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 boundaryelement 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 widt~h. The argeement between theory and experiment is discussed in terms of the likelihood of achieving in practical situations the modeling assumptions.The fabrication of electronic devices may require the etching of thin metal films that are coverd by a photoresist mask and supported by an insulating material. This is accomplished by dry or wet etching processes, with the latter being done either chemically or electrochemically. Datta and Romankiw (1) reviewed the advantages of different wet-etching procedures, and Allen (2) discussed many of the practical considerations. Figure 1 shows the initial, unetched assembly that is considered here. As indicated, both two-dimensional lines and axisymmetric holes are investigated. The thickness of the photoresist mask is d, and b is the metal film thickness. The half-width of the initial, unetched two-dimensional line is L, and r0 is the radius of the unetched axisymmetric hole.The prediction of the final shape requires a moving boundary simulation where, at each time step, the reaction rate distribution on the surface is determined. Dukovic (3) reviewed the developments in the 1980's in movingboundary calculations for electrodeposition. Electrochemical etching has received less attention from a theoretical viewpoint. In nearly all of the studies, which are reviewed briefly below, the local etch rate along the metal is assumed to be mass-transfer controlled. Kuiken et al. (4,5) studied by a perturbation analysis shape changes near the edge of the photoresist for masstransfer controlled etching. Their work, which is valid for infinitesimally thin masks (i.e., d/L = 0), was verified experimentally (6). Vuik and Cuvelier (7) also investigated diffusion-controlled etching through a thin photoresist mask. They discuss two numerical ...

High-throughput patterning of photonic structures with tunable periodicity

“…The localization of oxidic Ge ridge pattern (rings and lines) forms at the point where the CV scan direction changes from anodic to cathodic sweep. The patterns appear similar to those generated from moving boundary simulations of etching processes (18). Though pattern formation appears electrochemically mediated, capillary flows leading to contact line pinning and depinning (19) at the periphery of the unetched parent material may intervene in the generation of periodic features.…”

Design and fabrication of two-axis micromachined steel scanners

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Through-Mask Electrochemical Micromachining of Aluminum in Phosphoric Acid

“…[38][39][40][41][42] The boundary was first discretized into line segments where the concentration was approximated along each segment using discontinuous, linear functions. 43 Such boundary elements are easy to implement and allow for discontinuities at corner points and at the edge between the metal and the insulator.…”

“…At each time step the amount of displacement in x-and y-direction of every point along the metal surface was calculated by splitting Equation 2 into its x-and y-component using a finite difference approximation. 44 The length of a time step was chosen small, so that the displacement in y-direction in the center of the evolving cavity (x = 0) equaled 0.005 × w in order to avoid convergence problems 39 and to increase accuracy. Due to symmetry, only half of the depicted solution domain was considered in order to reduce the computational effort.…”