Nucleation versus instability race in strained films

Abstract

Under the generic term ``Stranski-Krastanov'' are grouped two different growth mechanisms of SiGe quantum dots. They result from the self-organized Asaro-Tiller-Grinfel'd (ATG) instability at low strain, while at high strain, from a stochastic nucleation. While these regimes are well known, we elucidate here the origin of the transition between these two pathways thanks to a joint theoretical and experimental work. Nucleation is described within the master equation framework. By comparing the time scales for ATG instability development and three-dimensional (3D) nucleation onset, we demonstrate that the transition between these two regimes is simply explained by the crossover between their divergent evolutions. Nucleation exhibits a strong exponential deviation at low strain while ATG behaves only algebraically. The associated time scale varies with $exp(1/{x}^{4})$ for nucleation, while it only behaves as $1/{x}^{8}$ for the ATG instability. Consequently, at high (low) strain, nucleation (instability) occurs faster and inhibits the alternate evolution. It is then this different kinetic evolution which explains the transition from one regime to the other. Such a kinetic view of the transition between these two 3D growth regimes was not provided before. The crossover between nucleation and ATG instability is found to occur both experimentally and theoretically at a Ge composition around 50% in the experimental conditions used here. Varying the experimental conditions and/or the system parameters does not allow us to suppress the transition. This means that the SiGe quantum dots always grow via ATG instability at low strain and nucleation at high strain. This result is important for the self-organization of quantum dots.