Reaction factorization for the dynamic analysis of atomic layer deposition kinetics

We develop a Gauss-Jordan factorization procedure to explicitly separate the slow (deposition), fast (equilibrium), and instantaneous (conserved) modes of thin-film deposition models describing the dynamics of the precursor, surface, and deposition chemical species, focusing primarily on the dynamics of atomic layer deposition (ALD) processes. Our reaction factorization procedure provides an unambiguous means of translating sequences of equilibrium and irreversible reactions characterizing a deposition system into a low-dimensional DAE system when the reaction kinetics are predicted using transition-state theory. The factorization eliminates redundant dynamic modes; an implicit Euler procedure then is used to solve the singular-perturbation problem describing the time-evolution of the reaction species on the manifold defined by the combination of the equilibrium relationships and conserved quantities. An alumina ALD process based on the TMA/water precursor system serves as the example used in this work; despite the intense study of this ALD process, several new observations regarding this reaction system are made and a number of new questions are raised.