Basics of simulations and carrier localization effects in semiconductor materials

Semiconductor alloys are at the heart of many optoelectronic devices. Among these alloys there are many prominent materials in which the virtual crystal approximation breaks down, including both highly-mismatched alloys such as GaAs_1−xN_x, and also the III-N alloys, (Al,Ga, In)N, where the difference in energy gap between InN and AlN is more than twice that between any of the more conventional III-V alloys. For such alloys one needs to describe the electronic structure taking atomic-scale disorder effects explicitly into account. Density functional theory can give some insight, but the limited supercell size that can be treated imposes artificial long-range ordering that can give misleading results. This has mandated the development of predictive empirical atomistic methods such as tight-binding and empirical pseudopotential models for large-scale calculations to quantitatively predict electronic and optical properties. Such atomistic models are, however, computationally too expensive for full device simulation, which then requires continuum models. But conventional continuum models are not sufficiently accurate for many disordered systems. Various quantum approaches have therefore been developed to overcome this challenge. These include explicitly incorporating random composition fluctuations into one- or multi-band k·p models, or the explicit introduction of localized states in the Hamiltonian, giving a band-anticrossing model to describe, e.g., the impact of N resonant defect levels on the band structure of GaAs_1−xN_x. Device simulations based, e.g., on the drift-diffusion model require semi-classical approaches that quantitatively treat disorder. We describe how the recently developed localization landscape method is addressing this question. Having overviewed the impact of disorder, we exemplify its effects by considering III-N alloys and heterostructures, where disorder effects play an increasingly important role as one moves from (Al,Ga)N to (In,Ga)N and then to (Al,In)N.