

40°35°

30°25°20°

15°10°

5°0°

Fig. 43. Cu(110). Angle-resolved photoelectron spectrataken at different polar angles θ along the ΓKWXazimuth of the bulk Brillouin zone. Photon energy hν =21.2 eV [81C2]. See also [79H1]. Analogous data takenalong the ΓKLU azimuth are reproduced in [81C1].


Cu(110)

IIn

tens

ity


0 = EF−2−4−6 −5 −3 −1−7

T [°C]= 25

200

400

600

800

Fig. 46. Cu(110). Angle-resolved photoelectron spectrataken in normal emission at hν = 45 eV with the sampleat different temperatures [77W]. See also [93G] for ashort review of temperature effects and [93M2] forfurther theoretical considerations.


0 = EF−2−4 −3 −1−6 −5−7

Cu(110)10

9

8

7

6

5

4

3

2

1

0

B D

E

F

G

S

A C

H

s-pol

p-pol

IIn

tens

ity[1

0co

unts

/3s]

4

(×5)I

Fig. 44. Cu(110). Normal-emissionphotoelectron spectra taken withlinearly-polarized photons at hν = 21.2eV. Sample temperature T = 130 K,photon incidence angle α = 45° along

the YΓ direction of the surfaceBrillouin zone. For ease ofcomparison, the s-pol spectrum isshifted vertically by two units of theordinate scale [98M3]. All transitionslabeled A-I are from bulk states[83B1], while S is a replica of peak Ginduced by a weak satellite line of thelight source. For normal emissionspectra taken with unpolarizedphotons of energies hν = 21.2 eV, 40.8eV and 48.4 eV, see [79C1]. For adetailed discussion of the effects oflinearly-polarized light on normalspectra see [82B, 82G2, 83B1, 83P].Normal emission intensities obtainedfor different polarizations at a widerange of photon energies are reportedand discussed in [79D]. See also[85W1] for off-normal results. Fordependence on ω and T see [01G].



















35

Cu(110)

0°

IIn

tens

ity


0 = EF−2−4−6−8

θ =

10°

20°

30°

40°

50°

60°

D

E10

5

0

0° 20° 40° 60°

Dtheory

experiment

Emission angle θTe

mp.

coef

f.[1

0K

]b

−−

41

Fig. 45. Cu(110). Left: Angle-resolved photoelectronspectra taken at room temperature at different polarangles θ in the ΓLUX plane of the bulk Brillouin zone.Photon energy hν = 21.2 eV. All curves are normalizedto the same amplitude. Right: Temperature dependence

of peak D as observed experimentally and calculated onthe basis of the inverse LEED formalism. Thetemperature coefficient b is defined to describe the peakintensity I by the equation lnI = –bT+a [83M].

Cu(110)

IIn

tens

ity

Energy [eV]E0 = EF

B 1

S3

S1

θ = 49°

40°

31°

22°

13°

8°

0°

2 4 6 8

Fig. 47. Cu(110). Inverse photoemission spectra takenat hν = 9.7 eV for different electron incidence angles θalong the ΓKLU bulk mirror plane [86J]. Transitionsinto bulk (surface) states are labeled B(S). For effect ofsample temperature see also [90S].

Cu(110)

IIn

tens

ity

Energy [eV]E0 = EF

B 1

S1

2 4 6 8

T = 320 K

410 K

480 K

520 K

570 K

Fig. 48. Cu(110). Temperature-dependent intensities ofbulk (B) and surface (S) peaks observed in inversephotoemission spectra taken at θ = 35° along the ΓKLUbulk mirror plane (hν = 9.7 eV) [86J]. See also [90S].








36

Cu(110)

IIn

tens

ity

Energy [eV]E0 = EF

B 1

B 2

S3

S2

θ = 44.5°

2 4 6 8

41°

35.5°

30°

24.5°

18°

Fig. 49. Cu(110). Inverse photoemission spectra takenat hν = 9.7 eV for different electron incidence angles θalong the ΓKWX bulk mirror plane [86J]. Transitionsinto bulk (surface) states are labeled B(S). For effect ofsample temperature see also [90S].

Cu(110)

IIn

tens

ity

Energy [eV]E0 = EF 2 4 6 8

T = 195 K265 K410 K545 K705 K

Fig. 50. Cu(110). Set of angle-resolved inversephotoelectron spectra taken at different sampletemperatures. Electron incidence angle θ = –57° along

the Γ X azimuth of the surface Brillouin zone.Photons (hν = 9.7 eV) detected at emission angle α =+55°. The estimated background is indicated by thedashed line [89F]. See also [90S].

Energy [eV]EEF

Cu (110)

IIn

tens

ity

0 = 5 10 15 20 25

E i [eV]32.4

30.429.4

28.4

27.4

26.4

24.4

23.3

22.4

21.4

20.4

19.4Fig. 51. Cu(110). Normal-incidence inversephotoemission spectra for different electron energies Eireflecting bulk band dispersion along the ΓKX directionof the Brillouin zone [90L].








37En

ergy

[eV]

E

0 = EF

2

4

6

8

1.5 1.0 0.5 0 0.5 1.0 1.5


XY ΓΓKLU Γ KWX

Cu(110)

Fig. 52. Cu(110). E(k||) diagram forinverse photoemission spectroscopyalong the ΓKLU and ΓKWX bulkmirror planes at a photon energy ofhν = 9.6 eV [90S]. For an explanationof the various symbols see the captionof Fig. 42.

Cu (111)

IIn

tens

ity

EF0 =Initial state energy [eV]E i

−2−4−6

h [eV]ν11.511.010.510.0

9.59.08.58.07.57.06.56.0

Fig. 53. Cu(111). Normal-emission photoelectronspectra taken with p-polarized synchrotron radiation atdifferent photon energies hν, showing the dispersionwith hν of several direct transition bulk emission peaksand an s,p-like surface state labeled S [79K2]. See also[80S]. For high-resolution normal emission data takenat hν = 40.8 eV and hν = 48.4 eV see [79C1].







38


Ener

gy[R

y]E

EF Λ

Λ

Λ

Λ

Λ

ΛΛ

Λ

ΛΛ

LL

L

LL

L

LL

ΓΓ

Cu(111)2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.50.40.30.20.1

0−0.1

1

1

1

1

1

1

13

3

2’

3’

3

3

3

3

3

2’

lower0.012

0.0080.004

0

0

Pm

f i

2 /2[R

y]P

mf i

2 /2[R

y]P

mf i

2 /2[R

y]

L

upper

0.24

0.200.160.12

0.08

0.040

Λ1

× 0.1

upper

lower0.008

0.016

0.024

Fig. 54. Cu(111). Band structure (left) and momentummatrix elements |Pfi|

2 along the (111) direction of theBrillouin zone [79S]. The calculation is based on thecombined interpolation scheme [79S] and refers tobulk→bulk band transitions. The panels on the right

show the variation of |Pfi|2 with k⊥ for transitions from

the initial-state bands indicated to final states in thelower Λ1 band. For the Λ1 initial states Pfi || [111], forΛ3 initial states Pfi ⊥ [111]. From [79S]. For a criticaldiscussion see [80S]. See also [81H3, 99M, 00M, 01P].

Cu (111)

IIn

tens

ity


−2−4−6

α

α

α = 30°

= 45°

= 85°

Fig. 55. Cu(111). Normal-emission photoelectronspectra excited by p-polarized HeI radiation (hν = 21.2eV) incident at three different angles α with respect tothe surface normal. Sample temperature T = 180K. Thespectra are normalized to equal maximum peakamplitude [98M3]. See also [01P].













39

Cu (111)

IIn

tens

ity

IIn

tens

ityInitial state energy [eV]E i Initial state energy [eV]E i

−7 −7− 6 − 6−5 −5−4 −4−3 −3−2 −2−1 −10 = E F 0 = E F

experiment

S

S

theory

Fig. 56. Cu(111). Left: Experimental normal-emission photoelectron spectrum taken with unpolarized HeI radiation(hν = 21.2 eV). Right: Corresponding spectra calculated within the fully relativistic one-step-model using muffin-tinpotential (triangles) and full-potential (solid line), respectively [98F]. S labels a surface state.

Cu (111)

IIn

tens

ity


−4 −3 −2 −1 0 = E F

θ = 1.5°−

3.5°

8.5°

13.5°

18.5°

23.5°

28.5°

33.5°

43.5°

48.5°

53.5°

58.5°

63.5°

68.5°

73.5°

78.5°

Fig. 57. Cu(111). Angle-resolved photoelectron spectrataken at different polar angles θ along the ΓLUX planeof the bulk Brillouin zone. Photon energy hν = 21.2 eV[79H1]. For further data see also [82G2].

Cu (111)


−2−4−6

α = 20°

α = 40°

α = 60°

IIn

tens

ity[1

0co

unts

/2s]

3

20

15

10

5

0

α = 0°

θ = 40°

B

A

C

DE

Fig. 58. Cu(111). Angle-resolved photoelectron spectrataken at a polar angle θ = 40° along the ΓLUX plane ofthe bulk Brillouin zone with p-polarized HeI-radiation(hν = 21.2 eV) incident at different angles α withrespect to the surface normal. For clarity, spectra areshifted by 5 units of ordinate scale against each other.Sample temperature T = 170 K [98G]. For data taken atθ = 10° see also [82G2].








40


−2.2 −2.0 −1.8 −1.6−2.8 −2.4−2.6

IIn

tens

ity[1

0co

unts

/s]

3

15

10

5

0

X 7+

X 7+X 6+ S

Cu (111)

Fig. 59. Cu(111). High-resolution photoelectronspectrum showing the spin-orbit splitting of d-bands atthe X-point of the bulk Brillouin zone. S labels asurface state. Photon energy hν = 21.2 eV, sampletemperature T = 105 K, electron emission angle θ = 46°along the ΓLKL plane, electron energy resolution ∆E =20 meV, angle-resolution ∆θ = ±0.4° [96M2]. For adiscussion on phonon contributions to photoholelinewidths see [96M1, 98M1, 01G] and referencesquoted therein.

Cu (111)


−1−2−3

IIn

tens

ity

100

6525

30 65

60

8.0

7.5

7.0

h [eV]ν

Fig. 60. Cu(111). Temperature-dependent normal-emission photoelectron spectra taken at different photonenergies hν. Thermally induced energy shifts are givenin meV, solid (dashed) curves refer to a sampletemperature T = 25°C (400°C) [79K1]. See also [82M].For one-step-model calculations see also [81L1] and[96M4, 98M1].


Cu (111)Cu (110)

IIn

tens

ity

IIn

tens

ity


T = 155 K

T = 145 K

10 1012 1214 1416 1618 1820 20

300 K405 K545 K 290 K705 K 705 K

Fig. 62. Cu(111), Cu(110). Inverse photoemissionspectra for a selected bulk transition observed by"triangulation" [95H] on two different surfaces forvarious sample temperatures. Left (Right): Electron

incidence at θ = –3°(–45°) within the ΓKLX bulkmirror plane. Photons (hν = 9.7 eV) are detected atemission angles θ = 55° (30°) [92S1], see also [90S]. Ewith respect to EF.















41

Cu (111)

0 0Initial state energy [eV]E i Initial state energy [eV]E i

−2 −2−4 −4−6 −6

IIn

tens

ity

S1

S2

θ = 0°exp.

θ

θ

θ= 0°

= 50°

= 50°calc.

ΓLUX

ΓLUX

exp.

calc.

Fig. 61. Cu(111). Upper panels: experimental angle-resolved photoelectron spectra (hν = 21.2 eV) taken atdifferent polar angles θ within the ΓLUX plane of thebulk Brillouin zone and at different sampletemperatures (thick lines: T = 125 K, thin lines: T =

703 K). Lower panels: corresponding one-step-modelcalculations (thick lines: T = 100 K, thin lines: T = 700K). Surface states labeled S1 and S2 are not reproducedby the bulk band calculation [98M1].

Ener

gy[e

V]E

0 = EF

2

4

6

8

1.5 1.0 0.5 0 0.5 1.0 1.5


MΓΓ LKL ΓLUX

Cu(111)

M‘

Fig. 63. Cu(111). E(k||) diagram forinverse photoemission spectroscopyalong the ΓLKL and ΓLUX bulkmirror planes at a photon energy ofhν = 9.6 eV [90S]. For an explanationof the various symbols see the captionto Fig. 42.





42

Cu (111)

Energy [eV]E

Wav

evec

tor k

Refle

ctiv

ityR

Refle

ctiv

ityR

d d2 2R E−−

0

0.4

0.3

0.2

0.1

0

1.0

0.5

0

ΓΓ Γ Γ

L16 18 20 22 24 26

‘ ‘2 15 25

Vi = 0.01 eV

Vi = 1 eV

Fig. 64. Cu(111). Bottom: Energy bands along the ΓL-direction of the Brillouin zone calculated from apseudopotential model [82J]. Middle: Elasticreflectivity R(E) calculated for small absorption(imaginary part of the potential Vi = 0.01eV). Top: R(E)calculated for realistic absorption (Vi = 1 eV) andcorresponding negative second derivative −d2R/dE2

[82J]. Note that E is defined with respect to the vacuumlevel. See also [01S1].

Cu (111)

Ener

gy[e

V]E

30

20

10

L LΓ d /dR EIm k Re kT T

Fig. 65. Cu(111). Left: Energy bandsalong the ΓL-direction of the Brillouinzone calculated with an optimizedpseudopotential including an energydependent absorption term Vi =0.05(E−EF) [96S]. Right: DerivativedR/dE of the elastic reflectivity atnormal incidence as observedexperimentally (bold line) andcalculated (thin line) [96S]. Note thatE is defined with respect to thevacuum level. See also [01S1].







Ref. p. 79] 2.9 Noble metals (Ag)


43

2.9.3 Ag (Silver) (Z = 47)

Lattice: fcc, a = 4.09 Å [63W]Brillouin zones: see section 1.3 of this volumeElectronic configuration: [Kr] 4d105s1


Typical errors are ± 0.15 eV

Table 5. Ag. Core-level binding energies in eVrelative to EF [78C2, 92F, 95H]. Typical scatterbeetween various sources is ± 0.1eV.

Level n = 3 n = 4

ns1/2 719.1 97.0np1/2 603.8 63.7np3/2 573.0 58.3nd3/2 374.0 –nd5/2 368.1 –


Table 6. Ag. Occupied valence bands. Comparison of theoretical and experimental determination of theΓ, X and L points in the BZ. Energy values are given in eV relative to EF. Experimental errors aretypically ± 0.04 eV if not given differently in parentheses. Symmetries are given in double groupnotation.

Symmetry Theory Theory Theory Theory ARUPS ARUPS ARUPSPoints [72C] [81J] [83B2] [84E] [85N] [85W3] [89W3]

Γ6+ –7.50 –7.92 –6.63 –7.21 – – –

Γ8+ –5.90 –5.97 –5.82 –6.23 –6.19 –6.15–4.69

Γ7+ –5.46 –5.49 –5.37 –5.80 –5.76 –5.70Γ8+ –4.75 –3.69 –4.73 –4.69 –4.95 –4.95 –4.95

X6+ –7.13 –6.54 –7.12 –7.00 –7.35 –7.38 –

X7+ –6.99 –6.22 –7.04 –6.82 –7.00 –7.32 –

X7+ –4.21 –2.93 –4.21 –4.25 –4.20 –4.35 –

X6+ –4.03 –2.64 –4.11 –4.04 – –4.12 –

X7+ –3.73 –2.64 –3.79 –3.71 –3.90 –3.82 –















2.9 Noble metals (Ag) [Ref. p. 79


44

Table 6 (cont.)

Symmetry Theory Theory Theory Theory ARUPS ARUPS ARUPSPoints [72C] [81J] [83B2] [84E] [85N] [85W3] [89W3]

L6+ –6.94 –6.34 –6.85 –6.74 –7.13 – –7.10

L4+ ,5+ –5.99 –5.97 –5.91 –6.28 –6.27 –6.25

–4.76

L6+ –5.53 –5.50 –5.44 –5.74 –5.74 –5.80

L6+ –4.20 –4.20 –4.23 –4.31 – –4.55

–2.87

L4+,5+ –3.97 –4.04 –4.01 –4.06 –4.11 –4.30

L6- –0.16 –0.59 –0.62 –0.03 – –0.20 –

For further data see also [84W1, 85N, 85W3]. For experimental d-hole lifetimes at X see [02G], forcalculations at X, L and Γ see [01Z, 02Z].

Table 7. Ag. Unoccupied bands of the bulk BZ. Energies of symmetry points are given in eV relative toEF.

Symmetry Theory Theory Theory Theory ARUPS ARUPS ARUPSPoints [72C] [81J] [83B2] [84E] [85N] [85W3] [84R]

Γ7– 16.84 – 17.17 16.98 17.0 17.1(2) –Γ6– 19.49 – 18.99 19.61 23.0 19.2(4) –

L6+ 3.33 3.79 3.82 3.44 – – 3.8(1)

X6– 2.02 1.70 1.88 2.27 – – 2.1(1)

For further data see [85W3, 99P1, 00L, 00P2].For Fermi surfaces see Landolt–Börnstein, Vol. III/13c (1984), p. 27.For information on the surface electronic properties see Landolt–Börnstein Vol III/24b and Vol. III/24d.



























45

Figures for 2.9.3

0 200 400 600 800 1000 1200 1400

Ag

4d3s

4p

5s

4s

3d

4s


102

10

1

10−1

10 −2

10−3

10−4

Cros

s sec

tion

[M

b]σ

4d

4p 3p

Fig. 66. Ag. Atomic subshell photoionization cross sections for photonenergies up to 1500 eV [85Y].

0 50 100 150 200 250 300 350

Ag

Photon energy [eV]hω Photon energy [eV]hω

102102

10

101

1

10−1

10 −2

Cros

s sec

tion

[M

b]σ

40 60 80 100 120 140 160 180a b

Phot

oion

izatio

n cr

oss s

ectio

n

[arb

.uni

ts]

σ

Fig. 67. Ag. Calculated (a) atomic 4d-subshell cross section near the Cooper minimum [85Y] and (b) experimentalphotoionization cross section for photon energies between 40 and 165 eV. In (b) the open circles are values for atoms[85K], filled circles with error bars are obtained from poly-crystalline metallic Ag [89K3].







46I

Inte

nsity

(

) /E

Eb

b

I


[eV]Eb

Ag(MNN)

992

901.5

1005 975 945 915 885

895.5M N V45 1 M N V45 23

M VV5

M VV4

1000 900 800 700 600 500 400 300 200 100 0

Ag(MNN)

Ag(3s)

Ag(3p )1/2

Ag(3p )3/2

Ag(3d )3/2

Ag(3d )5/2

(×4)

Ag(4s)Ag(4p)

Ag( VB)

MgK α

Ag

Fig. 68. Ag. Overview XPS spectrum.The insert shows a blow-up of the Ag(MNN) Auger-electron spectrum[79W1]. Data taken with unmono-chromatized MgKα-radiation.


IIn

tens

ity

(3d )3/2

(3d )5/2Ag

380 370 360

6.00

Fig. 69. Ag. XPS data showing the region of the spin-orbit-split 3d core level taken with unmonochromatizedMgKα radiation [79W1].

IIn

tens

ity

Ag

DOS


0 = EF−9 − 8 −7 − 6 −5 − 4 −3 −2 −1

Fig. 70. Ag. XPS valence band spectrum (dotted) takenwith monochromatized (0.5eV) AlKα radiation. The

solid curve is the corresponding density-of-states curve,calculated within the combined interpolation scheme[74S1] and smoothed with a Lorentzian broadening toaccount for the experimental resolution [74S2].







47I

Inte

nsity

Ag


0 = EF−9 − 8 −7 − 6 −5 − 4 −3 −2 −1

IIHe (40.8eV)

IHe (21.2eV)

Fig. 71. Ag. Photoelectron spectra obtained frompolycrystalline samples at different photon energies hν.Energy resolution ∆E = 80 meV at hν = 40.8 eV and 30meV at 21.2 eV [77B].

IIn

tens

ity

Ag


−10 − 8 − 6 − 4 −2

h [eV]ν = 1487

150

130

120

110

100

90

80

70

60

Fig. 72. Ag. Valence band photoemission ofpolycrystalline samples taken at different photonenergies hν [76W]. See also [89K3] for an experimentalinvestigation of the Cooper minimum at hν between 40and 165 eV.

IIn

tens

ity

Ag

DOS

Energy [eV]E0 = EF 2 4 6 8 10

Fig. 73. Ag. Top: Experimental bremsstrahlungisochromat spectrum (photon energy hν = 1486.7 eV,total resolution 0.7 eV). Bottom: Calculated density-of-states. Dotted line without broadening, solid lineincluding broadening to simulate instrumental andlifetime-widths [84S].

Ag

Photon energy [eV]hν

Refle

ctiv

ityR

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 75. Ag. Experimental normal-incidence reflectivitydata [81W] obtained from different experiments. Fordetails and tables of the "most recommended" data see[81W]. See also [85P, 01S2].












48I

Inte

nsity

Ag

DOS

Energy [eV]E0 = EF

BIS

DOS

10 20 30 40 50 60 70 80

Fig. 74. Ag. Bremsstrahlung-isochromat spectrum taken at hν =1486.7eV (dotted) and calculateddensity-of-states (thin line:unbroadened, thick line: broadened totake experimental resolution and life-time width into account). Thecorrespondence of structures in themeasured spectrum with features inthe broadened DOS is indicated [85S].See also [92F].

Ag

Photon energy [eV]hν0 5 10 15 20 25 30

10

8

6

4

2

Diel

ectri

c con

stan

t2ε

Fig. 76. Ag. Experimental ε2 spectra [81W] obtained

from different experiments. For details and tables of the"most recommended" data see [81W]. See also [85P,01S2].

Wavevector k

Ener

gy[e

V]E

Ag

Γ ΓX W L K,U

24

20

16

12

8

4

0

− 4

− 8

Fig. 77. Ag. Band structure calculatedby a second-principles method usingthe combined interpolation scheme.Spin-orbit coupling and otherrelativistic corrections are included[81L2]. See also [74S1] and [83B2].For a calculation using the relativisticaugmented plane wave method see[72C].













49

6

5

4

3

2

1

0

1.5

1.0

0.5

0−10 − 5 0 5 10 15 20 25

EF

Ag

(×4)

X(6)

L(7) X(7)

X(8)

X(11)

X(9) L(8)

Energy [eV]E E− F

DOS

[ele

ctro

ns/a

tom

eV]

⋅

DOS

[ele

ctro

ns/a

tom

eV]

⋅

Fig. 78. Ag. Density-of-states histogram calculated withthe combined interpolation scheme and the bandstructure of Fig. 77. High-symmetry critical-pointlocations are indicated [81L2]. See also [74S2].

Ag5

4

3

2

1

0 4 8 12 16 20 24

Diel

ectri

c con

stan

tε 2


Fig. 79. Ag. Calculated ε2 spectrum (solid line) in

comparison with experimental data (dots). Thecalculations were performed using a combinedinterpolation scheme and include spin-orbit effects andmomentum matrix elements [81L2]. The correspondingband structure is shown in Fig. 77. See also [01S2].


Ener

gy[e

V]E

Ag

Γ ΓΛ ΛL L

1

1

1

1

33’

2’

2’

2’

15

3

333

111

1225’

8+

7 +

8 +

6+ 6

6−6

4+566

4+5

4 +5+ +

4 +5+ +

6+

6+

6+

6+

4+5

66

6

6−

6−4 +5− −20

15

10

5

0

−5

a b

Fig. 80. Ag. Band structure calculated along the ΓL direction (a) without and(b) with spin-orbit interactions [83B2].








50

Wavevector kΓ Λ L

Ag

0.10

0.05

0

Squa

red

mat

rix e

lem

ent I

If i

2π

[arb

.uni

ts]

Fig. 81. Ag(111). Calculated momentum matrixelements |πfi|

2 for bulk band→bulk band transitions in

parallel polarization vector A || ΓL. The initial state isthe lowest relativistic Λ6 band (see the right panel in

Fig. 80). The solid (dashed) curve corresponds to thefinal state being the first (second) unoccupied Λ6 bands

(see Fig. 80) [83B2]. See also [80S] for a criticaldiscussion of the applicability of momentum matrixelements to photoemission intensities. The units for|πfi|

2 are arbitrary, but identical for Figs. 81-84.

Wavevector kΓ Λ L

Ag

0

2

4

6

0.2

0.1

0

Squa

red

mat

rix e

lem

ent I

If i

2π

[arb

.uni

ts]

Squa

red

mat

rix e

lem

ent I

If i

2π

[arb

.uni

ts]


2 as explained in legend to Fig. 81 but now

with the fourth Λ6 band (counted from bottom to top) as

the initial state [83B2]. See also Fig. 81.

Wavevector kΓ Λ L

Ag0.036

0.032

0.028

0.024

0.020

0.016

0.012

0.008

0.004

0

Squa

red

mat

rix e

lem

ent I

If i

2π

[arb

.uni

ts]


2 as explained in legend to Fig. 81 but now

in perpendicular polarization vector A ⊥ ΓL and thefirst (lowest) Λ6 band as the initial state [83B2]. See

also Fig. 81.

Wavevector kΓ Λ L

Ag

0

0.2

0.1

Squa

red

mat

rix e

lem

ent I

If i

2π

[arb

.uni

ts]


2 as explained in legend to Fig. 81, but

now with perpendicular polarization vector A ⊥ ΓL andthe fourth Λ6 band as initial state [83B2]. See also Fig.

81.








51

Wavevector k

Ener

gy[e

V]E

EF

Σ

Ag


7+

7+

7+

7+7+

7+

7+

7+

4

2

0

−2

− 4

− 6

− 8

−10S X

8+

8+

8+

8+

6 + 6 +

6 +

6 +

6 +

6 + 6 +

6 +6 +

6 +

4 +5+ +

4 +5+ +

6

6

6

6

7

7

7

6

5 5 55

7

6 66

6

767

3+4

6 −

6 −

6 −

4+5

4+5

Fig. 85. Ag. Relativistic band structurealong high-symmetry directions. Thecalculation rests on Kohn-Sham-typerelativistic one-particle equations witha local exchange-correlation potential[84E].

Wavevector k

Ener

gy[e

V]E

EF

Σ

Ag


7+

7+

7+

7+

0

− 4

− 8

S X

8+ 8+

6 +

6 +

6 +

6 +

6 +

6 +

6 +

6 +

6 +

4 +5+ +

4--+5-

6

66

6

6

6

6

66

6

6

6

6

7

7

7

6

6

5 5 55

7

77

76

6

6

76

7

3+4

6 −

6 − 6 −

6 −

6 −6 −

6 −

8 − 8 −

7 − 7 −

7 −

7 −

7 −

7 −

6 −

6 −

6 −

6 −

4+54+5

28

24

20

16

12

8

4

Fig. 86. Ag. Scalar-relativistic energybands. The calculation uses a set ofenergy parameters optimized for theenergy region above EF and is based

on Kohn-Sham-type relativistic one-particle equations with a localexchange-correlation potential [84E].For a first-principles relativisticaugmented plane wave (APW)calculation see [72C]. Symmetries indouble group notation.






52En

ergy

[Ry]

E

Σ

AgΓΓ

Γ

Γ

Γ

Γ

ΓΓΓΓ

∆ Z Q Λ

W

W

W

W W

W W

W

L L

LL

L

L

L

L K

K

K

K

K

K

KK

KK K

S

X

X

X

X

X

X

X

X XX

Wavevector k

EF

Γ ΓX X

X

X

X

X

X

XXXX

W L K,U

0

2.0

1.6

1.2

0.8

0.4

− 0.4

− 0.8

55

25’25’

25’

25’

15

15

12 12

11

11

1

1 1

1

1

1

1

1

1

1

1 1 1

1

1

3

3

3

3

33

3

3

3

3

33

4

4

4’

1’

5’5’

2

2

2

2’

2’

2’

3’

4’

5

1

2’

15

12

5 2’2’1 1

13

4

14

1

3

2 1

31

4

21 1

2

1

2

1

1

2

12

1

21

11

33

3

1

33

1

11

13

4

1

4

2

31

1

3

3

1241

31 3 1

11

24

1

1

4

1

1

Fig. 87. Ag. Band structure resultingfrom a nonrelativistic self-consistent,all-electron, local-density-functionalcalculation [90F]. Symmetries insingle group notation.


Ag

Optic

al co

nduc

tivity

[

10s

]14

1−σ

50

40

30

20

10

0 2 4 6 8 10 12 14 16

A

B

Fig. 88. Ag. Optical conductivity. Curve A representsthe calculated interband contribution using the energyband structure of Fig. 87 and includes calculatedmomentum matrix elements. Curve B shows theinterband plus the Drude optical conductivity.Experimental results are reproduced by data points[90F]. See also [01S2].

Wavevector k

EF

EFAg

Γ ΓL

0

− 4

− 8

− 6

−

− 7

− 3

− 2

− 1

Σ Σ∆Λ K

7+

7+

7+

7+

7+

X

8+

8+ 8+

8+6 +

6+

6 +

6 +

6 + 6 + 6 +

4 +5+ +

4 +5+ +

6 −

Initi

al st

ate

ener

gy[e

V]E i

=

5

‘

(theory)

dHvA dHvA

Fig. 89. Ag. Compilation ofexperimental data for the occupiedvalence band structure [85W3].Different symbols reflect resultsobtained using different experimentaltechniques and/or by different researchteams, for details see [85W3]. Thesolid lines represent the calculatedbands of [84E], compare also Fig. 85.Band symmetries are given in doublegroup notation. For further data seealso [85N, 89W2, 89W3, 99P1, 00L,00P2]. For d-hole lifetimes at X, L andΓ see [02G, 01Z, 02Z] and Fig. 22.


















53

Wavevector k

EFEFAg

Γ

Γ Γ

Γ

Γ0

− 4

− 8

− 6

−

− 7

− 3

− 2

− 1

Σ

Σ

∆

∆

K

7+

7+

7+

7+

7+

X

8+

8+8+

8+

6+

6 + 6 + 6 +

Initi

al st

ate

ener

gy[e

V]E i

=

5

(theory)

S

(110)

Fig. 90. Ag(110). Band structure along the ΓKXKΓdirection in the extended zone scheme of the bulkBrillouin zones. All data points [89C] are obtained fromangle-resolved photoemission spectra using final statesin bulk band gaps ("gap emission method" [95H]). Thefull curves are from a local density calculation [72C]with the Fermi energy shifted by 0.2 eV as indicated[89C]. See also [02G]. Symmetries in double groupnotation.

EF

Ag

Γ0

− 4

− 8

− 6

− 2

ΣK K

7+

X

8+

8+

Initi

al st

ate

ener

gy[e

V]E i

=

(110)

2 3 4Extended zone wavevector [Å ]k −1T

Fig. 91. Ag(110). Comparison of energy eigenvaluesE(k⊥) along the ΓKX direction determined from

normal-emission photoelectron spectra. Solid lines:energy bands obtained by methods using absolute k-determination [85W3]. Data points: the "free-electron-like" final-state band shown in Fig. 93 was exploited todetermine k⊥ from the experimental final state energy

[86G2]. See also [00L, 00P2, 02G].

Wavevector k

Ag

Γ ΓL Σ∆Λ KX

6 +

6 +

6 −

7 −

7 −

7 − 7 −

6 −

6 −

6 −8 −

6 −

Ener

gy[e

V]E

EF 0=S

25

20

15

5

10

4 − 5 −+

Fig. 92. Ag. Compilation ofexperimental data for the unoccupiedbands above EF [85W3]. Different

symbols reflect results obtained usingdifferent experimental techniquesand/or by different research teams, fordetails see [85W3]. The solid linesrepresent the calculated bands of[84E], see also Fig. 86. Bandsymmetries are given in double groupnotation. For further data see also[89W2, 89W3]. See also [00P2].



















54

Wavevector kΓΣKX

Fina

l sta

te e

nerg

y[e

V]E f

EF 0=

25

20

15

10

5

7+(1)

6 +(3)

6 − (5’)

7 −(5’)

6 + (1)

6 − (4’)

Ag (110)

Fig. 93. Ag(110). Final state bands for normal emissionphotoelectrons along the ΓKX direction of the Brillouinzone. Solid lines: calculated [84E], open circles:experimental results using methods for absolute k⊥-

determination [85W3]. Dotted and dashed lines: "free-electron"-parabolas fitted to the calculated bands[86G2]. Thick solid lines characterize branches ofcalculated bands with free-electron-like character[86G2]. Band symmetries in double (single) groupnotation.

Fig. 95. Ag(100). Normal-emission photoelectronspectra taken at different photon energies hν [77R]. Forthe temperature-dependence of off-normal spectra alongΓXWK see [85M]. See also [97H].

Ag (100)


IIn

tens

ity

−7 −6 −5 −4 −3 −2 −1 0 = EF

h =11.6 eVν

11.0

10.2

9.4

8.6

7.8

7.0 eV

Fig. 94. Ag(100). Normal-emission photoelectronspectra taken at different photon energies hν [78H2].See [78H2] also for photoelectrons (hν = 10.2 eV)emitted at different polar angles θ. See also [97H].

Initial state energy [eV]Ei

EF 0=

Ag (100)

IIn

tens

ity

h = 21.22 eV

h = 16.85 eV

h = 11.83 eV

ν

ν

ν

−8 −6 −4 −2













55


EF0 =

Ag (100)

IIn

tens

ity

h = 45 eVν

−8−10 −6 −4 −2

40

38

36

34

32

30

2827

2625 eV


EF0 =

Ag (100)

IIn

tens

ity

−1−2

θ = 34°

32°

30°

28°

26°

24°

22°

20°

18°

16°

←←←←Fig. 96. Ag(100). Angle-resolved electron energydistribution curves measured for normal emission withdifferent photon energies hν with (full lines) s-polarizedand (broken) s-p-polarized light [89W2]. For effects ofcircularly polarized light see [89S].


EF0 =

Ag (100)

IIn

tens

ity

h = 105 eVν

−8−10 −6 −4 −2

100

95

90

85

80

75 eV

Fig. 97. Ag(100). Angle-resolved electron energydistribution curves measured for normal emission withdifferent photon energies hν with s-polarized light[89W2].

←Fig. 98. Ag(100). Angle-resolved photoemissionspectra taken at a photon energy hν = 14 eV showing as, p-like initial state as it approaches and crosses EF

with variation of the polar angle θ along the ΓXULazimuth of the Brillouin zone. Sample temperature T =130 K [92H1]. See also [00P2].








56

Energy [eV]EEF = 0

Ag (100)

IIn

tens

ity

θ = 50°

2 4 6 8 10 12

B 3

S1B1

45°

40°

37.5°

35°

30°

32.5°

25°

20°

15°

10°

5°

0°

Fig. 99. Ag(100). Inverse photoemission spectra takenat hν = 9.5 eV for different electron incidence angles θalong the ΓXWK bulk mirror plane. Transitions intobulk (surface) states are labeled B(S) [86A].

Energy [eV]E

IIn

tens

ity

Ag(100)

EF = 0 2 4 6−2

1

Fig. 101. Ag(100). Normal-incidence inversephotoemission spectrum taken at an electron energyEi = 14.5 eV. The peak labeled 1 is due to an image

potential surface state [92H2].

Energy [eV]E

IIn

tens

ity

Ag(100)

EF = 0 2 4 6 8

S1

S2

B 1

B 2θ = 50°

47.5°

45°

42.5°

40°

37.5°

35°

30°

25°

20°

15°

10°

5°

0°

Fig. 100. Ag(100). Inverse photoemission spectra takenat hν = 9.5 eV for different electron incidence anglesalong the ΓXUL bulk mirror plane. Transitions intobulk (surface) states are labeled B(S) [86A]. See also[85R]. For an extension to energies up to 33 above EF

see [86A] and [89K1].

IIn

tens

ity

Ag (110)


0 = EF−7 − 6 −5 − 4 −3 −2 −1

h =11.6 eVν

11.0

10.2

9.4

8.6

7.8

7.0 eV

Fig. 102. Ag(110). Normal-emission photoelectronspectra taken at different photon energies hν [78H2].See [78H2] also for photoelectrons (hν = 10.2 eV) takenat different polar angles θ.











57


EF 0=

Ag (110)

IIn

tens

ity

h = 21.22 eV

h = 16.85 eV

h = 11.83 eV

ν

ν

ν

−8 −6 −4 −2

Fig. 103. Ag(110). Normal-emission photoelectronspectra taken at different photon energies hν [77R].


IIn

tens

ity

Ag (110)

−7−8 − 6 −5 − 4 − 3

θ = 34°36.5°

39°41.5°

44°

46.5°

49°51.5°

54°56.5°

59°61.5°

64°


IIn

tens

ity

ΣΓ Γ

Ag (110)

−7−8 − 6 −5 − 4Γ

KSX X X X X X

Γ Γ

G ABC676

7 86

7

8

7

C

BA

G F E D

C BA

G F E D

A

Γunpol

KLU

Γp-pol

KLU

Γs-pol

KLU

Γs-pol

KWX

Γp-pol

KWX

a

b

c

d

e

5

5

5

5

5

×

×

×

×

×

Fig. 104. Ag(110). Angle-resolved normal-emissionphotoelectron spectra taken at hν = 21.2 eV withdifferently polarized photons: (a) unpolarized (lightincident in the ΓKLU bulk mirror plane), (b) p-pol(ΓKLU), (c) s-pol (ΓKLU), (d) s-pol (ΓKWX), (e) p-pol(ΓKWX). Bottom: corresponding band structure andlocalization of several direct transitions [82G2]. Energyis with respect to EF.

Fig. 105. Ag(110). Angle-resolved photoelectronspectra taken at hν = 21.2 eV for different polar anglesθ along the ΓKLU bulk mirror plane [85W3]. Fornormal emission spectra taken at photon energies hνbetween 11eV and 36.7eV see [86G2].







58


IIn

tens

ity

Ag (110)

− 6 −2− 4

− 4°

θ

α

= 58°

= 79°

69°

59°

49°

36°

26°

16°

6°

EF = 0

Fig. 106. Ag(110). Angle-resolvedphotoelectron spectra taken at fixedpolar angle θ along the ΓKWX bulkmirror plane with p-polarized NeI-radiation (hν = 16.8 eV). The variableparameter is the angle α of lightincidence [85W2]. The shaded peakresults from a s,p-like initial state withΣ1 symmetry. Its excitation is for-

bidden at α = 0. See also [00M, 01P,02B].

Energy [eV]E

IIn

tens

ity

Ag(110)

EF = 0 2 4 6 8

S1

S4B’ 1

B 5

B’ 2

θ = 60°

55°

50°

45°

40°

35°

30°

0°

Fig. 107. Ag(110). Inverse photoemission spectra takenat hν = 9.7 eV for different electron incidence angles θalong the ΓKWX bulk mirror plane. Transitions intobulk (surface) states are labeled B(S) [86A].

Energy [eV]E

IIn

tens

ity

Ag(110)

EF = 0 2 4 6 8

S1

S2

S3

B 1

θ50°

40°

30°

25°

20°

15°

10°

5°

=

Fig. 108. Ag(110). Inverse photoemission spectra takenat hν = 9.7 eV for different electron incidence angles θalong the ΓKLU bulk mirror plane. Transitions intobulk (surface) states are labeled B(S) [86A]. For anextension to energies up to 33 eV above EF see [86A].










59I

Inte

nsity

Ag (111)


0 = EF−8 − 6 − 4 −2

h =ν 12 eV

11

10

9

8

7

6

Fig. 109. Ag(111). Normal-emission photoelectronspectra taken at different photon energies hν. The sharppeak closest to EF results from a surface state [85N].

See also [00N].


EF 0=

Ag (111)

IIn

tens

ity

h = 21.22 eV

h = 16.85 eV

h = 11.83 eV

ν

ν

ν

−8 −6 −4 −2

Fig. 111. Ag(111). Normal-emission photoelectronspectra taken at different photon energies hν [77R].

IIn

tens

ity

Ag (111)


0 = EF−3 − 1−2

Fig. 110. Ag(111). Normal-emission photelectronspectrum taken at hν = 8 eV with p-polarized light[97M], see also [96M3]. For similar results on Ag(100)see [97H]. See also [00M, 00N, 01P]. Dotted line:background.

IIn

tens

ity

Ag (111)


0 = EF− 15 − 10 −5

h =ν 32 eV

30

28

25 eV

Fig. 112. Ag(111). Normal-emission photoelectronspectra taken at different photon energies hν [90E]. Thedispersing peak marked by a vertical dash has aconstant final state energy Ef = 17 eV and results from

secondary electron emission around the Γ7-point (com-pare Fig. 92), see also [79W2]. For spin-resolvednormal photoemission spectra excited by circularlypolarized synchrotron radiation between hν = 14 eV and24 eV see [89T].















60I

Inte

nsity


− 6 −3−5−7−8 − 4Initial state energy [eV]Ei

− 6 −3−5−7−8 − 4

αα

= 70°= 25°Ag (111)

h =h =νν 25.5 eV25.5 eV

24.524.5

3,23,244 5,65,6

23.523.5

23.022.4

13.313.3

12.212.211.211.2

4,54 66

11

22

33

21.921.9

21.421.4

20.420.4

19.419.4

18.418.4

17.317.3

16.316.3

15.315.3

14.314.3

22.423.0

5

Fig. 113. Ag(111). Normal-emission photoelectronspectra taken at different photon energies hν. The lightwas p-polarized and incident at angles α = 70° (leftpanel) and α = 25° (right panel) with respect to thesurface normal [85W3]. See also [85N]. For an analysis

of the resonance-like variation of peak intensities withhν see [85W3]. These intensity resonances have alsobeen studied using constant initial state spectroscopy in[89W3] and in Fig. 114.


IIn

tens

ity

IIn

tens

ity

Initial state energy [eV]Ei Initial state energy [eV]Ei

−3 −3−5 −5−7 −7−9 −9

Ag (111)

h =h =

νν

65 eV65 eV

6060

5858

5555

5050

4545

4040

35

35

Fig. 115. Ag(111). Normal-emission photoelectron spectra taken at different photon energies hν. Left panel: s-polarized light, right panel: 25% p-polarized light [89W3]. See also [90E].









61I

Inte

nsity


− 6 −3 −2 −1−5−7−8 − 4

Ag (111)

h =ν 28.2 eV

45,6

EF = 0

27.2

26.2

25.2

24.2

23.2

22.2

21.2

20.2

19.2

18.2 eV

2,3

IIn

tens

ity

I

I

I

T = 196 K

T = 193 K

T = 191 K




2,3

5,6

4

268

260

254

349

337

327

447

428

410

520

491

467

659

601

554

18

18

18

20

20

20

22

22

22

24

24

24

26

26

26

28

28

28

Fig. 114. Ag(111). Left panel: Normal photoemissionspectra taken at different photon energies hν. Sample atT = 180 K. Right panel: constant initial state (CIS)spectra taken at initial state energies indicated byvertical dotted lines in the left panel [96M4]. The CIS-

results reveal resonance-like maxima which exhibit avery strong dependence on sample temperature T[96M4]. See also [85W3] and [89W2]. For inter-pretations in terms of final state scattering see [96O].


IIn

tens

ity

Ag (111)

−8 − 6 − 4 − 2

θ = 0°

EF = 0

2°

5°

7°

10°

12.5°

15°

40

50

20

50

SS

×

×

×

×

Fig. 116. Ag(111). Angle-resolved photoelectronspectra taken at different polar angles θ along theΓLUX bulk mirror plane. Photon energy hν = 21.2 eV[82G2]. SS labels the surface state seen prominent justat EF in Fig. 110. For results taken at θ = 10° withdifferently linear-polarized light see [82G2].










62


IIn

tens

ity

Ag (111)

−5 − 4.5 − 4 − 3.5

θ = 20°

22°24°26°27°28°29°30°31°32°33°34°35°36°37°38°40°41°42°43°44°

48°50°

46°45°

52°54°

Fig. 118. Ag(111). Angle-resolved photoelectronspectra taken at hν = 16.9 eV (NeI-radiation) fordifferent polar angles θ along the ΓLK bulk mirrorplane [85W3].

Energy [eV]E

IIn

tens

ity

Ag(111)

EF = 0 2 4 6 8

S1

B 1 B ’1

B ’1B 1

θ = 45°

S230°

15°

0°

-15°

-30°

-45°


IIn

tens

ity

Ag (111)

−8 − 6 − 4 − 2

θ = 38°

EF = 0

36°34°33°32°30°28°26°24°22°20°18°17°16°15°14°12°10°

8°6°5°

0°2°4°

Fig. 117. Ag(111). Angle-resolved photoelectronspectra taken at different polar angles θ along theΓLUX bulk mirror plane. Photon energy hν = 16.9 eV(NeI-radiation) [85W3]. For angle dependent spectrataken at hν = 10.2 eV along the ΓKLX bulk mirrorplane see [78H2].

Fig. 119. Ag(111). Inverse photoemission spectra takenat hν = 9.7 eV for different electron incidence angles θalong the ΓLU bulk mirror plane. Transitions into bulk(surface) states are labeled B(S) [86A]. For an extensionto energies up to 33eV above EF see [86A]. For earlier

work see [85M].







Ref. p. 79] 2.9 Noble metals (Au)


63

2.9.4 Au (Gold) (Z = 79)

Lattice: fcc, a = 4.08 Å [63W]Brillouin zones: see section 1.3 of this volumeElectronic configuration: [Xe] 4f145d106s1



Table 8. Au. Core-level binding energies in eV relative to EF [78C2, 92F, 95H]. Typical scatter betweenvarious sources is ± 0.1 eV.

Level n = 4 n = 5 n = 7

ns1/2 762.1 107.2 –np1/2 642.7 74.2 –np3/2 546.3 57.2 –nd3/2 353.2 – –nd5/2 335.1 – –nf5/2 – – 87.7nf7/2 – – 84.0

The 4f7/2 core-level is an often used and convenient energy-calibration standard at Eb = 83.99(5) eV[81H2]. For core-hole lifetime broadenings see [92F].

Table 9. Au. Occupied valence bands. Comparison of theoretical and experimental determination of the Γand L point in the BZ. Energies are given in eV relative to EF. If not specified, experimental errors aretypically ± 0.15 eV.

Symmetry Theory Theory Theory ARUPS ARUPS ARUPSPoints [71C] [81L2] [84E] [80M] [83B3] [86C]

Γ6+ –9.44 –8.60 –9.01 – – –

Γ8+ –5.65 –5.72 –5.75 –5.90 –6.0 –6.01(2)

Γ7+ –4.34 –4.43 –4.33 –4.45 –4.6 –4.68(5)

Γ8+ –3.29 –3.39 –3.38 –3.55 –3.65 –3.71(2)

L6+ –7.35 –7.24 –7.14 – –7.8(2) –L4+,5+ –5.82 –5.71 –5.88 – –6.2(2) –6.20(5)L6+ –4.34 –4.46 –4.52 – –4.9(1) –5.00(5)L6+ –2.81 –2.71 –3.02 – – –3.2(1)L4+,5+ –2.10 –2.20 –2.29 – – –2.3(1)L6– –0.72 –1.27 –0.37 – – –

For further data see also [79C2, 86C, 94W1].


















2.9 Noble metals (Au) [Ref. p. 79


64

Table 10. Au. Occupied valence bands. Theoretical and experimental determination of the X points.Energies are given in eV. relative to EF.

Symmetry Theory Theory Theory ARUPS ARUPSPoints [71C] [81L2] [84E] [84W1]*) [84W2]

X6+ –7.39 –7.46 –7.27 – –X7+ –7.01 –7.17 –6.89 –7.36(2) –7.5(1)X7+ –2.77 –2.94 –3.00 –3.03(2) –3.0(1)X6+ –2.60 –2.62 –2.77 –2.90(2) –2.5(1)X7+ –1.53 –1.86 –1.72 –1.85(2) –1.8(1)

*) See also [89C].

Table 11. Au. Unoccupied bands of the bulk BZ. Energies of symmetry points are given in eV relative toEF.

Symmetry Theory Theory Theory *) Experimentspoints [71C] [81L2] [84E]

Γ7– 15.58 15.54 15.8 16.0(1) 1), 15.9 2)Γ6– 18.03 16.84 18.1

18.8(5) 1)Γ8– 18.03 18.16 19.5

L6+ 3.01 3.68 3.0 3.4(1) 3), 3.6(1) 4)L6– 14.45 14.84 14.5 –

X6– 1.47 0.91 1.6 1.9(3) 5)X6+ 5.80 5.89 5.8

1) [86C] ARUPS. 2) [82J] LEER. 3) [84M] BIS. 4) [86W2] ARIPES. 5) [92H2] ARIPES.

*) Data taken from a figure.

Fermi surface radii (in units of 2π/a): kF [100] = 0.878, kF [110] = 0.736 [78H4]. For Fermi surfaces seealso Landolt-Börnstein, Vol. III/13c (1984), p. 47.

For information on the surface electronic properties see Landolt-Börnstein Vol. III/24b and Vol. III/24d.

Several authors have studied bulk and surface properties of Cu3Au(100) and Cu3Au(111), bothexperimentally and theoretically. For information we refer to [89K2, 93H, 93L1, 93L2, 96L, 99C].
























65

Figures for 2.9.4

0 200 400 600 800 1000 1200 1400

102

10

1

10−1

10 −2

10−3

10−4

Cros

s sec

tion

[M

b]σ

4d

5d

5s

4s

5p

6s

4p

4f

Au

5d


Fig. 120. Au. Atomic subshellphotoionization cross section forphoton energies from 0 to 1500 eV[85Y].

102

10

1

10−1

10 −2

0 50 100 150 200 250 300 350

Cros

s sec

tion

[M

b]σ

Au


Fig. 121. Au. Atomic 5d-subshellcross section near the Cooperminimum [85Y].


Au

I

Inte

nsity

()/

EE

bb

1000 900 800 700 600 500 400 300 200 100

MgKα

Au(4s)

AuVB

Au(4p )1/2

Au(4p )3/2

Au(4d )3/2

Au(5p )3/2

Au(4d )5/2

Au(4f )5/2

Au(4f )7/2

0

Fig. 122. Au. Overview XPS spectrumtaken with unmonochromatized MgKαradiation [79W1].






66


Au

I

Inte

nsity

4f5/2

4f7/2

90 86 82

Fig. 123. Au. XPS spectrum of the 4f spin-orbit splitcore-levels taken with monochromatized (0.5eV) AlKα-

radiation [83B4]. For results from gold-55-clusters see[91Q]. Eb relative to EF.


Au (110)- (2 1)×

I

Inte

nsity

B

S

85 84 83

Fig. 125. Au(110). Photoemission of the 4f7/2 core level

taken at a photon energy hν = 110 eV. Solid line:experimental result after background subtraction. Dashedlines: result of decomposition into bulk (B) and surface (S)components, both with a width of 0.35 eV. The observedsurface core level shift is 0.35 eV. [81H2]. Eb relative to EF.

→Fig. 126. Au(111). Photoemission of the 4f7/2 core level

taken at a photon energy hν = 110 eV. Solid line:experimental result after background subtraction.Dashed lines: result of decomposition into bulk (B) andsurface (S) components, both with a FWHM of 0.35 eV.The observed surface core level shift is 0.35eV. [81H2].Eb relative to EF.


Au (100)- (1 1)×

I

Inte

nsity

Au (100)- (5 20)×

BS

B S

85 84 83

Fig. 124. Au(100). Photoemission of the 4f7/2 core level

taken at a photon energy hν = 110 eV on (top) theunreconstructed (1x1) and the reconstructed (5x20)surface. Solid lines: experimental result afterbackground subtraction. Dashed lines: result ofdecomposition into bulk (B) and surface (S)components, both with a FWHM of 0.35 eV. Theobserved surface core level shifts are (top) 0.38 eV and(bottom) 0.28 eV [81H2]. Eb relative to EF.


Au (111)

I

Inte

nsity

B

S

85 84 83








67


IIn

tens

ity

Au

−8 −5 −1 1−3−7−9 − 6 − 4 − 2 EF = 0

Fig. 127. Au. XPS valence band spectrum [74S2] takenwith monochromatized AlKα radiation (hν = 1486.7 eV,

resolution 0.5eV).


IIn

tens

ity


− 6 −2−8 − 4

Au h =ν 40.8 eV

EF = 0

h =ν 21.2 eV

h =ν 26.9 eV

Fig. 130. Au. Angle-integrated photoelectron spectrataken at different photon energies hν frompolycrystalline (dashed) and liquid (solid lines) samples[71E].


Au

−2−8 − 6 − 4

θθ

EF = 0

0.5 eV

= 70°= 0°

15

10

5

0

1.2

0.8

0.4

4

2

0

a

b

c

d

e

IIn

tens

ity[a

rb.u

nits

]

Fig. 128. Au. XPS spectra taken withmonochromatized (0.25eV) AlKαradiation from polycrystallinesamples, at (a) normal emission and(b) at θ = 70° off-normal [78C1].Using weighting factors from thecorresponding 4f7/2 core-levelintensities, the spectra could bedecomposed into a surface DOS (c)and a bulk DOS (d) [78C1]. The shiftbetween the bulk d-band center-of-gravity (vertical solid line at −4.7 eV)and the corresponding surface value(dotted, −4.2 eV) is 0.5 eV. Trace (e)is a calculated bulk DOS from [74S2].For results obtained from gold-55-clusters see also [91Q].









68I

Inte

nsity


− 6 −2−8 − 4

Au

h =ν 40.8 eV

EF = 0

h =ν 21.2 eV

Fig. 129. Au. Photoelectron spectraobtained from polycrystalline samplesat different photon energies hν.Energy resolution ∆E = 80 meV athν = 40.8 eV and 30 meV at 21.2 eV[77B].


Refle

ctiv

ityR

0 5 10 15 20 25 30

1.0

0.8

0.6

0.4

0.2

Au

Fig. 131. Au. Experimental normal-incidence reflectivity data [81W]obtained from different experiments.For details and tables of the "mostrecommended" data see [81W]. Seealso [85P].


Diel

ectri

c con

stan

tε 2

Au8

6

4

2

0 5 10 15 20 25 30

Fig. 132. Au. Experimental ε2 spectra

[81W] obtained from differentexperiments. For details and tables ofthe "most recommended" data see[81W]. See also [85P, 02S].











69

Wavevector k

Ener

gy[R

y]E

EF

∆X

ΣΓ Γ

Λ

4.64.44.24.03.83.63.43.23.02.82.62.42.22.01.81.61.41.21.00.80.60.40.2

0− 0.2

Au

ZW

QL K,U

SX

8+

8+

7+

6+

Wavevector k

Ener

gy[e

V]E

XΓ Γ

Au

W L K,U X

24

20

16

12

8

4

0

−4

−8

Energy [eV]E - EF

DOS

[ele

ctro

ns/a

tom

eV]

⋅

DOS

[ele

ctro

ns/a

tom

eV]

⋅

EF

4

3

2

1

0−10 −5 0 5 10 15 20 25

1.0

0.5

Au L(9)L(8)

X(8)

X(9)W(9)

L(7)

X(7)

( 4)×

Γ(9)

Fig. 133. Au. Energy band structurecalculated using the relativisticaugmented-plane-wave (APW) method[76C]. The variation with temperature(simulated by calculations at differentlattice constant a) has been investi-gated in [79C2]. Symmetries in doublegroup notation.

Fig. 134. Au. Band structurecalculated by a second-principlesmethod using a combined inter-polation scheme [81L2].

Fig. 135. Au. Density-of-stateshistogram calculated with the com-bined interpolation scheme and theband structure of Fig. 134. High-symmetry critical-point locations areindicated [81L2].







70Di

elec

tric c

onst

ant

ε 2


Au

6

4

2

0 2 4 6 8 10 12 14 16 18 20 22 24

Fig. 136. Au. Calculated ε2 spectrum (solid line) in

comparison with experimental data (dots). Thecalculations were performed using a combinedinterpolation scheme and include spin-orbit effectsand momentum matrix elements [81L2].

Wavevector k

Ener

gy[e

V]E

EF

Σ

Au

Γ Γ∆ Z Q ΛX W L K55

S X

4

2

0

−2

−4

−6

−8

−10

6

78+

7

6

76

6+

8+

7 +

5

6-

7+

6+

7+

7 +

6+

6+

6+7

6

7

67

6+

6-

6

4+5

6

4+5

6

6+

6 6

6+

8+

7+

8+

5

6-

7 +

6+

7 +

7+

6+

3+4

4 +5+ +

4 +5+ +

Fig. 137. Au. Relativistic band structure along high-symmetrydirections. The calculation rests on Kohn-Sham-type relativistic one-particle equations with a local exchange-correlation potential [84E].Symmetries in double group notation.





71

Wavevector k

Ener

gy[e

V]E

EF

Σ

Au

Γ Γ∆ Z Q ΛX W L K5 5

S X

4

0

−4

−8

6

7

7

7

7

7

8+

7

67

66+

7 +

5

6-

7+

6+

7+

6+

6

6

7

6

6+

8- 8-6-

6-

6-

6-

6-

6-6-

6-

6-

7- 7-

7-

7-

7-

7- 6

6

6

6

4+5

6

4+5

6

6

6

6

6+

6

6+

6+

8+7+

5

6-

6+

6+

8

12

16

20

24

28

3+4

4 +5+ +

4 +5− −

6

Fig. 138. Au. Relativistic energybands. The calculation uses a set ofenergy parameters optimized for theenergy region above EF [84E]. Seealso Fig. 137. Symmetries in doublegroup notation.

Wavevector k

Au

Γ ∆ X

7 +

7+

6+

8+

7+

EF= 0

−1

−2

−3

− 4

−5

Initi

al st

ate

ener

gy[e

V]E i

Fig. 139. Au(100). Experimental band structure dataalong ΓX (open circles) obtained from photoemission[89C] compared to the results of a relativistic APWcalculation [71C] (solid lines). For d-hole lifetimes see[00C2, 01Z].

Wavevector k

Au

X

EF= 0

−2

−8

− 4

−6

Initi

al st

ate

ener

gy[e

V]E i

Σ ΣK K

Fig. 140. Au(110). Occupied energy bands along Σaround the X-point. Experimental points from [84W2]compared with calculated bands from [71C]. For d-holelifetimes see [00C2, 01Z].












72

Au

−2

−8

− 4

−6

−5

−7

−9

Initi

al st

ate

ener

gy[e

V]E i

Wavevector kΓΛL

0

−1

−3

−2

−8

− 4

−6

−5

−7

−9In

itial

stat

e en

ergy

[eV]

E i

0

−1

−3

6+

6+

6+

4 +5+ +

4 +5+ +

EF

Wavevector kΓΛL

7+

8+

8+

6+

(theory)

Λ6

Λ 4+5

Λ4+5

Λ 6

Λ 6

Λ6

Fig. 141. Au(111). Occupied valence band structurealong ΓL. Left panel: Solid lines represent result offirst-principles calculation [84E]. The data points arefrom [86C] and the corresponding k⊥-values wereobtained using the calculated [84E] lowest final stateband shown in Fig. 138. Right panel: Now the experi-

mental final state band (dashed in Fig. 142) was used toderive k⊥for the experimental data points. In addition,the calculated ground state bands have been rigidlyshifted down by 0.3 eV to improve visual agreement[86C]. For d-hole lifetimes see [00C2, 01Z].

Au

Ener

gy[e

V]E

Wavevector kΓΛL

6+

6−

Λ 6(3)

Λ6(1)

Λ6(1)

6−

6−

8−

7−

20

15

10

5

EF = 0

Fig. 142. Au(111). Unoccupied energy bands above EF

along ΓL [86C]. Experimental results [86C] (data pointsand dashed line) are compared with calculated firstprinciples bands [84E]. Symmetries at L and Γ indouble group notation.

IIn

tens

ity

Au (100)


0 = EF− 6 −5 − 4 −3 −2 −1

h =11.6 eVν

11.0

10.2

9.4

8.6

7.8

7.0 eV

Fig. 143. Au(100). Normal-emission photoelectronspectra taken at different photon energies hν [78H3].For photoelectrons emitted at different polar angles θ(hν = 10.2 eV) see also [78H3].














73I

Inte

nsity

Au (001)-(5 20)×


0 = EF− 6−8 − 4 −2

h =24 eVν

23

22

2120.520

14 eV

19

18171615

Fig. 144. Au(100)-(5x20). Normal-emission photoelectron spectrarecorded with s-polarized light at different photon energies hν[94W1]. For normal-emission with 25% p-polarized light see[94W1].


IIn

tens

ity

IIn

tens

ity

Au (100) Au (100)

−8 −8− 6 − 6− 4 − 4− 2 − 2

θ θ= 0° = 0°

EF = 0 EF = 0

(1 1)× (5 20)×

S45°

45°

50°50°

55°55°

60°60°

Fig. 145. Au(100). Angle-resolved photoelectron spectra taken at different polar angles along the ΓXWK bulk mirrorplane from (left) the unreconstructed and the (5x20)-reconstructed surface (right). Photon energy hν = 21.2 eV[79H3]. The peak labeled S is a d-like surface state [79H3].







74


− 7 − 7− 3 − 3− 5 − 5− 6 − 6− 4 − 4− 2 − 2

IIn

tens

ity

IIn

tens

ity

θ θ= 45° = 45°

40° 40°

35° 35°

30° 30°

20° 20°

25° 25°

15° 15°

Au (100)-(5 20)× Au (100)-(1 1)×

Fig. 146. Au(100). Angle-resolved photoelectronspectra taken at different polar angles θ along theΓXUL bulk mirror plane. Left: (5x20) reconstructedsurface, right: (1x1) surface. Sample temperature T =

60 K in both cases [95M]. The intense bulk bandtransition observed at Ei = –6.2 eV shows an intensity-resonance around θ = 35°, which is extremelytemperature dependent [95M].

IIn

tens

ity

Energy [eV]E

Au(100)

0 = EF−2 2 4 6

1

(1 1)×

(5 20)×

Fig. 147. Au(100). Normal-incidence inversephotoemission spectrum taken at an electron initial stateenergy Ei = 14.5 eV.The peaks labeled 1 are due to

image potential states. Dashed line: results for the(100)-(1x1) surface, data points refer to the (100)-(5x20) reconstructed surface [92H2].

IIn

tens

ity

Au (110)


0 = EF− 6 −5 − 4 −3 −2 −1

h =11.6 eVν

11.0

10.2

9.3

8.6

7.8

7.0 eV

Fig. 148. Au(110). Normal-emission photoelectronspectra taken at different photon energies hν [78H3].See also [78H3] for photoelectrons excited by hν = 10.2eV and emitted at different polar angles θ. For surfaceoptical properties see [02S].









75I

Inte

nsity

IIn

tens

ity

Au (110)


0 = EF− 6− 8− 9− 10 − 7 −5 − 4 −3 −2 −1Initial state energy [eV]E i

0 = EF− 6− 8− 9− 10 − 7 −5 − 4 −3 −2 −1

h =30 eVν h =

16 eVν

18 eV 8 eV

29 15

28 14

26 13

24 12.5

22 12.25

21.2 12

21 11.5

20 10

Fig. 149. Au(110)-(2x1). Normal-emission photo-electron spectra taken at different photon energies hν.p-polarized light was incident at α = 60°, with thevector potential A oriented within the ΓKLU bulk

mirror plane [89H]. See also [89H] for band mappingresults along ΓKX. The sharp and intense featureobserved at 1.8 eV below EF at 12.25 eV ≤ hν ≤ 28 eVwas interpreted as a surface resonance [89H].

IIn

tens

ity

Au (110)


0 = EF− 6−12 −3−9

h =150 eVν

90

80

70

60

50

30 eV

40

Fig. 150. Au(110)-(2x1). Normal-emission photo-electron spectra taken at different photon energies hν.p-polarized light was incident at α = 60°, with thevector potential A oriented within the ΓKLU bulkmirror plane [89H]. See also [89H] for band mappingresults along ΓKX.

Energy [eV]E

IIn

tens

ity

Au(110) -(2 1)×

EF = 0 5 10 15

S1

S1S2

S2

B 1

B 5

B 2

B 2

B 3B 4

B 6

θ = 45°

40°

35°

30°

0°

25°

20°

15°

10°

5°

‘ ‘

Fig. 151. Au(110)-(2x1). Angle-resolved inverse photo-emission spectra taken from the reconstructed surface atdifferent polar incidence angles θ along the ΓKLU bulkmirror plane. Photon energy hν = 9.4 eV, sample atroom temperature [89D]. Several transitions into bulk(B) and surface (S) states are identified [89D].










76

Energy [eV]E

IIn

tens

ity

Au(110) -(1 1)×

EF = 0 5 10 15

S1

S2

S2

B 1

B 5

B 2B 3

B 4B 6

θ = 45°

40°

35°

30°

0°

25°

20°

15°

10°

5°Fig. 152. Au(110)-(1x1). As Fig. 151 but with thesample held at T = 1000 K to obtain the unreconstructedsurface. Dashed lines indicate structures only seen at thereconstructed phase [89D].

IIn

tens

ity


− 6 −3 −2 −1−5−7−8−9 − 4

Au (111)

h =ν 27 eV

EF = 0

26252423

22

21

20191817

16151413.51312.5121110

9

SE

S

2,3

4

5,6

2

34

5,6

D1

D3

D2

Fig. 153. Au(111). Normal-emissionphotoelectron spectra taken at differentphoton energies hν [86C].The featureslabeled D1-D3 are assigned [86C, 86Z]to surface resonances. Peak S issurface state. SE labels weak structurefrom secondary electron emission. Theresonance-like variation of peakamplitudes with hν has been studiedand discussed in [86C]. See also Figs.154 and 155, and see [80M] for earlierwork. For photoelectrons emitted atdifferent polar angles with hν = 10.2eV see [78H3]. Ei relative to EF.










77I

Inte

nsity


− 6 −3 −2−5−7−8 − 4

Au (111)

h =ν 23.3 eV

2,34

5 6

D1

D1

D3

D3

D2

D2

23.0

22.7

22.3

22.0

21.7

21.3

21.0

20.720.320.019.719.319.018.618.3

←←←←Fig. 154. Au(111). Normal-emissionphotoelectron spectra recorded at differentphoton energies hν [86C]. The featureslabeled D1-D3 are assigned to surfaceresonances [86Z]. For d-hole lifetimes see[00C2, 01Z].

Fig. 155. Au(111). Normal-emissionphotoelectron spectra taken at a sampletemperature T = 150 K for different photonenergies hν (left panel). Dotted line: initialstate energies 2, 4 used to record the CISspectra I2, I4 in the right panel in theirdependence on sample temperature T[96M4]. See also [78H1] for earlier work.For off-normal data and corresponding one-step-model calculations see [96P].↓↓↓↓


− 6 −3 −2 −1−5−7−8 − 4

Au (111)

h =ν 26.2 eV

EF = 0

25.2

24.2

23.2

22.2

21.2

20.2

19.2

18.2

17.2

16.2 eV

IIn

tens

ityI

Inte

nsity

IIn

tens

ity

I

I

T = 180 K

T = 181 K

299

280

412

400

558

569

663

677

2 4

Photon energy [eV]hν18 20 22 24 2616

Photon energy [eV]hν18 20 22 24 2616

2

4










78


− 6 −3−5 − 4

Au (111)

IIn

tens

ity

A

A

IIn

tens

ity

T = 70 K1.0

0.8

0.6

0.4

0.2

1.0

0.8

0.6

0.4

0.2

1.0

0.8

0.6

0.4

0.2

1.0

0.8

0.6

0.4

0.2

T = 0 K

Emission angle [ ° ]0 10 20 30

θ0 200 400 600

Temperature [K]T

θ = 20°

θ = 10°

θ = 5°

θ = 20°

θ = 10°

θ = 0°

a b c

d e f

exp.

calc.

Fig. 156. Au(111). Angle-resolved photoelectronspectra (a) taken at a sample temperature of T = 30 K(thick line) and T = 560 K (thin line). Photon energyhν = 21.2 eV, electron polar angle θ = 20° along theΓLUX bulk mirror plane. The intensity of the peaklabeled A in (a) shows a strong intensity variation with θ,

as displayed in (b) for T = 70 K. Panel (c) shows thetemperature dependence of peak A at different emissionangles θ. Panels (d)-(f) show the same quantities ascalculated within the framework of the fully-relativisticone-step model of photoemission [98M1].


2.9 Noble metals (References)


79

2.9.5 References for 2.9

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(1979) 6164.80E Eberhardt, W., Himpsel, F. J.: Phys. Rev. B 21 (1980) 5572.



80

80M Mills, K. A., Davis, R. F., Kevan, S. D., Thornton, G., Shirley, D. A.: Phys. Rev. B 22 (1980)581.

80P Petroff, Y., Thiry, P.: Appl. Opt. 19 (1980) 3957.80S Smith, N. V., Benbow, R. L., Hurych, Z.: Phys. Rev. B 21 (1980) 4331.81B Borstel, G., Neumann, M., Wöhlecke, M.: Phys. Rev. B 23 (1981) 3121.81C1 Courths, R.: Solid State Commun. 40 (1981) 529.81C2 Courths, R., Bachelier, V., Cord, B., Hüfner, S.: Solid State Commun. 40 (1981) 1059.81H1 Hussain, Z., Kono, S., Petersson, L.-G., Fadley, C. S., Wagner, L. F.: Phys. Rev. B 23 (1981)

724.81H2 Heimann, P., van der Veen, J. F., Eastman, D. E.: Solid State Commun. 38 (1981) 595.81H3 Holloway, S., Grider, D. E., Sass, J. K.: Solid State Commun. 39 (1981) 953.81J Jepsen, O., Gloetzel, D., Mackintosh, A. R.: Phys. Rev. B 23 (1981) 2683.81L1 Larsson, C. G., Pendry, J. B.: J. Phys. C: Solid State Phys. 14 (1981) 3089.81L2 Lässer, R., Smith, N. V., Benbow, R.: Phys. Rev. B 24 (1981) 1895.81W Weaver, J. H., Krafka, C., Lynch, D. W., Koch, E. E.: Optical properties of metals, Vol. 2,

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50 (1984) 47.84R Reihl, B., Schlittler, R. R.: Phys. Rev. B 29 (1984) 2267.84S Speier, W., Fuggle, J. C., Zeller, R., Ackermann, B., Szot, K., Hillebrecht, F. U., Campagna,

M.: Phys. Rev. B 30 (1984) 6921.84W1 Wern, H., Leschik, G., Hau, U., Courths, R.: Solid State Commun. 50 (1984) 581.84W2 Wöhlecke, M., Baalmann, A., Neumann, M.: Solid State Commun. 49 (1984) 217.84Z Zimmer, H. G., Westphal, D., Kleinherbers, K. K., Goldmann, A., Richard, A.: Surf. Sci. 146

(1984) 425.85B Baalmann, A., Neumann, M., Braun, W., Radlik, W.: Solid State Commun. 54 (1985) 583.85G Goldmann, A., Dose, V., Borstel, G.: Phys. Rev. B 32 (1985) 1971.85H Hulbert, S. L., Johnson, P. D., Stoffel, N. G., Smith, N. V.: Phys. Rev. B 32 (1985) 3451.85K Krause, M. O., Sevensson, W., Carlson, T. A., Leroi, G., Ederer, D. E., Holland, D., Parr, A.

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81

85N Nelson, J. G., Kim, S., Gignac, W. J., Williams, R. S., Tobin, J. G., Robey, S. W., Shirley, D.A.: Phys. Rev. B 32 (1985) 3465.

85P Palik, E. D., (ed.): Handbook of Optical Constants of Solids, Academic, Orlando 1985.85R Reihl, B.: Surf. Sci. 162 (1985) 1.85S Speier, W., Zeller, R., Fuggle, J. C.: Phys. Rev. B 32 (1985) 3597.85W1 Wern, H., Courths, R.: Surf. Sci. 152/153 (1985) 196.85W2 Wern, H., Courths, R.: Surf. Sci. 162 (1985) 29.85W3 Wern, H., Courths, R., Leschik, G., Hüfner, S.: Z. Phys. B: Condens. Matter 60 (1985) 293.85Y Yeh, J. J., Lindau, I.: At. Data Nucl. Data Tables 32 (1985) 1.86A Altmann, W., Dose, V., Goldmann, A.: Z. Phys. B: Condens. Matter 65 (1986) 171.86C Courths, R., Zimmer, H.-G., Goldmann, A., Saalfeld, H.: Phys. Rev. B 34 (1986) 3577.86D Donath, M., Glöbl, M., Senftinger, B., Dose, V.: Solid State Commun. 60 (1986) 237.86G1 Goldmann, A.: Surf. Sci. 178 (1986) 210.86G2 Goldmann, A., Zimmer, H.-G., Courths, R., Saalfeld, H.: Solid State Commun. 57 (1986) 523.86J Jacob, W., Dose, V., Kolac, U., Fauster, Th., Goldmann, A.: Z. Phys. B: Condens. Matter 63

(1986) 459.86W1 White, R. C., Fadley, C. S., Sagurton, M.: Solid State Commun. 59 (1986) 633.86W2 Woodruff, D. P., Royer, W. A., Smith, N. V.: Phys. Rev. B 34 (1986) 764.86Z Zimmer, H.-G., Goldmann, A., Courths, R.: Surf. Sci. 176 (1986) 115.87W White, R. C., Fadley, C. S., Sagurton, M., Roubin, P., Chandesris, D., Lecante, J., Guillot, C.,

Hussain, Z.: Phys. Rev. B 35 (1987) 1147.88A Altmann, W., Desinger, K., Dose, V., Goldmann, A.: Solid State Commun. 65 (1988) 1411.89C Courths, R., Wern, H., Leschik, G., Hüfner, S.: Z. Phys. B.: Condens. Matter 74 (1989) 233.89D Drube, R., Dose, V., Derks, H., Heiland, W.: Surf. Sci. 214 (1989) L253.89F Fauster, Th., Schneider, R., Dürr, H.: Phys. Rev. B 40 (1989) 7981.89H Hansen, J. C., Benson, J. A., Wagner, M. K., Tobin, J. G.: Solid State Commun. 69 (1989)

1197.89K1 Kim, B., Hong, S., Lin, R., Lynch, D. W.: Phys. Rev. B 40 (1989) 10238.89K2 Krummacher, S., Sen, N., Gudat, W., Johnson, R., Grey, F., Ghijsen, J.: Z. Phys. B: Condens.

Matter 75 (1989) 235.89K3 Kwawer, G. N., Miller, T. J., Mason, M. G., Tan, Y., Brown, F. C., Ma, Y.: Phys. Rev. B 39

(1989) 1417.89S Schneider, C. M., Garbe, J., Bethke, K., Kirschner, J.: Phys. Rev. B 39 (1989) 1031.89T Tamura, E., Feder, R., Vogt, B., Schmiedeskamp, B., Heinzmann, U.: Z. Phys. B: Condens.

Matter 77 (1989) 129.89W1 Wu, S. C., Sokolov, J., Lok, C. K. C., Quinn, J., Li, Y. S., Tian, D., Jona, F.: Phys. Rev. B 39

(1989) 12891.89W2 Wu, S. C., Lok, C. K. C., Sokolov, J., Quinn, J., Li, Y. S., Tian, D., Jona, F.: J. Phys. Condens.

Matter 1 (1989) 4795.89W3 Wu, S. C., Li, H., Sokolov, J., Quinn, J., Li, Y. S., Jona, F.: J. Phys.: Condens. Matter 1 (1989)

7471.90E Edamoto, K., Miyazaki, E., Skimokoshi, K., Kato, H.: Phys. Scripta 41 (1990) 91.90F Fuster, G., Tyler, J. M., Brener, N. E., Callaway, J., Bagayoko, D.: Phys. Rev. B 42 (1990)

7322.90L Lange, C., Mandel, T., Laubschat, C., Kaindl, G.: J. Electron Spectrosc. Relat. Phenom. 52

(1990) 49.90S Schneider, R., Dürr, H., Fauster, Th., Dose, V.: Phys. Rev. B 42 (1990) 1638.91G Goldmann, A., Altmann, W., Dose, V.: Solid State Commun. 79 (1991) 511.91Q Quinten, M., Sander, I., Steiner, P., Kreibig, U., Fauth, K., Schmid, G.: Z. Phys. D: At. Mol.

Clusters 20 (1991) 377.92F Fuggle, J. C., Inglesfield, J. E., (eds.): Unoccupied Electronic States, Vol. 69, Topics Appl.

Phys., Springer, Berlin-Heidelberg, 1992.92H1 Hwu, Y., Lozzi, L., La Rosa, S., Onellion, M., Almeras, P., Gozzo, F., Lévy, F., Berger, H.,

Margaritondo, G.: Phys. Rev. B 45 (1992) 5438.



82

92H2 Himpsel, F. J., Ortega, J. E.: Phys. Rev. B 46 (1992) 9719.92S1 Schneider, R., Dose, V.: Chapter 9 in [92F], p. 277 ff.92S2 Smith, N. V.: Comments Condens. Matter. Phys. 15 (1992) 263.93G Goldmann, A., Matzdorf, R.: Progr. Surf. Sci. 42 (1993) 331.93H Halilov, S., Gollisch, H., Tamura, E., Feder, R.: J. Phys.: Condens. Matter 5 (1993) 4711.93L1 Lau, M., Löbus, S., Courths, R., Halilov, S., Gollisch, H., Feder, R.: Ann. Phys. 2 (1993) 450.93L2 Löbus, S., Lau, M., Courths, R., Halilov, S.: Surf. Sci. 287/288 (1993) 568.93M1 Matzdorf, R., Meister, G., Goldmann, A.: Surf. Sci. 286 (1993) 56.93M2 Matzdorf, R., Meister, G., Goldmann, A.: Surf. Sci. 296 (1993) 241.93S1 Smith, N. V., Thiry, P., Pétroff, Y.: Phys. Rev. B 47 (1993) 15476.93S2 Starnberg, H. I., Bauer, H. E., Nilsson, P. O.: Phys. Rev. B 48 (1993) 621.94A Aebi, P., Osterwalder, J., Fasel, R., Naumovic, D., Schlapbach, L.: Surf. Sci. 307-309 (1994)

917.94M1 Matzdorf, R., Goldmann, A.: Solid State Commun. 91 (1994) 163.94M2 Matzdorf, R., Paniago, R., Meister, G., Goldmann, A.: Solid State Commun. 92 (1994) 839.94W1 Wu, S. C., Li, H., Quinn, J., Tian, D., Li, Y. S., Begley, A. M., Kim, S. K., Jona, F., Marcus, P.

M.: Phys. Rev. B 49 (1994) 8353.95H Hüfner, S.: Photoelectron Spectroscopy - Principles and Applications, Vol. 82 Springer Ser.

Solid-State Sci., Springer, Berlin-Heidelberg, 1995.95K Krasovskii, E. E., Schattke, W.: Solid State Commun. 93 (1995) 775.95M Matzdorf, R., Paniago, R., Meister, G., Goldmann, A., Courths, R.: Surf. Sci. Lett. 343 (1995)

L1182.95Q Qu, Z., Goonewardene, A., Subramanian, K., Karunamuni, J., Mainkar, N., Ye, L., Stockbauer,

R. L., Kurtz, R. L.: Surf. Sci. 324 (1995) 133.96L Löbus, S., Courths, R., Halilov, S., Gollisch, H., Feder, R.: Surf. Rev. Lett. 3 (1996) 1749.96M1 Matzdorf, R., Meister, G., Goldmann, A.: Phys. Rev. B 54 (1996) 14807.96M2 Matzdorf, R., Goldmann, A.: Surf. Sci. 359 (1996) 77.96M3 Miller, T., McMahon, W. E., Chiang, T.-C.: Phys. Rev. Lett. 77 (1996) 1167.96M4 Matzdorf, R., Paniago, R., Meister, G., Goldmann, A., Zubrägel, Ch., Braun, J., Borstel, G.:

Surf. Sci. 352-354 (1996) 670.96O Osterwalder, J., Greber, T., Aebi, P., Fasel, R., Schlapbach, L.: Phys. Rev. B 53 (1996) 10209.96P Paniago, R., Matzdorf, R., Meister, G., Goldmann, A., Braun, J., Borstel, G.: Surf. Sci. 347

(1996) 46.96S Strocov, V. N., Starnberg, H. I., Nilsson, P. O.: J. Phys.: Condens. Matter 8 (1996) 7539.97H Hansen, E. D., Miller, T., Chiang, T.-C.: Phys. Rev. B 55 (1997) 1871.97M Miller, T., Hansen, E. D., McMahon, W. E., Chiang, T.-C.: Surf. Sci. 376 (1997) 32.97O Ogawa, S., Nagano, H., Petek, H.: Phys. Rev. B 55 (1997) 10869.97P1 Pawlik, S., Bauer, M., Aeschlimann, M.: Surf. Sci. 377-379 (1997) 206.97P2 Petek, H., Ogawa, S.: Progr. Surf. Sci. 56 (1997) 239.97W Wolf, M.: Surf. Sci. 377-379 (1997) 343.98A Aebi, P., Fasel, R., Naumovic, D., Hayoz, J., Pillo, Th., Bovet, M., Agostino, R. G., Patthey,

L., Schlapbach, L., Gil, F. P., Berger, H., Kreutz, T. J., Osterwalder, J.: Surf. Sci. 402-404(1998) 614.

98F Fluchtmann, M., Bei der Kellen, S., Braun, J., Borstel, G.: Surf. Sci. 402-404 (1998) 663.98G Gerlach, A., Matzdorf, R., Goldmann, A.: Phys. Rev. B 58 (1998) 10969.98H Hansen, E. D., Miller, T., Chiang, T.-C.: Phys. Rev. Lett. 80 (1998) 1766.98K Knoesel, E., Hotzel, A., Wolf, M.: Phys. Rev. B 57 (1998) 12812.98M1 Matzdorf, R.: Surf. Sci. Rep. 30 (1998) 153.98M2 Matzdorf, R., Goldmann, A.: Surf. Sci. 400 (1998) 329.98M3 Matzdorf, R., Gerlach, A., Hennig, R., Lauff, G., Goldmann, A.: J. Electron Spectr. Relat.

Phenom. 94 (1998) 279.98P Pawlik, S., Burgermeister, R., Bauer, M., Aeschlimann, M.: Surf. Sci. 402-404 (1998) 556.99C Courths, R., Löbus, S., Halilov, S., Scheunemann, T., Gollisch, H., Feder, R.: Phys Rev. B 60

(1999) 8055.



83

99H Hüfner, S., Claessen, R., Reinert, F., Straub, Th., Strocov, V. N., Steiner, P.: J. ElectronSpectrosc. Relat. Phenom. 100 (1999) 191.

99M Matzdorf, R., Gerlach, A., Goldmann, A., Fluchtmann, M., Braun, J.: Surf. Sci. 421 (1999)167.

99P1 Paggel, J. J., Miller, T., Chiang, T.-C.: Phys. Rev. Lett. 83 (1999) 1415.99P2 Petek, H., Ogawa, S.: Phys. Rev. Lett. 83 (1999) 832.00C1 Campillo, I., Pitarke, J. M., Rubio, A., Echenique, P. M.: Phys. Rev. B 62 (2000) 1500.00C2 Campillo, I., Rubio, A., Pitarke, J. M., Goldmann, A., Echenique, P. M.: Phys. Rev. Lett. 85

(2000) 3241.00C3 Chiang, T.-C.: Chem. Phys. 251 (2000) 133.00E Echenique, P. M., Pitarke, J. M., Chulkov, E. V., Rubio, A.: Chem. Phys. 251 (2000) 1.00K Kliewer, J., Berndt, R., Chulkov, E. V., Silkin, V. M., Echenique, P. M., Crampin, S.: Science

288 (2000) 1399.00L Luh, D. A., Paggel, J. J., Miller, T., Chiang, T.-C.: Phys. Rev. Lett. 84 (2000) 3410.00M Michalke, T., Gerlach, A., Berge, K., Matzdorf, R., Goldmann, A.: Phys. Rev. B 62 (2000)

10544.00N Nicolay, G., Reinert, F., Schmidt, S., Ehm, D., Steiner, P., Hüfner, S.: Phys. Rev. B 62 (2000)

1631.00P1 Petek, H., Nagano, H., Weida, M. J., Ogawa, S.: Chem. Phys. 251 (2000) 71.00P2 Paggel, J. J., Miller, T., Chiang, T.-C.: Phys. Rev. B 61 (2000) 1804.01G Gerlach, A., Berge, K., Goldmann, A., Campillo, I., Rubio, A., Pitarke, J. M., Echenique, P.

M.: Phys. Rev. B 64 (2001) 085423.01P Pforte, F., Michalke, T., Gerlach, A., Goldmann, A., Matzdorf, R.: Phys. Rev. B 63 (2001)

115405.01S1 Strocov, V. N., Claessen, R., Nicolay, G., Hüfner, S., Kimura, A., Harasawa, A., Shin, S.,

Kakizaki, A., Starnberg, H. I., Nilsson, P. O., Blaha, P.: Phys. Rev. B 63 (2001) 205108.01S2 Stahrenberg, K., Herrmann, Th., Wilmers, K., Esser, N., Richter, W.: Phys. Rev. B 64 (2001)

115111.01Z Zhukov, V. P., Aryasetiawan, F., Chulkov, E. V., Echenique, P. M.: Phys. Rev. B 64 (2001)

195122.02B Berge, K., Gerlach, A., Meister, G., Goldmann, A., Braun, J.: Surf. Sci. 498 (2002) 1.02G Gerlach, A., Berge, K., Michalke, T., Goldmann, A., Müller, R., Janowitz, C.: Surf. Sci. 497

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115116.

2.10 Noble metal halides (Introduction) [Ref. p. 156


84

2.10 Noble metal halides

2.10.1 Introduction

This chapter collects data on CuCl, CuBr, CuI, AgF, AgCl, AgBr and AgI. These I-VII compoundsexhibit Phillips ionicities fi just at the border line between tetrahedral and octahedral coordination. Valuesof fi for the Cu- and Ag-halides are as follows: CuF (fi =0.766), CuCl (0.746), CuBr (0.735), CuI (0.692),AgF (0.894), AgCl (0.856), AgBr (0.850) and AgI (0.770). Whereas the Cu-halides and AgI still form thezincblende or the wurtzite lattice at normal pressure and room temperature, in AgF, AgCl and AgBr theionicity is already so large that the rocksalt structure is favoured energetically. Thus the Cu- and Ag-halides are situated in the region between tetrahedral and octahedral coordination, which in turn leads tothe existence of a variety of high-pressure phases, polymorphs and a rather complex phase diagram. Fordetails we refer to Landolt-Börnstein volumes on “Semiconductors”, i.e. Vol. III/41B or previousvolumes III/17b and III/22a, and to references [77G, 81V, 86B, 98H].

Since CuF is chemically very unstable, no photoemission experiments were performed so far. Incontrast CuCl, CuBr and CuI have received very much attention, both from experiment and theory. Thisinterest results from the fact that their valence bands originate from the filled d10-shell of the metal+ -ionsand the s2p6 rare gas configuration of the halogen-ions. This is in contrast to the III-V and many other I-VII compounds whose valence bands also originate from a s2p6 configuration, but with the metal d-levelsenergetically well below the valence region. In the Cu-halides the spatial extent of the d-levels is large,their energies are close to those of the halogen p-levels, and a strong p-d hybridization results. Thus thezincblende lattice of the Cu-halides is built up by directed sp3 - sd3 bonds. In consequence thesecompounds show several physical properties significantly altered if compared to the other members of thegroup IV, III-V and II-VI isomorphic series. For example it was observed already very early [63C] that inCuCl the spin-orbit splitting of the edge exciton is reversed from that of "normal" zincblendesemiconductors. The bulk moduli are very much smaller than those of their isostructural neighbours[72H]. Also, the small magnitude [81V, 83B, 84C] of the deformation potentials of gaps and valence-state splittings related to hydrostatic and uniaxial strains can be attributed to strong d-p hybridization[86B]. The d10-admixture increases the number of valence electrons per formula unit from 8 (sp3-bonds)to 18, and this fact considerably complicates the task of calculating the energy-band structure of thesematerials. In consequence, a variety of techniques was used, both in nonrelativistic and relativisticversions, to figure out to which extent the calculated energy bands and the corresponding densities ofstates may explain the experimental data. Many of these theoretical results are reproduced in the presentchapter.

The silver halides are of important technical interest as photographic material. The promotion ofelectrons from the valence to the conduction bands by light absorption plays a major role in thephotographic process [88H, 93K]. Also they are of importance as solid electrolytes [82M, 87E], with α-AgI having an ionic conductivity similar to molten salts, and as liquid semiconductors [90E]. Moreover,the growth of bulk silver halide adlayers as well as halide-modified Ag surfaces are of relevance forcatalytic surface properties, interfacial electrochemistry, sensors and the development of thin-film solidlubricants. Besides this technical importance the nearly energetic degeneracy of the metal d orbitals withthose of the halogen attracts basic interest. The strong p-d hybridization causes AgF, AgCl and AgBr tohave indirect band gaps, in contrast to their isoelectronic neighbours CuCl and CuBr. In consequencethere was and still is considerable effort to understand the electronic properties of both the Cu- and Ag-halides and this ongoing interest explains the large amount of data available for these compounds.
















Ref. p. 156] 2.10 Noble metal halides (Introduction)


85

As a result of the p-d orbital mixing the photoelectron spectra are composites of both the halogen andmetal partial densities of states. Their relative intensities will therefore vary with photon energy accordingto the corresponding photoionization cross sections, and these variations may be drastic. For examplegoing from hν = 21.2 eV (HeI) to hν = 40.8 eV (HeII) decreases the metal cross sections by a factor ofabout 1.3 (Cu) and 1.04 (Ag), respectively [74G1]. In contrast the excitation probabilities for the halogenatoms go down by factors of about 15.2, 10.9 and 30.3 for Cl, Br and I [74G1]. Using either experimentalor theoretical cross-section ratios (at appropriate photon energies) as an input allows approximate partialp and d densities to be deduced from the experimental photelectron energy distribution curves. Thisprocedure was applied in several studies, and for further details of the analysis, various sources ofexperimental or calculated cross-section data and a discussion on possible p-d interference effects, werefer to the literature [72K1, 72K2, 73K, 74E2, 74G1, 74K1, 74K2, 74T, 75T, 77G, 78P, 79L, 80B, 80M,86S, 90M, 91S, 93M1].

Most experimental data reported in the following are taken from thin films, typically at a thickness ofonly a few hundred Å. These films, deposited either epitaxially or as polycrystalline material, generallyhave enough photoconductivity to avoid sample charging. Special care is necessary since during exposureto ultraviolet photons and soft X-rays at room temperature severe damage effects may be observed, inparticular if high-intensity synchrotron radiation is used [93M2]. Photolysis is, however, almostcompletely quenched at liquid nitrogen temperature [78C, 89K, 91W, 93M2]. At these low temperaturesinterstitial Cu+ and Ag+ migration is significantly slowed and this fact inhibits latent-image formation bymetal atom clustering. Taking photoelectron spectra at low temperatures has the additional advantage thatlinewidths are significantly narrowed [76B1, 76B2, 76L].

Landolt-Börnstein Vol. III/41B as well as previous volumes III/17b and III/22a summarize veryextensively data on the following quantities: gap energies, corresponding pressure coefficients anddeformation potentials, exciton parameters like energies and splittings and masses, g-factors, biexcitons,lattice properties, phonon frequencies and linear as well as non-linear optical constants. These data aretherefore not collected systematically in this chapter. For most recent data on nanocrystals we refer to[99E, 99O, 99Z, 00G, 00V], see also Landolt-Börnstein Vol. III/34C1, Chap. 6 (publ: in 2001).


































2.10 Noble metal halides (CuCl) [Ref. p. 156


86

2.10.2 CuCl (Cuprous chloride)

At normal conditions CuCl crystallizes in the zincblende structure (γ-CuCl):Lattice fcc, a = 5.4057 Å [63W],space group Td

2 - F 4 3m,Brillouin zones see section 1.3 of this volume.

Work-function (γ-CuCl):φ (polycrystalline) = 6.8(4) eV [74G1], 7.0(2) eV [79P], 6.9(2) eV [83G]φ (100) = 7.0(2) eV [83G]φ (111) = 6.8(2) eV [83G]

Direct band gap at Γ with Eg = 3.395 eV at T = 4K as best value extrapolated from various optical results[77G]. At room temperature Eg = 3.17eV (at zero pressure) has been derived from experiments studying

the absorption edge under hydrostatic pressure [81V]. Bulk plasmon energy ωp = 20.9(5)eV [74G1]. Forexcitonic and phononic properties of CuCl nanocrystals see [99E, 99O, 99Z] or Landolt-Börnstein, Vol.III/34C1, Chap. 6.

For the phase diagram and structural details of high-temperature / high pressure phases see Landolt-Börnstein Vols. III/41B, III/17b and [81V, 86B].

Table 1. γ-CuCl. Copper core-level binding energiesin eV relative to the top of the valence band [74G1].

Level n = 2 n = 3

ns1/2 1095.3(2) 121.2np1/2 950.8 76.5(2)np3/2 931.0 74.0(2)

Errors ±0.1eV unless otherwise stated. If referred to the vacuum level the Cu-ion core levels show achemical shift of 1.1(5)eV and are more tightly bound in CuCl than in metallic copper [74G1].

Table 2. γ-CuCl. Occupied valence bands. Critical point energies determined bydifferent experiments. Experimental errors are ± 0.1eV if not explicitly given inparentheses. Energy values are given in eV with respect to the top of the valence band.Symmetries are indicated in double (single) group notation.

SymmetryPoints

UPS[77G]

ARUPS[80W]

ARUPS[83G]

Reflectivity[83L]

Γ7,8 (Γ15) Γ8 (Γ12)

b)

Γ7,8 (Γ15) Γ6 (Γ1)

0–1.9–3.5–15.8(2)a)

0–2.0–5.0–

0–1.9–4.9–15.8(2)a)

0–1.5–3.4–15.7

X6,7 (X5)X6 (X3)X6,7 (X5)X6 (X3)X7 (X3)

–1.3–1.5–5.1–6.9–15.8(2)a)

–1.05–1.5––6.15–

–1.0–1.5–4.9–6.1–15.8(2)a)

–––3.4–4.9–15.7

cont.





















Ref. p. 156] 2.10 Noble metal halides (CuCl)


87

Table 2 (cont.)

SymmetryPoints

UPS[77G]

ARUPS[80W]

ARUPS[83G]

Reflectivity[83L]

L4,5,6 (L3)L4,5,6 (L1)L6 (L3)L4,5,6 (L1)L6 (L1)

–1.0–1.5–4.6–6.8–15.8(2)a)

–0.55–1.35––6.3–

–0.6–1.9–4.9–6.1–15.8(2)a)

–0.9–3.4–4.9––15.7

a) Data taken from [74G1].b) The Γ12 point has been located at –1.79 eV by two-photon absorption at T = 4.3 K [82F1].

Table 3. γ-CuCl. Unoccupied bands of the bulk. Experimental energies of symmetry points are given ineV with respect to the top of the valence band. Symmetries are given in single group notation.

Symmetry Γ15 X1 X5 X3 Γ15 L1 L3 L1

ARUPS 9.6(2) 7.8(2) 9.6(2) 12.1(2) – 8.1(2) 9.6(2) 11.4(3)[83G]

Reflectivity 9.7 7.2 – 12.6 17.5 8.7 – 11.4[83L]

Others – 7.3 a) – 12.3 b) 17.5 a) 8.5 a) – 11.7 a)

17.7 b) 8.6 b)

a) Deduced from Cl(2p) core-level absorption [71S].b) Deduced from Cl(1s) core-level absorption [73S].

Table 4. γ-CuCl. Calculated critical point energies at Γ according to different authors. All data given ineV relative to the top of the valence band. Symmetries are given in double (single) group notation.

Symmetry [67S] [73C] [79D] [79K1] [79K2] [79Z] [80O] [83L]Point

Γ7,8 (Γ15) +10.9 +9.4 +10.1 +10.13 – +9.6 – +9.7

Γ6 (Γ1) +3.4 +3.4 +3.07 +4.32 +3.1 +2 +3.57 +3.4

Γ7,8 (Γ15) 0 0 0 0 0 0 0 0

Γ8 (Γ12) –0.6 –1.41 –1.0 –3.4 –1.5 –1.33 –1.14 –1.47

Γ7,8 (Γ15) –2.7 –4.42 –3.13 –7.46 –3.8 –4.9 –4.3 –3.4

Γ6 (Γ1) –18 –16 –15.6 –25.7 –15.7 –16.8 – –15.7

The occupied Γ12 state has been calculated at –1.80eV using a quasimolecular approach [83E].

The fraction of p-like density of states at the γ-phase valence band edge has been determined in manyexperimental and theoretical studies. All experimental data range between 21 and 25% [77G], whilecalculated values scatter between 21 and 40% [83L]. The percentage of different symmetry types (s,p,d)integrated within each band has been calculated in [83L].

























88

Figures for 2.10.2

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ

Photon energy [eV]hν600 1200

102

10–2

10–1

1

10–3

10

Cl

2p

2s

3p

3s

4

2

68

4

2

68

4

2

68

4

2

68

4

2

68

Fig. 1. CuCl. Atomic subshellphotoionization cross sections ofchlorine for photon energies from0 to 1500 eV [85Y]. For atomiccopper see Fig. 1 in section 2.9.

0.5

0

1.0

1.5

2.0

2.5

3.0


–11 – 9 – 7 – 5 – 3 – 1 1

CuCl

EF

0

Fig. 2. γ-CuCl. XPS valence band spectrum taken froma polycrystalline sample with unmonochromatizedMgKα radiation at hv = 1253.6 eV [73K]. See also

[74G1]. For the results of a deconvolution whichcorrects for experimental broadening see [73K].







89

0

6

12

18

0– 2– 6 – 4– 8Initial state energy [eV]Ei

0

2

4

60

0.6

1.2

1.80

2

4

60

0.2

0.4

0.6

CuCl

EVBM

hν = 48.4 eV

(× 6)

(× 7)

hν = 40.8 eV

hν = 26.9 eV

hν = 21.2 eV

hν = 16.8 eV

Fig. 3. γ-CuCl. Photoelectron spectra taken for differentphoton energies from polycrystalline films. Dashed linesindicate estimated secondary electron background[74G1]. →Fig. 4. γ-CuCl. Photoelectron spectra taken at differentphoton energies hv from polycrystalline films [74I].

0.5

1.0

1.5

2.0

2.5

0


–12 – 10 – 8 – 4– 6 – 2 0 2

CuCl hν = 76 eV

EF

1

2

3

4

7

0


–12 – 10 – 8 – 4– 6 – 2 0 2

hν = 61 eV

EF

0.5

1.0

1.5

2.0

3.5

0


–12 – 10 – 8 – 4– 6 – 2 0 2

hν = 40 eV

EF

2.5

3.0

5

6





90

2 4 6 8 1210 14 16 2218 20Final state energy [eV]Ef

CuCl

Fig. 5. γ-CuCl. Bremsstrahlung-isochromat spectrum(BIS) taken at hv = 1486.6 eV, sample holder kept atliquid nitrogen temperature [94L]. The energy scale wascalibrated by the author of this chapter using Fig. 1 in[90H]. It may be accurate to ±1 eV and refers to energyzero at valence band maximum.

Abso

rptio

n co

effic

ient

[10

cm]

α5

–1

2.5

5.0

7.5

10.0

12.5

15.0


CuCl

Fig. 6. γ-CuCl. Absorption spectrum taken from apolycrystalline sample at liquid nitrogen temperature[72I].

5.0 7.5 10.0 15.0 17.5 20.0 30.00

5

10

20

15

25

35

30

40


Refle

ctiv

ity[%

]R

12.5 22.5 25.0 27.5

CuCl

5.90

11.17

12.07

13.10

13.90

8.47

14.65

7.35

9.70

9.30

10.30

6.80

Fig. 7. γ-CuCl. Reflectionspectrum taken at a sampletemperature of T = 6 K [83L]. Allenergies given in eV. For datataken at other temperatures see[80G1, 80G2] and [77L].










91

0 10 20 30 40 50Energy [eV]E

a

b

Abso

rptio

n

CuCl

Fig. 8. γ-CuCl. X-ray absorption spectra measured at(a) the CuK edge and (b) the ClK edge [90H]. Theenergy is referred to the valence band maximum.


Γ X W L Γ K X– 7

– 6

– 4

– 5

– 3

– 1

– 2

0

Wavevector k

Initi

alst

ate

ener

gy[e

V]E i

CuCl EVBM

5 315 5

3 1 3

1 3 12 1

5 1

15

5

3

Fig. 10. γ-CuCl. Semirelativisticband structure obtained from aself-consistent local-density poten-tial with the LMTO-ASA method[81V, 82G]. For the effects of a2% reduced lattice constant see[81V]. Symmetries given in singlegroup notation.







92

Γ X Γ L– 6

– 5

– 2

– 4

0

– 1

– 3

1

3

2

4

Ener

gy[e

V]E

Wavevector k

5

6

7

8 CuCl

EVBM

6

6

7

6

6

7 7 6

8 8 4,57

4,5

8 7 8 6

8 6 8 6

7 7 7 4,5

6 6

6

Fig. 9. γ-CuCl. Energy bandscalculated using the relativisticKKR method and neutral atomicpotentials [80O]. Symmetries givenin double group notation.

– 4

0

– 3

– 2

– 8

– 1

– 7

– 6

– 5

Initi

alst

ate

ener

gy[e

V]E i

CuClEVBM Γ15 (d)

Γ12 (d)

Γ15 (p)

X (p)3

Fig. 11. γ-CuCl. Energy position of critical points asobtained experimentally (broken lines [82W]) and fromvarious calculations: + [67S], o [79D], x [79K1], ❏

[79K2], ∆ [80H], ▲ [73C], ∇ [80O], ● [79Z], ■

[81V, 82G], ◊ [79V].
















93

XΓ

– 6.0

– 5.0

–2.0

– 4.0

0

–1.0

–3.0

Wavevector k

CuCl

EVBM

K ΓL

– 5.5

–2.5

– 4.5

–1.5

–3.5

– 0.5

15

(7)

(8)

(8)

(7)

12

(8)

15

Initi

alst

ate

ener

gy[e

V]E i

Fig. 12. γ-CuCl. Band structure calculated with the self-consistent relativisticLMTO-ASA method with "empty spheres" [82B]. Energy with respect toVBM. Symmetries given in (double) and single group notation.




94

X Γ–16

0

Ener

gy[e

V]E

Wavevector k

CuCl

EVBM

L K ΓW

–15

–14

–13

–6

–5

–4

–3

–2

–1

1

2

3

4

5

6

7

8

9

10

11

12

13

4 6216,7

2 6 16

7,8

36 17 6

46

2,16,7 8

2 4,51

6,6,71

6,6 2

7,8

1

617

6

4

6 1

6

7,8

61

1,2

4,5

26,73

2 3

1

4,5

4,5

–15 –5 –3 –1 1 13–16

DOS

3 5 7 9 11Energy [eV]E – EVBM

0

CuCl

Fig. 13. γ-CuCl. Parametrizedband structure obtained by aSlater-Koster fit to high-symmetrypoints (Γ,X,L) derived experimen-tally from reflection spectra [83L].Symmetries given in double groupnotation.

Fig. 14. γ-CuCl. Total density ofvalence and conduction statescalculated from the parametrizedband structure shown in Fig. 13.Energy referenced to the valenceband maximum [83L].





95

XΓ

0

Ener

gy[e

V]E

Wavevector k

CuCl

L KΓ–5

–4

–3

–2

–1

1

2

3

4

5

6

7

X∆ Λ Σ

6 ,+ +7

8 ,7+ +

8–

6–

7+

6+

7+

7–

6–

6–

6+

4+

6+

6+

4+

6+

4+

6+

6+

6+

8+

Fig. 15. CuCl (rocksalt phase). Relativistic bandstructure calculated from a standard muffin-tin potentialwith the KKR method [81V]. This phase is observedonly at high pressures above about 9 GPa [81V]. Theseauthors also present a semirelativistic band structure of

CuCl in the rocksalt phase obtained from a self-consistent local-density-potential with the LMTO-ASAmethod. For a scalar-relativistic LMTO self-consistentband structure of the high pressure tetragonal phase ofCuCl see [86B].






96

–16ΓL X

–12

– 8

– 4

0

4

8

12

1617

.5

Ener

gy[e

V]E

Wavevector k

CuCl

EVBM

16.1

12.1

10.3

8.5

7.4

8.2

14.6

5.9

6.8

9.3

9.7

11.2

13.1

20.7

1(5)

3(4)1(4)

1(3)

3(4)

5(3)

1(3)

3(3)

3(3) 5(2)3(2)1(2)

3(2)

1(2)

15(2)

15(3)

15(1)5(1)3(1)

1(1) 1(1)1(1)

3(1)1(2)

12(1)

Evac

Fig. 16. γ-CuCl. Empirical band structure model basedon experimental critical point energies obtained fromphotoemission spectra [83G]. The vertical arrows givethe interpretation [83G] of structures observed inreflection spectra [80G1, 80G2] in terms of directtransitions between critical points at Γ, L and X [83G].See also [80G2]. – Energy referenced to VBM.


– 8 –7

EF

– 6 –5 – 4 –3 –2 –1 0 1Initial state energy [eV]Ei

CuCl(100)

A

clean

a

– 8 –7

EF

– 6 –5 – 4 –3 –2 –1 0 1

C


S2

10 L O42

b

B

S2

B

C

S1

A

S1

EVBM

EVBM

Fig. 18. γ-CuCl (100). Normal-emission photoelectronsrecorded at hν = 21.2 eV from a clean (a) sample and asurface (b) contaminated by exposure to 104L O2 atroom temperature. Both spectra taken at T = 130 K[80W]. The difference curve a-b is shown shaded in (a)and identifies peaks S2 and S1 as surface state andsurface resonance, resp. [80W]. Labels A, B, C identifybulk band emission. See also [98T] for a surface state atE ≈ 9 eV below valence band maximum.












97

6 8 10 14 22 244

S2

12 16 18 20Final state energy [eV]Ef

CuCl(100)

a a

b

F1

b

c

F2 F3

C

B

A

S1

∆ νh∆ νh

∆ νh

hν = 16.8 eV

VBM + hν

hν =21.2 eV

hν =21.2 eV

Fig. 17. γ-CuCl (100). Normal-emission photoelectron spectra observedafter excitation by photons with hν = 21.2 eV (a,b) and hν = 16.8 eV (c),and plotted versus the final state energy [83G]. The low-energy cut-off islocated at about 6.9 eV. Structures labeled F1-F3 are due to SEE from finalstate bulk critical points. The other labels refer to surface state (S2), surfaceresonance (S1) and bulk band (A, B, C) photoemission, respectively. Alldata taken at T = 130 K. Spectra (a,b) differ slightly due to better surfacequality of (a) as judged by a more brillant LEED pattern and additional SEEfine structures a, b [83G]. Energy referenced to VBM.





98

– 8 –7

EVBM

– 6 –5 – 4 –3 –2 –1 0 1

B


S2

a

S1

AX5

sec

EVBMS2

b

S1

CX5

C

EVBM

S2

c

S1

A X5

CuCl(100)

EVBM

S2

d

S1

X5

hν = 40.8 eV

hν = 21.2 eV

hν = 16.9 eV

hν = 11.8 eV

A

B

X3

X5X3

Γ12

Fig. 19. γ-CuCl (100). Normal-emission photoelectronspectra taken at different photon energies with thesample at T = 130 K [82W]. "Sec" indicates thesecondary electron cut-off. Energy referred to VBM =0. Labels Γ and X indicate position of critical pointenergies of the valence band structure. The other labelsidentify peaks resulting from surface (S1, S2) and bulk(A, B, C) emission, respectively.


– 8 –7

EVBM


CuCl(100)

θ = 60°

50°

40°

30°

20°

10°

0°

– 9

Fig. 21. γ-CuCl (100). Photoelectron spectra taken at hν= 21.2 eV for different polar angles θ in the ΓXWKplane [82W]. For similar data at hν = 23 eV see [98T].See also [80W].







99

EF

– 6 –5 – 4 –3 –2 –1 0Initial state energy [eV]Ei

CuCl(100)

hν = 12.7 eV

14.4 eV

17.1 eV

19.5 eV

EF

– 6 –5 – 4 –3 –2 –1 1Initial state energy [eV]Ei

hν = 26.3 eV

30.4 eV

34.5 eV

40.7 eV

0 2– 7– 8– 9–10

Fig. 20. γ-CuCl (100). Normal-emission photoelectron spectra taken at different photon energies with the sample atroom temperature [98T]. The energy references to EF = 0.




100

– 8 –7

EVBM


A

CuCl(111)

– 9

a

hν = 11.8 eV

sec

EVBMb

hν = 16.9 eV

sec

EVBMc

hν = 21.2 eV

EVBM

d

hν = 40.8 eV

L3

L3

L1

Γ12

BC

A

Fig. 22. γ-CuCl (111). Normal-emission photoelectronspectra taken at different photon energies with thesample at T = 130 K [82W]. "Sec" labels features due tothe low-energy secondary electron cut-off. Labels Γ, Lindicate critical point energies of the valence bandstructure; A, B, C identify emission from bulk bands.

– 8 –7

EVBM


CuCl(111)

θ = 65°

50°

40°

30°

20°

10°

0°

– 9

5°

Fig. 23. γ-CuCl (111). Angle-dependent photoelectronspectra recorded at hν = 21.2 eV for different polarangles θ along ΓXWK. Sample temperature T = 130 K[82W].



Ref. p. 156] 2.10 Noble metal halides (CuBr)


101

2.10.3 CuBr (Cuprous bromide)

At normal conditions CuBr crystallizes in the zincblende structure (γ-CuBr):Lattice fcc, a = 5.6905 Å [63W],space group T2

d - 3m4F ,Brillouin zones see section 1.3 of this volume.

Work function (γ-CuBr):φ (polycrystalline) = 7.1(4) eV [74G1]Bulk plasmon energy ωp = 17.7(5) eV [74G1].

Direct band gap at Γ with Eg = 3.077 eV at T = 4K as best value extrapolated from various optical results

[77G]. At room temperature Eg = 2.91eV (at zero pressure) has been derived from experiments studyingthe absorption edge under hydrostatic pressure [81V].

For the phase diagram and structural details of high-temperature / high-pressure phases see Landolt-Börnstein Vol. III/41B and 17b, and [81V, 86B]. For an investigation of the lattice dynamics inisotopically tailored CuBr see [01S].

Table 5. γ-CuBr. Copper core-level binding energiesin eV relative to the top of the valence band [74G1].

Level n = 2 n = 3

ns1/2 1095.5 121.2np1/2 951.0 76.3(2)np3/2 931.2 73.9(2)

Errors ± 0.1 eV unless otherwise stated. If referred to the vacuum level the Cu-ion core levels show achemical shift of +1.5(5) eV and are more tightly bound in CuBr than in metallic copper [74G1].

Table 6. γ-CuBr. Occupied valence bands. Critical point energies determined by several authors. Allenergy values given in eV with respect to the top of the valence band. Symmetries are indicated in double(single) group notation.

Critical ARUPS UPS Theory a) Theory c)Point [93M2] [77G] [80O] [83E]

Γ8 (Γ15) 0 0 0 0

Γ7 (Γ15) –0.8(3) – –0.12 –Γ8 (Γ12) –2.05(1) –2.1 –1.1 –1.80Γ8 (Γ15) –4.2(2) –3.3 –3.7 –5.03Γ7 (Γ15) –4.8(3) – –4.3 –Γ6 (Γ1) –15.4(3) b) –15.4 b) – –

L4,5,6 –0.8(3) – –0.3 –

L6 –1.4(3) –1.1 –1.8 –0.41L4,5,6 –2.05(1) –1.8 –1.2 –1.66L4,5 –4.2(2) –4.1 –3.7 –4.72L6 –4.7(3) – –4.0 –L6 –5.6(3) –6.3 –5.1 –7.61L6 –15.4(3) b) –15.4(3) b) – –

a) Data read from a band structure calculated with the relativistic KKR method in [80O]. b) Taken from [74G1].c) Calculated by a quasimolecular approach [83E].


















2.10 Noble metal halides (CuBr) [Ref. p. 156


102

Table 7. γ-CuBr. Unoccupied bulk conduction band structure. Experimental critical pointenergies as obtained from constant-initial-state spectroscopy (CIS) and from secondaryelectron emission (SEE) spectra. The energies are referred to the top of the valence band.

CIS [91S] SEE [76L] SEE [93M2] Orbital character [93M2]

7.7(5) 7.5 7.4(2) p8.9(2) 8.8 8.9(3) s,d10.2(2) – – s,d12.0(5) – – ?14.1(2) – – p,f15.2(2) – – s,d17.2(2) – – p,f

The fraction of p-like density of states at the γ-phase valence band edge has been determined bothexperimentally and theoretically: The various data range between 28 and 51% [77G], a "best value"average of the experimental numbers [77G] is 37(5)%.

Figures for 2.10.3

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


102

10–2

10–1

1

10–3

10

Br

3p

3s

4p

4s

3d

Fig. 24. CuBr. Atomic subshell photoionization cross sections of brominefor photon energies from 0 to 1500 eV [85Y]. For atomic copper see Fig. 1in section 2.9.










103

0.5

0

1.0

1.5

2.0

2.5

3.0


–11 – 9 – 7 – 5 – 3 – 1 1

CuBr

EF

0

Fig. 25. γ-CuBr. XPS valence band spectrum takenfrom a polycrystalline sample with unmonochromatizedMgKα radiation at hv = 1253.6 eV [73K]. See also[74G1]. For the result of a deconvolution which correctsfor experimental broadening see [73K].

– 8 –7

EVBM


C

A

D

CuBr

hν = 24 eV

26

31

36

41

46 eV

B

0

0.1

0.2

0.3

EVBM

0.4

0.5

0

1

2

3


CuBr

EVBM

4

5

60

1

2

3

EVBM

4

50

1

2

3

EVBM

40

1

2

3

EVBM

4

5

(×3)

(×3)

hν = 48.4 eV

hν = 40.8 eV

hν = 26.9 eV

hν = 21.2 eV

hν = 16.8 eV

Fig. 26. γ-CuBr. Photoelectron spectra recorded fordifferent photon energies from polycrystalline films atroom temperature [74G1]. Dashed lines indicateestimated secondary electron background [74G1].

←Fig. 27. γ-CuBr. Photoelectron spectra measured atdifferent photon energies from polycrystalline filmswith the sample kept at T = 90 K [91S].









104In

tens

ity ra

tio

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

10 15 20 30 35 40 50Photon energy [eV]hν

25 45

CuBrC/B

D/B

Fig. 28. γ-CuBr. Experimental intensity ratios (areas) ofpeaks labeled B, C and D in Fig. 27 in their dependenceon photon energy [91S].

6 8 10 12 1614 18 20 2622 24 28Final state energy [eV]Ef

CuBr

c

b

a

peak BEi = –2.05 eV

peak DEi = – 5.63 eV

peak CEi = – 4.45 eV

Fig. 29. γ-CuBr. Constant initial state (CIS) spectrareferring to photoexcitation out of occupied bandslabeled B(Ei = –2.05 eV), C(–4.45 eV) and D(–5.63 eV)in Fig. 27. Polycrystalline film sample kept at T = 90 K[91S]. The final state energy is referred to the valenceband maximum.


CuBr

Fig. 30. γ-CuBr. Bremsstrahlung isochromat spectrum(BIS) taken at hν = 1486.6 eV, with the sample holderkept at liquid nitrogen temperature [94L]. The energywas calibrated by the author of this chapter using Fig.29. It may be accurate to ±1 eV and refers to energyzero at valence band maximum.

Abso

rptio

n co

effic

ient

[10

cm]

α5

–1

2.5

5.0

7.5

10.0

12.5

15.0


CuBr

Fig. 31. γ-CuBr. Absorption spectrum taken from apolycrystalline sample at liquid nitrogen temperature[72I].







105

5.0 7.5 10.0 15.0 17.5 20.0 30.00

5

10

20

15

25

35

30


Refle

ctiv

ity[%

]R

12.5 22.5 25.0 27.5

CuBr

5.30

6.05

6.55

7.01

7.22

8.40

11.02

11.90

13.40

14.95

12.25

9.62

7.75

10.55

9.07

Γ X Γ L– 6

– 5

– 2

– 4

0

– 1

– 3

1

3

2

4

Ener

gy[e

V]E

Wavevector k

5

6

7

8 CuBr

EVBM

7

6

6

6

6

8

7

8

7

7

7

8

7

8

6

4,56

4,56

8

6

8

67

6

7

6

4,57

Fig. 32. γ-CuBr. Reflectionspectrum taken at a sampletemperature T = 6 K [80G2]. Allenergies in eV. For data at roomtemperature see [77L].

Fig. 33. γ-CuBr. Energy bandscalculated along three different k-space directions using therelativistic KKR method andneutral atomic potentials [80O].See also [88C]. Symmetries givenin double group notation.







106

– 6

– 5

– 4

– 3

–2

–1

0

2

3

4

Ener

gy[e

V]E

5

1

Γ LWavevector k

6

Λa

Γ LΛb

CuBr

EVBM EVBM

7

8

6

4,5

64,5

6

6

4,5 64,5

6

6

7

8

8

6

4,56

6

8

7

6

6

4,5

6

6

8

7

8

Fig. 34. γ-CuBr. Energy bands along ΓL calculatedusing the relativistic KKR method from (a) neutralatomic potentials and (b) from ionic potentials [80O].Symmetries given in double group notation.

– 20

– 18

– 5.0

– 16

0

– 2.5

– 7.5

2.5

7.5

5.0

10.0

12.5

Ener

gy[e

V]E

ΓLWavevector k

CuBr

EVBM

X

3(3)

1(3)

3(2)

1(2)

3(3)

15(2)

3(2)5(2)

1(2)

5(1)3(1)

1(2)

12(1)

15(1)

1(1)

1(1)

3(1)

1(1)

Fig. 35. γ-CuBr. Semiempiricalenergy band structure calculated[98B] by fitting tight-bindingeigenvalues to six energies (at Γ, Land X) obtained from angle-resolved photoelectron spectra in[82W, 83G]. Energy scale referen-ced to the valence band maximum.Symmetries given in single groupnotation. Numbers in bracketscount bands upward from bottom.







107

–18 –16 – 6.0 – 4.5 – 3.0 6.0–20

DOS

–1.5 0 1.5 3.0 4.5Energy [eV]E – EVBM

CuBr


Fig. 36. γ-CuBr. Density of statescalculated from the semiempiricalband structure shown in Fig. 35[98B]. Energy scale referenced tovalence band maximum.

– 6.0

– 5.5

– 5.0

– 4.5

– 4.0

– 3.5

– 3.0

– 2.0

– 1.5

– 1.0

Initi

al st

ate

ener

gy[e

V]E i

– 0.5

– 2.5

LWavevector k

0

Γ

CuBr

EVBM

Λ LΓ

EVBM

Λ

calculation experiment

4,5

8

67

8

6

4,5

6

8

7

4,5

6

6

Fig. 38. γ-CuBr. Left panel reproduces part of the calculated band structure shown in Fig. 33 [80O]. Right panel:corresponding experimental band mapping data obtained from angle-resolved uv-photoemission [93M2]. Symmetriesgiven in double group notation.






108

XΓ

0

Ener

gy[e

V]E

Wavevector k

CuBr

L KΓ–5

–4

–3

–2

–1

1

X∆ Λ Σ

2

3

4

5

6

7

8–

6–

4+

6+

8+

6+6+

6+

6+

7+

8+

8–

7+

8+

6+

6+

6–4+6+

4+

7+

6+

6–

6–

7–

7+

7+6+

8+

6+

Fig. 37. CuBr (rocksalt phase). Relativistic band structure calculated from a standard muffin-tin potential with theKKR method [81V]. This phase is observed only at high pressures above about 7 GPa [81V]. Symmetries given indouble group notation.





109

CuBr(111)

– 8 –7

EVBM


hν = 40.8 eV

EVBM

hν = 21.2 eV

Fig. 39. γ-CuBr (111). Normal-emission photoelectronspectra taken at two different photon energies. Datataken while the sample was at T = 120 K and shieldedagainst visible light [93M2].

EVBM

– 4.0 –3.0 –2.0 –1.0 0 1.0Initial state energy [eV]Ei

CuBr(111)

θ = 20.0°

10.0°

7.5°

5.0°

2.5°

0°

–3.5 –2.5 –1.5 0.5 0.5 1.5

Fig. 40. γ-CuBr (111). Angle-resolved photoelectronspectra at hν = 40.8 eV for different polar angles θalong the ΓLUX plane of the bulk Brillouin zone, withthe sample at T = 120 K and shielded against visiblelight [93M2].



2.10 Noble metal halides (CuI) [Ref. p. 156


110

2.10.4 CuI (Cuprous iodide)

At normal conditions CuI crystallizes in the zincblende structure (γ-CuI):Lattice fcc, a = 6.0427 Å [63W],space group T2

d - 3m4F ,Brillouin zone see section 1.3 of this volume.

Work-function (γ-CuI):φ (polycrystalline) = 6.0(1) eV [74G1]Bulk plasmon energy ωp = 15.1(5) eV [74G1]

Direct band gap at Γ with Eg = 3.12eV at T = 4K as best value extrapolated from various optical results[77G]. At room temperature Eg = 2.95eV at zero pressure has been derived from experiments studying the

absorption edge under hydrostatic pressure [81V].

For the phase diagram and structural details of high-temperature / high-pressure phases see Landolt-Börnstein Vols. III/41B and III/17b, and [81V, 86B, 98H]. For the absorption spectra of CuInanocrystallites embedded in a glass matrix and the determination of some band parameters of bulk CuIcrystals see [00G] or Landolt-Börnstein, III/34C1, Chap. 6.

Table 8. γ-CuI. Copper core-level binding energiesin eV relative to the top of the valence band [74G1].

Level n = 2 n = 3

ns1/2 1094.4 –

np1/2 951.4 76.8(3)

np3/2 – 74.4(3)

Errors ± 0.1eV unless otherwise stated. If referred to the vacuum level the Cu-ion core levels show achemical shift of + 0.8(5)eV and are more tightly bound in CuI than in metallic copper [74G1].

Table 9. γ-CuI. Occupied valence bands. Critical point energies in eV (± 0.1eV if not stated differently inparentheses) referred to top of valence band. Symmetries are indicated in double (single) group notation.

Symmetry UPS ARUPS Symmetry UPS ARUPSPoint [77G] [88G] Point [77G] [88G]

Γ8 (Γ15) 0 0 X7 – –0.6

Γ7 (Γ15) – –0.6 X6 –1.7 –1.2

Γ8 (Γ12) –2.5 –2.4 X6 –2.2 –2.2

Γ8 (Γ15) –3.1 –3.5 X6,7 –2.5 –2.4

Γ7 (Γ15) – –3.9 X7 – –3.8

Γ6 (Γ1) –13.3(4) – X6 –4.4 –4.2

X6 –6.0 –5.1

X7 (Γ1) –13.3(4) –

The fraction of p-like density of states at the γ-phase valence band edge has been determinedexperimentally by several methods [77G], a "best value" average of the data [77G] is 47(5)%.


















Ref. p. 156] 2.10 Noble metal halides (CuI)


111

Figures for 2.10.4

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


102

10–2

10–1

1

10–3

10

Ι

3d

3p4d

3s

4p

4s5p5sFig. 41. CuI. Atomic subshellphotoionization cross sections ofiodine for photon energies from 0to 1500 eV [85Y]. For atomiccopper see Fig. 1 in section 2.9.

0.5

0

1.0

1.5

2.0

2.5

– 0.5


–11 – 9 – 7 – 5 – 3 – 1 1

Cu

EF

0

Ι

Fig. 42. γ-CuI. XPS valence-band spectrum taken froma polycrystalline sample with unmonochromatizedMgKα radiation at hν = 1253.6 eV [73K]. See also[74G1]. For the result of a deconvolution which correctsfor experimental broadening see [73K].







112

0

1

2

3


EVBM

4

1– 1– 5 – 3– 7

0

1

2

3

EVBM

4

0

1

2

3

EVBM

4

5

6

0

3

6

9

EVBM

12

0

0.1

0.2

0.3

EVBM

0.4

0.5

0.6

0.7hν = 48.4 eV

hν = 40.8 eV

hν = 26.9 eV

hν = 21.2 eV

hν = 16.8 eV

(×3)

(×3)

Cu Ι

Fig. 43. γ−CuI. Photoelectron spectra recorded fordifferent photon energies from polycrystalline films[74G1]. Dashed lines indicate estimated secondaryelectron background [74G1].

0

2

4

1

3

5

–12 –10 – 8 – 4– 6 – 2 0 2Initial state energy [eV]Ei

EF

0

1.0

2.0

0.5

1.5

2.5

EF

0

1.0

2.0

0.5

1.5

EF

2.5

3.0

hν = 76 eV

hν = 61 eV

hν = 40 eV

3.5Cu Ι

Fig. 44. γ-CuI. Photoelectron spectra recorded atdifferent photon energies hv from polycrystalline films[74I].






113

→→→→Fig. 46. γ-CuI. X-ray absorption spectra measured at (a)the Cu K edge, (b) the I L1 edge and (c) the I L3 edge[90H]. The energy is referred to the valence bandmaximum.


EVBM

Cu Ι

Fig. 45. γ-CuI. Bremsstrahlung isochromat spectrumtaken at hv = 1486.6 eV, sample holder kept at liquidnitrogen temperature [94L]. The energy scale wascalibrated by the author of this chapter using Fig. 1 in[90H]. It may be accurate to ±1eV and refers to energyzero at valence band maximum.

0 10 20 30 40 50Energy [eV]E

a

b

Abso

rptio

n

c

Cu Ι

EVBM

5.0 7.5 10.0 15.0 17.5 20.0 30.00

5

10

20

15

25

35

30


Refle

ctiv

ity[%

]R

12.5 22.5 25.0 27.5

4.78

8.10

5.10

7.62

5.376.75

12.50

6.48

8.458.97

9.90

10.9711.80

10.55

7.17

6.33

6.25

6.04 Cu Ι

Fig. 47. γ-CuI. Reflectivityspectrum taken at a sampletemperature of T = 6K [88G]. Fordata at room temperature see[77L]. All energies in eV.








114

– 14

– 4

– 5

– 3

0

– 1

– 2

Initi

al st

ate

ener

gy[e

V]E i

ΓLWavevector k

EVBM

Γ

– 6

– 13

X K

3

1

3

1

1

15

15

12

15

15

5

1

31 1

∆ + ∆3 4

∆ + ∆3 4

∆1

∆1

Cu Ι5

3

12

Fig. 48. γ-CuI. Band structureresulting from a semiempiricalLCAO calculation which treats thematrix elements of the crystalHamiltonian as parameters adjust-ed to photoemission results[74G1]. Symmetries given insingle group notation.

Γ X Γ L– 6

– 5

– 2

– 4

0

– 1

– 3

1

3

2

4

Ener

gy[e

V]E

Wavevector k

5

6

7

EVBM

7

8

6

7

8

6

7

6

6

8

7

8

7

7

8

7

8

4,5

664,5

6

4,5

6

6

7

8

6

6

8

7

Cu Ι

Fig. 49. γ-CuI. Energy bandscalculated along three different k-space directions using the relati-vistic KKR method and neutralatomic potentials [80O]. Symme-tries given in double group nota-tion.





115

XΓ

– 5.0

– 4.0

–1.0

– 3.0

0

0.5

–2.0

Ener

gy[e

V]E

Wavevector k

EVBM

K ΓL

– 4.5

–1.5

– 3.5

– 0.5

–2.5

1.5

1.0

8

7

8

8

7

Cu Ι

Fig. 50. γ-CuI. Band structure obtained from the self-consistent relativisticLMTO-ASA method with "empty spheres" [82B]. Energy referenced tovalence band maximum. Symmetries given in double group notation.




116

– 15

– 14

– 5.0

– 13

0

– 2.5

– 7.5

2.5

7.5

5.0

10.0

Ener

gy[e

V]E

ΓLWavevector k

EVBM

X

3(3)

1(3)

3(2)

1(2)

3(3)

15(2)

3(2)

5(2)

1(2)

5(1)3(1)

1(2)

12(1)

15(1)

1(1)

1(1)

3(1)

1(1)

Cu Ι

Fig. 51. γ-CuI. Semiempiricalband structure calculated [98B] byfitting tight-binding eigenvalues tosix energies (at Γ, L and X)obtained from angle-resolvedphotoelectron spectra in [82W,83G]. Energy scale referenced tothe valence band maximum.Symmetries given in single groupnotation. Numbers in bracketscount bands upward from bottom.

–13 –12 – 6.0 – 4.5 – 3.0 6.0–14

DOS

–1.5 0 1.5 3.0 4.5Energy [eV]E – EVBM

Cu Ι

Fig. 52. γ-CuI. Density of statescalculated [98B] from the semi-empirical band structure shown inFig. 51. Energy scale referenced tovalence band maximum.







117

XΓ

0

Ener

gy[e

V]E

Wavevector kL KΓ

–5

–4

–3

–2

–1

1

X∆ Λ Σ

2

3

5

6

7

8

8–

6–

4+

4+

6+

,8+

6+

6+

6+

7+

8+

6+

6+

4+

6+

6–

6–

7+

7+6+

7–

6+

6+

Cu Ι

Fig. 53. CuI (rocksalt phase). Relativistic band structurecalculated from a standard muffin-tin potential with theKKR method [81V]. This phase is observed only athigh pressures above about 10 GPa [81V]. For a scalar

-relativistic LMTO self-consistent band structure of thehigh-pressure tetragonal phase of CuI see [86B].Symmetries given in double group notation.






118DO

S[s

tate

s (at

om e

V)]

–1

0

1

2

3

10–1–3–4–5–7Energy [eV]E – EVBM

–2–6

0

1

2

3

4

5

Energy [eV]E – EVBM

0

1

2

3

4

5

6


total

d-like

p-like

EVBM

EVBM

10–1–3–4–5–7 –2–6

10–1–3–4–5–7 –2–6

DOS

[sta

tes (

atom

eV)

]–1

DOS

[sta

tes (

atom

eV)

]–1

EVBM

Cu Ι

Fig. 54. γ-CuI. From top to bottom: total, partial d andpartial p density of valence states deduced [74G2] fromthe photoemission spectra shown in Fig. 43 compared tothose from a semiempirical model calculation using aparametrized seven-function basis set [74G1]. Thecorresponding energy bands are shown in Fig. 48.


– 4.0

0

– 3.0

– 2.0

– 1.0

– 5.0In

itial

stat

een

ergy

[eV]

E i

EVBM Γ8

7X

– 4.5

– 3.5

– 2.5

– 1.5

– 5.5

– 0.5

6X

6X

7X

6X

6X

Γ7

Γ8

Γ8

Γ7

CuI(110)

22.5Photon energy [eV]hν

20.017.515.0 32.530.027.525.0

Cu Ι

Fig. 56. γ-CuI (110). Initial state energies of dispersingphotoelectron peaks observed in Fig. 55 andinterpretation in terms of critical point energies at Γ andX [88G]. For the resulting empirical energy bands alongΓX and a comparison to experimental optical spectra see[88G]. See also [80G2] for earlier work.

CuI(110)

Evac

0 1Electron energy [eV]E – Evac

2 3 4 5 6 7 8 9 10

Cu Ι

Fig. 57. γ-CuI (110). Normal-emission electronspectrum observed after excitation by photons with hv =40 eV showing secondary electron structures indicatedby arrows located above the vacuum level [88G].









119

–6.5–7.0Initial state energy [eV]Ei

–5.5–6.0 –4.5–5.0 –3.5–4.0 –2.5–3.0 – 1.5–2.00 – 0.5– 1.0 0.50 1.0

hν = 34.0 eV

CuI (110)

32.0

30.0

29.0

28.0

27.0

26.0

25.0

24.0

23.0

22.0

21.0

20.0

19.0

18.5

18.0

17.0

16.5

16.015.0 eV

E

D

C

B

A

31.0

F

Cu Ι

EVBM

Fig. 55. γ-CuI (110). Normal-emission photoelectron spectra taken at different photon energies from cleaved singlecrystals [88G]. In some curves the arrows indicate secondary electron emission features.


2.10 Noble metal halides (AgF) [Ref. p. 156


120

2.10.5 AgF (Silver fluoride)

At normal conditions AgF crystallizes in the rocksalt structure:Lattice: fcc, a = 4.936 Å [71M],space group: O5

h – Fm3m,Brillouin zones: see section 1.3 of this volume.

The fact that silver monofluoride AgF is hygroscopic and highly reactive, together with the existence ofsilver subfluoride Ag2F and silver difluoride AgF2 have made it difficult to prepare samples suitable forphotoelectron spectroscopy. This explains why not much experimental data is available for AgF.

Indirect band gap with an exciton energy of Egx = 2.8(3) eV at T = 4.8K [71M], direct exciton transition

energy Egx = 4.63(2) eV at T = 4.8K and assigned to a transition at Γ [71M]. For a comparison of these

numbers with XPS valence–band data see [75M].

Table 10. fcc–AgF. Core–level binding energies in eV relative to EF.

Level n = 1 n = 2 n = 3 Assignment

ns1/2 682.7(2) a) 27.2(6) b) – F in AgF

np1/2 – – 603.1(4) c) Ag in AgF

np3/2 – – 572.3(4) c) Ag in AgF

nd3/2 – – 373.6(2) c) Ag in AgF

nd3/2 – – 374.0(1) Ag in Ag metal

nd5/2 – – 367.6(3) b); 367.8(2) a) Ag in AgF

nd5/2 – – 368.1(1) c) Ag in Ag metal

a) [98W]. b) Obtained from data given in [75M].c) Obtained from figures in [98W].

Table 11. fcc-AgF. Occupied valence band critical point energies determinedexperimentally and from different calculations. Energy values in eV referred totop of the valence band.

Symmetry XPS a) TheoryPoint [72F] [82K]b) [83E]

Γ12 –1.6(4) –1.48 –0.7 –1.27

Γ25' –3.2(1) – –1.9 –1.72

Γ15 –5.3(4) –4.04 –5.3 –1.62

Γ1 –25.8(6) – – –22.3

a) Data obtained from [75M] by assuming that the top of the valence band is located at 1.4 eV below EF.b) Read from a figure in [82K].

In contrast to AgCl and AgBr, where p-like (halogen) density of states is dominant at the top of thevalence band, the highest valence band of AgF is formed largely by d-like (silver) contribution [75M,83E].















Ref. p. 156] 2.10 Noble metal halides (AgF)


121

Figures for 2.10.5

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

F

1s

2s

2p

4

2

68

4

2

68

4

2

68

4

2

68

4

2

68

10–4

Fig. 58. AgF. Atomic subshellphotoionization cross sections offluorine for photon energies from0 to 1500 eV [85Y]. For atomicAg see Fig. 66 in section 2.9.




122

378 376 374 372 370 368Binding energy [eV]Eb

Inte

nsity

I

366 364

AgFAg0

AgF

Ag0

a

b

AgF

Ag metal

Fig. 59. fcc-AgF. XPS spectra of the Ag 3d doublettaken with unmonochromatized MgKα radiation from(a) a pressed-powder sample of AgF and (b) Ag metal.Energies referred to EF [98W]. See [98W] for an XPSoverview spectrum at binding energies between zeroand 1000 eV.

610 600Binding energy [eV]Eb

Inte

nsity

I

AgF

F

590 580 570 560

Fig. 60. fcc-AgF. XPS spectrum of the Ag 3p doublettaken with unmonochromatized MgKα radiation from apressed-powder sample of AgF. Energy referred to EF.F is an Auger line of fluorine [98W].

Inte

nsity

I

–10 10Initial state energy [eV]Ei

AgF

–1–2–3–4–5–6–7–8–9

EF

Fig. 61. fcc-AgF. XPS spectrum taken from apolycrystalline film with monochromatized (0.5 eV)AlKα-radiation. Sample kept at 100 K and protectedfrom exposure to visible light. Energy scale referred toEF [75M].





Ref. p. 156] 2.10 Noble metal halides (AgF)


123

L Γ XWavevector k

AgF

Ener

gy[R

y]E

3'

1

1

5,3

1

–1.1

–1.2

–1.3

–1.4

–1.5

–1.6

–1.7

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'12

25'

5'

2'

3'

2'

15

4'

L Γ XWavevector k

Ener

gy[R

y]E

2'

1

1

5

3

1

–1.1

–1.2

–1.3

–1.4

–1.5

–1.6

–1.7

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'

12

25'

5'

2'

3'

2'

15

4'

3'

2

5

3'

25'

3

1

51

3, 2

Fig. 62. fcc-AgF. Left panel: self-consistent Hartree-Fock band structure. Right panel: same but with inclusion ofcorrelation and relaxation corrections [82K]. Symmetries given in single group notation.




124

– 8 – 7 – 6 – 5 – 4 – 3 – 2 –1 10

DOS


EVBM

AgF

Fig. 63. fcc-AgF. Density of valence states calculatedfrom the band structure shown in the left panel in Fig.62 [82K]. Energy referred to the top of the valenceband.

→Fig. 64. fcc-AgF. Partial densities of states for (a) Ag,(b) F and (c) total DOS calculated self-consistently bythe tight-binding LMTO-ASA method [96O]. 0

8

14

4

10

16

6

12

Energy [eV]E – EF

DOS

[sta

tes

(eV

cell)

]–1

– 6 – 3 0 3 6 9 12

2

0

8

6

4

2

10

Energy [eV]E – EF

– 6 – 3 0 3 6 9 12

DOS

[sta

tes

(eV

cell)

]–1

0

8

14

4

10

16

6

12

Energy [eV]E – EFDO

S[s

tate

s(e

Vce

ll)]

–1

– 6 – 3 0 3 6 9 12

2

c

b

a

AgF Ag-like

F-like

total



Ref. p. 156] 2.10 Noble metal halides (AgCl)


125

2.10.6 AgCl (Silver chloride)

At normal conditions AgCl crystallizes in the rocksalt structure:Lattice: fcc, a = 5.5502 Å [55B],space group: O5

h - Fm3m,Brillouin zones: see section 1.3 of this volume.

Work-function (fcc):φ (polycrystalline) = 6.3(3) eV [75T]

Indirect optical band gap (from L to Γ) with Eg = 3.2476 eV at T = 1.8K [83N]. The direct gap occurs at Γ[75M] with Eg = 5.15(5) eV at T = 4K [71C]. For exciton self-trapping in AgCl nanocrystals see [00V].

Table 12. fcc-AgCl. Core-level binding energies in eV referred to the top of the valence band for thecompound and to EF for the metal. All errors are ± 0.1eV unless otherwise stated.

Level n = 2 n = 3 n = 4 Assignment

ns1/2 – – 94.9(3) a) Ag in AgCl

96.8 a) Ag in metalnp1/2 – 601.9a) – Ag in AgCl

np3/2 196.0(3)b) – – Cl in AgCl

np3/2 – 571.0a) – Ag in AgCl

nd3/2 – 372.3a) – Ag in AgCl

nd5/2 – 366.1a) – Ag in AgCl

365.6(3)b) – Ag in AgClnd5/2 – 368.3a) – Ag in metal

a) [75T]. b) Data from [75M] but referred to top of valence band.

If referred to the vacuum level, all Ag levels have the same binding energy within ± 0.3eV in both thehalide and the metal. For an interpretation see [75T].

Table 13. fcc-AgCl. Calculated and experimental peak positions in the valence band density of states (ineV, referred to the top of calculated valence band).

Character Theory [98V] a) XPS [75M] b) UPS [76B2] UPS [74T, 75T]

Cl 3p – 1.0 – 1.4 (4) – 0.8 (2) – 0.6 (2)Cl 3p – 2.5 – 2.5 (2) – 2.6 (2) – 2.5 (2)Ag 4d – 3.1 – 3.2 (1) – 3.3 (2) – 3.2 (1)Ag 4d – 4.6 – 4.4 (2) – – 4.6 (3)Cl 3s – 15.0 – – – 14.3 (6)

a) Ab initio calculated with self-interaction and relaxation-corrected pseudopotential.b) Original data [75M] are referred to EF. These are shifted rigidly by 1.3 eV to make the comparison with [98V] easier (this brings theoretical and measured top of valence band in direct agreement).

For further calculations see [83E, 97V]. The electronic structure of the states at the bottom of the conductionband (using an ab initio method) and the corresponding orbital character are calculated in [00O].




















2.10 Noble metal halides (AgCl) [Ref. p. 156


126

Figures for 2.10.6

– 7 – 6 – 5 – 3 –1 0– 8

EF

AgCl

– 4 – 2Initial state energy [eV]Ei

T = 83 K222 K300 K

Fig. 65. fcc-AgCl. XPS valenceband spectra taken from apolycrystalline film with mono-chromatized (0.5 eV) AlKα-radia-tion at three different temperatures[75M].


XL Γ K X

– 4

– 5

– 3

– 1

– 2

0

Wavevector k

Ener

gy[e

V]E

5

3

1

3

1

3

12

1

4

115

5

3

1

1

1

1

3

5

1

25' 1,2

1,4

1,2 3,5

AgCl

EVBM

1

2

3

4

5

6

Fig. 67. fcc-AgCl. Band structureresulting from a semiempiricalLCAO calculation which treats thematrix elements of the crystalHamiltonian as parameters adjust-ed to photoemission results [75T].For a different tight-binding bandcalculation see [76S1]. Symme-tries given in single groupnotation.






127


AgCl

EVBM

hν = 1486.6 eV

hν = 40.8 eV

hν = 26.9 eV

hν = 16.8 eV

hν = 21.2 eV

– 1– 5 – 3 1

EVBM

EVBM

EVBM

EVBM

Fig. 66. AgCl. Photoelectron spectra recorded fordifferent photon energies from polycrystalline films[75T].

DOS

[sta

tes (

atom

eV)

]–1

0

0.5

1.0

1.5


–2–6

0

0.5

1.0

1.5

2.0

2.5


total

d-like

p-like

EVBM

EVBM

10–1–3–4–5–7 –2–6

3.0

0

0.5

1.0

1.5

2.0

2.5


EVBM

10–1–3–4–5–7 –2–6

3.0AgCl

DOS

[sta

tes (

atom

eV)

]–1

DOS

[sta

tes (

atom

eV)

]–1

Fig. 68. fcc-AgCl. From top to bottom: total, partial dand partial p densities of valence states deduced [75T]from the photoemission spectra shown in Fig. 66compared to those from a semiempirical modelcalculation using a parametrized basis set. Thecorresponding energy bands are reproduced in Fig. 67.





128

ΛL ΣU,KX– 6

– 4

– 5

– 3

– 1

– 2

0

Wavevector k

Ener

gy[e

V]E

AgCl

EVBM

5

3'

25'

3

12

1

4

12

1

5'

1

15

5

4

Γ ∆ Γ

3

1

1

1

1

1

151

3

1

3'

3'

2'

2'

1

2'

2

1

4'

5

3

1

2

1

31

2,3

1

4 4

1

2,3

1

3

1

25'

1

2

3

4

5

6

7

8

9

Λ LΣ X

– 4

– 5

– 3

– 1

– 2

0

Wavevector k

Ener

gy[e

V]E

AgCl

EVBM

8–

Γ∆Γ

1

1

2

3

4

5

6

7

8

9

6–

8+

6+

10

11

12

13

6+

6+

6–

6–

6–

4–

6–

7+

6–

7+

7–

6+

7+

8–

6–

8+

8+

8+

7+ 7

+

6+

4+

4+

6+

6+

6+

6+

, 4+

Fig. 69. fcc-AgCl. Band structurecalculated by means of theempirical pseudo-potential methodneglecting spin-orbit coupling.Energy referred to top of valenceband. The symmetry labelscorrespond to the origin at the Clatom [76W]. Symmetries given insingle group notation.

Fig. 70. fcc-AgCl. Band structurecalculated by means of therelativistic KKR method. Thesymmetry labels are referred to theorigin at the Ag-atom [81O]. For asemirelativistic band structureobtained from a self-consistentlocal-density potential with theLMTO-ASA method calculated attwo different lattice constants see[81V]. Symmetries given indouble group notation.






129

L Γ XWavevector k

AgCl

Ener

gy[R

y]E

3

11

5

3

1

–1.1

–1.2

–1.3

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'

12

25' 5

2'

3'

2'

15

4'

L Γ XWavevector k

Ener

gy[R

y]E

2'

1

1

5

3

–1.1

–1.2

–1.3

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'

12

25'5

2'

3'

2'

15

4'

3'

2

1

3

25'

3'

25'

1

12

4'15

2'

1

5',3

15

3

2'

Fig. 71. fcc-AgCl. Left panel: self-consistent Hartree-Fock band structure. Right panel: same but with inclusion ofcorrelation and relaxation corrections [82K]. Symmetries given in single group notation.

–7 – 6 –5 – 4 –3 –2 –1 0Energy [eV]E – EVBM

DOS

AgCl

exp.

theor.

EVBM Fig. 72. fcc-AgCl. Density of valence states (solid line)calculated from the band structure shown in the rightpanel of Fig. 71 [82K] and compared to the exper-imental total DOS (dashed line) obtained fromphotoemission spectra [75T, 82K].







130

X WL Γ K– 6

– 4

– 5

– 3

– 1

– 2

8

Wavevector k

Ener

gy[e

V]E

AgCl

EVBM

Γ

0

1

2

3

4

5

6

7

Fig. 73. fcc-AgCl. Energy bandscalculated by the density-functional pseudopotential method[94K]. Zero of energy at the top ofthe valence band. For a contourplot of the valence electronpseudodensity on a (100) planepassing through Ag and Cl sitessee also [94K].


– 15

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

WWavevector k

AgCl

EVBM

– 6

– 12

X WΓL K

– 14

– 13

1

2

3

4

5

6

Fig. 75. fcc-AgCl. Band structurecalculation employing a full-potential linear augmented-Slater-type-orbital implementation of thelocal-density approximation [97V].Energy zero referred to top of thevalence band.






131

0

Energy [eV]E – EF

DOS

[sta

tes

(eV

cell)

]–1

– 6 – 3 0 3 6 9 12

0

4

3

2

1

5

Energy [eV]E – EF

– 6 – 3 0 3 6 9 12

DOS

[sta

tes

(eV

cell)

]–1

0

12

6

15

21

9

18

Energy [eV]E – EF

DOS

[sta

tes

(eV

cell)

]–1

– 6 – 3 0 3 6 9 12

3

c

b

a

AgCl Ag-like

Cl-like

total

12

6

15

21

9

18

3

–7 – 6 –5 – 4 –3 –2 –1 0 1Initial state energy [eV]Ei

– 8

AgCl

EVBM

DOS

EVBM

calc.

exp.

2

Fig. 77. fcc-AgCl. Top: bulk density of states calculatedusing the energy band structure shown in Fig. 76 [98V].Bottom: XPS valence band spectrum taken with 0.5 eVresolution from a polycrystalline film kept at T = 83 K[75M].


←Fig. 74. fcc-AgCl. Partial densities of states for (a) Ag,(b) Cl and (c) total DOS calculated self-consistently bythe tight-binding LMTO-ASA method [96O].






132

– 15

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

WWavevector k

AgCl

EVBM

– 6

XΓL K

– 14

– 16

1

2

3

4

5

6

7

8

9

10

11

12

Γ

Fig. 76. fcc-AgCl. Band structure LDA calculation based on self-interactionand relaxation-corrected pseudopotentials. Spin-orbit coupling is included.The horizontal dashed lines indicate the experimental energy gap. Energyreferred to top of the valence band [98V]. See also [98N].



Ref. p. 156] 2.10 Noble metal halides (AgBr)


133

2.10.7 AgBr (Silver bromide)

At normal conditions AgBr crystallizes in the rocksalt structure:Lattice fcc, a = 5.7747 Å [55B]space group Oh

5 - Fm3m,Brillouin zones see section 1.3 of this volume.

Work-function (fcc):φ (polycrystalline) = 6.3 (3) eV [75T].

Indirect optical band gap (from L to Γ) with Eg = 2.6845 eV at T = 1.8 K [84S]. The direct gap occurs at Γwith Eg = 4.292(2) eV at T = 4.2 K [71C]. Growth, surface structure and phonon dynamics of thinepitaxial AgBr(100) films grown on NaCl are reported in [99G].

Table 14. fcc-AgBr. Core-level binding energies in eV referred to the top of thevalence band for the compound and to EF for the metal. All errors are ± 0.1 eV unlessotherwise stated.

Level n = 3 n = 4 Assignment

ns1/2 – 94.9 (3) a) Ag in AgBr96.8 a) Ag in metal

np1/2 602.0 a) – Ag in AgBrnp3/2 571.3 a) – Ag in AgBr

180.3(3) b) – Br in AgBrnd3/2 372.4 a) – Ag in AgBrnd5/2 366.4 a) – Ag in AgBr

365.9(2) b) – Ag in AgBr368.3 a) – Ag in metal

a) [75T]. b) Data from [75M] but referred to top of valence band.

If referred to the vacuum level, all Ag levels have the same binding energy within ± 0.3 eV in both thehalide and the metal. For an interpretation see [75T].

Table 15. fcc-AgBr. Calculated and experimental peak positions in the valence band density of states (ineV, referred to the top of the calculated valence band).

Character Theory [98V] a) XPS [75M] b) UPS [74T, 75T] c) PES [90M] UPS[93M1]

Br 4p –1.9 –2.0(4) –2.0(2) –1.4(2), –2.0(2) –1.8(2)Br 4p –3.1 –3.2(1) –3.1(2) –3.1(2), –4.2(2) –2.8(2)Ag 4d –4.0 –3.9(1) –3.9(2) –3.9(2) –3.7(2)Ag 4d –4.9 –4.9(1) –4.9(2) –4.2(5) –4.3(4)Br 4p ≈–4.9 –5.1(3) –5.2(2) –5.3(3) –4.5(3),

–5.2(2)Br 4s –15.3 – –15.0(6) – –

a) Ab initio calculated with self-interaction and relaxation-corrected pseudopotential.b) Original data [75M] are referred to EF. These are shifted rigidly by 0.8 eV to make the comparison with [98V]easier (this brings theoretical and measured top of valence band in direct agreement).c) Shifted rigidly by 0.2 eV. See also [76B2].

For further calculations see [83E, 97V]. The electronic structure of the states at the bottom of the conductionband (using an ab initio method) and the corresponding orbital character are calculated in [00O].





















2.10 Noble metal halides (AgBr) [Ref. p. 156


134

Figures for 2.10.7

– 7 – 6 – 5 – 3 –1 0– 8

EF

AgBr

– 4 – 2Initial state energy [eV]Ei

T = 83 K190 K300 K

Fig. 78. fcc-AgBr. XPS valenceband spectra taken from apolycrystalline film with mono-chromatized (0.5 eV) AlKα radia-tion at three different temperatures[75M].


AgBr

676869707172

Fig. 79. fcc-AgBr. Photoemission of the Br 3d core-levels excited by photons of hv = 120 eV [91W]. Thesample is a polycrystalline, closed film condensed atT = 83 K and studied at this temperature. For detailedstudies of its annealing behaviour as well as of samplesdeposited at T = 403 K see [91W].






135

0

1

2

3

Inte

nsity

[arb

.uni

ts]

I

129 118Energy [eV]E

1076

AgBr

40

1

2

3

40

1

2

3

40

1

2

3

40

1

2

3

40

1

2

3

4

hν = 10.8 eV

hν = 11.0 eV

hν = 11.2 eV

hν = 11.4 eV

hν = 11.6 eV

T = 80 K295 K

hν = 11.8 eV

Fig. 80. fcc-AgBr. Photoelectron spectra, normalized toincident photon flux, from polycryst-alline samples keptat T = 80 K (solid lines) and 295 K (dashed), for differentphoton energies hν [76B1]. E is energy above VBM.

20Initial state energy [eV]Ei

–1–2–3–4–5–6–7

c

1

EVBM

b

hν = 40.8 eV

AgBr

EVBM

a

hν = 21.2 eV

Fig. 81. fcc-AgBr. Photoelectron spectra taken frompolycrystalline samples at T = 90 K for different photonenergies (a,b). Trace c reproduces the calculated DOS[82K], but shifted in energy to make the sharp peaks at3.8 eV coincide [93M1]. For data recorded at RT see[75T]. Energy scale referred to the experimental VBM.







136

–10.0Initial state energy [eV]Ei

hν = 140 eV

–7.5 –5.0 –2.5 0 2.5 5.0

EVBM

(× 1)

hν = 120 eV

EVBM

(× 3.75)

hν = 100 eV

EVBM

(× 20)

hν = 80 eV

EVBM

(× 33)

AgBr

Fig. 82. fcc-AgBr. Photoelectronspectra recorded at differentphoton energies from poly-crystalline samples kept at 77 K[89K]. Since the photon energytunes the intensity through theCooper minimum around hv = 150eV, the intensities are normalizedto equal maximum amplitude[89K]. See also [90M].






137

–1.0

0

1.0

2.0

– 0.5

0.5

1.5

Asym

met

rypa

ram

eter

β

40 60 80 120100 140 160 180Photon energy [eV]hν

AgBr

p/d band

d bands

Fig. 83. fcc-AgBr. Experimental asymmetry parameterβ( hv) for the angular distribution of photoelectronintensities for photon energies moving across theCooper minimum around hv = 150 eV [89K]. Filledcircles refer to low lying bands with dominant Ag(4d)partial valence density of states, while open circlescorrespond to the upper bands with strongAg(4d)/Br(4p) hybridized DOS. Solid (dashed) lines aredrawn to guide the eye. A polycrystalline sample wasused, checked for random orientation and kept at T = 88K [89K].

– 5

– 1

0

1

3

2

4

Ener

gy[e

V]E

Wavevector k

5

6

7

AgBr

EVBM

9

8

10

11

12

13

8–

6–

8+

6+

6+

6+

6–

6–

6–

4–

6–

7+

6–

7–

6+

7+

8–

6–

8+

8+8

+

7+ 7

+

6+

4+

6+

6+

6+

6+

, 4+

4+

Λ LΣ X Γ∆Γ

– 2

– 3

– 4

8+

7+

8+

7+

Fig. 84. fcc-AgBr. Band structurecalculated by means of therelativistic KKR method. Thesymmetry labels are referred to theorigin at the Ag atom [81O].Symmetries given in double groupnotation.






138

L Γ XWavevector k

AgBr

Ener

gy[R

y]E

4'

11

5

3

1

–1.1

–1.2

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'

12

25'

5'2'

3'

2'

15

4'

L Γ XWavevector k

Ener

gy[R

y]E

2'

1

1

5

3

1

–1.1

–1.2

0

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–0.9

–1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3'

12

25'

5'2'

3'

2'

15

4'

3'

3

25'

1

3

15

2'

2'2'

25'

3'

15

2,3

12

23

5

Fig. 85. fcc-AgBr. Left panel: self-consistent Hartree-Fock band structure. Right panel: same but with inclusion ofcorrelation and relaxation corrections [82K]. Symmetries given in single group notation.

DOS

exp.

theor.

AgBr


–2–6

EVBM

Fig. 86. fcc-AgBr. Density of valence states (solid line)calculated from the band structure shown in the rightpanel of Fig. 85 [82K] and compared to theexperimental total DOS (dashed line) obtained fromphotoemission spectra [75T, 82K].







139

0

15

25

20

30

10

Energy [eV]E – EF

DOS

[sta

tes

(eV

cell)

]–1

– 6 – 3 0 3 6 9 12

5

0

4

3

2

1

5

Energy [eV]E – EF

– 6 – 3 0 3 6 9 12

DOS

[sta

tes

(eV

cell)

]–1

0

15

25

10

30

20

Energy [eV]E – EF

DOS

[sta

tes

(eV

cell)

]–1

– 6 – 3 0 3 6 9 12

5

c

b

a

AgBr Ag-like

Br-like

total

←←←←Fig. 87. fcc-AgBr. Partial densities of states for (a) Ag,(b) Br and (c) total DOS calculated self-consistently bythe tight-binding LMTO-ASA method [96O].

For Figs. 88, 89 see next page


AgBr

EVBM

DOS

calc.

exp.

2 3

Fig. 90. fcc-AgBr. Top: bulk density of states calculatedusing the energy band structure shown in Fig. 89 [98V].Bottom: XPS valence band spectrum taken with 0.5 eVresolution from a polycrystalline film kept at T = 83 K[75M].






140

X

– 13

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

ΓWWavevector k

AgBr

EVBM

– 6

– 12

L W

– 14

– 15

1

2

3

4

5

6

K

Fig. 88. fcc-AgBr. Band structurecalculation employing a full-potential linear augmented-Slater-type-orbital implementation of thelocal-density approximation [97V].Energy with respect to the top ofthe valence band.

X

– 14

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

Γ WWavevector k

AgBr

EVBM

– 6

– 13

L

– 15

– 16

1

2

3

4

5

6

K

7

Γ

Fig. 89. fcc-AgBr. Band structureLDA calculation based on self-interaction and relaxation-correct-ed pseudopotentials. Spin-orbitcoupling is included. Energyreferred to top of the valence band[98V].





141


– 6 – 4– 5 – 2 0– 3 1

0.75

0

1.00

1.25

1.50

1.75

2.00

0.50

0.25

2.25

DOS

[ele

ctro

nseV

]–1

–1– 7

p-like

7.5

0

10.0

12.5

15.0

17.5

5.0

2.5

DOS

[ele

ctro

nseV

]–1

d-likeAgBr

EVBM

EVBM

Fig. 91. AgBr. Partial d- and p-densities of valencestates calculated from the band structure of Fig. 85[93M3].

DOS

[sta

tes

(eV

atom

)]

–1

– 7 – 1– 6 0– 5 1– 4 2– 3 – 2

0

DOS

[sta

tes

(eV

atom

)]

–1

0.5

1.0

1.5

2.0

2.5

0

1

2

3

4

5


p-like

d-likeAgBr calc.

p-like

d-like

EVBM

exp.

DOS

[arb

.uni

ts]

Fig. 92. fcc-AgBr. Bottom: experimental [93M1] partialp-like and d-like densities of valence states, derivedfrom the spectra shown in Fig. 81. Top: calculated[90M] partial densities of states (see also Fig. 91) afterconvolution with a 0.95 eV (FWHM) Gaussian lineshape and a rigid shift in energy to make the prominentd-peaks at 3.8 eV coincide [93M1]. For furtherexperimental results see also [90M] and [75T].







2.10 Noble metal halides (AgI) [Ref. p. 156


142

2.10.8 AgI (Silver iodide)

At normal conditions AgI crystallizes in the γ-(zincblende-) phase which, however, is metastable andoften coexisting with the β-(wurtzite-)phase:zincblende lattice: a = 6.473 Å [63W], space group T2

d - F 4 3mwurtzite lattice: a = 4.580 Å, c = 7.494 Å [63W], space group C4

6v - P63mc.Both phases may coexist up to 420 K. Depending on the deposition conditions, the β-γ mixing ratio ofthin films can be varying between the pure β-phase and a practically pure γ-phase.

Work-function (γ-AgI): φ (polycrystalline) = 6.7(3) eV [74G1].

Direct band gap at Γ with Eg = 2.82 eV [81V] for γ-AgI. Bulk plasmon energy ωp = 12.6(5) eV [74G1].The direct gap energy (at Γ) is Eg = 3.025(1) eV for β-AgI at T = 1.6 K [76D].

Under normal pressure AgI crystallizes in the stable α-phase between T = 420 and 831 K. In this phasethe iodine atoms form a bcc lattice, while the two Ag atoms are distributed statistically over 24 latticepoints. In an electric field the Ag atoms can easily migrate. The conductivity is three to four orders ofmagnitude larger than in β-AgI. At pressures above 0.7 GPa (at room temperature) AgI goes over to therocksalt structure and its optical gap becomes indirect from L to Γ [81V]. For phase diagrams, structuraldetails and electronic properties of high-temperature/high-pressure phases see Landolt-Börnstein Vols.III/41B, III/17b, III/22a and [77G, 81V].

Table 16. AgI. Core-level binding energies in eV referred to top of valence band forthe compound and to EF for the metal. All errors are ± 0.1 unless otherwise stated.

Level n = 3 n = 4 Assignment

ns1/2 717.6(2) 95.7 Ag in AgI a)

719.4(3) 96.8 Ag in metal b)

np1/2 602.7 – Ag in AgI a)

np3/2 571.8 – Ag in AgI a)

nd3/2 373.0 – Ag in AgI a)

nd5/2 367.0 – Ag in AgI a)

367.1(2) – Ag in AgI c)

368.3 – Ag in metal b)

617.3(4) – I in AgI c)

a) For γ-AgI [74G1].b) [74G1].c) For γ-AgI [75M].

If referred to the vacuum level, the Ag-ion core levels show a chemical shift of + 0.9 (5) and are moretightly bound in AgI than in metallic silver [74G1].














Ref. p. 156] 2.10 Noble metal halides (AgI)


143

Table 17. AgI. Calculated and experimental peak positions in the valence band density of states (in eV),referred to the top of the calculated valence band.

Character Theory [98V] a) XPS [75M] b) UPS [76B2] c) UPS [74G1] d)

I 5p –1.7 –2.3(2) –1.7 –2.1(2)I 5p –3.9 – –4.0(1)

–4.4Ag 4d –5.1 –5.0(1) –4.9(1)Ag 4d –5.7 –5.7(1) – –5.7(1)I 5s –13.4 – – –14.1(6)

a) Ab initio calculated for γ-AgI with self-interaction and relaxation-corrected pseudopotential.b) β-AgI. Original data [75M] referred to EF. These are shifted rigidly by 0.1 eV to make comparison with [98V] easier.c) β-AgI.d) γ-AgI. Original data [74G1] shifted rigidly by 0.8 eV to make comparison with [98V] easier. The averaged fraction of p-like density of states at the γ-phase top of the valence band has been determined as 68% [63C] and 66% [74G1], respectively.

Ab initio electronic structure calculations for all three phases (α, β, γ) of AgI are presented in [97V].These employ the full-potential linear augmented-Slater-type-orbital implementation of the local-densityapproximation. Spin-orbit interaction is not taken into account. Although band-gap magnitudes areunderestimated, their location and relative ordering as well as bandwidths are in good agreement withexperiment.

Figures for 2.10.8


30– 3– 6– 12– 15– 18

EVBM

– 9

Ag I

Fig. 93. γ-AgI. XPS valence band spectrum taken withunmonochromatized AlKα radiation (hv = 1486.6 eV)from a polycrystalline film at room temperature. Thearrow indicates the position of the iodine 5s band.Energy referred to top of valence band [74G1].















144

– 7 – 6 – 5 – 4 – 3 – 2 – 1 0– 8

EF


1– 9

Ag I

Fig. 94. AgI. XPS spectra takenwith 0.5 eV resolution (mono-chromatized photons at hv =1486.6 eV) from β-AgI at T = 100K (dotted line) and α-AgI at T =441 K (solid line). Energy referredto EF [75M].

– 7 – 6 – 5 – 4 – 3 – 2 – 1 0– 8

EVBM


– 9–10

hω = 30 eV

22.5 eV

15 eV

EVBM

EVBM

1

Ag I

Fig. 95. γ-AgI. Photoelectronspectra taken from a poly-crystalline film at different photonenergies hv [74E1]. For spectra atother photon energies see also[74E2].






145In

tens

ity ra

tio

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 40 50 60 80Electron kinetic energy [eV]Ek

30 70

Ag I

Fig. 96. γ-AgI. Experimental intensity ratio (areas) of5p-like intensity from iodine (observed at bindingenergy 0…3.7 eV, compare Fig. 95) and 4d-likeintensity from silver (observed at 3.7…6.0 eV belowtop of valence band, compare Fig. 95) versus electronkinetic energy [74E2].

0

2

4

6


hν = 16.8 eV

8

100

2

4

6hν = 21.2 eV

0

0.6

1.2

1.8hν = 26.9 eV

0

0.2

0.4

0.6

EVBM

0.8

hν = 40.8 eVAg I

EVBM

EVBM

EVBM

Fig. 97. γ-AgI. Photoelectron spectra taken for differentphoton energies from polycrystalline films. Dashedlines indicate estimated secondary electron background[74G1].





146

ΓL Γ KX– 14

– 12

– 8

– 10

– 6

– 2

– 4

0

Wavevector k

Initi

alst

ate

ener

gy[e

V]E i

EVBM

15

1

3

12

1

5

1

15

3

2

53

1

1

1 1

15

12

15

∆ + ∆3 4

∆1

Ag I

Fig. 98. γ-AgI. Band structure resulting from a semiempirical LCAOcalculation which treats the maxtrix elements of the crystal Hamiltonian asparameters adjusted to photoemission results [74G1, 77G]. For a modifiedtight-binding approach to calculate the band structures and correspondingdensities of states of the AgI polymorphs (fcc, α, β, γ) see [76S2].Symmetries given in single group notation.






147

0

1

2

3

4

5

6


10–1–3–4–5–7 –2–6

DOS

[sta

tes (

atom

eV)

]–1

0

1

2

3


–2–6

d-like

p-like

EVBM

DOS

[sta

tes (

atom

eV)

]–1

0

1

2

3

4

5

6


10–1–3–4–5–7 –2–6

DOS

[sta

tes (

atom

eV)

]–1

7

8

9

7

8

total

EVBM

EVBM

Ag I←←←←Fig. 99. γ-AgI. From top to bottom: total, partial d andpartial p density of valence states deduced from thephotoemission spectra reproduced in Fig. 97 [74G1].Histograms show the corresponding DOS from thecalculated model bands reproduced in Fig. 98 [74G1].


10–1–3–4–5Energy [eV]E – EVBM

–2–6

EVBM

DOS

AgI

exp.

calc.

Fig. 101. γ-AgI. Upper curve: experimental total densityof states from [74G1]. Histograms: total (dash-dottedline) and partial-p (dotted line) density of valence statescalculated [77O] from the band structure reproduced inFig. 100 [77O]. Energy zero refers to calculated top ofvalence band. The experimental curve is rigidly shiftedin energy to improve visual agreement.








148

Λ LΣ X

–2.0

–2.5

–1.5

–0.5

–1.0

0

Wavevector k

Ener

gy[e

V]E

AgI

EVBM

8

Γ∆Γ

6

7

4

4

4

0.51.01.5

2.02.53.03.5

4.04.5

5.0

5.56.06.57.0

7.58.0

8.59.0

9.510.0

10.5

–4.5–5.0

–4.0

–3.0

–3.5

6

7

8

6

7 6

6

4

6

8

8

8

7

7

6

7

7

7

8

8

8

7

7

6

6

6

66

6

6

6

6

Fig. 100. γ-AgI. Band structure calculated with the fully relativistic KKRmethod employing a muffin-tin potential constructed from neutral atomicpotentials [77O]. Symmetries given in double group notation.




149

Λ LΣ X

–2.0

–2.5

–1.5

–0.5

–1.0

0

Wavevector k

Ener

gy[e

V]E

EVBM

Γ∆Γ

0.51.01.5

2.02.53.03.5

4.04.5

5.0

5.56.06.57.0

7.58.0

8.59.0

9.510.0

10.5

–4.5–5.0

–4.0

–3.0

–3.5

11.0

8–8–

6–

4+

4+

6+

8+

8+

8+

6+

8+ 8+

7+

7+ 7+

6+

6+

6+

6+

4+

6+

7+

6–6–

7–

7+

7+7+

6+

6–

6–

6–

4–

6–

6+

Ag I

Fig. 102. fcc-AgI. Band structure calculated with the fully relativistic KKRmethod employing a muffin-tin potential constructed from neutral atomicpotentials [77O]. Symmetries given in double group notation




150

XΓ

Ener

gy[e

V]E

Wavevector kL KΓ

–5

–4

–3

–2

–1

0

X∆ Λ Σ

1

2

3

4

5

6

8–

6–

4+8+

6+ 6+

7+

8+

6+

6+

4+

6+

7+

6–

6–

7+

7+

6+

6–

6–

6+

6+

Ag I

–6

4+

Fig. 103. fcc-AgI. Relativistic band structure obtained from a standard muffin-tin potential by means of the KKRmethod [81V]. Symmetries given in double group notation.




151

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

Wavevector k

α-

EVBM

– 6

– 12

Γ H' P– 14

– 13

1

2

3

4

5

6

N' P N H Γa

Ag I

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

Wavevector k

β-

EVBM

– 6

– 12

H– 14

– 13

1

2

3

4

5

6

A M KΓb

L

Ag I

Fig. 104 a,b. For caption see next page



152

– 4

– 5

– 3

0

– 1

– 2

Ener

gy[e

V]E

WWavevector k

γ-

EVBM

– 6

– 12

X WΓL K– 14

– 13

1

2

3

4

5

6

Ag I

c

Fig. 104. AgI. Band structurecalculations for (a) α-AgI, (b) β-AgI and (c) γ-AgI. The calculationsemploy a full-potential linearaugmented-Slater-type-orbital im-plementation of the local-densityapproximation. Energies referredto the top of the valence band[97V].


– 8

EVBM

DOS

calc.

exp.

Ag I

2


Fig. 106. β-AgI. Top: bulk density of states calculatedusing the energy band structure shown in the left panelof Fig. 105 [98V]. Bottom: valence band spectrumtaken with 21.2 eV photons from a polycrystalline filmkept at room temperature [74G1].






153

Γ XWavevector k

Ener

gy[R

y]E

– 4

– 5

– 3

0

– 1

– 2

γ-

EVBM

– 6

– 14

– 13

1

2

3

4

5

6

L W ΓK

7

ΓMWavevector k

Ener

gy[R

y]E

– 4

– 5

– 3

0

– 1

– 2

β-AgI

EVBM

– 6

– 14

– 13

1

2

3

4

5

6

A K ΓH

7

L A

– 7 – 7

Ag I

Fig. 105. AgI. Left panel shows band structure LDA calculation for γ-AgI (zincblende), based on self-interaction andrelaxation-corrected pseudopotentials. Spin-orbit coupling is included. Right panels show the same for β-AgI(wurtzite). Energies referred to top of the valence band [98V].




154

–7

EVBM


AB

AgI

T = 251 °C

218 °C

149 °C

147 °C

146 °C

142 °C

29 °C

CD

BA

CD

hν = 21.2 eV

a–7

EVBM


AB

T = 251 °C

218 °C

186 °C

139 °C

108 °C

29 °C

CD

hν = 40.8 eV

b

Fig. 107. AgI. Photoelectron spectra collected from a polycrystalline film at various temperatures after excitationwith photons of hv = 21.2 eV (a) and 40.8 eV (b). The shape of the spectra reflects the structural phase transitionfrom γ-AgI to α-AgI at about T = 147°C [79O].




155

0

0.25

0.50

0.75

0– 3 –1– 4Energy [eV]E – EVBM

– 2– 5– 6

1.00T = 35 °C

– 7

DOS

[sta

tes (

atom

eV)

]–1

p-like

0

0.25

0.50

0.75

1.00T = 145 °C

0

0.25

0.50

0.75

1.00T = 147 °C

0

0.25

0.50

0.75

1.00T = 230 °CAgI

Fig. 108. AgI. Partial p-density of valence statesderived from the photoelectron spectra shown in Fig.107 [79O]. The temperature dependence reflects thephase transition from γ-AgI to α-AgI between T =145°C and 147°C [79O].

5.70 40 80 120 160 200

Temperature [°C]T

p-ba

ndw

idth

[eV

]

Ener

gy g

ap(0

) –(

) [e

V]E

ET

gg

240 280

5.8

5.9

6.0

6.1

6.2

6.3

6.4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T = 147 °Cc

( γβ + ) (α)

b

0 40 80 120 160 200Temperature [°C]T

240 280

0.94

0.96

1.14

a

1.12

1.10

1.08

1.06

1.04

0.98

1.00

1.02

AgI

3 K

Fig. 109. AgI. The phase-transition from γ-AgI to α-AgI as reflected in photoemission spectra (compareFigs. 107, 108). (a) Amplitude ratio of peaks labeled C,D in Fig. 107 as a function of temperature (dots). Thesolid lines are a guide to the eyes. (b) Experimentalwidth of the partial p-density of states (see Fig. 108)versus temperature (dots, left scale) compared to thechange in size of the optical band gap with temperature(solid line, scale on the right) [79O].




2.10 Noble metal halides (References)


156


55B Berry, C.: Phys. Rev. 97 (1955) 676.63C Cardona, M.: Phys. Rev. 129 (1963) 69.63W Wyckoff, R. W. G.: Crystal Structures, Vol. 1, John Wiley and Sons, 1963.67S Song, K. S.: J. Phys. (Paris) 28 (1967) 195.71C Carrera, N. J., Brown, F. C.: Phys. Rev. B 4 (1971) 3651.71M Marchetti, A. P., Bottger, G. L.: Phys. Rev. B 3 (1971) 2604.71S Sato, S., Ishii, T., Nakagura, I., Aita, O., Nakai, S., Yokota, M., Ichikawa, K., Matsuoka, G.,

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161.77O Overhof, H.: J. Phys. Chem. Solids 38 (1977) 1214.78C Copperthwaite, R. G., Steinberg, M.: Solid State Commun. 28 (1978) 915.78P Potts, A. W., Lyus, M. L.: J. Electron Spectrosc. Relat. Phenom. 13 (1978) 305.79D Doran, N. J., Woolley, A. M.: J. Phys. C.: Solid State Phys. 12 (1979) L321.79F Farberovich, O. V., Akopdzhanov, R. G., Kurganskii, E. P., Domashevskaya, E. P.: Sov. Phys.

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157

79L Lamoureux, M., Farnoux, F. C.: J. Phys. (Paris) 40 (1979) 545.79O Ostrow, M., Goldmann, A.: Phys. Status Solidi (b) 95 (1979) 509.79P Pong, W., Okada, S. K.: Phys. Rev. B 20 (1979) 5400.79V Van der Laan, G., Sawatzky, G. A., Haas, C., Myron, H. W.: Phys. Rev. B 20 (1979) 4287.79Z Zunger, A., Cohen, M. L.: Phys. Rev. B 20 (1979) 1189.80B Berkowitz, J., Batson, C. H., Goodman, G. L.: J. Chem. Phys. 72 (1980) 5829.80G1 Gross, J. G., Lewonczuk, S., Khan, M. A., Pinchaux, R., Ringeissen, J.: Solid State Commun.

35 (1980) 445.80G2 Gross, J. G., Lewonczuk, S., Khan, M. A., Ringeissen, J.: Solid State Commun. 36 (1980) 907.80H Herman, F., Kasowski, R. V.: private communication.80M McNaughton, R. M., Allen, J. D., Schweitzer, G. K.: J. Electron Spectrosc. Relat. Phenom. 18

(1980) 363.80O Overhof, H.: Phys. Status Solidi (b) 97 (1980) 267.80W Westphal, D., Goldmann, A.: Solid State Commun. 35 (1980) 441.81F Farberovich, O. V., Timoshenko, Y. K., Bugakov, A. M., Domashevskaya, E. P.: Solid State

Commun. 40 (1981) 559.81O Overhof, H.: private communication. [Fig. 70 is reproduced from Landolt-Börnstein III/22a,

1987, p. 447].81V Ves, S., Glötzel, D., Cardona, M., Overhof, H.: Phys. Rev. B 24 (1981) 3073.82B Blacha, A., Cardona, M., Christensen, N. E., Ves, S., Overhof, H.: Solid State Commun. 43

(1982) 183.82F1 Fröhlich, D., Volkenandt, H.: Solid State Commun. 43 (1982) 189.82F2 Farberovich, O. V., Timoshenko, Y. K., Bugakov, A. M., Domashevskaya, E. P.: Sov. Phys.

Solid State 24 (1982) 349.82G Glötzel, D.: private communication.82K Kunz, A. B.: Phys. Rev. B 26 (1982) 2070.82M Mellander, B. E.: Phys. Rev. B 26 (1982) 5886.82R Ren, S. Y., Allen, R. E., Dow, J. D., Lefkowitz, I.: Phys. Rev. B 25 (1982) 1205.82W Westphal, D., Goldmann, A.: J. Phys. C.: Solid State Phys. 15 (1982) 6661.83B Blacha, A., Vers, S., Cardona, M.: Phys. Rev. B 27 (1983) 6346.83E Ermoshkin, A. N., Evarestov, R. A., Kuchinskii, S. A., Zakharov, V. K.: Phys. Status Solidi (b)

118 (1983) 191.83G Goldmann, A., Westphal, D.: J. Phys. C.: Solid State Phys. 16 (1983) 1335.83L Lewonczuk, S., Gross, J. G., Ringeissen, J., Khan, M. A., Riedinger, R.: Phys. Rev. B 27

(1983) 1259.83N Nakamura, K., von der Osten, W.: J. Phys. C: Solid State Phys. 16 (1983) 6669.84C Christensen, N. E.: Phys. Status Solidi (b) 123 (1984) 281; 125 (1984) K59.84G Guimaraes, P. S., Parada, N. J.: J. Phys. C.: Solid State Phys. 17 (1984) 1695.84P Podloucky, R.: J. Phys. Chem. Solids 45 (1984) 609.84S Sliwczuk, U., Stolz, H., von der Osten, W.: Phys. Status Solidi (b) 122 (1984) 203.85Y Yeh, J. J., Lindau, I.: Atomic Data and Nuclear Data Tables 32 (1985) 1.86B Blacha, A., Christensen, N. E., Cardona, M.: Phys. Rev. B 33 (1986) 2413.86E Edamatsu, K., Ikezawa, M., Tokailin, H., Takahashi, T., Sagawa, I.: J. Phys. Soc. Jpn. 55

(1986) 2880.86S Samson, J. A. R., Shefer, Y., Angel, G. C.: Phys. Rev. Lett. 56 (1986) 2020.87E Ebbsjö, I., Vashishta, P., Dejus, R., Sköld, K.: J. Phys. C 20 (1987) L441.88C Cardona, M., Christensen, N. E., Fasol, G.: Phys. Rev. B 38 (1988) 1806.88G Gross, J. G., Fliyou, M., Lewonczuk, S., Ringeissen, J., Pinchaux, R.: Phys. Rev. B 37 (1988)

3068.88H Hamilton, J. F.: Adv. Phys. 37 (1988) 359.89K Kwawer, G. N., Miller, T. J., Mason, M. G., Tan, Y., Brown, F. C., Ma, Y.: Phys. Rev. B 39

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158

90H Hamza, S., Khan, M. A., Lewonczuk, S., Ringeissen, J., Petiau, J., Sainctavit, Ph.: Solid StateCommun. 75 (1990) 29.

90M Mason, M. G., Tan, Y. T., Miller, T. J., Kwawer, G. N., Brown, F. C., Kunz, A. B.: Phys. Rev.B 42 (1990) 2996.

91S Skonieczny, J., Lodders, F., Engelhard, H., Goldmann, A., Johnson, R. L. Ghijsen, J.: Z. Phys.B: Condens. Matter 85 (1991) 211.

91W Wagner, M. K., Hansen, J. C., deSouza-Machado, R., Liang, S., Tobin, J. G., Mason, M. G.,Brandt, S., Tan, Y. T., Yang, A.-B., Brown, F. C.: Phys. Rev. B 43 (1991) 6405.

93K Kapecki, J., Rodgers, J.: in: Kirk-Othmer Encyclopedia of Chemical Technology, Howe-Grant,M., (ed.), 4th edition, Vol. 6, Wiley, New York 1993.

93M1 Matzdorf, R., Goldmann, A.: J. Electron Spectrosc. Relat. Phenom. 63 (1993) 167.93M2 Matzdorf, R., Skonieczny, J., Westhof, J., Engelhard, H., Goldmann, A.: J. Phys.: Condens.

Matter 5 (1993) 3827.93M3 Mason, M. G.: private communication of results obtained by A. Barry Kunz (unpublished).

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Kamilli, A., Send, W., Gerthsen, D.: Phys. Rev. B 62 (2000) 13053.00O Overhof, H., Gerstmann, U.: Phys. Rev. B 62 (2000) 12585.00V Vogelsang, H., Husberg, O., Köhler, U., von der Osten, W., Marchetti, A. P.: Phys. Rev. B 61

(2000) 1847.01S Serrano, J., Ruf, T., Widulle, F., Lin, C. T., Cardona, M.: Phys. Rev. B 64 (2001) 045201.

Ref. p. 337] 2.11 Nonmagnetic transition metals (Introduction)


159

2.11 Nonmagnetic transition metals

2.11.1 Introduction

Transition metals are a group of elements which exhibit valence d-shells filled only partially withelectrons. There are eight 3d transition metals: Sc, Ti, V which are nonmagnetic and the magneticelements Cr, Mn, Fe, Co and Ni. The five magnetic transition metals are treated separately in Landolt-Börnstein Vol. III/23c2 and are therefore not under further consideration in the present chapter. Then wehave eight 4d transition metals: Y, Zr, Nb, Mo, Tc, Ru, Rh and Pd. Among these Tc is not easilyaccessible for experimental work since it is radioactive and no stable isotope exists. Finally we haveseven transition metals with outer 5d-shells: Hf, Ta, W, Re, Os, Ir and Pt. Formally also the rare earthelements La to Lu have 5d orbitals which can be filled with an electron. However, the Lanthanides aretreated separately in Landolt-Börnstein Vol. III/23a and, most important, their relevant physical propertiesare in general determined by the 4f electron shell. Therefore the present chapter is confined to Sc, Ti, Vwith 3d electrons, the 4d-shell metals Y to Pd and the elements with partially filled 5d-shell ranging fromHf to Pt. In all of these materials, the physical properties of both the bulk and the surface are largelydetermined by the partially filled valence d-shell.

The nd transition elements (n = 3, 4, 5) elements exhibit a wide variety of structural andelectromagnetic properties. For detailed bulk structure data, including phase transitions and other changeswith temperature, we refer to Landolt-Börnstein Vols. III/6 and III/14a. A key factor in the understandingof transition metals is the peculiar nature of their electronic energy bands. The valence states may beconsidered to arise from the nearly degenerate nd- and (n+1)s atomic levels. Their orbitals have differentspatial distribution, with the s electrons generally extending beyond the corresponding d-shell. Alreadyearly studies of photoemission from d-band metals examined, to which extent experimental spectra maybe explained within the one-electron band theory [74S1]. This is of relevance since transition metals areconsidered a class of materials in which electronic correlations considerably influence the excitationspectrum as well as ground-state properties [94U]. Moreover, the hexagonal-close-packed (hcp) structureis the most common among the transition metals, and this crystal structure is more complex than that ofthe cubic metals. The combination of the uniaxial symmetry and the two atoms per unit cell results in anelectronic structure which is also more complex than that of the cubic metals [75J1]. Furthermore,deviations from the ideal c/a ratio of 1.63 may impose anisotropies, which make band calculations evenmore difficult [88B]. In addition, there is no doubt that the heavier elements require the use of a fullyrelativistic description. There is no clear consensus, however, regarding the form in which relativity hasto be implemented into an electronic energy band calculation [00T1]. Several transition metals showstructural phase transitions at elevated temperatures [71L, 88L] and the theoretical prediction of phasestability trends is of considerable interest [00G]. Theoretical ab initio studies of optical properties in theultraviolet energy range are still very rare. The reason is that very accurate band structure calculations arerequired in a wide energy range, and the problem is complicated by the need to compute a full dielectricmatrix [01K1]. Finally some transition metals are of interest since they show high superconductingtransition temperatures (as compared to their neighbours) as well as anomalies in their phonon dispersioncurves. These metals are often also building blocks in transition-metal compounds having both theoreticaland technological importance.

In the context of photoemission and related spectroscopies with their extreme surface sensitivity it isnot only the three-dimensional bulk band structure and its change with subsequent filling of the d-bandswhich attracted considerable interest. In general, transition metal surfaces show high chemical and/orcatalytic activity due to the presence of unfilled d-states around the Fermi level. The d-holes may providean easy escape channel for electron transfer from an adsorbate thereby allowing for strong bonds. Inconsequence interest, both experimentally and theoretically, is focused to occupied as well as to emptybands. Moreover, electronic surface properties may be of crucial relevance for surface reactions. Forexample, surface core level shifts reflect the difference in potential at the surface and in the bulk due tothe modified structural environment. Thus, while the present chapter concentrates on electronic bulkproperties, we have also included some experimental data concerning surface states and core-level shifts










2.11 Nonmagnetic transition metals (Introduction) [Ref. p. 337


160

where considered necessary or unavoidable: both surface and bulk properties often appear simultaneouslyin photoelectron spectra. A comprehensive treatment of surface properties is, however, not within thescope of the present chapter. Such information can be found elsewhere in Landolt-Börnstein volumes.Details on surface crystallography and structural parameters, referring to ideal surfaces as well as tosurface reconstruction and relaxation, are collected in Vol. III/24A. Extensive summaries of dataconcerning the electronic structure of transition metal surfaces are available in Vol. III/24B and in Vol.III/24D.

With respect to metals crystallized in the hcp structure we remember the fact that alternativecoordinate systems are used in the literature to describe the hexagonal lattice. Some authors use acoordinate system referring to the three primitive basis vectors: two axes in the hexagonal plane with anangle of 60° between them, and the third axis normal to the hexagonal plane. The alternative system usesfour components: three axes in the hexagonal plane with angles of 120° between them, and the fourth axisnormal to the hexagonal plane. In consequence e.g. the D-direction normal to the hexagonal plane(compare Fig. 10 and 11 in chapter 1.3 of the present volume) is labeled [0001] in the four-axes system

and [001] in the alternative one and similarly [11 2 0] equals [110]. For more details we refer to theappendix (on Bravais lattices, primitive unit cells, reciprocal lattices and first Brillouin zones) of Landolt-Börnstein Vol. III/13c. Both index systems are in use and in the data section we left the labels given bythe respective authors to make comparison with the original literature easier.

Ref. p. 337] 2.11 Nonmagnetic transition metals (Sc)


161

2.11.2 Sc (Scandium) (Z = 21)

Lattice hcp, a = 3.309 Å, c = 5.273 Å, c/a = 1.594 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Ar) 3d1 4s2

Work-function [95H]:φ (poly) = (3.5 ± 0.3) eV

Table 1. Sc. Core-level binding energies in eVrelative to EF [95H]. Typical scatter betweenvarious sources is ± 0.5 eV. See also [95M].

Level n = 2 n = 3

ns1/2 498.0 51.1np1/2 403.6

28.3np3/2 398.7


Table 2. Sc. Occupied valence bands. Experimental and theoretical determination of high symmetry pointenergies. Energy values are given in eV w.r. to EF.

Point Level Experiment Theory[94P1] [91M] [80S1] * [76D]

Γ Γ1+ – 4.65(10) – 5.1 – 6.3 – 5.1Γ4– – 1.85(10) – 1.6 – 1.0 – 1.6

* taken from a figure.










2.11 Nonmagnetic transition metals (Sc) [Ref. p. 337


162

Figures for 2.11.2

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s

3d

Photon energy [eV]h�

102

10–2

10–1

1

10–3

10

Sc

2p2s

3p

3s

Fig. 1. Sc. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].

EFBinding energy [eV]Eb

Eb [eV]

IIn

tens

ity

= 020040060080010001200

LMM

Ar Ar 3s3p

2s

2p1/2

2p3/2

LMM

I

940 870

Sc

Fig. 2. Sc. Overview XPS spectrum. Insert shows blow-up of the Sc(LMM) Auger-electron spectrum [95M]. Data taken withunmonochromatized MgKα radiation. For results obtained with

monochromatized AlKα radiation see [95M].






163


IIn

tens

ity

2p1/2

2p3/2Sc

P

425 415 405 395

Fig. 3. Sc. XPS spectrum showing 2p core levels andplasmon satellite (P) from polycrystalline film excitedwith unmonochromatized MgKα radiation [77G]. See

also [95M]. Eb w.r. to EF


IIn

tens

ity

3pSc

P

60 50 40 30

3s

20

Fig. 4. Sc. XPS spectrum showing 3s and 3p core levelstaken from poly-crystalline film with unmono-chromatized AlKα radiation. Feature P is dominated by

bulk plasmon excitation, but contains also a weakcontribution from excitation of the 3s core level by theAlKα3,4 satellite[77G].


IIn

tens

ity

Sc (0001)

38 36 34 32 30 28 26

Fig. 5. Sc (0001). 3p core levels for normal (filledcircles) and 60° off-normal (empty symbols) emission.Photon energy hν = 80 eV [92B].

IIn

tens

ity

Sc

EFInitial state energy [eV]E i

= 0−12 −8 −4

Fig. 6. Sc. XPS spectrum of the valence band obtainedwith monochromatized (0.5 eV) AlKα radiation (hν =

1487 eV) [77L1].








164I

Inte

nsity

Sc

Photon energy [eV]hν0 50 100 150

Fig. 7. Sc. Photoionization cross section of the 3d valenceband for a polycrystalline film in its dependence onphoton energy, measured at an initial state energy 0.5 eVbelow EF by CIS spectroscopy [85B].

IIn

tens

ity

Sc

20 30 40 50

M 2,3

3dE i [eV]44.2543.2542.25

40.25

38.25

36.2534.25

32.25

30.2529.25

27.2526.25

24.2522.25

28.25

Photon energy [eV]hνFig. 9. Sc. Inverse photoemission spectra taken for apolycrystalline film in normal electron incidence atvarious electron energies Ei, showing strong variation in

the 3d features (tick marks). Fermi level indicated byarrows [89H]. →Fig. 10. Sc. Inverse photoemission spectra for apolycrystalline film taken at electron incidence angles θand (resonant) electron energy Ei = 42.25 eV. Peaks A,

B and C reflect Sc3d empty-state features, thefluorescent decay of the Sc3p core hole, and plasmon-related effects, respectively [88H].

Energy [eV]E E− F

IIn

tens

ity

Sc

DOS

0 2 4 6 8 10

0

0

Fig. 8. Sc. Top: Experimental bremsstrahlungisochromat spectrum (photon energy hν = 1486.7 eV,total resolution 0.7 eV). Bottom: Calculated density ofstates. Dashed without broadening, solid line includingbroadening to simulate instrumental and lifetime widths[84S].

IIn

tens

ity

Sc

20 30 40

M 2,3

A

A

A

A

B

B

B

B

C

C

C

θ = 45°

30°

15°

0°

EF








165

Wavevector k

Ener

gy[R

y]E

Σ

Sc

Γ Γ∆ L

1’

1’

1

1

1

1

1

2

2

2

2

2

2

22

3

4’

2’3

1

1

2

2

1

2

2

3’

2’

3

31

4

1

1

1 1

14

4

44

4-

4-

4-

3

3 3

3

3

1 1

1

11

1

11

1

1

1

1

1

1

4’

2

31

2

4

1

0

0.2

0.4

0.6

6 +6 +

5 +

1+ 1+

1+

1+

1+

1+

3+

3+

3+

6-6-

1-2-

2-

2+

6

6

5

5

EF

1,3

2,4

1,3

1,3

1,3

A S H P K T M U L R A S’ H’ M T’ K’

= 0.493Ry

Fig. 11. Sc. Band structure calculated by the KKRZ method inconjunction with a quantum defect method [80S1]. See also [76D].Symmetry labels in single group notation

Wavevector k

Ener

gy[R

y]E

Sc

Γ Γ L

EF

A H HK KM L A M

0.5

0.7

0.3

0.1

− 0.13 1.5 0 3 0 30 0 60 0

DOS

s p d total

Fig. 12. Sc. Right panel: Energy bands calculated self-consistently by means of the full potential linearizedaugmented-plane-wave method [88B]. See also [91M]. Left panel: Density of states with s,p,d orbital character (instates/Ry/atom) and corresponding total DOS (states/Ry/unit cell) [88B].








166

Energy [Ry]E

Sc

EF

DOS

[sta

tes/

atom

/Ry]

10

5

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7

dz 2

d dxy x y, -2 2

d dxz yz,

Fig. 13. Sc. Symmetry decomposition of the partial d-density ofstates (normalized to one d-state without degeneracy) resulting fromthe energy bands shown in Fig. 12 [88B].


Refle

ctiv

ityR

1.0

0.8

0.6

0.4

0.2

0 1 2 3 4 5

Sc

Fig. 14. Sc. Experimental normal-incidencereflectivity data taken from single crystals withelectric field vector E parallel (solid line) andperpendicular (dashed line) to the c-axis [81W2].





167I

Inte

nsity


0 = EF−2−4−5 −3 −1

Sc(0001) exp.


0 = EF−2−4−5 −3 −1

calc.

h [eV]ν5048

4644

4240

38

36

3432

30

2826

24

2220

Fig. 15. Sc(0001). Experimental (left) and calculated (right) results for photo-electron normal emission, i.e. along theΓA direction of the bulk Brillouin zone, at various photon energies hν. P-polarized light is incident at 30° withrespect to the surface normal [94P1]. See also [92B].


0 = EF−2−4 −3 −1

θ = 50°

40°

30°

20°

10°

0°

−10°

−20°

−30°


0 = EF−2−4 −3 −1

Sc(0001)

IIn

tens

ityI

Inte

nsity

θ = 60°

50°

40°

30°

20°

10°

0°

−10°

−20°

−30°

IIn

tens

ity

Fig. 16. Sc(0001). Off-normal photoemission spectra taken along the ΓK (left) and ΓM (right) azimuths. Photonincidence at 30° with respect to surface normal. Photon energy hν = 40 eV [92B].






168

Wavevector kII Wavevector kII

Γ ΓΓ K KK MM M M

Initi

al st

ate

ener

gy[e

V]E i

Initi

al st

ate

ener

gy[e

V]E i

0 0

−2 −2

−4 −4

−5 −5

−3 −3

−1 −1

Sc (0001)

Fig. 17. Sc(0001). E(k||) values derived from data in Fig. 16 [92B].


0 = EF−2−4−5 −3 −1

IIn

tens

ity

α= 80°

70°

60°

50°

40°

30°

20°

10°

0°

Sc (0001)

Fig. 18. Sc(0001). Photoelectron spectra collected atpolar angle θ = 20° in the ΓM direction as a function ofphoton incidence angle α. Photon energy hν = 40 eV,electric field vector confined to the ΓM mirror plane,i.e. α = 0 corresponds to fully s-polarized light [94P1].



Ref. p. 337] 2.11 Nonmagnetic transition metals (Ti)


169

2.11.3 Ti (Titanium) (Z = 22)

Lattice hcp, a = 2.951 Å, c = 4.684 Å, c/a = 1.587 [71L]See also [71L] for other phasesBrillouin zones: see section 1.3 of this volumeElectronic configuration: (Ar) 3d2 4s2


Table 3. Ti. Core-level binding energies in eVrelative to EF [95H]. Typical scatter between varioussources is ± 0.5 eV. See also [95M].

Level n = 2 n = 3

ns1/2 560.9 58.6np1/2 461.2

32.6np3/2 453.7

For core-hole lifetime broadenings see [92F]. For a measurement of the Kβ-to-Kα X-ray intensity ratioand the resulting valence electron configuration see [02R1].

Figures for 2.11.3

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s


102

10–2

10–1

1

10–3

10

Ti

2p2s

3p3s

3d

3d

Fig. 19. Ti. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].









2.11 Nonmagnetic transition metals (Ti) [Ref. p. 337


170


IIn

tens

ity

= 020040060080010001200

LMM

Ar Ar 3s3p

2s

2p1/2

2p3/2Ti

Fig. 20. Ti. Overview XPS spectrum. Data taken withunmonochromatized MgKα radiation. For spectrum excited with



IIn

tens

ity

2p1/2

2p3/2Ti453.8

6.15

470 460 450

Fig. 21. Ti. XPS data showing region of the spin-orbit-split 2p core levels taken with unmonochromatizedMgKα radiation [79W]. See also [83P] and [95M].

IIn

tens

ity

Ti


= 0−12 −8 −4

Fig. 22. Ti. XPS spectrum of the valence band obtainedwith monochromatized (0.5 eV) AlKα radiation (hν =

1487 eV) [77L1].








171I

Inte

nsity


EF= 0

Ti

8 6 4 2

( )a

( )b

( )c

−− − −

Fig. 23. Ti. Angle-integrated UPS data from a Ti(0001)surface using photon energies hν = 16.8 eV (a), 21.2 eV(b) and 40.8 eV (c) [80F1].

IIn

tens

ity

T i


Fig. 24. Ti. Photoionization cross section of the 3dvalence band for a polycrystalline film in the photonenergy range between 15 and 150 eV, measured by CISspectroscopy (initial state energy 0.5 eV below EF )

[85B]. See also [96K].

Energy [eV]E E− F

IIn

tens

ity

T i

DOS

0 2 4 6 8 10

0

0

Fig. 25. Ti. Top: Experimental bremsstrahlungisochromat spectrum (photon energy 1486.7 eV, totalresolution 0.7 eV). Bottom: Calculated DOS. Dashedwithout broadening, solid line including broadening tosimulate instrumental and lifetime widths [85S]. Seealso [82R].

IIn

tens

ity

Ti

Energy [eV]E0 = EF

h [eV]ν

2 4 6 8

22.5

20.4

18.7

15.7

14.5

12.7

11.1

Fig. 26. Ti. Bremsstrahlung isochromat spectra taken atdifferent photon energies hν from polycrystallinesample [92P].







2.11 Nonmagnetic transition metals (Ti) [Ref. p. 337


172

Wavevector k

Ener

gy[R

y]E

Ti

Γ Γ L

EF

A H HK KM L A M

0.6

0.8

0.4

0.2

3 1.5 0 2 0 25 0 60 0DOS

s p d total

0

Fig. 27. Ti. Right panel: Energy bands calculated self-consistently by means of the full potential linearized APWmethod. Left panel: corresponding s,p,d (states/Ry/atom) and total densities of states (states/Ry/unit cell) [88B]. Seealso [75J2] and [87L].

64 64

56 56

48 48

40 40

32 32

24 24

16 16

8 8

0 0

11.2 11.2

9.8 9.8

8.4 8.4

7.0 7.0

5.6 5.6

4.2 4.2

2.8 2.8

1.4 1.4

0 00 00.06 0.060.12 0.120.18 0.180.24 0.240.30 0.300.36 0.360.42 0.420.48 0.48

Energy [Ry]E Energy [Ry]E

α −Ti (hcp) −Ti (hex)

DOS

[ ele

ctro

n st

ates

/ato

m/R

y]

DOS

[ ele

ctro

n st

ates

/ato

m/R

y]

NOS

[ele

ctro

ns/a

tom

]

NOS

[ele

ctro

ns/a

tom

]

EFEF

ω

Fig. 28. Ti. Electronic densities of states (left scale) and integrated number of electrons (right scale) calculated for theα-phase (hcp, left panel) and the ω-phase (simple hexagonal, right) using the nonrelativistic APW method [79V2].For experimental data see [78F] and [79V2].









173


0 = EF 0 = EF

EF

−4 −4−8 −8−10 −10−6 −6−2 −2

IIn

tens

ity

1.5

1.0

0.5

0

DOS

[sta

tes/

eV/a

tom

]

2 2

spd

Ti

BG

Fig. 29. Ti. Comparison of the XPS valence band spectrum (right, dots) with a simulated one (right, solid line) usinga partial DOS calculation (left) after inclusion of several broadening mechanisms [81H2]. BG: estimated secondaryelectron background.


Ti1.0

0.8

0.6

0.4

0.2

05 10 15 20 25 30

Refle

ctiv

ityR


0 = EF−10 −5−15

IIn

tens

ity

Ti

h [eV]ν

47

37

←←←←Fig. 30. Ti. Experimental normal-incidence reflectivitydata [81W1] obtained from different experiments. Fordetails and tables of the "most recommended" data see[81W1].


Diel

ectri

c con

stan

tε2

ε

ε

2

2

Ti10

8

6

4

2

05 10 15 20 25 30

ε210

10

Fig. 31. Ti. Experimental ε2 spectra [81W1] from

different experiments. See also caption to Fig. 30.

←Fig. 32. Ti. Angle-integrating UPS spectra taken from aTi(0001) surface showing resonant electron emission:(top) spectrum on resonance (hν = 47 eV) and (bottom)off-resonance (hν = 37 eV) [83B2].






2.11 Nonmagnetic transition metals (V) [Ref. p. 337


174

2.11.4 V (Vanadium) (Z = 23)

Lattice bcc, a = 3.024 Å [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Ar) 3d34s2


Table 4. V. Core-level binding energies in eVrelative to EF [95H]. Typical scatter between varioussources is ± 0.5 eV. See also [95M].

Level n = 2 n = 3

ns1/2 626.7 66.3np1/2 519.8

37.2np3/2 512.1

For core-hole lifetime broadenings see [92F]. For a measurement of the Kβ-to-Kα X-ray intensity ratioand the resulting valence electron configuration see [02R1].

Figures for 2.11.4

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s3d

3d


102

10–2

10–1

1

10–3

10

2p2s

3p3s

V

Fig. 33. V. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].








Ref. p. 337] 2.11 Nonmagnetic transition metals (V)


175


Eb [eV]IIn

tens

ity

= 020040060080010001200

LMM

Ar Ar 3s3p

2s

2p1/2

2p3/2 LMM

I

795 775785

V

Fig. 34. V. Overview XPS spectrum.The insert shows a blow-up of theV(LMM) Auger-electron spectrum[95M]. Data taken withunmonochromatized MgKα radiation.

Spectrum excited with mono-chromatized AlKα is shown in [95M].


IIn

tens

ity

2p1/2

2p3/2 V (100)

507 512 517 532522 527

Fig. 35. V. XPS spectrum of the 2p levels taken withunmonochromatized MgKα radiation from a V(100)

surface after background subtraction [94V]. See also[79W], [86R] and [95M].

Fig. 37. V. XPS spectrum of the valence band obtainedwith monochromatized (0.5 eV) AlKα radiation [77L1].

See also [82A2].


IIn

tens

ity3p

V

60 50 40 30

3s

7080

Fig. 36. V. Photoemission from the 3p and 3s corelevels taken with hν = 130 eV [92S].

IIn

tens

ity

V


= 0−12 −8 −4












176I

Inte

nsity

IIn

tens

ity


0 = EF−2−4−8−10 −6

h [eV]ν

6458545048464544434241403938

AA

A

A

A

AA

A

h [eV]ν52

48A

A

20 16 12 8 4 0− − −−−

V

Fig. 38. V. Photoemission spectra taken at differentphoton energies hν from a polycrystalline film sample[92S]. The large enhancement near EF with increasing

hν is due to resonant photoemission. Label A indicatescontribution from an Auger process [92S].

Fig. 40. V. Top: Experimental bremsstrahlungisochromat spectrum (hν = 1486.7 eV, total resolution0.7 eV). Bottom: calculated density of states. Dashedwithout broadening, solid line including broadening tosimulate instrumental and lifetime widths [84S].

IIn

tens

ity

V


Fig. 39. V. Photoionization cross section of the 3dvalence band for a polycrystalline film in itsdependence on photon energy, measured at an initialstate energy 0.5 eV below EF by CIS spectroscopy

[85B].

Energy [eV]E E− F

IIn

tens

ity

V

DOS

0 2 4 6 8 10 12

0

0







177I

Inte

nsity

V

Energy [eV]E0 = EF

h [eV]ν

2 4 6 8

22.5

20.4

18.7

15.7

14.512.711.1

10

Fig. 41. V. Bremsstrahlung isochromat spectra taken atdifferent photon energies hν from polycrystallinesample [92P].

Energy [Ry]EDO

S [ s

tate

s Ry

]−1

EF

V50

40

30

20

10

−1.0 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4

Fig. 43. V. Density of states calculated from the bandstructure reproduced in Fig. 42 [78L].

Wavevector k

Ener

gy[R

y]E

Σ

V

Γ Γ∆

1’

1’

1

1

1

1

222

3

3

1

1

2

2

1

2

2’

3

3

1

4 4

1

4 44

4

4 4

3

3

3333

3

3

1

11

1

1

1

1

1

1

5

EF

H HG

0.1

0

− 0.1

−0.2

−0.3

−0.4

−0.5

−0.6

−0.7

−0.8

−0.9

−1.0N ND P PΛ F

12

1212

12

25’

25’

25’

25’

Fig. 42. V. Energy bands along somelines of high symmetry in the bulkBrillouin zone calculated using a self-consistent LCAO method [78L].Symmetry labels in single groupnotation.






178

Energy [Ry]E Energy [Ry]E

DOS

[ ele

ctro

n st

ates

/ato

m /

Ry]

DOS

[ ele

ctro

n st

ates

/ato

m /

Ry]

EF

EF

60

50

40

40

30

30

20

20

10

10

0 00.4 0.40.6 0.60.8 0.81.0 1.01.2 1.21.4 1.40.2 0.21.6 1.6

V

Fig. 44. V. Density of states calculated from a bandstructure based on a self-consistent APW method withexchange parameter α = 2/3. Left: Calculated at normalroom temperature lattice constant a0 , interpolation of

the lowest six bands. Right: Calculated at reducedlattice constant a = 0.95 a0, interpolation of the lowestfour bands [72P].

Energy [Ry]E

DOS

[ sta

tes/

Ry/a

tom

/spi

n]

EF

0.4 0.6 0.8 1.0 1.2 1.40.2

V

NOS

[ele

ctro

ns/a

tom

]25

20

15

10

5

02015

10

5

010

5

04040

10

8

6

4

2

0

total

d :Γ12

d :Γ25’

p

s

Fig. 45. V. Density of states (top panel) and partial s,p,d densities ofstates calculated from a self-consistent APW band structurecalculation using the exchange approximation with α = 2/3 [77B].





179

V


Refle

ctiv

ityR

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 46. V. Experimental normal-incidence reflectivitydata [81W1] obtained from different experiments. Fordetails and tables of the "most recommended" data see[81W1].

V


Diel

ectri

c con

stan

tε2

20

15

10

5

20

10

ε 2

1 2 30[eV]hν

Fig. 47. V. Experimental ε2 spectra [81W1] from

different experiments. See also caption to Fig. 46.


0 = EF−8 −6 −4 −2

IIn

tens

ity

V (100)

2

0

Fig. 48. V(100). Normal-emission photoelectronspectrum taken at hν = 21.2 eV [96P1]. For results frompolycrystalline sample at hν = 21.2 eV see [82A2].

V (100)


= 0−10 −8 −4 −2

θ = 50°

45°

40°

35°

30°

25°

20°

15°

10°

0°

IIn

tens

ity[a

rb.u

nits

]

10000

8000

6000

4000

2000

0

Fig. 49. V(100). Valence band photoemission spectrarecorded at hν = 21.2 eV at different electron emission

angles θ varied in the (01 1 ) plane by sample rotationabout the [011] axis [94P2].









180

Wavevector k

Γ M

Initi

al st

ate

ener

gy[e

V]E i

0

−2

V (100)

H G N

EF

Fig. 50. V(100). Energy dispersion along Γ-Σ-M of thesurface Brillouin zone, derived from data shown in Fig.49 and compared to the calculated bulk band dispersionfrom [72P].

IIn

tens

ity

V (100)

Energy [eV]E0 = EF

h = 11.5 eV

h = 10 eV

ν

ν

2 4 6

Fig. 51. V(100). Normal-incidence inversephotoelectron spectra taken at two different photonenergies hν in the isochromat mode [96P1].

IIn

tens

ity

V (100)


θ = 45°

30°

15°

0°

Fig. 52. V(100). Inverse photoemission spectrarecorded in the isochromat mode at photon energy hν =11.5 eV for various electron incidence polar anglesindicated [96P1].






181I

Inte

nsity

V (100)

Energy [eV]E0 = EF 2 4 6 8−1−2 1 3 5 7

Ei = 32.2 eV

29.5

26.9

25.2

23.7

20.9

19.7 eV

Fig. 53. V(100). Normal-incidence inverse photoemission spectrataken at different incident electron energies Ei [96O].

IIn

tens

ity

V (100)

Energy [eV]E

Ei = 28.4 eV

20.9 eV

26.9

25.2

22.7

23.7

8 9 10 11 12 13 14 15 16 17 18

Fig. 54. V(100). Normal-incidence inverse photoemission spectrataken at different incident electron energies Ei [96O]. Energy with

respect to EF.



2.11 Nonmagnetic transition metals (Y) [Ref. p. 337


182

2.11.5 Y (Yttrium) (Z = 39)

Lattice hcp, a = 3.647 Å, c = 5.731 Å, c/a = 1.571 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d1 5s2


Table 5. Y. Core-level binding energies in eVrelative to EF [95H]. Typical scatter between varioussources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 392.0 43.8np1/2 310.6 24.4np3/2 298.8 23.1nd3/2 157.7 –nd5/2 155.8 –


Table 6. Y. Occupied valence bands. Experimental and theoreticaldetermination of high symmetry point energies (given in eV w.r. to EF).

Point Level Experiment Theory[87B1] [88B] [91M]

Γ Γ1+ – –4.9 –4.8Γ4– –1.7 –1.9 –1.8









Ref. p. 337] 2.11 Nonmagnetic transition metals (Y)


183

Figures for 2.11.5

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s

3d


102

10–2

10–1

1

10–3

10

Y

3p

3s

3p

4d

4d

5s

4p

3d

Fig. 55. Y. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].

Cros

s sec

tion

[M

b]σ


10–2

10–1

1

10

Y

0 50 100 150 200 250 300 350

Fig. 56. Y. Atomic 4d-subshell cross section near the Cooperminimum [85Y].





184


IIn

tens

ity

= 020040060080010001200

MNN

Ar

4s4p

3s

3p1/2

3p3/2

3d3/23d5/2Y

Fig. 57. Y. Overview XPS spectrum.Data taken with unmonochromatizedMgKα radiation [95M]. See also

[95M] for spectrum excited bymonochromatized AlKα radiation.


IIn

tens

ity

Y (0001)

2224262830 20

Fig. 58. Y(0001). 4p core level spectrum taken withphoton energy hν = 60 eV in normal (solid line) andoff-normal (dashed, 60° w.r. to surface normal)emission geometry [89B, 92B].

Energy [eV]E E− F

IIn

tens

ity

Y

DOS

0 2 4 6 8 10

0

0

Fig. 59. Y. Top: Experimental bremsstrahlungisochromat spectrum (hν = 1486.7 eV, total resolution0.7 eV). Bottom: Calculated DOS. Dashed withoutbroadening, solid line including broadening to simulateinstrumental and lifetime widths [84S].








185

Energy [eV]E E− F

EFY

DOS

0 2−6 4−4 6−2

Fig. 60. Y. Density of states calculated using the self-consistent ASW method [84S].

Wavevector k

Ener

gy[R

y]E

Y

Γ Γ L

EF EF

A H HK KM L A M

0.6

0.8

0.4

0.2

3 1.5 0 2 0 15 0 40 0DOS

s p d total

0

Fig. 61. Y. Right panel: Energy band structure calculated self-consistently by means of the full potential linearized APW-method. Left panel: corresponding partial (in states/Ry/atom) and total (states/Ry/unit cell) densities of states [88B].

Wavevector k

Ener

gy[e

V]E

Y

Γ Γ

EF

A HKML A

0

1

2

−1

−2

−3

−4

−5

Γ4−

Γ1+Fig. 62. Y. Self-consistent LMTO-ASA band structure calculation [92B].






186

Energy [eV]E E− F

0−4 −1−5 −3 −2

DOS

[sta

tes e

V]

−1

2

spd

Y5

4

3

2

1

0

total

1

Fig. 63. Y. Total and partial densities of valence states calculatedwith the bandstructure shown in Fig. 62 [92B].

Energy [eV]E E− F

0−4−6 −2

DOS

[sta

tes e

V]

−1

2

Ytotal d

d − eg

d − t2g

3

2

1

02

1

03

2

1

04 6

Fig. 64. Y. Partial d-like DOS in the bcc phase. Energyzero at EF [00G].

YE cII

E cII


Refle

ctiv

ityR

E cT

10 R

E c

T

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 65. Y. Experimental normal-incidence reflectivitydata [81W1] obtained with light polarization vector Eparallel (solid line) and perpendicular (dashed) to the c-axis of the sample.






187

Y

E cII


E c

T

10

E c

T

0 2 4 8 12 16

E cII

Diel

ectri

c con

stan

t2ε

ε

20

15

10

5

20 24scale change

2

Fig. 66. Y. Experimental ε2 results [81W1] obtained with linearly

polarized light. See legend to Fig. 65 for details.

IIn

tens

ity


0 = EF−2−4−8 −6−10−14 −12

Y(0001)h [eV]ν= 60

55

50

45

40

35

30

25

Fig. 67. Y(0001). Photoemission spectra at normalemission taken for various photon energies hν [87B1].

IIn

tens

ity


0 = EF−2−4 −3 −1

Y(0001)

h [eV]ν = 50

48

46

44

42

40

38

36

34

32

30

28

26

24

22

20

Fig. 68. Y(0001). Normal-emission photoelectronspectra taken for various photon energies hν [92B].






188I

Inte

nsity


0 = EF−2−4−6−12 −10 −8

Y(0001)

Y(1120)

T = 340 K

600

610

620

630

640 K Fig. 69. Y. Photoemission spectra recorded at photonenergy hν = 40 eV in normal-emission geometry from

(top) Y(0001) at room temperature and from Y(11 2 0)at various temperatures as indicated [92B].


0 = EF−2−4 −3 −1

Y(0001)

IIn

tens

ity

θ = 30°

20°

10°

0°

−10°

−20°

−30°


0 = EF−2−4 −3 −1

θ = 30°

20°

10°

0°

−10°

−20°

−30°

IIn

tens

ity

Fig. 70. Y(0001). Angle-dependent photoelectron spectra recorded for hν = 40 eV for electron emission along the ΓK(left) and ΓM (right) azimuths, resp. [92B].





189

Wavevector kII Wavevector kII

Γ Γ ΓΓ K KK MM M M

Initi

al st

ate

ener

gy[e

V]E i

Initi

al st

ate

ener

gy[e

V]E i

0 0

−2 −2

−4 −4

−5 −5

−3 −3

−1 −1

Y (0001)

Fig. 71. Y(0001). E(k||) values derived from the spectra shown in Fig. 70 [92B].

IIn

tens

ity

Energy [eV]E0 = EF

Y(0001) h [eV]ν = 17

16

15

14

13

12

2 4 6 8

Fig. 72. Y(0001). Isochromat normal-incidence inversephotoemission spectra taken over the photon energyrange 12-17 eV [91B, 92B].

IIn

tens

ity

Energy [eV]E0 = EF

Y(0001) h [eV]ν = 23

2 4 6 8 10

22

21

20

19

18

Fig. 73. Y(0001). Normal-incidence isochromat inversephotoemission spectra taken over the photon energyrange 18-23 eV. Tick marks indicate the onset offluorescence due to the decay of a 4p core hole [91B].





2.11 Nonmagnetic transition metals (Zr) [Ref. p. 337


190

2.11.6 Zr (Zirconium) (Z = 40)

Lattice hcp, a = 3.232 Å, c = 5.148 Å, c/a = 1.593 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d2 5s2


Table 7. Zr. Core-level binding energies in eVrelative to EF [95H]. Typical scatter between varioussources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 430.3 50.6np1/2 343.4 28.5np3/2 329.7 27.7nd3/2 181.2 –nd5/2 178.8 –


Figures for 2.11.6

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ


102

10–2

10–1

1

10–3

10

Zr

3d

3d

4d

3p

3p

3s

4p4s

5s

Fig. 74. Zr. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].







Ref. p. 337] 2.11 Nonmagnetic transition metals (Zr)


191Cr

oss s

ectio

n

[Mb]

σ


10–2

10–1

1

10Zr

0 50 100 150 200 250 300 350

Fig. 75. Zr. Atomic 4d-subshell crosssection near the Cooper minimum[85Y].


Zr

50 100 150 200

IIn

tens

ity

Fig. 76. Zr. Partially angle-integrated photoionizationcross section for the 4d subshell taken frompolycrystalline sample: experimental data (open circles)and result of calculation taking solid-state effects intoaccount [83A].


Eb [eV]

IIn

tens

ity

= 020040060080010001200

MNN

MNN

Ar

3s

4p

4s

3p1/2

3p3/2

3d3/2

3d5/2

I

1120 1105 1090

Zr

Fig. 77. Zr. Overview XPS spectrum.The insert shows the Zr (MNN)Auger-electron spectrum [95M]. Datataken with unmonochromatized MgKαradiation. Spectra with mono-chromatized AlKα are shown in

[95M].







192


IIn

tens

ity

3d3/2

3d5/2Zr178.7

2.4

193 183 173

Fig. 78. Zr. XPS spectrum showing the region of thespin-orbit-split 3d core levels taken withunmonochromatized MgKα radiation [79W]. See also

[95M].


0 = EF−1−3 −2

IIn

tens

ity

Zr

1

Fig. 80. Zr. Photoemission at hν = 21.2 eV frompolycrystalline sample [87N]. For data taken at hν = 80eV see [83A].


0 = EF 0 = EF

EF

−4 −4−8 −8−10 −10−6 −6−2 −2

IIn

tens

ity

1.5

1.0

0.5

0

DOS

[sta

tes/

eVat

om]

⋅

2 2

spd

Zr

BG

Fig. 79. Zr. Right (data): XPS spectrum of the valenceband obtained with monochromatized (0.6 eV)AlKα radiation [81H2]. Left: Partial densities of s,p,d-like valence states used to calculate (including several

broadening mechanisms) the XPS spectrum shown as asolid line through the data points. BG = estimatedsecondary electron background [81H2]. See also[79V1].










193

Energy [eV]E E− F

IIn

tens

ity

Zr

DOS

0 2 4 6 8 10

0

0

Fig. 81. Zr. Top: Experimental bremsstrahlungisochromat spectrum (photon energy 1486.7 eV, totalresolution 0.7 eV). Bottom: Calculated DOS withoutbroadening (dashed) and (solid line) broadened tosimulate instrumental and lifetime widths [84S].

Zr

IIn

tens

ity

Energy [eV]E0 = EF

h [eV]ν

2 4 6 8 10

= 22.5

20.4

18.7

15.7

14.5

12.7

11.1

Fig. 82. Zr. Bremsstrahlung isochromat spectra taken atdifferent photon energies hν from polycrystallinesample [92P].


Zr1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Refle

ctiv

ityR

Fig. 83. Zr. Experimental normal-incidence reflectivitydata obtained from different experiments [81W1]. Fordetails and tables of "most recommended" data see[81W1].

Zr

Photon energy [eV]hν0

Diel

ectri

c con

stan

t2ε 2

ε

2ε

20

15

10

5

10

5 10 15 20 25 30

Fig. 84. Zr. Experimental ε2 spectrum [81W1]. See also

legend to Fig. 83.








194

64

56

48

40

32

24

16

8

0

11.2

9.8

8.4

7.0

5.6

4.2

2.8

1.4

00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48

Energy [Ry]E

α − Zr (hcp)

DOS

[ ele

ctro

n st

ates

/ato

m/R

y]

NOS

[ele

ctro

ns/a

tom

]

EF

64

56

48

40

32

24

16

8

0

11.2

9.8

8.4

7.0

5.6

4.2

2.8

1.4

00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48

Energy [Ry]E

− Zr (hex)

DOS

[ ele

ctro

n st

ates

/ato

m/R

y]

NOS

[ele

ctro

ns/a

tom

]

EF

ω

Fig. 85. Zr. Electronic densities of states (left scale) and integrated number of electrons (right scale) calculated for theα-phase (hcp, left panel) and the ω-phase (simple hexagonal, right) using the nonrelativistic APW method [79V2].For experimental data see [79V2].

Wavevector k

Ener

gy[R

y]E

Zr

Γ Γ L

EF

A H HK KM L A M

0.7

0.9

0.5

0.3

3 1.5 0 1.5 0 15 0 35 0DOS

s p d total

0.1

Fig. 86. Zr. Electronic band structure (right panel) calculated self-consistently by means of the full potentiallinearized APW method and (left panel) partial s,p,d-like densities of states (in states/Ry/atom) and total DOS(states/Ry/unit cell), respectively [88B]. See also [75J1, 84C2, 87L].









195

Energy [eV]E E− F

0−4−6 −2

DOS

[sta

tes e

V]

−1

2

Zrtotal d

d − eg

d − t2g

3

2

1

02

1

03

2

1

04 6

Fig. 87. Zr(bcc). Calculated total and d-like partialdensities of states [00G].


2.11 Nonmagnetic transition metals (Nb) [Ref. p. 337


196

2.11.7 Nb (Niobium) (Z = 41)

Lattice bcc, a = 3.299 Å [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d4 5s1

Work-function [95H]:φ (poly) = 4.3 eVφ (001) = 4.02 eVφ (110) = 4.87 eVφ (111) = 4.36 eV


Table 8. Nb. Core-level binding energies in eVrelative to EF [95H]. Typical scatter betweendifferent sources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 466.6 56.4np1/2 376.1 32.6np3/2 360.6 30.8nd3/2 205.0 –nd5/2 202.3 –


Table 9. Nb(110). Energy of critical points above EF determined in different calculations andexperimentally using inverse photoemission. Energies in eV with respect to EF [88J2].

Point Level Experiment Theory[88J2] [77E] [83S] [87S]

Γ Γ25' 1.6 0.52 0.19 0.43Γ12 3.5 3.45 3.18 2.72

For theoretical studies of electron and hole quasiparticle lifetimes see [02Z].












Ref. p. 337] 2.11 Nonmagnetic transition metals (Nb)


197

Figures for 2.11.7

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ


102

10–2

10–1

1

10–3

10

Nb

3d

3d

4d

4d

3p

3p

3s

4p4s

5s

Fig. 88. Nb. Atomic subshell photoionization cross sections forphoton energies from 0 to 1500 eV [85Y].

Cros

s sec

tion

[M

b]σ


10–2

10–1

1

10

Nb

0 50 100 150 200 250 300 350

Fig. 89. Nb. Atomic 4d-subshell cross section near the Cooperminimum [85Y].





198


Eb [eV]

IIn

tens

ity

= 020040060080010001200

MNV

MNV

3s

4p4s

3p1/2

3p3/2

3d3/2

3d5/2

I

1100 1085 1070

Nb

Fig. 90. Nb. Overview XPS spectrumtaken with unmonochromatized MgKαradiation. The insert shows a blow-upof the MNV Auger electron spectrum[95M]. For data with mono-chromatized AlKα see [95M].


IIn

tens

ity

Nb

210 208 206 204 202 200

Fig. 91. Nb. XPS spectrum of the 3d core level doublettaken with monochromatized (0.6 eV) AlKα radiation

from a polycrystalline sample [81H2]. See also [95M].


IIn

tens

ity

EF = 0

Nb

×5

VB

40 30 20 10

4p

Fig. 92. Nb. XPS spectra of valence band (VB) and 4pcore levels [81H2] taken with monochromatized (0.6eV) AlKα radiation.








199


IIn

tens

ity

Nb (001)

h = 240 eV

h = 250 eV

ν

ν

BS1

S2

204.0 203.5 203.0 202.5 202.0 201.5 201.0

Fig. 93. Nb(001). High-resolution 3d5/2 core level

photoemission spectra taken at two different photonenergies hν. Solids circles: experimental data. Solidlines: fit with three identical Doniach-Sunjic line shapesconvoluted with a Gaussian function and backgroundcurve, where S1, S2 and B denote surface, subsurface

and bulk components [95L].

IIn

tens

ity


0 = EF−5.0 −2.5

Nb

h [eV]ν =120

100

80

60

Fig. 95. Nb. Photoelectron spectra from apolycrystalline sample taken at different photonenergies hν [82M].

IIn

tens

ity


EF

0−2−4−8 −6−10−12

Nb

2 4

Fig. 94. Nb. XPS valence band spectrum frompolycrystalline sample taken with monochromatized(0.5 eV) AlKα -radiation [76H1].

Energy [eV]E E− F

IIn

tens

ity

Nb

DOS

0 2 4 6 8 10

0

0

Fig. 96. Nb. Top: Experimental bremsstrahlungisochromat spectrum (photon energy 1486.7 eV, totalresolution 0.7 eV). Bottom: Calculated DOS withoutbroadening (dashed) and (solid line) broadened tosimulate instrumental and lifetime widths [84S].







200I

Inte

nsity

Energy [eV]E0 = EF

Nbh [eV]ν= 22.5

2 4 6 8

20.4

18.7

15.7

14.5

12.7

11.1

10

Fig. 97. Nb. Bremsstrahlung isochromat spectra takenat different photon energies hν from polycrystallinesample [92P].

Nb

Photon energy [eV]hνRe

flect

ivity

R

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 98. Nb. Experimental normal-incidence reflectivitydata obtained from different experiments [81W1]. Fordetails and tables of the "most recommended" data see[81W1].

Nb


Diel

ectri

c con

stan

t2ε

ε

ε20

15

10

5

10

2

2

5 10 15 20 25 30

Fig. 99. Nb. Experimental ε2 spectra [81W1] from

different experiments. See also legend to Fig. 98.


EF

Energy [Ry]E

DOS

[sta

tes/

(Ry

atom

spin

)]⋅

⋅

Nb20

16

12

8

4

012

8

4

012

8

4

02

2

0.4 0.6 0.8 1.0 1.2 1.4

10

8

6

4

2

0

total

d − Γ12

d − Γ25’

s

NOS

[ele

ctro

ns /

ato

m]

p

Fig. 102. Nb. Total and partial densities of states fromself-consistent energy bands using the α = 2/3 exchangeapproximation [77B].








201

Wavevector k

Ener

gy[R

y]E

Σ

Nb

Γ Γ∆

1’

1’

111

1

1

1

2

2

2

3

3

3

3

3

1

1

2

2

1

2

2’

3

3

14

4

4

1

4 4

4 44

3

3

3

3

3

3

3

31

1

1

1

11

1

1

1

1

15

5

EF

H HG

0.1

0

− 0.1

−0.2

−0.3

−0.4

−0.5

−0.6

−0.7N ND P PΛ F

1212

12 12

25’25’

25’25’

1515

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 100. Nb. Energy bands from a self-consistent all-electroncalculation, employing density-functional theory and the linearcombination of Gaussian orbitals method [88J1]. See also [77E, 78M,79L]. Symmetry labels in single group notation.

Energy [Ry]E

Nb

DOS

[ sta

tes R

yat

om]

−−

11

EF

72

60

48

36

24

12

0− 0.5 − 0.3 − 0.1 0.1 0.3 0.5 0.7 0.9

Fig. 101. Nb. Density of states calculated from the band structure shownin Fig. 100. [88J1]. See also [77E].









202

Energy [eV]E E− F

0−4−6 −2

DOS

[sta

tes e

V]

−1

2

Nb

total d

d − eg

d − t2g

3

2

1

0

2

1

03

2

1

04 6

Fig. 103. Nb. Partial d-like densities of states calculatedfor the bcc phase [00G].

Wavevector k

Ener

gy[e

V]E

Nb

Γ ∆

1

2

1

2’

1

1

1

5

EF

H

−4

−8

12

12

25’

25’

15

24

20

16

12

8

4

0

Fig. 105. Nb. Solid lines: bulk band structure calculatedin [79L]. Filled circles represent experimental dataderived from spectra shown in Fig. 104 [98F2].

→Fig. 106. Nb(001). Angle-resolved photoelectronspectra taken at various relative k|| values between Γand X of the surface Brillouin zone showing dispersionof several surface states (resonances). Photon energy21.2 eV [94F]. See also [93F].


0 = EF−2−10−12 −8 −6 −

IIn

tens

ity

Nb (100)∆1 s1

s ’1

h = 26 eVν

25

2321

191817

15

13

4

Fig. 104. Nb(100). Normal-emission photoelectronspectra taken at different photon energies hν. Peakslabeled s1 and s′1 originate from surface resonances atk|| = 0, solid line labeled ∆1 shows the dispersion of the

lower ∆1 bulk band [98F2].

X


−2 −1−6 − −

IIn

tens

ity

Nb (001)

4 3

Γ

− 5 0 = EF 1 2 3

0.00

0.10

0.17

0.26

0.39

0.51

0.58

0.64

0.68

0.81

0.91

1.00









203

M


−2 −1−6 − −

IIn

tens

ity

Nb (001)

4 3

Γ

− 5 1 2 3

0.00

0.11

0.160.220.270.32

0.37

0.520.56

0.660.71

0.80

0.92

1.00

0.42

0.47

0.61

0.76

0.84

0.88

0 = EF

Fig. 107. Nb(001). Angle-resolved photoelectronspectra taken at various relative k|| values between Γand M of the surface Brillouin zone showing dispersionof several surface states (resonances). Photon energy21.2 eV [94F]. See also [94F] for data taken along theM-X direction.

IIn

tens

ity

Nb (100)

Energy [eV]E0 = EF 10 20

E i [eV]32.2

31.230.229.2

28.227.2

26.225.2

24.223.2

22.621.6

20.619.6

16.615.5

14.3


−2− −4−6−16 −14 −12 −10

IIn

tens

ity

Nb (110)

8 0 = EF

Fig. 108. Nb(110). Normal-emission photoelectronspectrum taken with photons of 21.2 eV [81S2].

IIn

tens

ity

Nb (110)

Energy [eV]E0 = EF 10

E i [eV]

5 15

= 33

31

29

27

25

23

2119

1715

Fig. 110. Nb(110). Normal-incidence inversephotoemission spectra as a function of the incidentelectron energy Ei. The dashed line indicates the positionof a plasmon peak at fixed photon energy [89P1].

←Fig. 109. Nb(100). Normal-incidence inversephotoemission spectra as a function of the incidentelectron energy Ei. The dashed line indicates theposition of a plasmon peak at fixed photon energy[89P1].








204I

Inte

nsity

Nb (110)

Energy [eV]Ei

14 18 22 26 30 34

Fig. 111. Nb(110). Intensity of the direct transition 3.5eV above EF in Fig. 110 as a function of incident

electron energy [89P1].

IIn

tens

ity

Nb (110)

E i [eV]38

28

36.534.532.530.528.526.524.522.5

Photon energy [eV]hνFig. 112. Nb(110). Normal-incidence inversephotoemission spectra showing photon intensity fordifferent incident electron energies Ei (given in 0.5 eV

steps from 28 to 38 eV) vs. energy of the emittedphotons [88J2].

Wavevector k

Ener

gy[e

V]E

Nb (110)

ΓΣ

1

2

3

3

44

1

1

1

1

EF

N

12

25’

25

25

20

15

10

5

0

Fig. 113. Nb(110). Dispersion of the unoccupied bandsabove EF as determined (vertical dashes) from the data

shown in Fig. 112 [88J2]. Solid lines show calculatedbands from [77E]. The calculated Σ1 band between 12

and 20 eV above EF was used to determine k⊥ [88J2].






Ref. p. 337] 2.11 Nonmagnetic transition metals (Mo)


205

2.11.8 Mo (Molybdenum) (Z = 42)

Lattice: bcc. a = 3.147 Å [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d5 5s1

Work function [95H]:φ (poly) = 4.6 eVφ (100) = 4.53 eVφ (110) = 4.95 eVφ (111) = 4.55 eV

Typical errors are ± 0.2 eV.

Table 10. Mo. Core-level binding energies in eVrelative to EF [95H]. Typical scatter betweendifferent sources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 506.3 63.2np1/2 410.6 37.6np3/2 394.0 35.3nd3/2 231.1 –nd5/2 227.9 –


Table 11. Mo. Energies (in eV w.r. to EF) of band structure criticalpoints determined experimentally and from different calculations[79Z].

Level Experiment Theory[76C2] [73I] [79Z]

Γ1 – –5.92 –5.67Γ25' –1.5 –1.49 –1.52Γ12 – 1.37 1.51H12 –5.0 –6.24 –5.21H25' – 4.16 3.21












2.11 Nonmagnetic transition metals (Mo) [Ref. p. 337


206

Figures for 2.11.8

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s

4s

3d


102

10–2

10–1

1

10–3

10

Mo

3p

4p

4d

4d

3d

5s

3p

3s

Fig. 114. Mo. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].

Cros

s sec

tion

[M

b]σ


102

10–2

10–1

1

10

Mo

0 50 100 150 200 250 300 350

Fig. 115. Mo. Atomic 4d-subshell cross section near the Cooperminimum [85Y].





207


Eb [eV]

IIn

tens

ity

= 020040060080010001200

MNV

4s4p

3s

3p1/2

3p3/2

3d3/2

3d5/2MNV

I

1080 10501065

Mo

Fig. 116. Mo. Overview XPSspectrum taken with unmono-chromatized MgKα radiation. The

insert shows a blow-up of theMNV Auger electron spectrum[95M]. For results obtained withmonochromatized AlKα radiation

see [95M].


IIn

tens

ity

3d3/2

3d5/2Mo

227.7

3.15

240 230 220

Fig. 117. Mo. XPS spectrum showing the region of thespin-orbit-split 3d core levels taken with unmono-chromatized MgKα radiation [79W]. See [83W] and

[95M] for similar results. Binding energy [eV]Eb

IIn

tens

ity

Mo (110)

229 228 227 226

hν [eV] = 340

320

300

290

280

270

265

260

Fig. 118. Mo(110). Photoemission from the 3d5/2 core

levels, taken at different photon energies hν in normalemission with the sample at 100 K [93L]. For ab initiocalculation of the surface-core level shift see [94A].










208

IIn

tens

ityInitial state energy [eV]E i

0 = EF−4−8−10 −6 −2 2

BG


0 = EF

EF

−4−8−10 −6 −2

1.5

1.0

0.5

0

DOS

[sta

tes/

eVat

om]

⋅

2

spd

Mo8

6

4

2

0

Fig. 119. Mo. Right panel: XPS valence band spectrumtaken with monochromatized (0.5 eV) AlKα radiationfrom a polycrystalline sample (data points) compared toa simulated one (solid line and assumed background,BG) employing partial DOS calculations shown in the

left panel [81H2]. See also [80A2] and [83W]. Forspectra taken at hν = 84…120 eV, including effect ofargon-ion bombardment, see [91K1]. For angle-integrated data from Mo(100) at 21.2 and 16.8 eV see[77W1].

Energy [eV]E E− F

IIn

tens

ity

Mo

DOS

0 2 4 6 8 10

0

0

Fig. 120. Mo. Top: Experimental bremsstrahlungisochromat spectrum (photon energy 1486.7 eV, totalresolution 0.7 eV). Bottom: calculated DOS withoutbroadening (dashed) and (solid line) broadened tosimulate experimental and lifetime widths [84S].









209


Refle

ctiv

ityR

Mo1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30


Mo

0 5 10 15 20 25 30

Diel

ectri

c con

stan

tε2

ε 2

ε 2

ε 2

20

15

10

5

/10

10

Fig. 121. Mo. Experimental normal-incidence reflectivity data obtainedfrom different experiments [81W1].For details and tables of "mostrecommended" data see [81W1].

Fig. 122. Mo. Experimental ε2 spectra

[81W1]. See also caption to Fig. 121.

Energy [eV]E E− F

E F

0− 4−6 −2 2

Mo

DOS

4 6


Fig. 124. Mo. Calculated DOS based on a bandstructure using the KKR method and first-principlesself-consistent potentials [84S]. See also [79Z].








210

Wavevector k

Energy

[Ry]

E

Energy

[eV]

EΣ

Mo

Γ Γ∆

0

0.2

0.4

0.6

EF

H P P

0.8

−0.2−2

−0.4

−4

−0.6

−6

−0.8

−8

−10

G N NΛ D D F H

12

10

8

6

4

2

0

1’

1

1

1

1

2

2

23

3

3

1

1

2

2

2

1

2’

3

3 1

4

1

4

4

44

44

4 33

3

3

33

3

3

1

1

1

1

1

1

1

1

1

1

1

1

5

5

1212

12

12

1515

25’ 25’

25’25’

Fig. 123. Mo. Band structure calculated using the RS-LMTO-ASAmethod in a non-relativistic treatment. Energy scale relative to EF [00L].

For bands at higher energies above EF see [79Z]. See also [73I].

Wavevector k

Energy

[eV]

E

Mo

ΓΓ

4+5

4+5

4+5

8

6+

7+

8+

8+

66

6

6

7

7

7

6

6

6

65 5

5

5

5

5

5

5

5

5

5

5

5

EF

H P P

2

−2

− 4

− 6

− 8N N H

Fig. 125. Mo. Energy bands calculated using a nonorthogonal tight-binding interpolation scheme including the spin-orbit-interaction [88J3].Symmetry labels in double group notation.







211

Wavevector k

Ener

gy[R

y]E

Mo

Γ

EF

− 0.5

−1.0

0

0.5

∆ H G N Σ Γ Λ P F H

Fig. 126. Mo. Orthogonal tight-binding band structure (dots) incomparison with an ab initio LMTO-ASA band structure (solid lines)[98H].

Energy [eV]E E− F

0−4−6 −2

DOS

[sta

tes e

V]

−1

2

Mototal d

d − eg

d − t2g

3

2

1

02

1

03

2

1

04 6

Fig. 127. Mo. Partial d-like densities of states calculatedfor the bcc phase [00G].


0 = EF−2−3 −1

IIn

tens

ity

Mo (100)

hν [eV]

40

25

20

17

15

Fig. 128. Mo(100). Normal-emission photoelectronspectra taken at different photon energies hν [91S1]. Forphoton energies up to 48 eV see [93S]. See also [77N] forearlier work. For spectra taken at hν = 10.2…21.2 eVwithin a 10°-cone around normal emission see [76C2].For influence of hydrogen-adsorption see [91S2].










212I

Inte

nsity

Mo (001)hν


0 = EF−2−4−5 −3 −1

= 21.22 eV

SB

SRSRB

( )A

( )B

Fig. 129. Mo(001). High-resolution normal-emissionphotoelectron spectra for a clean (A) and a hydrogencovered (B) surface, demonstrating sensitivity ofsurface state S at Ei = –0.3 eV. B and SR denote bulk

emission and surface resonance emission, respectively[93S].

IIn

tens

ity

Mo (001)


0 = EF−2−4 −3−5 −1

B SR

SR

SRB S

θ

25°

20°

15°

10°

5°

0°

=

Fig. 131. Mo(001). Angle-resolved photoelectronspectra taken with hν = 21.2 eV at different angles θalong the ∆-direction of the surface Brillouin zone[93S]. Sample at 52 K. For the meaning of S, SR, B seeFig. 129.

IIn

tens

ity

Mo (001)


0 = EF

EF

−2−3 −1

k II1[Å ]−

0.99

0.93

0.860.800.740.67

0.610.54

0.41

0.340.270.21

0.14

0

Fig. 130. Mo(001). Angle-resolved photoemissionspectra taken with ω = 20 eV at different k|| along theΣ direction of the surface Brillouin zone [91S1]. Seealso [79I] for earlier work.

IIn

tens

ity

Mo (001)

Energy [eV]E0 = EF−2 2 4 6

kII / MΓ0.46

0.41

0.33

0.24

0.14

0.06

0

Fig. 132. Mo(001). Inverse photoemission spectra takenat different k|| of the incident electrons along ΓM of the

surface Brillouin zone at fixed electron energy Ei = 14.3

eV [86D1].








213I

Inte

nsity

Mo (110)


0 = EF−2−4 −3−5 −1

Fig. 133. Mo(110). Normal-emission photoelectronspectrum using monochromatized HeI (21.2 eV)radiation [00K2]. For effects of residual gas exposureeven in UHV see [00K1]. See also this source forsurface Fermi contours.

IIn

tens

ity

Mo (011)


0 = EF−2−3 −1

k II1[Å ]−

0.67

0.640.60

0.540.490.460.440.430.42

0.410.400.390.380.350.310.27

Fig. 134. Mo(011). Angle-resolved photoelectronspectra taken with hν = 24 eV at different k|| along the ∆direction of the surface Brillouin zone [88J3]. For anexperimental surface Fermi contour see [89J].

IIn

tens

ity

Mo (112)


0 = EF−2−3−4 −1

hν [eV]

28

26

24

22

20

18

16

Fig. 135. Mo(112). Normal-emission photoelectronspectra taken for photon energies 16…28 eV [01Y].

IIn

tens

ity

Mo (112)


0 = EF−2−3−4−5−6−7−8 −1

hν [eV]

83

80

77

74

71

68

65

62

59

56

53

50

47

44

4135

32

Fig. 136. Mo(112). Normal-emission photoelectronspectra taken for photon energies 32…83 eV [00Y].








214In

itial

stat

e en

ergy

[eV]

E i

−2.0

−3.0

−4.0

−5.0

−0.5

0


Mo (112)

−1.0

−1.5

−2.5

−3.5

−4.5

2515 35 45 55 65 75 85 95

Fig. 137. Mo(112). Experimental band dispersionobserved in normal-emission as a function of photonenergy [01Y], see also Figs. 135 and 136. See [01Y] fora detailed analysis separating bulk and surface sensitivefeatures.

IIn

tens

ity

Mo (112)

Energy [eV]E0 = EF 1 2 3

30°

25°

20°

15°

10°

5°

0°

= 35°θ

−1_2

Mo (112)

IIn

tens

ity


0 = EF−2−3−4−5−6 −1

T [ ]K

320

350

378

405

430

454

476

Fig. 138. Mo(112). Normal-emission valence bandspectra for various temperatures. Photon energy 55 eV[96W].

Fig. 139. Mo(112). Angle-resolved inversephotoemission spectra taken in the isochromat mode(hν = 9.5 eV) at different electron incidence anglesθ along the Γ-Y surface Brillouin zone direction [01J].





Ref. p. 337] 2.11 Nonmagnetic transition metals (Tc)


215

2.11.9 Tc (Technetium) (Z = 43)

Lattice: hcp. a = 2.743 Å, c = 4.400 Å, c/a 1.604 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d5 5s2

Work-function:φ (poly) = (4.88 ± 0.3) eV [95H]φ (poly) = (5.0 ± 0.3) eV [84C1]

Table 12. Tc. Core-level binding energies in eVrelative to EF [90K1, 95H]. Estimated accuracy is ±0.2 eV [90K1].

n = 3 n = 4

ns1/2 544.0 69.9np1/2 447.6 42.3np3/2 427.6 39.9nd3/2 257.5 –nd5/2 253.9 –

For core-level widths see [90K1] and [92F].

Figures for 2.11.9

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s

4s

3d

νPhoton energy [eV]h

102

10–2

10–1

1

10–3

10

Tc

3p

4d

4d

3d

5s

4p

3s

Fig. 140. Tc. Atomic subshellphotoionization cross sections forphoton energies between 0 and 1500eV [85Y].










2.11 Nonmagnetic transition metals (Tc) [Ref. p.337


216Cr

oss s

ectio

n

[Mb]

σ


10–2

10–1

1

10

0 50 100 150 200 250 300 350

Tc

Fig. 141. Tc. Atomic 4d-subshell cross section near the Cooperminimum [85Y].

Kinetic energy [eV]Ek

IIn

tens

ity

Tc

M4

M5

1904 1908 1912 1916 1920 1924

Fig. 142. Tc. The M4,5 internal-conversion electron spectrum from

polycrystalline metallic 99mTc (dotted). The result of theseparation of the M5 line is shown by a continuous line [90K1].



Ref. p. 337] 2.11 Nonmagnetic transition metals (Tc)


217

Wavevector k

Ener

gy[R

y]E

Tc

Γ Γ L

EF

A H HK KM L A M

0.9

1.1

0.7

0.5

3 1.5 0 1 0 15 0 30 0DOS

s p d total

0.3

Fig. 143. Tc. Right panel: Band structure calculated self-consistently by means of the full potential linearized APW-method [88B] and (left panel) resulting s,p,d-like partial densities of states (in states/Ry/atom) as well as total DOS(states/Ry/unit cell) [88B]. For earlier work see also [77F, 79A, 83C].

Tc

IIn

tens

ity


0 = EF−2−4−6−8

He

I

I

Ne

Fig. 144. Tc. Angle-integrated photoemission spectrataken at hν = 21.2 eV (HeI) and hν = 16.8 eV (NeI),respectively [84C1]. The dashed curve reproduces theDOS calculated in [79A].








2.11 Nonmagnetic transition metals (Ru) [Ref. p. 337


218

2.11.10 Ru (Ruthenium) (Z = 44)

Lattice: hcp. a = 2.706 Å, c = 4.281 Å, c/a = 1.582 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d7 5s1

Work-function:φ (poly) = (4.7 ± 0.3) eV [95H]φ (0001) = (5.4 ± 0.1) eV [81H1]

Table 13. Ru. Core-level binding energies in eV w.r.to EF [95H]. Typical scatter between differentsources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 586.1 75.0

np1/2 483.5 46.5

np3/2 461.3 43.2

nd3/2 284.1 –

nd5/2 280.0 –


Table 14. Ru. Energies of band structure critical points determined experimentally and theoretically,given in eV w.r. to EF. Error bars estimated from the experimental data to be about ± 0.2 eV.

Critical Point Experiment Theoryenergy level [81H1] [86L2] [75J1] [81H1]

Γ1+ –7.5 –7.3 –8.2 –7.0Γ4– –5.6 – –6.0 –5.8Γ6–,1+ –2.4 –2.45 –2.75 –2.6

–2.5 –2.3–2.3

Γ5+ –1.7 – –2.05 –1.8–1.75

Γ6+ – –1.2 –1.45 –1.2–1.3

Γ2+ +16.4 +16.5 – +15.0











Ref. p. 337] 2.11 Nonmagnetic transition metals (Ru)


219

Figures for 2.11.10

0 200 400 600 800 1000 1200 140010−4

Cros

s sec

tion

[M

b]σ

4s

3d


102

10–2

10–1

1

10–3

10

Ru

3p

4d

4d

3d

5s

4p

3s

Fig. 145. Ru. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].

νPhoton energy [eV]h0 50 100 150 200 250 300 350

Ru

Cros

s sec

tion

[M

b]σ

102

10–2

10–1

1

10

Fig. 146. Ru. Atomic 4d-subshell cross section near the Cooperminimum [85Y].





220


Eb [eV]

IIn

tens

ity

= 020040060080010001200

MNV

3s

4p4s

3p1/23p3/2

3d3/2

3d5/2

I

Ru 1102

10521023

979.2

M N N45 1 23

M N V45 1M N V45 23 M VV45

1115 1065 1015 965

MNN

Fig. 147. Ru. Overview XPS spectrumtaken with unmonochromatized MgKαradiation [95M]. The insert shows a blow-up of the MNN Auger electron spectrum[79W]. For data with monochromatizedAlKα radiation see [95M].


IIn

tens

ity

3d3/2

3d5/2

Ru

292 282 272

280

4.1

Fig. 148. Ru. XPS spectrum showing the region of thespin-orbit-split 3d core levels taken with unmono-chromatized MgKα radiation [79W]. See also [95M].


IIn

tens

ity

Ru (0001) S2 b S1

h [eV]ν400

370

352

280.8 280.4 280.0 279.6 279.2

Fig. 149. Ru(0001). High-resolution study of surfacecore level shifts at the 3d5/2 peak performed at three

different photon energies. Energy resolution better than80 meV. Solid lines indicate decomposition into threecomponents, related to emission from bulk (b), firstlayer atoms (S1) and second layer atoms (S2) [00L].









221


IIn

tens

ity

Ru (1010)

S2

bS1

281.5 281.0 280.5 280.0 279.5

clean (1 1)×

279.0 278.5

Fig. 150. Ru(10 1 0). High-resolution study of the 3d5/2

core levels. Photon energy 400 eV, resolution 65 meV.Solid line indicates emission from bulk atoms, S2 and

S1 result from second and first layer atoms [01B]. For

more details and spectra recorded at different photonenergies see [00B1].

Energy [eV]E E− F

IIn

tens

ity

Ru

DOS

0 2 4 6 8 10

0

0

Fig. 151. Ru. Top: Experimental bremsstrahlungisochromat spectrum (photon energy 1486.7 eV, totalresolution 0.7 eV). Bottom: calculated DOS withoutbroadening (dashed) and (solid line) broadened tosimulate experimental and lifetime widths [84S].

Ru


Refle

ctiv

ityR

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25 30

Fig. 152. Ru. Experimental normal-incidence reflectivity dataobtained from different experiments [81W1]. For details and tables of"most recommended" data see [81W1].








222

Ru


Diel

ectri

c con

stan

t2ε ε10 2

5 10 15 20 25 30

40

30

20

10

Fig. 153. Ru. Experimental ε2 spectra [81W1]. See also caption to Fig.

152.

Wavevector k

Ener

gy[R

y]E

Ru

Γ Γ L

EF

A H HK KM L AM

EF

1.0

0.8

0.6

0.4

0.2

0∆ΣT T’ U P S’ R S

Fig. 154. Ru. Relativistic energy band structure calculated by means of the linear muffin-tin-orbital method [75J1].See also [78M, 86C].







223

EF

Energy [Ry]E

DOS

[sta

tes/

( ato

mRy

)]⋅

Ru

0.4 0.5 0.6 0.7 0.8 0.9

10

8

6

4

2

0

NOS

[ele

ctro

ns /

atom

]

35

30

25

20

15

10

5

00.2 0.3

12

14

Fig. 155. Ru. Density of states calculated from the bandstructure shown in Fig. 154 [75J1].

EF

Energy [eV]E - EF

DOS

Ru

0

− 6 −4 −2 0 2 4 6

Fig. 156. Ru. Calculated DOS based on a band structureusing the KKR method and first-principles self-consistent potentials [84S].

Wavevector k

Ener

gy[R

y]E

Ru

Γ Γ L

EF

A H HK KM L A M

0.9

1.1

0.7

0.5

3 1.5 0 1 0 15 0 30 0DOS

s p d total

0.3

Fig. 157. Ru. Right panel: Band structure calculated self-consistently by means of the full potential linearized APW-method [88B]. Left panel shows corresponding s,p,d-like partial densities of states (in states/Ry/atom) and the totalDOS (states/Ry/unit cell) [88B]. See also [78M, 86C].









224

Wavevector k

Ener

gy[e

V]E

Ru (001)

Γ Γ∆ ∆∆

EF

A A Γ ∆∆ A

15

10

5

−5

0 =

40

35

30

25

20

65

60

55

50

45

ss1

ss2

2

1

2

5

2

65

6

21

1

5

1

26

5

6

1

2

Fig. 158. Ru(001). Calculated occupied and empty energy bands along ΓΑ [86L2]. Dots correspond to free-electron-like bands fitted to experimental critical points marked with squares, dashed lines present photoemission final-statebands. SS1 and SS2 refer to surface states [86L2].


0 = EF 0 = EF−2 −2−4 −4−8 −6 −6−10

IIn

tens

ity

IIn

tens

ity

Ru (001)hν [eV]

hν [eV]

24

24

22

22

20

21

19

19

18

18

17

17

16

16

14

14

12

122

Fig. 159. Ru(001). Left panel: experimentalphotoelectron spectra excited by p-polarized light innormal emission at different photon energies between12 and 24 eV. Arrows indicate structure due to finalstates [86L2]. For results obtained with mixed

polarization see [81H1]. Right panel: Theoreticalphotoemission spectra corresponding to the parametersof the left panel. Dashed line displays background forhν = 12 eV [86L2]. For a spectrum taken at hν = 21.2eV see also [99B].









225


0 = EF 0 = EF−2 −2−4 −4−8 −6 −6−10

IIn

tens

ity

IIn

tens

ity

Ru (001)hν [eV]

hν [eV]50

50

48

48

46

4644

444242

383836

3634

3432

3230

3028

2826

26

2

Fig. 160. Ru(001). As figure 159 but for higher photon energies between 26 and 50 eV [86L2].

Initi

al st

ate

ener

gy[e

V]E i

Ru (001)

Wavevector kΓA

−2

−4

−6

−8

EF0 =

Γ ‘

Fig. 161. Ru(001). Experimental occupied bandsderived from normal-emission spectra (squares: lightincidence angle α = 20°, circles: α = 75°) compared tocalculated bands (solid lines) [86L2].

IIn

tens

ity

Ru (001)


0 = EF

−5°−10°−15°−20°−30°

−40°−50°

−55°

−10 −5

θ

20°15°

10°

5°

0°

=

30°

40°

50°

Fig. 162. Ru(001). Experimental off-normalphotoemission spectra taken at different polar angles θalong ΓK of the surface Brillouin zone. Photon energy38 eV [86L2].






226I

Inte

nsity

Ru (001)


B1

B2

S1

S2

Fig. 163. Ru(001). Inverse photoemission spectrumtaken in the isochromate mode at hν = 9.7 eV [87B2].Labels B and S denote emission of bulk and surfaceorigin, respectively.

IIn

tens

ity

Ru (001)

Energy [eV]E10 15 20 25 30

Fig. 164. Ru(001). Unoccupied electronic statesreflected in different electron spectroscopies. Top:Very-low-energy electron diffraction (VLEED)intensity versus energy curve taken near (3° off) normalincidence. Bottom: Normal-emission photoelectronspectrum excited by photons of 38 eV, showing intensesecondary-electron emission structure at electronenergies below 20 eV [86L1]. From the originalphotoemission spectrum (dashed line) a smoothbackground was subtracted.



Ref. p. 337] 2.11 Nonmagnetic transition metals (Rh)


227

2.11.11 Rh (Rhodium) (Z = 45)

Lattice: fcc. a = 3.804 Å [71L].Brillouin zones: see section 1.3 of this volume.Electronic configuration: (Kr) 4d8 5s1

Work-function:φ (111) = (5.4 ± 0.1) eV [89G2].

Table 15. Rh. Core-level binding energies in eV w.r.to EF [95H ]. Typical scatter between differentsources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 628.1 81.4np1/2 521.3 50.5np3/2 496.5 47.3nd3/2 311.9 –nd5/2 307.2 –


Table 16. Rh. Experimental and theoretical critical point energies (in eV relative to EF) [89G2].Symmetries in double (single) group notation.

Energy Experiment Theorylevel [89G2] [73C] [74S1] [79B1] [81B]

L6+ (L1) –5.6(5) –5.54 –6.0 –5.8 –5.2

X7+ (X3) –5.0(1) –5.36 –5.5 –5.2 –5.0

Γ8+ (Γ25') –3.1 –3.00 –2.8 –2.9–2.75(10)

Γ7+ –2.8 –2.74 –2.5

L6+ (L3) –3.07 –3.3 –3.1 –3.0–2.65(10)

L4+, 5+ –2.78 –3.0 –2.7

Γ8+ (Γ12) –0.85(10) –1.09 –1.2 –1.0 –1.0

L6+(L1) 9.0(5) 8.17 8.7 8.7 8.7

Γ7− (Γ2') 16.1(5) 16.4 – 16.4 17.8

Γ6– (Γ15) 20.3 21.1 22.420.5(5) –

Γ8– 20.4 23.1














2.11 Nonmagnetic transition metals (Rh) [Ref. p. 337


228

Figures for 2.11.11

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


102

10–2

10–1

1

10–3

10

4d

4p

5s

4

2

68

4

2

68

4

2

68

4

2

68

4

2

68

10–4

4

2

68

Rh

3p3d

4d

4s

3s

Fig. 165. Rh. Atomic subshellphotoionization cross sections forphoton energies from 0 to 1500 eV[85Y].

2

4

6

89

7

5

3

2

4

6

89

7

5

3

2

4

3

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–1

1

50Rh

10

Fig. 166. Rh. Atomic 4d-subshellcross section near the Cooperminimum [85Y].





229In

tens

ityI


0900 800 700 600 500 400 300 200 100

1000Eb V[e ]

1050

I

M V103145 1N

M V100145 23N

M V952.1

45V

900950

MNN

Rh

3d5/2

3d3/2

3p3/2

3p1/2

3s

4s4p

(× 4)

MNN

EF

Fig. 167. Rh. Overview XPS spectrum taken with unmonochromatized MgKα radiation. The insert shows a blow-up

of the MNN Auger electron spectrum [79W]. For results with monochromated AlKα radiation see [95M].

320 318 316 314 310312 308 306 300304 302

3d5/2

3d3/2

307.0


Rh

Inte

nsity

I

4.75

Fig. 168. Rh. XPS spectrum showing the region of thespin-orbit-split 3d core levels taken withunmonochromatized MgKα radiation [79W]. For the

core line asymmetry of data taken with mono-chromatized AlKα radiation see [74H1]. See also

[95M].








230

309.0 308.5 308.0 307.5 307.0 306.5 306.0 305.5 305.0

Inte

nsity

I


Rh(100) hν = 370 eVb

s

Fig. 169. Rh(100). Photoemission spectrum of the 3d5/2

core level and (solid lines) its decomposition intoemission from bulk (b) and surface (s) atoms [00R]. Forresults obtained at different photon energies anddetailed discussions see also [94B, 96Z1, 96Z2, 01K2].


–10 – 8 – 6 – 4 – 2 0 2

Inte

nsity

I

Rh

DOS

EF

Fig. 171. Rh. XPS valence band spectrum (dotted)taken with monochromatized (0.5 eV) AlKα radiation.

The solid curve is the corresponding density-of-statescurve, calculated within the combined interpolationscheme [74S1] and smoothed with a Lorentzianbroadening to account for experimental resolution[74S2]. See also [74H2].

310 309 308 307 306 305 304

Inte

nsity

I


Rh b

s

(110)

(111)

Fig. 170. Rh. High-resolution spectra of the 3d5/2 level

for the (111) surface (bottom) and the (110) surface(top) taken at photon energies hν = 380 eV (bottom)and 370 eV (top). Dots are experimental data, solidlines show individual bulk (b) and surface (s)components [94A]. For Rh(110) spectra taken at hν =397 eV see [96Z2]. For Rh(111) see also [01G].














231

2.50Initial state energy [eV]Ei

Inte

nsity

I

Pd

–17.5 –15.0 –12.5 –10.0 –7.5 –5.0 –2.5

hν = 80 eV

70

60

55

50

48

46

44

42

40

30 eV

EF

Fig. 172. Rh(poly). Spectra of the valence band taken atvarious photon energies between 30 and 80 eV [84I].For similar results measured between 40 and 70 eVfrom Rh(111) in an angle-integrated mode see [84H2].

Refle

ctiv

ityR

0.2

0.4

0.6

0.8

1.0


Rh

Fig. 173. Rh. Experimental normal-incidencereflectivity data obtained from different experiments[81W1]. For details and tables of "most recommended"data see [81W1].

Diel

ectri

c co

nsta

ntε 2

7.5

10.0

12.5

15.0

17.5

20.0

5.0

2.5

0 15.02.5 17.55.0 20.07.5 22.510.0 12.5Photon energy [eV]hν

Rh

Fig. 174. Rh. Experimental ε2 spectra [81W1]. See also

legend to Fig. 173.








232


– 6

– 4

– 2

0

Wavevector k

Ener

gy[e

V]E

EF

Rh

2

4

6

8

10

12

14

Fig. 175. Rh. Band structure calculated by a second principles methodusing the combined interpolation scheme [74S1].

– 8

DOS

[sta

tes

(eV

atom

)]

–1

Energy [eV]E – EF

– 6 – 4 – 2 0 2 4 6 8 10 12

DOS

[sta

tes

(eV

atom

)]

–1

Rh

0

0.15

0.05

0.10

0.20

0.35

0.25

0.30

0.40

0.55

0.45

0.50

0.60

(× 8)

0

0.5

2.0

1.0

3.0

2.5

1.5

3.5

4.5

4.0

5.0

EF

Fig. 176. Rh. Density-of-states calculated with the combined interpolationscheme and the band structure of Fig. 175 [74S2].





233

0.3 0.5 0.7 1.1 1.5 1.90.1

EF

Rh

DOS

0.9 1.3 1.7Energy [Ry]E

LX

– 5.0

0

2.5

Ener

gy[e

V]E

Wavevector k

Rh

EF

WΓ X

– 2.5

– 7.5

5.0

7+ 7+

7+

7+

7+ 7+

7+

7+

7–

7–

8+ 8+

ZQKΣ'Γ ∆ Σ Λ

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

6

7

6

55

56+

6+

6+

6+

6+

6–

6–

6–

6–

6+ 6+ 6+

8+ 8+

6

7

6

6

6

6

6

7

7

5

6,7

3+4

4 +5+ +

6+

6+

6 ,7– –

4 +5– – –,6

7

6

6

6

6

6.7

8–6

76–

7+ 8–

6–

4+5,6

4+5

7

7+

6 ,7– –

6+

Fig. 177. Rh. DOS calculated froma band structure computed bymeans of the RAPW method[73C].

Fig. 178. Rh. RAPW bandstructure. Exchange part ofmuffin-tin potential has beencalculated using a nonlocalapproach [81B]. Symmetry labelsin double group notation.





234

W L Γ K X

– 0.6

– 0.7

– 0.5

– 0.2

– 0.4

0

Wavevector k

Ener

gy[R

y]E

1

3

1

3

1

4

11

125' 25'

Rh

EF

0.1

0.2

0.3

5

12 1

2

X Z Λ ΣΓ ∆ Q S

– 0.3

– 0.1

0.4

0.5

0.6

0.7

2'

1

5' 1'1

21

11

32

2

2'

12

11

4

3

2'

3

1

3

3

3

1

1

2

4

3

1

1

1

1

3

1

3

4

2

22

4'

3

2

11

3

3

4'

311

3

2 5'

0

4

DOS

[sta

tes

(ato

mRy

)]

–1

–0.7

8

12

16

20

24

28

32

36

40

44

48

Energy [Ry]E–0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

EF

Rh

Fig. 179. Rh. Band structure fromlocal density, all electron, selfconsistent calculations [88T].Symmetry labels in single groupnotation.

Fig. 180. Rh. DOS calculated fromthe band structure shown in Fig.179 [88T].





235

– 6.0

– 5.5

– 5.0

– 4.5

– 4.0

– 3.5

– 3.0

– 2.0

– 1.5

– 1.0

Initi

al st

ate

ener

gy[e

V]E i

– 0.5

– 2.5

LWavevector k

0

Γ

Rh(111)

EF

Λ LΓ Λ

0.5

1.0

1.5

EF

7+

6+

4 +5+ +

4 +5+ +

7+

8+ 8+

8+8+

6+

6+

6–

6+

6+

– 8.0

– 7.5

– 7.0

– 6.5

Fig. 181. Rh(111). Comparison of band mapping results (data points) and theoretical band structures (solid lines)along ΓL. Left panel: bands calculated within the combined interpolation scheme [74S2]. Right panel: calculation of[81B]. Experimental data from [89G2].






236

LΛWavevector k

Rh

Ener

gy[e

V]E

3'

1

1

3

1

0

–2.512

25'

2'

3

1

Γ

–5.0

–7.5

–10.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

27.5

30.0

32.5

35.0

37.5

40.0

42.5

2'

1

1

3

3

3

3'

2'1

25'

15

12

1

33

11

11

A B C

EF3

2'

15

Fig. 182. Rh. Energy bands calculated [79B1] alongΓL. Vertical arrows indicate direct transitions excited athν = 14 eV, compare Fig. 186. Heavy lines characterizebands with significant free-electron-like character,dotted line connects calculated bands via free-electronparabola. Open symbols above EF indicate experimental

data obtained from photo-emission and/or secondaryelectron emission [89G2].


→Fig. 185. Rh(111). Normal-emission photoelectronspectra excited with 21.2 eV photons with the sample at(a) room temperature and (b) at 100 K [89G2].

Inte

nsity

I–7 –6 –5 –4 –3 –2 –1 0 1


Rh(100)

EF

Fig. 183. Rh(100). Normal-emission photoelectronspectrum taken at hν = 130 eV [01K2]. For earlier workusing laboratory line sources see [79B1]. For existenceand properties of an occupied surface state just belowEF around the M point of the surface Brillouin zone see

[90M, 94W].

Inte

nsity

I

–6 –5 –4 –3 –2 –1Initial state energy [eV]Ei

–7–8 0 1

Rh(111)

a

b

Inte

nsity

I

EF

EF










237In

tens

ityI


–7–8 0 1 2

polarization : z

11.8 eV

16.8 eV

hν = 21.2 eV

Inte

nsity

I

polarization : y

11.8 eV

16.8 eV

hν = 21.2 eV

Inte

nsity

I

Rh(110) polarization : x

11.8 eV

16.8 eV

hν = 21.2 eV

a

b

c

EF

EF

EF

←←←←Fig. 184. Rh(110). Normal-emission photoelectronspectra for different polarization of the incident light:

(a) E parallel [001], (b) E parallel [1 1 0] and (c) Eparallel [110]. From [81B]. For earlier work see also[79B1].

Inte

nsity

I


–7–8

Rh(111)

–9–10 0

10.9 eV

12.0

13.0

C B A14.0

15.0

16.2

hν = 17.3 eV B,C

A

EF

Fig. 186. Rh(111). Normal-emission photoelectronspectra taken at different photon energies between 10.9and 17.3 eV [89G2].






238

→Fig. 188. Rh(111). Angle-resolved secondary electronemission spectra, with emission angle θ oriented alongthe ΓLUX plane [89G2]. Ef referred to EF.

Inte

nsity

I


–7–8

Rh(111)

–9–10 0

17.3 eV

19.6

20.7

21.8

22.9

24.8

hν = 25.8 eV

18.4

23.7S2

S3

S1

EF

Fig. 187. Rh(111). As Fig. 186 but at photon energiesbetween 17.3 and 25.8 eV. The labels S1, S2 and S3

indicate structure due to secondary electron emission[89G2].

→Fig. 189. Rh(111). Experimental conduction bandpoints obtained from angle-resolved secondary electronspectra [89G2] compared with calculated bands from(solid line) [73C] and (dashed) [79B1]. Differentsymbols refer to different kinematical conditions forexcitation of secondary electron emission. See also[89G2] for experimental results along different k-spacedirections.

5.0 7.5 10.0 12.5 15.0 17.5 20.0

Inte

nsity

I

Final state energy [eV]Ef

Rh(111)

θ = 20°

S2S3

25°

30°

35°

40°

45°

50°

55°

S2

S3

E0 = 40.3 eV

8

9

10

11

12

13

14

15

16

17

18

Γ Σ KWavevector k

Fina

l sta

te e

nerg

y[e

V]E f

Rh(111)

S2







Ref. p. 337] 2.11 Nonmagnetic transition metals (Pd)


239

2.11.12 Pd (Palladium) (Z = 46)

Lattice: fcc. a = 3.891 Å [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Kr) 4d10 5s0

Work-function:φ (poly) = (5.2 ± 0.3) eV [95H]φ (110) = 5.13 eV [90Y]φ (111) = (5.6 ± 0.1) eV [95K]

Table 17. Pd. Core-level binding energies in eVwith respect to EF [95H]. Typical scatter betweendifferent sources is ± 0.5 eV. See also [95M].

Level n = 3 n = 4

ns1/2 671.7 87.6np1/2 560.0 55.7np3/2 532.3 50.9nd3/2 340.5 –nd5/2 335.2 –


Table 18. Pd. Experimental and calculated critical point energies (in eV w.r. to EF).

Critical Experiment Theorypoint [78H] [88S3]* [90Y]* [76C1]

Γ – – –2.8 –2.79–2.55(15) – –2.5 –2.49–1.15(10) –1.2 –1.1 –1.17+21.7(5) +21.8 – +21.65

L –0.4(2) –0.3 – –0.14–0.1(1) –0.1 – +0.05+7.7(3) +7.8 – +7.3– +17.0 – +17.2

X – – +13.3 +12.9; +13.3– – +22.0 +21.3

* Taken from a figure. For states above EF see also [82J].















2.11 Nonmagnetic transition metals (Pd) [Ref. p. 337


240

Figures for 2.11.12

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


40

10–2

10–1

1

6 10⋅ –3

10

4d

4p

4

2

68

20Pd

3p3d

4s

3s

4

2

68

4

2

68

4d

Fig. 190. Pd. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].

2

4

6

89

7

5

3

2

4

6

89

7

5

3

20

4030

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–1

1

Pd

10

Fig. 191. Pd. Atomic 4d-subshell cross section near the Cooper minimum [85Y].





241

1000Binding energy [eV]Eb

0900 800 700 600 500 400 300 200 100

1000Eb V[e ]

1050

M V101145 1N

M V980

45 23N

M V925.6

5V

900950

MNN

Pd

3d5/2

3d1/2

3p3/2

3p1/2

3s

4s

4p

(× 4)

MNN

Fig. 192. Pd. Overview XPS spectrum taken with unmonochromatized MgKα radiation. The insert shows a blow-up

of the MNN Auger electron spectrum [79W]. For data taken with monochromatized AlKα radiation see [95M].





242

350 348 346 344 340342 338 336 330334 332

3d5/2

3d3/2

334.9


Pd

5.25

Fig. 193. Pd. XPS spectrum showing the region of thespin-orbit-split 3d core levels taken withunmonochromatized MgKα radiation [79W]. For the

line asymmetry of data taken with monochromatizedAlKα radiation see [74H1]. See also [95M].


Pd

DOS

–10 – 8 – 6 – 4 – 2 0 2

EF

338 337 336 335 334 333 332Binding energy [eV]Eb

Pd b

s

(110)

(111)

(100)

b s

Fig. 194. Pd. 3d5/2 photoelectron spectra from the

Pd(110), Pd(100), and Pd(111) surfaces measured at aphoton energy of 390 eV. The binding energy of thebulk (b) and surface (s) emission is indicated [94A]. Forother high resolution results see also [96P2] and [92N]for Pd(100), and [00S] for Pd(111). For ab initiocalculation of surface core level shifts see [94A]. ForPtxPd1-x(111) alloy surfaces see [02R2].

←Fig. 195. Pd. XPS valence band spectrum (dotted) takenwith monochromatized (0.5 eV) AlKα radiation. The

solid curve is the Pd DOS calculated within thecombined interpolation scheme [74S1] and smoothedwith a Lorentzian to account for experimental resolution[74S2]. See also [74H2]. The agreement betweenexperimental and calculated data may be improvedconsiderably by inclusion of corrections for matrix-element modulation, lifetime of the photohole andinelastic electron electron scattering, see [76H2].
















243


Pd

–8 –7 –6 –5 –4 –3

hν = 36 eV

30

28

26

24

23

19

18

16

14 eV

EF

20

21.2

22


EF

(× 20)

(× 20)

(× 10)

hν = 150 eV

120

100

70

50 eV

–9 –2 –1 10–8 –7 –6 –5 –4 –3–9 –2 –1

Fig. 196. Pd. Valence-band photoemission spectra of polycrystalline film for photon energies 14…36 eV (left panel)and 50 - 150 eV (right panel) [97K]. For valence band spectra from disordered PdxAu1−x (0 ≤ x ≤ 1) see [98N], for

similar data from random PdxAg1−x alloys see [01A].






244

0 10 20 30 40 50 80–10Energy [eV]E

Pd

60 70

DOS

EF

Fig. 197. Pd. Bremsstrahlung-isochromat spectrum taken at hν =1487 eV (dots) and calculatedDOS (solid line, bottom) ofunoccupied states. Correspondenceof structures in the experimentalspectrum and features in the DOS(solid, middle: broadened to mimicresolution and lifetime effects) isindicated [85S]. For data shown onan expanded scale up to 10 eV andfor results obtained fromdisordered PdxAu1−x alloys see

[98N]. For further isochromatstudies and theory see [88S5,88S6, 91S3].

30.00 2.5 5.0 7.5

0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5Photon energy [eV]hν

Pd

Refle

ctiv

ityR

Fig. 198. Pd. Experimentalnormal-incidence reflectivity dataobtained from different experi-ments [81W1]. For details andtables of "most recommended"data see [81W1]. For a calculationof the full dielectric matrix andoptical properties see [01K1].











245

30.00 2.5 5.0 7.5

0.5

1.5

1.0

2.5

3.5

2.0

3.0

4.5

4.0

5.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Diel

ectri

c co

nsta

ntε 2


Pd

ε2

ε2⋅10–1Fig. 199. Pd. Experimental ε2

spectra [81W1]. See also legend toFig. 198. For theoretical results see[01K1].

0 0.1 0.2 0.3 0.4 0.5 0.80.6 0.90.7 1.0

DOS

[sta

tes

(ato

mRy

)]

–1

Energy [Ry]E

5

20

10

30

25

15

35

45

40

50

55

EF

PdFor Fig. 200 see next page

Fig. 201. Pd. Density-of-statesfunction in the d-band rangecalculated from the RAPW bandsof Fig. 200 [76C1].






246

Γ X W L Γ KU X0

Wavevector k

Ener

gy[R

y]E

EF

Pd

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

∆ Z Q Λ Σ S

Fig. 200. Pd. Energy bands calculated by means of the relativisticaugmented-plane-wave method [76C1]. For a self-consistent full-potentialtotal energy KKR calculation including all relativistic effects see [96B].





247


– 6

– 4

– 2

0

Wavevector k

Ener

gy[e

V]E

EF

Pd

2

4

6

8

10

12

14

Fig. 202. Pd. Band structure calculated by a second principles method usingthe combined interpolation scheme [74S1].

– 8

DOS

[sta

tes

(eV

atom

)]

–1

Energy [eV]E – EF

0

0.5

2.0

1.0

3.0

2.5

1.5

3.5

4.5

4.0

5.0

– 6 – 4 – 2 0 2 4 6 8 10 12

DOS

[sta

tes

(eV

atom

)]

–1

Pd

0

0.15

0.05

0.10

0.20

0.35

0.25

0.30

0.40

0.55

0.45

0.50

0.60

(× 8)

EF

Fig. 203. Pd. Density-of-states calculated with the combined interpolationscheme and the band structure of Fig. 202 [74S2].





248DO

S

–6 –5 –4 –3 –2 –1 0 6Energy [eV]E – EF

Pd

EF

1 2 3 4 5

Fig. 204. Pd. DOS curve calculated with the KKRmethod in the local-density approximation [84S]. ForPdxAg1–x alloys see [01A].

–3.0

–2.5

–2.0

–1.5

–1.0

–0.5

0

ΓΛLWavevector k

Initi

al st

ate

ener

gy[e

V]E i

Pd(111)

3

1

3

EF

Fig. 205. Pd(111). Experimental band structure dataalong Λ [78H].

LΛWavevector k

Pd(111)

Ener

gy[e

V]E

0

–1

Γ

–2

–3

–4

1

2

3

4

EF

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

Λ61

Λ61

Λ4,53

Λ63

Λ61

Λ4,53

Fig. 206. Pd(111). Experimental band structure dataobtained above and below EF and compared to

calculated bands (solid lines). Symmetry labels aresuperscribed with single group notation and subscribedwith double group notation. The calculated empty bands(solid) are shifted by an energy dependent valuebetween 0.4 eV and 1.1 eV towards higher energies(dashed curves) in order to improve agreement with theexperimental data points above EF. The dashed emptybands were used to determine k⊥ for the occupied bands[88S3].







249

LΛWavevector k

Pd(111)

Ener

gy[e

V]E

0

–5

Γ

–6

–7

–8

1

2

4

EF

3

–1

–2

–3

–4

5

6

7

9

8

10

11

12

14

13

15

16

17

19

18

20

21

22

23

25

24

13

2

1

3

6

7

9

8

10

11

12

14

13

15

16

17

19

18

20

21

22

23

25

24

1

2

3

Ener

gy[e

V]E

Im kz

0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 207. Pd(111). Relativistic bulk band structure along ΓL with point-group symmetries Λ6 (solid lines) and Λ4+5

(long-dashed lines). Zero energy at EF. Inclusion of an imaginary potential yields short-dashed bands labelled 1,2,3

and associated parts of Imkz shown in the right-hand-side panel. Symbols below EF indicate some experimental

results [89T].




250

2 25. 2 50. 2 75. 3 00. 3 25. 3 50. 3 75. 5 00.– 8

– 7

– 4

– 6

– 2

– 3

– 5

– 1

EF = 0

4 00. 4 25. 4 50. 4 75.Wavevector [Å ]k⊥

–1

Initi

alst

ate

ener

gy[e

V]E i

K Σ ΓXWavevector k

1

1

3

4

Pd(110)

Fig. 208. Pd(110). Experimentalband mapping results along ΓKXcollected at different experimentalconditions [90Y]. Solid curvesshow calculated bands from[76C1].


–7–8

Pd(110)

0

18 eV

24

26

28

30

34

hν = 40 eV

22

32

EF

1

20

36

38

Fig. 209. Pd(110). Normal-emission photoelectronspectra from the (1x1) surface taken at different photonenergies with light incident at α = 25° and thepolarization vector in the (001) mirror plane [00B2].For data at hν from 24 to 68 eV see also Fig. 210[90Y]. See also [77L2], [80A1] and [85L] for earlierwork. For surface Fermi contours on Pd(100) see[91E1].











251In

tens

ityI


–7 0 1

EF

Pd(110)

hν = 24 eV

26

28

30

32

34

36

38

40

42

44

46

48

52

56

60

68 eV

Fig. 210. Pd(110). Normal-emission photoelectron spectra from the (1x1)surface taken at different photon energies. The incident light angle is α =

25°, with the polarization vector in the (1 1 0) mirror plane. Dashed linesindicate dispersion (or nondispersion) of experimental peaks or shoulders[90Y].




252


–6 –5 –4 –3 –2 –1

hν = 30 eV

28

26

2423

22

20

18

11

10

9 eVEF

Pd(111)

12

13

14

15

16

17

19

21

Fig. 211. Pd(111). Normal-emission photoelectronspectra taken at various photon energies hν [78H]. Forearlier work see also [77L2, 79D, 81N, 84H1].

–14 –12 –10 – 8 – 6 – 4 – 2 0 2

Inte

nsity

IInitial state energy [eV]Ei

EF

Pd(111)

Fig. 212. Pd(111). Normal-emission photoelectronspectrum collected at hν = 81 eV [01W].

0.25

0.50

2.25

1.75

0.75

2.00

1.00

1.25

0

1.50

– 3.5 – 3.0 – 2.5 – 1.5– 2.0 – 1.0 0.5

2.50

– 0.5 0

Inte

nsity

I


EF

Pd(111)

Fig. 213. Pd(111). Photoelectron spectra collected innormal-emission at hν = 16 eV using circularlypolarized radiation. Solid line: data taken withoutpolarization analysis. Dashed, dotted lines: separation intwo partial transition intensities by means of the emittedelectron spin polarization [88S3].










253

– 6 – 5 – 4 – 3 – 2 –1 0 1Initial state energy [eV]Ei

Pd(111)

c

– 6 – 5 – 4 – 3 – 2 –1 0 1Initial state energy [eV]Eia

– 6 – 5 – 4 – 3 – 2 –1 0 1Initial state energy [eV]Eib

Γ – M

Γ – 'M Γ – K

θ = – 6°

0°

10°

20°

30°

40°

50°52°55°60°66°

θ = – 8°

0°

10°

20°

32°

40°

28°

θ = – 6°

0°

10°

20°

30°35°40°46°50°

– 4°

– 2°

EF EF

EF

Fig. 214. Pd(111). Angle-dependent photoemissionspectra taken at hν = 21.2 eV along (a) the Γ-M′azimuth of the surface Brillouin zone, (b) along Γ-K and (c) along Γ-M [97K]. See [97K] also for datawith hν = 16.85 eV.





254

–2 0 2 4 6 8 10Energy [eV]E

12 14 16 18 20 22 24 26

Pd(110)

θ = – 41°

EF

B

S

L

S

B

B

– 36°

– 31°

– 26°

– 21°

– 16°

– 11°

– 6°

– 1°

4°

9°

14°

19°

24°

29°

34°

39°

Fig. 215. Pd(110). Inverse photoemission spectrarecorded in the isochromat mode at hν = 9.6 eV forelectrons incident at indicated angles θ along the ΓYsurface Brillouin zone azimuth [90J]. Spectral features

are labeled B (bulk), S (surface) and L (low-energy-electron diffraction), respectively. For results taken witha grating monochromator and parallel photon energydetection see [88S4].





255

–1 0 1 2Energy [eV]E

Pd(110)

θ = 77°

EF

B

S

L

B

B

61°

41°

31°

21°

B

B

11°

1°

BB

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fig. 216. Pd(110). Inverse photoemission, similar to Fig. 215 but with electrons incident along the ΓX direction ofthe surface Brillouin zone [90J].




256

5 10 15 20 25 30 35 40 45Energy [eV]E

Pd(110)

Fig. 217. Pd(110). Low-energy portion of a normal-emission photoelectron spectrum taken at hν = 50 eVshowing significant secondary electron emissionstructure [90Y]. For detailed earlier investigation ofsecondary electron spectra see [83L]. E w.r. to EF.

12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5

Wav

evec

tork

Energy [eV]E

Pd(111)

Γ2' Γ15 Γ25'

Γ

L

Fig. 218. Pd(111). Excited-band signatures observed inlow-energy electron reflectance. Top: sample current Icversus energy of normally incident electrons andcorresponding second derivative spectrum Ic". Bottom:

relevant section of the bulk bands [82J]. E w.r. to EF.






257

0 2.5 5.0Energy [eV]E

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

10°

15°

20°

25°

30°

35°

40°

45°

50°

55°

θ = 60°

Pd(111) Γ – M Γ – 'M

0 2.5 5.0Energy [eV]E

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

10°

15°

20°

25°

30°

35°

40°

45°

50°

55°

θ = 60°

Fig. 219. Pd(111). Inverse photoemission showingisochromats at hν = 9.8 eV for electrons incident atdifferent polar angles in the ΓLUX plane [87I]. Forearlier work and model calculations see also [86H,

84W3]. For an inverse photoemission study of the (100)surface see [92W]. For two-photon photoelectronspectra see [87K1]. See also [89K] for theoretical workon unoccupied states at Pd(111).







2.11 Nonmagnetic transition metals (Hf) [Ref. p. 337


258

2.11.13 Hf (Hafnium) (Z = 72)

Lattice: hcp. a = 3.195 Å, c = 5.051 Å, c/a = 1.581 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d2 6s2

Work-function:φ (poly) = (3.9 ± 0.3) eV [95H]

Table 19. Hf. Core-level binding energies in eV w.r. to EF [95H]. Experimental uncertainty estimated tobe up to 1 eV. See also [95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 538.0 438.2 380.7 220.0 211.5 15.9 14.2

n = 5 64.2 38.0 29.9 – – – –

For core-hole lifetime broadenings see [92F]

Figures for 2.11.13

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

4

2

68

Hf20

68

4

2

68

4

2

68

4

2

68

4 10⋅ –4

5p

4p

3d

5s

4s

4d4f

5d

6s

Fig. 220. Hf. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].







Ref. p. 337] 2.11 Nonmagnetic transition metals (Hf)


259


0900 800 700 600 500 400 300 200 100

Hf

4d5/2

4d3/2

4p3/2

4p1/24s

5s

5p

4f

Ni

NNN

1100 1000

Fig. 221. Hf. Overview XPS spectrum taken with unmonochromatized MgKα radiation [95M]. See also [95M] for

data taken with monochromatized AlKα radiation.





260

25 23 21 19 1517 13 11 59 7

4f7/2

4f5/2

14.3 ev


Hf

16.0 eV

Fig. 222. Hf. XPS data showing region of the spin-orbit-split 4f core levels taken with unmonochromatizedMgKα radiation [95M]. For data recorded with

monochromatized AlKα radiation see [79S] and [95M].

For surface core level shift in polycrystalline Hf see [84N].

–2 0 2 4 6 8 10Energy [eV]E

Hf

EF

hν = 22.5 eV

20.4

18.7

15.7

14.5

12.7

11.1 eV

DOS

[sta

tes

(eV

atom

)]

–1

0.25

0

0.50

0.75

1.00

1.25

1.50

Hf


–10 – 8 – 6 – 4 – 2 0

EF


–10 – 8 – 6 – 4 – 2 0

EF

2

2

spd

BG

Fig. 223. Hf. Bottom: XPS valence band spectrumtaken with monochromatized (0.6 eV) AlKα radiation

from polycrystalline sample (data points) compared to asimulated one (solid line and assumed background, BG)employing partial DOS calculations shown in the upperpanel [81H2].

←Fig. 224. Hf. Bremsstrahlung isochromat spectra takenat different photon energies hν from polycrystallinesample [92P].









261

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Hf

Fig. 225. Hf. Experimentalnormal-incidence reflectivity dataobtained from differentexperiments [81W1]. For detailsand tables of "most recommended"data see [81W1].

30.00 2.5 5.0 7.5Photon energy [eV]hν

1

3

2

5

7

4

6

9

8

10

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Hf

Diel

ectri

c co

nsta

ntε 2

ε2⋅10–1

10 ε2

ε2 E cIIE c⊥

Fig. 226. Hf. Experimental ε2

spectra [81W1]. Dashed line E c,dotted line E ⊥ c. See also captionto Fig. 225.






262

Γ K L,K LΓ A H0

Wavevector k

Ener

gy[R

y]E

EF

Hf

0.10

0.05

∆T T' Σ SHM A,M U P S' R

0.15

0.25

0.20

0.30

0.40

0.35

0.45

0.55

0.50

0.60

0.70

0.65

0.75

0.85

0..80

0.90

1.00

0.95

1.05

1.15

1.10

1.20

Fig. 227. Hf. Relativistic band structure based on the linear muffin-tin-orbital method [75J1].




263

0

2.5

10.0

5.0

15.0

12.5

7.5

17.5

22.5

20.0

25.0

27.5

0 0.1

DOS

[sta

tes

(Ry

atom

)]

–1

NOS

[ele

ctro

nsat

om]

–1

EF

Energy [Ry]E

Hf

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

30.0

0

1

4

2

6

5

3

7

9

8

10

11

12

Fig. 228. Hf. Density-of-states calculated from the band structure shown inFig. 227 [75J1].


2.11 Nonmagnetic transition metals (Ta) [Ref. p. 337


264

2.11.14 Ta (Tantalum) (Z = 73)

Lattice: bcc. a = 3.303 Å [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d3 6s2

Work-function:φ (100) = (4.15 ± 0.3) eV [95H]φ (100) = 4.1 eV [90P]φ (110) = (4.8 ± 0.3) eV [95H]φ (111) = (4.0 ± 0.3) eV [95H]

Table 20. Ta. Core-level binding energies in eV w.r. to EF [95H]. Experimental errors estimated to be±0.5 eV. See also [95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 563.4 463.4 400.9 237.9 226.4 23.5 21.6n = 5 69.7 42.2 32.7 – – – –


Figures for 2.11.14

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

4

2

68

Ta20

68

4

2

68

4

2

68

4

2

68

4 10⋅ –4

5p

4p

5s

4s

4d4f

5d

6s

4f

Fig. 229. Ta. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].










Ref. p. 337] 2.11 Nonmagnetic transition metals (Ta)


265

2

4

6

89

7

5

3

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–2

1

20Ta

10

10–1

2

4

6

89

7

5

3

2

4

6

89

7

5

3

Fig. 230. Ta. Atomic 5d-subshell cross section near the Cooper minimum [85Y].


35 33 31 29 2527 23 21 1519 17

4f7/2

4f5/2

21.9 ev


Ta

Inte

nsity

I

23.8 eV

5p3/2

Fig. 232. Ta. XPS spectrum showing the region of thespin-orbit-split 4f core levels taken with unmono-chromatized MgKα radiation [95M].

23.0 22.6 22.2 21.8 21.4

Inte

nsity

I


S2

S1

140 meV

740 meV

21.65 eVTa(100)

B

Fig. 233. Ta(100). High-resolution photoemissionspectrum of the 4f7/2 core level and its decomposition

into bulk (B) and surface (S1, S2) components [85G].

Photon energy hν = 70 eV. See also [88S7] and [96R].








266In

tens

ityI


0900 800 700 600 500 400 300 200 100

Ta

4d5/2

4d3/2

4p3/2

4p1/24s

5s

5p

4f

NNN

1100 1000

Fig. 231. Ta. Overview XPS spectrum taken with unmonochromatized MgKα radiation [95M]. For results obtained

with monochromatized AlKα radiation see [95M].





267Co

rele

vel s

hift

[meV

]∆

E b

Temperature [K]T

–700

–705

–710

–715

50 100 150 200 250 300

–720Ta(100)

Fig. 234. Ta(100). Experimental surface core level shift(energy distance between bulk and surface componentof the 4f7/2 core level) in its dependence on sampletemperature [96R].

22.5 22.4 22.3 22.2 21.922.1 21.8 21.7 21.321.6 21.4Binding energy [eV]Eb

Ta(110)

s

b

22.0 21.5

Fig. 235. Ta(110). Photoemission spectrum of the 4f7/2

core level showing the contributions from bulk (b) andsurface (s) atoms [97S]. Photon energy hν = 120 eV. Eb

w.r. to EF. See also [85G] and [88S7].

20

80

40

120

100

60

140

180

160

200

25.0 23.5 23.0 22.5 22.0 21.5 20.521.024.024.5Binding energy [eV]Eb

Ta(111)

Fig. 236. Ta(111). High-resolution photoemission from the 4f doublet. Eachspin-orbit component is decomposed into (starting from lowest bindingenergy) a bulk, a sub-surface and a surface line [84W2]. The background usedfor decomposition is shown as a dotted line and has a general parabolic shape.








268

–2 0 2 4 6 8 10Energy [eV]E

Ta

Inte

nsity

I

EF

hν = 25.0 eV

20.4

18.7

15.7

14.5

12.7

11.1 eV

22.5

Fig. 237. Ta. Bremsstrahlung isochromat spectra takenat different photon energies hν from polycrystallinesample [92P].

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Ta

Fig. 238. Ta. Experimentalnormal-incidence reflectivity dataobtained from different experi-ments [81W1]. For details andtables of "most recommended"data see [81W1].






269

500 2 4 6Photon energy [eV]hν

1

3

2

5

7

4

6

9

8

10 15 20 25 30 35 40 45

Ta

Diel

ectri

c co

nsta

ntε 2

ε2 10–1⋅

ε2

scale change

8

27.5 25.0 22.5 15.0 7.5 –2.530.0 20.0 12.517.5 10.0Binding energy [eV]Eb

5.0 02.5

Ta(100)

Fig. 239. Ta. Experimental ε2

spectra [81W1]. See also legend toFig. 238.

For Figs. 240, 241 see nextpages

Fig. 242. Ta(100). Normal-emission photoelectron spectrumtaken at hν = 30 eV. Light-incidence angle α = 60°, withlinear-polarization vector Aoriented in the mirror-plane alongthe ΓM direction of the surfaceBrillouin zone [90P]. Some datapoints are reproduced to indicatestatistical accuracy. For surfaceelectronic properties of Ta(110)see [90K2] and [91K2].







270

Γ H NΓ H0

Wavevector k

Ener

gy[R

y]E

EF

Ta

0.2

0.1

∆ FP PΣ ΛG N

0.4

0.3

0.6

0.5

0.8

0.7

1.0

0.9

1.2

1.1

1.4

1.3

1.5

25'

12

1

2'

5

2

1

1

12

1

1

1

1

3

42

2

1

3

3

1

41

1'

1

4

15

25' 2

4 3

3

1 1

1

3 3

3 1 1

1

332423

1

1

1'

3

4

4 24

4

1

31

1

1

12

25'

15

1

3

Fig. 240. Ta. Nonrelativistic band structure [77B].




271

0.1 0.2

DOS

[sta

tes

(Ry

atom

spin

)]

–1

Energy [Ry]E

2

0

3

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

2

0

3

1

4

s

p

0

2

d – Γ25'

4

6

8

10

12

140

2

d – Γ12

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

18

20

22 Ta

EF

NOS

[ele

ctro

nsat

om]

–1

DOS

[sta

tes

(Ry

atom

spin

)]

–1DO

S[s

tate

s(R

yat

omsp

in)

]–1

DOS

[sta

tes

(Ry

atom

spin

)]

–1

0

2

4

6

10

8

1

3

5

7

11

9

12

total

Fig. 241. Ta. Total (top) and partialdensities-of-states calculated fromthe bandstructure reproduced inFig. 240 [77B].




272


kII

Ta(100)

Γ [1]

M

Γ [0]center

1– 2 –1– 4 – 3– 6 – 5 0Initial state energy [eV]Ei

kII

Γ [1]

Modd

1– 2 –1– 4 – 3– 6 – 5a b

Fig. 243. Ta(100). Angle-resolved photoelectronspectra taken at various polar angles along the Σ (ΓM)direction of the surface Brillouin zone. Photon energyhν = 40 eV. The polarization vector is ((a), left panel)

in the mirror plane of collection or ((b), right panel)perpendicular to the mirror plane of collection, thusexciting only even (a) or odd (b) states, respectively[90P].




273


kII

Ta(100)

Γ [1]

X

Γ [0]center

1– 2 –1– 4 – 3– 6 – 5 0Initial state energy [eV]Ei

kII

Γ [1]

1.0–1.0 – 0.5– 2.0 –1.5– 3.0 – 2.5a b

0.5

Γ [0]center

X

Fig. 244. Ta(100). Angle-resolved photoelectron spectra taken at various polar angles along the ∆ (ΓX) direction ofthe surface Brillouin zone. Ei w.r. to EF. For details see legend to Fig. 243 [90P].




274

–2Energy [eV]E

Ta(100) hν = 20 eV

hν = 15 eV

EF

–1 0 1 2 3 4 5 6 7 8 9

Fig. 245. Ta(100). Experimental isochromat spectrarecorded at normal electron incidence and photonenergies hν = 15 and 20 eV [89A]. For angle-of-incidence dependent spectra recorded at hν = 9.7 eV see[87B3].



Ref. p. 337] 2.11 Nonmagnetic transition metals (W)


275

2.11.15 W (Tungsten) (Z = 74)

Lattice: bcc. a = 3.165 Å [71L].Brillouin zones: see section 1.3 of this volume.Electronic configuration: (Xe) 4f14 5d4 6s2

Work-function [95H]:φ (poly) = 4.6 eVφ (100) = 4.63 eVφ (110) = 5.25 eVφ (111) = 4.47 eV

Errors estimated to be ± 0.3 eV.

Table 21. W. Core-level binding energies in eV w.r. to EF [95H ]. Experimental scatter between differentsources ± 0.5 eV. See also [95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 594.1 490.4 432.7 256.0 243.4 33.6 31.5n = 5 75.6 45.3 36.8 – – – –


Table 22. W. Comparison of theoretical and experimental energies at high-symmetry points of the bulkBrillouin zone [98F1]. All energies in eV relative to EF.

Critical Calculation Experimentspoint [74C1, 78W2] [84B1]

Γ8+ –1.17 –1.53 –1.32(10) a) ; ≈ – 1.3 b)

Γ7+ –0.61 –1.01 –0.75(5) a); ≈ – 0.4 b)

Γ8+ 1.99 2.15 2.6(2) c)

Γ 14.4 14.9 15.3(5) a); 14.6 (6) b); ≈ 15 d)Γ 30.2 – 29.7(17) c)

N5+ –3.35 –3.66 –3.40(5) a); –3.5 e)

N5+ 1.96 1.98 2.2(2) c)

N5+ 2.89 2.94 ≥ 3.2 c)

N5+ 5.90 5.88 6.3(5) d)

N5+ 10.7 9.9710.8(5) d)

N5– 11.1 11.7

N 26.1; 26.9 – 26.5 e)

H8+ –6.1 –5.9 –5.7 b)H8– 9.0 9.2 9.3 b)

a) Photoemission [98F1]; b) Photoemission [76S]; c) Inverse Photoemission [93D]; d) Photoemission [78W2];e) Photoemission [82B3].















2.11 Nonmagnetic transition metals (W) [Ref. p. 337


276

Figures for2.11.15

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

4

2

68

W20

68

4

2

68

4

2

68

4

2

68

4 10⋅ –4

5p

4p

5s

4s

4d4f

5d

6s

40

4f

2

4

6

89

7

5

3

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–2

1

20W

10

10–1

2

4

6

89

7

5

3

2

4

6

89

7

5

3

4030

Fig. 246. W. Atomic subshellphotoionization cross sections forphoton energies from 0 to 1500 eV[85Y].

Fig. 247. W. Calculated atomic5d-subshell cross section near theCooper minimum [85Y].





277


0900 800 700 600 500 400 300 200 100

W

4d5/2

4d3/2

4p3/2

4p1/24s

5s

4f

NNN

1100 1000

Fig. 248. W. Overview XPS spectrum. Data taken with unmonochromatized MgKα radiation [95M]. For data

obtained with monochromatized AlKα see also [95M].





278

26 27 28 30 34 3525

W(110)

29 31 32 33Kinetic energy [eV]Ek

4f5/2

5p3/2

4f7/2

Fig. 249. W(110). Wide scanencompassing the 5p3/2 and 4f

region. High resolution data (∆E =83 meV) taken with 70 eV photons[90R]. The spin-orbit-split 4f5/2

and 4f7/2 levels are each split

additionally due to appearance ofthe bulk component and a surface-shifted line, see also Fig. 250.

32.00 31.75 31.50 31.25 31.00 30.75 30.50 30.25Binding energy [eV]Eb

B

SW(110)

Fig. 250. W(110). Analysis of the 4f7/2 photoemission

spectrum. The data, taken with 70 eV photons, are fittedwith a linear background and two independent linesrepresenting the surface (right) and bulk (left)contributions [90R]. For effects of sample temperaturesee [89P2], for intensity variation with emission anglesee [87J]. Holographic images from surface and bulkatoms are reported in [99L].

32.00 31.50 31.00 30.50 30.00Binding energy [eV]Eb

W(100)

Fig. 251. W(100). High-resolution photoemission fromthe 4f7/2 core level, indicating decomposition in (from

left to right) a bulk, subsurface and surface line [84W2].Background used for decomposition is shown as adotted line and has a general parabolic shape.









279

32.00 31.50 31.00 30.50 30.00Binding energy [eV]Eb

W(111) B

S

Fig. 252. W(111). Energy distribution curve of the 4f7/2

photoemission spectrum showing bulk (left) and surface(right) contributions [88W]. See also [84W2]. For thethermal shift in the binding energy of the bulk 4f7/2

component see [97T].

Fig. 253. W(100). XPS valence band spectra recordedwith monochromatized AlKα radiation at fixed polar

angle θ = 63° but different azimuth angles Φ [80H]. Foreffect of temperature variation on XPS spectra fromW(100) and W(110) see [86W1].


Inte

nsity

I

W(100)

–10 –1

F = 45°

EF

– 2– 3– 4– 5– 6– 7– 8– 9

40°

35°

30°

25°

20°

15°

10°

5°

0° [102]








280

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

W

Fig. 254. W. Experimentalnormal-incidence reflectivity data[81W1] obtained from differentexperiments. For details and tablesof the "most recommended" datasee [81W1].


5

15

10

25

35

20

30

45

40

50

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

W

Diel

ectri

c co

nsta

ntε 2

10 ε2

ε2

Fig. 255. W. Experimental ε2

results [81W1] obtained fromdifferent experiments. For detailsand tables of the "mostrecommended" data see [81W1].







281

Γ H0

Ener

gy[R

y]E

Wavevector kH

–12

0

Ener

gy[e

V]E

W

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

N Γ P N P FDDΛΣG∆

–10

– 8

– 6

– 4

– 2

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

⟨ ⟩100 ⟨ ⟩110 ⟨ ⟩111

EF

Evac

Evac

Evac

Fig. 256. W. Energy bands along high-symmetrydirections of the bulk Brillouin zone [78W2] ascalculated by a relativistic augmented-plane-wavemethod [74C1]. The work functions of each low-indexface are indicated by the vacuum level Evac relative to

the Fermi level at EF = 0 eV. A prominent feature is the

band gap (shaded) which extends throughout theBrillouin zone, except for the region along the PH line.For the calculated density-of-states see [74C1]. For anapproach using an interpolation scheme see also [88S1].







282

Γ H NΓ H–10

Wavevector k

Ener

gy[e

V]E

EF

W

– 9

∆ FP PΣ ΛG N

15

12

1

2'

5

2

1

1

12

1

1

1

1

3

42

2

1

3

1

4

1

1

4

15

25' 2

4

3

1

3

3

3

1

1 1

3

4

1

3

4'

4

2

4

4

1

3

1

1

1

12

25'

15

0

– 8

– 7

– 6

– 5

– 4

– 3

– 2

– 1

1

2

11

3

4

5

6

7

8

9

10

12

13

14

1

1 1

1

25'

12

1

4 3

3

3

3

1'

1

5

25'

1

3

1 1

1

1

1

1

4

3

3

1

2

4

4

1

1'

4'

D

Fig. 257. W. Result of a self-consistent semirelativistic pseudopotential calculation of energy bands along high-symmetry directions of the bulk Brillouin zone [83B1]. Fermi level at zero of energy scale.




283

–10 –5 5

W

DOS

Energy [eV]E – EF

0

totalQ = 6.000

–10 –5 50

s × 50Q = 0.254

–10 –5 50

p × 10Q = 0.842

–10 –5 50

dQ = 4.828

–10 –5 50

f × 100Q = 0.075

Fig. 258. W. Total and partial (s,p,d,f) densities of states calculated from the semirelativistic energy bands shown inFig. 257. Q is the integrated charge density up to EF [83B1].




284

Γ H NΓ H–10

Wavevector k

Ener

gy[e

V]E

EF

W

– 9

∆ FP PΣ ΛG N

15

6

7

7

7

6

6

6

8–

7+

5– 6

4

4

6

4

4

4

6

6

6

0

– 8

– 7

– 6

– 5

– 4

– 3

– 2

– 1

1

2

11

3

4

5

6

7

8

9

10

12

13

14

6+

6

7

6

5+

6

6–

8+

5+

5+

5+8+

6

7

8

8

6

6

5–

8+

7+

5+

5+

6

4

6

6 46

6+

6

8+

8

7

6

D

Fig. 259. W. Result of a self-consistent relativistic pseudopotential calculation of the energy bands [84B1]. See also[84J] and [85W2]. – Symmetry labels in double group notation.






285

0

– 1

1

– 2

2

Γ H NΓ H–0.8

Wavevector k

Ener

gy[R

y]E

EF

W

∆ FP PΣ ΛG NEn

ergy

[eV]

E

– 3

– 4

– 5

– 6

– 7

– 8

– 9

– 10

DD

–0.7

–0.6

–0.5

–0.4

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3

4

5

6

7

8

9

10

11

12

13

12

2'

5

2

1

1

121

1

1

1

42

1

3

4

1

15

25'

2

3

1 3

3

3

4

1

1

3

42

44

3

1

1

1 12

25'

15

11

1

1

25'

12

1

4 333

3

1'

1

5

25'

1

3

1

1

2

4

1

2

1

1'

33

Fig. 260. W. Energy bands calculated using a first-principles, self-consistent real-space linear muffin-tin orbitalmethod in the atomic sphere approximation [00L]. Symmetry labels in single group notation.




286

–10

– 8

– 6

– 4

– 2

0

2

6

8

10

12

4

H∆Wavevector k

Ener

gy[e

V]E

Γ

EF

1

2'

5

1 2

W

a

–10

– 8

– 6

– 4

– 2

0

2

6

8

10

12

4

H∆Wavevector k

Ener

gy[e

V]E

Γ

EF

1,6

2',7

5,7

1,6

2,7

b

5,62,7

Fig. 261. W. Band structure along the [001] axis, the ΓH direction, for (a) non-relativistic calculation and (b) fullyrelativistic calculation [91C]. Symmetry labels in (a) and first label in (b) indicate single-group representations towhich the bands belong in the absence of spin-orbit coupling. Second label in (b) indicates corresponding double-group representations.

–10

– 8

– 6

– 4

– 2

0

2

6

8

4

NΣWavevector k

Ener

gy[e

V]E

Γ

EF

W

a

–10

– 8

– 6

– 4

– 2

0

2

6

8

4

NΣWavevector k

Ener

gy[e

V]E

Γ

EF

4,5

3,5

1,5

1,5

2,5

b

1,5

3

1

2

1

4

1

1,5

3,5

4,5

Fig. 262. W. Band structure along the [110] axis, the ΓN direction, for (a) non-relativistic calculation and (b) fullyrelativistic calculation [91C]. Symmetry labelling as defined in Fig. 261.





287

–10

– 8

– 6

– 4

– 2

0

2

6

8

10

4

N ΓWavevector k

Ener

gy[e

V]E

Γ

EF

1

4

3

1

2

W(110)

1

1

NΣ ∆

Fig. 263. W(110). Nonrelativisticband structure calculated along theΓN line and the correspondingprojected band structure in the(001) mirror plane [00T2]. Verti-cally and horizontally hatchedareas denote even and odd bands,respectively.

N– 4

– 2

–1

0

1

2

3

4

– 3

Wavevector k

Ener

gy[e

V]E

Γ

W(110)

Σ

EF

8+

7+

8+

Fig. 264. W(110). Experimentally determined energybands along the ΓN line of the bulk Brillouin zone.Occupied bands below EF from photoemission [98F1],

empty bands above EF from inverse photoemission

[93D]. The full curves correspond to the relativisticcalculation of [74C1]. The diamonds at EF are from de

Haas-van Alphen data. Symmetry labels in doublegroup notation.







288

–20 0

EF

hν =22 eV

11

W(001)

21

20

19

18

17

16

15

14

13

12

10 eV


–16 –12 – 8 – 4

←←←←Fig. 265. W(001). Normal-emission photoelectronspectra taken at different photon energies hν between10 and 22 eV. Polarized Synchrotron radiation wasnormally incident on the (001) face, i.e. s-polarization[76S]. See also [78A]. For earlier work on W(100),W(110) and W(111) at hν = 8…12 eV see [73F, 74C2].Normal-emission photoelectron spectra from W(111) athν = 13 - 30 eV are reported in [82C]. For excitation ofspin-polarized photoelectrons see [81F, 81K].

– 5 0 5 10 15 20 25 30 35

hν =13 eV

W(100)

15

18

21

25

29

33

35 eV

Kinetic energy [eV]Ek

Fig. 266. W(100). Normal-exit photoemission spectrameasured with various photon energies. P-polarizedlight was incident at α = 45°. Arrows indicate peaksinterpreted as surface resonances [78W1]. See also[77W2]. For surface resonances and surface Fermicontours see [80C, 81C, 90S, 91E2].
















289

0 2 4 6 8 10Energy [eV]E

Evac

Ei = 140 eV

12 14 16 18 20

80

50

4030

20 eV

W(100)

Fig. 267. W(100). Normal-emission secondary electronspectra taken at different electronincidence energies Ei. All spectra

are referred to the zero energy E atthe vacuum level [81S1]. Forearlier work see [78W2].

0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0Energy [eV]E

W(100)

Evac

c

b

a

Fig. 268. W(100). (a) Normal-emission experimentalsecondary electron spectrum after subtraction of asmooth "background cascade" spectrum [81S1]. (b)Model calculation based on the "inverse LEED"formulation which takes the details of the band structureas well as absorptive and surface effects into account[81S1]. (c) Fine structure obtained in the experimentalelectron reflection coefficient [81S1].








290

–2 0 2 4 6 8Energy [eV]E

EF

16.3

14.3

12.3 eV

Ei = 18.3 eV

W(001)

S

B

Ι

–2 0 2 4 6Energy [eV]E

EF

–1 1 3 5–1 1 3 5 7

kII /ΓM

0.87

0.73

0.57

0.35

0.14

0

Fig. 269. W(001). Left: Normal-incidence inversephotoemission spectra taken at different energy Ei ofthe incident electron. Each spectrum corresponds to theenergy distribution of the emitted photons at fixed Ei ,with high photon energies towards the left. S, B, and I

label emission from surface (S), bulk (B) and imagepotential (I) states. Right: Angular dependence forelectrons incident at Ei = 14.3 eV along the [110] bulkazimuth [86D1]. See also [87K2], [92C], and [94L].







291

0.50Initial state energy [eV]Ei

Inte

nsity

I

W(110)

–1.0

EF

– 2.0– 3.0– 4.0

SR

A

C

D

DA

–1.5– 2.5– 3.5 –0.5 0.50Initial state energy [eV]Ei

Inte

nsity

I

–1.0

EF

– 2.0– 3.0– 4.0

SR

–1.5– 2.5– 3.5 –0.5

hν = 19.2 eV

18.8

18.3

17.8

17.3

16.8

16.3

15.8

15.3

14.8

14.3

13.8

12.8

11.8 eV

25.2

24.8

24.3

23.8

23.2

22.8

21.8

21.0

20.8

hν = 27.3 eV

26.8

26.3

25.8

19.8 eV

Fig. 270. W(110). Normal-emission photoelectronspectra taken at different photon energies hν between11.8 and 19.2 eV (left) and between 19.8 and 27.3 eV(right). All spectra are normalized to equal maximum

peak amplitude [98F1] and shifted vertically againsteach other. The feature labeled SR represents emissionfrom a surface resonance, see also [87G, 89G3].






292


W(110)

C

D

A

Fig. 271. W(110). Relative variation of peak amplitudesof several dispersing features labeled A, C, and D inFig. 270 with photon energy hν [98F1].

– 8 – 7 – 6 – 5 – 4 – 3 – 2 –1 0Initial state energy [eV]Ei

W(110)1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

kk

II/

(H)

EF

Fig. 274. W(110). Angle resolved photoelectron spectrataken at hν = 21.2 eV along the NΓH azimuth of thebulk Brillouin zone. The parameter on the right givesthe approximate position of k|| (the wavevector parallelto the surface) in the surface Brillouin zone along the Γ-H symmetry line, where k||/k(H) refers to the ratio of k||

relative to its value at the H zone boundary [92H].


–10 – 9 –8 – 5 – 2 1–11 – 7 – 4– 6 – 3 –1 0Initial state energy [eV]Ei

W(110)

6s,p 5d

(× 3)

EF

Fig. 273. W(110). Normal-emission photoelectron spectrum taken with hν =62.5 eV [01R]. For data taken at hν = 40.8 eV see [01S].







293

a b

Inte

nsity

I

– 6 – 5 – 4 – 3 – 2 – 1Initial state energy [eV]Ei

W(110)

0 1

EF

Inte

nsity

I– 6 – 5 – 4 – 3 – 2 – 1


0 1

EF

c d

Inte

nsity

I


0 1

EF

Inte

nsity

I


0 1

EF

Fig. 272. W(110). Normal-emission photoelectron spectra taken at ω = 21.2 eV with different light polarizations:Light incidence in (110) plane p-polarized (panel (a)) or s-polarized (b), and incident in (100) plane with p-polarization (c) and s-polarization (d), resp. [02B].




294

–2 –1 0 1 2 3 4 5 6

EF

W(110)

Σ1

Σ1

Σ4

Ι

Energy [eV]E

Fig. 275. W(110). Normal-incidence inverse-photoemission spectrum taken at fixed electron energyEi = 14.5 eV showing emission labeled Σ1 , Σ4 from

three bulk bands (compare Fig. 262) and an imagepotential state (label I) [93D].

–1 0 1 2 3 4 5Energy [eV]E

W(110)

hν = 30 eV

28

25

22

20

17

15 eV

EF

Fig. 276. W(110). Normal-incidence inversephotoemission spectra taken in the isochromat mode fordifferent photon energies hν between 15 and 30 eV(crosses) compared to photocurrent calculations (fullcurves) based on the one-step model of inversephotoemission [91C]. See also [94S].




Ref. p. 337] 2.11 Nonmagnetic transition metals (Re)


295

2.11.16 Re (Rhenium) (Z = 75)

Lattice: hcp. a = 2.761 Å, c = 4.458 Å, c/a = 1.615 [71L]Brillouin zones: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d5 6s2

Work-function:φ (poly) = (4.7 ± 0.3) eV [95H]

Table 23. Re. Core-level binding energies (in eV relative to EF) [95H, 95M]. Estimated error ± 0.5 eV.

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 625.4 518.7 446.8 273.9 260.5 42.7 40.3

n = 5 99 45 35 – – – –


Figures for 2.11.16

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

4

2

68

Re20

68

4

2

68

4

2

68

4

2

68

4 10⋅ –4

4p

5s

4s

4d4f

5d

6s

40

5p

4f

Fig. 277. Re. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].







2.11 Nonmagnetic transition metals (Re) [Ref. p. 337


296

2

4

6

89

7

5

3

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–2

1

20Re

10

10–1

2

4

6

89

7

5

3

2

4

6

89

7

5

3

4030

Fig. 278. Re. Calculated atomic5d-subshell cross section near theCooper minimum [85Y].


54 52 50 48 4446 42 40 3438 36

40.1


Inte

nsity

I

2.4

Re 4f7/2

4f5/2

Fig. 280. Re. XPS data showing the region of the spin-orbit-split 4f core levels taken with unmonochromatizedAlKα radiation [79W]. For angle-integrated spectra

taken with different photon energies frompolycrystalline Re foil see also [80F2].

38.5Binding energy [eV]Eb

Re(0001) 4f7/2

4f5/2

39.039.540.040.541.041.542.042.543.043.544.0

Fig. 281. Re(0001). Photoelectron spectrum in normalemission within the range of the 4f core levels excitedwith photons of hν = 102 eV. Overall energy resolutionwas about 250 meV [89M]. See also [95M].








297


0900 800 700 600 500 400 300 200 100

Re

4d5/2

4d3/2

4p3/2

4p1/24s

5s

NNN

1100 1000

4f7/2

4f5/2

Fig. 279. Re. XPS overview spectrum taken with unmonochromatized MgKα radiation [95M]. See also [80F2]. For

spectra obtained with monochromatized AlKα radiation see [95M].






298


Re(0001)

43.8 43.6 43.4 43.2 43.0 42.8 42.6 42.4 42.2 42.0 41.8 41.6b


43.8 43.6 43.4 43.2 43.0 42.8 42.6 42.4 42.2 42.0 41.8 41.6a

Fig. 282. Re(0001). Normal-emission spectrum of the4f5/2core level component taken with hν = 102 eV and

reproduced (data points) in both panels. Top (a): thespectrum can be well described by one Doniach-Sunjicfunction (solid line). Bottom (b): Describing the samespectrum by two Doniach-Sunjic functions yields asurface core level shift smaller than 0.125 eV [89M].



Re(0001)

–15 –13 –11 – 9 – 7

θ = 45°

EF

– 5 –1

40°

35°

30°

25°

20°

15°

10°

5°

0°

– 3–17

Fig. 285. Re(0001). Photoelectron spectra taken at hν =21.2 eV for different emission angles θ along theΓAHK bulk mirror plane [79B3].





299

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Re

Fig. 283. Re. Experimentalnormal-incidence reflectivity dataobtained from different experi-ments [81W1]. For details andtables of "most recommended"data see [81W1].


2

6

4

10

14

8

12

18

16

20

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Re

Diel

ectri

c co

nsta

ntε 2

ε2

E cII E c⊥

Fig. 284. Re. Experimental ε2 data

[81W1] for light polarizationvector parallel (solid line) andperpendicular (dashed) to the c-axis. See also legend to Fig. 283.






300

–14 –12 –10 – 8 – 6 – 4 – 2 0 2Initial state energy [eV]Ei

θ = 35°

EF

EF

EF

EF

EF

θ = 25°

θ = 15°

θ = 5°

θ = 45°Re(0001)

Fig. 286. Re(0001). Photoelectron spectra taken at hν =16.8 eV for different emission angles θ along theΓAHK bulk mirror plane [79B2].


Ref. p. 337] 2.11 Nonmagnetic transition metals (Os)


301

2.11.17 Os (Osmium) (Z = 76)

Lattice: hcp. a = 2.735 Å, c = 4.319 Å, c/a 1.579 [71L]Brillouin zone: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d6 6s2

Work-function:φ (poly) = (5.9 ±0.3) eV [95H]

Table 24. Os. Core-level binding energies (in eV relative to EF). Estimated error ± 0.5 eV [95H, 95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 658.2 549.1 470.7 293.1 278.5 53.4 50.7

n = 5 88.0 58.0 44.5 – – – –


Figures for 2.11.17

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


40

10–2

10–1

1

10–3

10

5d

4

2

68

4

2

68

4

2

68

4

2

68

20

4⋅10–468

Os

4p4f

4s

5s

4d

5p

6s

4f

Fig. 287. Os. Atomic subshell photoionization cross sections for photonenergies from 0 to 1500 eV [85Y].







2.11 Nonmagnetic transition metals (Os) [Ref. p. 337


302

2

4

6

89

7

5

3

20

30

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–1

1

40Os

10

4 10⋅ –2

2

4

6

89

7

5

3

6

89

7

Fig. 288. Os. Calculated atomic 5d-subshell cross section near the Cooper minimum [85Y].

For Figs. 289, 290 see next pages

Refle

ctiv

ityR

0.2

0.4

0.6

0.8

1.0


Os

Fig. 291. Os. Experimental normal-incidencereflectivity data obtained from different experiments[81W1]. For details and tables of "most recommended"data see [81W1].

Diel

ectri

c co

nsta

ntε 2

7.5

10.0

12.5

15.0

17.5

20.0

5.0

2.5


Os

0 5 10 15 20 25 30

ε2ε2 10–1⋅

10 ε2

Fig. 292. Os. Experimental ε2 spectrum [81W1].







303In

tens

ityI


0900 800 700 600 500 400 300 200 100

Os

4d5/2

4d3/2

4p3/2

4p1/24s

5p

NNN

1100 1000

4f7/2

4f5/2

Fig. 289. Os. XPS overview spectrum taken with unmonochromatized MgKα radiation [95M]. For results obtained

with monochromatic AlKα radiation see also [95M].





304

51.75 51.50Binding energy [eV]Eb

B

S

51.25 51.00 50.75 50.50 50.25 50.00 49.75 49.50


Os(0001)

53.0 52.5 52.0 51.5 51.0 50.5 50.0 49.554.555.0

4f7/2

4f5/2

Fig. 290. Os(0001). Top: Photoelectron spectrum in normal emission within the energy range of the 4f core levelsexcited with hν = 110 eV [89M]. Bottom: Decomposition of the 4f7/2 core level spectrum taken at hν = 110 eV into

bulk (B) and surface (S) emission [89M].





305

Γ K L,K LΓ A H0

Wavevector k

Ener

gy[R

y]E

EF

Os

0.10

0.05

∆T T' Σ SHM A,M U P S' R

0.15

0.25

0.20

0.30

0.40

0.35

0.45

0.55

0.50

0.60

0.70

0.65

0.75

0.85

0..80

0.90

1.00

0.95

1.05

1.15

1.10

1.20

Fig. 293. Os. Relativistic band structure calculated by the linear-MTO method including spin-orbit coupling [75J1].




306

0

2.5

10.0

5.0

15.0

12.5

7.5

17.5

22.5

20.0

25.0

27.5

0 0.1

DOS

[sta

tes

(Ry

atom

)]

–1

NOS

[ele

ctro

nsat

om]

–1

EF

Energy [Ry]E

Os

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

30.0

0

1

4

2

6

5

3

7

9

8

10

11

12

32.5 13

35.0 14

Fig. 294. Os. Density of states calculated from the band structure shown inFig. 293 [75J1]. NOS is the integrated number of electrons per atom.


Ref. p. 337] 2.11 Nonmagnetic transition metals (Ir)


307

2.11.18 Ir (Iridium) (Z = 77)

Lattice: fcc. a = 3.839 Å [71L]Brillouin zone: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d7 6s2

Work-function:φ (100) (1x1) = 6.1 ± 0.1 eV [92D1]φ (100) (5x1) = 5.9 ± 0.1 eV [92D1]φ (110) = 5.4 ± 0.3 eV [95H]φ (111) = 5.8 ± 0.3 eV [95H]

Table 25. Ir. Core-level binding energies (in eV relative to EF). Estimated error ± 0.5 eV [95H]. See also[95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 691.1 577.8 495.8 311.9 296.3 63.8 60.8n = 5 95.2 63.0 48.0 – – – –


Table 26. Ir. Experimental and calculated critical point energies (in eV withrespect to EF).

Energy Experiment Calculationlevel [80V1] [82N]

Γ8+ –4.07(8) –3.94Γ7+ –3.18(8) –3.06Γ8+ –1.04(5) –1.00

Γ7– 15.2(5) 14.67Γ6– 18.92

19.5(5)Γ8– 19.49

L4+,5+ –4.25 (10) –4.27L6+ –3.35 (10) –3.39L6– –1.0 (2) –0.92

L6+ 7.6(5) 7.44L6– 14.5(5) 13.54X6+ 10.5(5) 10.80











2.11 Nonmagnetic transition metals (Ir) [Ref. p. 337


308

Figures for 2.11.18

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

10

4

2

68

20

68

4

2

68

4

2

68

4

2

68

4 10⋅ –4

4p

5s

4s

4d4f

5d

6s

40

r

5p

4f

Fig. 295. Ir. Atomic subshellphotoionization cross sections forphoton energies from 0 to 1500 eV[85Y].

2

4

6

89

7

5

3

20

30

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–1

1

40

10

4 10⋅ –2

2

4

6

89

7

5

3

6

89

7

r

Fig. 296. Ir. Photoionization crosssection for the 5d subshell near theCooper minimum [85Y].





309


0900 800 700 600 500 400 300 200 100

4d5/2

4d3/2

4p3/2

4p1/24s

5p

NNN

1100 1000

4f7/2

4f5/2

r

Fig. 297. Ir. Overview XPS spectrum taken with unmonochromatized MgKα radiation [95M]. For data taken with






310

75 73 71 69 6567 63 61 5559 57

60.9 eV


4f7/2

4f5/2

r

63.9 eV

Fig. 298. Ir. XPS data showing the region of the spin-orbit-split 4f core levels taken with unmonochromatizedMgKα radiation [95M]. For data measured usingmonochromatized AlKα radiation and a line-shape

analysis see [74H1] and [95M].


DOS

–10 – 8 – 6 – 4 – 2 0 2

EF

r

Fig. 299. Ir. Valence band XPS photoelectron spectrumtaken with monochromatized (0.5 eV) AlKα radiation

(closed circles) [74S2], compared with a smoothedversion of the occupied DOS calculated for bandsobtained from the combined interpolation scheme, seealso Fig. 305 [74S1, 74S2]. Valence band XPS spectrafrom Ir(100) are reported with high energy resolution(0.4 eV) as a function of the electron emission angle θin the (100) and (110) mirror planes in [92K].

2

r

EF


–10 – 8 – 6 – 4 – 2 0–12

Fig. 300. Ir. Angle-integrated photoelectron spectrumtaken with hν = 40.8 eV from a polycrystalline film[86W2].

r

EF


–10 – 8 – 6 – 4 – 2 0–12

Fig. 301. Ir. Angle-integrated photoelectron spectrumtaken with hν = 21.2 eV from a polycrystalline film[86W2]. See also [80V2].













311

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

r

Fig. 302. Ir. Experimental normal-incidence reflectivity data obtainedfrom different experiments[81W1]. For details and tables of"most recommended" data see[81W1].


2

6

4

10

14

8

12

18

16

20

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Diel

ectri

c co

nsta

ntε 2

r

573 K

313 KFig. 303. Ir. Experimental ε2

spectra [81W1]. See also legend toFig. 302.






312

Γ X W L Γ K X

– 8

– 6

– 4

– 2

0

Wavevector k

Ener

gy[e

V]E

EF

2

4

6

8

10

12

14

r

– 10

Fig. 304. Ir. Model band structurecalculated within the combinedinterpolation scheme. Spin-orbitcoupling and other relativisticcorrections are included [74S1].

– 8

DOS

[sta

tes

(eV

atom

)]

–1

Energy [eV]E – EF

0

0.25

1.00

0.50

1.50

1.25

0.75

1.75

2.25

2.00

2.50

– 6 – 4 – 2 0 2 4 6 8 10 12

DOS

[sta

tes

(eV

atom

)]

–1

0

0.15

0.05

0.10

0.20

0.35

0.25

0.30

0.40

0.45

0.50

(× 5)

EF

r

–10

Fig. 305. Ir. Density of statescalculated from the band structureshown in Fig. 304 [74S2].





313

W L Γ K X

– 10

– 12

– 8

– 2

– 6

0

Wavevector k

Ener

gy[e

V]E

1

3

1

3

1

4

11

1

25' 25'

EF

2

4

512 1

2

X Z Λ ΣΓ ∆ Q S

– 4

2'

1

5'

1'

1

21

1

1

3

2

2

2'

12

11

4

3

2'

3

1

3

3

3

1

2 4

3

1

11

1

3

1

34

2 5

2

2

4'

3

21

1

3

3

4'

33

1

5

1

1

4

2

3

1

1

1

1

4

41

4215

2'

2'

5'

1

1

2'

3'

15

2'

11

3

1

4

1

2'

r

6

8

10

12

14

16

18

20

5

2

1

Fig. 306. Ir. Scalar relativistic band structure based on the self-consistentlattice potential of a fully relativistic calculation [82N]. Symmetry labelsrefer to representation in single group notation.




314

W L Γ K X

–10

–12

0

Wavevector k

Ener

gy[e

V]E

EF

2

X Z Λ ΣΓ ∆ Q S

– 2

r

– 4

– 6

– 8

4

6

8

10

12

14

16

18

20

22

7+

7+

7+7+

7+

7–

8+

6

7

5

5

56+

6+

6+

6–

6–

6+

6+

6+

8+ 8+

67 6

6

6

6

4 +5+ +

6+

7

6

6

6

7

6–

8–

6–

4+5

4+5

7–

6+

3+4

3+4

3+4

3+4

3+4

3+4

5

5

5

5

5

5

5

5

6

8+ 7+

6+

7+6–

6+

6–

6+

4 +5+ +4+5

7

7

5

5

5

7+

5

6–

5

55

5

53+4

5

6–

6+

6

6

7

7

6

6

5

57–

8–5

5

5

6

5

3+4

3+4

3+4

6 75

5

7–6–

6

5

5

5

5

5

5

5

57

Fig. 307. Ir. Fully relativistic band structure [82N]. Symmetry labels refer torepresentations in double group notation. See also [96B].





315DO

S[s

tate

s(a

tom

eV)

]–1

– 9 – 6 – 3Energy [eV]E – EF

0 3

EF

r

0.4

0.2

0–12

f

EF

0.4

0.2

0

d

0.8

0.6

1.2

1.0

1.6

1.4

EF

0.4

0.2

0

p

EF

0.4

0.2

0

s

EF

0.4

0.2

0

total

0.8

0.6

1.2

1.0

1.6

1.4

2.0

1.8

Fig. 308. Ir. Total DOS (top) and s,p,d,f-like partialdensities of states calculated with the energy bandstructure shown in Fig. 307 [82N].

LΛWavevector k

Ener

gy[e

V]E

0

–1

Γ

–2

–3

–4

1

2

3

4

EF

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

8

7

65

4

3

2

1

∆E = 0.8 ± 0.3 eV

16.4 eV

15.1 eV

17.6 eV

–5

–6

–7

–8

–9

–10

–11

–12

8+

7–

6+

6–

7+

8+

r (111)

Fig. 309. Ir(111). Band structure along ΓL. Solid anddotted lines represent calculation [82N] shown also inFig. 307. Broken lines show empty calculated bandsshifted to higher energies by 0.8 eV to better matchexperimental results. Experimental band mapping dataare marked by various empty and filled symbols,respectively. Vertical arrows indicate direct transitionslabeled by the corresponding photon energies [87M].All data taken with circularly polarized light. For detailssee [87H].







316

LΛWavevector k

Ener

gy[e

V]E

0

–5

Γ

–6

–7

–8

1

2

4

EF

3

–1

–2

–3

–4

5

6

7

9

8

10

11

12

14

13

15

16

17

19

18

20

21

22

23

25

24

13

2

1

3

6

7

9

8

10

11

12

14

13

15

16

17

19

18

20

21

22

23

25

24

1

2

3

Ener

gy[e

V]E

5

–9

–10

3

+ –+

––

r (111)

A B C D F Im kz

0 0.1 0.2 0.3 0.4 0.5 0.6

hν = 16 eV

3

L

– 4

– 2

–1

0

– 3

Wavevector k

Initi

al st

ate

ener

gy[e

V]E i

Γ X

– 5

– 6

EF

r (111) r(100)–(1×1)

Fig. 311. Ir. Experimental band mapping results (openand filled circles) along ΓL and ΓX [80V1]. Arrowsdenote Fermi level crossings derived from variousexperiments, solid lines are calculated bands. For detailssee [80V1].

Fig. 310. Ir(111). Relativistic bulkbands calculated along ΓL withsymmetry types Λ6 (solid lines) and

Λ4+5 (long-dashed). Inclusion of

the imaginary part of the potentialyields the short-dashd empty bands(labeled 1, 2, 3) and the associatedimaginary parts of the wavevectorshown in the right-hand-side panel.The various symbols shown belowEF represent experimental band

mapping results. Vertical linesindicate direct transitions at hν =16 eV [89T]. See also Fig. 317.






317


–10 –1

EF

– 2– 3– 4– 5– 6– 7– 8– 9

r (100)–(1×1)hν = 28 eV

26

24

23

22

21

20

19

18

17.5

17

16

15

14

13 eV

←←←←Fig. 312. Ir(100). Normal-emission photoelectronspectra collected at various photon energies hν from the(1x1) unreconstructed surface [80V1]. See also [80V2].Band dispersion indicated by dashed lines.


–1

EF

– 2– 3– 4– 5– 6– 7– 8– 9

r (100)–(5×1)

hν = 27 eV

26

25

24

23

21

20

19

18.5

18

17

16 eV

Fig. 313. Ir(100). Similar to Fig. 312 but spectracollected from the reconstructed (5x1) surface [80V1].See also [80V2].







318

θ = 66°

4 24Energy [eV]E – EF

–16°

6 8 10 12 14 16 18 20 22

θ = 66°

r (100)–(1×1) r(100)–(1×5)


6 8 10 12 14 16 18 20 22


6 8 10 12 14 16 18 20 224 24Energy [eV]E – EF

6 8 10 12 14 16 18 20 22

–16°

60°

50°

40°

30°

18°

10°

0°

–10°

θ = 66°

–16°

60°

50°

42°38°

16°

10°

0°

–12°

θ = 66°

60°

50°

34°

30°

24°

10°

0°

–16°

60°

50°

40°

30°

20°

10°

0°

–10°–10°

Fig. 314. Ir(100). Top panels: target current spectra from the unreconstructed (1x1) and the reconstructed (1x5)surfaces. Bottom panels: corresponding first derivatives. The numbers on the right side of each spectrum give theangle of electron incidence in the ΓXUL azimuth [92D1].




319


–1

EF

– 2– 3– 4– 5– 6– 7– 8– 9

r (111)

hν = 23 eV

22

21

20

19

18

17

16

14

11.5

11

10.5

10

9.5

9 eV

ss

Fig. 315. Ir(111). Normal-emission photoelectronspectra collected at various photon energies hν [80V1].See also [80V2]. ss denotes a surface state.


Pola

rizat

ion

P

– 1.0

– 6 – 5 – 4 – 2– 3 – 1 0 1

– 0.8

– 0.6

– 0.4

– 0.2

0

0.2

0.4

0.6

0.8

EF

r (111)

Tota

lint

ensit

iyI

0

EF

Part

iali

nten

sitie

s+

,–

II

0

EF

D

C

BA

F

D

C

B

A

F

D

C

BA

F

C

Fig. 317. Ir(111). Normal-emission photoelectronspectra excited by normally incident circularlypolarized light at hν = 16 eV [87M]. Top panel shows

total electron intensity, bottom panel gives partial intensities excited with different spin directions (filled symbols:spin up, open symbols: spin down). Middle panel shows the resulting electron spin polarization [87M]. See also[87M] for normal-emission data taken at various photon energies. See also Fig. 310.








320

–12.5 –10.0 –7.5 –2.5 0

EF

– 5.0

A

B C

r(111)ΓLW

θ = 0°

3°

6°

9°

30°


–15.0

Fig. 316. Ir(111). HeI-excited photoelectron spectra collected at differentelectron exit angles θ [86M]. The features labeled A, B, C are due tosecondary electron emission, compare Fig. 318.




321

7.5 10.0 12.5 17.5 22.5 25.05.0 15.0 20.0Energy [eV]E

A

B

C

r (111)ΓLW

θ = 0°

6°

10°

12.5°

15°

20°

25°

30°

35°

40°

45°

50°

D

Fig. 318. Ir(111). Angle-resolved secondary electron emission spectra taken atvarious exit angles θ along the ΓLW bulk azimuth [86M]. Primary electronenergy 40 eV. E w.r. to EF.




322

7.5 10.0 12.5 17.5 22.5 25.05.0 15.0 20.0Energy [eV]E

A

B

C

r (111)ΓLK

θ = 0°

10°

15°

25°

40°

D

θ = 0°

10°

40°

45°

50°

ΓLU

A

B

C

D

Fig. 319. Ir(111). As Fig. 318 butwith electron emission angle θalong ΓLK (top) and ΓLU(bottom), respectively [86M]. Fora detailed interpretation in terms ofthe bulk band structure see [86M].Primary electron energy 40 eV. Ew.r. to EF.



Ref. p. 337] 2.11 Nonmagnetic transition metals (Pt)


323

2.11.19 Pt (Platinum) (Z = 78)

Lattice: fcc. a = 3.924 Å [71L]Brillouin zone: see section 1.3 of this volumeElectronic configuration: (Xe) 4f14 5d9 6s1

Work-function:φ (poly) = (5.5 ± 0.3) eV [95H]φ (100) (1x1) = (5.5 ± 0.2) eV [92D1]φ (100) (5x20) = (5.4 ± 0.2) eV [92D1]φ (111) = (5.9 ± 0.3) eV [95H]

Table 27. Pt. Core-level binding energies in eV relative to EF. Typical scatter between different sources is± 0.5 eV [95H]. See also [95M].

ns1/2 np1/2 np3/2 nd3/2 nd5/2 nf5/2 nf7/2

n = 4 725.4 609.1 519.3 31.6 314.6 74.7 71.1n = 5 101.7 65.3 51.7 – – – –


Table 28. Pt. Experimental and calculated energies at critical points of the bulk band structure (in eV,with respect to EF).

Critical Experiments Theorypoint [80T] a) [84L] b) [84L, 84E2]

Γ8+ –4.08(7) –4.12(10) –4.11Γ7+ –2.8(1) –2.79(5) –3.07Γ8+ –1.4(1) –1.49(3) –1.40

Γ6– – +19.2 c) +18.5

X7+ –0.45(7) –0.38(3) –0.32

X6+ – +9.7(5) d) +9.0

L6+ – –0.95(5) –0.92L 6– – –0.34(5) –0.36

L4+, 5+ – +0.3(2) d) +0.2

a) ARUPS; b) ARUPS; c) ARUPS [85W1]; d) IPES [88D].















2.11 Nonmagnetic transition metals (Pt) [Ref. p. 337


324

Figures for 2.11.19

0 200 400 800 1000 1400 1600

Cros

s sec

tion

[Mb]

σ


10–2

10–1

1

10–3

4

2

68

10–4

4p

5s

4s

4d4f

5d

6s

Pt

5p

102

10

4

2

68

4

2

68

4

2

68

4

2

68

4

2

68

4f

5d

Fig. 320. Pt. Atomic subshellphotoionization cross sections forphoton energies from 0 to 1500 eV[85Y].

20

30

0 50 100 200 250 350 400

Cros

s sec

tion

[Mb]

σ


10–1

1

40

10

6 10⋅ –2

2

4

6

89

7

5

3

89

2

4

6

89

7

5

3

Pt

Fig. 321. Pt. Photoionization crosssection for the 5d subshell near theCooper minimum [85Y]. Forexperimental data of bulk Pt in theenergy range 10…25 eV see[93V].






325


0900 800 700 600 500 400 300 200 100

4d5/2

4d3/2

4p3/2

4p1/24s

5p

NNN

1100 1000

4f7/2

4f5/2

Pt

Fig. 322. Pt. Overview XPS spectrum taken with unmonochromatized MgKα radiation [95M]. For results with






326

85 83 81 79 7577 73 71 6569 67

71.2 eV


4f7/24f5/2Pt

74.5 eV

Fig. 323. Pt. XPS data showing the region of the spin-orbit-split 4f core levels taken with unmonochromatizedMgKα radiation [95M]. For data measured usingmonochromatized AlKα radiation and a line-shape

analysis see [74H1]. See also [95M].


Inte

nsity

I

b

s

72.0 71.5 71.0 70.5 70.0 69.5 69.0

Pt(111)

Fig. 324. Pt(111). Decomposition of the 4f7/2 core level

photoemission into bulk (b) and surface (s) component[00R]. See also [86D2] and[82B1]. For similar datafrom the (110)-(1x2) surface see [82B1] and [02J]. ForPtxPd1-x(111) surfaces see [02R2].


DOS

–10 – 8 – 6 – 4 – 2 0 2

EF

Pt

Fig. 325. Pt. Valence band XPS spectrum taken withmonochromatized (0.5 eV) AlKα radiation (closed

circles) [74S2], compared with a smoothed version ofthe occupied DOS calculated from the combinedinterpolation scheme, see also Fig. 329 [74S1, 74S2].For a comparison between theory and experiment seealso [76H2]. Results of inverse photoemission in the20…40 eV range are presented for a polycrystallinesample in [82B2].

















327

30.00 2.5 5.0 7.5

Refle

ctiv

ityR


0.1

0.3

0.2

0.5

0.7

0.4

0.6

0.9

0.8

1.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5

Pt

Fig. 326. Pt. Experimental normal-incidence reflectivity data obtainedfrom different experiments[81W1]. For details and tables of"most recommended" data see[81W1]. For theoretical results see[01K1].

500 2 4 86Photon energy [eV]hν

1

3

2

5

7

4

6

8

10 15 20 25 30 35 40 45

Pt

Diel

ectri

c co

nsta

ntε 2

ε2 10–1⋅ε2

scalechange Fig. 327. Pt. Experimental ε2

spectra [81W1]. See also legend toFig. 326. For theoretical results see[01K1].








328

Γ X W L Γ K X

– 8

– 6

– 4

– 2

0

Wavevector k

Ener

gy[e

V]E

EF

Pt

2

4

6

8

10

12

14

– 10

Fig. 328. Pt. Model band structurecalculated within the combinedinterpolation scheme. Spin-orbitcoupling and other relativisticcorrections are included [74S1].

– 8

DOS

[sta

tes

(eV

atom

)]

–1

Energy [eV]E – EF

0

0.50

2.00

1.00

3.00

2.50

1.50

– 6 – 4 – 2 0 2 4 6 8 10 12

DOS

[sta

tes

(eV

atom

)]

–1

Pt

0

0.15

0.05

0.10

0.20

0.35

0.25

0.30

0.40

0.55

0.45

0.50

0.60

(× 5)

EF

–10

0.25

0.75

2.25

1.25

2.75

1.75

Fig. 329. Pt. Density of statescalculated from the band structureshown in Fig. 328 [74S2].





329

KX

4.0

4.2

Ener

gy[R

y]E

Wavevector k

Pt

UΓ X

4.4

Z sWΓ ∆ ΣΛ

EF

3.4

3.6

3.8

2.8

3.0

3.2

2.6

2.5

2.7

2.9

4.1

4.3

3.5

3.7

3.9

3.1

3.3

L LQ

Fig. 330. Pt. Fully relativistic bandstructure based on density-functional theory in the local-density approximation [00T1]. Seealso [96B].

–10

–9

–8

–7

–6

–5

–4

–3

–2

–1

0

XWavevector k

Initi

al st

ate

ener

gy[e

V]E i

∆Γ

Pt(100) EF


Fig. 332. Pt(100). Experimental bulk band dispersion(filled circles) along the ΓX direction [80T]. See also[84L], [84W1] and [88D]. For gap emission inultraviolet photoemission experiments see also [89C].For the surface bands of Pt(100) see [95S].











330

LΛWavevector k

Ener

gy[e

V]E

0

Γ

–6

–8

2

4

EF

–2

–4

6

8

10

12

14

16

18

20

22

24

1 3

2

1

3

6

8

10

12

14

16

18

20

22

24

1

2

3

Ener

gy[e

V]E

–10

3Pt(111)

Im kz

0 0.1 0.2 0.3 0.4 0.5 0.6

1 2

2626

Fig. 331. Pt(111). Relativistic bulk bands calculatedalong ΓL with symmetry types Λ6 (solid lines) and Λ4+5

(dashed). Inclusion of the imaginary part of thepotential yields the dotted empty bands (labeled 1, 2, 3)and the associated imaginary parts of the wavevector

shown in the right-hand-side panel. The varioussymbols shown below EF represent experimental bandmapping results. Vertical lines indicate direct transitionsat hν = 17 eV [89T].




331

L

–4.0

–2.0

–1.0

0

–3.0

Wavevector k

Initi

al st

ate

ener

gy[e

V]E i

Γ X–5.0

EFPt

4 + 5

6

6

6

8+7

6

7

6

7

7+

8+

6–

6+

6+

4 + 5

4 + 5+ +

Λ ∆

–4.5

–2.5

–1.5

–3.5

– 0.5

Fig. 333. Pt. Experimental valenceband mapping results along ΓLand ΓX (various open and filledsymbols resulting from differentexperiments) [85W1] compared tothe band structure calculation of[84E2]. Symmetry labels in doublegroup notation. For data above EF

see [85W1] and [88D].

Pt(110)

–11

– 8

– 6

– 4

– 2

0

1

5

6

3

XΣWavevector k

Ener

gy[e

V]E

Γ

EF

–10

– 7

– 5

– 3

– 1

– 9

5,3

5,4 5,3

5,2

5,4

5,2

6 ,4'–

7 ,5+

6 ,5+

7 ,2+

7 ,3+

6 ,1+

8 ,12+

7 ,25'+

8 ,25'+

6 ,1+

4

2

K

5,1

5,1

5,1

5,1

Fig. 334. Pt(110). Bulk band mapping results alongΓKX (symbols) [86V] compared to calculated bandsfrom [84E2]. Symmetry labels refer to double group,single group notation. Data are recorded for the (1x2)reconstructed surface using spin-polarizedphotoemission with circularly polarized, normallyincident light [86V]. For other spin-resolvingphotoemission experiments see [95I, 96I].












332

–5.0

–4.5

–4.0

–3.5

–3.0

–2.5

–2.0

–1.5

–1.0

–0.5

0

LWavevector k

Initi

al st

ate

ener

gy[e

V]E i

Λ Γ

Pt(111)0.5

4,3 5,3

6,36,1

6,3

6,1

4,3 5,3

6,3

EF

Fig. 335. Pt(111). Bulk band mapping results (filledcircles) from spin-resolved normal-emissionphotoelectron spectra excited with circularly polarizedlight [89G1]. Solid lines represent band structurecalculation of [84E2]. Symmetry labels refer to doublegroup, single group notation. Different symbols areexperimental data from various sources.

–3.5 –3.0 –2.5 – 2.0 – 1.5 – 1.0 – 0.5 0 0.5Initial state energy [eV]Ei

EF

Pt(001)

Fig. 337. Pt(001). Normal-emission photoelectronspectrum taken at hν = 16.85 eV [84L].


–1

EF

– 2– 3– 4– 5– 6– 7

hν = 20.5 eVPt(100)

20.0

19.5

19.0

18.5

18.0

16.0

14.0

11.0 eV


–1

EF

– 2– 3– 4– 5– 6– 7

hν = 30 eV

28

21 eV

1 2 1

26

25

24

23

22

Fig. 336. Pt(100). Normal-emission photoelectron spectra recorded at different photon energies hν [80T].







333

Energy [eV]E–2 0 2 4 5 7 8

Pt(100)

(5 × 20)

Pt(111)

631–1

EF

EF

EF

(1×1)

Fig. 338. Pt(100), Pt(111). Normal-incidenceisochromat spectra from the unreconstructed (100)-(1x1) surface (top), the reconstructed (100)-(5x20)surface (middle) and Pt(111) (bottom). Photon energy9.5 eV [88D]. For results from target-currentspectroscopy at Pt(100) see [92D1].

EF = 0

1

2

3

4

5

6

7

8

9

10

0 1.25Wavevector kII [Å ]–1

0.25 0.50 0.75 1.00

Fina

l sta

te e

nerg

y[e

V]E f

Γ

S

B

B

S

B

X

Pt(001) ΓXUL

Fig. 339. Pt(001). Experimental final state energies as afunction of k|| derived from angle-dependent inverse

photoemission spectra. Unshaded areas denote gaps ofthe projected bulk band structure. Label B and S denotebulk and surface character, respectively. Full (empty)symbols result from prominent (weak) spectral features.Solid lines connect data points to guide the eye. Thedashed line results from a calculation using theoreticalbulk bands and assuming bulk direct transitions [88D].






334


EF

hν = 29 eVPt(111)

26

22

18

17

16

15

14

13 eV


–1

EF

– 2– 3– 4– 5– 6– 7

hν = 29 eV

26

13 eV

2

22

18

17

16

15

14

1– 8– 9– 100–1– 2– 3– 4– 5– 6– 7 21– 8– 9– 10

Fig. 340. Pt(111). Normal-emission photoelectron spectra recorded with p-polarized (left) and s-polarized (right)light at various photon energies hν [80M].




335

– 2 0Initial state energy [eV]Ei

EF

hν = 25 eV

Pt(111)

– 4– 6– 8–10–12–14–16–18

EF

hν = 24 eV

EF

hν = 23 eV

EF

hν = 22 eV

X

X

X

Fig. 341. Pt(111). Normal-emission photoelectron spectrarecorded at photon energiesbetween 22 and 25 eV. The arrowsindicate peaks due to secondaryelectron emission [89T]. For spin-resolving photoemission experi-ments see [84E1, 85O, 88S2].







336


–1– 2– 3– 4– 5

hν = 24.9 eV

Pt(111)

23.9

23.0

22.0

21.0

20.0

19.0

18.1

17.1

16.1

15.1

14.2

13.2

12.2 eV

EF

Fig. 342. Pt(111). Normal-emission photoelectronspectra recorded at different photon energies hνshowing dispersion of bulk bands (dashed lines) andstrong intensity resonances between hν = 20 and 22 eV[85W1]. For angle-dependent spectra see also [92D2].



2.11 Nonmagnetic transition metals (References)


337


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noble metals, noble metal halides and nonmagnetic transition metals

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