Stability and accuracy control of k · p parameters

Abstract

The k·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 k·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 k·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 Γ-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.

A comprehensive study of g-factors, elastic, structural and electronic properties of III-V semiconductors using hybrid-density functional theory

“…We fitted the HSE α band structure using the secular equation of the 8×8 Hamiltonian proposed in the Ref. 36, determining simultaneously all the parameters. All points have the same weight and the same distance for all materials.…”

“…All points have the same weight and the same distance for all materials. Using different percentages of the FBZ around Γ point, we determined different parameter sets and the choice of the final set of parameters was done by root mean square deviation (RMSD) analysis, 36 using the euclidean distance between the band structures from HSE α and the effective Hamiltonian k·p with the adjusted parameters. Technical details about the fitting are available in the Supplementary Material.…”

“…As we have previously shown, 36 to correctly assign a value to P , it is necessary to include the first nonparabolicity in the range used for the fitting. If only the values below it are included, there is a fast variation of the values of P depending on the range used.…”

“…34 As the band increases almost linearly by increasing the magnitude of the nonlocal Fock exchange, 35 several studies have proposed a fitting of the α parameter to improve the description of the band gap. [34][35][36] However, those studies have employed, in most cases, atomic structures optimized with the local or semilocal functionals, [37][38][39] i.e., the differences in the structural parameters are neglected. This is a good approximation but it might fail in cases in which the fine details of the electronic structure depend strongly on the lattice parameters, e.g., III-V systems with large SOC.…”

Development and application of the k.p method to investigate spin and optical properties of semiconductor nanostructures

“…Therefore, a numerical approach to extract the k.p parameters has to be employed. (120)(121)(122)(123)(124)(125)(126)(127) In this thesis, we provide for the first time the parameter sets for InAs and InP in WZ phase including the relativist k-dependent SOC terms in 8×8 k.p Hamiltonian to correctly model the BIA splittings. (127) Our Hamiltonian is numerically fitted to ab initio band structure in multiple directions of the FBZ simultaneously.…”