Scale-up Analysis of Continuous Cross-flow Atomic Layer Deposition Reactor Designs

Anders Holmqvist, Fredrik Magnusson, Stig Stenström

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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)2 and H2O precursors that was experimentally validated in our previous work (Holmqvist et al., 2012, 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.
Original languageEnglish
Pages (from-to)301-317
JournalChemical Engineering Science
Publication statusPublished - 2014

Subject classification (UKÄ)

  • Chemical Engineering
  • Control Engineering


  • Atomic layer deposition
  • Mathematical modeling
  • Dynamic optimization
  • Scale-up analysis
  • Limit-cycle kinetics
  • Numerical analysis


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