Effect of sample thickness on etching rate: Simulations and experiments

Precision optical elements such as computer generated holograms (CGH) for optical testing or optical elements for high-power lasers, e.g., pulse compression gratings, are often many millimeters thick. This study investigates the effect of substrate thickness on dry etching in an inductively coupled plasma discharge (ICP). We present a combined fluid and equivalent electric circuit (EEC) model to simulate the plasma sheath in the presence of the dielectric sample. The model demonstrates that the sheath voltage and ion energy at the sample surface are reduced due to lower sample capacitance for thicker samples. This effect becomes critical at high ICP power levels, where ion energy can fall below the threshold for effective chemical etching or sputtering. Etching experiments on fused silica samples of different thickness confirm these findings, showing strong agreement with simulation predictions. A modified etching rate model is proposed and validated against experimental results.