Analytic expressions for atomic layer deposition: Coverage, throughput, and materials utilization in cross-flow, particle coating, and spatial atomic layer deposition

In this work, the authors present analytic models for atomic layer deposition (ALD) in three common experimental configurations: cross-flow, particle coating, and spatial ALD. These models, based on the plug-flow and well-mixed approximations, allow us to determine the minimum dose times and materials utilization for all three configurations. A comparison between the three models shows that throughput and precursor utilization can each be expressed by universal equations, in which the particularity of the experimental system is contained in a single parameter related to the residence time of the precursor in the reactor. For the case of cross-flow reactors, the authors show how simple analytic expressions for the reactor saturation profiles agree well with experimental results. Consequently, the analytic model can be used to extract information about the ALD surface chemistry (e.g., the reaction probability) by comparing the analytic and experimental saturation profiles, providing a useful tool for characterizing new and existing ALD processes.