The Multi-Band k⋅p Hamiltonian for Heterostructures: Parameters and Applications

In this contribution all the various definitions of the k⋅p parameters available in the literature are summarized, and equations that relate them to each other are provided. We believe that such a summary for both zinc blende and wurtzite crystals on a few pages is very useful, not only for beginners but also for experienced researchers that quickly want to look up conversion formulas. Results of k⋅p calculations for bulk semiconductors are shown for diamond, and for unstrained and strained InAs. Several examples of k⋅p calculations for heterostructures are presented. They cover spurious solutions, a spherical quantum dot and heterostructures showing the untypical type-II and type-III band alignments. Finally, self-consistent k⋅p calculations of a two-dimensional hole gas in diamond for different substrate orientations are analyzed. Wherever possible, the k⋅p results are compared to tight-binding calculations. All these calculations have been performed using the nextnano software (nextnano: The nextnano software can be obtained from http://www.nextnano.com ; Birner et al., IEEE Trans. Electron Dev. 54:2137–2142, 2007). Therefore, this contribution provides some specific details that are relevant for a numerical implementation of the k⋅p method.