Simulating anisotropic etching of silicon in any etchant: evolutionary algorithm for the calibration of the continuous cellular automaton

Abstract

An evolutionary algorithm is presented for the automated calibration of the continuous cellular automaton for the simulation of isotropic and anisotropic wet chemical etching of silicon in as many as 31 widely different and technologically relevant etchants, including KOH, KOH+IPA, TMAH and TMAH+Triton, in various concentrations and temperatures. Based on state-of-the-art evolutionary operators, we implement a robust algorithm for the simultaneous optimization of roughly 150 microscopic removal rates based on the minimization of a cost function with four quantitative error measures, including (i) the error between simulated and experimental macroscopic etch rates for numerous surface orientations all over the unit sphere, (ii) the error due to underetching asymmetries and floor corrugation features observed in simulated silicon samples masked using a circular pattern, (iii) the error associated with departures from a step-flow-based hierarchy in the values of the microscopic removal rates, and (iv) the error associated with deviations from a step-flow-based clustering of the microscopic removal rates. For the first time, we present the calibration and successful simulation of two technologically relevant CMOS compatible etchants, namely TMAH and, especially, TMAH+Triton, providing several comparisons between simulated and experimental MEMS structures based on multi-step etching in these etchants.

Evolutionary continuous cellular automaton for the simulation of wet etching of quartz

“…These removal rates have been obtained traditionally by deriving and solving a set of equations that relates the etch rates of certain macroscopic planes to the sequence of occupation reductions and atom removals appearing on those planes [6]. Nevertheless, it has been demonstrated recently that the use of an Evolutionary Algorithm (EA) provides a reliable method to determine the removal rates based on macroscopic etch rates as input data [8]. The EA has made possible the calibration of the CCA for a wide range of silicon etchants, including KOH, KOH+IPA, TMAH, TMAH+Triton and isotropic etching [8].…”

“…Nevertheless, it has been demonstrated recently that the use of an Evolutionary Algorithm (EA) provides a reliable method to determine the removal rates based on macroscopic etch rates as input data [8]. The EA has made possible the calibration of the CCA for a wide range of silicon etchants, including KOH, KOH+IPA, TMAH, TMAH+Triton and isotropic etching [8].…”

“…Only recently, it has been demonstrated that the use of Evolutionary Algorithms can perform this task automatically, requiring only an atom classification/equation derivation for the main cristallographic planes [8].…”

“…In silicon, the etching of the main planes is simpler, consisting on the successive removal of layers of the same type of atoms. This complexity and the good results obtained in [8] for silicon etching justify the use of an evolutionary algorithm instead of manually deriving the equations for a large number of different surface orientations.…”

“…E 2 : Underetching, 3-fold symmetry and floor corrugation. Although the etching of a sphere allows to obtain the etch rates for a wide range of orientations, several artifacts may appear when simulating the etching of a MEMS structure, such as an incorrect symmetry in the etched structure, disproportionate underetching at convex corners and/or excessive floor corrugation, all of which are features not obviated by the etching of the hemisphere [8]. To avoid such artifacts, we monitor the etching of a masked (0001) quartz chip, focusing on promoting three-fold symmetry, minimum underetching and minimum floor corrugation, as observed in experiments [13].…”