Development of a Deep Silicon Phase Fresnel Lens using Gray-scale Lithography and Deep Reactive Ion Etching

Abstract

A phase Fresnel lens (PFL) could achieve higher sensitivity and angular resolution in astronomical observations than the current generation of gamma and hard x-ray instruments. For ground tests of a PFL system, silicon lenses must be fabricated on the micro-scale with controlled profiles to enable high lens efficiency. Thus, two MEMS-based technologies, gray-scale lithography and deep reactive ion etching (DRIE), are extended to create multiple controlled step heights in silicon on the necessary scale. A Gaussian approximation is introduced as a method of predicting a photoresist gray level height given the amount of transmitted light through a gray-scale optical mask. Etch selectivity during DRIE is then accurately controlled by introducing an oxygen-only step to a standard Bosch cycle to produce the desired scaling factor between the photoresist and silicon profiles. Finally, a profile evaluation method is developed to calculate the expected efficiency of measured silicon profiles. Calculated efficiencies above 87% have been achieved.