On the modeling of shape evolution in through-mask electrochemical micromachining of complex patterned substrates

This study is about the optimization of the shape evolution of a printed circuit board (PCB) by means of an auxiliary electrode. Predicting the shape evolution of such complex workpieces calls for a significant reduction of the nodal points in discretization. The authors applied a hierarchic modeling strategy, which breaks the overall problem into three spatial scales: the macroscopic, the mesoscopic and the microscopic scale. Simulations on each scale are performed by considering influences from the other scales in a simplified way. The strategy yields the shape evolution of any chosen trench of the workpiece and allows for the consideration of an auxiliary electrode. The auxiliary electrode was optimized in terms of its geometry and potential. The uniformity of the etch rate was governed by an interplay of different extrema caused by the complex patterning of the workpiece. This interplay was cleared up by investigating the current density of each extremum as a function of the parameters.