Effect of elastic strain energy on self-organized pattern formation

This paper studies the growth of self-organized quantum dots in strained semiconductors in the Stranski-Krastanov growth mode using the kinetic Monte Carlo simulation method. The four nearest and four next nearest neighbours of each atom in the square lattice grid with a periodic boundary condition are considered in the calculation of the binding energy among atoms. The elastic strain energy is accurately evaluated by the rigorous point eigenstrain half-space Green's function and is incorporated for the first time into the kinetic Monte Carlo model. The set of relevant growth parameters such as growth temperature, surface coverage, flux rate, and growth interruption time, is investigated and optimal values are identified. It is shown clearly that when the long-range elastic strain energy is included in the simulation, uniform size and ordered spatial distribution can be achieved. Furthermore, the growth of stacked quantum dot layers is also simulated briefly and vertical alignment is observed that could lead to progressively uniform island size and spatial ordering.