Model-based Analysis of Atomic Layer Deposition Growth Kinetics and Multiscale Process Dynamics
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A first principles model describing the reaction kinetics and surface species dynamics for the trimethylaluminum (TMA) and water half-reactions of alumina atomic layer deposition (ALD) is coupled with a dynamic film growth model and reactor-scale species transport model. The reaction kinetics model is based on reported enthalpies and transition state structures from published quantum-chemical computational studies; these data are used to determine kinetic parameters using statistical thermodynamics and absolute reaction rate theory. Several TMA half-reactions were modeled to account for TMA adsorption and subsequent reaction on a range of growth surfaces spanning bare to fully hydroxylated states. Several water reactions were also considered. By coupling the reaction rate models with surface species conservation equations, a dynamic model is created which is useful for examining the relative rates of competing surface reactions. To describe the continuous cyclic operation of the deposition reaction system, a numerical procedure to discretize limit-cycle solutions is developed and used to distinguish saturating growth per cycle from non-saturating conditions. The transition between the two regimes is studied as a function of precursor partial pressure, exposure times, and temperature. Finally, a cross-flow tubular ALD reactor system model is derived with components describing the precursor thermophysical properties, precursor delivery system, reactor-scale gas-phase dynamics, and surface reaction kinetics derived from absolute reaction rate theory. These model components are integrated to simulate the complete multiscale ALD process. Limit-cycle solutions defining continuous cyclic ALD reactor operation are computed with a fixed point algorithm based on temporal and spatial discretization within the reactor, resulting in an unambiguous definition of film growth per cycle. The use of the simulator for assisting in process design decisions and optimization frameworks is presented.