Analysis of stresses and shape changes in thin substrates with stressed film patterning using femtosecond laser micromachining

Abstract

The accurate, high-throughput fabrication of light weight optical systems for applications like next-generation space telescopes and semiconductor wafers is both crucial and challenging. A potential solution is to first fabricate thin substrates with traditional methods, then apply surface stress to bend them into desired shapes to correct residual height errors. We have developed a stress-based figure correction method for thin silicon mirrors using a femtosecond laser micromachining technique to generate patterned stress fields, through the removal of selective stressed film regions and adjacent substrate regions. In this paper, we present an in-depth analysis for the laser-induced stresses and resulting shape changes of thin mirrors due to the periodic patterning of a stressed film (silicon oxide) on silicon substrates using femtosecond laser surface ablation. Experimental results are presented, and a 3D finite element model (FEM) is developed to study the substrate curvature in directions parallel and perpendicular to the patterned troughs in the substrates. We simulate the stress relief process in the thin-film/substrate system, and the numerical predictions compare reasonably well with curvature measurements for several different geometrical combinations of depth, width and spacing of the patterned troughs, achieving >82% quantitative agreement with the experiments. It is also shown in the simulations that certain geometries of patterned troughs induce more dramatic shape changes and counter-intuitive reversals of curvature in the direction perpendicular to the troughs, and a qualitative explanation involving the Poisson effect is presented. The 3D finite element methods and findings of this paper can be used to determine the optimal parameters of the stressed film patterns for figure correction of thin telescope mirrors and other types of thin substrates used in the semiconductor industry.