Stability and accuracy control of $\mathbf{k}\cdot \mathbf{p}$ parameters

Abstract

The $\mathbf{k}\cdot \mathbf{p}$ method is a successful approach to obtain band structure, optical and transport properties of semiconductors, and it depends on external parameters that are obtained either from experiments, tight binding or ab initio calculations. Despite the widespread use of the $\mathbf{k}\cdot \mathbf{p}$ method, a systematic analysis of the stability and the accuracy of its parameters is not usual in the literature. In this work, we report a theoretical framework to determine the $\mathbf{k}\cdot \mathbf{p}$ parameters from state-of-the-art hybrid density functional theory including spin-orbit coupling, providing a calculation where the gap and spin-orbit energy splitting are in agreement with the experimental values. The accuracy of the set of parameters is enhanced by fitting over several directions at once, minimizing the overall deviation from the original data. This strategy allows us to systematically evaluate the stability, preserving the accuracy of the parameters, providing a tool to determine optimal parameters for specific ranges around the $\Gamma$-point. To prove our concept, we investigate the zinc blende GaAs that shows results in excellent agreement with the most reliable data in the literature.

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Cited by in corpus (7)

• Ab initio Investigation of Structural Stability and Exfoliation Energies in Transition Metal Dichalcogenides based on Ti-, V-, and Mo-Group Elements
• A Comprehensive Study of $g$-Factors, Elastic, Structural and Electronic Properties of III-V Semiconductors using Hybrid-Density Functional Theory
• High-harmonic generation in GaAs beyond the perturbative regime
• Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires
• Invariant expansion of the 30-band k.p model and its parameters for III-V compounds
• DFT2kp: effective kp models from ab-initio data
• Revisiting semiconductor bulk hamiltonians using quantum computers