Mesoscopic scale modeling of microloading during low pressure chemical vapor deposition

A model designed to deal with pattern dependences of deposition processes is discussed. It is a mesoscopic scale model in the sense that it deals with spatial scales on the order of 10^-3 to 10^-2 m, which is intermediate between reactor scale and feature scale. This model accounts for the effects of the microscopic surface structure via suitable averages obtained by a homogenization technique from asymptotic analysis. Two studies on the low pressure chemical vapor deposition of silicon dioxide from tetraethoxysilane are presented to demonstrate the mesoscopic scale model. The first study shows the effects of microloading in regions of higher feature density. The second study shows the effects of varying operating conditions on loading and introduces a generalized Damkoehler number, which includes information about the surface patterns, for quantifying the degree of transport limitations. Some thoughts on how this model can be used to bridge reactor scale and feature scale models are presented.