Evolution of Material Boundaries under Ion Bombardment

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Abstract
The conservation law model of ion etching is applied to the problem of etching configurations of two materials. The basic problem is to describe the evolution of the point on the surface at which the two materials meet and to determine boundary conditions at this point. Such a point is called a material boundary. The equations that govern the evolution of a material boundary are derived. These nonlinear equations relate the motion of the boundary to the slopes of the two materials. Centered waves are introduced and are used to derive conditions that uniquely define boundary values at material boundaries.

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