Diffusion-Reaction Model of ALD in Nanostructured Substrates: Analytic Approximations to Dose Times as a Function of the Surface Reaction Probability

We have developed a transport model for Atomic Layer Deposition (ALD) in nanostructured substrates. The model comprises a non-linear advection-diffusion-reaction equation coupled to a surface kinetic equation that incorporates the self-limiting nature of ALD. In their nondimensional forms, these equations show that coverage dynamics in ALD depend only on two parameters: the Damkoeler number and the precursor excess number. These parameters depend on the surface chemistry and experimental conditions and can be readily calculated for a wide range of substrate geometries including trenches and vias, anodized alumina, and powders.