Analytical Solution of the Continuous Cellular Automaton for Anisotropic Etching

The fabrication of micro- and nanoelectromechanical systems (MEMS/NEMS) is based on a wide variety of growth and etching technologies sequentially applied throughout process flows which may involve a dozen or more steps, their realistic simulation having become an essential part of the overall design. By focusing in the simulation of anisotropic etching as a complex example of microfabrication, in this paper, we show how to solve analytically the time evolution of the continuous cellular automaton method, thus providing a particularly suitable choice for the realization of realistic simulations for MEMS and NEMS applications. This paper presents a complete theoretical derivation of the analytical solution based on geometrical and kinetic aspects of step flow on any surface, including a new classification of the surface sites based on a mean-field treatment of the propagation of the steps. The results of the corresponding simulations are in good agreement with the experiments. The study can be seen as an example of a general procedure that is applicable to other interface propagation problems.