Evolutionary Kinetic Monte Carlo Simulation of Anisotropic Wet Etching of Sapphire at Different Concentrations and Temperatures

This study focuses on the simulation of wet etching of sapphire at different concentrations and temperatures. We use the Evolutionary Kinetic Monte Carlo (E-KMC) method, which combines (i) a removal probability function (RPF), to reduce the large collection of adjustable removal rates to a smaller number of energy parameters, and (ii) an evolutionary algorithm, to optimize those parameters by minimizing errors between simulated and experimental rates for a selected group of surface orientations. To improve the resemblance between simulated and experimental etch rate distributions at different concentrations, additional surface orientations located in the region with worst similarity are used. This is validated by a comparison of experimental and simulated trench profiles obtained on C-plane sapphire wafers with rectangular mask openings. Most importantly, this study addresses for the first time the temperature dependence considered in traditional formulations of the RPF, concluding that it is only partially correct. To overcome this deficiency, a physically meaningful modified removal probability function (M-RPF) is formulated as the product of a standard prefactor and a standard Boltzmann factor, in agreement with Transition State Theory. Effectively, the prefactor transforms the facet-specific orientation-dependence of the etch rate at a given temperature into the atom-specific site-dependence of removal rates on the local neighborhood, while the Boltzmann factor assigns a different activation energy to every surface atom type. It is shown that the M-RPF provides a suitable approach to correctly model the overall temperature dependence. The study extends the range of wet etching applications of the E-KMC method. [2021-0221]