Plane-Wave approaches to the electronic structure of semiconductor nanostructures

This chapter is dedicated to different plane-wave based approaches to calculate the electronic structure of semiconductor nanostructures. We introduce semi-analytical and numerical methods to achieve a plane-wave based description of such systems. This includes use of plane-wave methods to calculate not just the electronic structure but also the built-in strain and the polarisation potential, with the strain and the polarisation potential each having a significant influence on the electronic properties of a semiconductor nanostructure. The advantages and disadvantages of different plane-wave based formulations in comparison to a realspace, finite element model will be discussed and we will present representative examples of semiconductor nanostructures together with their elastic and electronic properties, computed from semi-analytical and numerical approaches. We conclude that plane-wave-based methods provide an efficient and flexible approach when using k p models to determine the electronic structure of semiconductor nanostructures.