Effect of substrate thickness on the etching rate of diffractive optical elements

The substrate thickness of multilayer dielectric (MLD) pulse compression gratings can reach several centimeters. These elements are often fabricated using holography combined with plasma etching. Even though the effect of substrate thickness on the etching performance is huge, literature on this problem is scarce. With this work, we attempt to fill this gap. We have performed etching experiments on fused silica samples of different thicknesses (2, 5, and 10mm) in fluorocarbon inductively coupled plasma discharge (ICP). We have observed a significant deviation in etching rates for samples with different thicknesses under the same conditions. In extreme cases, the etching on a thick sample stops completely, while for thin substrates, the etching rate reaches its maximum. Results are analyzed with a specific one-dimensional fluid model of a plasma sheath coupled with an equivalent electric circuit model. The developed model allows to predict variations in potential and ion energy distributions at a substrate surface. We found that the thick substrate acts as a weak capacitor and reduces the energy of incident ions. This results in a change of the etching-passivation rates balance. 86 aktive optische Elemente U. Böhm