A MATHEMATICAL-MODEL FOR PLANARIZATION OF MICROELECTRONIC TOPOGRAPHIES

A model has been developed to predict free surface profiles over topog raphic features for nonvolatile fluids. The degree of planarity of the free surface is shown to depend on two geometric ratios and the relat ive magnitude of centrifugal and surface tension forces. Previous mode ls have used a lubrication model to approximate the flow field. One pu rpose of this work is to make a comparison between the full two-dimens ional model and a one-dimensional lubrication model. The lubrication m odel compares favorably to the 2D model for large features. For small features, there is a difference between the free surface predictions o f the two models, which depend on the geometric ratios.