436664 Atomic Layer Deposition Processes: Understanding the Algebraic and Geometrical Structure of Dynamic Reaction Models

Wednesday, November 11, 2015: 12:30 PM
Salon G (Salt Lake Marriott Downtown at City Creek)
Raymond A. Adomaitis and David Arana-Chavez, Department of Chemical & Biomolecular Engineering; Institute for Systems Research, University of Maryland, College Park, MD

While substantial effort has been invested in understanding the fundamentals of atomic layer deposition (ALD) surface reaction mechanisms and how surface reaction models are integrated with reactor-scale precursor transport simulations (see, e.g., [1-3]), ambiguities remain in modeling the surface species dynamics during the different phases of an ALD process cycle. For example, open questions exist regarding how reactive surface species in amorphous ALD films are defined, how rate-limiting steps are identified in surface reaction networks, how equilibrium processes are distinguished from their finite-rate counterparts, and how redundant modeling equations can be pruned from the ALD surface reaction network. Therefore, the objective of this work is to take the first steps towards developing a mathematical framework that can be used to decompose ALD surface reaction dynamics according to the time-scales of the elementary reactions and to assess whether the resulting simulation problem is well-posed and so will provide physically meaningful simulation results.

In this paper, we present a recently developed reaction factorization procedure [4] that explicitly separates 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 for ALD processes. The reaction factorization procedure provides an unambiguous means of translating sequences of adsorption, equilibrium, and irreversible reactions characterizing a deposition system into a low-dimensional differential-algebraic (DAE) system when the reaction kinetics are predicted using transition-state theory, an approach that builds directly on such ALD DFT studies as those described in [1]. The factorization eliminates redundant dynamic modes and provides a wealth of other structural information about the deposition model. An implicit Euler procedure then is used to numerically 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.

Our modeling and analysis approach will be described in the context of an alumina ALD process based on the TMA/water precursor system. Even with the existing bodies of modeling research for these two systems, our approach to reaction kinetics modeling will reveal new insights into the rate-limiting processes of each deposition reaction network by quantifying the flux of ALD precursors and surface species through the nodes of an ALD reaction graph.

References

[1] Elliott, S. D., Semicond. Sci. Tech. 27, 1–10 (2012)
[2] Holmqvist, A., T. Torndahl and S. Stenstrom, Chem. Eng. Sci. 81, 260–272 (2012) [3] Travis, C. D. and R. A. Adomaitis, Processes 1, 128–152 (2013)
[4] Remmers, E., C. D. Travis, and R. A. Adomaitis, Chem. Eng. Sci., in press, (2015) 


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