An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface diffusion, and long range effects due elastic interaction. The algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection-reduced kinetic Monte Carlo based on using upper bounds for the rates. The former is achieved by using a multigrid method for global updates of the displacement field and an expanding box method for local updates. The simulations show the importance of intermixing on the growth of a strained film. Further the method is used to simulate the growth of self-assembled stacked quantum dots.
We present a fast Monte-Carlo algorithm for simulating epitaxial surface growth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and Lebowitz. When simulating realistic growth regimes, much computational time is consumed by the relatively fast dynamics of the adatoms. Continuum and continuum-discrete hybrid methods have been developed to approach this issue; however in many situations, the density of adatoms is too low to efficiently and accurately simulate as a continuum. To solve the problem of fast adatom dynamics, we allow adatoms to take larger steps, effectively reducing the number of transitions required. We achieve nearly a factor of ten speed up, for growth at moderate temperatures and large D/F .
We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 ± 0.002 and its leading correction to scaling are the same as in the radial case. The average cluster, defined as the average conformal map, is similar but not identical to Saffman-Taylor fingers.
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique to simulate Dielectric Breakdown Model growth which is governed nonlinearly by the Harmonic Measure. Recurrence times are shown to be accurate and effective in probing the multifractal growth measure of diffusion limited aggregation. For the Dielectric Breakdown Model our new technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.
We use an island dynamics model for heteroepitaxial growth to study the narrowing and sharpening of the island-size distribution as a function of the strain in the submonolayer growth regime. Our island dynamics model is coupled to an elastic model that is based on atomistic harmonic interactions. The elastic equations are solved self-consistently at every time step during the simulation for the entire system. This is possible because the numerical time steps in the island dynamics model that is based on the level set technique are significantly larger than the time step of a typical atomistic event such as adatom diffusion and detachment while we still retain all the relevant physics that are associated with adatom diffusion and detachment.
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