HYDROFLUORIC-ACID ETCHING OF SILICON DIOXIDE SACRIFICIAL LAYERS .2. MODELING

Modeling of sacrificial layer etching can be done by combining the diffusion rates of etchants in solution and the chemical reaction rate. Steady-state diffusion is estimated for HF diffusion coefficients in water on the range of 5 X 10(-6) to 5 X 10(-5) cm2/s as observed from an independent experiment. Likewise, the chemical reaction rates (or initial etch rates) for each silicon dioxide/hydrofluoric acid system as a function of HF concentration are obtained from independent experiments. The etching kinetics of SiO2 with HF are nonlinear. An analytical method is used with power law kinetic reaction rate expressions and Newton's method to linearize the problem. This allows the calculation Of the surface HF concentration as a function of etching time. By equating the diffusive and reactive fluxes at the SiO2 action surface, the surface HF concentration is calculated. Applying a forward Euler integrated etch rate relationship, the surface HF concentration can be used to plot the etch front location as a function of time.