Particle swarm optimization of model parameters: Simulation of deep reactive ion etching by the continuous cellular automaton

As a widespread form of Deep Reactive Ion Etching (DRIE), the Bosch process alternates etching and passivation cycles, typically leading to characteristic scalloping patterns on the sidewalls. Measurements of the etch depth per cycle l_d and undercut length per cycle l_u show a strong dependence of the undercut ratio l_u/l_d on the trench aspect ratio for a wide range of opening sizes. Although various simulation models have been proposed, the determination of the corresponding parameters from experimental data remains unsolved. We present the use of (i) the Continuous Cellular Automaton (CCA), to simulate the process reliably in three dimensions, (ii) the Particle Swarm Optimization (PSO) method, to determine suitable values for the atomistic CCA parameters directly from experimental data, and (iii) a GPU, parallel implementation of the CCA, to increase the computational efficiency of the simulations. The resultant, parameter-optimized CCA simulations show good agreement with the experiments. The approach has a large potential for the simulation of other MEMS processes.