3-D Topography Simulation of Via Holes Using Generalized Solid Modeling

A 3-D deposition and etching simulator using “generalized solid modeling (GSM) method” has been developed. This simulator uses the boundary representation model to define solids, forming the individual materials of the wafer. Then, basic solid modeling operations are used to deform the solids without the need for complex loop removal algorithms. In this simulator, the “3-D unified equation,” whose parameters are the same as those of the 2-D equation, is.used to calculate a local deposition and/or etching rate. To precisely calculate the movement vector of each vertex for complex 3-D structures, the “3-D plane model” and “semi-sphere mesh method” have been developed. This simulator has been applied to the patterning and metallization of via holes, and its results closely agree with experimental results.