Analytical modelling of sputter induced surface morphology

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Abstract
A review is presented of the mathematical treatment of the development of surface topography of amorphous materials bombarded by an energetic beam of particles. In the first section the relevant analytical equations are presented and extended to include surface diffusion. In general the complete analytical approach is shown to be intractable, but in the second section some of the equations are adapted to suit computer programmes which allow calculation of the development of a surface contour provided the original contour and the functional relationship between sputtering coefficient and angle (S(θ)) are specified. Finally, geometrical construction techniques, which allow the topographical development to be predicted, are discussed and a new cursor, which evolves from the appropriate S,θ relationship, is shown to be significantly simpler to use than the erosion slowness curve when making a geometrical construction of the evolving surface.