Perspective: Theory and simulation of highly mismatched semiconductor alloys using the tight-binding method

The electronic structure of highly mismatched semiconductor alloys is characterized by carrier localization and strongly influenced by the local alloy microstructure. First-principles calculations can deliver valuable quantitative insight, but their associated computational expense limits alloy supercell size and imposes artificial long-range ordering, which can produce misleading results. The empirical tight-binding method (ETBM) provides a transparent approach to investigate large-scale supercells on an atomistic level, to quantitatively predict the electronic structure of semiconductor alloys. Here, we overview key aspects and considerations for establishing ETBMs. Additionally, we discuss and highlight, given that the ETBM matrix elements are described in the language of overlaps between localized atomic orbitals, that ETBMs have proven highly successful in analyzing the impact of localized and resonant impurity states, as well as disorder, on the optoelectronic properties of highly mismatched alloys. The ETBM continues to provide valuable insight for emerging material systems, including two-dimensional materials, perovskites and their heterostructures, and provides a framework to address technologically relevant questions including the importance of short-range disorder for loss mechanisms such as non-radiative Auger-Meitner recombination. Moreover, the ETBM furnishes a quantitative basis for continuum models such as k ⋅ p or localization landscape theories, allowing to explicitly incorporate disorder effects in nanostructures to underpin predictive device-level analysis.