Empirical atomic pseudopotentials for AlAs/GaAs superlattices, alloys, and nanostructures

There are numerous instances in semiconductor nanostructure physics where effective-mass approximations are deemed insufficient and ‘‘direct diagonalization’’ approaches that retain the microscopic quasiperiodic potential are needed. In many of these cases there are no free surfaces and charge transfer effects are small, so fixed, non-self-consistent potential approaches suffice. To this end we have developed a continuous-space, fully relativistic empirical pseudopotential for AlAs/GaAs, which is carefully fitted to the measured electronic structure of bulk AlAs and GaAs, and to ab initio local-density calculations on short- and long-period AlAs/GaAs superlattices. Variations in the anion-cation charge transfer in AlAs and GaAs are simulated by using an As pseudopotential that depends on the number of Al and Ga nearest neighbors. Excellent agreement is demonstrated between the results of the present empirical-pseudopotential method and experiment or ab initio calculations for crystal structures exhibiting a variety of local atomic arrangements. The method is suited for large-scale electronic-structure calculations, where a realistic, three-dimensional band structure is important. We illustrate this in the context of plane-wave calculations on (i) 512-atom supercells describing (001) AlAs/GaAs superlattices with rough interfaces, (ii) 2000-atom supercells describing (AlAs${)}_{\mathit{n}}$/(GaAs${)}_{\mathit{m}}$ superlattices with randomly selected periods (n,m), and (iii) 512-atom AlAs supercells containing clusters of isoelectronic Ga impurities.