The Influence of Lithographic Patterning on Current Distribution: A Model for Microfabrication by Electrodeposition

Abstract

A model has been developed to predict current distribution in electrodeposition onto substrates that contain lithographic patterns. The aim of the work was to understand the strong effects that substrate patterning can exert on the thickness distribution of plated films. Based on the familiar potential-theory model for secondary current distribution in electrochemical cells, the model is applicable at length scales that are large compared to the individual features of a pattern. The pattern is described entirely as a continuous distribution of “active-area density,” a property that reflects any relative change in the electroactive area of the substrate due to the pattern. The active-area density enters the expression that relates the surface overpotential to the current density. An implementation of the model, using the boundary element method, has been applied to several problems that illustrate the effects of substrate patterning on current distribution. For each example, the dimensionless groups that characterize the current distribution have been identified, general solutions have been obtained over wide parameter ranges, and behavioral trends have been interpreted. © 1991, The Electrochemical Society, Inc. All rights reserved.