Angel Yanguas-Gil and Jeffrey W. Elam Self-Limited Reaction-Diffusion in Nanostructured Substrates: Surface Coverage Dynamics and Analytic Approximations to ALD Saturation Times Chemical Vapor Deposition 18
We present a general model based on a time-dependent reaction-diffusion equation to determine the dosing times and coverage profiles in structured substrates during atomic layer deposition (ALD). Using the assumptions of molecular flow in a circular pore, we derive a general, analytic equation to predict saturation exposure times. To demonstrate the utility of our model, we derive additional expressions incorporating a precursor loss term relevant to predicting exposure times during ozone-based ALD. Because our model makes no assumptions about the diffusion coefficient or sample geometry, it can easily be adapted to describe a broad range of ALD systems.
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