Simulation of anisotropic wet chemical etching using a physical model

Abstract

We present a method to describe the orientation dependence of the etch rate in anisotropic etching solutions of silicon, or any other single crystalline material, by analytical functions. The parameters in these functions have a simple physical meaning. Crystals have a small number of atomically smooth faces, which etch (or grow) slowly as a consequence of the removal (or addition) of atoms by rows and layers. However, smooth faces have a roughening transition (well known in statistical physics) [P. Bennema, Growth and morphology of crystals: integration of theories of Roughning and Hartman-Perdok theorie, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, vol. I, Elsevier, Amsterdam (1993) 477; M. Elwenspoek, On the mechanism of anisotropic etching of silicon, J. Electrochem. Soc., 140 (1993) 2075]; at increasing temperature they become rougher, and accordingly, the etch and growth rates increase. Consequently, the basic physical parameters of our functions are the roughness of the smooth faces and the velocity of steps on these faces. We have applied our method to the practical case of etching of silicon in KOH solutions. The maximum deviation between experimental data and simulation using only nine physically meaningful parameters is less than 5% of the maximum etch rate. The method can easily be adapted to describe the growth or etching process of any other crystal.