Reaction Network Analysis for Thin-Film Deposition Processes: Physical Interpretation of Reaction Invariants

Modeling the dynamics of atomic layer deposition processes is challenging because of the nonlinear behavior of these systems, their multiple and widely-ranging timescales, and by the relative lack of validated reaction kinetics information. Those data that do exist are typically derived from quantum chemical computations or experimental examinations of reaction sequences that define only a portion of the complete ALD reaction cycle.

In this talk, we will describe our efforts to develop mathematical methods that address the numerical challenges of simulating dynamic Atomic Layer Deposition (ALD) and Chemical Vapor Deposition (CVD) processes while providing a rational path to creating well-posed models of these deposition processes. Our model reduction approach is based on a two-step procedure where in the first, the chemical species surface balance dynamic equations are factored to decouple the (nonlinear) reaction rates, eliminating redundant dynamic modes. The second phase further reduces the dynamic dimension when species relatively minor in concentration can be identified. The overall technique extracts physically significant reaction invariants [1-3] and points to potential model structural problems if they exist. An alumina ALD process is used for an example consisting of nineteen reactions and twenty-three surface and gas-phase species. Using our approach, the model is reduced by nineteen modes to a four-dimensional dynamic system without any knowledge of the reaction rate values. Results are interpreted in the context of identifying rate limiting steps and validating the predicted dynamic behavior.

[1] Asbjornsen, O.A., Reaction invariants in the control of continuous chemical reactors. Chemical Engineering Science, 27(4), 709-717 (1972).

[2] Rodrigues, D., S. Srinivasan, J. Billeter, and D. Bonvin, Variant and invariant states for chemical reaction systems. Computers Chemical Engineering, 73, 23-33 (2015).

[3] Zhao, Z., J. M. Wassick, J. Ferrio, and B. E. Ydstie, Reaction variants and invariants based observer and controller design for CSTRs, DYCOPS 2016 (2016).