Atomistic k ⋅ p theory

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 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-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.

Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires

“…To correct this problem, we follow the ideas of Refs. [88,89] and we symmetrize the discretization operator, defined here as…”

Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

“…In addition, it turns out that correcting the effective mass equation by the second term in Eq. (12) has an opposite effect on the two models: it decreases the accuracy for the homogeneous QD, while it improves it (to a larger degree) for the trumpet-shape model. We were not able to find a plausible explanation of this fact.…”

“…The applicability of the k k k· p p p method for modulated systems (nanostructures) has been confirmed by providing a rigorous derivation from the full Schrödinger equation 10,11 . Recent developments bring the k k k· p p p methods down to the atomistic level 12 . Currently, the 8-band k k k· p p p model is a widely tested and generally trusted standard for calculating carrier states (including magnetic effects) in mesoscopic structures, in particular in strained, self-assembled systems [13][14][15][16] .…”

Electron ground state g factor in embedded InGaAs quantum dots: An atomistic study

“…A complication that arises in most of these magnetoluminescence-based measurements is the extraction from the excitonic g factor that of the electronic contribution [6,8,27,28,30,31,33,34], which hinders its sign, a concern also shared by the magnetocapacitance [29], and photocurrent spectroscopy experiments [35]. Naturally, they need to be supplemented by an electronic structure theory, which has been routinely a variant of the k • p model [36][37][38][39][40], even though more sophisticated alternatives are being developed [41][42][43][44]. Another difficulty that virtually affects all experimental studies stems from not knowing the precise structural information such as the alloy composition, geometry, and hence the strain profile of the probed single QD.…”