The atomic geometry of GaAs(110) revisited

L135

Surface Science 127 (1983) L135-L143 North-Holland Publishing Company

SURFACE

SCIENCE

THE ATOMIC C.B. DUKE,

LETTERS

GEOMETRY

OF GaAs(ll0)

S.L. RICHARDSON

Xerox Webster Research Center, W-114,

REVISITED

* and A. PATON Webster, New York 14580, USA

and A. KAHN Department of Electrical Engineering and Computer Science, Princeton Jersey 08544, USA Received

6 December

1982; accepted

for publication

24 January

University,

Princeton, New

1983

Improvements in surface structure determination methodologies based on the analysis of experimental low-energy electron diffraction intensities are utilized to perform an R-factor structure determination for GaAs(ll0). In addition to the commonly-accepted structure (a top-layer bond-length-conserving rotation of the As outward and the Ga inward characterized by w, = 27’, relaxation of the top layer toward the bulk by 0.05 A,, and a relaxation of the second-layer Ga outward and As inward by 0.06 A), a new structure is found which consists of a top-layer bond-length-conserving rotation of w, = 7”. relaxation of the top layer away from the bulk by 0.05 A, and a converse second-layer relaxation of the Ga and As by 0.03 A. This new structure may be distinguished from the accepted one and refinements thereof by examining the integrated intensities of the diffracted beams. When these are considered, a refinement of the accepted structure still provides the best description of measured low-energy electron diffraction intensity data, and is manifestly compatible with other recent analyses of photoemission and isochromat data.

GaAs( 110) occupies a singular position in the history of surface structure determinations because it is the first semiconductor surface for which the atomic geometry was determined [l], and its structure is by far the most thoroughly verified one for any semiconductor surface [2]. Nevertheless, it is our purpose in this letter to demonstrate the existence of another possible structure which provides a description of measured elastic low-energy-electron diffraction (ELEED) intensity profiles which is marginally better than that afforded by any of the previously proposed structures and comparable to that obtained with a refinement of the previous “best-fit” structure [3]. If we * Xerox Research 43210. USA.

Fellow

at Department

0039-6028/83/0000-0000/$03.00

of Physics,

Ohio

State

University,

0 1983 North-Holland

Columbus,

Ohio

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C. B. Duke et al. / Atomic geometry of GaAs(l IO) revisited

compare the integrated intensity in each beam with the values predicted by the various models [4], however, we find that our refinement of the previous best fit structure is superior to all of the various alternatives. The experimental ELEED intensities were obtained at T = 125 K and reported earlier [3]. The intensities of fourteen beams, i.e., those with the beam indices (10) = (io), (01) (Oi), (1 I) = (il), (li) = (ii), (02) (02) (20) = (IO), (12) = (i2), (12) = (iz), (21) = (21) (2i) = (zi), (13) = (i3) and (13) = (i3) were used in the structure analysis. The scattering model of the diffraction process which we reported previously [3] was utilized to perform our dynamical calculations of the ELEED intensities. In the model, the scattering species are represented by energy-dependent phase shifts in terms of which the ELEED intensities from the surface are computed. The scattering amplitudes associated with the uppermost three atomic bilayers are evaluated exactly, as are those of each of the individual atomic layers beneath. These amplitudes are superposed, weighted by appropriate phase factors, to obtain the diffracted intensities. Six phase shifts are included in the analysis. Revisions of the intensity-calculation computer programs to optimize their performance on vector processors (the CYBER-205 in this case) has reduced the cost of a complete calculation (14 beams, 100 energies) for GaAs(ll0) to less than $100.00 and thereby enabled the study reported herein. The electron-ion-core interaction is described by a one-electron muffin-tin potential. The one-electron crystal potential is formed from a superposition of overlapping ionic charge densities. In contrast to earlier structure analyses for GaAs( 1 lo), an energy-dependent (“Hara”) exchange potential was employed to calculate the electron-ion-core phase shifts. A description of the construction of the potential and the resulting phase shifts has been given elsewhere [S]. The electron-electron interaction is incorporated into the model via a complex inner potential with a constant real part V, and an imaginary part characterized by the inelastic collision mean free path X,, [6]. We selected V, to minimize the X-ray R factor, R, (given by eqs. (3) (8) (13) (14) and (16) of Zanazzi and Jona [7]). Our structure searches were performed using X,, = 8 A. The structure analysis was conducted by minimizing the X-ray R factor. Rx. in a systematic fashion as described earlier for GaSb [8,9] and ZnTe [9]. The reasons for selection of the X-ray rather than other possible R factors are documented by Duke et al. [lo]. In addition, we evaluated the integrated beam R factor, R,,defined by I/,k =

/

Z,,,(E)

dE,

R, = c {[Ihk(calc) h.k

(la) - I,,(obs)l/l,,(obs)}2.

In eqs. (l), Ihk( E) is the intensity

(lb)

of the beam with indices (h, k) as a function

C.B. Duke et al. / Atomic geometry of GaAs(ll0)

revisited

L137

of the incident energy E; the integral over E in eq. (la) extends over the range of energies for which the observed intensities are available; “obs” designates the observed intensities and “talc” designates the calculated intensities. For typical best-fit structures, values of R, lie in the range of 0.10 I R ,< 0.15. The structural variables which characterize the atomic geometries of the (110) surfaces of zincblende structure compound semiconductors are specified in fig. 1. In addition, the values of these parameters associated with our overall best fit structure for GaAs(ll0) are indicated, using the dimensions of the surface unit cell obtained from the bulk structure of GaAs [3,11]. The vector shear between the Ga and the As in each layer, A, has two independent components: one normal to the surface, A,,, , and one along the y axis, A,,,. The symmetry of the measured intensities requires that A,,, equal its value m the bulk [3]. It has become customary to perform structure searches by initially linking the values of A,,, and A,,, in such a fashion that all the bond lengths remain constant as the surface species are displaced from their bulk positions (“bond-length-conserving” rotations). In this case the angle o, between the plane of the uppermost chain of Ga and As and that of the truncated bulk surface is utilized as the independent structural variable. We follow that procedure here, utilizing variations in w, for bond-length-conserving rotations to fix A,., and subsequently varying A,,, independently in order to determine the shear vector A,, characteristic of the uppermost layer of Ga and As species. The third independent structural variable is taken to be the uppermost layer spacing, d,,, . Finally, we define the shear vector in the second layer, A,, by its perpendicular component, A,., , alone because the ELEED analysis is not GaAs (110)

*As o Ga

Fig. 1. Schematic indication of the surface atomic geometry for the (110) surface of GaAs. The symbols utilized in table 1 are defined in the upper panel of the figure. The numerical values shown are taken from row (d) of table I. The surface unit cell parameters are those given by Wyckoff [ 1I].

Ll38

C. B. Duke ef al. / Atomic geomerry of GaAs(l IO) revisited

sufficiently accurate bond-length-conserving

to determine w2 and AZ._”separately, although we expect structures for the second layer [ 121. Therefore A,., , quantities in terms of which the A 1.Y’ 4z.l and A,,, are the four independent two-layer reconstructions of the (110) surfaces of zincblende structure semiconductors are specified. Having defined the independent structural variables, we can proceed with a description of the R-factor structure analysis. First, we calculated the ELEED intensities and from them the X-ray structure factors for a range of bondlength-conserving top-layer reconstructions described by 0 I w, 5 34.8”. The resulting values of R, are shown in the uppermost panels of figs. 2 and 3. We find that two comparable minima occur for which R.(min) = 0.2: one for w, = 7O and the other for w, = 29”. Second, we refine the w, = 7” and w, = 29” structures by varying the spacing between the uppermost layer and substrate, i.e., d,z,l . The resulting values of R, are shown in panels (b) of figs. 2 and 3 for w, = 7” and o, = 29”, respectively. Third, we further refine these two structures by introducing shear into the second atomic layer with the R factors given in panels (c) of figs. 2 and 3. Finally, we examine the sensitivity of the resulting structures on the magnitude of the Ga-As shear in the top layer parallel to the surface: i.e., to the value of A,, ,.. The consequences of this examination are presented in panels (d) of figs. 2 and 3. It is noteworthy that both best-fit structures occur for values of A,,,. which differ from those characteristic of a bond-length-conserving rotation Hence, for these structures the value of w, varies accordingly as evident in rows (b) and (d) of table 1. Further small refinements about the minimum-Rx structures were attempted in order to recover any additional effects of interactions among the structural variables in their four-parameter space. -The resulting best fit structures are specified in rows (b) and (d) of table 1 for w, - 7’ and w, - 29”, respectively. The previous “best fit” structure [3,12], obtained via visual fitting procedures, is given in row (c) of table 1. All three structures provide a significantly better description of the observed intensities (i.e., 0.18 5 R, 2 0.19) than the unreconstructed structure (R, = 0.30). Within the accuracy [lo] of this analysis the two best-fit structures are indistinguishable both from each other and from their bond-length-conserving counterparts characterized by w, = 7” and w, = 29”, respectively. While both are marginally superior to the previous “best-fit” structure [3], the distinction also is insignificant within the accuracy of the of the quality of their methodology (i.e., AR, = 0.04 [lo]). A n indication description of the measured intensities is afforded by figs. 4 and 5 for two beams which are particularly sensitive to the fine details of the surface reconstruction [ 121. Our major new result is self-evident from figs. 2 and 3. We have discovered an unexpected surface structure for GaAs(ll0) (w, - 7’ and an expanded value of d,,,,) which seems to yield a description of the ELEED intensities comparable to that afforded by the “accepted” [2] atomic geometry (25” -< w,

C.B. Duke et al. / Atomic geometry of GaAs(ll0)

L139

revisited

0.45 (a)

0.40

:q

0.35 rr”0.30 0.25 0.20 I

I

20 30 w1 (deg 1

1

40

J;0

IO

20 30 w1 (deg)

40

-0.1

0.1 0 ~duz(~)

0.2

0.30 a* 0.25 0.20 -0.2 0.35

-02

-0.2

-0.1

0 A24

-0.1

0.1

0.2

(8)

AzJ.~~)

-0.2

0 01 -0.1 8A,,Y (A)

0.2

Fig. 2. Values of the X-ray R factors associated with systematic variations of the parameters characteristic of the surface reconstruction of GaAs(l10) for w, - 7”. Panel (a): Variations of w, for a bond-length-conserving top-layer rotation. Panel (b): Variations of the spacing between the top layer and the layer beneath relative to its value for an w, = 7’ bond-length-conserving, top-layer rotation. Panel (c): Variations in the second-layer shear relative to an o, = 7O top-layer rotation and a value of d,, I which is expanded relative to its bulk value by 0.04 A. Panel (d): Variations in the positions of the top layer As parallel to they axis (see fig. 1) relative to its value for the minimum Rx structure defined by panel (c) above. Fig. 3. Values of the X-ray R factors associated with systematic variations of the parameters characteristic of the surface reconstruction of GaAs( 110) for w, - 29”. Panel (a): Variations of w, for a bond-length-conserving top-layer rotation. Panel (b): Variations of the spacing between the top layer and the layer beneath relative to its value for an w, = 29” bond-length-conserving top-layer rotation alone. Panel (c): Variations in the second-layer shear relative to an w, = 29’ top-layer rotation and a value of d12,* which is contracted relative to its bulk value by 0.04 A. Panel (d): Variations in the position of the top layer As parallel to they axis (see fig. 1) relative to its value for the minimum Rx structure defined by panel (c), above.

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C. B. Duke et al. / Atomic geometry of GaAs(ll0)

revisited

Table 1 Candidate structures for the surface atomic geometry of GaAs(ll0); the structural symbols A and d are defined in fig. 1; the angle between the actual plane of the uppermost chain of Ga and As and the plane of the truncated bulk surface is designated by w,; the values of w, given in the first column (entitled structure) and those obtained for bond-length-conserving rotations (see, e.g., Structure

64

Layer

As

Ga

A *I,1 (4

A .2.I 6%

0

d j2.L (4

d 23.1

A .‘a

(4

(A)

1.99

1.99

4.241

0

0

0

(b) WI - 70

to.117 J 0.030

J 0.055 T 0.030

o.‘72

- 0.060

1.914

2.029

4.412

(c) Old best fit

to.144 JO.060

’ oSo6 t 0.060

0.650

-0.120

1.434

2.059

4.395

(d) w, - 29”

TO.159 JO.030

* o.527 t 0.030

0.686

- 0.060

1.442

2.029

4.518

Unreconstructed

5 29” and a contracted value of d,2,1). These two structures can be distinguished clearly from each other, however, by assessing how well they predict the integrated intensities in the various individual beams. (In this context it is useful to recall that in evaluating R, each calculated beam is scaled, by definition [7,10], to yield the same integrated area as the experimental beam with which it is compared.) This assessment is accomplished by evaluating the integrated-beam R factor, R,, defined by eqs. (1). The values of R, obtained for the four structures of interest are given in the final column of table 1. It is immediately evident that the w, - 7” structure gives an unsatisfactory value of RI, i.e., one even larger than that obtained for the unreconstructed surface (i.e., structure derived from the w, = 29” R, = 0.25). In contrast, the minimum-Rx bond-length-conserving initial structure gives R, = 0.12 which is better than the value (R, = 0.15) afforded by the previously-obtained visual best fit [3]. Consequently, this structure, which is a minor refinement of the “accepted” structure [2], provides the most satisfactory description of the measured low-temperature ELEED intensities from GaAs( 110). The results of our analysis assume particular significance in the light of recent studies GaAs(ll0) by isochromat spectroscopy [13,14]. These studies indicate that a bond-length-conserving rotation of the uppermost layer of GaAs( 110) is inconsistent with the isochromat data, which are more compatible with the perpendicular displacement model. A detailed account of a controversy on this topic arising from analyses of photoemission spectra has

C.B. Duke et al. / Aromic geometv

of ~aAs(l~~~

L14l

revisited

panels (a) of figs. 2 and 3), whereas those given in the column labeled wt are obtained including relaxations parallel to the surface (see, e.g., panels (d) of figs. 2 and 3); the inner potential symbol, Vc, as well as the R factors are defined in the text; h,, = 8 A for all of the calculated R factors in the table

d 12.Y

a1

f4

(de&

Ga,-As, X bond length change

Ga,-As, % bond length change

0

0

As,-Ga, 5%bond length change

YO

X,,

tev)

(A)

RX

RI

10

8

0.301

0.252

2.821

0

2.953

7.3

- 1.31

2.31

1.65

10

8

0.182

0.289

3.313

27.34

0.0

0.30

- 4.02

10

8

0.194

0.153

3.339

31.1

- 1.94

- 0.68

10

8

0.180

0.120

-0.17

appeared in the review literature [2]. Panels (d) of figs. 2 and 3 reveal that the displacement parallel to the surface of the top-layer As is determined very imprecisely by ELEED intensity analysis. There is an indication of a reduced As displacement parallel to the surface, as suggested by isochromat [ 13,141 and angle-resolved photoemission [15] data, but the uncertainties in A,<, are of the order of f0.2 A or larger because differences in R, of less than 0.04 are not adequate to discriminate definitively against a structural model [lo]. Therefore our R-factor intensity analysis reveals explicitly that the ELEED data are consistent with considerably reduced relaxations of the top-layer As (and Ga) parallel to the surface relative to those characteristic of a simple bond-lengthconserving-rotation model, provided that the same perpendicular displacement between these species (i.e., A,,, = 0.69 rt: 0.05 A) is maintained. This result removes any vestiges of incompatibility between the results of ELEED intensity analysis and those of either photoemission [ 151 or isochromat [ 13,141 spectroscopy. In summary, a new R-factor search has uncovered an unexpected candidate for the atomic geometry of GaAs(l IO). This structure consists of w, - 7”, an expanded top layer spacing, and a small second-layer relaxation as described in row (b) of table I. Although this structure provides a description of the shapes of the normal incidence intensity profiles which is marginally better than that afforded by its predecessors, it fails to describe adequately the relative magnitudes of the various diffracted beams. A refinement of the

L142

C.B. Duke et al. / Atomic geometry of GaAs(ll0)

(IO) BEAM

0

30

revisited

I

I

I

I

I

I

60

90

120

150

180

210

ENERGY

240

WI

Fig. 4. Comparison of calculated (solid lines) and measured (dashed lines) intensities of electrons normally incident on GaAs( 110) diffracted into the (10) beam. Panel (a): Calculated intensities for the unreconstructed surface structure as specified in row (a) of table 1. Panel (b): Calculated intensities for the structure that minimizes the X-ray R factor with w, - 7” as specified in row (b) of table 1. Panel (c): Calculated intensities for the previous best fit structure [3] as specified in row (c) of table 1. Panel (d): Calculated intensities for the structure that minimizes the X-ray R factor with w, - 29’ as specified in row (d) of table 1.

accepted structure [2], given in row (d) of table 1, provides by far the best description of these relative magnitudes, as well as a description of the intensity profiles which is equivalent to that afforded by the o, - 7” candidate structure. Moreover, the R-factor methodology provides bounds on the absolute accuracy of the ELEED structure analysis which reveal its explicit compatibility with recent analyses of photoemission [15] and isochromat [13,14] spectra. The authors are indebted to L.J. Kennedy for assistance and to M.D. Tabak for his continuing support of this work. In particular one of us (S.L. Richardson) wishes to express his gratitude and appreciation to Drs. C.B Duke and H.I. James, and the other members of the Xerox Webster Research Center, for their support and hospitality during his recent visit as a Xerox Summer Intern.

C.B. Duke et al. / Atomic geometry of GaAs(ll0) revisited

I

I

I

I

I

Ll43

I

(1.i) BEAM

30

I

60

I

90

I

120

ENERGY

I

150

(eV)

I

180

I

210

240

Fig. 5. Same as fig. 4 for the (11) beam.

References Ill A.R. Lubinsky, C.B. Duke, B.W. Lee and P. Mark, Phys. Rev. Letters 36 (1976) 1058. PI C.B. Duke, Appl. Surface Sci. 11/12

(1982) 1. 131 R.J. Meyer, C.B. Duke, A. Paton, A. Kahn, E. So, J.L. Yeh and P. Mark, Phys. Rev. B19 (1979) 5194. I41 C.W. Tucker, Jr. and C.B. Duke, Surface Sci. 29 (1972) 237. (51 R.J. Meyer, C.B. Duke and A. Paton, Surface Sci. 97 (1980) 512. PI C.B. Duke, Advan. Chem. Phys. 27 (1974) 1. r71 E. Zanazzi and F. Jona, Surface Sci. 62 (1977) 61. (81 C.B. Duke, A. Paton and A. Kahn, Phys. Rev. B, submitted. [91 C.B. Duke, A. Paton and A. Kahn, J. Vacuum Sci. Technol., to be published. IlO1 C.B. Duke, A. Paton, W.K. Ford, A. Kahn and J. Care& Phys. Rev. B24 (1981) 562. 1111 R.W.G. Wyckoff, Crystal Structures (Wiley, New York, 1963) Vol. I, p. 108. 1121 C.B. Duke, R.J. Meyer, A. Paton, P. Mark, A. Kahn, E. So and J.L. Yeh, J. Vacuum Sci. Technol. 16 (1979) 1252. 1131 V. Dose, H.-J. Grossman and D. Straub, Phys. Rev. Letters 47 (1981) 608. 1141 V. Dose, H.-J. Grossman and D. Straub, Surface Sci. 117 (1982) 387. 1151 D.J. Chadi, J. Vacuum Sci. Technol. 15 (1978) 631, 1244.