Electronic Structure and Transport for Nanoscale Device Simulation

In this chapter, we discuss the physical models that are commonly used for the quantum simulation of electronic states and currents in nanostructures. Since most of these structures are too large for an atomistic description, we focus here on continuum models with empirically adjusted material parameters. In specific, after a short introduction into the band structure theory of crystalline solids, we first present the k·p-equations for semiconductors. Next, we discuss the envelope function approximation for heterostructures and consider the effects of elastic deformations and strain. Furthermore, we also examine carrier densities at non-zero temperature and consider the interplay of the Poisson and Schrodinger equation. After describing the electronic structure, we now discuss the Boltzmann equation and the numerically more tractable drift-diffusion equations as semi-classical models for carrier transport in semiconductors. We then extend the drift-diffusion model to take quantum corrections for size quantization into account, and we outline the principles of ballistic quantum transport. Finally, we present nextnano 3, a software package for the simulation of nanostructures that has been developed by the authors, and give an example application.