Shape Changes during Through‐Mask Electrochemical Micromachining of Thin Metal Films

Abstract

Shape change simulations of the electrochemical etching of lines and holes into thin metal films sandwiched between a photoresist mask and an insulating support are presented. For the moving‐boundary simulations, which use a boundary‐element method, it is assumed that the primary current distribution is applicable. The Appendix explains how formulating the current distribution problem in terms of a stream function instead of an electric potential can improve the efficiency of the numerical procedure. Two aspect ratios of photoresist thickness to cavity width are considered. In one case, large aspect ratios are assumed, and various metal film thicknesses are investigated. At long times, but before the insulating support is first exposed to the electrolyte, the shapes of the profiles can be fit to an ellipse. The simulations are continued following exposure of the support, and these results are summarized by a design curve that gives the cavity width necessary to etch a groove of a desired width or a hole of a desired radius into a metal of a given thickness. The second case that is investigated was studied experimentally by Rosset et al. [17]. The aspect ratio of this geometry is 0.08, and the thickness of the metal is large compared to the cavity width. The argeement between theory and experiment is discussed in terms of the likelihood of achieving in practical situations the modeling assumptions.