First-principles study of (2 1) and (2 2) phosphorus-rich InP(001) surfaces

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1 Surace Science 464 (2000) First-principles study o (2 1) and (2 2) phosphorus-rich InP(001) suraces Olivia Pulci a,*, Kathy Lüdge b, W.G. Schmidt a, F. Bechstedt a a Institut ür Festkörpertheorie und Theoretische Optik, Friedrich-Schiller-Universität, Max-Wien Platz 1, D Jena, Germany b Institut ür Festkörperphysik, Technische Universität Berlin, Hardenbergstrasse 36, D Berlin, Germany Received 26 May 2000; accepted or publication 11 July 2000 Abstract The dependence o the InP(001) surace reconstruction on the chemical potentials o its constituents is explored. Based on irst-principles pseudopotential plane-wave calculations the surace phase diagram is constructed. 17 structural models are studied or the phosphorus-rich InP(001) suraces, with (2 1), p(2 2) and c(2 2) translational symmetry. P-top dimer reconstructions are avoured. Under less P-rich preparation conditions a tendency or disorder is predicted. STM images are also calculated in order to contribute to a solution o the structural puzzle Elsevier Science B.V. All rights reserved. Keywords: Density unctional calculations; Indium phosphide; Low index single crystal suraces; Surace electronic phenomena (work unction, surace potential, surace states, etc.) 1. Introduction ( III) are unoccupied and those on the surace anions ( V ) are doubly occupied. This guiding The understanding o the structure and com- principle, usually reerred to as the electron countposition o semiconductor suraces during growth ing rule [ 2], explains the relatively large reconstrucis one o the keys to controlling the evolution o tions built up by dimers or missing dimers. This epitaxial ilms on the atomic level, or instance picture o the III V( 001) suraces is at least well using techniques like molecular beam epitaxy established or the ( 2 4)/c(2 8) and c(4 4) (MBE), chemical beam epitaxy (CBE) or metalor- surace phases o GaAs [3]. ganic vapour-phase epitaxy (MOVPE) [1]. This In contrast to those o arsenides, the (001) holds in particular or the polar (001) suraces o suraces o other III V compounds, however, III V semiconductors crystallizing in the zinc- exhibit several peculiarities, which seem to contrablende structure. Their phases in dependence on dict the basic reconstruction mechanism. Whereas substrate temperature and material luxes, i.e. stoi- AlSb(001) orms an insulating c(4 4) reconstrucchiometry, have been studied in detail. It is widely tion, GaSb possesses (2 10) suraces that are accepted that these suraces reconstruct in such a weakly metallic and, hence, violate the electron way that the dangling bonds on the surace cations counting model [4]. Also the reconstruction mechanism acting on (001) suraces o phosphides is * Corresponding author. Fax: under discussion. For the InP( 001) surace several address: pulci@ito.physik.uni-jena.de (O. Pulci) translational symmetries have been observed. For /00/$ - see ront matter 2000 Elsevier Science B.V. All rights reserved. PII: S ( 00 )

2 O. Pulci et al. / Surace Science 464 (2000) suraces prepared under MBE, CBE and MOVPE a (2 2) phase, which shows only a diuse boundary conditions with varying phosphorus partial pressure, with the (2 1) reconstruction [ 7]. Recently, (2 4), (2 1) and (2 2) relection high several observations o this P-rich phase have been energy electron diraction ( RHEED) patterns published [17 19]. A (2 1/2 2) LEED pattern have been monitored or substrate temperatures in and STM images o a surace with poor longrange the interval 300 to 590 C [5 7] and varying material ordering have been reported [17 19]. A high luxes. A weak c(4 4) reconstruction has also number o deects characterize this more P-rich been observed at lower temperatures [7,8]. Since surace, that can only locally be described in terms P atoms desorb rom the surace with increasing o P dimers on top o a complete irst P layer, temperature, the surace becomes less P-rich. giving rise to local (2 2), c(2 2) and c(4 2) Consequently, the (2 4) phase is known as In- structures. Observations suggest that this surace rich, whereas lower temperature phases should be contains more than 1 ML o P atoms, possibly up represented by P-rich suraces. to 2 ML. We call the occurring phases 2 ML For the In-rich (2 4) phase, images o scanning phases. tunneling microscopy (STM) [9] and results o The present study aims to elucidate the atomic time-o-light scattering and recoiling spectrometry structure o the nominal (2 2)/(2 1) InP sur- [10] have been interpreted as indications or P aces in dependence on their preparation. A large trimers or a trimerization o the topmost In atoms. variety o models representing (2 1) and ( 2 2) However, also P In P bridge bonds have been translational symmetries are analysed. To connect suggested [11,12]. The experimental observations our data energetically with previous theoretical can, however, be described by conventional P P and experimental work, we also include the meanwhile dimers or mixed In P dimers as shown recently well established mixed-dimer model [13 [13 15]. 15,20]. In the extreme P-rich limit we ocus our For the more P-rich phase, STM observations attention on some o the reconstructions that have or MOVPE material show that the nominally been proposed [17 19] in order to discuss the (2 1) surace, as indicated by low energy electron experimental indings. We address the question o diraction (LEED), seems to consist o zig zag whether the dimer ormation is still appropriate chains along the [110] direction. The corresponding or InP(001) suraces, where atoms with a remark- surace geometry has been interpreted as a able size dierence are involved and the bonds are mixture o p(2 2) and c(4 2) domains [16,17], more ionic than in the GaAs case. The validity o with P P dimer buckling in-phase [resulting in the electron counting rule and the dimer buckling p(2 2)] or out-o-phase [resulting in c(4 2)]. are discussed. To that end we perorm irst-prin- One expects, however, that buckling is reduced in ciples total-energy ( TE) calculations and construct the presence o ionic bonds. Buckled dimers o the surace phase diagram. Furthermore, the identical atoms have only been observed at (001) atomic geometries, surace electronic structures suraces o the covalent materials Si and Ge. As and calculated STM images o the energetically and P dimers exhibit practically no buckling on avoured structures are presented. GaAs and InP suraces [3,9 12]. The observed P-rich suraces seem to have an overlayer o about 1 ML o P atoms. We will call suraces o this type 2. Computational methods 1 ML phases. Besides dimer buckling, other reasons or the electronic inequivalence o the two The calculations are based on the density unctional P atoms in a dimer, e.g. electron correlation eects theory in the local density approximation between dangling bonds on neighbouring dimers, (DFT-LDA) [21,22]. A pseudopotential planewave have been discussed [16]. Very recently, a stabilization code [23,24] is used. The electron ion interhave o this surace type by alkyl groups and action is treated by using ully separable, normconserving hydrogen atoms has been considered [18,19]. pseudopotentials [25]. The single-parhydrogen For even more P-rich conditions one approaches ticle orbitals are expanded into plane waves up to

3 274 O. Pulci et al. / Surace Science 464 (2000) an energy cut-o o 15 Ry. The k-space integrations are replaced by a sum over eight special points in the irreducible part o the two-dimensional Brillouin zone (BZ) o the (2 2) phases and equivalent sets o points or the larger surace unit cells. The suraces are modelled using periodic slab geometries along the (001) surace normal. Each unit cell includes an atomic slab with six to seven atomic layers and a vacuum region corresponding to ive layers. The cation-terminated bottom layer o the slab is saturated with ractionally charged H atoms [26]. Two layers on this side o the slab are kept rozen, whereas all other atoms are allowed to relax. The minima o the TE unctional with respect to both the atomic and electronic degrees o reedom are ound by means o a Car Parrinello molecular dynamical approach [27]. The atoms are assumed to be in their ully relaxed positions when orces acting on the ions are smaller than ev/å. The calculations are perormed with the theoretical equilibrium lattice constant o 5.87 Å. The TE calculations are perormed or a variety o structural models, shown in Figs. 1 and 2. In addition to the already known In-rich (2 4) mixed-dimer reconstruction, test structures or the (2 1) and ( 2 2) reconstructed P-rich InP(001) suraces with dierent phosphorus overlayers are Fig. 1. Top view o surace structures with P coverages H less considered. The coverages H reer to an ideal than 1 ML. Dierent arrangements o mixed dimers (md) and top-p dimers (td) as well as single P adatoms (aa) are consid- In-terminated slab. The considered structures realered. In the case o two md dimers per (2 2) surace unit cell ize dierent P coverages, ranging rom H=0 or parallel (p) or antiparallel (a) arrangements are distinguished. the In-rich (2 4) mixed dimer ( Fig. 1) up to H= Two dimers can orm a staggered (s) arrangement. Filled circles: 2 in the case o adsorption o eight P atoms on a P atoms; open circles: In atoms. (2 2) cell (Fig. 2). We consider adsorption on the In-terminated InP( 001) surace with P cover- monolayers (H=1.5) or i=2 ( Fig. 2). The age H 1 as shown in Fig. 1, and with 1<H 2 p(2 2) top-dimer adsorbates td1 and td1s ( Fig. 1) as shown in Fig. 2. As reconstruction elements in stand or complete P monolayers with H=1, where the adlayer we consider mixed dimers (md) in s indicates a staggered dimer coniguration. The parallel (p) or antiparallel (a) conigurations, buck- p(2 2) td2 and p(2 2)td2s, shown in Fig. 2, led and unbuckled top-p dimers (td), possibly in represent two top-dimer adsorbates on a complete a staggered arrangement (s), and phosphorus ada- P monolayer (H=2). toms (aa). The mixed dimer structures mdi represent Because o the variation o the number o either an In P dimer on the indium-terminated surace atoms in the unit cell, the energetical surace (i=1) or an In P dimer on top o a comparison o the structures in Figs. 1 and 2 complete P adsorbate layer (i=2). The (2 2) depends on the chemical potentials m( X ) o the surace constituents X= P, In [28]. In the zero- temperature limit this corresponds to the study o the surace energy V versus the chemical potential top-p dimer and adatom structures, tdi and aai, correspond to a coverage o hal a P monolayer (H=0.5) or i=1 (Fig. 1), and o one and a hal

4 O. Pulci et al. / Surace Science 464 (2000) Fig. 2. As Fig. 1 but or P coverages H between 1 and 2 ML (1<H 2). phase. It is below the bulk chemical potential in the cases where the elemental bulk is not stable and the surace is in equilibrium with a gaseous phase, e.g. the gas o two atomic molecules P. 2 According to the mass action law and the deinition o the heat o ormation, the chemical potential m( In) varies between the value or the corresponding metal mbulk(in) and a value mbulk(in) DH ( InP) reduced by the heat o ormation o the compound InP. With Dm( In)=m( In) mbulk( In), it holds that 1 Dm(In)/DH (InP) 0. Extreme In-rich (P-poor) preparation conditions are described by Dm(In)=0, whereas Dm(In)= DH ( InP) characterizes more P-rich ( In-poor) conditions. The surace energy V is represented in Fig. 3 versus the variation Dm( In) o the In chemical potential with respect to its bulk value. Since, due to the various possible modiications, the white phosphorus does not unambiguously deine the elemental condensed bulk phase in equilibrium with the surace and, moreover, the heat o orma- o one constituent. Since bulk solid InP with the chemical potential mbulk( InP) is a reservoir which can exchange atoms with the surace, the mass action law, m( In)+m(P)=mbulk( InP), holds. It allows the representation o the surace energy V as a unction o m(in) or m(p). The bulk energy per pair, mbulk(inp)=mbulk(in)+mbulk(p) DH (InP), is equal to the sum o the energies o the bulk elemental In and P minus the heat o ormation DH (InP). Elemental In occurs in the orm o a bulk tetragonal metal with mbulk( In). Elemental phosphorus shows a wide structural variety, the most common allotropes being the white, black, violet and red phosphorus and some amorphous orms. For the ormation o InP rom white phosphorus, the solid high-temperature phase, the experimental value amounts to DH (InP)= 0.92 ev or the heat o ormation [29]. Fig. 3. Surace energy (with respect to the ideal unrelaxed The chemical potential o each element cannot P-terminated surace) per (1 1) unit cell versus the variation be above that o the bulk elemental phase being o the In chemical potential. The thermodynamically allowed stable at the substrate temperature. It approaches range is given by 1 Dm(In)/DH 0.0. The energetically most avourable surace reconstruction models are shown. 1: the elemental bulk chemical potential in the case p(2 2)td2; 2: p(2 2)td2s; 3: (2 2)td2; 4: c(2 2)aa2; 5: that bulk material is present and the surace is in p(2 2)td1; 6: p(2 2)md2ps; 7: p(2 2)td1s; 8: (2 1)td1; 9: equilibrium with the elemental condensed bulk (2 2)td1; 10: c(2 2)aa1; 11: (2 1)md1p; 12: (2 4)md1.

5 276 O. Pulci et al. / Surace Science 464 (2000) tion DH (InP) varies with temperature [30], we unit cell become inequivalent; or that reason no have also checked the inluence o dierent values c(2 2) symmetry occurs in the staggered case. o DH (InP) on the phase diagram in Fig. 3. There The two P dimers occur at dierent distances o is, however, only an inluence on the thermodynamically about 2.2 Å on average rom the underlying In allowed range without major conse- atomic layer. As a consequence, the surace quences on the stability o the dierent surace becomes semiconducting. The hybridization o the phases. dangling bonds tends towards s and p (p and z sp2 ) or upper (lower) dimers. Four and six xy electrons are accommodated on the s- and p-states 3. Results o the corresponding dimer. Another possibility to explain zig zag chains along [110] are mixed 3.1. Geometry and bonding dimers o P and In atoms which are automatically buckled [13 15]. In the 1 ML ramework we Geometries with 1 ML phosphorus consider our mixed-dimer (md) overlayers with The suraces with P coverage H 1 and our or c(2 2) and p( 2 2) reconstructions [ which correspond less adatoms per (2 2) unit cell are shown in to (2 1) in the case o a parallel arrangeless Fig. 1. They may represent reconstruction elements ment o the two dimers] (c. Fig. 1). Among these occurring in the surace phases experimentally mixed-dimer geometries, the energetically most prepared under intermediate P-rich conditions avourable one is the md1p structure, consisting [16,17]. This holds in particular or the pure P o two identical parallel In P dimers per p(2 2) adlayers. cell on an In layer and, hence, describing in reality However, any attempt to buckle the top-p dimer a 2 1 reconstruction. The dimer buckling (td1) structures ailed within the (2 1), (2 2) amounts to 0.48 Å, with the P atoms moving out and p(2 2) translational symmetries. We ound o the surace and the In ones down towards the local minima on the Born Oppenheimer TE ace bulk. However, the resulting equal arrangement o only or unbuckled top dimers. This is in P and In adatoms can only explain linear chains. agreement with indings or dimers o equal atoms Moreover, experimental indings rom inrared at other (001) suraces o III V compounds [3,13 spectroscopy rule out the possibility o In atoms 15]. Dimer buckling increases the electrostatic on the top o the surace [16]. Also, the observation energy o the system and, hence, is unlikely in the o the dimer lipping seems to conclusively presence o partially ionic bonds. Our TE calcula- rule out mixed dimers [17]. In order to explain the tions thus do not conirm the existence o buckled obvious discrepancies between theory and experi- dimers used to explain the zig zag chains observed ment, at least or the p(2 2) translational symmetry by STM or intermediate P coverages [16,17]. observed in STM and assumed in the TE Another possibility or the ormation o zig zag calculations, other reasons have to be considered, chains along the [110] direction could be a corresponding arrangement o phosphorus atoms in the adlayer structure aa1 in Fig. 1. This c(2 2) overlayer is characterized by a zig zag arrangement o two P atoms on top o a complete In layer Structures with >1 ML phosphorus The suraces with more than one monolayer o P are shown in Fig. 2. We have considered several possible dimer reconstructions and adatom arrangements, ranging rom 1.5 to 2 ML o P and exhibiting a p(2 2) or c(2 2) translational sym- metry. The (2 2)td2 structure ( Fig. 2) has just one P dimer per (2 2) cell, on top o a complete P monolayer (H=1.5). It is buckled with a buck- However, this adatom structure is unstable. I we instead allow the ormation o a dimer, i.e. the (2 2) td1 structure in Fig. 1, the energy decreases by about 0.3 ev per atom. The complete coverage o the In-terminated (001) surace by top-p dimer td1 with p(2 2) td1 or p(2 2)td1s translational symmetries oers urther possibilities or the ormation o chain structures. The two dimers per or instance a deect stabilization o local structures at real suraces, adsorption o urther species, such as hydrogen, or electron correlation eects.

6 O. Pulci et al. / Surace Science 464 (2000) ling amplitude o 0.69 Å. The driving orces or layers o the P adsorbate, we discuss the two this reconstruction seem to be the same as in the reconstructions p( 2 2)td2 and p(2 2)td2s with case o Si and Ge(001) suraces o bulk systems a P coverage o H=2 in more detail. The most with a small energy gap [31]. A charge transer important geometry parameters are listed in rom the lower to the upper P atom o the dimer Table 1 and deined in Fig. 4. The interesting point occurs. Nevertheless, the buckled dimers cannot is that the reconstruction is not only characterized explain the observed zig zag rows since each by the ormation o two P dimers in the uppermost second dimer is missing. The c( 2 2)aa2 structure P layer with dierent distances to the In termina- ( Fig. 2), with the same surace stoichiometry but tion o the bulk. Rather, there is also a remarkable without dimer bonds between the two extra P displacement o the dimers parallel to the [1: 10] adatoms on top o the complete P monolayer, is direction. Consequently, bonds between the dimer also unstable. This structure is about 0.1 ev/atom displaced outward and the second atomic layer are higher in energy than the (2 2) td2 one, thus stretched considerably. Actually, the distances L= showing that the dimer ormation is always energetically 3.3 and 3.6 Å are too long or covalent bonds. A more avourable. The two top-p dimer typical measure o a bond is the sum o the structures p(2 2)td2 and p( 2 2)td2s with H= covalent radii, about 2.12 Å. On the other hand, 2 ( Fig. 2) show again no buckling. In contrast to the bonds o the dimers displaced towards the the case o smaller coverage, e.g. H=1.5 represented bulk and the second atomic layer are shortened to by (2 2)td2, the dimer dimer interaction l=2.0 or 2.30 Å. A similar trend is observed or makes buckling unavourable. The insulating character o the surace is again a consequence o the lower dimers and d =2.1 Å in the upper dimers. 2 the dimer bond lengths o d =2.4/2.61 Å in the 1 geometrical and electronic inequivalence o the There seems to be a tendency or a two-old two dimers. As in the monolayer case, they dier coordination o the atoms in the uppermost P with respect to the distance rom the underlying layer. Each P atom possesses two strong bonds complete P layer and with respect to their dimer and a weak bond. In the second atomic layer this lengths. These vertical and horizontal dierences tendency is accompanied by the trend o a three- are 0.30 Å and 0.57 Å or the p(2 2)td2 structure, old coordination o hal o the atoms. Altogether, and 0.64 Å and 1.00 Å or the p(2 2)td2s one. the adlayer shows eatures known rom solid black The two dimers can accommodate eight and six phosphorus consisting o bilayers, where a P atom electrons, hence the surace can be semiconducting. has three nearest neighbours at about 2.2 Å and On the other hand, the mixed-dimer structures the minimum P P distance in adjacent layers md2, with parallel and antiparallel arrangement o amounts to 3.8 Å. the dimers and p( 2 2) translational symmetry ( Fig. 2), show a signiicant buckling. Among them, 3.2. Phase diagram the energetically most avourable one is the p(2 2)md2as structure with In P buckling o In Fig. 3 we plot the surace energies V o the about 0.6 Å. As an example or the characteristic arrangement o the phosphorus atoms in the two atomic energetically most avourable structures versus the In chemical potential in an interval slightly larger than the allowed range. The ideal unrelaxed surace Table 1 Structural parameters (Å) or P-rich InP(001) suraces with p(2 2)td2 and p(2 2)td2s geometry. The parameters are explained in Fig. 4 D 1z D1 1z D 2z D 3z d d 12 L l d 1 d 2 p(2 2)td p(2 2)td2s

7 278 O. Pulci et al. / Surace Science 464 (2000) Fig. 4. Top (a) and side (b) view o the P-rich (H=2) InP(001) suraces with p(2 2)td2 and p(2 2)td2s geometries. Open (illed) circles are In (P) atoms. The largest size o circles indicates the topmost layer. with one complete P layer is used as energy zero. translational symmetry. However, a complete comparison The surace phase diagram o InP(001) also o experimental and theoretical results is includes the (2 4) boundary o the In-rich phase. hardly possible. On the one hand, disorder eects It is known [13 15] that under In-rich preparation play an essential role. STM images indicate a conditions the (2 4) reconstruction is represented random distribution o the local structures and by a single mixed dimer on top o the In-terminated many deects [ 17]. Hence, long-range order is surace (c. Fig. 1). The phase diagram shows that absent, in contrast to the assumption in the TE under more P-rich conditions, (2 2) overlayer calculations. Furthermore, in particular during the structures with 2 or 1.5 ML P become more avour- MOVPE growth o the P-rich InP( 001) suraces, able. In the ramework o the restriction to (2 2) alkyl groups and H atoms adsorb onto the P translational symmetries, several dierent surace overlayer [18,19]. The adsorption onto hal o the geometries can be distinguished in dependence on exposed phosphorus atoms in the uppermost layer the chemical potential o In. Under the most P-rich may completely change the reconstruction conditions the p( 2 2)td2 reconstruction is the behaviour. most energetically avourable one. The staggered The situation becomes even more complicated arrangement o the two P dimers, the p(2 2)td2s in an intermediate range o P-rich surace prepara- structure, is close in energy. Thereore its existence tion conditions with Dm(In)/DH (InP) between cannot be excluded. Deect-induced strain ields 0.3 and 0.5 (c. Fig. 3). The TE calculations may stabilize other arrangements o the surace indicate a tendency or coexistence o several surace dimers. However, all avourable structures under phases o dierent structure and stoichiomedimers. P-rich conditions should contain two P monolayers try, at least the two top-p dimer structure with dierent P P dimers in the uppermost p(2 2)td2 with H=2, the one top-p dimer struc- atomic layer. ture (2 2)td2 with H=1.5, and the one mixeddimer Vogt et al. [17] and Hicks and coworkers [18,19] structure ( 2 4)md1 with H=0. However, observed or very P-rich growth conditions a mix- also a variety o other structures are close in ture o domains o c(4 2), (2 2) and c(2 2) energy. They involve the mixed-dimer structures

8 O. Pulci et al. / Surace Science 464 (2000) on top o a P layer [e.g. p( 2 2)md2ps in Fig. 2], correlation. Since the dimer interaction is weak, as well as the P monolayer structures td1 with the dispersion o the electronic surace-state bands p(2 2) or (2 1) translational symmetry ( Fig. 1). related to the p- and p1-dimer states is nearly All these structures represent a H=1 surace stoichiometry. vanishing. Consequently, a Mott Hubbard mechaindicates The similarity o their surace energies nism may correlate the electrons as recently that randomness may reduce the ree observed or Si-rich SiC(0001) suraces [ 32]. Other energy o the surace system or a given substrate eects are also possible. The obviously dierent temperature T. A conigurational entropy o about electron occupation o the two dimer atoms may 2k may already give a lowering o the ree energy also be related to a negative-u behaviour as predicted or alkali-covered GaAs(110) suraces [33]. B by about 0.1 ev per (1 1) unit cell at a temperature o about 600 K. Consequently, taking into In order to check this idea, spin-polarized calculations consideration the error bars o the calculations, need to be perormed. we cannot exclude the coexistence o several structural elements on one and the same surace: 3.3. Band structures unbuckled P dimers on a P monolayer, buckled dimers on a P monolayer, mixed dimers on a P In Fig. 5 the surace-state energy bands o the monolayer, unbuckled P dimers on the In termination, energetically most avourable P-rich structures, the and mixed dimers on the In termination. p(2 2) td2 ( Fig. 5a) and the p(2 2)td2s These structural elements can be combined to orm ( Fig. 5b), are shown together with the projected local arrangements, which may then give p( 2 2), InP bulk band structure. Both suraces are semiconducting. In both cases, V, the highest occupied 1 c(2 2) and ( 2 1) translational symmetries. Our calculations do not conirm the STM inter- surace band, lies slightly above the bulk valence pretation o the intermediate phase in terms o band maximum (VBM). The maximum occurs at one monolayer o buckled P P dimers [16,17]. The the J K line (closer to J) o the surace BZ. Empty TE optimizations o the ideal suraces show that surace-related bands also appear in the undamendimer buckling is energetically unavourable, as tal gap. The lowest band, C, exhibits one pronounced minimum on the C J line near J. The 1 or other suraces o polar semiconductors. According to our calculations, buckled dimers only other extremum at C corresponds more to a saddle occur or the missing-dimer (2 2)td2 and or point in the p( 2 2)td2 case, whereas it is a mixed-dimer structures. This indicates a discrep- minimum in the p( 2 2)td2s case. Consequently, ancy between theoretical results and STM indings both suraces possess an indirect gap JJ or intermediate variations o the In chemical [p(2 2) td2] or JC [p( 2 2)td2s]. The gap energies potentials [16]. The P zig zag chains being are 0.60 and 0.45 ev. In Fig. 6 we discuss the in-phase [generating p(2 2)] or out-o-phase orbital character o the two lowest empty (C, 1 [generating c( 4 2)] on an In atomic layer cannot C ) and the two highest occupied surace bands 2 be realized since the buckling o these dimer- (V,V) at the K point. As a consequence o the 1 2 related structures is unstable. However, there is an stretching o the back bonds, practically dangling additional problem. The semiconducting character bond-like surace states occur at the second layer o such a surace [16] needs urther consideration. P atoms. In the p(2 2)td2 case, the maximum With two exceptions [(2 1)td1 and (2 2)td1 in o V occurs between J and K about 0.3 ev above 1 Fig. 1], all overlayer structures studied theoretically the VBM. This band is related to the occupied ulil the electron counting rule and, hence, dangling bonds (p -like) o the P atoms in the z give rise to an insulating behaviour o the surace. second layer, since the bond to the uppermost However, this is not automatically the case or dimer is extremely weak. Also V is related to these 2 zig zag chain arrangements o, apart rom the dangling bonds. Additionally, antibonding p1 orientation, equally buckled P dimers derived rom the STM studies [16,17]. Additional eects may be involved, or instance eects o strong electron orbitals at the lower dimer and backbonds contribute strongly. The lowest empty surace band, C, 1 is related to antibonding s1-like orbitals located

9 280 O. Pulci et al. / Surace Science 464 (2000) Fig. 5. Surace band structure or the p(2 2)td2 (a) and p(2 2)td2s (b) suraces. Grey regions indicate the projected bulk band structure. at the lower dimer. The state belonging to the c(4 2) [16 19] domains are observed may be higher band, C, at K is an antibonding state traced back to the dierent geometry and 2 localized at the uppermost dimer (see Fig. 6a). electronic structure o the two top dimers in a In the p(2 2)td2s case, V is, around J, about 1 (2 2) cell. In order to investigate this idea, we 0.5 ev above the VBM. Also or this structure V 1 have perormed calculations o STM images or is a dangling bond state o the P atoms at the the most phosphorus-rich dimerized overlayer second layer, but also an antibonding orbital structures (2 2)td2, p(2 2)td2 and p(2 2)td2s p1-like o the lower dimer does contribute. The (c. Fig. 2). Calculating the STM images we use orbital corresponding to V has mainly a mixed 2 the same approach as in Re. [34]. In this approach s+p1 character, located at the lower dimer (see the tunneling current is proportional to the spa- Fig. 6b), but also the dangling bonds o the second tially resolved density o states integrated over a P layer do contribute (not shown in the igure). certain energy interval. Depending on the number The empty surace states C and C are antibondo either empty or occupied energy bands one can 1 2 ing combinations o orbitals o the upper and simulate STM images corresponding to dierent lower dimer, respectively. voltages applied to the sample with respect to From the analysis o these states, it is clear that the tip. a picture o the dimer states as purely s, p, s1 Results or images o the occupied states are and p1 orbitals is oversimpliied. Moreover, the plotted in Fig. 7. We have integrated states over an uppermost dimer has two rather weak bonds with energy interval o 1.5 ev below the VBM in order the P atoms at the second layer, as shown by the dangling bond character o V and V. Also the to simulate a negative bias o about 2.5 V. The 1 2 interpretation o the other surace states lying in simulated STM images mainly show the occupied the gap is quite diicult, since many contributions dimer states. The buckling o the top dimer in the rom dimer and backbond states appear. missing-dimer structure (2 2)td2 in Fig. 7a gives rise to a square lattice o the STM spots. In the 3.4. STM images case o the p(2 2)td2 structure rows o dimers with dierent intensity can be seen along the [1:10] The act that in several STM images o the direction. Indications or these reconstructions are most P-rich phase local ( 2 2), c(2 2) and not seen experimentally [16 19]. Interestingly,

10 O. Pulci et al. / Surace Science 464 (2000) Fig. 6. Contour plots o the squared wave unctions at K or highest occupied (V 1,V 2 ) and lowest unoccupied (C 1,C 2 ) surace states. (a) p(2 2)td2; (b) p(2 2)td2s. The states are plotted in a (1:10) plane (side view), with the exception o V 2 (a), plotted in the (110) plane, and V 1 (b), plotted in the (001) plane (top view). Grey circles indicates P atoms in the lower dimer. in-phase zig zag chains along [110] occur in the p(2 2)td2s case. This allows an interpretation o the experimental indings, provided that each dimer gives only one oval spot due to the limited experimental resolution. Then, at least the in-phase zig zag chain structures observed by Vogt et al. [17] and Hicks and coworkers [18,19] or extremely P-rich preparation conditions could be explained. Fig. 7. Filled state STM images calculated or the (2 2)td2 (a), p(2 2)td2 (b) and p(2 2)td2s (c) top-p dimer geometries, shown in Figs. 2 and 4. The dimer bonds are along the [110] direction.

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