# Band structure of Ge$_{1-x}$Sn$_{x}$alloy: a full-zone 30-band $k$$\cdot$$p$ model

## TL;DR

This paper introduces a comprehensive 30-band k·p model for Ge$_{1-x}$Sn$_{x}$ alloy, enabling efficient and accurate electronic band structure calculations across a range of compositions, facilitating device optimization.

## Contribution

The paper develops and calibrates a full-zone 30-band k·p model for Ge$_{1-x}$Sn$_{x}$ alloy, validated against empirical and ab initio methods, with reduced computational requirements.

## Key findings

- Accurate reproduction of band structures in Ge and α-Sn.
- Material properties like effective masses and Luttinger parameters obtained.
- Model enables efficient device optimization for Ge$_{1-x}$Sn$_{x}$ alloys.

## Abstract

A full-zone 30-band $k$$\cdot$$p$ model is developed as an efficient and reliable tool to compute electronic band structure in Ge$_{1-x}$Sn$_{x}$ alloy. The model was first used to reproduce the electronic band structures in Ge and $\alpha$-Sn obtained with empirical tight binding and \textit{ab initio} methods. Input parameters for the 30-band $k$$\cdot$$p$ model are carefully calibrated against prior empirical predications and experimental data. Important material properties such as effective mass for electrons and holes, Luttinger parameters, and density of states are obtained for Ge$_{1-x}$Sn$_{x}$ alloy with the composition range $0<x<0.3$. The 30-band $k$$\cdot$$p$ model that requires far less computing resources is a necessary capability for optimization of sophisticated devices made from Ge$_{1-x}$Sn$_{x}$ alloy with a large parameter space to explore.