Modeling of Through-Mask Electrochemical Micromachining

The through-mask electrochemical machining of features of micron dimensions was studied theoretically. The Laplace equations for the electric field potential and the equation of workpiece surface evolution were used as the mathematical model of the process. The problem was solved numerically using the methods of finite and boundary elements, and also the "Level Set" method. By using the numerical experiments, the effect of parameters, which characterize the mask geometry and the process conditions, on the initial distribution of current density over the workpiece surface and the variation of current distribution in the course of etching was studied. In particular, the dependences of dimensionless average current density on a fraction of unprotected areas were obtained at various values of mask thickness and unprotected areas (rectangular grooves or circles). It is shown that the higher is the unprotected area density, the mask thickness, and unprotected area width, the higher is the initial average current density. It is shown that the initial nonuniformity of average current density changes in the course of machining leading to a change in a ratio between the anodic dissolution rates of unprotected areas of different widths. In the initial period of treatment, the smaller is the width of uncovered area, the higher is the anodic dissolution rate. Then, in the course of machining, the anodic dissolution rate on the narrow unprotected areas steeply decreases and can become lower than that on the wider areas. As a result, the depth of unprotected areas of different sizes will be different. The result of modeling enables one to predict the final depth of the features on the workpiece surface.