Kinetic theory of bombardment induced interface evolution

An interface evolution equation has been formulated to describe bombardment‐induced etching by an axisymmetric angular distribution of energetic particles where the yield per incident particle is assumed to be a function of its energy and its angle relative to the surface normal. These assumptions result in a nonlinear integro differential equation, but this equation reduces to a partial differential equation in several important special cases. At points that are not shadowed by a remote part of the surface, the interface evolution equation reduces to a nonlinear hyperbolic conservation law. Such equations have been applied to bombardment‐induced etching by a monodirectional beam with angle‐dependent yields; however, this form of equation applies more generally to raised isolated convex regions (e.g., etching masks) regardless of the angular distribution of the incident particles or the angle dependence of the yield. The essential qualitative feature of the solution in these cases is the spontaneous evolution of facet edges (slope discontinuities) from smooth initial conditions. Shadowing by remote parts of the surface may occur in concave regions (e.g., trenches) where it results in proximity effects.