Step flow model in continuous cellular automata method for simulation of anisotropic etching of silicon

Abstract

A continuous cellular automaton (CCA) is presented for the simulation of anisotropic wet chemical etching in the fabrication of microstructures. Based on the step-flow model, the surface atoms are divided into categories according to the atom configurations on different crystal planes. An analytical solution for the dependence of the etch rate on orientation is derived, and the CCA approach makes a direct conversion of experimental macroscopic rates into calibrated microscopic parameters for realistic and reliable simulations. The presented model has been extended to a simulation system based on a CCA method. Linear search and variable time stepping are used to simulate a silicon wafer in various etching condition and mask shapes. The simulation results agree well with the experiments. This improved CCA makes possible for the realization of accurate simulations of anisotropic etching in engineering applications. Downloaded From: http://nanolithography.spiedigitallibrary.org/ on 05/16/2015 Terms of Use: http://spiedl.org/terms J. Micro/Nanolith. MEMS MOEMS 023004-7 Apr-Jun 2013/Vol. 12(2) Rezvankhah et al.: Step flow model in continuous cellular automata method. . . Downloaded From: http://nanolithography.spiedigitallibrary.org/ on 05/16/2015 Terms of Use: http://spiedl.org/terms

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“…Several studies have been carried out to examine overall cases of anisotropic silicon etching [ 161 , 162 , 163 ]. Good predictions for shapes of etched wafers can be found using numerical analysis [ 164 , 165 , 166 ].…”