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.

Microelectromechanical Systems

“…These effects need to be minimized in order to achieve uniform, flat shapes and reproducible material properties. At the pattern scale, it was found that a higher average current density is obtained in regions having a low density of patterns to be filled [19], as schematically shown in Figure 28.5. Design rules for MEMS thus suggest that the pattern should have a uniform density of features of similar size [20].…”

The Path from Invention to Product for the Magnetic Thin Film Head

“…pattern being plated [38,39]. In 1969, however, the required mathematics was not available, and even if it were, the modeling would have required a lot of expensive computer time on a main frame system.…”

Manufacturing Tools

“…Wafer-to-wafer repeatability is very important in order to ensure uniform product characteristics, and within-die or within-feature thickness or alloy composition uniformity may also be critical factors. Some of these considerations mean that the microscale pattern density of the substrate may be important in terms of determining the results on the wafer or substrate [37][38][39].…”