Phase-Field Simulation of Quantum Dot Formation
Tomohiro TAKAK, Tadashi HASEBE and Yoshihiro TOMITA
Abstract:Self-assembled quantum dot formation in heteroepitaxial growth attracts much attention of many researchers. Although a large number of experimental studies are made on the quantum dot, it is also very important to establish the numerical method which can examine the shape, size and arrangement of the quantum dots growing on the substrate surface. In this study, phase-field model, which can simulate the growth process of the quantum dot in which the thin film with planer surface transforms to the periodic islands, is developed. The driving force of the surface morphology change is elastic strain energy generated by the lattice mismatch of substrate and thin film. Two dimensional simulations are performed by using finite difference method for phase-field and finite element method for stress field. The time evolutions of the surface morphology, stress distribution and free energy are evaluated. As a result, it is clarified that the surface of thin film changes to the island morphology so as to reduce the elastic strain energy while the surface energy increases. Phase-field model developed here, furthermore, is applied to the dislocation network, substrate steps and multilayer structure, which are utilized in order to achieve uniform size and distribution of the quantum dots arrangement. The preferential island formations on top of dislocation, step and embedded inclusion are observed and the island size becomes more uniform. Key Words:Quantum dot, Self-assembly, Heteroepitaxial thin film, Lattice misfit strain, Phase-field method