The surface geometry of GaAs(110)

L789

Surface Science 164 (1985) L789-L796 North-Holland. Amsterdam

SURFACE

SCIENCE

THE SURFACE M.W. PUGA,

LETTERS

GEOMETRY

OF GaAs(ll0)

G. XU * and S.Y. TONG

Luboratory for Surface SIU&S and Depcrr~men~ of Phwics, Milwaukee, Wisconsin 53201. USA Received

22 March

1985; accepted

for publication

Unruersic~ of Wuconsin - Mdwmkee.

17 July 1985

Results of a fully dynamical low-energy electron diffraction calculation show that the GaAs(l10) surface reconstructs with a top-layer tilt-angle of 27” 5 w 5 31”. The smaller tilt angle 7” 5 w I 10” reported earlier is outside the error limits of the analysis and can be clearly ruled out. The results are independent of which R-factor or which set of existing experimental data is used. Lateral shifts larger than 0.1 A for the surface atoms are necessary to obtain acceptable agreement with the measured intensity spectra.

The geometric structure of GaAs(ll0) has been determined by low-energy electron-diffraction (LEED) intensity-voltage (Z-V) spectra analysis [1,2], as well as a host of other spectroscopies [3]. The results generally agree with one another and converge on the following points [3]. In the surface diatomic layer, the Ga atoms recede towards the bulk and As atoms rotate outwards with an angle of tilt w between 27” and 31”. In the second diatomic layer, there are strain relieving distortions of the order 0.03-0.09 A [2,3]. The atomic displacements cause surface bonds to rehybridize, and surface bond lengths vary somewhat from that of the bulk. Lateral displacements have been found to be relatively large for both Ga and As atoms in the surface layer. These results were challenged by recent studies. First a high energy ion channelling work [4] found that a surface model with large lateral displacements was incompatible with the measured surface peak intensity. This analysis predicted an upper bound of less than 0.1 A in lateral displacements for either the surface Ga or As atom. Adding to the confusion was a recent LEED study [5] in which multiple scattering theory was used for the first three layers and a modified kinematical calculation for deeper layers. This study found that for a bond-length-conserving top-layer rotation model, a small angle of tilt, w = 7.3” gave a slightly better X-ray R-factor (R,) than larger angles of tilt w z 27”-31”. However, by using a different R-factor, the so called integrated beam R,, the authors preferred a large tilt angle of w = 31.1”. These two works raised important issues concerning the surface geometry of * Permanent

address:

Department

of Physics,

Zhongshan

University.

of China.

0039~6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

Guangzhou,

People’s

Rep.

L790

M. W. Pup

et ul. /’ Surfucr geometry of GaAs(llO)

GaAs(l10). The latter work also raised serious questions concerning structural analysis by the LEED technique. In particular the following questions need to be answered: (i) Are lateral displacements of less than 0.1 A compatible with analysis by accurate dynamical LEED theory? (ii) If one uses an accurate dynamical LEED theory, would one still find an ambiguity of R, between w = 7.3” and w = 27”-31°? If so, this would call into question the procedure of using R-factors in LEED 1-V curve analysis. It would mean that different R-factors would select vastly different structures. In fact, if and when this happens, one should not believe either structure, since there is no a priori way to justify accepting the result of one R-factor while rejecting a contradictory result of another R factor. To answer the above questions we have carried out a fully convergent multiple scattering calculation for GaAs(l10). We used three R-factors in the analysis: The Van Hove-Tong R-factor [6-Q (RVHT), the Zanazzi-Jona R-factor [9] (R,,) and the X-ray R-factor [5,6] (R,). Since the integrated beam R-factor [5] (R,) did select the larger tilt angles, w = 27”-31”. we did not repeat that analysis. We have carried out the same bond-length-conserving top-layer rotation model and plotted the three R-factors versus w in fig. 1. For easy comparison, the three R-factors have been normalized to the same value at the global minimum of w = 30’. The actual R-factor values are listed in table 1. From the figure. it is clear that there is no ambiguity between o = 7” and o = 30”. All three R-factors R,, R,,, RVHT strongly prefer the w = 30” value. There is a local minimum at 10” but its R, value is 78% larger than that at w = 30”. Local minima, besides the global minimum, in an R-factor curve are very common. This is so because LEED IV spectra have many peaks. As surface geometric parameters (e.g. the value of w) are changed, the calculated peak positions shift in energy. This leads to an oscillatory behavior in the comparison between calculated and measured I-1/ curves. As long as the global minimum is well below each local minimum, as it is the case in fig. la, there is no ambiguity in selecting the correct structure. To ensure that our finding is not due to using different experimental data in the analysis we digitized the data of Duke and coworkers [5,10] in table 2 we data of list the values of R, versus o obtained by using the experimental Duke et al. and our calculated I- V curves. Again, the global minimum occurs at w = 30”. The small angle local minimum moves to w = 7’. However, the value of R, at w = 7” is 80% larger than that at w = 30”, again indicating that there is no ambiguity in the surface geometry. Thus, using the same R-factor ( R,), and the same experimental data, our calculations do not show the ambiguity found in the previous work [5]. We conclude that the different results are due to real differences in the two calculations. Of the two calculations, only our calculation unambiguously gave the correct structure independently of which R-factor was used.

M. W. Puga et al. / Surface geometry

of GaAs(ll0)

L791

.69

.63

57

.51

g

.45

.39 .32 --

.30 --

.33

.2a -5 7

10

15

20

25

30

35

.27

Angle of tilt Fig. 1. Plots of R-factor values versus tilt angle rotation model. Solid line: RVHT, broken line: R,;

w for the bond-length-conserving chained line: R,,.

top-layer

Once the optimal value of w has been found via a bond-length-conserving model, we relaxed the structure to optimize the rest of the parameters. This search was performed by keeping the relative positions between the Ga and As atoms of the first layer constant (i.e. at w = 30”) and optimizing their positions with respect to the second layer. A second layer tilt in the range 0.03-0.09 A was implemented to relieve strain. The results are shown in table 3 where we quote the value of the lowest R-factor found as a function of this tilt. The best structure corresponds to a situation in which the Ga atom in the second layer moves vertically up by 0.03 A and the As atom moves down by the same amount, yielding a combined tilt of 0.06 A with an R-factor (RvHT) of 0.256.

L792

M. W. Puga et al. / Surface geometry of GaAs(ll0)

Table 1 R-factor versus tilt angle w for the bond-length-conserving top-layer rotation R-factor, R zJ = Zanazzi-Jona R-factor, Rvw, = Van Hove-Tong R-factor

w Cd%) 0 10

15 20 25 27 29 30 31 34.7

model;

Rx

RLJ

R

0.750 0.572 0.521 0.604 0.574 0.375 0.322 0.296 0.293 0.298 0.390

0.673 0.519 0.454 0.466 0.417 0.333 0.320 0.311 0.310 0.314 0.359

0.461 0.407 0.383 0.394 0.371 0.305 0.288 0.280 0.278 0.283 0.320

Rx = X-ray

VHT

Table 2 Rx values versus tilt angle w for the bond-length-conserving top-layer rotation model; the Rx values are obtained by comparing the experimental data of Duke et al. with our calculated I-V curves

Rx

w Cd%) 0

0.753 0.416 Local minimum 0.437 0.667 0.829 Maximum 0.368 0.269 0.230 Global minimum 0.234 0.440

10

15 20 25 27 30 31 34.7

Table 3 RVHT values as a function of the second layer tilt A,; the As atoms displaced vertically downward by A 2/2 while the Ga atoms are displaced equal amount

A, (A)

Rvnr

Change

0.00

0.278 0.271 0.256 0.258

7.1 5.8 0 1.8

0.03 0.06 0.09

from minimum

in the second layer are vertically upwards by an

(W)

M. W. Puga et al. / Surface geometry of Table 4 Displacements

of the first layer atoms which produce

GaAs(lIO)

the smallest

L793

RVHT values for each value of

w (As).

t

(As),,

@a).

I

Ga),,

RVHT

(a)

27

tb) cc) (d) (e)

28 29 30 31

Change

from minimum

(4%)

SegJ 0.155 0.157 0.161 0.193 0.195

0.163 0.165 0.167 0.169 0.170

0.487 0.507 0.525 0.515 0.535

0.317 0.331 0.345 0.359 0.373

0.261 0.258 0.258 0.256 0.260

1.9 0.8 0.8 0 1.6

This result, however, does not discriminate against other possible tilts. In fact we observe from the table that tilts of 0.03 and 0.09 A yield structures with values of RVHT higher by only 5.8% and 1.8% respectively. Such variations are within the error bars of the method and we therefore conclude that a second layer tilt in the range 0.03-0.09 A is compatible with the experimental data. We then kept the second layer tilt at 0.06 A and optimized the positions of the first layer atoms relative to the bulk. We also searched over other tilt angles near 30”. For each value of w, we kept the intralayer distances of the first layer fixed and optimized their positions by moving rigidly the first layer atoms vertically to five different positions and laterally to three different ones. We show the results in table 4 where we have chosen the best structure obtained out of the 15 structures tested for each w, with their corresponding R-factors. For each structure we show vertical and lateral displacements of both surface atoms. The numbers in table 4 show a fairly consistent trend in which the optimal structures select very similar values of the four displacements of the surface atoms regardless of the numerical value of the tilt angle w. This means that the parameters most sensitive to the Z-V curve are the physical displacements of the atoms from their bulk positions. The tilt angle w can be varied by changes in the vertical as well as horizontal distances between surface Ga and As atoms. Its value varies from 27” to 31”, while the R-factor changes by less than 2%. These findings indicate that w is not a sensitive indicator of the structure and that the physical quantities that affect the I-V curves are the displacements of the atoms themselves. The effect is particularly pronounced for the parallel displacement of the As atom. The optimal structures listed in table 4 (one for each different value of w) have variations in this parameter of I 0.007 A although w varies from 27” to 31’. Because the R-factor values, for the structures listed in table 4, are so similar all these structures are acceptable. Of these, structure (d) has the least R-factor value. It corresponds to parallel shifts of 0.17 and 0.36 A for the As and Ga top-layer atoms respectively. These shifts fall outside the 0.1 A upper bound limit suggested by the ion scattering results [4]. To address this question

hf. W. Pug-a et al. / Surfacegeomerry

L794

of GaAs( I1 0)

.28 --

.28--

20

25

I 30

I 35

Angle of tilt Fig. 2. Plot of RVHT versus tilt angle w. Upper and lower curves correspond to one and two layer reconstruction models, respectively. Points (a)-(d) correspond to reducing the surface Ga and As lateral shifts.

and study the effects of reducing lateral shifts, we started with our best structure (table 4, structure (d)) and systematically reduced the lateral shifts. The results are shown in fig. 2 where we have redrawn part of the RVWT curve already shown in fig. 1 and added the points listed in table 4 which included a second layer tilt of 0.06 A. We found that as the lateral shifts are reduced, the R VHT values increase rapidly. Points (a)-(c) of the broken line in fig. 2 values corresponding to reducing the lateral shifts of Ga represent the R,,, and As by l/3, 2/3, and 3/3 respectively. We note that as we do this, the two

M. W. Puga et al. / Surface geometry

of GaAs(lIO)

L795

Table 5 R vHT values corresponding

to reducing

Shift

(As),,

(Ga),,

R “HT

Change

A,,

0.169 0.113 0.056 0.000

0.359 0.240 0.120 0.00

0.256 0.267 0.289 0.318

0 4 13 24

0.00

0.190

0.280

9

24,,/3 A,,/3 0

the surface

Ga and As lateral

shifts (%)

Equal shifts of A,, = 0.169 A

atoms are shifted by different amounts. Hence the tilt angle w changes value. Reducing the shifts by 2/3 (i.e. (b): A As,, = 0.056 A, AGa ,,= 0.120 A) has the Ga atom lying outside the ion scattering upper bound of 0.1 A [4]. The corresponding R VHT value at (b) is 13% worse, which is well above the error bar of our LEED analysis. We find therefore that our LEED result would rule out a structure whose surface atom lateral displacements are I 0.1 A. There is an additional point in fig. 2. This point (d) corresponds to reducing the lateral shifts by subtracting 0.169 A from both the top-layer AGa,, and AAs,,. In this structure the surface As atom has zero lateral shift and the Ga atom has a lateral shift of 0.19 A. This point (d) yields an R-factor which is worse by 9%. Further reduction of the surface Ga lateral shift (e.g. to I 0.1 A) again pushes the RvHT values above the error limit of our method. We list the R VHT values corresponding the points (a)-(d) in table 5 for easy reference. In summary we conclude that the results of a fully dynamical theory of LEED unambiguously select an angle of tilt 27” I w I 31”. The optimal structures are listed in table 4. The smaller tilt angle 7” 2 w I 10” result is clearly outside the error bar of our analysis. Moreover lateral shifts > 0.1 A for the surface atoms are necessary to obtain acceptable agreement with the experimental data. The reconstructed GaAs(ll0) surface, under these conditions, is almost totally electronically relaxed [ll]. Also our results are consistent with those found by the medium-energy ion scattering experiments of Smit et al. [12]. This work is supported 1154-AC5,6.

in part by NSF grant DMR-8405049

and PRF grant

References [l] S.Y. Tong, A.R. Lubkinsky. B.J. Mrstik and M.A. Van Hove, Phys. Rev. B17 (1978) 3303. [2] A. Kahn, G. Cisneros, M. Bonn, P. Mark and C.B. Duke, Surface Sci. 71 (1978) 387. [3] See, for example, S.Y. Tong, W.N. Mei and G. Xu, J. Vacuum Sci. Technol. B2 (1984) 393, and references therein.

Ll96 (41 [5] [6] [7] [8] [9] [lo] [II] (121

M. W. Puga et al. / Surface geometp of GaAs(l IO) W.M. Gibson and H.J. Gossman, J. Vacuum Sci. Technol. 82 (1984) 343. C.B. Duke, S.L. Richerdson, A. Paton and A. Kahn, Surface Sci. 127 (1983) L135. M.A. Van Hove, S.Y. Tong and M.H. Elconin, Surface Sci. 64 (1977) 85. S.Y. Tong, W.M. Kang, D.H. Rosenblatt, J.G. Tobin and D.A. Shirley. Phys. Rev. 827 (1983) 4632. S.Y. Tong and K.H. Lau. Phys. Rev. B25 (1982) 7382. E. Zanazzi and F. Jona, Surface Sci. 62 (1977) 61. We digitized a total of 9 beams, using published curves contained in R.J. Meyer, C.B. Duke, A Paton, A. Kahn, E. So, J.L. Yeh and P. Mark, Phys. Rev. B19 (1979) 5194. and ref. [5]. S.Y. Tong, G. Xu, W.Y. Hu and M.W. Puga, J. Vacuum Sci. Technol. B3 (1985) 1076. L. Smit. T.E. Derry and J.F. van der Veen, Surface Sci. 150 (1985) 245.