Tight binding models derived from k-dot-p theory

Calculations of the electronic properties of semiconductor nanostructures rely on one of three different methods: tight-binding, pseudopotentials, or k-dot-p theory. The first two are well suited to modeling small scale structures, however their parameters must be fitted to bulk properties, which can be a complicated procedure, especially for tight-binding. In contrast, k-dot-p theory is best at describing large nanostructures in which the placement of individual atoms is not important, and the parameters of k-dot-p theory are directly related to experimentally determined quantities. To bridge the gap between atomistic and large scale models, we will present a method for constructing tight-binding models directly from k-dot-p theory by considering a real-space representation of k-dot-p theory with finite differences on a grid which matches the desired crystal lattice. Conversely, given a tight-binding model it is also possible to construct an equivalent k-dot-p theory in the long wavelength limit