Scale-up analysis of continuous cross-flow atomic layer deposition reactor designs

• Novel model-based methodology for scaling up cross-flow ALD reactors.
• Dynamic similarity was investigated by means of the non-dimensionalized ALD reactor model.
• ALD limit-cycle dynamic solution was numerically computed using Radau collocation schemes.
• The maximum precursor utilization was enhanced by scaling up the substrate dimensions.
• Optimal scaling rules to keep deposition profiles identical in scaled-up systems were identified.

This paper presents the development of a non-dimensional model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing and a structured model-based methodology for scaling up the substrate dimensions. The model incorporates an ALD gas–surface reaction kinetic mechanism for the deposition of thin ZnO films from Zn(C2H5)2Zn(C2H5)2 and H2OH2O precursors that was experimentally validated in our previous work (Holmqvist et al., 2012 and Holmqvist et al., 2013a). In order to maintain dynamic similarity, a scaling analysis was applied based on the dimensionless numbers, appearing in non-dimensionalized momentum and species mass conservation equations, that describe the convective laminar flow, mass transfer and heterogeneous reaction. The impact on these dimensionless numbers and, more importantly, the impact on the limit-cycle deposition rate and its relative uniformity was thoroughly investigated when linearly scaling up the substrate dimensions. In the scale-up procedure, the limit-cycle precursor utilization was maximized by means of dynamic optimization, while ensuring that identical deposition profiles were obtained in the scaled-up system. The results presented here demonstrated that the maximum precursor yields were promoted at higher substrate dimensions. Limit-cycle dynamic solutions to the non-dimensionalized model, computed with a collocation discretization in time, revealed that it is a combination of the degree of precursor depletion in the flow direction and the magnitude of the pressure drop across the reactor chamber that governs the extent of the deposition profile non-uniformity. A key finding of this study is the identification of optimal scaling rules for maximizing precursor utilization in the scaled-up system while maintaining fixed absolute growth rate and its relative uniformity.