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. Sec., 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. (C) 2000 Elsevier Science S.A. All rights reserved.