Effects of diffusional processes on crystal etching: Kinematic theory extended to two dimensions

The effects of diffusional processes on etching of crystalline materials are investigated using a model that combines an atomistic, kinetic Monte Carlo simulation with a step-density dependent model of diffusional effects. Diffusion may be driven by processes such as etchant depletion, product buildup, or reaction exothermicity. In effect, this model extends traditional kinematic theory (KT), a one-dimensional continuum model, to two dimensions. The case of relatively isotropic step flow etching with locally accelerating diffusional effects is examined in detail. When the effects of diffusion are included, the etching surface spontaneously develops step bunches separated by relatively step-free areas. Since diffusional processes accelerate etching, the step bunches travel faster than individual etching steps. The steady state size of the bunches is determined by the competition between step incorporation and step detachment. Both of these observations are in agreement with the original KT. In contrast, the characteristic concave bunch profile predicted by one-dimensional KT is not reproduced in two dimensions. Instead, the bunches have a relatively flat profile that is in agreement with recent experiments. The implications of this observation on experimental measurements are discussed.