Development of a deep silicon phase Fresnel lens using Gray-scale lithography and deep reactive ion etching

We report the first fabrication and development of a deep phase Fresnel lens (PFL) in silicon through the use of gray-scale lithography and deep-reactive ion etching (DRIE). A Gaussian tail approximation is introduced as a method of predicting the height of photoresist gray levels given the relative amount of transmitted light through a gray-scale optical mask. Device mask design is accomplished through command-line scripting in a CAD tool to precisely define the millions of pixels required to generate the appropriate profile in photoresist. Etch selectivity during DRIE pattern transfer is accurately controlled to produce the desired scaling factor between the photoresist and silicon profiles. As a demonstration of this technology, a 1.6-mm diameter PFL is etched 43 μm into silicon with each grating profile designed to focus 8.4 keV photons a distance of 118 m.