Spontaneous Atomic Ordering in Semiconductor Alloys: Causes, Carriers, and Consequences
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sition x were tacitly assumed to have the same excess enthalpy AH(x). Clearly the option for ordering was eliminated at the outset. While these theories served to produce very useful depictions of the immiscibility of many semiconductor alloys (and continue to guide strategies of crystal growth), they also cemented the paradigm that semiconductor alloys don't order, they just phase-separate. This was true, at the time. When I approached this problem in early 1984, one glaring exception to the accepted paradigm stood out: Despite a huge ( — 40%) lattice-constant mismatch between diamond and silicon, the isovalent alloy Si^Ci-* was known to order crystallographically at x = 0.5 (much like Cu and Au). In this system, the excess enthalpy of the ordered phase AH(ordered) was negative.4 In contrast, we knew that III-V alloys behaved differently, having positive AH(x) > 0, at least for the random phase. While HumeRothery knew already four decades ago that when AH(x) < 0 (which is the case in "compound-forming systems," such as Cu-Au or Si-C), size differences can lead both to short- and to long-range order, in compound semiconductors, we were faced with a completely different situation: AH(x) was known to be positive, so Hume-Rothery's ideas did not apply. Could a system with AH(random,x) > 0 order crystallographically?
When Srivastava, Martins, and I5 looked into the problem, we found theoretically that ordered and disordered atomic configurations of III-V alloys at the same composition x could have very different enthalpies—in principle, even different signs of AH(x), a situation that is extremely rare in metallurgy. Thus we predicted5 that even though it was not observed at the time, long-range atomic ordering in III-V alloys was in principle possible despite AH(random) > 0. A detailed phase-diagram calculation illustrating coexistence of ordering and phase separation followed.6 The reason that AH(ordered) < 0 could coexist with AH(random) > 0 [or at least that 0 < AH(ordered) < AH(random)] was4'5 that certain ordered three-dimensional (3D) atomic arrangements minimize the strain energy resulting from the large lattice-constant mismatch between the constituents, while random arrangements do not. Clearly the key was that in strained systems, different atomic arrangements could have very different enthalpies at the same composition. After our paper (Reference 5) was received by Physical Review, I visited the IBM T.J. Watson Research Laboratory. T. Kuan stood up after the seminar I gave, and said that he had just observed ordering in Al t Gai v As alloys and was planning to submit a paper soon.7 (Ironically the ordering in the lattice-matched AlrGai vAs system is still the least understood case.) Soon after, many other sightings of spontaneous ordering in III-V alloys were reported—for example, by Nakayama and Fujita8 (liquid-phase epitaxy [LPE]—InGaAs), by Jen et al." (metalorganic chemical vapor deposition [MOCVD]—GaAsSb), by Shahid et al.10 (vapor levitation epitaxy—InGaAs), and by Gomyo et al. 1 " 2 (MOCVD—GalnP and m
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