Fast Kinetic Monte Carlo Simulation of Strained Heteroepitaxy in Three Dimensions

Abstract

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 Green's function formalisms for boundary values in the associated lattice 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. PACS numbers:Epitaxial growth techniques enable deposition of a dislocation-free thin film on a substrate of a different material with a mismatched lattice constant. For film-substrate combinations such as Ge/Si, InAs/GaAs and InAs/InP, arrays of three-dimensional (3D) coherent islands self-assemble spontaneously beyond certain film thicknesses under appropriate growth conditions [1,2,3,4]. These studies are of much current interest since they are expected to find applications in future microelectronic devices.One of the most widely studied examples is Ge/Si(100) with a 4% lattice misfit. Relatively flat islands called pre-pyramids start to emerge at 3 monolayers (MLs) of Ge coverage [5,6,7]. Upon further deposition, they quickly grow into truncated pyramids bounded by four (105) facet planes on the sides and subsequently into fully grown pyramids which are also called hut islands. Upon still further deposition, they become dome islands bounded mainly by (113) facet planes. Finally, large dislocated islands appear. For the closely related alloy variant Si 1−x Ge x /Si(100) with a generally lower 4x% misfit, the development is rather similar and goes through stages characterized by ripples, hut islands, dome islands and finally dislocated islands [8,9,10]. The structures are however larger and each transition is postponed to occur at a larger film thickness. The islands are also more closely packed.Islands self-assemble because they can relieve the elastic stress in the heteroepitaxial films. There is theory for island formation that emphasizes nucleation. It suggests that islands must overcome an energy barrier associated with a critical size so that the elastic energy gained can balance the extra surface energy cost [11]. The theory is reasonably consistent with experiments at relatively high misfit. At low misfit, the critical island size and hence the energy barrier are expected to increase and make nucleation prohibitively difficult. Island formation mechanisms which do not have a barrier then offer a more promising explanation. For example, according to the Asaro-Tiller-Grinfeld (ATG) theory [12,13,14], strained surfaces are unstable at sufficiently long wavelengths. Therefore, shallow ripples first develop from small random initial perturbations and then into islands. For this mechanism to oper...

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