Employing first principles total energy calculations we have studied the
behavior of Ga and Al adatoms on the GaAs(001)-beta2 surface. The adsorption
site and two relevant diffusion channels are identified. The channels are
characterized by different adatom-surface dimer interaction. Both affect in a
novel way the adatom migration: in one channel the diffusing adatom jumps
across the surface dimers and leaves the dimer bonds intact, in the other one
the surface dimer bonds are broken. The two channels are taken into account to
derive effective adatom diffusion barriers. From the diffusion barriers we
conclude a strong diffusion anisotropy for both Al and Ga adatoms with the
direction of fastest diffusion parallel to the surface dimers. In agreement
with experimental observations we find higher diffusion barriers for Al than
for Ga.Comment: 4 pages, 2 figures, Phys. Rev. Lett. 79 (1997). Other related
  publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Alexander Kley

B. D. Yu

C. Roland

D. M. Bylander

E. Kapon

E. Kaxiras

G. B. Bachelet

G. Brocks

G. H. Vineyard

J. E. Northrup

J. H. Neave

J. M. Hove

J. Neugebauer

J. P. Perdew

J. Tersoff

J. W. Haus

K. Ohta

K. Shiraishi

L. Däweritz

M. Hata

M. Kawabe

Matthias Scheffler

Paolo Ruggerone

R. Z. Bachrach

S. Koshiba

T. Hashizume

T. Nishinaga

T. Shitara

X. Q. Shen

Y. Horikoshi

English

arXiv

Kley, Alexander

Ruggerone, Paolo

Scheffler, Matthias

Max Planck Society eDoc Server

Novel diffusion mechanism on the GaAs (001) surface: the role of adatom-dimer interaction

Crossref

Novel Diffusion Mechanism on the GaAs(001) Surface: The Role of Adatom-Dimer Interaction

Kley, A.

Ruggerone, P.

Scheffler, M.

MPG.PuRe

arXiv:cond-mat/9710180v1  [cond-mat.mtrl-sci]  17 Oct 1997Novel diffusion mechanism on the GaAs (001) surface: the role ofadatom–dimer interactionAlexander Kley, Paolo Ruggerone, and Matthias SchefflerFritz-Haber-Institut der Max-Planck-Gesellschaft,Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany(February 1, 2008)Employing first principles total energy calculations we havestudied the behavior of Ga and Al adatoms on the GaAs(001)–β2 surface. The adsorption site and two relevant diffusionchannels are identified. The channels are characterized bydifferent adatom–surface dimer interaction. Both affect in anovel way the adatom migration: in one channel the diffusingadatom jumps across the surface dimers and leaves the dimerbonds intact, in the other one the surface dimer bonds arebroken. The two channels are taken into account to derive ef-fective adatom diffusion barriers. From the diffusion barrierswe conclude a strong diffusion anisotropy for both Al and Gaadatoms with the direction of fastest diffusion parallel to thesurface dimers. In agreement with experimental observationswe find higher diffusion barriers for Al than for Ga.PACS numbers: 68.35.Fx, 68.35 JaGrowth techniques, such as molecular beam epitaxy,operate under conditions far away from thermodynamicequilibrium. Particularly for growth at low tempera-tures or for structures with length scales smaller than theadatom diffusion length, features driven by the growthkinetics have been observed. [1] In the GaAs/AlAs het-eroepitaxy the differences between the growth kinetics ofAlAs and GaAs have been utilized to create low dimen-sional structures. [2] Recently Kapon et al. [3] success-fully fabricated quantum wire heterostructure in whichstimulated emission has been observed.Despite these successes the underlying microscopicprocesses such as adsorption, surface diffusion, desorp-tion, and nucleation are poorly understood. A key mech-anism in growth is cation surface diffusion which is con-sidered to be a rate limiting process. [4,5] Experimentallythe surface diffusion is difficult to access. The deducedmigration barriers [6–10] for Ga adatoms span a rangebetween 1.1 and 4.0 eV. Even the anisotropy of surfacediffusion on the (001) surface is controversially debated:Shitara et al. [11] speculate that fastest diffusion is alongthe [110] direction; in contrast, Kawabe et al. [4] pro-pose the [110] direction. We have therefore performedfirst-principles total-energy calculations which constitutea powerful tool to study surface diffusion.Adatoms on solid surfaces occupy well defined bind-ing sites. The migration of the chemisorbed adatoms canbe described as a hopping between these sites. The ac-tivation energies for the individual hops are determinedby the energy differences between the binding and thetransition sites. These positions can be identified as theminima and saddle points of the potential energy surfaceover the configurational space spanned by the the coor-dinates of the adatom and the substrate atoms. In orderto find all minima and transition sites a mapping of theentire configurational space is in principle required. How-ever, this is computationally neither possible nor useful.For the study of surface diffusion the mapping is com-monly restricted to a subspace given by the lateral coor-dinates of the adsorbate. [12–16] This mapping gives thepotential energy surface (PES) E(x, y) for a given lateralposition (x, y) of the adatom where all substrate atomsand the z coordinate of the adatom are fully relaxed.This implies that all minima and saddle points relevantfor the description of surface diffusion can be found onone single PES. However, in this Letter the results of ourfirst principles study on the cation diffusivity show thatthis assumption fails for the migration on the GaAs(001)surface.In this paper we focus on the GaAs(001)–(2×4) sur-face in the β2 phase. This structure has been shownto be stable at the equilibrium [17] as well as to be thedominating surface structure over a wide range of growthconditions. [18,19] As shown in Fig. 1, each (2×4) unitcell consists of two As dimers and two missing dimers inthe topmost layer, a missing Ga pair in the second layerand a As dimer in the third layer.Our calculations of the PESs employ density func-tional theory in the generalized gradient approxima-tion (GGA). [20] The electron-ion interaction is de-scribed by fully separable, norm-conserving pseudopoten-tials. [21,22] The adatom-substrate system is modeled bya supercell geometry with a (4×4) periodicity parallel tothe surface. This supercell has been tested to be suffi-ciently large to have a negligible adatom-adatom interac-tion. Perpendicular to the surface our supercell containsa vacuum of 6 layers GaAs and an additional layer ofpseudo H-atoms (Z=0.75) to saturate the bonds of thelower surface. [23] To prevent a dipole-dipole interactionbetween the inequivalent upper and lower surface of ourslab we use a dipole correction. [24] The wave functionsare expanded in a plane-wave basis with a cutoff energyof 10Ry. The k–space integration was performed witha special k-point set, with a density equivalent to 64 k-points in the Brillouin zone of the (1×1) surface cell.1The PES has been mapped on an equidistant grid witha spacing of 1 A˚ along the [110] and the [110] direction.At each position the upper four substrate layers and theadatom height were fully relaxed, starting from the posi-tions of the clean surface for the substrate and an adatomheight of 3 A˚ above the surface. In a second step we in-terpolated the PES from the energy values on the mesh.Subsequently we repeated our mapping around the in-terpolated saddle points using a finer mesh. The exactpositions of the local minima were obtained by puttingthe adatom on the interpolated minima and relaxing allatomic positions without constraints.The resulting PES for a Ga adatom is shown in Fig.1(a). In each (2×4) unit cell we find the binding sites:A1 and the two equivalent positions A2 and A2′ . Allthree binding sites are on long bridge positions betweensurface As–dimer. This agrees with previous first princi-ples calculations [15] for the metastable (2×4)–β struc-ture (assuming near-equilibrium growth conditions [25],at T = 900 K, a typical growth temperature, the surfacearea covered with the β2 phase and the area covered bythe β phase differ by more than two orders of magnitude).At the three binding sites our calculations yield a stronginward relaxation of the adatom which resides almostin the center between the neighboring As atoms. Thesubstrate atoms display only minor deviations (< 0.2 A˚)from their clean surface positions; in particular the sur-face dimer bonds remain intact.From PES shown in Fig. 1(a) migration on GaAs(001)can be described as a sequence of random hops on a pe-riodic (2×4) lattice with the three binding sites. Theeffective diffusion barrier is determined by applying theformalism of continuous time random walk (CTRW) [26]that yields the diffusion tensor as a function of the indi-vidual hopping rates between neighboring binding sites.Within transition state theory [27] the individual hop-ping rate from a site Ai to a site Aj via a transitionstate Tk can be written asΓij = Γ0ij exp[(E(Tk)− E(Ai))/kBT ] (1)where E(Ai) and E(Tk) are the energies given in Tab. I.Γ0ij is a temperature independent prefactor and assumedto be roughly the same for all individual hops. This as-sumption leads to only minor errors as long as solely theeffective diffusion barrier are discussed. [12,13,15] Apply-ing the CTRW formalism [28] and considering the size ofthe individual activation energies we find for the diffusionconstants along the [110] and [110] directionsD[110] =Γ12Γ21(2Γ22+Γ22′ )(2Γ12+Γ21)(4Γ22+Γ21+2Γ22′ )8a20≈Γ1228a20 (2)D[110] =4Γ12Γ22+Γ11Γ212Γ12+Γ212a20 ≈ Γ11 2a20 (3)a0 is the lattice constant of GaAs. From the approx-imated solutions we get as effective diffusion barriers∆E[110] = E(T1)−E(A1) and ∆E[110] = E(T4)−E(A1),i.e. ∆E[110] = 0.8 eV and ∆E[110] = 0.6 eV.In the above discussion we have implicitly assumedthat all relevant minima in the configuration space couldbe found by relaxing the adatom from a position in thevacuum and the substrate from its ideal position in theclean case. This is true if all other minima of the totalenergy are either energetically much higher or separatedfrom the first minima by a large barrier. The assump-tion should be correct when the surface exhibits mainlybulk-like bonds, as it is the case for most metal surfaces.For reconstructed semiconductor surfaces, however, sur-face bonds exist which differ significantly from the bulkbonds, as for example anion–anion dimers. On those sur-faces stable adsorption sites for a cation could be realizedby breaking these weak surface bonds and forming bulk-like cation-anion bonds instead.Since in the PES shown in Fig. 1(a) the adatom doesnot break any surface As-dimer, we investigate in moredetails the adatom–dimer interaction. Fig. 2(a) showsthe binding energy of the adatom as a function of itsheight za−d on the dimer center with its lateral coor-dinates (x, y) fixed above the dimer center [site A3 inFig. 1(b)] and the substrate fully relaxed. Approachingthe surface from the vacuum we find a first local mini-mum at za−d ≈ 2 A˚ which corresponds to a saddle pointin the PES shown in Fig. 1(a). Coming closer to thesurface there is a barrier at za−d ≈ 1.2 A˚ and anothermuch deeper minimum at za−d ≈ 0.1 A˚. Such a doublepotential well was already predicted for Si on Si (001)by Roland and Gilmer. [16] The origin of the barrierand the presence of the second minimum can be under-stood by analyzing the bonding situation of the adatomto the dimer. At the first minimum the adatom interactswith the completely filled dangling bonds of the dimer[Fig. 2(c)], at the second one it breaks the dimer bondand forms directional bonds with the adjacent anions[Fig. 2(b)]. The barrier between the minima is due tothe energy cost required to break the As–dimer. Thebinding energy at the second minimum is higher thanthat at the previously found binding sites A1, A2 andA2′ . This shows that the adsorption site which is de-fined as the site with the highest binding energy cannotbe on the PES displayed in Fig. 1(a).To find the real adsorption site and to include the in-fluence of the dimer breaking on the diffusion proper-ties we map the PES a second time. In contrast to themapping of the first PES the adatom height z is nowrelaxed starting from a position 0.5 A˚ above the surfaceand the surface As atoms are relaxed from a initial po-sition where the As–As dimer bond length is 3.5 A˚, i.e.the directional dimer bonds are broken. Fig. 1(b) dis-plays the resulting PES. Figs. 1(a) and (b) show thatthe two PESs are similar over a wide area but they dif-fer significantly around the dimers. In addition to thebinding sites already present on the first PES we find2three new binding sites in each unit cell: A3 and the twoequivalent positions A4 and A4′ . The comparison of thebinding energies of the whole set of binding sites yieldsas adsorption site A3, a short bridge site between the Asatoms of one dimer.At A3, A4 and A4′ the adatom breaks the dimer, andcharge accumulations between the adatom and the adja-cent anions confirm the formation of directional bonds.The angle between the two adatom-As bonds is about175◦, i.e. the adatom is almost incorporated into the Astop layer. This is accompanied by a strong horizontalrelaxation of the As atoms bonded to the adatom. Theyrelax along the [110] direction, and the As–As distanceincreases from ≈ 2.5 A˚ (the As–dimer bond length) to4.4 A˚ which is close to the As-As distance in bulk GaAs(4.0 A˚). The relaxation keeps the nearest neighbor bondlength of the substrate atoms nearly unchanged and re-sults in bulk like adatom–As bond lengths. Such a relax-ation has been observed experimentally for an Al termi-nated (2×1) reconstructed GaAs (001) surface. [29] Thedriving mechanism for the flat incorporation of the cationis analogous to that which leads to the well known inwardrelaxation of the surface Ga atoms on GaAs(110). Thetwo–fold coordinated adatom with only partially occu-pied dangling bonds rehybridizes to a planar sp or sp2bonding configuration. At the same time the three–foldcoordinated As atoms bonded to the adatom gain energyfrom rehybridization to a p3 bonding configuration.To find the exact binding energies at the transitionsites T5, T6 and T7 between the short bridge and thelong bridge binding sites the PES has been mappedaround the interpolated transitions sites as a functionnot only of the lateral adatom coordinates but also ofthe dimer atoms. Note that we found an energy bar-rier to break the dimer for every pathway of the adatomtoward A3, A4, and A4′ .Including the new binding sites, surface diffusion is de-scribed by a random hopping on a periodic (2×4) latticewith six sites in each unit cell: A1, A2, A2′ , A3, A4,and A4′ . With the CTRW formalism we approximatethe diffusion constants (the rather long exact expressionwill be published elsewhere [28]) as:D[110] ≈Γ12Γ31 + Γ13Γ322Γ138a20 (4)D[110] ≈Γ11Γ31Γ132a20 (5)From theses equations we find as effective diffusion bar-riers ∆E[110] = E(T1) − E(A3) and ∆E[110] = E(T4) −E(A3). Inserting the energies given in Tab. I we findfor the Ga adatom diffusion ∆E[110] = 1.5 eV and∆E[110] = 1.2 eV. From these values a significant dif-fusion anisotropy with fastest diffusion parallel to thesurface dimers can be concluded.The inclusion of the binding sites of the second PESchanges the diffusion barriers dramatically. At firstglance, taking into account only the second PES seems tobe sufficient for the calculation of the diffusion barriers.However, from Eq. (5) it is clear that the description ofthe diffusion parallel to the surface dimers demands hop-ping rates from both PESs. If the contributions from onePES are neglected [as in the Eqs. (2) and (3)], wrong bar-riers are obtained. The reason for involving both PESsis that the energy barrier to hop from a site A1 to asite A3 (which requires the breaking of a dimer) is onlyslightly higher than the one to migrate from the site A1to a neighboring A1 site. Thus, once an adatom occupiesa weakly bound A1 site it performs a number of hops toneighboringA1 sites (like surfing on the first PES) beforebeing trapped again in a strongly bound A3 site.Our calculated diffusion barriers for a Ga adatom areat the lower limit of the experimentally deduced diffusionbarriers (1.1 – 4.0 eV). This seems reasonable because theexperimental results were derived rather indirectly fromgrowth experiments and therefore they are affected byadatom–adatom and adatom–step interactions. Further,the adatom mobility depends on the As supply and de-creases with increasing As flux. [30] Accounting for sucheffects should result in an effective diffusion barrier higherthan that calculated here for a single adatom.We have performed similar calculations also for an Aladatom. The PESs are almost identical to those of aGa adatom, i.e. the positions of the minima and ofthe saddle points for the two cations differ by less than0.1 A˚. The main difference is a slightly stronger corru-gation for Al adatoms leading to higher diffusion barri-ers: ∆E[110] = 1.6 eV and ∆E[110] = 1.3. The enhancedcorrugation can be understood in terms of the higher co-hesive energy of AlAs (EcohAlAs = 3.78 eV) compared toGaAs (EcohGaAs = 3.26 eV) implying that Al-As bonds arestronger than Ga-As bonds. From the higher barriers weconclude a lower mobility of Al adatoms which is in ac-cordance with several experiments. [1,8] Our calculateddifference in the barrier height of about 0.1 eV for Al com-pared to Ga adatoms agrees rather well with the value of0.16 eV obtained by Shitara et al. [8] from Monte–Carlosimulations of RHEED measurements of the growth ofAlAs and GaAs.In conclusion, we have shown that the adatom–surfacedimer interaction is crucial for determining the adsorp-tion site as well as the effective diffusion barrier. The ori-gin of the very stable new adsorption site is that a weaksurface bond (As–As) is replaced by almost bulk–likecation–As bonds. This mechanism should also work onother semiconductor surfaces exhibiting surface dimersor trimers.Stimulating discussions with E. Pehlke and K. Shi-raishi are acknowledged. We thank the SFB–296 for fi-nancial support.3[1] S. Koshiba et al., J. Appl. Phys. 76, 4138 (1994).[2] X. Q. Shen, M. Tanaka, K. Wada, and T. Nishinaga, J.Crystal Growth 135, 85 (1994).[3] E. Kapon, D. H. Hwang, and R. Bhat, Phys. Rev. Lett.63, 430 (1989).[4] M. Kawabe and T. Sugaya, Jpn. J. Appl. Phys. 28, L1077(1989).[5] Y. Horikoshi, M. Kawashima, and H. Yamaguchi, Jpn.Apl. Phys. 25, l868 (1986).[6] T. Nishinaga and K. Cho, Jpn. J. Appl. Phys. 27, L12(1988).[7] J.H. Neave, P.J. Dobson, B.A. Joyce, and J. Zhang, Appl.Phys. Lett. 47, 100 (1985).[8] T. Shitara, J. H. Neave, and B. A. Joyce, Appl. Phys.Lett. 62, 1658 (1993).[9] K. Ohta, T. Kojima, and T. Nakagawa, J. Cryst. Growth95, 71 (1989).[10] J.M. Hove and P.I. Cohen, J. Cryst. Growth 81, 13(1987).[11] T. Shitara et al., Phys. Rev. B 46, 6825 (1992).[12] G. Brocks, P.J. Kelly, and R. Car, Phys. Rev. Lett. 66,1729 (1991).[13] B.D. Yu and A. Oshiyama, Phys. Rev. Lett. 72, 3190(1994).[14] E. Kaxiras, Thin Solid Films 272, 386 (1996).[15] K. Shiraishi, Thin Solids Films 272, 345 (1996).[16] C. Roland and G.H. Gilmer, Phys. Rev. B 46, 13428(1992).[17] J.E. Northrup and S. Froyen, Phys. Rev. B 50, 2015(1994).[18] L. Da¨weritz and R. Hey, Surf. Sci. 236, 15 (1990).[19] T. Hashizume et al., Phys. Rev. Lett. 73, 2208 (1994).[20] J.P. Perdew et al., Phys. Rev. B 46, 6671 (1992).[21] G.B. Bachelet, D.R. Haman, and M. Schlu¨ter, Phys. Rev.B 26, 4199 (1982).[22] D.M. Bylander and L. Kleinman, Phys. Rev. B 41, 3509(1990).[23] K. Shiraishi, J. Phys. Soc. Jap. 59, 3455 (1990).[24] J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067(1992).[25] J. Tersoff, M.D. Johnson, and B.G. Orr, Phys. Rev. Lett.78, 282 (1997).[26] J.W. Haus and K.W. Kehr, Phys. Rep. 150, 264 (1987).[27] G.H. Vineyard, J. Phys. Chem. Solids 3, 121 (1957).[28] A. Kley, unpublished.[29] R.Z. Bachrach, R.S. Bauer, P. Chiaradia, and G.V. Hans-son, J. Vac. Sci. Techn. 18, 335 (1981).[30] M. Hata, A. Watanabe, and T. Isu, J. Crystal Growth111, 83 (1991).TABLE I. Binding energies (eV) of a Ga adatom at varioussurface sites on the GaAs(001)–(2×4) β2 structuresite A1 A2 A3 A4 T1 T2 T3 T4 T5 T6 T7Ga -2.5 -2.2 -3.2 -2.6 -1.7 -1.8 -1.6 -2.0 -1.45 -1.5 -1.9 A1A2A20T3T4T1T2(a) [001][110][110]side viewtop view(b)A1A2A20T3T6T5T7T1T2A4A40A3FIG. 1. Total energy surfaces for a Ga adatom on theGaAs(001)–(2×4) β2 surface. (a) PES obtained when theadatom is relaxed from 3 A˚ above the surface (b) PES ob-tained when the adatom is relaxed from 0.5 A˚ above the sur-face with the surfac e dimers initially broken. The dashed boxshows the unit cell. The contour–line spacing is 0.2 eV. Theatomic positions of the clean surface are indicated for atomsof the upper two layers and for the As-dimers in the thirdlayer (As: empty circles, Ga: filled circles). −1.0 0.0 1.0 2.0 3.0−4.0−3.0−2.0−1.00.0za d(A)bindingenergy(eV)(a)(b) (c)FIG. 2. (a) Binding energy of an Ga adatom as functionof its height za−d above the center of an As-dimer. (b) and(c) charge density cross section through the adato m and thedimer atoms at the two minima of the binding energy.4

http://hdl.handle.net/11858/00-001M-0000-0011-1F79-2

Novel diffusion mechanism on the GaAs(001) surface: the role of
  adatom-dimer interaction

Novel diffusion mechanism on the GaAs(001) surface: the role of adatom-dimer interaction

Abstract

Similar works

Full text

Available Versions

Max Planck Society eDoc Server

Crossref

MPG.PuRe

MPG.PuRe