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Bradley et. al. recently provided an explanation of nanodot and defect-freeordered ripple production from binary compounds, for normal and obliqueincidence ion sputtering respectively, by the inclusion of the effect of thepreferential sputtering of one type of atom relative to the other type on thesurfaces of binary compounds. In this paper, we propose an extended anisotropicmodel of such surfaces of type AxB1-x that addresses anisotropy in thevariations of the specie-composition as well. We show that this model gives theanisotropic Cuerno-Barabasi model as x approaches unity, and analyze thegeneral properties of the model. Further, the complexity of the solutions ofnon-linear higher-order differential equations in general has led to thecreation of great number of highly technical and computationally intensivenumerical schemes. We introduce a simple conformal map method which allows fora fast and accurate simulation of the dynamical evolution of ion-sputteredsurfaces based on any stochastic continuum model. An optimization algorithm foran efficient application of the scheme is also introduced. In this scheme thenoise term has a physical meaning which allows one to go beyond the usual whitenoise approximation by actually being able to assign physical parameters to it.

Theory of off-normal incidence ion sputtering of surfaces of type A_xB_{1-x} and a conformal map method for stochastic continuum models