E. van Veenendaal,   A. J. Nijdam and J. van Suchtelen
 

Abstract
We present a simulation tool for the prediction of the evolution of macroscopic crystal growth and etching shapes that can be represented in a two-dimensional setting. It is assumed that the advance rate of the crystal surface depends solely on the surface orientation, which implies that the classical kinematic wave theory applies. We present an algorithm to calculate the crystal shape at any given point in time in a single time step for initial crystal shapes that are either completely convex or completely concave. We show that calculation of the crystal shape for mixed convex/concave crystal shapes may require a series of time steps. Boundary conditions imposed at imperfections in the crystal surface or at boundaries with a container wall or a mask are treated. The possibility of two or more disconnected crystal shapes that meet at some point in their evolution is also taken into account. The simulation tool is used to predict crystal shape evolution for the technologically relevant case of wet chemical etching of masked silicon {1 0 0} wafers with multiple mask openings. It is shown that the experimental evolution of Si{1 1 0} surfaces cannot be reproduced using any simulation tool based on the assumption that the etch rate depends solely on the surface orientation. The differences between experiments and simulations are explained on the basis of the etching mechanism of Si{1 1 0} surfaces.