Atomistic k ⋅ p theory
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2015-12-08 |
| Journal | Journal of Applied Physics |
| Authors | Craig Pryor, Mats‐Erik Pistol |
| Institutions | Lund University, University of Iowa |
| Citations | 12 |
Abstract
Section titled “Abstract”Pseudopotentials, tight-binding models, and k ⋅ p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here, we present the first new method in decades, which we call atomistic k ⋅ p theory. In its usual formulation, k ⋅ p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however, it is insensitive to the locations of individual atoms. We construct an atomistic k ⋅ p theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or ab initio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamond/zincblende crystal and show that it is equivalent to the sp3 tight-binding model. We can thus directly derive the parameters in the sp3 tight-binding model from experimental data. We then take the atomistic limit of the widely used eight-band Kane model and compute the band structures for all III-V semiconductors not containing nitrogen or boron using parameters fit to experimental data. Our new approach extends k ⋅ p theory to problems in which atomistic precision is required, such as impurities, alloys, polytypes, and interfaces. It also provides a new approach to multiscale modeling by allowing continuum and atomistic k ⋅ p models to be combined in the same system.
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
Section titled “References”- 2009 - The k.p Method: Electronic Properties of Semiconductors