Calculation of Elastic Strain Fields for Single Ge/Si Quantum Dots

TL;DR

This paper presents an atomistic simulation approach using the Keating potential and conjugate gradient method to calculate strain fields in single Ge/Si quantum dots, revealing rapid decay of strain with distance from the dot.

Contribution

It introduces a large-scale atomistic modeling technique for strain fields in quantum dots, considering about three million atoms, which improves understanding of strain distribution in these nanostructures.

Findings

Strain energy density decreases rapidly away from the quantum dot.

Cluster boundary effects are negligible for sufficiently large quantum dots.

Strain fields influence electron potential energy in silicon.

Abstract

An atomistic model based on the Keating potential and the conjugate gradient method are used for simulation of the strain fields for single Ge/Si quantum dots. Calculations are performed in the cluster approximation using clusters containing about three million atoms belonging to 150 coordination spheres. The spatial distributions of the strain energy density and electron potential energy are calculated for different valleys forming the bottom of the silicon conduction band. It is shown that the strain field in silicon decreases sufficiently rapidly with distance from the center of the quantum dot, so the influence of the cluster boundary is observed only for very large quantum dots.