The inverse band-structure problem of finding an atomic configuration with given electronic properties

Modern crystal-growth techniques, such as molecular beam epitaxy or metal–organic chemical-vapour deposition, are capable of producing prescribed crystal structures, sometimes even in defiance of equilibrium, bulk thermodynamics. These techniques open up the possibility of exploring different atomic arrangements in search of a configuration that possesses given electronic and optical properties. Unfortunately, the number of possible combinations is so vast, and the electronic properties are so sensitive to the details of the crystal structure, that simple trial-and-error methods (such as those used in combinatorial synthesis) are unlikely to be successful. Here we describe a theoretical method that addresses the problem of finding the atomic configuration of a complex, multi-component system having a target electronic-structure property. As an example, we predict that the configuration of an Al0.25 Ga0.75As alloy having the largest optical bandgap is a (GaAs) 2(AlAs)1(GaAs)4(AlAs)1 superlattice oriented in the [201] direction.