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 expla
ined 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 $zetaalt 2$ 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.
Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Greens function formalisms for boundary values in the associated l
attice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.
