Atomistic k ⋅ p theory
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)
- NanoLund and Solid State Physics, Lund University, P.O. Box 118, 221 00 Lund (Sweden)
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 sp{sup 3} tight-binding model. We can thus directly derive the parameters in the sp{sup 3} 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.
- OSTI ID:
- 22493039
- Journal Information:
- Journal of Applied Physics, Vol. 118, Issue 22; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
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