Linköping Studies in Science and TechnologyDissertation No. 1303Atomic and Electronic Structures ofClean and Metal AdsorbedSi and Ge Surfaces:An Experimental and Theoretical Study

Johan Eriksson

Surface and Semiconductor Physics DivisionDepartment of Physics, Chemistry and BiologyLinköping University, S-581 83 Linköping, SwedenLinköping 2010

The �gure on the cover shows a top view of the calculated charge density redistribu-tion needed to reach self consistency on a c(4×2) Si(001) surface, see Fig. 1.6(a) onpage 7. The blue large triangular shaped features are positioned at the sites of thedimer down atoms and illustrate volumes that are depleted of charge. The �gurewas rendered using the XCrysDen software.

Copyright © Johan Eriksson 2010, unless otherwise notedISBN: 978-91-7393-433-6ISSN 0345-7524Printed by LiU-Tryck, Linköping, Sweden 2010

AbstractIn this work, a selection of unresolved topics regarding the electronic and atomicstructures of Si and Ge surfaces, both clean ones and those modi�ed by metal ad-sorbates, are addressed. The results presented have been obtained using theoreticalcalculations and experimental techniques such as photoelectron spectroscopy (PES),low energy electron di�raction (LEED) and scanning tunneling microscopy (STM).Si(001) surfaces with adsorbed alkali metals can function as prototype systems forstudying properties of the technologically important family of metal-semiconductorinterfaces. In this work, the e�ect of up to one monolayer (ML) of Li on the Si(001)surface is studied using a combination of experimental and theoretical techniques.Several models for the surface atomic structures have been suggested for 0.5 and1 ML of Li in the literature. Through the combination of experiment and theory,critical di�erences in the surface electronic structures between the di�erent atomicmodels are identi�ed and used to determine the most likely model for a certain Licoverage.In the literature, there are reports of an electronic structure at elevated temper-ature, that can be probed using angle resolved PES (ARPES), on the clean Ge(001)and Si(001) surfaces. The structure is quite unusual in the sense that it appears atan energy position above the Fermi level. Using results from a combined variabletemperature ARPES and LEED study, the origin of this structure is determined.Various explanations for the structure that are available in the literature are dis-cussed. It is found that all but thermal occupation of an ordinarily empty surfacestate band are inconsistent with our experimental data.In a combined theoretical and experimental study, the surface core-level shiftson clean Si(001) and Ge(001) in the c(4×2) reconstruction are investigated. Inthe case of the Ge 3d core-level, no previous theoretical results from the c(4×2)reconstruction are available in the literature. The unique calculated Ge 3d surfacecore-level shifts facilitate the identi�cation of the atomic origins of the components inthe PES data. Positive assignments can be made for seven of the eight inequivalentgroups of atoms in the four topmost layers in the Ge case. Furthermore, a similar,detailed, assignment of the atomic origins of the shifts on the Si surface is presentedthat goes beyond previously published results.At a Sn coverage of slightly more than one ML, a 2√

3 × 2√

3 reconstructioniii

can be obtained on the Si(111) surface. Two aspects of this surface are exploredand presented in this work. First, theoretically derived results obtained from anatomic model in the literature are tested against new ARPES and STM data. Itis concluded that the model needs to be revised in order to better explain theexperimental observations. The second part is focused on the abrupt and reversibletransition to a molten 1×1 phase at a temperature of about 463 K. ARPES and STMresults obtained slightly below and slightly above the transition temperature revealthat the surface band structure, as well as the atomic structure, changes drasticallyat the transition. Six surface states are resolved on the surface at low temperature.Above the transition, the photoemission spectra are, on the other hand, dominatedby a single strong surface state band. It shows a dispersion similar to that of acalculated surface band associated with the Sn-Si bond on a 1×1 surface with Snpositioned above the top layer Si atoms.There has been extensive studies of the reconstructions on Si surfaces induced byadsorption of the group III metals Al, Ga and In. Recently, this has been expandedto Tl, i.e., the heaviest element in that group. Tl is di�erent from the other elementsin group III since it exhibits a peculiar behavior of the 6s2 electrons called the �inertpair e�ect�. This could lead to a valence state of either 1+ or 3+. In this work,core-level PES is utilized to �nd that, at coverages up to one ML, Tl exhibits a 1+valence state on Si(111), in contrast to the 3+ valence state of the other group IIImetals. Accordingly, the surface band structure of the 1

3ML √

3×√

3 reconstructionis found to be di�erent in the case of Tl, compared to the other group III metals.The observations of a 1+ valence state are consistent with ARPES results fromthe Si(001):Tl surface at one ML. There, six surface state bands are seen. Throughcomparisons with a calculated surface band structure, four of those can be identi�ed.The two remaining bands are very similar to those observed on the clean Si(001)surface.

iv

Populärvetenskaplig sammanfattningArbetet som presenteras i den här avhandlingen rör egenskaper hos ytor av kristallintkisel (Si) och germanium (Ge). Atomstrukturen hos dessa material är mycket likaoch kan, likt de �esta fasta grundämnen, beskrivas av en enhetscell bestående av eneller �era atomer som upprepas med en periodicitet given av ett gitter i tre dimen-sioner. Periodiciteten i en riktning bryts vid en yta och den kan därför väsentligenbetraktas som tvådimensionell. Den brutna periodiciteten ger upphov till lokaliser-ade elektrontillstånd, s.k. yttillstånd, som kan vara både fyllda och tomma. Kristall-ytornas orientering anges med beteckningar såsom t.ex. (001) eller (111). På grundav de brutna kristallbindningarna är det, för både Si och Ge, ofördelaktigt ur en-ergisynpunkt att låta ytatomerna behålla samma positioner som om de suttit i etttredimensionellt gitter. En energisänkning kan åstadkommas genom att atomerpå ytan spontant ändrar position och skapar nya bindningar, man säger att ytanrekonstrueras. Rena ytor, och de som är modi�erade av adsorbat, kan uppvisa enrad olika mer eller mindre komplicerade rekonstruktioner med olika egenskaper. Idet här arbetet har egenskaper som laddningsfördelningen på ytan studerats medsveptunnelmikroskopi (STM), ytans periodicitet med elektrondi�raktion (LEED)och yttillståndens egenskaper med vinkelupplöst fotoelektronspektroskopi (ARPES).Samma egenskaper kan studeras för olika atommodeller med hjälp av datorbaseradeberäkningar. Genom att jämföra experimentella och beräknade data har man möj-lighet att identi�era den atommodell som beskriver ytan och tolka de experimentellaobservationerna.På de rena (001)-ytorna av Si och Ge bildas s.k. 2×1-rekonstruktioner närytatomerna bildar par. Dessa ytor är föremål för två studier. I den ena visas attett ovanligt fenomen, där elektroner besätter de vanligtvis tomma tillstånden, bästförklaras av termiska e�ekter. Vid låga temperaturer övergår Si- och Ge-ytornatill att istället uppvisa c(4×2)-periodiciteter. Dessa undersöks i den andra studiendär beräknade energiskillnader hos relativt hårt bundna elektroner används för attförklara experimentella data. Det visar sig att bidrag från grupper av atomer ändaner till fjärde lagret går att identi�era.Tre olika adsorbat har använts för att modi�era Si-ytor. Gemensamt för de tre,litium (Li), tenn (Sn) och tallium (Tl), är att de tillhör gruppen metaller i detperiodiska systemet. De kan dock antas bete sig olika vid adsorption på en Si-ytaeftersom de skiljer sig markant på �era sätt, till exempel storleksmässigt och i antaletv

elektroner som deltar i bindningarna. Ytor modi�erade genom adsorption av Li, Sneller Tl bjuder därför på goda möjligheter att studera många olika fenomen.I litteraturen �nns �era olika modeller för (001)-ytan på Si när den modi�eratsmed Li. I avhandlingen presenteras en studie där experimentella data från ARPESjämförs med beräknade elektronstrukturer och de mest troliga atommodellerna förtvå olika täckningsgrader av Li identi�eras.Vid en täckning som motsvarar cirka en Sn-atom per Si-atom (ett monolager) påen Si(111)-yta bildas en 2√

3 × 2√

3-rekonstruktion. Denna uppvisar en enhetscellsom är tolv gånger större än den för en orekonstruerad yta. Trots den stora enhets-cellen med många atomer, har STM bara påvisat fyra atomer. En dubbellagermodellför ytan �nns beskriven i literaturen. I avhandlingen kombineras alla ovan nämndaexperimentella och teoretiska tekniker för att testa om modellen är rimlig. NyaSTM-resultat visar att det undre lagret förmodligen har en annan struktur och attmodellen bör revideras. Arbetet har också fokuserat på, en för ytan, karaktäris-tisk övergång till en smält fas vid ca 190 ◦C. Observationer av förändringar hosytans elektronstruktur, mätt något under respektive över övergångstemperaturen,kombineras med beräknade resultat och nya slutsatser dras om ytans beska�enhet.Ovanför övergångstemperaturen uppvisar ytan egenskaper som kan förknippas meden blandning av en �ytande och en fast fas.Ordnade efter ökande atommassa består grupp III-metallerna i periodiska sys-temet av aluminium, gallium, indium och tallium. De har alla tre valenselektronersom kan delta i atombindningar (trivalenta). Tl-atomen skiljer sig från de övrigagrupp III-metallerna då den ibland kan bete sig som om den bara hade en valenselek-tron (monovalent). Den här märkliga egenskapen kommer av en relativistisk e�ektsom ger sig till känna för tyngre grundämnen. I tre studier, en på Si(001) och två påSi(111), visas att Tl uppträder i den monovalenta formen för täckningar upp till ettmonolager. Ytans elektronstruktur skiljer sig från den som uppvisas vid adsorptionav de lättare, trivalenta, metallerna i grupp III. En jämförelse med en beräknadelektronstruktur visar att vid en täckning motsvarande ett monolager av Tl, bildasen rekonstruktion som liknar den som de monovalenta alkalimetallerna ger upphovtill på Si(001).vi

PrefaceThis doctorate thesis presents results that were obtained from experimental andcomputational work performed between 2004 and 2009 within the Surface and Semi-conductor Physics Division at the Department of Physics, Chemistry and Biology(IFM) at Linköping University, Sweden. The photoemission and electron di�ractionmeasurements were conducted at beamlines 33, I311 and I4 at the MAX-lab syn-chrotron radiation facility in Lund, Sweden. Scanning tunneling microscopy datawas acquired using a variable temperature microscope at IFM. Density functionaltheory calculations were performed on a computer cluster at IFM and later also onthe Neolith cluster at the National Supercomputer Centre in Linköping.The thesis contains three parts. First a brief introduction to the topic and apresentation of the experimental and theoretical methods used. It is followed by asection with summaries and additional comments to the included papers. The lastsection contains the scienti�c output in the form of seven papers that have eitherbeen published, or have been submitted for publication.

ix

x

List of papersPaper ILithium-induced dimer reconstructions on Si(001) studied by pho-toelectron spectroscopy and band-structure calculationsP.E.J. Eriksson, K. Sakamoto and R.I.G. UhrbergPhysical Review B 75, 205416 (2007)Paper IIOrigin of a surface state above the Fermi level on Ge(001) andSi(001) studied by temperature-dependent ARPES and LEEDP.E.J. Eriksson, M. Adell, K. Sakamoto and R.I.G. UhrbergPhysical Review B 77, 085406 (2008)Paper IIISurface core-level shifts on clean Si(001) and Ge(001) studiedwith photoelectron spectroscopy and DFT calculationsP.E.J. Eriksson and R.I.G. UhrbergSubmitted to Physical Review BPaper IVAtomic and electronic structures of the ordered 2√3×2√3 andthe molten 1×1 phase on the Si(111):Sn surfaceP.E.J. Eriksson, J. R. Osiecki, K. Sakamoto and R.I.G. UhrbergSubmitted to Physical Review BPaper VElectronic structure of the thallium induced 2×1 reconstructionon Si(001)P.E.J. Eriksson, K. Sakamoto and R.I.G. UhrbergSubmitted to Physical Review BPaper VICore-level photoemission study of thallium adsorbed on a Si(111)-(7×7) surface: Valence state of thallium and the charge state ofsurface Si atomsK Sakamoto, P.E.J. Eriksson, S. Mizuno, N. Ueno, H. Tochihara and R.I.G.UhrbergPhysical Review B 74, 075335 (2006)Paper VIIPhotoemission study of a thallium induced Si(111)-√3×

√3 surfaceK. Sakamoto, P.E.J. Eriksson, N. Ueno and R.I.G. UhrbergSurface Science 601, 5258 (2007) xi

My contribution to the papersPaper IPerformed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.Paper IIPerformed the experimental work in collaboration with the co-authors, an-alyzed the data and wrote the manuscript.Paper IIIPerformed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.Paper IVPerformed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.Paper VPerformed the experimental work in collaboration with the co-authors, per-formed the calculations, analyzed the data and wrote the manuscript.Paper VIParticipated in the experimental work and in the discussion of the data.Paper VIIParticipated in the experimental work and in the discussion of the data.

xii

Papers not included1 Abrupt rotation of the rashba spin to the direction perpendicularto the surfaceKazuyuki Sakamoto, Tatsuki Oda, Akio Kimura, Koji Miyamoto, MasahitoTsujikawa, Ayako Imai, Nobuo Ueno, Hirofumi Namatame, Masaki Taniguchi,P. E. J. Eriksson, and R. I. G. UhrbergPhysical Review Letters 102, 096805 (2009)2 Electronic structure of the Si(110)-(16×2) surface: High-resolutionARPES and STM investigationsKazuyuki Sakamoto, Martin Setvin, Kenji Mawatari, P. E. J. Eriksson,Kazushi Miki, and R. I. G. UhrbergPhysical Review B 79, 045304 (2009)3 Surface electronic structures of the Eu- and Ca-induced so-calledSi(111)-(5×1) reconstructionsKazuyuki Sakamoto, P. E. J. Eriksson, A. Pick, Nobuo Ueno, and R. I. G.UhrbergPhysical Review B 74, 235311 (2006)

xiii

xiv

AcknowledgmentsThis work would have been impossible without the help of several individuals andorganizations. They have, in di�erent ways, supported me through the ups anddowns during the studies. I would therefore like to acknowledge:My supervisor, Prof. Roger Uhrberg. I am truly grateful for all his help andsupport in every aspect of my work through the years. His positive spirit has beeninvaluable and I have always felt welcome with my concerns, big or small.Dr. Kazuyuki Sakamoto. I want to thank him as I have had the opportunity tolearn much from his expertise on photoemission and labwork in general. His endlesspatience and good humor has been an inspiration and motivation during the MAX-lab weeks we shared.Mainly Dr. Balasubramanian Thiagarajan, but also Dr. Martin Adell andthe other members of the MAX-lab sta�, for their technical support and trou-bleshooting skills.Dr. Jacek Osiecki, for the time we shared at the STM.Dr. Alexander Pick, for our friendship during my �rst year at IFM.My mentor Prof. Bo Ebenman, for keeping an eye on my progress.Kerstin Vestin, for her immaculate administrative skills.The Swedish Research Council (VR) and the Knut and Alice WallenbergFoundation (KAW), for �nancial support.Andreas G. I am thankful for the time we spent together and for his unreservedway of kindly sharing his opinions on everything.Arvid L and the other students, for making life at IFM enjoyable.My wife Ylva, for her love and support, and our children Hedvig and Arvid, forshowing me the meaning of life.

xv

xvi

List of abbreviations1D, 2D, 3D One, two, three dimensionARPES Angle resolved photoelectron spectroscopyBZ Brillouin zoneDFT Density functional theoryEF Fermi levelESCA Electron spectroscopy for chemical analysisGGA Generalized gradient approximationLAPW Linearized augmented plane waveLDA Local density approximationLDOS Local density of statesLEED Low energy electron di�ractionML MonolayerPES Photoelectron spectroscopyRT Room temperatureSBZ Surface Brillouin zoneSCF Self consistent �eldSCLS Surface core-level shiftSTM Scanning tunneling microscopySTS Scanning tunneling spectroscopyUHV Ultra high vacuumUPS Ultraviolet photoelectron spectroscopyUV UltravioletVBM Valence band maximumXPS X-ray photoelectron spectroscopy xvii

xviii

Contents1 Crystal Structure and Surfaces 11.1 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Electronic structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Si and Ge surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Methods 92.1 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Photoelectron spectroscopy . . . . . . . . . . . . . . . . . . . 102.1.2 Low energy electron di�raction . . . . . . . . . . . . . . . . . 142.1.3 Scanning tunneling microscopy . . . . . . . . . . . . . . . . . 162.2 Computational techniques . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Slab geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Electronic band structure . . . . . . . . . . . . . . . . . . . . 202.2.3 Core-level shift . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Summary and Comments to the Papers 253.1 Paper I: Si(001):Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Paper II: Warm Ge(001) and Si(001) . . . . . . . . . . . . . . . . . . 263.3 Paper III: Surface core-level shifts on clean Si(001) and Ge(001) . . . 283.4 Paper IV: Si(111):Sn . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Paper V: Si(001):Tl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.6 Paper VI and VII: Si(111):Tl . . . . . . . . . . . . . . . . . . . . . . 32Bibliography 354 The Papers 41Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Paper V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Paper VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Paper VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125xix

xx

1.0 Crystal Structure and SurfacesCHAPTER 1

Crystal Structure and Surfaces1.1 Crystal structureAll systems seek to minimize their energy. In nature, this is beautifully manifestedby the crystalline structure of solids. The fundamental components of a crystal arethe lattice and the primitive unit cell. In three dimensions there exist 14 fundamentallattice types [1], also known as the Bravais lattices, which de�ne the symmetry andperiodicity of a crystal. The unit of repetition is de�ned by the primitive unit cell.It can contain a single atom, groups of atoms, ions or combinations of these [2].Truncation of solids gives rise to surfaces. Through the study of the orientation ofthe surface planes in the late 18th century [3], the crystalline properties of solidswere systematically investigated for the �rst time. An important contribution camein 1839, when Miller presented [4] a convenient notation for the orientation of planesand directions in crystals. This index system is widely used and came to be knownas the Miller indices.In Fig. 1.1(a) is an example of a cubic structure. The Bravais lattice is simple cu-bic de�ned by the lattice vectors a, b and c. The primitive cell contains one atom inthis case. Two crystal planes are denoted by their Miller indices and two directionsare illustrated with arrows in the �gure. For many applications, where the momen-tum of the electron is important, e.g. di�raction or electronic band dispersions, itis useful to also de�ne the reciprocal lattice, which is an arrangement of imaginarypoints in reciprocal space described by the vectors a∗, b∗ and c∗. These vectors canbe generated from the three crystal lattice vectors using eq. 1.1. Figure 1.1(b) shows1

Chapter 1. Crystal Structure and Surfaces

Figure 1.1: (a) Crystal lattice of a simple cubic structure with lattice constant a0. TheBravais lattice is de�ned by the vectors a, b and c. Two crystal planes (shaded) are denotedby Miller indices in parenthesis. Two directions, corresponding to the normal directionsof the crystal planes are shown with arrows and denoted by square brackets. (b) Thecorresponding reciprocal lattice de�ned by a∗, b∗ and c∗.the corresponding reciprocal lattice of the simple cubic Bravais lattice in Fig. 1.1(a).The position of the reciprocal lattice points have the form Ghkl, as given by eq. 1.2.Two important concepts of the crystal are related to the reciprocal lattice. First,for every family of equidistant lattice planes in the crystal, there exists a vector be-tween two reciprocal lattice points that is parallel to the normal direction. Second,the interplanar spacing, d, in a family of equidistant crystal planes determines thelength of its corresponding reciprocal lattice vector as 2πd.

a∗ = 2πb × c

a · (b × c)b∗ = 2π

c × a

a · (b × c)c∗ = 2π

a × b

a · (b × c)(1.1)

Ghkl = ha∗ + kb∗ + lc∗ (h, k, l = 0,±1,±2...) (1.2)The primitive unit cell, containing one reciprocal lattice point, can be de�ned inmany di�erent ways. It is often convenient to choose the Wigner-Seitz cell as theprimitive cell. The Wigner-Seitz cell is centered around a reciprocal lattice point andis comprised of all points in reciprocal space which are closer to that lattice pointthan to any other lattice point. Figure 1.2(a) shows the Wigner-Seitz cell (shaded)in the cubic case. Another, more commonly used, name for the Wigner-Seitz cell isthe �rst BZ.It is possible to reach any reciprocal lattice point by translation using a reciprocal2

1.2. Electronic structure

Figure 1.2: (a) The Wigner-Seitz cell (�rst Brillouin zone) of a simple cubic structurecontaining one reciprocal lattice point (dot). (b) High symmetry points and labels.lattice vector. Due to the translational symmetry, an arbitrary vector, k, can betranslated (folded) back into the �rst BZ. High symmetry points in the BZ are givenspecial labels, as shown in Fig. 1.2(b) for the cubic case.1.2 Electronic structureAn electron can be characterized by the wave vector, k, or momentum, ~k. In freespace, the electron has a kinetic energy, Ekin, given by eq. 1.3, and is described bya traveling wave, eq. 1.4. The wave vector must be real-valued since ψk(r) must be�nite. In 1D, the dispersion relation, E(k), has the shape of a parabola. Due to therequirement of conservation of energy and momentum, a free electron cannot absorba photon as illustrated in the 1D case in Fig. 1.3(a).Ekin =

~2|k|22me

(1.3)ψk(r) = eik·r (1.4)In a crystal the situation is di�erent. Here, reciprocal space is partitioned bythe BZ boundaries and momentum can be exchanged with the lattice in units of

~G. The parts of the parabola outside the �rst BZ become accessible by folding,employing reciprocal lattice vectors, G, see Fig. 1.3(b). This situation describesthe electronic band structure of a crystal. Excitation by means of a photon ispossible in this case, provided that the energy of the photon, hν, matches the energyseparation between the initial state and an unoccupied state at higher energy. Thetransition is nearly vertical since the momentum carried by the photon, hνc, is several3

Chapter 1. Crystal Structure and Surfaces

Figure 1.3: One dimensional example of electronic energy dispersions. (a) Energy disper-sion of an electron in free space. Excitation by a photon with energy hν is not possible asthis would require a much larger addition to the momentum than what is provided by thephoton. (b) Energy dispersion of an electron in a crystal with a weak periodic potential.Photoexcitations are possible through interaction with the lattice. Crystal momentum canbe transferred in units of ~G, where G is a reciprocal lattice vector. Bragg re�ections occurwhere the wave vector is a multiple of 1

2G, dotted lines. As a consequence, forbidden en-ergy gaps appear. (c) Schematic examples of three electron wave functions; 1) an electronin an in�nite crystal, 2) and 3) show a bulk state and a surface state, respectively, near acrystal surface.orders of magnitude smaller than the crystal momentum, ~G. As the electrons arein�uenced by a periodic potential, they are described by Bloch functions [1]. Theseare traveling waves modulated by a function, uk(r), as illustrated in Fig. 1.4. Atcertain points, or planes in 3D, the electron wave vector ful�lls eq. 1.5. These areso called Bragg planes [2]. Electrons with such wave vectors cannot propagate asstrong backscattering results in the formation of standing waves. This is referredto as Bragg re�ections, and it introduces further changes to the band structure. InFig. 1.3(b) this is shown by the opening of band gaps at the BZ boundaries.

|k| = |k − G| (1.5)When a crystal is terminated by a surface, the requirement that the wave vectoris real-valued is lifted due to the partitioning of space that the surface brings about.Additional solutions are possible when the exponentially decaying wave functionoutside the crystal is matched to the Bloch functions inside. Exponentially decayingwave functions inside the crystal describe surface states when modulated by uk(r),see Fig. 1.3(c). The energy levels associated with states localized at the surface canonly exist in the band gap regions of the in�nite crystal [5]. A surface resonanceis a state that is a mix of a surface state and bulk states. Energy levels of surfaceresonances can therefore overlap with the bulk band structure. The discovery of4

1.3. Si and Ge surfaces

Figure 1.4: Examples of the complex part of Bloch wave functions in 1D. (a) A function,uk(x), with the same periodicity, a, as the crystal lattice. b) Wave functions of freeelectrons, eq. 1.4, with various values of k are drawn with dotted curves. The solid curvesillustrate the corresponding Bloch functions of electrons in a crystal.surface states immediately started intense research activities. See Ref. [6] for ahistorical overview.Being con�ned to the surface plane implies that the surface states have a 2Dcharacter, i.e., the surface bands show no dispersion in the direction perpendicularto the surface. Utilizing this property, and the fact that they appear in bulk bandgaps facilitate an identi�cation of the surface states experimentally. Furthermore,surface states are more a�ected by contamination from the gas environment thanbulk states.1.3 Si and Ge surfacesSi and Ge are very similar elements. They belong to the group of semiconductors inthe periodic table and both exhibit a tetrahedrally bonded atomic structure. Bothhave attracted a lot of attention from a scienti�c point of view. Furthermore, Sihas gained strong commercial interest as well [7]. Surface and interface properties ofsemiconductors play an important role in the development of electronic components.In the study of various surface and interface phenomena, Si and Ge surfaces o�erseveral bene�ts. They can provide well ordered surfaces with a low defect density [8]and can be used, clean or modi�ed by adsorbates, as model systems for more com-plicated structures. The band gap of semiconductors enables the study of surfaceelectronic states without interference from bulk states. 5

Chapter 1. Crystal Structure and Surfaces

Figure 1.5: (a) Conventional cubic unit cell of the diamond lattice. Crystal axes and the(001) and (111) planes are indicated. (b) and (c) Reciprocal lattice and surface Brillouinzones of the (001) and (111) surfaces, respectively. The directions of the basis vectors areshown.Si and Ge both exhibit the diamond structure, i.e., a face centered cubic struc-ture with two atoms in the basis as illustrated in Fig. 1.5(a). A layer of surfaceatoms shows no translational symmetry in the normal direction. As a result, thereciprocal lattice of a surface is a two-dimensional grid spanned by two reciprocallattice vectors, a∗ and b∗. The reciprocal lattices and SBZs of the two surfaces usedin this work, (001) and (111), are shown in Figs. 1.5(b) and (c).The formation of a surface involves the breaking of atomic bonds. It is howeverenergetically unfavorable to have unpaired electrons, dangling bonds, at the surface.As a consequence, the surface reconstructs. Bonds and atoms are rearranged atthe surface to facilitate a lowering of the surface energy. If the periodicity of thesurface is altered as a consequence of the reconstruction, a superlattice [9] is usedto describe the new reconstructed surface. The commonly used notation is afterWood [10] and has the form (p × q) − R◦. The length of the basis vectors of thesuperlattice are given by the integers p and q, in units of the lattice vector lengthsof the bulk terminated structure. If there is any rotation of the superlattice vectorsrelative to the underlying lattice, it is indicated by an angle R◦.Si(001) and Ge(001)Ideal bulk truncated Si(001) and Ge(001) surfaces consist of atoms with two danglingbonds each in a square lattice. In 1957, Schlier and Farnsworth showed that Si(001)exhibits a (2×1) surface periodicity after cleaning in UHV. It was suggested thatthe surface atoms shift laterally to form pairs, dimers. By participating in the dimerbond, one dangling bond per atom is eliminated. In this model, a half �lled danglingbond state would exist at each surface atom. Following these results there was a6

1.3. Si and Ge surfaces Figure 1.6: (a) Atomic structure of thec(4×2) reconstruction on clean Si(001)and Ge(001). The dimer atoms areshown in gray and, in addition, the up-atom is drawn with a larger circle. Theshaded area shows the unit cell. In (b),the c(4×2) and 2×1 SBZs are drawn bysolid and dotted lines, respectively. Dueto the existence of two surface domains,the c(4×2) and 2×1 SBZs appear withtwo orientations as illustrated by 1) and2).discussion on how these symmetric dimers could explain the semiconducting natureof the surface. This was resolved in 1979, when theoretical calculations by Chadishowed that tilted dimers are energetically preferable over symmetric ones. SeeRef. [7] for a historical summary of the advancements in the understanding of theSi(001) surface.Above a temperature of about 200 K the dimers change tilt direction rapidly.Ge(001) behaves in a similar way. At reduced temperature, the rate of �ippingis reduced. Through interaction between neighboring dimers, both Si(001) andGe(001) can then assume a c(4×2) reconstruction with alternating tilt directionboth along and perpendicular to the dimer rows, as shown in Fig. 1.6(a). At elevatedtemperatures, on the other hand, both surfaces transform into a 1×1 phase.The similarities between Si(001) and Ge(001) are also evident from the surfaceband structure. Figure 1.7 shows ARPES data from low temperature c(4×2) re-constructed Si(001) and Ge(001). The data was obtained along the [010] direction,see Fig. 1.6(b). This direction is special since identical k|| points in the SBZs of thetwo domains on the surface, shown as 1) and 2) in the �gure, are probed. The twodomain surface is a consequence of ML high atomic steps that are always present.Papers II and III deal with di�erent aspects of the clean Si(001) and Ge(001)surfaces. In papers I and V, the Si(001) surface was studied when modi�ed byadsorbates.Si(111)The ideal bulk truncated Si(111) surface consists of atoms in a hexagonal lattice withone dangling bond each. In UHV, it forms a metastable 2×1 reconstruction of π-bonded chains when prepared by cleaving [11]. Upon annealing to about 650 K, theSi surface irreversibly converts into a 5×5 phase, and at about 800 K it transforms7

Chapter 1. Crystal Structure and Surfaces

Figure 1.7: Band structure of the c(4×2) reconstructed Si(001) and Ge(001) surfaces,measured at 100 K using ARPES along the [010] direction as shown in Fig 1.6(b). Thedata was acquired using linearly polarized photons with 21.2 eV energy.into a 7×7 structure [12]. In 1985, the 7×7 reconstruction was described by thedimer-adatom-stacking fault (DAS) model proposed by Takayanagi et al. [13]. TheDAS model can be generalized to (2n+1)×(2n+1) models, and describes the 5×5phase as well. At about 1100 K the Si(111) surface transforms to a 1×1 phase.Adsorbate modi�ed Si(111) surfaces are discussed in Papers IV, VI and VII.

8

2.0 MethodsCHAPTER 2

Methods2.1 Experimental techniquesTo minimize the disturbance from unintentional reactions during experiments a con-trolled environment is required for the study of the atomic and electronic propertiesof surfaces. Molecules in a gas environment will adsorb on surfaces until equilib-rium is reached. All experiments must therefore be conducted in vacuum in orderto minimize the e�ect of adsorbed species. The quality of the vacuum ultimatelydetermines the time until the surface becomes too contaminated for further exper-iments. Equation 2.1 [14] gives the adsorption time, τ , for one ML as a functionof the partial pressure, p, and the molecular mass of the gas species, m. Also thenumber of atoms in a ML, n0, and the temperature, T , are important parameters.Some typical values are given in Ref. [14].

τ(p) =n0

√2πmkBT

p(2.1)To maintain a su�cently clean surface during the experiment, a base pressure ofabout 10−10-10−11 torr is required. This is what is referred to as the UHV regime.See Ref. [14] for a review of UHV technology.Synchrotron radiation sources, see Ref. [15] for a thorough introduction, havebeen used for the photoelectron spectroscopy studies in this work. These sourceso�er many advantages over conventional laboratory sources [14] such as gas dischargelamps or X-ray tubes. The ability to tune the photon energy is perhaps the most9

Chapter 2. Methodsstriking one, but also the high �ux and polarization of the photons are importantproperties.2.1.1 Photoelectron spectroscopyPES is one of the most important techniques in surface science [9], and has beenso for many decades. The method is based on fundamental discoveries in the late19th and early 20th centuries by Hertz (1887), Lenard (1894), Thomson (1899) andEinstein (1905), see Ref. [16] for a historical review. The use of PES in materialanalysis was however delayed due to technical challenges like the construction ofelectron energy analyzers, electron detectors, UHV compatible photon sources andgeneral UHV equipment. Eventually the technology matured and, with the workled by Siegbahn [17], su�cient resolution was reached to turn X-ray PES into atruly useful tool in 1957. Shortly thereafter, in 1962, Turner [18] demonstrated asetup with UV excitation. It was in 1964, in the group led by Siegbahn, that PESin the form of ESCA [19] was �rst used as a method to study material propertieslike chemical composition and chemical environment of atoms.In PES, electrons in a sample are excited by photons with a well de�ned energy,hν, that is higher than the work function, φ, of the material studied. The intensityof the emitted electrons is measured as a function of their kinetic energies, Ekin,using an electron analyzer either in the spatial domain, hemispherical or cylindricalmirror analyzers [20], or in the temporal domain, time-of-�ight analyzer [21].For the analysis of the electronic states in a material, it is often useful to displaythe recorded electron distribution curves as a function of electron binding energy,Eb, instead of Ekin. The expression for Eb is given by eq. 2.2.

Eb = hν − φ − Ekin (2.2)Of the emitted photoelectrons, those originating from states at EF will have thehighest kinetic energy, hν − φ. The Fermi energy is used as the reference level,corresponding to Eb = 0, as illustrated by the schematic spectrum in Fig. 2.1. Theenergy position of EF cannot be determined from spectra recorded from all materials,e.g., in non-metallic samples there are no electronic states at the Fermi energy, andhence no photoelectron intensity. Instead the position of EF can be measured on ametallic part of the sample holder that is in electrical contact with the sample.10

2.1. Experimental techniquesB

ind

ing

ene

rgy

Photoelectron intensity

Valence band

ARPES

Core states

XPS

Inelastically

scattered

electrons

Valence band

Fermi level

Vacuum level

Core states

Kin

tetic e

ne

rgy

0

Bin

din

g e

ne

rgy

0

Sample Electron analyzer Spectrum

Figure 2.1: Schematic overview of the energy levels involved in photoelectron spec-troscopy. Electrons in bound states in a sample with a work function, φ, are excitedby photons with energy hν. The intensity of the photoemitted electrons are measured as afunction of their kinetic energies, Ekin. Electrons from states at EF have a kinetic energyof hν − φ. This energy position is used as the zero level in the resulting spectrum, wherekinetic energy has been converted to binding energy.Angle resolved photoelectron spectroscopyBy adding the ability to control and measure the angle at which the photoelectronsare detected, one enters the �eld of ARPES. This technique is particularly useful forstudying electronic structures in surface science. Figure 2.2 shows the geometry ofan ARPES experiment. Emitted electrons are characterized by their wave vector,k, in momentum space, the polar angle, Θe, and the azimuthal angle, ϕ. The wavevector can be decomposed into two components as shown in eq. 2.3, one parallel andone perpendicular to the surface.

k = k|| + k⊥ (2.3)Transport across the material boundary changes the perpendicular componentas a consequence of the energy loss due to the work function. The two-dimensionalcharacter of the surface states implies that their dispersion relations are functions11

Chapter 2. Methods

Figure 2.2: Geometry of an ARPES experiment. Photons hitting the sample at anincidence angle of Θi emit electrons from the sample. The electron intensity is analyzedas a function of k and the polar, Θe, and azimuthal, ϕ, emission angles. The surface bandstructure is obtained when these parameters are converted to binding energy and k||.of k||. This component remains unchanged, modulo a two-dimensional reciprocallattice vector G||, when electrons cross the sample boundary. Using the geometry inFig. 2.2, the parallel component can be extracted from eq. 2.4.

|k||| = |k|· sin Θe (2.4)By combining eq. 2.4 with the expression for the kinetic energy of a free electron,eq. 1.3, an expression relating the momentum parallel to the surface to the kineticenergy of the electrons is obtained, see eq. 2.5.k|| =

√2me

~

√

Ekin· sin Θe (2.5)The photoelectron intensity in the entire 2D k||-space can be probed by varyingΘe and ϕ. Figure 1.7 shows two examples of ARPES data, where the surface bandstructures of the Si(001) and Ge(001) surfaces were probed along the [010] directionusing 21.2 eV photons from beamline I4 at the MAX-III synchrotron radiation sourceat MAX-lab in Lund, Sweden.12

2.1. Experimental techniques Figure 2.3: The universal mean freepath curve calculated in units of MLequivalents. The curve is valid for bothSi and Ge since their ML spacings ac-cording to eq. 2.6, Si: 0.272 nm andGe: 0.282 nm, are very similar.Core-level photoelectron spectroscopyCore electrons are more tightly bound than valence electrons and their wave func-tions are more localized. As a consequence, they do not show any energy dispersionand are of limited interest for ARPES studies. Instead they can be used to examinecomposition of a sample and the chemical environment of the atoms in a crystal[19]. Core-level spectroscopy can also be used to determine the contamination of asurface during sample preparations. No intensity from the C 1s or O 1s core-levelsindicates that the surface is atomically clean. Core-levels are accessible using bothXPS (e.g. C 1s, Eb=284 eV and O 1s, Eb=543 eV) and UPS (Ge 3d, Eb=29.8-29.2 eVand Sn 4d, Eb=24.9-23.9 eV) [22].Core-level spectra consist of a background and superimposed contributions fromatoms in di�erent environments. They can be analyzed through a peak �ttingprocedure where the spectra are decomposed into components with a suitable lineshape. The background can be modeled as proportional to the integrated spectralintensity of photoelectrons with higher kinetic energy [23], or as an exponentialfunction if the kinetic energy of the core-level electrons is low so that inelasticallyscattered electrons constitute the major part of the background.Information of the depth from which the measured electrons originate is valuablesince it allows for a characterization of di�erent atomic layers. The degree of surfacesensitivity in an experiment is determined by the energy of the incoming photonbeam and by the geometry of the experiment. The photon energy determines thekinetic energy of the photoelectrons.It has been found empirically [24] that the mean free path of the electrons, λm,as a function of their kinetic energy follows what is often referred to as the universalcurve. It quite accurately describes the behavior of electrons with kinetic energiesbetween a few to a few thousand eV. Figure. 2.3 shows the electron mean free path in13

Chapter 2. Methodsunits of ML. It was calculated using the best �t expression for elemental solids, seeeq. 2.6 [24], and is valid for Si and Ge since their ML spacings, a, are very similar.From the geometry of the experiment it follows that at a higher emission angle,Θe, electrons originating from a depth z must travel a longer distance of z

cos Θebefore they reach the surface. This results in an enhanced surface sensitivity aselectrons from sub surface layers su�er a greater risk of energy loss through scatteringbefore being emitted.λm(ML) =

538

E2kin

+ 0.41 ·√

a ·√

Ekinwhere a(nm) =

(

Molecular weight(g/mol)

ρ(kg/m−3) · NA(mol−1)

)1/3

· 108 (2.6)Knowing the mean free path, one can use a Beer-Lambert type expression, eq. 2.7[25], to estimate the photoelectron yield, I, from di�erent depths, z.I(z) ∝ e

“

−zλ·cos Θe

” (2.7)Most electrons su�er losses through inelastic scattering on their way out. UsingPES, these electrons can be seen as a high background at lower kinetic energies.This is shown schematically in Fig. 2.1.2.1.2 Low energy electron di�ractionLEED is a quick and simple tool, which can provide information on e.g. surfacequality, geometry of the unit cell and the disposition of atoms in the unit cell onthe surface [26]. In a LEED experiment, electrons, with kinetic energies usually inthe range 30 to 300 eV and a momentum vector k0, typically hit the sample surfaceat normal incidence. It is the wave nature of the electrons that is utilized as theyare di�racted by the atoms in the �rst few layers of the surface due to the shortmean free path. To make the analysis of the di�racted electrons feasible, thosethat have su�ered energy losses due to some inelastic process are �ltered out bymetallic meshes at di�erent voltages in the LEED optics. The remaining, elasticallyscattered, electrons pass through and hit a �uorescent screen which is monitoredeither by a camera or inspected directly by eye.The di�racted electrons, with momentum vector k, ful�ll the 2D analog of theLaue equations in the surface plane, eq. 2.8 [9], and give rise to a spot pattern14

2.1. Experimental techniques

Figure 2.4: a) A schematic representation of the two c(4×2) reconstructions with di�erentorientations that are present on both Si(001) and Ge(001). b) The corresponding reciprocallattices. c) The two reciprocal lattices superimposed. d) The experimentally observedLEED pattern of Ge(001) c(4×2).on the screen. Ghk is a reciprocal lattice vector in the surface plane, as de�nedby eq. 2.9. The coherence length of the electrons in the incoming beam is usuallyaround 100 Å [27]. This imposes two limitations on the size of the structures thatcan be resolved using LEED. First, only structures with a periodicity smaller thanthe coherence length can produce di�raction spots in a LEED experiment. Second,ordered regions that are smaller than the coherence length will result in di�use spots.The smaller the ordered regions are, the more di�use the spots become.Ghk = k|| − k0|| (2.8)

Ghk = ha∗ + kb∗ (h, k = 0,±1,±2...) (2.9)As an example of LEED, consider the c(4×2) reconstruction which was intro-duced in Sect. 1.3. Figure 2.4(a) schematically shows the surface with two orien-tations of the unit cell as a result of the two surface domains. In Fig. 2.4(b) arethe corresponding reciprocal lattices. LEED is an area integrating technique due15

Chapter 2. Methods

Figure 2.5: Energy levels in an STM experiment with a semiconducting sample and ametallic tip. (a) A negative sample bias, V, results in a shift of the sample density ofstates to higher energy relative to the tip. Tunneling from occupied states of the sampleis possible within the energy range eV from EF . (b) Tunneling to unoccupied states of thesample is illustrated for a positive sample bias.to the spot size of the electron beam (∼1 mm2), thus the resulting LEED patternhas contributions from both domains. Figure 2.4(c) shows two overlapping recipro-cal lattices and the real LEED pattern, in the case of Ge(001) c(4×2), is shown inFig. 2.4(d). In the analysis of the pattern, the shape, size, position and intensity ofthe spots contain information on the surface structure.2.1.3 Scanning tunneling microscopyThe quantum mechanical concept of tunneling can be used to obtain atomicallyresolved images of surfaces. Electrons in a solid sense a barrier, the work function,which prevents them from leaving the material. As this barrier height is �nite, partof the electron wave function will extend outside the surface of the material, cf.Fig. 1.3(c). When two pieces of material are brought close to each other, electronshave a probability to tunnel through the barrier to the other side. By utilizing the16

2.1. Experimental techniques

Figure 2.6: Two constant current STM images acquired at RT showing the same 50×45Å2 area on a Si(111) sample with an average Sn coverage of approx. 1 ML. Empty and �lledstates on the surface are probed using sample biases of +0.5 and -0.8 V in the respectiveimage. A 2√

3 × 2√

3 unit cell is shown by dotted lines and an adjacent area with lowerSn coverage shows a √3 ×

√3 reconstruction as seen in the top left corner of the images.electron tunneling between a metallic tip and a sample surface separated by a verysmall distance, Binnig and Rohrer managed to construct the �rst STM in 1981 [28].In 1982 they could, together with Gerber and Weibel, present topographic picturesof surfaces on an atomic scale [29].Using STM, the electronic states a few eV around EF can be probed. Twomodes of operation are commonly used as the tip is swept over the surface. Inthe constant current mode, a feedback system regulates the tip z position, i.e., theheight over the sample, so that the tunneling current is kept at a preset value. Theimages are obtained from the z variation of the tip. In the constant height mode,no feedback is used and variations in the tunneling current are used to image thesurface. By changing polarity of the bias voltage between the tip and the sampleboth occupied and unoccupied states can be probed as illustrated in Figs. 2.5(a) and(b). By acquiring images at di�erent bias voltages, information about the spatialdistribution of the orbitals, that are contributing to surface states at di�erent energypositions relative to EF , can be obtained. Figure 2.6 shows two images where emptyand �lled states on the 2√

3 × 2√

3 Si(111):Sn surface are probed. It is apparentthat the empty and �lled states are distributed di�erently. Four features can beresolved inside the 2√

3 × 2√

3 unit cell in the image showing empty states, whileessentially only one feature is seen when �lled states are probed. The features inthe STM images are the combined result of electronic and topographical variationson the surface and do not necessarily re�ect the atomic positions.Current vs. voltage curves, I-V curves, can be obtained if the tip is held sta-17

Chapter 2. Methodstionary over the surface while the tunneling current is measured over a range ofbias voltages. This is an STS method that can be used for estimating the LDOSaccording to eq. 2.10 [14].LDOS ∝ dI/dV

I/V(2.10)2.2 Computational techniquesAll calculated material properties presented in this work were obtained using meth-ods in the DFT based software package WIEN2k [30]. The framework of DFT wasestablished in two papers, by Hohenberg and Kohn [31] in 1964 and by Kohn andSham [32] in 1965. With DFT, the complicated many-body Schrödinger equationis reduced to a series of single particle equations which are solved using a self con-sistent scheme. The total energy, E, is in DFT given as a functional of the electrondensity, ρ(r), as shown in eq. 2.11, see [33]. All material speci�c parameters, likegeometry and atomic species, are contained in the external potential Vext(r). F [ρ] isa universal functional of ρ, and the framework of DFT states that the ground statedensity yields the minimum value of E, i.e., the ground state energy.

E[ρ] = F [ρ] +

∫

ρ(r)Vext(r)dr (2.11)Even though DFT is formally exact (within the Born-Oppenheimer approxima-tion) [34], usually not all parts of the universal functional F [ρ] are known exactly [35].More speci�cally, it is the form of the exchange-correlation energy functional thatis unknown. LDA and GGA are the two most common methods for approximationsof this term.The method implemented in WIEN2k for the practical use of DFT is LAPW,see [36]. Compared to pseudopotential methods, it is an all electron scheme. Theelectrons are divided into core electrons and valence electrons by a cut-o� energy.Space is partitioned [33] into non-overlapping atomic spheres centered on the nuclei,called mu�n-tin spheres, where core electrons are described by linear combinationsof radial functions and spherical harmonics. There is an interstitial region, withvalence electrons described by plane wave expansions. The use of all electron meth-ods permits direct access to the core electrons for obtaining, e.g., surface core-levelshifts.18

2.2. Computational techniques

Figure 2.7: Examples of symmetric and H-terminated Si(001):Tl 2×1 slabs are shownin (a) and (b). The shaded region is the unit of repetition. (c) shows the band structurenear EF obtained using the two slabs. The use of a symmetric slab can induce an arti�cialsplitting of the surface bands as indicated by A and B.2.2.1 Slab geometryThe calculations were performed on structures that, in the computational scheme,are repeated in all directions. To do a surface calculation, a slab structure withvacuum as spacing in one direction is necessary. Two examples of surface slabs areshown in Figs. 2.7(a) and (b). The unit of repetition, shaded, contains a vacuumregion which separates the slabs in the direction perpendicular to the surface. Thedistance between consecutive slabs must be su�ciently large to avoid interactionbetween surfaces of neighboring slabs. The interior of the slab serves a similarpurpose. It acts as a bulk bu�er region and separates the surface from the arti�cialbackside of the slab. It must therefore be su�ciently thick.In a slab geometry, two surfaces are created, i.e., the top and bottom ones. Thereare two ways of dealing with this situation. One can either use a symmetric slab,Fig. 2.7(a), or one can create an arti�cial bulk termination using hydrogen atoms(H), Fig. 2.7(b). A disadvantage with the symmetric slab approach is shown inFig. 2.7(c). Interaction between surface states on opposite sides of the slab cancause a splitting of the surface bands. The disadvantage with a H-terminated slabis the computational cost. The lack of inversion symmetry necessitates complex-valued calculations, instead of real-valued in the symmetric case. Furthermore,the small bond length associated with the H-termination layer demands a small19

Chapter 2. Methods

Figure 2.8: Calculated band structure near EF of a Si(001) surface in a 2×1 reconstruc-tion as shown in (a). The path in the SBZ that is traversed is shown in Fig. 2.9(a). (b)Surface bands with contributions from U, D and the second layer atoms, S. In (c) thecontribution from atom U is decomposed into di�erent orbitals, s, px, py and pz. The sizeof the circles is proportional to the contribution to the band from the respective atom andorbital.mu�n-tin radius, that in turn results in an increased cut-o� energy for the planewave expansion. These calculations can be extremely time consuming since thecomputational time scales as the ninth power [36] of the plane wave cut-o�.2.2.2 Electronic band structureSurface band structure calculations are useful for comparing with ARPES results.Surface band dispersions can be compared e.g. to test a theoretical model or toidentify experimentally obtained bands. In Fig. 2.8 the contributions to the surfaceband structure of a Si(001) 2×1 surface, see Fig. 2.8(a), is resolved down to speci�corbitals on individual atoms.Two strong surface bands are associated with atoms U and D. Furthermore, aback bond state associated with atom U and a second layer atom, S, can be seen inthe band structure around Γ in Fig. 2.8(b). From the orbital decomposition of thecontribution from atom U in Fig. 2.8(c) it is evident that the strong band mainlyoriginates from dangling bond pz orbitals, but also some s contribution is seen nearthe SBZ boundaries. The back bond contribution comes from py orbitals around Γ.20

2.2. Computational techniques

Figure 2.9: Calculation of the bulk band projection onto the SBZ. (a) A path Γ − J −K − J ′− Γ− J ′

2 is shown in a 2×1 SBZ (dotted lines). The underlying bulk truncated 1×1SBZ is shaded. (b) The same path shown at three di�erent heights, A-C, in the bulk BZ.(c) Band structures along the path at A, B and C. (d) The bulk band projection estimatedby 26 superimposed band structures obtained at di�erent heights between A and C.Even though a study might be aimed at the surface band structure, it can alsobe useful to keep track of the bulk band structure. In Fig. 1.7 the shaded areasindicate the projection of the bulk bands onto the SBZ. Bands that are not inside theprojection originates from surface states. The projection of the bulk band structureonto the 1×1 SBZ was calculated using a bulk 1×1×1 cell such as the one shownin Fig. 1.5(a). Figure 2.9(a) shows the same path in the SBZ as was traversedin the calculation presented in Fig. 2.8. In Fig. 2.9(b) this path is shown in the3D conventional reciprocal lattice cell. The projection of the band structure ontothe SBZ (shaded), is obtained by traversing this path at di�erent heights in theBZ, i.e., at di�erent k⊥ values. Figure 2.9(c) shows the band structure at threedi�erent heights, A-C. The bulk band projection is built by superimposing severalsuch images. Figure. 2.9(d) shows the situation when the BZ has been sampled at26 di�erent values of k⊥. 21

Chapter 2. MethodsEtotal

Enon-ionized

With screening

Total energies

Etot-bulk

Etot D Etot U

Ebinding

D U

E2p

E2p-bulk

E2p D E2p U

No screening

Core-state eigenenergies

Ebinding

D U

E =0B E =0BFigure 2.10: Energy levels in SCLS calculations. Results for the Si 2p SCLSs obtainedfor a Si(001) c(4×2) surface, see Fig. 1.6(a), are shown schematically in the �gure. Uand D refer to the up- and down-atoms of the dimer. In the case of no screening 2peigenenergies are compared. The average of the 2p eigenenergies of atoms in the centerof the slab, E2p−bulk, serves as bulk reference. The 2p SCLS of atoms U and D are 2peigenenergy deviations from this value. When screening is included, total energies areinstead compared. The average total energy obtained when atoms in the center of the slabare ionized Etot−bulk is used as bulk reference. The 2p SCLS of atoms U and D are totalenergy deviations from this value when atoms U and D are ionized, respectively.2.2.3 Core-level shiftIn core-level studies, the possibility to resolve the core-level shift of individual atomsis of great value. In theoretical calculations, these shifts can be computed with vari-ous degrees of screening included, i.e., relaxation of the valence electrons in responseto the core-hole. When screening is included, the SCLS calculations can becomecomputationally very demanding. There are three reasons for this. One stems fromthe fact that each atom must be treated individually. The second reason is the iso-lation of the core-hole, i.e., interaction laterally between core-holes in adjacent slabsshould be avoided. Thus, the unit of repetition must in general be larger or havea lower symmetry than in a band structure calculation. Finally, the perturbationthat the core-hole introduces can lead to slow convergence in the calculations. Fig-ure 2.10 illustrates the energy levels involved in the SCLS calculations, without andwith screening. Screening e�ects are important for metals [37] where the valenceelectrons are very mobile and respond strongly to core-holes. It has also been shownto be important for Si and Ge surfaces [38].In the case of Ge, the electrons in the 3d states are in the calculations normallytreated as valence electrons. In experiments, however, they are considered as coreelectrons with no energy dispersion despite their low binding energy. Treating themas core electrons in the calculations results in core charge leakage out of the mu�n-tin spheres. Calculations with screening included can still be performed using a22

2.2. Computational techniquestwo window semi-core approach [36]. The procedure starts with one electron beingremoved from a 3d state on one of the Ge atoms. One single iteration of the SCFprocedure is run with the 3d states treated as core states, despite the charge leakage.The result is a shift of the 3d state of the ionized Ge atom to a slightly higher bindingenergy compared to the other, neutral, Ge atoms. In the next step, the 3d levels ofthe ionized atom as well as the neutral atoms, are then treated as valence states.The energy range of the valence states are separated into two windows by an energycut-o�, which is chosen to be between the down shifted 3d level and the 3d levels ofthe other Ge atoms. By keeping the occupancy one electron short in the window ofthe down shifted state, one is e�ectively creating a localized hole in the distributionof valence electrons. In the second window the occupation is not changed. Thistechnique is applied to all individual atoms of interest and the corresponding SCFprocedures are completed, this time with no core leakage. The SCLSs are extractedfrom the converged total energy di�erences in the same manner as is illustrated inFig. 2.10. The Si 2p core-level can be treated properly without core charge leakagewith the regular approach as well as the two window technique. Tests have shownthat the two methods produce very similar results of the SCLSs.

23

24

3.0 Summary and Comments to the PapersCHAPTER 3

Summary and Comments to the Papers3.1 Paper I: Si(001):LiMetal-semiconductor interfaces are important from a technological point of view.The alkali metals have a single s electron in the valence band and can, in com-bination with semiconductor surfaces, be used as prototype systems for studyingsuch interfaces. In paper I, the adsorption sites of Li on Si(001) are investigatedusing photoelectron spectroscopy and band-structure calculations. In the literature,four di�erent models of a 2×2 reconstruction with 0.5 ML of Li have been pro-posed [39, 40], while three di�erent models for a 2×1 reconstruction with 1 ML of Lihave been proposed [40, 41, 42]. ARPES results from the [110] and [110] directionswere obtained through the use of a Si(001) sample with the surface normal 4◦ o�the [001] direction where the majority domain constitutes 80% of the surface area.These new ARPES results from the 2×2 and 2×1 reconstructions were compared totheoretical results from the literature. Using additional band structure calculationsin the [010] direction and total energy comparisons we were able to discriminatebetween the di�erent atomic models.On the 2×2 surface, two models were found to be indistinguishable as theyshowed similar surface band structures and total energies. This stems from the verysimilar atomic structures of these two models. Both share a Si dimer structure withalternating strongly and weakly buckled Si dimers, and in addition, one Li atompositioned above a fourth layer Si atom in the trough between the Si dimers. Thesecond Li atom occupies a bridge site above a second layer Si atom in one model,25

Chapter 3. Summary and Comments to the Paperswhile it is instead positioned close to a pedestal site between the Si dimers in adimer row but slightly shifted toward a bridge site in the second model.The total energy calculations favored two of the 2×1 models and the energydi�erence between them was found to be very small. These are, like in the case ofthe 2×2 models mentioned above, quite similar in atomic structure. They share astructure with symmetric Si dimers and one Li atom at the pedestal sites betweenthe dimers along the dimer rows. However, the position of the second Li atom in thetrough di�er. Surface band structure comparisons revealed that the ARPES datawas better reproduced by the model where this second Li atom occupies the sitesabove the third layer Si atoms.Analysis of the dimer atom components in high resolution Si 2p core-level spectracon�rmed that the arrangement of the Si dimers in the models are indeed plausible.3.2 Paper II: Warm Ge(001) and Si(001)The surface band structures of clean Si(001) and Ge(001) are very similar as theexample in Fig. 1.7 on page 8 shows. Filled, π, and empty, π∗, surface bandsare associated with dangling bond states of the up atom and the down atom of thedimers as illustrated for Si(001) 2×1 in Fig. 2.8 on page 20. In this paper, the emptyband is in focus. In addition to calculations, it has been probed experimentallyusing inverse photoemission [43] and STS [44]. Following an early report [45] of astructure seen in normal emission with ARPES near EF on heated Ge(001), morerecent studies [46, 47] have shown that this structure is actually positioned aboveEF . It was attributed to the minima of the π∗ surface band of the dimer down atomsas it was found to show a k|| dependence as expected from calculated dispersionsof that band [46]. Since the �rst report, where the occupation of the structure wasassociated with the c(4×2) to 2×1 phase transition, the origin of the electrons inthe band minima has been under discussion.In paper II, ARPES and LEED data from Ge(001) at various temperatures arepresented which show that the phase transition and appearance of the structure inphotoemission are not connected. Furthermore, the intensity of the structure aboveEF monotonically increases up to about 625 K, and becomes higher than that of theπ band positioned 0.17 eV below EF at Γ. Above that temperature the intensitydrops steeply, possibly re�ecting a change in the dimer reconstruction. A similarstructure, but much weaker in intensity, was found on Si(001). Here, no decrease26

3.2. Paper II: Warm Ge(001) and Si(001) Figure 3.1: Normal emission ARPESspectra from a highly n-doped (n+)clean Si(001) sample at 100 K (gray)and a Si(001) sample with very low (dot-ted curve) and slightly higher Cs cov-erage (thin black curve) at RT. Datafrom a clean Si(001) sample at elevatedtemperature is shown with thick blackcurves.in intensity could be observed up to 875 K, only a saturation. As neither the π,nor the π∗ surface bands on Ge and Si cross EF , both surfaces must be consideredas semiconducting in the entire temperature range. By dividing by the Fermi-Diracdistribution function, the energy position of the structures were estimated to be 0.13and 0.24 eV above EF for Ge(001) and Si(001), respectively. These values result inseparations between the VBM and the π∗ band minimum at Γ that are consistentwith earlier reports.More recent results have been published on Si(001), where the conclusion is thatelectron donation by thermal adatoms is the cause of the �lling of the π∗ bandminima [48]. The authors argue that the temperature for the onset of the �lling istoo low to explain thermal excitations of electrons to the π∗ band. Furthermore,the unusual energy position of the structure is explained by the number of donatedelectrons, which is thought to be too low to align the π∗ band minima to EF [48].The π∗ band minima can be probed using ARPES by supplying additional elec-trons to the surface. In Fig. 3.1, this is illustrated by the use of i) a highly n-dopedsample (n+) and ii) Cs adsorption. The result when using an n+ sample is shownin gray. From this it is apparent that the photoemission cross-section of the π∗band minima is very high in this geometry using 21.2 eV photons. It is thereforenot unreasonable to have a measurable photoemission intensity from this structureat about 500 K, contrary to what was claimed in Ref. [48]. Both in the n+ spec-trum and in the spectra showing the two Cs adsorbed surfaces (dotted and thinsolid curves), the energy position of the π∗ band minimum is very close to EF . Thelow coverage Cs case would correspond to the situation of initial �lling by thermaladatoms. Despite the low intensity, the π∗ band minimum has been aligned withEF . Compare this to the thick solid curves that show a spectrum from the Si(001) at27

Chapter 3. Summary and Comments to the Paperselevated temperature. There is a clear di�erence in energy position of the structurecompared to the two Cs cases as well as compared to the n+ case.3.3 Paper III: Surface core-level shifts on clean Si(001)and Ge(001)In paper III, the Si 2p and Ge 3d core-levels are studied using high resolution PESand DFT calculations. Both the Si(001) and the Ge(001) surfaces show a c(4×2)reconstruction at lower temperatures. Even though the atomic model, see Fig. 1.6on page 7, is well established, calculated SCLSs in the literature only cover the Sisurface. No results from Ge(001) in the c(4×2) reconstruction have been reportedin the literature. Calculations on the similar p(2×2) surface structure have beenpresented in Ref. [38]. There it was found that screening plays an important rolefor the SCLSs on both the Si(001) and Ge(001) surfaces. Screening is a �nal statee�ect, which is the result of the response from the valence electrons on the creationof a vacancy in the core state. The phenomenon of valence charge redistribution isalways present when there are localized charges in solids. It becomes important inSCLS calculations when there is, as pointed out in Ref. [38], a site dependence, i.e.,the e�ciency of the screening varies between di�erent atoms.When screening e�ects are included, the calculated SCLSs presented in this paperwere found to describe the experimentally obtained core-level spectra from both Siand Ge very well. From the comparison between experiments and calculations, sevenof the eight calculated components from the four topmost layers could be assignedto the components used to �t the spectra in both the Si and Ge case. A strongsite dependence of the screening was seen as the change in relative binding energydue to screening was signi�cantly larger for the dimer down atom compared to theother atoms. This has been attributed to occupation by screening electrons of theordinarily empty dangling bond state at the down atom [38]. Figure 3.2 shows threeexamples of the spatial valence charge redistribution in the Si(001) c(4×2) case. Theatoms with the core holes are recognized by the surrounding electron cloud, shownby large oversaturated red areas in the �gure. In a larger shell around the coreholes, beyond the relatively dense electron cloud, there is a depletion region that is,in many cases, followed by a region with excess charge in an oscillatory manner asshown in Fig. 3.2(b). The change in core-level shift due to screening was found tobe more similar for atoms in deeper layers. Also, in contrast to the surface atoms,28

3.4. Paper IV: Si(111):Sn

0.01 e/Å-3

-0.01 e/Å-3

Up Down

4th layer

1 2 3 4-0.5

0.51

1.5

0

-0.5

0.51

1.5

0

-0.5

0.51

1.5

0

Up

Down

4th layer

Radius (Å)

ρ(r

) (

e/Å

)

-3

Figure 3.2: In a), a cross sectional view of the valence charge density of Si(001) c(4×2)is showing the di�erence between the charge distribution of a slab with a core hole and aneutral slab. The three panels show the situations when core holes are introduced in the2p level of the dimer up atom, dimer down atom and a fourth layer atom. Both the atomwith the core hole and the Si dimer are in the plane of the plot. Note that the color scaleis heavily saturated in order to show small variations. In b) the spherical average of thecharge density di�erence around each of the three core-holes in a) is shown. Red (blue)indicate an accumulation (depletion) of charge in shells of di�erent radius.the accumulation/depletion oscillations in the spatial charge redistribution for thesebulk-like atoms are virtually identical to that of the 4th layer atom in Fig. 3.2(b).3.4 Paper IV: Si(111):SnWhen Sn is adsorbed on Si(111) a √

3×√

3 reconstruction is initially formed. Withincreasing Sn coverage the surface starts to exhibit a 2√

3 × 2√

3 periodicity. Ina narrow coverage interval slightly above 1 ML, the 2√

3 × 2√

3 reconstruction ispresent without coexistence of the √3×√

3 phase [49]. The 2√

3×2√

3 phase showsa remarkable transition at 463 K. As observed in LEED, the entire surface abruptly,and reversibly, switches between the 2√

3 × 2√

3 and a 1×1 di�raction pattern atthe transition temperature.In this paper, calculated results obtained from an atomic two-layer model inthe literature [50] are compared to detailed STM data and low temperature ARPESresults from the 2√

3×2√

3 surface. It is found that several of the six experimentallyresolved surface state dispersions are not reproduced by the calculated surface bands.However, in calculated STM images the empty states, in combination with the29

Chapter 3. Summary and Comments to the Papersgeometry of the top layer, indicate some agreement with STM data. The conclusionis, despite this, that the model needs to be revised, since, in addition to the poorcorrelation with ARPES data new STM images show an under layer that is notcompatible with the atomic positions in the model. The under layer shows eightatoms, and with four atoms in the top layer a new model would require a Sn coverageof 1.0 ML. The geometry of this new model remains unknown since force relaxationshave so far not resulted in any stable con�guration that reproduces the STM images.The phase transition of the surface is studied with ARPES and STM. It is foundthat the electronic structure slightly below the transition temperature is quite similarto that at low temperature. Aided by STM images showing the transition, thedi�erent surface states can be associated with either the top or the under layer.One surface state survives the transition. Model calculations performed on a bulktruncated 1×1 surface with Sn in di�erent positions reveal that this state is verysimilar to the surface state induced by the Sn-Si bond when Sn occupies T1 sites,i.e., above the topmost Si atoms. Such a con�guration is analogous to what hasbeen found on the similar Ge(111):Sn surface [51]. From the ARPES spectra, it isevident that the appearance of the surviving surface state changes very little at thephase transition. Sn atoms in the base layer of a revised model for the 2√

3 × 2√

3surface would, according to these observations, show preference for T1 sites.3.5 Paper V: Si(001):TlStudies of the adsorption of group III metals on semiconductor surfaces have throughthe years mainly been focused on Al, Ga and In. It is only recently that attentionhas turned towards Tl. The Tl adsorbed surfaces have been shown to exhibit severalinteresting phenomena that are not observed with the other group III metals. Someexamples are the spin splitting by the Rashba e�ect which has been reported onSi(111):Tl [52], and the observation of both a 3+ and 1+ valence state dependingon sample conditions [53]. These observations are connected with spin-orbit e�ectsthat become increasingly important for elements with higher atomic numbers, e.g.,Tl. An e�ect of the variable valence state is the formation of a 2×1 phase at 1 MLcoverage on the Si(001) surface at RT. This phase has been suggested, see Ref. [54],to be similar to the double layer structure induced by adsorption of the monova-lent alkali metals [55]. In Paper V, the surface band structure of this 2×1 phase30

3.5. Paper V: Si(001):Tl

Figure 3.3: ARPES spectra in the [110] and [010] azimuths from a 2×1 Si(001):Tl samplewith 1 ML coverage at 100 K, obtained using linearly polarized 21.2 eV photons.31

Chapter 3. Summary and Comments to the Papersis investigated using ARPES and band structure calculations. Figure. 3.3 showsARPES spectra obtained at 100 K along the [110] and the [010] azimuths. Foursurface state bands associated with the Tl induced reconstruction can be identi�edin the data. Even though the surface, as observed in LEED, undergoes a phasetransition to what appears to be a mix of reconstructions with larger unit cells atlow temperature, the surface band structure remains very similar to that at RT andit still displays a 2×1 periodicity. The calculated surface band structure, obtainedusing the �pedestal + valley-bridge� model, shows similar features as in the ARPESdata. From this it is concluded that the atomic structure used in the calculations isa plausible model for the surface reconstruction and that the phase transition hasno e�ect on the surface band structure.3.6 Paper VI and VII: Si(111):TlPapers VI and VII deal with thallium induced reconstructions on Si(111). At acoverage of 1

3ML, a √

3×√

3 reconstruction is formed on the surface. This behavioron Si(111) is common to that of the other group III metals, Al, Ga and In. Tl,being the heaviest atom in that group, behaves di�erently at 1 ML coverage. A 1×1phase is formed due to the peculiar behavior in the form of the so-called inert paire�ect. It arises due to the reluctance of the 6s2 electrons to participate in chemicalbonds. As a consequence, Tl can show a 1+ oxidation state. It has been suggestedthat Tl shows a variable valence, i.e., in addition to the 1+ state, it can also showthe 3+ state that is expected for group III metals [53, 56]. However, in paper VI, acoverage dependent SCLS study is presented which shows that Tl on Si(111) preferthe 1+ oxidation state at coverages up to 1 ML, i.e., no evidence of variable valencyis found.The √3×√

3 phase on Si(111) at 1

3ML coverage is, as mentioned above, sharedamong all the group III metals. The monovalent behavior of Tl can be expected toresult in a surface band structure which is di�erent from the other group III metals.This is the topic of paper VII. Using ARPES, three surface states are identi�ed inthe gap of the bulk band projection. One nearly dispersionless state about 0.3 eVbelow EF is similar to a state associated with defects on the other group III surfaces.However, since the two other surface states di�er between Tl and the other group IIImetals, the Tl surface is suggested to have a di�erent atomic structure. Therefore,the origin of the three surface states are not necessarily the same as for those of the32

3.6. Paper VI and VII: Si(111):Tlother group III metal surfaces.

33

34

BibliographyBibliography

[1] Charles Kittel, Introduction to Solid State Physics, seventh edition, John Wiley& Sons, Inc., ISBN 0-471-11181-3 (1996).[2] Neil W. Ashcroft and N. David Mermin, Solid State Physics, Thomson Learn-ing, Inc., ISBN 0-03-083993-9 (1976).[3] M. R.-J. Haüy, An Elementary Treatise on Natural Philosophy, translated fromfrench by Olinthus G. Gregory, printed for George Kearsley, Fleet-Street, Lon-don (1807) ch. II.5.[4] W. H. Miller, A Treatise on Crystallography, J. & J. J. Deighton, Trinity Street,London (1839).[5] M. Lannoo and P. Friedel, Atomic and Electronic Structure of Surfaces,Springer Verlag, ISBN 3-540-52682-X (1991).[6] Sydney G. Davison and Maria St¦±licka, Basic Theory of Surface States, OxfordUniversity Press, ISBN 0-19-851896-X (1996) ch. 9.[7] Jarek D¡browski and Hans-Joachim Müssig, Silicon Surfaces and Formation ofInterfaces, Basic Science in the Industrial World, World Scienti�c PublishingCo. Pte. Ltd., ISBN 981-02-3286-1 (2000).[8] Arantzazu Mascaraque and Enrique G. Michel, J. Phys.: Condens. Matter 14,6005 (2002).[9] H. Lüth, Surfaces and Interfaces of Solid Materials third edition, Springer Ver-lag, ISBN 3-540-58576-1 (1995). 35

Bibliography[10] Elizabeth A. Wood, J. Appl. Phys. 35, 1306 (1964).[11] K. C. Pandey, Phys. Rev. Lett. 47, 1913 (1981).[12] R. I. G. Uhrberg, E. Landemark and L. S. O. Johansson, Phys. Rev. B 39,13525 (1989).[13] K. Takayanagi, Y. Tanishiro, S. Takahashi and M. Takahashi, Surf. Sci. 164,367 (1985).[14] K. Oura, V. G. Lifshits, A. A. Saranin, A. V. Zotov and M. Katayama, SurfaceScience An Introduction, Springer Verlag, ISBN 3-540-00545-5 (2003).[15] David Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principlesand Applications, Cambridge University Press, ISBN 0-521-65214-6 (1999)ch .5.[16] Friedrich Reinert and Stefan Hüfner, New J. of Phys. 7, 97 (2005).[17] Carl Nordling, Evelyn Sokolowski and Kai Siegbahn, Phys. Rev. 105, 1676(1957).[18] D. W. Turner and M. I. Al Jobory, J. Chem. Phys. 37, 3007 (1962).[19] S. Hagström, C. Nordling and K. Siegbahn, Phys. Letters 9, 235 (1964).[20] J. C. Rivière and S. Myhra (eds.), Handbook of Surface and Interface Analysis,second edition, CRC Press, ISBN 978-0-8493-7558-3 (2009) p. 46.[21] G. Lebedev, A. Tremsin, O. Siegmund, Y. Chen, Z.-X. Shen and Z. Hussain,Nucl. Instrum. Methods Phys. Res. A 582, 168 (2007).[22] Albert C. Thompson and Douglas Vaughan (eds.), X-Ray Data Booklet (2001),(Available at http://xdb.lbl.gov/).[23] D. A. Shirley, Phys. Rev. B 5, 4709 (1972).[24] M. P. Seah and W. A. Dench, Surf. Interface Anal. 1, 2 (1979).[25] D. J. O´Connor, B. A. Sexton, R. St. C. Smart (Eds.), Surface Analysis Meth-ods in Materials Science, second edition, Springer-Verlag, ISBN 3-540-41330-8(2003) p. 25.36

Bibliography[26] J. B. Pendry, Low Energy Electron Di�raction, Academic Press Inc. (London)Ltd. ISBN 0-12-550550-7 (1974) ch. 1.[27] John B. Hudson, Surface Science: An Introduction, John Wiley & Sons, Inc. ,ISBN 0-471-25239-5 (1998) p. 203.[28] K. J. Stout and L. Blunt, Three Dimensional Surface Topography, second edi-tion, Penton Press, ISBN 1-85718-026-7, (2000) p. 77.[29] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Phys. Rev. Lett. 49, 57(1982).[30] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka and J. Luitz,WIEN2k,An Augmented Plane Wave + Local Orbitals Program for Calculating CrystalProperties (Karlheinz Schwarz, Tech. Universität Wien, Austria), 2001. ISBN3-9501031-1-2.[31] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).[32] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).[33] S. Cottenier, Density Functional Theory and the Family of (L)APW-methods: A Step-by-Step Introduction (Institut voor Kern- en Stralingsfys-ica, K.U. Leuven, Belgium), 2002, ISBN 90-807215-1-4 (to be found athttp://www.wien2k.at/reg_user/textbooks).[34] C. Y. Fong (ed.), Topics in computational materials science, World Scienti�cPublishing Co. Pte. Ltd. ISBN 981-02-3149-0 (1997) p. 2.[35] David S. Sholl and Janice A. Steckel, Density Functional Theory : A PracticalIntroduction, John Wiley and Sons, Inc, ISBN 978-0-470-37317-0 (2009) p. 28.[36] David J. Singh and Lars Nordström (eds.), Planewaves, Pseudopotentials, andthe LAPW Method, second edition, Springer Verlag, ISBN: 0-387-28780-9(2006).[37] Börje Johansson and Nils Mårtensson, Phys. Rev. B 21, 4427 (1980).[38] E. Pehlke and M. Sche�er, Phys. Rev. Lett. 71, 2338 (1993).[39] H. Q. Shi, M. W. Radny and P. V. Smith, Phys. Rev. B 69, 235328 (2004). 37

Bibliography[40] Y.-J. Ko, K. J. Chang and J.-Y. Yi, Phys. Rev. B 56, 9575 (1997).[41] Y. Morikawa, K. Kobayashi and K. Terakura, Surf. Sci. 283, 377 (1993).[42] H. Q. Shi, M. W. Radny and P. V. Smith, Surf. Sci. 574, 233 (2005).[43] J. E. Ortega and F. J. Himpsel, Phys. Rev. B 47, 2130 (1993).[44] O. Gurlu, H. J. W. Zandvliet and B. Poelsema, Phys. Rev. Lett. 93, 066101(2004).[45] S. D. Kevan, Phys. Rev. B 32, 2344 (1985).[46] K. Nakatsuji, Y. Takagi, F. Komori, H. Kusuhara and A. Ishii, Phys. Rev. B72, 241308(R) (2005).[47] C. Jeon, C. C. Hwang, T.-H. Kang, K.-J. Kim, B. Kim, Y. Chung and C. Y.Park, Phys. Rev. B 74, 125407 (2006).[48] C. Jeon, C. C. Hwang, T.-H. Kang, K.-J. Kim, B. Kim, Y. Kim, D. Y. Nohand C. Y. Park, Phys. Rev. B 80, 153306 (2009).[49] T. Ichikawa, Surf. Sci. 140, 37 (1984).[50] C. Törnevik, M. Hammar, N. G. Nilsson and S. A. Flodström, Phys. Rev. B44, 13144 (1991).[51] M. F. Reedijk, J. Arsic, F. K. de Theije, M. T. McBride, K. P. Peters and E.Vlieg, Phys. Rev. B 64, 033403 (2001).[52] K. Sakamoto, T. Oda, A. Kimura, K. Miyamoto, M. Tsujikawa, A. Imai, N.Ueno, H. Namatame, M. Taniguchi, P. E. J. Eriksson and R. I. G. Uhrberg,Phys. Rev. Lett. 102, 096805 (2009).[53] V. G. Kotlyar, A. A. Saranin, A. V. Zotov and T. V. Kasyanova, Surf. Sci. Lett.543, 663 (2003).[54] A. A. Saranin, A. V. Zotov, V. G. Kotlyar, I. A. Kuyanov, T. V. Kasyanova, A.Nishida, M. Kishida, Y. Murata, H. Okado, M. Katayama and K. Oura, Phys.Rev. B 71, 035312 (2005).[55] T. Abukawa and S. Kono, Phys. Rev. B 37, 9097 (1988).38

Bibliography[56] S. S. Lee, H. J. Song, N. D. Kim, J. W. Chung, K. Kong, D. Ahn, H. Yi, B. D.Yu and H. Tochihara, Phys. Rev. B 66, 233312 (2002).

39