Generalized Electron Counting in Determination of Metal-Induced Reconstructionof Compound Semiconductor Surfaces

Lixin Zhang,1 E. G. Wang,1 Q. K. Xue,1 S. B. Zhang,2 and Zhenyu Zhang3,4

1International Center for Quantum Structures and Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China2National Renewable Energy Laboratory, Golden, Colorado 80401, USA

3Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA4Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA(Received 31 July 2005; revised manuscript received 30 April 2006; published 19 September 2006)

Based on theoretical analysis, first-principles calculations, and experimental observations, we establisha generic guiding principle, embodied in generalized electron counting (GEC), that governs the surfacereconstruction of compound semiconductors induced by different metal adsorbates. Within the GECmodel, the adsorbates serve as an electron bath, donating or accepting the right number of electrons as thehost surface chooses a specific reconstruction that obeys the classic electron-counting model. Thepredictive power of the GEC model is illustrated for a wide range of metal adsorbates.

DOI: 10.1103/PhysRevLett.97.126103 PACS numbers: 68.35.Bs, 68.43.Bc, 75.70.Ak

On a typical semiconductor surface, atoms in the toplayers often rearrange themselves to form a reconstructedsurface. For compound semiconductors such as GaAs andZnSe, a simple electron-counting (EC) model [1–3] hasproven to be exceptionally instrumental in identifying thevarious forms of surface reconstruction. Since its proposal,the EC model has been applied successfully to manyhomogeneous semiconductor systems [4]. It has alsobeen extensively invoked in determining the structures ofsurface defects, such as vacancies, steps, and islandsformed during homoepitaxial growth [1,5,6].

Metal growth on semiconductors is indispensable formany important technological applications. At the earlieststages of growth, adsorption of a submonolayer of metaloften leads to the appearance of much richer surface re-construction patterns than that in the corresponding homo-geneous case. Because the reconstruction influences manyimportant properties of the metal/semiconductor contactssuch as the Schottky-barrier heights [7], it is vital to under-stand the precise form of reconstruction for a given system.More recently, such reconstructions have also been shownto play an important role in influencing the growth ofdiluted magnetic semiconductors at the growth front [8–10]. To date, determination of metal-induced reconstruc-tion of compound semiconductor surfaces has been pri-marily relying on a trial-and-error approach, typically withstructural characterization using scanning tunneling mi-croscopy (STM) or other techniques and results from ex-tensive first-principles calculations as inputs on a case-by-case basis.

In this Letter, we establish a generic guiding principle,embodied in generalized electron counting (GEC), thatgoverns the surface reconstruction of compound semicon-ductors induced by different metal adsorbates. Within theGEC (consisting of three ingredients or rules as detailedbelow), the metal adsorbates serve primarily as an electronbath by donating or accepting the right number of elec-trons, as the host surface chooses a specific reconstruction

that obeys the classic EC model. Whereas the classic ECmodel demands that the surface be nonmetallic upon re-construction, the GEC allows the combined metal/semi-conductor system to be metallic. A straightforwardapplication of the GEC model can greatly narrow downthe possible low-energy reconstruction patterns out ofmany candidate structures in the configuration space. Thepredictive power of the GEC model is illustrated for differ-ent classes of metal adsorbates, with direct comparisonwith experiment made wherever possible.

The classic EC model is rooted in an equal partitioningof the valence electrons within the nominal number of‘‘bonds,’’ e.g., four for zinc blende semiconductors. There-fore, for bulk GaAs, a Ga atom would provide 3=4 elec-trons to each bond, while an As atom would provide 5=4electrons, resulting in a total number of (3=4� 5=4 � 2)electrons in each bond, as it should be. On a surface, thereare partially occupied dangling bonds, which will drive thereconstruction of the surface toward a state in which all ofthe dangling bonds on electronegative As atoms are filledwhile those on electropositive Ga atoms are empty, pre-serving the nonmetallic nature of the system [1– 4].

When metal atoms are adsorbed, we encounter a morecomplex, ternary system. Hence, the first GEC rule isconcerned with where the metal adsorbates prefer to locateon the surface. An extensive literature search reveals thatthe d-active metals such as Cr, Mn, Fe, and Co prefer theinterstitial sites around the GaAs surfaces [8–10], while thes and sp metals such as Ag, Au, Al, and Cs prefer thesubstitutional sites [11,12]. This difference stems from thefact that the d-active elements prefer to be multicoordi-nated, a requirement more easily satisfied at the interstitialsites. In contrast, the spmetals tend to bind in an sp or sp2

configuration, a requirement more easily satisfied at sub-stitutional sites.

The second GEC rule is rooted in the realization that themetal adsorbates are generally less demanding in formingstrongly directional chemical bonds than the semiconduc-

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tor atoms, making them more susceptible to charge trans-fer. Therefore, this rule stipulates that the classic EC modelis still valid for the binary host, while the metal adsorbatesserve as only an electron bath. Given a surface, whether ametal adsorbate is likely to serve as a donor or an acceptordepends on its relative electronegativity � within the ter-nary system and the chemical hardness, defined as thederivative of � with respect to the occupation of the orbital[13]. For simplicity, however, here we primarily focus onthe leading order effect of �. The Pauling electronegativ-ities [14] of the various metals relative to those of Ga andAs are shown in Fig. 1. Here we see that all the alkalimetals are more electropositive than Ga. Therefore, theyare expected to behave as donors; in particular, even thedangling bonds on Ga could be filled when in close contactwith the donors. In contrast, all the metals above bothdashed lines are more electronegative than As. Therefore,they are expected to behave as acceptors; in particular,even the dangling bonds on As could be empty when inclose contact with the acceptors. Among the transitionmetals, Mn is expected to clearly be a donor, while theelectronegativities of the others fall within the boundsdefined by the electronegativity of Ga and As.

For an arbitrary slab containing, respectively, nM, nAs,and nGa metal, As, and Ga atoms, the total number ofvalence electrons on the metal atoms can be rigorouslygiven as

nR � �MnM � 3nGa � 5nAs � 2nbonds; (1)

where �M is the number of valence electrons on an isolatedmetal atom, and nbonds is the total number of chemicalbonds formed in the slab, including both the � bonds andthe occupied dangling bonds (ODBs). The third GEC rulestates that the lowest-energy surface reconstructions arethose that minimize nR for metal donors and maximize nRfor metal acceptors. Here the expression (�MnM�nR) mea-sures the net charge transfer from the metal adsorbates tothe substrates. The classic EC model is a special case of theGEC, where nM � 0, and nR � 0 for all the low-energysurface reconstructions.

To establish the validity of the GEC model, we study thereconstructions of GaAs surfaces induced by five different

classes of metals: (i) Cs from the alkali metals, whoseelectronegativity is much lower than Ga; (ii) Mn fromtransition metals, whose electronegativity is less than Ga;(iii) the trivalent sp metals such as Al and In, whoseelectronegativities are close to Ga; (iv) the group V metalssuch as Sb and Bi, whose electronegativities are close toAs; and (v) Au, whose electronegativity is higher than As.For each case, we first predict the preferred surface struc-tures based on the GEC. These GEC predictions are thencompared with the results of detailed first-principles totalenergy calculations within density functional theory(DFT), or with experiments, or both. The DFT calculationsuse the generalized gradient approximation and ultrasoftpseudopotentials as implemented in the VASP code [15,16].The cutoff energy in the plane wave expansion is 200, 227,and 200 eV for cases (i), (ii), and (v), respectively. We use a2� 2 surface lattice for the slab with thickness of 10 layers,of which 6 are GaAs layers for the (110) surface, and8 bilayers, of which 4 are GaAs bilayers for the (001)surface, respectively. Pseudohydrogen atoms with 5=4and 3=4 electrons are used to passivate the bottom Gaand As atoms, respectively. A 2�2�1 k-points mesh isused for the Brillouin-zone integration. Based on the totalenergy results, the formation energies of the related sur-faces were calculated as described in Ref. [17].

For case (i), taking Cs=GaAs�110� as a widely studiedexample, the GEC model requires that each Cs adsorbatedonate its one and only valence electron to the GaAs(110)surface, with nR � 0. The donated electrons will occupythe dangling bonds on the Ga atoms, with two electrons perbond. Therefore, the elemental building block should con-tain a pair of substitutional Cs atoms.

Detailed DFT calculations show that the structure shownin Fig. 2 is energetically the most favorable at the low Cscoverage of 0.25 ML. The two Cs adatoms are diagonallylocated at the epitaxial Ga sites at the surface and form a

Number of valence electrons

Pau

ling

elec

tron

egat

ivity

2

1

Au

InGa

MgSc

Be TiV

AlZr

Li

Cs

NaK

Ca SrBa

Rb

As

FeW

MnCr

P

Sb Bi

Ru

CuCoNi

Pd Pt

Ag

Rh

Don

ors

Acc

epto

rs

Am

phot

eric

1 3 5 7 9 11

Pb

FIG. 1 (color online). Pauling electronegativity of variousclasses of metals with respect to that of Ga and As [14].

2x2Cs

AsGa

Empty DB on Ga

ODB on Ga

ODB on As

(a)

[001]

[110]

(c)

(b)

FIG. 2 (color online). (a) Schematic top and (b) side views ofthe elemental building block for the Cs=GaAs�110� surface.(c) Corresponding simulated STM image of the Cs chains at abias voltage of �2 V. The various bond notations used here alsoapply to Figs. 3 and 4.

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building block for surface reconstruction at this and higherCs coverages. We note that, on a pure GaAs(110) surface,the Ga atoms relax inward (sp2) and the As atoms relaxoutward (p3) due to charge transfer from Ga to As [18].Upon adsorption of two Cs atoms, one nearby Ga atom islifted vertically [19]. This uplifting is caused by the fillingof the Ga dangling bond, causing it to evolve from sp2

bonding to p3 bonding. Further increases of the Cs cover-age will lift more Ga atoms, at the rate of one Ga atom perCs pair. Therefore, all of the low-energy configurationsmust have an even number of Cs atoms within the elemen-tal building block, in agreement with experimental obser-vations [20,21]. The simulated STM image shown inFig. 2(c) also agrees with experiments [22].

For case (ii), we focus on Mn=GaAs�001�, an importantsystem related to growth of dilute magnetic semiconduc-tors [23]. According to the GEC model, the Mn adatomswith the electronic configuration �Ar3d54s2 will try todonate all of their s electrons to the surface, while keepingthe half-filled d shell untouched. As a result, at a given Mncoverage, the total number of s electrons left on the Mnadatoms should be minimized for energetically favorablestructures. On the other hand, by accepting electrons, Aswill keep its dangling bonds occupied, and Ga may fill itsotherwise empty dangling bonds as well. Furthermore, it isknown that, on a GaAs(001) dimerized surface, every As-As dimer lacks one electron and every Ga-Ga dimer hasone extra electron within the classic EC model. Therefore,the unit cell of Mn-induced GaAs(001) surface has a basic2� 2 geometry, as dictated by its ability to accept twoextra s electrons from one Mn adsorbate.

At �Mn � 1=2 ML, four s electrons from the two ad-sorbed Mn atoms will be donated to one surface unit cell,more than the cell can accommodate. In order for the Mnatoms to reach their optimal charge state of (2�), thesurface atoms have to rearrange, by either breaking theAs-As dimer(s) or transferring As or Ga atoms from theirrespective reservoirs [17]. After considering various likelyscenarios, we conclude that the structure shown in Fig. 3(a)is the preferred one. In this structure, one extra As and oneextra Ga atom have been ferried to the 2� 2 surface cell.Counting the bonds in Fig. 3(a) yields n�bonds � nODB �5� 6 � 11, and nR��7�2�5��4=2�1��3�1�2�11�10, leaving each Mn atom in its optimal chargestate of (�2).

At �Mn � 1 ML, eight s electrons from four Mn atomswill be donated. The 2� 2 surface unit cell can accom-modate only six electrons even after the breaking of all As-As dimers. Therefore, the system prefers further recon-struction to minimize nR. In this case, losing a surface Asatom is a straightforward way, as it removes five electronsalong with four ODBs but also exposes two ODBs on theGa in the second layer [see Fig. 3(b)]. The net electronreduction is, thus, one. Counting the bonds in Fig. 3(b)yields n�bonds � nODB � 6� 8 � 14, and nR � �7� 4�5� 3� 3� 4=2� � 2� 14 � 21. This number is oneelectron more than that for the optimal charge state (4�

5 � 20) but is the lowest value possible, leaving the Mnadatoms in a different charge state than (2�).

Detailed DFT calculations [17] have shown that thestructures predicted by the GEC model at the three differ-ent Mn coverages indeed have the lowest formation ener-gies among many other possibilities. Figure 3 shows thecorresponding simulated STM images for 1=2 and 1 ML ofMn, which compare favorably with experimental observa-tions [17,24]. Here the bright spots in the STM imagescorrespond to surface As or Ga atoms other than Mn atoms.The formulation of the GEC concept in the present studyrationalizes the findings from the extensive DFT calcula-tions performed earlier [17].

For case (iii), the trivalent sp metals of In and Al areisovalent with and close in electronegativity to Ga; there-fore, such metals are expected to behave just like Ga,leading to a natural extension of the classic EC model. Inthis case, nR is zero, as revealed in previous studies ofGaInP(001) [25] and In=GaAs�001� surfaces [26].

For case (iv), the group-V metals of Sb and Bi areisovalent and close in electronegativity to As; therefore,such metals are expected to behave just like As, againleading to a natural extension of the classic EC model.The energetically preferred surface patterns on GaAs(001)are to preserve the 2� 4 structure, with Sb or Bi substitut-ing for As, and nR is zero. Indeed, extensive experimentalstudies of Sb adsorption on GaAs(100) confirm the prefer-ence of the 2� 4 structure upon annealing [27].

As an example for case (v), we consider Au onGaAs(001). It is known that a 2� 2-dimerized Ga-terminated GaAs(001) surface has two net electrons (nR �2) and is unstable. Upon adsorption, Au can accept onemore electron to fill its s orbital and take the (1� ) chargestate, thereby helping to stabilize the surface. Figure 4shows two structures at �Au � 1=4 and 1=2 ML, as pre-

FIG. 3 (color online). The two Mn=GaAs�001� surfaces at Mncoverage of (a) 1=2 and (b) 1 ML. The left column of each panelshows the top (up) and side (down) views of the atomic struc-tures. The right column displays the experimental (up) and thecorresponding simulated (down) STM images at a bias voltageof�2 V. The bright spots in the simulated STM images indicatethe highest points in the charge contour. They correspond to theoutermost surface Ga or As sites. Here and in Fig. 4, the broadersolid lines are the � bonds considered in the electron counting.

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dicted by the GEC model. In Fig. 4(a), one Au atomreplaces one Ga on the surface. In the counting slab shownin Fig. 4(a), nAu�1, nAs�4=2�2, nGa � 3, and nbonds �n�bonds � nODB � 7� 2 � 9. By applying Eq. (1), we ob-tain nR � �1� 1� 5� 2� 3� 3� � 2� 9 � 2, just asthe GEC requires. Figure 4(b) shows a structure with twobridge-site Au atoms. Here nAu�2, nAs�0, nGa � 4=2 �2, and nbonds � n�bonds � nODB � 2� 0 � 2. By applyingEq. (1), we obtain nR � �1� 2� 5� 0� 3� 2� � 2�2 � 4, again with two electrons on each Au atom.

The two structures predicted above are fully confirmedin detailed total energy calculations, showing that they areboth energetically the lowest among more than ten con-figurations considered at �Au � 1=4 and 1=2 ML, respec-tively. In addition, on an otherwise As-terminated surface,our calculations show a strong tendency of intermixingbetween As and Au. Such intermixing will enhance theOhmic contact between Au and GaAs and will disruptordered reconstruction, in agreement with experiment [28].

In summary, a generalized electron-counting model hasbeen proposed to serve as the guiding principle in under-standing metal-induced surface reconstruction of com-pound semiconductors. The validity of the GEC modelhas been demonstrated by its ability to predict the likelylow-energy reconstruction patterns induced by a wide va-riety of metal adsorbates on different GaAs surfaces.

Though the GEC model was developed using GaAs as aprototype substrate, the underlying concepts empoweringthe model are expected to be applicable to many othercompound semiconductors.

This work was partially supported by the NSF andMOST of China, by BES and EERE of the U.S. DOE underDE-AC36-99GO10337, by ORNL, managed by UT-Battelle, LLC for the U.S. DOE under DE-AC05-00OR22725, and by U.S. NSF under DMR-0306239.

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FIG. 4 (color online). Top (top) and side (middle) views of thetwo stable structures for Ga-terminated GaAs(001) surfaces withAu coverage of (a) 1=4 and (b) 1=2 ML and the correspondingsimulated STM images (bottom) at a bias voltage of �2 V.

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