Dynamic parameter estimation of atomic layer deposition kinetics applied to in situ quartz crystal microbalance diagnostics

Abstract

This paper presents the elaboration of an experimentally validated model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing encoded in the Modelica language. For the experimental validation of the model, in situ quartz crystal microbalance (QCM) diagnostics was used to yield submonolayer resolution of mass deposition resulting from thin film growth of ZnO from Zn(C2H5)2 and H2O precursors. The ZnO ALD reaction intrinsic kinetic mechanism that was developed accounted for the temporal evolution of the equilibrium fractional surface concentrations of precursor adducts and their transition states for each half-reaction. This mechanism was incorporated into a rigorous model of reactor transport, which comprises isothermal compressible equations for the conservation of mass, momentum and gas-phase species. The physically based model in this way relates the local partial pressures of precursors to the dynamic composition of the growth surface, and ultimately governs the accumulated mass trajectory at the QCM sensor. Quantitative rate information can then be extracted by means of dynamic parameter estimation. The continuous operation of the reactor is described by limit-cycle dynamic solutions and numerically computed using Radau collocation schemes and solved using CasADi׳s interface to IPOPT. Model predictions of the transient mass gain per unit area of exposed surface QCM sensor, resolved at a single pulse sequence, were in good agreement with experimental data under a wide range of operating conditions. An important property of the limit-cycle solution procedure is that it enables the systematic approach to analyze the dynamic nature of the growth surface composition as a function of process operating parameters. Especially, the dependency of the film growth rate per limit-cycle on the half-cycle precursor exposure dose and the process temperature was thoroughly assessed and the difference between ALD in saturating and in non-saturating film growth conditions distinguished.