Simulation of anisotropic wet chemical etching using a physical model

We present a method to describe the orientation dependence of the etch rate in anisotropic etching solutions of silicon, or any other single crystalli ne material, by analytical functions. The parameters in these functions hav e a simple physical meaning. Crystals have a small number of atomically smo oth 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 roughen ing transition (well known in statistical physics) [P. Bennema, Growth and morphology of crystals: integration of theories of Roughning and Hartman-Pe rdok theorie, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, vol. I, E lsevier, Amsterdam (1993) 477; M. Elwenspoek. On the mechanism of anisotrop ic etching of silicon, J. Electrochem. Sec., 140 (1993) 2075]; at increasin g temperature they become rougher, and accordingly, the etch and growth rat es increase. Consequently, the basic physical parameters of our functions a re the roughness of the smooth faces and the velocity of steps on these fac es. We have applied our method to the practical case of etching of silicon in KOH solutions. The maximum deviation between experimental data and simul ation using only nine physically meaningful parameters is less than 5% of t he maximum etch rate. The method can easily be adapted to describe the grow th or etching process of any other crystal. (C) 2000 Elsevier Science S.A. All rights reserved.