GaAs interfaces: a case of Fermi level pinning by surface states

Solid State Communications, Vol. 108, No. 6, pp. 361–365, 1998 c 1998 Elsevier Science Ltd. All rights reserved

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SCHOTTKY BARRIER FORMATION AT ErAs/GaAs INTERFACES: A CASE OF FERMI LEVEL PINNING BY SURFACE STATES W.R.L. Lambrecht a,1 , A.G. Petukhov b,2 and B.T. Hemmelman b Department of Physics, Case Western Reserve University, Cleveland, OH 44106-7079, U.S.A. b Physics Department, South Dakota School of Mines and Technology, Rapid City, SD 57701-3995, U.S.A. a

(Received 11 November 1997; in revised form 20 July 1998; accepted 4 August 1998 by S.G. Louie)

Schottky barrier heights and electronic structure are calculated for two model ErAs/GaAs (001) interfaces, using the linear muffin-tin orbital method, showing a clear pinning of the Fermi level by GaAs surface states. Implications for other ErAs/GaAs interfaces are discussed. c 1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION In 1947, Bardeen [1] proposed pinning of the Fermi level by the high density of states in the semiconductor gap localized at the interface to explain the observed insensitivity of the Schottky barrier heights (SBH) on the metal. This model is in contrast with the Mott-Schottky model [2, 3], which predicts a linear variation of the SBH on the metal workfunction: ΦBn = φM − χS with φM the metal workfunction and χS the electron affinity of the semiconductor and the subindex n specifies that we mean the SBH for electrons rather than for holes. The origin and nature of these localized states has been controversial for a long time. Bardeen suggested semiconductor surface states as a possible origin. Since the original proposal by Bardeen, however, there have been very few, if any, cases in which it was clearly shown that the free semiconductor surface states actually play a direct role. Many other models were advanced to describe the origin of levels in the gap which are responsible for the pinning. These include the model of metal induced gap states (MIG) [4–6], which are the exponentially decaying tails of the metallic continuum states into the semiconductor gap, sometimes called virtual gap states (VIG) [4,7–9], and the unified defect model [10], in which pinning is assumed to originate in intrinsic semiconductor defect levels, such as those associ1

[email protected], Supported by Air Force Office of Scientific Research F49620-95-10043 2 [email protected], Supported by Air Force Office of Scientific Research F49620-96-1-0383

ated with antisites. In this paper, we present evidence from model first-principles calculations that the epitaxial ErAs/GaAs Schottky barriers are controlled by the semiconductor surface states. This results essentially from the frustration in bonding between the octahedral bonds in rocksalt ErAs and the tetrahedral bonds in GaAs. That leads to a weak bonding at the interface and hence the occurence of interface states which are very closely resembling those of the GaAs surface. This is somewhat similar to Louie and Cohen’s result [5,6] that the MIGs pinning the Fermi level at a Al/Si interface retain to some extent the dangling bond character of the free Si surface. The complex behavior of the ErAs/GaAs interfaces presents a challenging problem to Schottky barrier theories. Significant variations of the SBH were reported depending on surface orientation, annealing and deposition temperatures [11]. The main experimental facts are: (i) ΦBn decreases linearly with miscut angle of vicinal surfaces from the (001) to the (1¯ 1¯ 1¯ ) direction; (ii) ΦBn of low temperature deposits (below 400◦C) increases by ∼0.2 eV after a 600◦C anneal while, (iii) a high temperature deposit results in a barrier height similar to that obtained for the initial low temperature deposit. While the annealing and deposition temperature dependence effects were shown to be correlated with different surface reconstructions, a full understanding of the data is lacking. The calculations presented here focus on the (001) interface. Our main conclusion, that the SBH in this case is determined primarily by semiconductor surface state pinning, however, allows us to speculate about the other interfaces and provides

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a new framework for future discussions of the surface reconstruction effects. Up to now, these have been discussed in terms of work-function variations in the spirit of the Schottky model. The present paper suggests that surface states may be the more important factor to consider.

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(b) (a)

2. COMPUTATIONAL METHOD AND MODELS Two distinct models of the (001) interface suggested by experimental studies on the interface structure are investigated using full-potential (FP) and atomicsphere-approximation (ASA) linear muffin-tin orbital (LMTO) calculations [12, 13] based on the density functional theory (DFT) in the local density approximation (LDA). ∗ Rutherford backscattering (RBS) channeling studies [15,16] reveal that the As sublattice at the interface is continuous. This, however, leaves two distinct candidate structural models, which are illustrated in Fig. 1. Structural relaxations have been previously studied by Tarnov [17] for the closely related case of ErAs/AlAs. We follow his nomenclature for the interface models. The first one is referred to as the chain model because of the occurence of Ga-As zigzag chains at the interface. Since the deposits all occur on initially As terminated GaAs, one may view this as Er atoms filling in the top layer of GaAs. That layer becomes in that way the first ErAs layer. Our calculations below provide evidence for this statement by showing that the bonding between the ErAs and remaining Ga-terminated GaAs surface is rather weak. The second model is called the shadow model because the Er atoms are placed on top of the top layer As atoms of GaAs. One may notice that this model is less rich in Er. Because of the near lattice match, (assumed to be ideal and fixed by the lattice constant of the substrate GaAs in the calculations), the common As sublattice completely determines the geometry of the initial models. We use supercells (ErAs)4 (Ga3 As2 ) for the chain and (ErAs)3 (Ga2 As3 ) for the shadow model. 3. RESULTS Structural relaxation of these models was carried out versus the various interplanar distances using FPLMTO calculations. The possibility of buckling the ∗

While LDA is not strictly applicable to Er 4f states, we treat the latter as open shell core states, which was found to provide a correct model for the valence states of ErAs in our prior work. See e.g. [14]

Fig. 1. Structural models of the ErAs/GaAs (001) interface: (a) chain model, (b) shadow model; light sphere: As, darker grey: Er, darkest grey: Ga. These models represent the local structure at the interface between two semi-infinite crystals. They do not correspond to the computational supercells. ErAs layers (i.e. the possibility of a relative displacement normal to the interface of the Er and As planes belonging to the same ErAs layers) was included. Our findings are that the shadow model requires essentially no relaxation while the distance between the first ErAs plane and the terminating Ga plane in the chain model expands by 60 %. Buckling is not found to be favorable in either case. This last result differs from Tarnov’s [17] conclusions. We note though that his calculations are for a few monolayers of ErAs with a free surface while ours are for a periodic superlattice model. The presence of a free surface in his case may explain the difference in results because buckling is known to occur at free surfaces of rocksalt structures. In both models, charge density plots reveal a weak bonding between the GaAs and ErAs. This is illustrated in Fig. 2 for the chain model. One can clearly see that the Ga–As bonding along the interface chain is weakened by the interface separation. In fact, one can recognize a Ga dangling bond character. This picture is confirmed by examining the partial densities of states (PDOS) at the interface (calculated in the ASA). Figures 3 and 4 show this for the chain and shadow models respectively. In these figures, the solid lines, represent the supercell model PDOS, the dotted lines represent corresponding bulk PDOS and the dashed lines represent PDOS for a free surface model of GaAs. The latter were obtained from the same supercell as the GaAs/ErAs one but with the atoms in the ErAs region replaced by empty spheres.

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Clearly, the interface PDOS on the GaAs layers resembles the surface (thin slab) GaAs PDOS more closely than the bulk PDOS, while the central Ga layer and bulk ErAs layers closely resemble their respective bulk PDOS, particularly in the valence band region. For the ErAs layers in the region E > 0, there is a noticeable shift of the peaks to higher energy compared to bulk. This reflects the size quantization effect on Er 5d bands of this very thin ErAs layer. The ErAs interface layer PDOS for the most part resembles bulk ErAs but with the addition of some tails of the GaAs gap states. Note that the ErAs layers exhibit a region of very small PDOS because of the nearly semiconductor like behavior of these thin layers. In other words, this semimetal/semiconductor interface resembles a semiconductor heterojunction. In these figures, the bulk and surface PDOS were aligned with the supercell PDOS by using the main features in the valence band. The GaAs PDOS were shifted downward by ∼0.4 eV to account for self-energy corrections as explained below. The Fermi level of the supercell, which is the energy zero in Figs 3–4, does not provide a good representation of the Fermi level position in bulk ErAs because the ErAs portion of our supercell is too small. To estimate the valence band SBH, we indicate the position of bulk Fermi level of ErAs with respect to its bulk PDOS peaks and of the bulk valence band maximum (VBM) Ev with respect to the bulk GaAs PDOS features. The coincidence of the bulk ErAs Fermi level with the GaAs surface states is consistent with the Bardeen Fermi level pinning model. A more careful calculation of the SBH was carried out using larger unit cell models and using the As 3d core level as a “local reference” level. That is, we obtain the difference in the As 3d core level in the most bulklike GaAs layer and in the most bulk-like ErAs layer of the supercell. The difference between this corelevel and the Fermi level (in ErAs) and VBM (in GaAs) are separately obtained from standard bulk unit cells. This allows one to obtain the alignment of VBM and EF . By subtracting ΦBp from the experimental gap of GaAs, we obtain ΦBn . Besides the gap correction to the LDA, we must also consider a quasiparticle self-energy correction to the VBM and EF on an absolute scale [18, 19]. For GaAs, using GW calculations for the quasiparticle spectrum, this correction ∆Ev = Ev(GW ) − Ev (LDA) was found by Godby, Schlu¨ ter and Sham [20] to be −0.36 eV when using the Ceperley-Alder [21,22] LDA exchange-correlation. For ErAs, no GW calculations have been performed. Our previous work on modeling the Shubnikov-deHaas measurements of the Fermi surface indicate that a 0.4 eV upward shift of the Er d bands is necessary to obtain the correct Fermi

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As Er As Ga As Ga Fig. 2. Charge density of the chain model projected on (110) plane. surface volume [23, 24]. This, however, only negligibly shifts the Fermi level position with respect to the peaks in the valence band DOS. Secondly, because the LDA is a better approximation for metals than for semiconductors, and, moreover in exact DFT, the quasiparticle and Kohn-Sham eigenvalues coincide at the Fermi-level, we assume tentatively that ∆EF ≈ 0. The SBHs obtained in this way are summarized in Table 1. We caution that GW calculations of absolute values of energy levels are in general still rather uncertain [20] and more so in the present case because of the absence of such data on ErAs. Nevertheless, corrections of this order of magnitude to LDA values of Schottky barriers are not uncommon [25].

4. DISCUSSION We emphasize that our calculations did not include the possibility of interface reconstructions (i.e. while relaxations were included, an increase in 2D unit cell size was not allowed). While reconstructions involving dimer formation are well established on the GaAs

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PDOS ( (states/eV)/cell )

ErAs b 4.0

EF

ErAs i

Ga-db

VBM

Ga i 2.0

As Ga b 0.0 -15.0

-10.0

-5.0

0.0

5.0

ENERGY (eV)

Fig. 3. Layer partial density of states for the chain model. Solid lines: supercell, dotted lines: bulk, dashed lines: ideal surface slab. Gai refers to the Gaterminated GaAs surface layer, As to the next layer down, and Gab to the “bulk-like” Ga layer in the center of the GaAs region of the cell. All GaAs PDOS were shifted down by a quasiparticle correction of ∼0.4 eV for reasons explained in the text. Unoccupied states in GaAs should be shifted up by the gap correction of GaAs but this was not done in the figure because we focus on the alignment of the valence band maximum (VBM) and the Fermi level EF .

PDOS ( (states/eV)/cell )

6.0

ErAs b 4.0

EF ErAs i As-db As i

2.0

VBM Ga As b

0.0 -15.0

-10.0

-5.0

0.0

5.0

ENERGY (eV)

Fig. 4. Layer partial density of states for the shadow model. Solid lines: supercell, dotted lines: bulk, dashed lines: ideal surface slab. Asi refers to the As-terminated GaAs surface layer, Ga to the next layer down, and Asb to the “bulk-like” As layer in the center of the GaAs region. Remarks similar to those in Fig. 3 apply here. Table 1. Shottky barrier heights (in eV). model chain shadow expt ∗

LDA 0.2 0.0

ΦBp LDA+GW(VBM) 0.6 0.4

ΦBn LDA+GW 0.9 1.1 0.87–1.06

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(001) surface, it was noted by Palmstrøm et al. [11] using Low Energy Electron Diffraction (LEED) that even in the very initial stages of ErAs deposition, the surface reconstructions change. Since the actual reconstructions of the well-formed interface are unknown, our calculations only represent qualitative model results. However, our main conclusion for both surface models that the interface electronic structure closely resembles that of the corresponding free GaAs surface should maintain its validity in more realistic models. While it is perhaps somewhat premature to attach too much meaning to the actual values of the SBH (in view of the LDA correction uncertainties and uncertainties of the actual structures), it is noteworthy that the value for the chain model is in excellent agreement with the experimental values for as-deposited samples while the shadow model is in better agreement with those for the high temperature annealed samples. This suggests that the annealing may result in Er out-diffusion and enrichment in As at the interface rather than the other way around as was suggested by Palmstrøm et al. [11]. Direct information on the interface composition after annealing (for example obtainable from Z-contrast electron microcopy) would be extremely helpful in resolving this issue. We also note that we find the chain model to have a lower interface energy than the shadow model. (Details on how we arrive at this conclusion will be provided elsewhere [26].) Assuming the shadow model to correspond to the annealed situation would then appear to contradict the intuitive notion that annealing must lead to the equilibrium lower energy configuration. However, more direct information on the stoichiometric changes accompanying the anneal are required before firm conclusions can be drawn. Next, we consider the interface orientation effect. As already explained by Palmstrøm et al. [11], the gradual variation with angle can easily be explained by the fact that the intermediate vicinal surfaces can be thought of as a combination of facets of (001) and (1¯ 1¯ 1¯ ) surfaces. We thus only need to consider the end cases. As yet we have not performed calculations for the (1¯ 1¯ 1¯ ) interface. However, we may speculate that the Er deposited on top of this As-terminated surface will bond more strongly to the interface As (as is the case for the chain model for the (001) interface). In that case, we are left with a very unusual GaAs termination with Ga atoms exposing three dangling bonds. While this is likely to be unstable and to reconstruct in some way, we can nevertheless make a qualitative argument about the expected change in SBH. In the case of the GaAs (001) surface, there are two dangling bonds per atom. As shown for example by Ivanov, Mazur and

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Pollman [27], rehybridization will lead to bonding and antibonding surface state bands, with the lowest one filled with two electrons. In the case of three dangling bonds, no matter what the details, we can expect that in between the bonding and antibonding levels, a band will appear which is closer to the pure dangling bond energy and which will be half-filled. Hence, we expect the Fermi level to be pinned higher up in the gap than for the (001) case. This at least qualitatively coincides with the experimental finding that ΦBn (1¯ 1¯ 1¯ ) < ΦBn (001). 5. CONCLUSION In conclusion, our model calculations for unreconstructed but relaxed ErAs/GaAs (001) interfaces show Fermi level pinning by interface states which closely resemble the surface states of the corresponding GaAs surfaces. These interface states are either Ga dangling bond like (in the chain model) or As dangling bond like (in the shadow model) and lead to a somewhat smaller ΦBn in the former than the latter case. Both values are in reasonable agreement with the range of experimental values. In the former case, which we find to be the lower energy structure, one may view the initial ErAs formation as resulting from a conversion of the top As layer of the GaAs into ErAs with subsequent partial debonding from the then Ga terminated GaAs surface. A qualitative explanation for the interface orientation effect was proposed, which will however require further calculations to be confirmed. The annealing and deposition temperature effects are presently not well understood. The hypothesis that the shadow model (which has the larger ΦBn ) is involved in the high temperature anneal situation, would predict an out-diffusion of Er or enrichment in As of the interface, a prediction which is open to experimental verification. Acknowledgements—We thank Mark van Schilfgaarde and Michael Methfessel for making available their FPLMTO codes, and Chris Palmstrøm and B. Segall for helpful discussions. REFERENCES 1. Bardeen, J., Phys. Rev., 71, 1947, 717. 2. Mott, N.F., Proc. Cambridge Phil. Soc., 34, 1938, 568.

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3. Schottky, W., Z. Phys., 113, 1939, 367. 4. Heine, V., Phys. Rev., 138, 1965, A 1689. 5. Louie, S.G. and Cohen, M.L., Phys. Rev. Lett. 35, 1975, 866. 6. Louie, S.G. and Cohen, M.L., Phys. Rev. B, 13, 1976, 2461. 7. Tejedor, C., Flores, F. and Louis, E., J. Phys. C, 10, 1977, 2163. 8. Tersoff, J., Phys. Rev. B, 32, 1985, 6968. 9. Monch, ¨ W., Phys. Rev. B, 37, 1988, 7129. 10. Spicer, W.E., Lindau, I., Skeath, P.R., Su, C.Y. and Thye, P., Phys. Rev. Lett., 44, 1980, 420. 11. Palmstrøm, C.J., Cheeks, T.L., Gilchrist, H.L., Zhu, J.G., Carter, C.B., Wilkens, B.J. and Martin, R., J. Vac. Sci. Technol. A, 10, 1992, 1946. 12. Methfessel, M., Phys. Rev B, 38, 1988, 1537. 13. Andersen, O.K., Phys. Rev. B, 12, 1975, 3060. 14. Petukhov, A.G., Lambrecht, W.R.L. and Segall, B., Phys. Rev. B, 53, ,1996, 4324. 15. Stoffel, N.G., Palmstrøm, C.J., and Wilkens, B.J., Nucl. Instrum. Methods B, 56/57, 1991, 792. 16. Guivarch, A., Ballini, Y., Minier, M., Guenais, B., Dupas, G., Ropars, G. and Regreny, A., J. Appl. Phys., 73, ,1993, 8221. 17. Tarnov, E., J. Appl. Phys., 77, 1995, 6317. 18. Zhang, S.B., Tom´anek, D., Louie, S.G., Cohen, M.L. and Hybertsen, M.S., Solid State Commun., 66, 1988, 585. 19. Zhang, S.B., Cohen, M.L., Louie, S.G., Tom´anek, D. and Hybertsen, M.S., Phys. Rev. B, 41, 1990, 10058. 20. Godby, R.W., Schlu¨ ter, M. and Sham, L.J., Phys. Rev. B, 37, 1988, 10159. 21. Ceperley, D.M. and Alder, B.I., Phys. Rev. Lett., 45, 1980, 566. 22. Perdew, J.P. and Zunger, A., Phys. Rev. B, 23, 1981, 5048. 23. Lambrecht, W.R.L., Segall, B., Petukhov, A.G., Bogaerts, R. and Herlach, F., Phys. Rev. B, 55, 1997, 9239. 24. Petukhov, A.G., Lambrecht, W.R.L. and Segall, B. Phys. Rev. B, 50, 1994, 7800. 25. Das, G.P., Blochl, ¨ P., Andersen, O.K., Christensen, N.E. and Gunnarsson, O., Phys. Rev. Lett., 63, 1989, 1168. 26. Hemmelman, B.T., Petukhov, A.G. and Lambrecht, W.R.L. unpublished. 27. Ivanov, I., Mazur, A. and Pollmann, J., Surf. sci., 92, 1980, 365.