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Local structure of pseudobinary semiconductor alloys: An x-ray absorption fine structure study
Journal of Crystal Growth 98 (1989) 37—43 North-Holland, Amsterdam
37
LOCAL STRUCTURE OF PSEUDOBINARY SEMICONDUCTOR ALLOYS: AN X-RAY ABSORPTION FINE STRUCTURE STUDY J.B. BOYCE and J.C. MIKKELSEN, Jr. Xerox Palo A Ito Research Center, Palo A Ito, California 94304, USA
Extended X-ray absorption fine structure (EXAFS) has been used to investigate the local bonding structure in several pseudobinary semiconductor alloy systems, (A 1 ~B~)C. Both cation- and anion-substituted pseudobinary alloys with x ranging from o to 1 were studied. It is found that the first neighbor cation—anion distance remains closer to that in the pure binary compound than to that of the average or virtual crystal distance, determined from the lattice constant, despite a large difference between the two. Some change in bond length with composition, however, does occur, but it corresponds to only 20—25% of the change predicted in the virtual crystal approximation. These results agree well with the predictions of recent theories. The second-neighbor structural results indicate that these alloys are solid solutions with negligible clustering. Also these bulk samples prepared at high temperatures have occupation of the mixed sublattice that is consistent with that of a random distribution. This differs from the ordered distributions observed for samples grown under special conditions.
I. Introduction
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A large number of semiconductor pseudobinary alloys with chemical formula (AI_XBX)C exist in the zincblende structure over the entire alloy range from x 0 to x 1. For these materials the C atoms occupy one face-centered cubic (FCC) sublattice and the A and B atoms are distributed over the other FCC sublattice. Under special growth conditions there can be ordering of the A and B atoms. But for bulk materials prepared at high temperatures, the ones discussed here, the A and B atoms are expected to be randomly distributed, The existence of these pseudobinary alloys plus the fact that the properties of one endpoint binary compound AC can differ from those of the other endpoint binary compound BC offer the opportunity to continuously vary these properties, such as the band gap, by varying x. Of fundamental importance in calculating and predicting the properties of these alloys is the location of the atoms. The actual atomic structure has implications for the electronic properties that one would want to change by varying x. Consider the band gap as an example. The band gap varies smoothly with x but exhibits a bowing or band gap reduction from a linear variation. This bowing =
is represented by ZIEg bx(x 1), where b is the bowing parameter [1,2]. Extensive efforts to cxplain the bowing have been made. The simplest of these models is the average or virtual crystal approximation (VCA). This model treats the chemical and structural disorder by assuming an average crystal. Lending support to such an approach is the fact that the lattice constants of these pseudobinary alloys follow Vegard’s Law [3]. This empirical law states that the lattice constant of the alloy, a(x), varies linearly with x from the lattice constant of the AC binary compound, aAC, to that of BC, aBc: a(x) (1 x)aAC + xaBC. This observation has led many workers to assume that the individual first nearest neighbor distances or bond lengths in the alloy are equal to one another and are linearly related to the lattice constant: rAC(x) rBc(x) ~Iia(x). This is one of the underlying assumptions of the VCA, and is one of the limiting possibilities for the bond lengths. When applied to the band gap bowing problem, this VCA model can account for a portion, but not all, of the bowing parameter. The effects of the chemical disorder have subsequently been included in the coherent potential approximation (CPA) [4] to try to account for the remainder of b. The early CPA calculations, in which a tight bind-
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0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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J. B. Boyce, J. C. Mikkelsen, Jr.
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Local structure ofpseudobinary semiconductor alloys
ing approximation to the valence band is used [4], yield only a small correction, too small to account for the remaining difference. Later CPA results [5], in which both the valence and conduction bands are done in an improved band structure calculation, do predict the bowing parameter to within the experimental accuracy. Another approach [1] used, as a starting point, the concept of the conservation of covalent radii of Bragg [6] and Pauling—Huggins [7]. This is the other limiting structural possibility and followed the experimental observation that the VCA result for the local structure is not correct [81. In this conservation of covalent radii case the bond lengths in the alloy are almost the same as in the binary compounds, are very different from the VCA value, and are independent of x: rAC(x) ~ and rBC(x) ~ This notion is that the bond lengths depend only on the pair of atoms involved and do not vary from one chemical environment to another similar chemical environment (i.e., covalent to covalent but not necessarily covalent to ionic). This other theoretical approach [1] takes into account the Pauling—Huggins bond-length differences in a chalcopyrite-type structure and can account for the observed bowing parameter for the special case of x 0.5. A CPA approach that is modified to take into account the bondlength disorder, the molecular CPA (MCPA) [9], arrives at a different conclusion, namely, that b is insensitive to chemical and bond-length disorder, A recent angle-resolved photoemission study [10], however, brings into question some of the effects of bond-length disorder in the MCPA model. In any event, the local atomic structure is needed for any detailed modeling of the band gap bowing as well as the other properties of these materials. To determine the actual first neighbor dis-
The alloys were prepared by quenching melts of the appropriate ratios of the binary compounds AC and BC. The resulting solids were repeatedly ground and sintered until the X-ray diffraction patterns were sharp. The determined lattice constants were used as a check on the composition, using Vegard’s Law. No other phases were visible in the X-ray diffraction pattern, indicating that the samples contained, at most, a few percent of a second phase. Also from the maximum observed broadening of the X-ray peaks, we estimate the maximum deviation in composition to be about ±2 mol%, assuming that broadening due to small crystallite size is negligible. Five semiconductors with the zincblende structure were studied. These consisted of four Ill—V compounds: (Ga,In)P, (Ga,In)As, (Ga,In)Sb, Ga(P,As); and one Il—VI compound: Zn(Se,Te). This list of materials includes alloys with substitution on the cation sublattice as well as alloys with substitution on the anion sublattice. The samples were ground into fine powders and cast in epoxy of the appropriate thickness to give approximately two X-ray absorption lengths at the K-edge of interest. In some case, the powders were brushed onto tapes which were stacked together to yield the proper thickness. Each sample was selected to be free of pinholes; an X-ray photograph of each sample
tances, we have performed extended X-ray ab-
was taken at the synchrotron to check this selec-
sorption fine structure (EXAFS) measurements on
tion process.
several pseudobinary alloys of varying composition. EXAFS being a local and a spectroscopic structural probe provides the near neighbor distance about a specific atom, selected by tuning the X-rays to the appropriate absorption-edge energy. Measuring the EXAFS on the K absorption edge
The X-ray absorption data were collected at each of the K-edges in the materials on one of the wiggler beamlines at the Stanford Synchrotron Radiation Laboratory during dedicated operation. All absorption measurements were taken in the transmission mode for temperatures of 77 and 300
of each of the elements in the alloys provides a
K. In a couple of cases, data were also taken at 4.2
total description of the near neighbor structure. In
K. The collection, reduction and analysis of the
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each case studied, we find that the Pauling—Hug-
gins concept is closer to experiment than the VCA prediction, but that there is a small but significant change in the alloy bond lengths with a change in the average lattice constant with alloy composition.
2. Experimental details
J.B. Boyce, J. C. Mikkelsen, Jr.
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39
Local structure of pseudobinary semiconductor alloys
EXAFS data were performed in the usual way [11]. For quantitative comparisons, the Fourier transforms of the k-space data, FT(k~(k)), into real space were fit to structural standards in order to determine the number of neighbors at specific distances and spreads in distance with temperature. For the analysis of the first-neighbor environment, the endpoint binary compound served as a structural standard. This provides an optimum situation for the EXAFS analysis since the tronically very similar. The analysis of the second neighbor structure proceeded in a similar fashion for the C—C standard and distances. unknown However, are structurally approximations, and dccas described previously [8,12], had to be used in analyzing the B—(A, B) and A—(A, B) secondneighbor environment.
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3. Experimental results We have analyzed the K-edge EXAFS for the elements A and B in order to determine A—C and B—C bond lengths. The EXAFS results on element C were used as a check on these results [8,12]. For (Ga,In)P, the K edge of the light element phosphorus were not readily accessible. In this case, this check was not performed. The details of the (Ga,In)As results have been reported previously [8]. Here we will concentrate on the results for Zn(Se,Te). As will be seen, the conclusions for these two systems, a Ill—V and a Il—VI, are very similar. The results for the other systems studied will also be listed below. 3.1. First-neighbor environment
Representative data for the system Zn(Se,Te) are shown in fig. 1. This shows the EXAFS in real space on the Se K edge for ZnSe and Zn(Se025 Te075). The first peak in each case is due to the 4 Zn first neighbors to the Se in zincblendestructured material. A feature of these data, and a general feature of all the first neighbor data in these alloy systems, is that the first peak is very close in position and almost identical in width to that in the binary compound. The latter observation on the width indicates that there is no signifi-
2
3
4 5 6 r (A) Fig. 1. The Fourier transform of the EXAFS data on the Se K-edge in (a) ZnSe and (b) Zn(Se 025Te075). Note the similarity of the first neighbor peak and dissimilanty of the second neighbor (Se,Te)Znpeaks. The the transform window is 3.4—15.7 A’, broadened by a Gaussian of width 0.7 A
cant static distribution in the bond lengths due to the alloy disorder. The first observation on the position indicates that the Pauling concept of the conservation of atomic radii is closer to the true situation than the VCA prediction. This is evident in fig. 2, which shows the results of detailed fits to the first neighbor peaks in the EXAFS data on the Se and Te K-edges for a number of Zn(Se,Te) alloys of varying composition. The first neighbor distances change very little with composition from those in the endpoint binary compounds, much less than the VCA prediction, the central line in fig. 2. This is very similar to the situation we have reported previously [8] on (Ga,In)As and similar to the results on other Il—VI alloys [13]. For this example of Zn(Se1 ~Te~),the Se—Zn distances are the following: rznse(x 0) r~°~5~ 2.454 A, the value in pure ZnSe, whereas r~~5~(x1) 2.491 ±0.010 A. This yields a total change of ~rznse [rznse(x 1) r~nse] 0.037 ±0.010 A. For the Te—Zn distance, we have rzflTe(x 1) rznTe 2.637 A for pure ZnTe, with rZflTC(x 0) 2.592 =
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40
J.B. Boyce, J. C. Mikkelsen, Jr.
/ Local structure of pseudobinary semiconductor are
2.65
/
-~ •
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I
2.55 ~CA
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/
2.50
/
1
// / 2.45 0
+
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-
~-
---
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ZnSe
~-~-‘----
0.4
-
.~rznse/.~riv
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0.20 ±0.04 and
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/
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2.60
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—0.25 ±0.04. These first-neighbor distances were confirmed by analyzing the data on the Zn K-edge. The first neighbor environment of the Zn atoms is more complex than that for the Se and Te since it consists of both Sc and Te atoms at two different distances. For Zn(Se1 _~Te~) the first neighbor environment consists of 4x Te atoms at rzflTe(x) and 4(1 x)Se atoms at rznse(x). Interference between the EXAFS for the two different distances is readily in the real-space (not shown here).apparent A detailed analysis yields data dis-
-
Te-Zn
~rznse//~riv
alloys
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Se—Zn —~-~
0.6
tances which agree with those of fig. 2 but which have larger error bars due to the more complicated two-peak environment. A similar analysis was performed on the EX-
~---~—~
0.8
1
x in Zn(SeI.XTeX)
ZnTe
Fig. 2. The composition dependence of the first neighbor Te—Zn and Se—Zn distances in Zn(Se~ Te ), obtained from the Te and the Se K-edge EXAFS data, respectively. The solid line is the virtual crystal distance, i.e., ~Iiao(x).
±0.010 A, for a total change of ~rzflTe —0.045 ±0.010 A. These actual changes in the bond lengths are only about 20% of the total change predicted by the VCA, namely, ~ T~nTe r~nse 0.183 A. The individual experimental ratios =
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AFS data for the other pseudobinary alloys. The results on the first neighbor distances are all very similar to those of fig. 2 and are listed in table 1. It is seen that for all these Ill—V and Il—VI semiconductors, the ratio ~r1/~r~~ is in the range of 0.20 to 0.25. These values are to be contrasted with those obtained for rocksalt-structured 1—VIl materials where ~r1/~r1~ is in the range of 0.33 to 0.5 [12,14]. We should mention that a similar study [15] of Ga(P1 ~As~) has been performed and the change in first neighbor distance is about twice our result,
Table I The first-neighbor bond length information in five pseudobinary alloys with the zincblende structure; listed are the EXAFS experimental results for the total bond-length change in (A1 .~B~)Con going from the binary compound (x = 0 or x = 1) to the dilute alloy (x —el or x —~ 0), ~5r1 these are compared with the corresponding change for the virtual crystal model, ~r1~ the theoretical results of the radial force model are from Shih et al. [211,the valence force field from Martins and Zunger [19], and the full perturbation theory from Chen and Sher [20]; good agreement between experiment and theory is seen Alloy (A,B)C B (A,
(Ga,ln)P (Ga,In)As (Ga,In)Sb Ga(P,As) Zn(Se,Te)
~ r1 v
Experiment,
(A)
~r1
A—C (A)
0.181 0.174 0.165 0.088 0.183
0.038 0.040 0.032 0.021 0.037
B—C
Experiment, ~ri/~riv A—C B—C
(A)
—0.044 —0.035 —0.035 —0.022 —0.045
0.21 0.23 0.21 0.24 0.20
0.24 0.20 0.22 0.25 0.25
Theory, Radial force model
Valence force field
Full perturbation theory
A-C and B-C
A-C
B-C
A-C
B-C
0.25 0.25 0.25 0.25 0.25
0.27 0.27 0.26 0.31 0.26
0.37 0.38 0.40 0.39 0.29
0.20 0.19 0.24 0.30 0.22
0.30 0.30 0.33 0.36 0.25
J.B. Boyce, iC. Mikkelsen, Jr.
/
Local structure ofpseudohinary semiconductor alloys
L~ri/~riv 0.4—0.5. The error bars on these re-
suits, however, are large and overlap our data. Our conclusion of ZXr1/Z~r1~ 0.25 for Ga(P5 _xASx) is consistent with their data. Also in a recent EXAFS investigation [16] of dilute Ga and As doped InP, Ga—P and As—In distances were obtained that agree with our results listed in table 1. 3.2. Second-neighbor environment
The second neighbor environment was also investigated. For Zn(Se5 _~Te~) the second neighbors to the Zn are also Zn. A single Zn—Zn distance did not fit the data; however, two Zn—Zn peaks did fit the data, and the distances are shown in fig. 3. The obtained distances and relative amplitudes indicate that the two distances correspond to Zn atoms bonded to Zn via a Te atom and via a Sc atom, i.e., Zn—Te—Zn and Zn—Se—Zn. For example, in Zn(Se075Te025) about 75% of the Zn second neighbors have the shorter distance of 4.02 A while the other 25% have the longer distance of 4.3 A. The ratio of the amplitudes is the same as the ratio of the mole fractions of ZnSe and ZnTe in the alloy. Also the obtained distances 4.4
.~
-
Zn-Te-Zn
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42
4.1
I 4.0
•
-~
Zn-Se-Zn
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i.o 0
0.2
0.4
0.6
ZnSe
0.8
are close to the Zn—Zn distances in the endpoint binary compounds, as seen in fig. 3. Similar second-neighbor results for the common-atom sublattice were obtained in the other alloy systems studied here. Aside from the small change in first neighbor distance with composition, one might be tempted to conclude from the results so far that the alloy is not a solid solution but rather consists of small clusters of ZnSe and ZnTe. This conclusion may be reasonable since the first-neighbor and the Zn—Zn second neighbor distances are close to those in the endpoint binary compounds. However, the conclusion that these alloys are indeed solid solutions comes from the Se and Te secondneighbor environments. This conclusion is evident from the Se second-neighbor peaks in fig. 1. If the alloy consisted of small microclusters of ZnSe and ZnTe in the proper proportions, then the Se second neighbors would be Se at the Se—Se distance appropriate to ZnSe. Referring to fig. 1, this implies that the structure between 3 and 4 A would be the same in part (a), ZnSe, and part (b), Zn(Se0 25Te0 ~). This is obviously not the case, and a detailed fit to this region yields that the second neighbors to a Sc atom are both Se and Te in the correct ratio, i.e., 25% Se and 75% Te. As a result, these alloys do not consist of clusters but rather are thoroughly mixed solid solutions on an
.~
f
41
1 ZnTe
x in Zn(Sei.~Te~)
Fig. 3. The two second neighbor Zn—Zn distances, Zn—Te—Zn and Zn—Se—Zn, in Zn(Se1 ~Te~) as a function of composition, x. The solid line is the virtual crystal distance, i.e., ~s/~a0(x).
atomic We should scale. mention that, from these data, one cannot definitively conclude that the alloys are totally random, only that they have the random value of composition on an atomic scale. Ordering of the type observed recently for materials grown under special conditions [17,18] cannot be ruled out. Only specific types of ordering can be ruled out since the second-neighbor environment has the same average Sc to Te ratio as a random solid solution. For example, in Zn(Se05Te05) the Se second neighbors are 6 Se and 6 Te. This would rule out the type of ordering observed in (Ga05A105)As grown at 600 to 880°Cby MBE and MOCVD on GaAs [17].In this case an ordered structure is observed in which the Ga atoms have 4 Ga and 8 Al second neighbors rather that the 6 and 6 value for a random arrangement. Nonetheless, our bulk materials are most likely random
42
J. B. Boyce, J.C. Mikkelsen, Jr.
/ Local structure of pseudobinary
since the number of second neighbors to the Se atom varies with composition in the way expected for a random solution: 25% Se has 3 Se and 9 Te second neighbors; 50% Se, 6 and 6; 75% Se, 9 Se and 3 Te. Similar and complimentary information
is obtained from the Te second neighbor data. This is also the case for the Ga and In second neighbors in (Ga5 _~In~)As[8].
4. Discussion
semiconductor alloys
stretching force constants are taken to be equal. With these assumptions, all the physical constants drop out of the problem and only geometry remains; i.e., the predicted value of /~r 1/~r1~ depends only on the crystal structure. The results are ~r1/~r1~ = 1/4 for zincblende and ~r1/L1r1~ = 1/2 for rocksalt. These are also listed in table 1. It is seen that this simple model agrees well with experiment. This good agreement is somewhat surprising considering all the simplifying assumptions involved. As discussed by Martins and
Zunger [19] and by Chen and Sher [20], This is Since, as seen in fig. 2, the variation of the near
due to the fact that there is a cancellation in the
neighbor distances with composition is small and linear (within the signal-to-noise ratio for these small changes), the relevant quantity to calculate is the bond-length relaxation around the impurity in the dilute limit, i.e., rH((x —sO) in (AI_~BX)C. Several theoretical calculations have been performed for the alloy structural properties. They all
effects due to second-shell relaxation and bond bending forces; so a good result is obtained even though both are ignored. More sophisticated calculations, using Monte Carlo techniques to indude the relaxation of more distant shells [22], refine the earlier results. Yet the experimental uncertainty of betweeli ±0.005 and ±0.01 A is
use a valence force field (VFF) model with differing approximations. In the calculation of Martins and Zunger [19], the VFF of Keating is used, including bond bending forces, and the first two shells of neighbors are allowed to relax. Results are obtained on 64 semiconductor—impurity systems and the appropriate ones for this study are given in table 1 (their parameter E equals (1 — ~r1/~1r1~)). Their calculation is in good agreement with experiment. It does, however, predict a
not sufficient to make a firm distinction between these various approximations. They all agree well with experiment. It is interesting to compare the local structure
somewhat larger pulling of the near neighbor dis-
recent theoretical study [23] predicts that the
tance by the host (larger ~r1/~r1v) for the strongly covalent systems. A second calculation by Chen
dopant can move more than 1 A away from one of its neighbors, along the bond, into a threefold-co-
and Sher [29] evaluated five different VFF models
ordinated site. Such a large distortion is contrary
as well as a full perturbation model, involving a combination of a VFF and an elastic continuum connected to the second shell. All but one of these models our The one thatagree can bewith ruled outexperimental consists of avalues. continuum connected to the first shell atoms, their model E. Their full theory results are listed in table 1, showing the good agreement. A third calculation, due to Shih et al. [21], uses a simple radial force model. Bond bending forces
to the conservation of covalent radii observed here and should be readily observable using EXAFS. Such a study [24] has been performed (Al~3 3 Sn. on The Sn Ga0 7)As containing 5 x 1018 cm substitutes for the Ga and Al in this system and forms a DX center. The EXAFS data show no evidence for a large shift in first-neighbor distance. The obtained four As neighbors at about 2.58 A agrees with the four As at 2.60 A in ordered ZnSnAs 2. This result is very similar to the situation described here for the pseudobinary alloys, namely, the first-neighbor bond lengths are preserved. No large distortion from the normal near-neighbor environment is seen. As a result,
are ignored and the second neighbors are assumed to be fixed at their virtual crystal distance, which for this dilute case is the pure AC crystal distance, As a further simplification, the A—C and B—C
obtained in these isovalent alloy systems with that for alloy systems containing dopant atoms, i.e., atoms with different valences. The specific case we compare with here is the DX center. One class of models for the DX center involves a large lattice relaxation around the dopant impurity atoms. A
J.B. Boyce, J. C. Mikkelsen, Jr.
/
Local structure of pseudobinary semiconductor alloys
any lattice relaxation, if it occurs, must change bond angles and not alter bond lengths or doordination substantially.
43
technology Resource Program, Division of Research Resources. References
5. Summary The extended X-ray absorption fine structure (EXAFS) has been used to investigate the local bonding structure in a variety of pseudobinary alloy systems ranging from the covalent, zincblende-structured Ill—V compounds to the less covalent Il—VI compounds. Both cation- and anion-substituted pseudobinary alloys with x ranging from 0 to 1 were studied. In all these materials, it is found that the first neighbor Calion—anion distance remains closer to that in the pure binary compound than to that of the average or virtual crystal distance, determined from the lattice constant, despite a large difference between the two. In addition, the widths of these firstneighbor distributions are not substantially larger than those for the pure binary compounds. Some change in bond length with composition, however, does occur, but it corresponds to only 20—25% of the change predicted in the virtual crystal approximation. These results agree well with the predictions of recent theories. The second-neighbor structural results indicate that these alloys arc solid solutions with negligible clustering. Also these specific bulk samples prepared at high temperatures exhibit A- and B-atom occupation of one of the sublattices that is consistent with that of a random distribution rather than that of some of the ordered distributions observed for epitaxial samples grown under special conditions. In addition, the first-neighbor results on these isovalent alloys are similar to recent conclusions on the local environment in the DX-center system (Al~ Gai~)As:Sn.
[1] See A. Zunger and J.E. Jaffe, Phys. Rev. Letters 51(1983) 662, and references contained therein. [21J. Van Vechten and T. Bergstresser, Phys. Rev. B1 (1970) 3351. [31L. Vegard, Z. Physik 5 (1921) 17. [4] A-B. Chen and A. Sher, Phys. Rev. B17 (1978) 4726. [5] A-B. Chen and A. Sher, Phys. Rev. B23 (1981) 5360. [6] W.L. Bragg, Phil. Mag. 40 (1920) 169. [71L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, NY, 1967); L. Pauling and M.L. Huggins, Z. Knst. Knstallgeom. Kristallphys. Kristallchem. 87 (1934) 205. [8] J.C. and J.B. Boyce, 1412. Phys. Rev. B28 (1983) 7130;Mikkelsen, Phys. Rev.Jr.Letters 49 (1982) [9] K.C. Hass, R.J. Lempert and H. Ehrenreich, Phys. Rev. Letters 52 (1984) 77; S. Knshnamurthy, M.A. Berding, A. Sher and A-B. Chen, Phys. Rev. B37 (1988) 425. 110] J. Hwang, P. Pianetta, Y.-C. Pao, C.K. Shen, PAP. Lindberg and R. Chow, Phys. Shih, Rev. Z.-X. Letters 61 (1988) 877.
1111 112]
1131
[14] [15] [16] [17] [18]
TM. Hayes and J.B. Boyce, in: Solid State Physics, Vol. 37, Eds. H. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York, 1982) p. 173. J.B. Boyce and J.C. Mikkelsen, Jr., Phys. Rev. B31 (1985) 6903. A. Balzarotti, in: Ternary and Multinary Compounds, Eds. 5K. Deb and A. Zunger (Materials Research Society, Pittsburgh, PA, 1987) p. 333. J.B. and J.C.Eds. Mikkelsen, Jr.,and in: Ternary and Multinary Boyce Compounds, S.K. Deb A. Zunger (Materials Research Society, Pittsburgh, PA, 1987) p. 359. T. Sasaki, T. Onda, R. Ito and N. Ogasawara, Japan. J. AppI. Phys. 25 (1986) 231. H. Oyanagi, Y. Takeda, T. Matsushita, T. Ishiguro, T. Yao and A. Sasaki, Solid State Commun., to be published. T.S. Kuan, T.F. Kuech, WI. Wang and E.L. White, Phys. Rev. Letters 54 (1985) 201. HR. Jen, M.J. Cherng and GB. Stringfellow, AppI. Phys. Letters 48 (1986) 1603.
Acknowledgments
[19] J.L. Martins and A. Zunger, Phys. Rev. B30 (1984) 6217. [20] A.-B. Chen and A. Sher, Phys. Rev. B32 (1985) 3695. [21] C.K. Shih, WE. Spicer, WA. Harrison and A. Sher, Phys. Rev. B31 (1985) 1139. [22] M. Podgorny, MT. Czyzyk, A. Balzarotti, P. Letardi, N.
The experiments were performed at SSRL, which is funded by the Department of Energy under contract DE-AC-03-82ER-13000, Office of Basic Energy Sciences, Division of Chemical Sciences, and the National Institutes of Health, Bio-
Motta, A. K.isiel and M. Zimnal-Starnawska, Solid State Commun. 55 (1985) 413. [23] D.J. Chadi and K.J. Chang, Phys. Rev. Letters 61(1988) [24] 873. T.M. Hayes. DL. Williamson, A. Outzourhit, P. Small, P. Gibart and A. Rudra, in: Proc. 5th Intern. Conf on X-Ray Absorption Fine Structure, 1988. unpublished.
37
LOCAL STRUCTURE OF PSEUDOBINARY SEMICONDUCTOR ALLOYS: AN X-RAY ABSORPTION FINE STRUCTURE STUDY J.B. BOYCE and J.C. MIKKELSEN, Jr. Xerox Palo A Ito Research Center, Palo A Ito, California 94304, USA
Extended X-ray absorption fine structure (EXAFS) has been used to investigate the local bonding structure in several pseudobinary semiconductor alloy systems, (A 1 ~B~)C. Both cation- and anion-substituted pseudobinary alloys with x ranging from o to 1 were studied. It is found that the first neighbor cation—anion distance remains closer to that in the pure binary compound than to that of the average or virtual crystal distance, determined from the lattice constant, despite a large difference between the two. Some change in bond length with composition, however, does occur, but it corresponds to only 20—25% of the change predicted in the virtual crystal approximation. These results agree well with the predictions of recent theories. The second-neighbor structural results indicate that these alloys are solid solutions with negligible clustering. Also these bulk samples prepared at high temperatures have occupation of the mixed sublattice that is consistent with that of a random distribution. This differs from the ordered distributions observed for samples grown under special conditions.
I. Introduction
=
A large number of semiconductor pseudobinary alloys with chemical formula (AI_XBX)C exist in the zincblende structure over the entire alloy range from x 0 to x 1. For these materials the C atoms occupy one face-centered cubic (FCC) sublattice and the A and B atoms are distributed over the other FCC sublattice. Under special growth conditions there can be ordering of the A and B atoms. But for bulk materials prepared at high temperatures, the ones discussed here, the A and B atoms are expected to be randomly distributed, The existence of these pseudobinary alloys plus the fact that the properties of one endpoint binary compound AC can differ from those of the other endpoint binary compound BC offer the opportunity to continuously vary these properties, such as the band gap, by varying x. Of fundamental importance in calculating and predicting the properties of these alloys is the location of the atoms. The actual atomic structure has implications for the electronic properties that one would want to change by varying x. Consider the band gap as an example. The band gap varies smoothly with x but exhibits a bowing or band gap reduction from a linear variation. This bowing =
is represented by ZIEg bx(x 1), where b is the bowing parameter [1,2]. Extensive efforts to cxplain the bowing have been made. The simplest of these models is the average or virtual crystal approximation (VCA). This model treats the chemical and structural disorder by assuming an average crystal. Lending support to such an approach is the fact that the lattice constants of these pseudobinary alloys follow Vegard’s Law [3]. This empirical law states that the lattice constant of the alloy, a(x), varies linearly with x from the lattice constant of the AC binary compound, aAC, to that of BC, aBc: a(x) (1 x)aAC + xaBC. This observation has led many workers to assume that the individual first nearest neighbor distances or bond lengths in the alloy are equal to one another and are linearly related to the lattice constant: rAC(x) rBc(x) ~Iia(x). This is one of the underlying assumptions of the VCA, and is one of the limiting possibilities for the bond lengths. When applied to the band gap bowing problem, this VCA model can account for a portion, but not all, of the bowing parameter. The effects of the chemical disorder have subsequently been included in the coherent potential approximation (CPA) [4] to try to account for the remainder of b. The early CPA calculations, in which a tight bind-
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0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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38
J. B. Boyce, J. C. Mikkelsen, Jr.
/
Local structure ofpseudobinary semiconductor alloys
ing approximation to the valence band is used [4], yield only a small correction, too small to account for the remaining difference. Later CPA results [5], in which both the valence and conduction bands are done in an improved band structure calculation, do predict the bowing parameter to within the experimental accuracy. Another approach [1] used, as a starting point, the concept of the conservation of covalent radii of Bragg [6] and Pauling—Huggins [7]. This is the other limiting structural possibility and followed the experimental observation that the VCA result for the local structure is not correct [81. In this conservation of covalent radii case the bond lengths in the alloy are almost the same as in the binary compounds, are very different from the VCA value, and are independent of x: rAC(x) ~ and rBC(x) ~ This notion is that the bond lengths depend only on the pair of atoms involved and do not vary from one chemical environment to another similar chemical environment (i.e., covalent to covalent but not necessarily covalent to ionic). This other theoretical approach [1] takes into account the Pauling—Huggins bond-length differences in a chalcopyrite-type structure and can account for the observed bowing parameter for the special case of x 0.5. A CPA approach that is modified to take into account the bondlength disorder, the molecular CPA (MCPA) [9], arrives at a different conclusion, namely, that b is insensitive to chemical and bond-length disorder, A recent angle-resolved photoemission study [10], however, brings into question some of the effects of bond-length disorder in the MCPA model. In any event, the local atomic structure is needed for any detailed modeling of the band gap bowing as well as the other properties of these materials. To determine the actual first neighbor dis-
The alloys were prepared by quenching melts of the appropriate ratios of the binary compounds AC and BC. The resulting solids were repeatedly ground and sintered until the X-ray diffraction patterns were sharp. The determined lattice constants were used as a check on the composition, using Vegard’s Law. No other phases were visible in the X-ray diffraction pattern, indicating that the samples contained, at most, a few percent of a second phase. Also from the maximum observed broadening of the X-ray peaks, we estimate the maximum deviation in composition to be about ±2 mol%, assuming that broadening due to small crystallite size is negligible. Five semiconductors with the zincblende structure were studied. These consisted of four Ill—V compounds: (Ga,In)P, (Ga,In)As, (Ga,In)Sb, Ga(P,As); and one Il—VI compound: Zn(Se,Te). This list of materials includes alloys with substitution on the cation sublattice as well as alloys with substitution on the anion sublattice. The samples were ground into fine powders and cast in epoxy of the appropriate thickness to give approximately two X-ray absorption lengths at the K-edge of interest. In some case, the powders were brushed onto tapes which were stacked together to yield the proper thickness. Each sample was selected to be free of pinholes; an X-ray photograph of each sample
tances, we have performed extended X-ray ab-
was taken at the synchrotron to check this selec-
sorption fine structure (EXAFS) measurements on
tion process.
several pseudobinary alloys of varying composition. EXAFS being a local and a spectroscopic structural probe provides the near neighbor distance about a specific atom, selected by tuning the X-rays to the appropriate absorption-edge energy. Measuring the EXAFS on the K absorption edge
The X-ray absorption data were collected at each of the K-edges in the materials on one of the wiggler beamlines at the Stanford Synchrotron Radiation Laboratory during dedicated operation. All absorption measurements were taken in the transmission mode for temperatures of 77 and 300
of each of the elements in the alloys provides a
K. In a couple of cases, data were also taken at 4.2
total description of the near neighbor structure. In
K. The collection, reduction and analysis of the
=
=
=
each case studied, we find that the Pauling—Hug-
gins concept is closer to experiment than the VCA prediction, but that there is a small but significant change in the alloy bond lengths with a change in the average lattice constant with alloy composition.
2. Experimental details
J.B. Boyce, J. C. Mikkelsen, Jr.
/
39
Local structure of pseudobinary semiconductor alloys
EXAFS data were performed in the usual way [11]. For quantitative comparisons, the Fourier transforms of the k-space data, FT(k~(k)), into real space were fit to structural standards in order to determine the number of neighbors at specific distances and spreads in distance with temperature. For the analysis of the first-neighbor environment, the endpoint binary compound served as a structural standard. This provides an optimum situation for the EXAFS analysis since the tronically very similar. The analysis of the second neighbor structure proceeded in a similar fashion for the C—C standard and distances. unknown However, are structurally approximations, and dccas described previously [8,12], had to be used in analyzing the B—(A, B) and A—(A, B) secondneighbor environment.
±II~.
><
~ _______________________________________
~
1
3. Experimental results We have analyzed the K-edge EXAFS for the elements A and B in order to determine A—C and B—C bond lengths. The EXAFS results on element C were used as a check on these results [8,12]. For (Ga,In)P, the K edge of the light element phosphorus were not readily accessible. In this case, this check was not performed. The details of the (Ga,In)As results have been reported previously [8]. Here we will concentrate on the results for Zn(Se,Te). As will be seen, the conclusions for these two systems, a Ill—V and a Il—VI, are very similar. The results for the other systems studied will also be listed below. 3.1. First-neighbor environment
Representative data for the system Zn(Se,Te) are shown in fig. 1. This shows the EXAFS in real space on the Se K edge for ZnSe and Zn(Se025 Te075). The first peak in each case is due to the 4 Zn first neighbors to the Se in zincblendestructured material. A feature of these data, and a general feature of all the first neighbor data in these alloy systems, is that the first peak is very close in position and almost identical in width to that in the binary compound. The latter observation on the width indicates that there is no signifi-
2
3
4 5 6 r (A) Fig. 1. The Fourier transform of the EXAFS data on the Se K-edge in (a) ZnSe and (b) Zn(Se 025Te075). Note the similarity of the first neighbor peak and dissimilanty of the second neighbor (Se,Te)Znpeaks. The the transform window is 3.4—15.7 A’, broadened by a Gaussian of width 0.7 A
cant static distribution in the bond lengths due to the alloy disorder. The first observation on the position indicates that the Pauling concept of the conservation of atomic radii is closer to the true situation than the VCA prediction. This is evident in fig. 2, which shows the results of detailed fits to the first neighbor peaks in the EXAFS data on the Se and Te K-edges for a number of Zn(Se,Te) alloys of varying composition. The first neighbor distances change very little with composition from those in the endpoint binary compounds, much less than the VCA prediction, the central line in fig. 2. This is very similar to the situation we have reported previously [8] on (Ga,In)As and similar to the results on other Il—VI alloys [13]. For this example of Zn(Se1 ~Te~),the Se—Zn distances are the following: rznse(x 0) r~°~5~ 2.454 A, the value in pure ZnSe, whereas r~~5~(x1) 2.491 ±0.010 A. This yields a total change of ~rznse [rznse(x 1) r~nse] 0.037 ±0.010 A. For the Te—Zn distance, we have rzflTe(x 1) rznTe 2.637 A for pure ZnTe, with rZflTC(x 0) 2.592 =
=
=
—*
—+
—
=
=
=
=
—~
=
=
40
J.B. Boyce, J. C. Mikkelsen, Jr.
/ Local structure of pseudobinary semiconductor are
2.65
/
-~ •
.
I
2.55 ~CA
/
/
2.50
/
1
// / 2.45 0
+
~
-
~-
---
0.2
ZnSe
~-~-‘----
0.4
-
.~rznse/.~riv
—
/
I
0.20 ±0.04 and
=
/
-~
I
2.60
=
—0.25 ±0.04. These first-neighbor distances were confirmed by analyzing the data on the Zn K-edge. The first neighbor environment of the Zn atoms is more complex than that for the Se and Te since it consists of both Sc and Te atoms at two different distances. For Zn(Se1 _~Te~) the first neighbor environment consists of 4x Te atoms at rzflTe(x) and 4(1 x)Se atoms at rznse(x). Interference between the EXAFS for the two different distances is readily in the real-space (not shown here).apparent A detailed analysis yields data dis-
-
Te-Zn
~rznse//~riv
alloys
-
I
Se—Zn —~-~
0.6
tances which agree with those of fig. 2 but which have larger error bars due to the more complicated two-peak environment. A similar analysis was performed on the EX-
~---~—~
0.8
1
x in Zn(SeI.XTeX)
ZnTe
Fig. 2. The composition dependence of the first neighbor Te—Zn and Se—Zn distances in Zn(Se~ Te ), obtained from the Te and the Se K-edge EXAFS data, respectively. The solid line is the virtual crystal distance, i.e., ~Iiao(x).
±0.010 A, for a total change of ~rzflTe —0.045 ±0.010 A. These actual changes in the bond lengths are only about 20% of the total change predicted by the VCA, namely, ~ T~nTe r~nse 0.183 A. The individual experimental ratios =
=
—
=
AFS data for the other pseudobinary alloys. The results on the first neighbor distances are all very similar to those of fig. 2 and are listed in table 1. It is seen that for all these Ill—V and Il—VI semiconductors, the ratio ~r1/~r~~ is in the range of 0.20 to 0.25. These values are to be contrasted with those obtained for rocksalt-structured 1—VIl materials where ~r1/~r1~ is in the range of 0.33 to 0.5 [12,14]. We should mention that a similar study [15] of Ga(P1 ~As~) has been performed and the change in first neighbor distance is about twice our result,
Table I The first-neighbor bond length information in five pseudobinary alloys with the zincblende structure; listed are the EXAFS experimental results for the total bond-length change in (A1 .~B~)Con going from the binary compound (x = 0 or x = 1) to the dilute alloy (x —el or x —~ 0), ~5r1 these are compared with the corresponding change for the virtual crystal model, ~r1~ the theoretical results of the radial force model are from Shih et al. [211,the valence force field from Martins and Zunger [19], and the full perturbation theory from Chen and Sher [20]; good agreement between experiment and theory is seen Alloy (A,B)C B (A,
(Ga,ln)P (Ga,In)As (Ga,In)Sb Ga(P,As) Zn(Se,Te)
~ r1 v
Experiment,
(A)
~r1
A—C (A)
0.181 0.174 0.165 0.088 0.183
0.038 0.040 0.032 0.021 0.037
B—C
Experiment, ~ri/~riv A—C B—C
(A)
—0.044 —0.035 —0.035 —0.022 —0.045
0.21 0.23 0.21 0.24 0.20
0.24 0.20 0.22 0.25 0.25
Theory, Radial force model
Valence force field
Full perturbation theory
A-C and B-C
A-C
B-C
A-C
B-C
0.25 0.25 0.25 0.25 0.25
0.27 0.27 0.26 0.31 0.26
0.37 0.38 0.40 0.39 0.29
0.20 0.19 0.24 0.30 0.22
0.30 0.30 0.33 0.36 0.25
J.B. Boyce, iC. Mikkelsen, Jr.
/
Local structure ofpseudohinary semiconductor alloys
L~ri/~riv 0.4—0.5. The error bars on these re-
suits, however, are large and overlap our data. Our conclusion of ZXr1/Z~r1~ 0.25 for Ga(P5 _xASx) is consistent with their data. Also in a recent EXAFS investigation [16] of dilute Ga and As doped InP, Ga—P and As—In distances were obtained that agree with our results listed in table 1. 3.2. Second-neighbor environment
The second neighbor environment was also investigated. For Zn(Se5 _~Te~) the second neighbors to the Zn are also Zn. A single Zn—Zn distance did not fit the data; however, two Zn—Zn peaks did fit the data, and the distances are shown in fig. 3. The obtained distances and relative amplitudes indicate that the two distances correspond to Zn atoms bonded to Zn via a Te atom and via a Sc atom, i.e., Zn—Te—Zn and Zn—Se—Zn. For example, in Zn(Se075Te025) about 75% of the Zn second neighbors have the shorter distance of 4.02 A while the other 25% have the longer distance of 4.3 A. The ratio of the amplitudes is the same as the ratio of the mole fractions of ZnSe and ZnTe in the alloy. Also the obtained distances 4.4
.~
-
Zn-Te-Zn
- --
42
4.1
I 4.0
•
-~
Zn-Se-Zn
~
i.o 0
0.2
0.4
0.6
ZnSe
0.8
are close to the Zn—Zn distances in the endpoint binary compounds, as seen in fig. 3. Similar second-neighbor results for the common-atom sublattice were obtained in the other alloy systems studied here. Aside from the small change in first neighbor distance with composition, one might be tempted to conclude from the results so far that the alloy is not a solid solution but rather consists of small clusters of ZnSe and ZnTe. This conclusion may be reasonable since the first-neighbor and the Zn—Zn second neighbor distances are close to those in the endpoint binary compounds. However, the conclusion that these alloys are indeed solid solutions comes from the Se and Te secondneighbor environments. This conclusion is evident from the Se second-neighbor peaks in fig. 1. If the alloy consisted of small microclusters of ZnSe and ZnTe in the proper proportions, then the Se second neighbors would be Se at the Se—Se distance appropriate to ZnSe. Referring to fig. 1, this implies that the structure between 3 and 4 A would be the same in part (a), ZnSe, and part (b), Zn(Se0 25Te0 ~). This is obviously not the case, and a detailed fit to this region yields that the second neighbors to a Sc atom are both Se and Te in the correct ratio, i.e., 25% Se and 75% Te. As a result, these alloys do not consist of clusters but rather are thoroughly mixed solid solutions on an
.~
f
41
1 ZnTe
x in Zn(Sei.~Te~)
Fig. 3. The two second neighbor Zn—Zn distances, Zn—Te—Zn and Zn—Se—Zn, in Zn(Se1 ~Te~) as a function of composition, x. The solid line is the virtual crystal distance, i.e., ~s/~a0(x).
atomic We should scale. mention that, from these data, one cannot definitively conclude that the alloys are totally random, only that they have the random value of composition on an atomic scale. Ordering of the type observed recently for materials grown under special conditions [17,18] cannot be ruled out. Only specific types of ordering can be ruled out since the second-neighbor environment has the same average Sc to Te ratio as a random solid solution. For example, in Zn(Se05Te05) the Se second neighbors are 6 Se and 6 Te. This would rule out the type of ordering observed in (Ga05A105)As grown at 600 to 880°Cby MBE and MOCVD on GaAs [17].In this case an ordered structure is observed in which the Ga atoms have 4 Ga and 8 Al second neighbors rather that the 6 and 6 value for a random arrangement. Nonetheless, our bulk materials are most likely random
42
J. B. Boyce, J.C. Mikkelsen, Jr.
/ Local structure of pseudobinary
since the number of second neighbors to the Se atom varies with composition in the way expected for a random solution: 25% Se has 3 Se and 9 Te second neighbors; 50% Se, 6 and 6; 75% Se, 9 Se and 3 Te. Similar and complimentary information
is obtained from the Te second neighbor data. This is also the case for the Ga and In second neighbors in (Ga5 _~In~)As[8].
4. Discussion
semiconductor alloys
stretching force constants are taken to be equal. With these assumptions, all the physical constants drop out of the problem and only geometry remains; i.e., the predicted value of /~r 1/~r1~ depends only on the crystal structure. The results are ~r1/~r1~ = 1/4 for zincblende and ~r1/L1r1~ = 1/2 for rocksalt. These are also listed in table 1. It is seen that this simple model agrees well with experiment. This good agreement is somewhat surprising considering all the simplifying assumptions involved. As discussed by Martins and
Zunger [19] and by Chen and Sher [20], This is Since, as seen in fig. 2, the variation of the near
due to the fact that there is a cancellation in the
neighbor distances with composition is small and linear (within the signal-to-noise ratio for these small changes), the relevant quantity to calculate is the bond-length relaxation around the impurity in the dilute limit, i.e., rH((x —sO) in (AI_~BX)C. Several theoretical calculations have been performed for the alloy structural properties. They all
effects due to second-shell relaxation and bond bending forces; so a good result is obtained even though both are ignored. More sophisticated calculations, using Monte Carlo techniques to indude the relaxation of more distant shells [22], refine the earlier results. Yet the experimental uncertainty of betweeli ±0.005 and ±0.01 A is
use a valence force field (VFF) model with differing approximations. In the calculation of Martins and Zunger [19], the VFF of Keating is used, including bond bending forces, and the first two shells of neighbors are allowed to relax. Results are obtained on 64 semiconductor—impurity systems and the appropriate ones for this study are given in table 1 (their parameter E equals (1 — ~r1/~1r1~)). Their calculation is in good agreement with experiment. It does, however, predict a
not sufficient to make a firm distinction between these various approximations. They all agree well with experiment. It is interesting to compare the local structure
somewhat larger pulling of the near neighbor dis-
recent theoretical study [23] predicts that the
tance by the host (larger ~r1/~r1v) for the strongly covalent systems. A second calculation by Chen
dopant can move more than 1 A away from one of its neighbors, along the bond, into a threefold-co-
and Sher [29] evaluated five different VFF models
ordinated site. Such a large distortion is contrary
as well as a full perturbation model, involving a combination of a VFF and an elastic continuum connected to the second shell. All but one of these models our The one thatagree can bewith ruled outexperimental consists of avalues. continuum connected to the first shell atoms, their model E. Their full theory results are listed in table 1, showing the good agreement. A third calculation, due to Shih et al. [21], uses a simple radial force model. Bond bending forces
to the conservation of covalent radii observed here and should be readily observable using EXAFS. Such a study [24] has been performed (Al~3 3 Sn. on The Sn Ga0 7)As containing 5 x 1018 cm substitutes for the Ga and Al in this system and forms a DX center. The EXAFS data show no evidence for a large shift in first-neighbor distance. The obtained four As neighbors at about 2.58 A agrees with the four As at 2.60 A in ordered ZnSnAs 2. This result is very similar to the situation described here for the pseudobinary alloys, namely, the first-neighbor bond lengths are preserved. No large distortion from the normal near-neighbor environment is seen. As a result,
are ignored and the second neighbors are assumed to be fixed at their virtual crystal distance, which for this dilute case is the pure AC crystal distance, As a further simplification, the A—C and B—C
obtained in these isovalent alloy systems with that for alloy systems containing dopant atoms, i.e., atoms with different valences. The specific case we compare with here is the DX center. One class of models for the DX center involves a large lattice relaxation around the dopant impurity atoms. A
J.B. Boyce, J. C. Mikkelsen, Jr.
/
Local structure of pseudobinary semiconductor alloys
any lattice relaxation, if it occurs, must change bond angles and not alter bond lengths or doordination substantially.
43
technology Resource Program, Division of Research Resources. References
5. Summary The extended X-ray absorption fine structure (EXAFS) has been used to investigate the local bonding structure in a variety of pseudobinary alloy systems ranging from the covalent, zincblende-structured Ill—V compounds to the less covalent Il—VI compounds. Both cation- and anion-substituted pseudobinary alloys with x ranging from 0 to 1 were studied. In all these materials, it is found that the first neighbor Calion—anion distance remains closer to that in the pure binary compound than to that of the average or virtual crystal distance, determined from the lattice constant, despite a large difference between the two. In addition, the widths of these firstneighbor distributions are not substantially larger than those for the pure binary compounds. Some change in bond length with composition, however, does occur, but it corresponds to only 20—25% of the change predicted in the virtual crystal approximation. These results agree well with the predictions of recent theories. The second-neighbor structural results indicate that these alloys arc solid solutions with negligible clustering. Also these specific bulk samples prepared at high temperatures exhibit A- and B-atom occupation of one of the sublattices that is consistent with that of a random distribution rather than that of some of the ordered distributions observed for epitaxial samples grown under special conditions. In addition, the first-neighbor results on these isovalent alloys are similar to recent conclusions on the local environment in the DX-center system (Al~ Gai~)As:Sn.
[1] See A. Zunger and J.E. Jaffe, Phys. Rev. Letters 51(1983) 662, and references contained therein. [21J. Van Vechten and T. Bergstresser, Phys. Rev. B1 (1970) 3351. [31L. Vegard, Z. Physik 5 (1921) 17. [4] A-B. Chen and A. Sher, Phys. Rev. B17 (1978) 4726. [5] A-B. Chen and A. Sher, Phys. Rev. B23 (1981) 5360. [6] W.L. Bragg, Phil. Mag. 40 (1920) 169. [71L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, NY, 1967); L. Pauling and M.L. Huggins, Z. Knst. Knstallgeom. Kristallphys. Kristallchem. 87 (1934) 205. [8] J.C. and J.B. Boyce, 1412. Phys. Rev. B28 (1983) 7130;Mikkelsen, Phys. Rev.Jr.Letters 49 (1982) [9] K.C. Hass, R.J. Lempert and H. Ehrenreich, Phys. Rev. Letters 52 (1984) 77; S. Knshnamurthy, M.A. Berding, A. Sher and A-B. Chen, Phys. Rev. B37 (1988) 425. 110] J. Hwang, P. Pianetta, Y.-C. Pao, C.K. Shen, PAP. Lindberg and R. Chow, Phys. Shih, Rev. Z.-X. Letters 61 (1988) 877.
1111 112]
1131
[14] [15] [16] [17] [18]
TM. Hayes and J.B. Boyce, in: Solid State Physics, Vol. 37, Eds. H. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York, 1982) p. 173. J.B. Boyce and J.C. Mikkelsen, Jr., Phys. Rev. B31 (1985) 6903. A. Balzarotti, in: Ternary and Multinary Compounds, Eds. 5K. Deb and A. Zunger (Materials Research Society, Pittsburgh, PA, 1987) p. 333. J.B. and J.C.Eds. Mikkelsen, Jr.,and in: Ternary and Multinary Boyce Compounds, S.K. Deb A. Zunger (Materials Research Society, Pittsburgh, PA, 1987) p. 359. T. Sasaki, T. Onda, R. Ito and N. Ogasawara, Japan. J. AppI. Phys. 25 (1986) 231. H. Oyanagi, Y. Takeda, T. Matsushita, T. Ishiguro, T. Yao and A. Sasaki, Solid State Commun., to be published. T.S. Kuan, T.F. Kuech, WI. Wang and E.L. White, Phys. Rev. Letters 54 (1985) 201. HR. Jen, M.J. Cherng and GB. Stringfellow, AppI. Phys. Letters 48 (1986) 1603.
Acknowledgments
[19] J.L. Martins and A. Zunger, Phys. Rev. B30 (1984) 6217. [20] A.-B. Chen and A. Sher, Phys. Rev. B32 (1985) 3695. [21] C.K. Shih, WE. Spicer, WA. Harrison and A. Sher, Phys. Rev. B31 (1985) 1139. [22] M. Podgorny, MT. Czyzyk, A. Balzarotti, P. Letardi, N.
The experiments were performed at SSRL, which is funded by the Department of Energy under contract DE-AC-03-82ER-13000, Office of Basic Energy Sciences, Division of Chemical Sciences, and the National Institutes of Health, Bio-
Motta, A. K.isiel and M. Zimnal-Starnawska, Solid State Commun. 55 (1985) 413. [23] D.J. Chadi and K.J. Chang, Phys. Rev. Letters 61(1988) [24] 873. T.M. Hayes. DL. Williamson, A. Outzourhit, P. Small, P. Gibart and A. Rudra, in: Proc. 5th Intern. Conf on X-Ray Absorption Fine Structure, 1988. unpublished.