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Arsenic Dimer Dynamics during MBE Growth: Theoretical Evidencefor a Novel Chemisorption State ofAs2 Molecules on GaAs Surfaces

C. G. Morgan,1,2 P. Kratzer,1 and M. Scheffler11Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany

2Physics Department, Wayne State University, Detroit, Michigan 48202(Received 9 December 1998)

Results of first-principles calculations are reported for the adsorption of As2 molecules on thestable surface reconstructions of the GaAs (001) surface, including adsorption paths and barristrongly bound sites. It is shown that a novel chemisorption state acts together with an intermphysisorbed plateau in the total energy to hold the As2 molecules near the surface and funnel theinto strongly bonding sites during epitaxial growth, and that this state can explain the transitionthe b2s2 3 4d to the cs4 3 4d reconstruction under low-temperature, very arsenic-rich conditio[S0031-9007(99)09336-9]

PACS numbers: 82.65.My, 68.45.Da, 81.10.Aj

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A wide variety of electronic and optoelectronic devices are based on multilayered structures composedIII-V semiconductors, such as GaAs. Understanding thfundamental kinetic processes of epitaxial growth is aimportant step toward optimizing the characteristics othese semiconductor layers by altering the growth condtions. Because of its technological importance as the mcommonly used surface for epitaxial growth of GaAsthe GaAs (001) surface has been extensively studieHowever, although the relative energies of various stareconstructions for this surface, with different surfacstoichiometries, have been thoroughly studied by firsprinciples calculations [1,2], gallium adatom diffusion isthe only kinetic process that has been thoroughly invesgated by such methods, including reaction paths and eergy barriers as well as the binding energies for stable ametastable adatom sites [3]. In particular, almost nothinis known about the microscopic reaction paths, reactibarriers, and kinetics of the important processes involing incoming arsenic, such as adsorption, diffusion, anincorporation into strongly bonded sites on the surface.

Experimental work, from the earliest studies of the interaction of gallium and arsenic beams with the GaAsurface [4–6] to recent scanning tunneling microscopstudies of island shapes and size distributions immediatfollowing a growth interruption [7], has shown that the kinetics of arsenic adsorption and attachment play an iportant role in GaAs growth. Although both As2 and As4sources are used for epitaxial growth of GaAs, it is simplto understand the growth processes when As2 is used, sincethe GaAs (001) surface reconstructions produced in stadard epitaxial growth are terminated with arsenic dimerso the As2 molecule does not necessarily have to breaup in order to become incorporated into the growing suface. For both As2 and As4 sources, in order to repro-duce growth without assuming unphysically large As:Gflux ratios, the growth models used in kinetic Monte Carlsimulations commonly assume that arsenic moleculesinitially adsorbed into a “molecular precursor” state [5–8

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However, no microscopic description of this precursstate has been given, and no microscopic model has bproposed for the incorporation of arsenic molecules frothe precursor state into the growing surface.

GaAs growth by molecular beam epitaxy (MBE) undmoderately arsenic-rich conditions produces theb2s2 3

4d reconstruction, shown in Fig. 1, which must grow bfilling the trenches and growing the new mountainsthe next layer up. In this Letter, we report resultsdensity-functional pseudopotential [9] calculations for A2adsorption at a large variety of sites on theb2s2 3 4dsurface, with and without additional gallium atoms—including both strongly bound sites where the arsedimer can attach to the dangling bonds of the surfaand sites where the ad-dimer cannot bind strongly—aadditional calculations on thecs4 3 4d surface, which isthe stable surface produced by MBE growth under vearsenic-rich conditions.

Our calculations were carried out using both the locdensity approximation (LDA) and the generalized gradieapproximation (GGA) [10]. We report the GGA resultfor the binding energies and adsorption barriers first, sinthese are known to be more reliable, followed by tLDA results in parentheses, for comparison to earlcalculations. The wave functions were expanded inplane-wave basis with a cutoff energy of 10 Ry, and t

FIG. 1. The b2s2 3 4d reconstruction of the GaAs (001surface with an incoming arsenic ad-dimer at the preferr“physisorbed” distance above the surface. Arsenic atomsgrey, and gallium atoms are white.

© 1999 The American Physical Society

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k-space integration was performed with a specialk-pointset, with a density equivalent to 64k points in theBrillouin zone of the (1 3 1) surface unit cell.

We have used a slab geometry to model the ad-dimesubstrate system, with slabs containing seven or eigatomic layers, passivated on the bottom by an additionlayer of pseudohydrogen atoms [11]. All the layers excethe bottom atomic layer and the pseudohydrogen atowere allowed to relax. The reported results were obtainfor a (4 3 4) periodicity parallel to the surface, which wehave found to be sufficient to model the interactions of aisolated As2 molecule with the surface.

When an arsenic molecule comes down on the surfaceis generally not in exactly the right position and orientatioto bind immediately to the dangling bonds of the GaAsurface. Instead, we find that the molecule will initiallycome into a region above the surface corresponding tointermediate plateau in the total energy, as shown in Fig.In this region, the ad-dimer behaves as if it is physisorbeit keeps the bond length of the isolated molecule (2.1 Årather than expanding to the bond length of the surfadimers (2.5 Å), and there is very little distortion of theGaAs surface below. While it remains in this regionthe arsenic ad-dimer has a binding energy to the surfaof about 0.2 eV (0.7 eV in the LDA). As long as thephysisorbed ad-dimer is located over the mountains of tb2s2 3 4d surface, it floats about 2.5 Å above the surfacHowever, its vertical position over the trenches is not swell defined, since it can float down into the trench withouencountering an energy barrier.

Estimating the lifetimet of As2 in the physisorbedregion by 1yt ­ C expf2EByskTdg, with an attemptfrequencyC ­ 1013 sec21 for escape back into the vaporphase [12] and a binding energyEB ø 0.2 eV, givesa lifetime t ø 2 3 10212 sec during standard epitaxialgrowth, around 800 K. Since physisorbed As2 moleculescan move around on the surface without significantchanging their energy or causing large relaxations of tsurface atoms below, they should be quite mobile, makiit easier for them to find favorable binding sites on thsurface and orient themselves so they can bind stronglythese sites before they desorb back into the vapor phas

If no gallium adatoms are present on theb2s2 3 4dsurface, we find that the strongest binding of the arsenad-dimer occurs when it comes down on top of the moutain, breaking the bonds of two adjacent arsenic surfadimers and inserting itself into these bonds, as shown

(b) FIG. 2. (a) Arsenic ad-dimerinserting itself into the secondsurface dimer bond and (b)arsenic ad-dimer chemisorbedon the top arsenic layer of theb2s2 3 4d surface. Arsenicatoms are grey, and galliumatoms are white.

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Fig. 2. The binding energy of the ad-dimer chemisorbeon the arsenic surface dimers of the mountain is abo1.6 eV (about 2.2 eV in the LDA); it remains practicallyunchanged (energy changes are less than 0.1 eV) whthere are arsenic ad-dimers chemisorbed on the mountain adjacent (2 3 4) unit cells, or gallium adatoms in thetrench nearby.

However, a favorable binding energy alone is nosufficient to ensure that the ad-dimer actually adsorbs othis site. There must also be at least one trajectory withsmall or nonexistent adsorption energy barrier for the addimer chemisorbing on this site. If the ad-dimer comedown parallel to the surface, breaking both dimer bondsimultaneously, we find that there is a prohibitively largebarrier (over 1 eV, even in the LDA). However, if thead-dimer comes down one end first, breaking one dimbond and inserting itself, and then tips over to break thsecond surface dimer bond [as shown in Fig. 2(a)], theis no adsorption barrier. Therefore the site on the arsensurface dimers of the mountain should be populated bincoming As2 molecules and depopulated by desorptionof As2. The desorption is activated, with an activationenergy equal to the binding energy.

Experimental work starting with the earliest studies[4–6] shows that arsenic can bind to the surface moreffectively when gallium adatoms are present. Earlietheoretical work [3] has shown that the most energeticallfavorable place for gallium adatoms on theb2s2 3 4dsurface is in the trenches, and it is particularly favorablif two gallium atoms in the trench occupy adjacent sitesfilling the gallium layer at the bottom of the trench andforming theas2 3 4d reconstruction in one unit cell [13].

Of all the configurations we have studied, we find thestrongest binding energy, 2.4 eV (3.5 eV in the LDA),for the arsenic ad-dimer coming down on top of suchpair of gallium adatoms in the trench, and locally formingthe bs2 3 4d reconstruction. This result is in agreemenwith earlier LDA calculations of Shiraishi and Ito [14],which showed that adding two gallium adatoms to filthe gallium layer at the bottom of the trench stabilizethe binding of an additional arsenic dimer in the arsenilayer above. We find that an As2 molecule coming downparallel to the surface can adsorb on top of a pair ogallium atoms in the trench with no adsorption barrier.

We find that the arsenic ad-dimer has a binding energof 1.9 eV (2.6 eV in the LDA) on top of a single galliumatom in the trench. The arsenic atom which has n

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gallium atom beneath it will tip slightly downward towardthe empty gallium site, but the dimer will not dissociateAs in all the other strongly bound adsorption sites whave investigated, the arsenic ad-dimer prefers to rema dimer: if we separate the arsenic atoms, placing oon top of the gallium atom and the other in the empgallium site beside, they will relax back to the tilted dimeconfiguration. Binding energies for the ad-dimer in othsites near gallium adatoms in the trench are less favorathan the binding energy for the ad-dimer chemisorbedthe arsenic surface dimers of the mountain.

We may estimate the desorption rate, or inverse lifetimD for arsenic ad-dimers at various strongly bonded siton the surface by usingD ­ 1yt ­ C expf2EByskT dg,with an attempt frequencyC ­ 1013 sec21 for escape backinto the vapor phase. The binding energiesEB and thecorresponding desorption ratesD for an arsenic ad-dimerchemisorbed on the top arsenic layer of the mountain,bound on top of one or two gallium adatoms in the trencare given in Table I. We use GGA energies, rather ththe overestimated LDA binding energies, in this table.

The estimated desorption rates can be compawith the incoming As2 flux during growth, e.g.,3 3 1014 moleculesyscm2 secd [15], or 4 moleculesysecfalling on each (2 3 4) unit cell. Since the estimated desorption rate for an arsenic ad-dimer bound on top of a pof gallium adatoms in the trench is very low at the commonly used temperatures for MBE growth, any ad-dimewhich desorb from these sites should be easily replacby incoming As2 molecules. However, ad-dimers bounon top of a single gallium adatom are predicted to desotoo rapidly at 800 K to be replaced by this incominflux; observation of these is predicted only for higheAs2 fluxes or lower temperatures. Arsenic ad-dimechemisorbed on the top arsenic layer of the mountain aalso expected to desorb too rapidly to be replaced durstandard, high-temperature MBE growth around 800 K.

Although the arsenic ad-dimers which adsorb on thmountain, on top of a single gallium adatom, or in othemore weakly bound configurations near gallium adatomare ultimately expected to desorb during growth at 800these adsorption sites still play an important role in extening the lifetime of As2 molecules on the surface. Whenan As2 molecule which has been temporarily adsorbedone of these sites desorbs, it enters the physisorbed regwhere it can move around reasonably freely—so it mbecome bound in another temporary adsorption site or fi

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TABLE I. Arsenic ad-dimer binding energyEB and desorption rateD (or inverse lifetime,in sec21) at different temperatures, for various ad-dimer sites.

EB D D DSite (eV) at 500 K (sec21) at 700 K (sec21) at 800 K (sec21)

On mountain: 1.6 6.9 3 1024 29 790On 1 Ga in trench: 1.9 6.5 3 1027 0.2 10On 2 Ga in trench: 2.4 5.8 3 10212 4.9 3 1025 7.1 3 1023

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its way into a strongly bound site before it escapes bainto the vapor phase. Since the As2 molecule does notdissociate in any of the adsorption sites we have fouwhich have a binding energy of 0.5 eV or more, these sondary adsorption sites, together with the physisorbedgion, which increases the mobility of As2 on the surface,can function as a molecular precursor state, increasinglikelihood that an incident As2 molecule will become in-corporated into the crystal. We note that kinetic MonCarlo simulations of growth require a “precursor statwith a binding energy of about 1.7 eV [16], which is quitclose to the calculated binding energy for an arsenicdimer chemisorbed on the mountain. Since mountain sshould significantly outnumber unpaired gallium adatomin the trenches, we would expect the mountain sites to pa dominant role in extending the lifetime of As2 moleculeson the surface.

When the temperature is lowered, desorption ratesstrongly reduced for arsenic ad-dimers at all adsorptsites. For example, if the temperature is reduced fr800 to 700 K, the estimated desorption rate for arsenicdimers chemisorbed on the top arsenic layer of the motain (shown in Table I) is reduced from790 to 29 sec21.If there is no incoming gallium flux to provide sites withstronger binding energies in the trench, it seems likethat these sites can be resupplied by an As2 flux of 4.5 3

1015 moleculesyscm2 secd, or 60 moleculesysec falling oneach (2 3 4) unit cell. So we would expect significannumbers of arsenic molecules to chemisorb and remainthe top arsenic surface layer if the surface is exposedan As2 flux of 4.5 3 1015 moleculesyscm2 secd at 700 K.This suggests that under such conditions the surface shtransform to a new reconstruction involving a top patial layer of arsenic chemisorbed on arsenic: thecs4 3 4dreconstruction.

The cs4 3 4d surface, which is shown in Fig. 3 witha single additional arsenic molecule chemisorbed onis terminated by a complete layer of arsenic, withadditional partial layer of arsenic on top. Like the arsenatoms in the top layers on the mountain and in the trenfor the b2s2 3 4d surface, the arsenic atoms in the topartial layer of thecs4 3 4d surface form dimers. Thelocal bonding for the arsenic in the top partial layerthe cs4 3 4d surface is quite similar to the local bondinfor the ad-dimer chemisorbed on the top arsenic layerthe mountain, shown in Fig. 2(b): each arsenic atomthe top partial layer is bonded to its dimer partner, a

VOLUME 82, NUMBER 24 P H Y S I C A L R E V I E W L E T T E R S 14 JUNE 1999

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FIG. 3. One arsenic ad-dimer chemisorbed on the surfadimers of the top partial layer of arsenic for thecs4 3 4dsurface. The arsenic atoms of the top partial layer and tad-dimer are black, arsenic atoms in lower layers are grey, agallium atoms are white. For ease of viewing, the atomic radare taken to be larger in this figure than in the other figures.

to two adjacent arsenic atoms in the layer below. Tharsenic atoms of the top partial layer and the additionchemisorbed arsenic molecule are shown black insteadgrey in Fig. 3, so that it easier to see that the dimersthe top partial layer are arranged in rows of three dimefollowed by an empty dimer site.

The transition from theb2s2 3 4d to the cs4 3 4dreconstruction has in fact been observed for GaAs surfacheld at 700 K under a somewhat lower As2 flux of 3 3

1014 moleculesyscm2 secd [15]. Although we predict sucha transition only at a somewhat higher flux, we cannexpect our simple method of estimating desorption ratfrom the calculated desorption energies to reproduce texact boundaries for theb2s2 3 4d to cs4 3 4d transition.

When an As2 molecule comes down on thecs4 3 4dsurface, we find that the molecule will initially comeinto a region above the surface where it acts as if itphysisorbed, just as incoming As2 molecules do on theb2s2 3 4d surface. While the ad-dimer remains in thphysisorbed region, it has a binding energy to the surfaof about 0.2 eV (0.8 eV in the LDA), and it keeps the bonlength of the isolated molecule rather than expanding to tbond length of the arsenic dimers in the top partial lay(2.5 Å).

If no gallium adatoms are present on thecs4 3 4d sur-face, we find that the arsenic ad-dimer can bind strongon top of two adjacent dimers in the top partial layer, bbreaking these dimer bonds and inserting itself. The boning configuration for the ad-dimer chemisorbed on thearsenic dimers looks very similar to the bonding configuration for the ad-dimer chemisorbed on the arsenic suface dimers of theb2s2 3 4d surface, shown in Fig. 2(b).Since the ad-dimer on thecs4 3 4d surface is chemisorbedon top of two layers of arsenic, rather than on top of onlayer, as it would be on theb2s2 3 4d surface, it has abinding energy of only 1.4 eV (2.2 eV in the LDA).

Figure 3 shows the top view of thecs4 3 4d surfacewith a single ad-dimer chemisorbed on the top partial layof arsenic. Under sufficiently low-temperature, arseni

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rich conditions, we expect that arsenic ad-dimers wichemisorb randomly at one end or the other of each groof three surface dimers, causing thecs4 3 4d RHEEDpattern to become fuzzier. If this is followed by furtherandom arsenic adsorption at more weakly bound sitethecs4 3 4d ordering may disappear completely. Suchchange from thecs4 3 4d pattern to a disordereds1 3 1dpattern has been seen [17,18] for GaAs gradually coolfrom from 700 to 500 K under an As2 pressure of1.5 3

1025 Torr, which corresponds to a flux of over1.5 3

1015 moleculesyscm2 secd.The enhanced chemisorption of As2 molecules on

the arsenic surface dimers which occurs under lowtemperature, arsenic-rich conditions can also explain twell-documented observation that MBE growth of GaAunder such conditions leads to incorporation of up to (12)% excess arsenic, which can produce technologicaattractive, high-resistivity material with ultrashort carrielifetimes [19].

This work was supported in part by AFOSR GranNo. F49620-96-1-0167. Cray T3E time was provided athe Fritz-Haber-Institut and the Computing Center of thMax-Planck-Gesellschaft at Garching, and by grantstime at the DOD HPC NAVO Center and at the NPACSan Diego Supercomputing Center.

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[14] K. Shiraishi and T. Ito, Phys. Rev. B57, 6301 (1998).[15] J. H. Neaveet al., Surf. Sci.133, 267 (1983).[16] M. Itoh (private communication).[17] K. G. Eyink et al.,J. Vac. Sci. Technol. B11, 1423 (1993).[18] K. G. Eyink et al., J. Electron. Mater.22, 1387 (1993).[19] Low Temperature GaAs and Related Materials,edited by

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