# Valence band structure calculations of strained Ge$_{1-x}$Sn$_x$ quantum well pFETs

## TL;DR

This paper investigates how Sn content, strain, and substrate orientation affect the valence band structure of GeSn quantum wells in pFETs, using empirical pseudopotential and k·p models to reveal effects on hole populations and effective mass.

## Contribution

It provides a detailed theoretical analysis of valence band structures in strained GeSn quantum wells, incorporating wave-function coupling effects influenced by cap thickness and band offsets.

## Key findings

- Increased Sn content raises hole population in the quantum well.
- Thinner caps and higher Sn content reduce the transport effective mass.
- Valence band structure depends on substrate orientation and strain conditions.

## Abstract

The dependence of valence band structures of Ge$_{1-x}$Sn$_x$ with 0 $\leq$ $x$ $\leq$ 0.2 on Sn content, biaxial strain, and substrate orientation is calculated using the nonlocal empirical pseudopotential method. The first valence subband structure in p-type Ge cap/fully strained Ge$_{1-x}$Sn$_x$ quantum well/Ge (001) and (111) inversion layers are theoretically studied using the 6$\times$6 k$\cdot$p model. A wave-function coupling of a Ge cap with respect to a strained Ge$_{1-x}$Sn$_x$ quantum well, which is influenced by the cap thickness, valence band offset, and confined effective mass, changes the energy dispersion relation in the two-dimensional $k$-space. The increase in Sn content and the decrease in cap thickness increase the hole population in the strained Ge$_{1-x}$Sn$_x$ quantum well to reduce the transport effective mass at the zone center in the Ge/strained Ge$_{1-x}$Sn$_x$/Ge inversion layers.