Kinetic Monte Carlo simulation of shape transition in strained quantum dots

TL;DR

This paper uses atomistic simulations to study the shape transition from pyramids to domes in strained quantum dots, revealing how island size and composition influence the transition under various growth conditions.

Contribution

It introduces a multi-state lattice model with surface reconstructions and a simple theory explaining the shape transition in quantum dots based on island size and composition.

Findings

Transition size scales with Ge concentration as n_c^{1/d} or all temperatures and rates.

Energy barrier for transition is mainly due to facet interface energy.

Fast deposition delays the shape transition to larger islands.

Abstract

The pyramid-to-dome transition in Ge$_{x}$Si$_{1-x}$ on Si(100) initiated by step bunching on pyramidal quantum dots is atomistically simulated using a novel multi-state lattice model incorporating effective surface reconstructions. Results are explained by a simple theory based on a shallow island approximation. Under given deposition conditions in $d$ dimensions, the shape transition is shown to occur at island size $n_c$ following $n_c^{1/d} \propto x^{-\zeta}$ independent of temperature and deposition rate, where $\zeta\alt 2$ and $x$ is the actual Ge concentration in the island. The transition has an energy barrier dominated by the facet interface energy. Fast deposition however can out-run and delay the transition to larger island sizes.