Diffusion vs. Surface Controlled Deposition

Before considering the full problem in all its complexity, it will be useful to understand the concept of surface or diffusion controlled CVD. At one extreme, with very low pressures (large diffusion coefficients) and low surface temperatures, there is a large flux of reactants to the surface where they react slowly so that there is an oversupply of reactants waiting to be consumed. This would be considered the surface controlled regime where the rate of 

At the other extreme, we have higher pressures (smaller diffusion coefficients) and high surface temperatures. Now, any molecule that can make it to the surface will react rapidly, so that the deposition rate will be more limited by diffusion through the gas adjacent to the surface. Since diffusion is weakly dependent on temperature, this type of diffusion controlled regime tends to be relatively insensitive to surface temperature. 

Similar boundary layers (transition regions) exist for temperature as well as species concentrations. 

Assume we have a mixture of ideal reacting gases, and a concentration boundary layer. Then the diffusion of species i from the body of the gas to the solid surface is governed by Fick s Law1 

When deposition is controlled by diffusion. Equation (28) shows that variations in boundary layer thickness, 5, influence the mass flux due to diffusion and thereby, the deposition rate. In practical CVD reactors, boundary layer thicknesses can vary so that thickness uniformity of deposition can be poor unless this phenomena is recognized and corrected. 

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