Short- and long-range-order effects on the electronic properties of III-V semiconductor alloys

First-principles and empirical pseudopotentials are used to study the effects of short-range and long-range atomic order on the electronic properties of III-V semiconductor alloys. The alloy structure with a given degree of long- or short-range order is modeled by two types of supercells: (a) Small (16-32 atom) supercells are constructed in the fashion of the special quasirandom structures (SQS) used previously to simulate random alloys [A. Zunger et al., Phys. Rev. Lett. 65, 353 (1990)]. Their electronic structure is treated via first-principles pseudopotential methods. (b) Large (∼ 1000 atom) supercells are found by a simulated-annealing technique which optimizes the atomic configuration until a given degree of short-range order is reproduced. The electronic structure is then determined using the empirical pseudopotential method. Statistical tests prove that the small cell SQS mimic the much larger supercells and thus provide an efficient means of studying the electronic band structure of disordered alloys in a non-mean-field approach. For the direct band gaps of ideally random ${\mathrm{Al}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}$, ${\mathrm{Ga}}_{1-x}{\mathrm{In}}_x\mathrm{P}$, and ${\mathrm{Al}}_{1-x}{\mathrm{In}}_x\mathrm{As}$ alloys, we find optical bowing parameters $b=0.48, 0.46, \mathrm{and} 0.52$ eV, respectively. In the presence of short-range order in the form of cation clustering, we find the following: (i) Clustering elongates the Ga-P bond and shortens the In-P bond in ${\mathrm{Ga}}_{0.5}$ ${\mathrm{In}}_{0.5}$P and (ii) the optical bowing of the direct band gap is greatly enhanced. This leads to an indirect-gap to direct-gap crossover in ${\mathrm{Al}}_{0.5}$ ${\mathrm{Ga}}_{0.5}$As with sufficient clustering. (iii) The band-gap reduction is accompanied by a localization of band-edge wave functions on certain types of clusters. The clusters act as "isoelectronic impurities" which localize states if their concentration (i.e., the degree of short-range order) is large enough. Electrons at the conduction-band minimum localize on the cations with lower $s$-orbital energies. The band-gap reduction and wave-function localization of alloys with short-range order is compared to the effects of long-range order, where the gap reduction is due to level repulsion between zone-folding conduction states. Numerical results are given for CuPt-type long-range order of AlGa${\mathrm{As}}_2$, GaIn${\mathrm{P}}_2$, and AlIn${\mathrm{As}}_2$. For complete ordering, the band-gap reduction relative to the random alloys are 0.36, 0.49, and 0.16 eV, respectively.