Exploration of the use of the kinetic Monte Carlo method in simulation of quantum dot growth

The use of Kinetic Monte Carlo (KMC) simulations in modeling growth of quantum dots (QDs) on semiconductor surfaces is explored. The underlying theory of the KMC method and the algorithms used in KMC implementations are explained, and the merits and shortcomings of previous KMC simulations on QD growth are discussed. Exploratory research has determined that on the one hand, quantitative KMC simulation of InAs/GaAs QD growth would need to be off-lattice, but that on the other hand, the available empirical interatomic potentials needed to make such off-lattice simulation tractable are not reliable for modeling semiconductor surfaces. A qualitative Kinetic Monte Carlo model is then developed for QD growth on a (001) substrate of tetrahedrally coordinated semiconductor material. It takes into account three different kinds of anisotropy: elastic anisotropy of the substrate, anisotropy in diffusion of isolated particles deposited onto the substrate (or single-particle diffusional anisotropy), and anisotropy in the interactions amongst nearest-neighboring deposited particles. Elastic effects are taken into account through a phenomenological repulsive ring model. The results of the qualitative simulation are as follows: (1) Effects of elastic anisotropy appear more pronounced in some experiments than others, with an anisotropic model needed to reproduce the order seen in some experimental results, while an isotropic model better explains the results from other experiments. (2) The single-particle diffusional anisotropy appears to explain the disorder in arrangement of quantum dots that has been seen in several experiments. (3) Anisotropy in interactions among nearest-neighboring particles appears to explain the oblong shapes of quantum dots seen in experiments of growth of InGaAs dots on GaAs(001), and to partially explain the presence of chains of dots as well. It is concluded that while the prospects of quantitative KMC simulations of quantum dot growth face difficulties, qualitative KMC simulations can lend some physical insights and lead to new questions that may be addressed by future research.