Optimization of the Monte Carlo Simulation for Sapphire in Wet Etching

Abstract

In this paper, the Monte Carlo simulation for sapphire in wet etching is optimized, which improves the accuracy and efficiency of simulated results. Firstly, an eight-index classification method is proposed to classify the kinds of surface atoms, which can make assigned removal probabilities more accurately for surface atoms. Secondly, based on the proposed classification method of surface atoms, an extended removal probability equation (E-RPE) is proposed, which makes the errors between simulated and experimental rates smaller and greatly improves the accuracy of the simulated result of the etch rate distribution under the experimental condition (H2SO4:H3PO4 = 3:1, 236 °C). Thirdly, a modified removal probability equation (ME-RPE) considering the temperature dependence is proposed based on the error analysis between the simulated and experimental rates under different temperature conditions, which can simulate etch rates under the different temperature conditions through a group of optimized energy parameters and improve the simulation efficiency. Finally, small errors between the simulated and experimental rates under the different temperature conditions (H2SO4:H3PO4 = 3:1, 202 °C and 223 °C) verify the validity of the ME-RPE for temperature change. The optimization methods for the Monte Carlo simulation of sapphire in wet etching proposed in this paper will provide a reference for the simulation of other crystal materials.

Analysis of Wet-Etched Structures on R-Plane Substrates of Sapphire in the Etchant of Sulfuric Acid and Phosphoric Acid

“…Typical crystal planes which belong to the family of crystal planes {Y} are labeled Y1, Y2, … Yn, respectively. 30,31 For the wet-etched square groove in Fig. 8a, the exposed typical crystal planes are marked as A, B, C1, C2, D1, D2, E1 and E2, respectively.…”