Kinetic Monte Carlo method for the simulation of anisotropic wet etching of quartz

Abstract

This study combines wet etching experiments and Kinetic Monte Carlo simulations to describe anisotropic etching of quartz for the manufacture of microelectromechanical systems (MEMS). Based on the particular atomistic structure of quartz we introduce a ‘quartz-based’ removal probability function with nine energy parameters. This enables describing the removal rate of any surface atom as an explicit function of the number of neighbors. An evolutionary algorithm is used to systematically transform the experimental (facet specific) etch rates of nine crystal planes parallel to the X (electric) and Y (mechanical) axes into suitable values for the nine energy parameters. To improve the computational efficiency of the evolutionary search we make use of a transformation matrix, effectively constraining the evolutionary search space. This leads to successful predictions for the etch rates of a wide range of crystallographic facets as well as for the three-dimensional etched shapes obtained on masked Z-cut substrates.