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Atomistic k . p theory
Journal article   Open access   Peer reviewed

Atomistic k . p theory

Craig E. Pryor and M. -E. Pistol
Journal of applied physics, Vol.118(22), p.225702
12/14/2015
DOI: 10.1063/1.4936170
url
https://arxiv.org/pdf/1503.00217View
Open Access

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 arc obtained from experimental results or ab natio 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/zinchlende crystal and show that it is equivalent to the sp(3) tight-binding model. We can thus directly derive the parameters in the sp(3) tight-binding model from experimental data, We then take the atomistic limit of the widely used eight-hand Kane model and compute the hand 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 he combined in the same system, (C) 2015 AIP Publishing LLC
 Physical Sciences Physics Physics, Applied Science & Technology

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