(317b) Coupling Ballistic Transport and Surface Reaction Models for Simulation of Atomic Layer Deposition Processes

This paper examines the connections that exist between precursor transport and surface reaction modeling elements in atomic layer deposition process simulators. In particular, we consider nanoporous materials modified by ALD, taking advantage of ALD’s potential for conformal deposition in high-aspect-ratio structures. Because of the very large Knudsen number associated with these processes, the diffusion of gas-phase species inside the nanostructures takes place in a purely ballistic manner. Closed-form expressions for the pore-feature precursor transmission probabilities describing the fluxes between the pore internal surfaces are developed and then compared to previous deterministic modeling studies (e.g., those described and cited in [1]).

The transport model elements then are coupled to ALD surface reaction models that describe precursor chemisorption, desorption, and surface reactions that form the ALD film and gas-phase products [2]. Mean-field and simple Monte-Carlo surface reaction models will be described. We will show that a distinct mathematical structure describes this coupling; understanding this structure is crucial to formulating the simulator in such a way that modifications to the surface reaction elements or transport geometry are simple to make. The combined system is spatially discretized and integrated over each precursor exposure and purge period to determine the spatio-temporal features of the reaction surface states during a complete ALD cycle, a computational task presenting its own set of numerical challenges.

Predictions from our dynamic model will be compared to previously published studies of conformal ALD [3]-[7] to validate our simulator and to gain further insight into the physical mechanisms at work in ALD processes. The consistency of our predictions relative to previous modeling work will be quantitatively assessed, and new perspectives on the cited studies will be provided when possible. Overall, our goal is to establish a baseline from which more refined models can be developed, to explore more intricate deposition surface topographies and more realistic surface reaction mechanisms and kinetic expressions. Ultimately, the physically based models of the type we develop can be exploited to determine optimal precursor exposure levels for ALD-based nanomanufacturing operations.

References

[1] Cale, T. S., M. O. Bloomfield, and M. K. Gobbert, Two deterministic approaches to topography evolution, Surface & Coatings Tech. 201 8873-8877 (2007).
[2] Elliott, S. D., Models for ALD and MOCVD growth of rare earth oxides, Rare Earth Oxide Thin Films, Topics Appl. Physics 106 7386 (2007).
[3] Dendooven, J., D. Deduytsche, J. Musschoot, R. L. Vanmeirhaeghe, and C. Detavernier, Modeling the conformality of atomic layer deposition: The effect of sticking probability, J. Electrochem. Soc., 156 (4) 63-67 (2009).
[4] Elam, J. W., D. Routkevitch, P. P. Mardilovich, and S. M. George, Conformal coating on untrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition, Chem. Mater. 15 3507-3517 (2003).
[5] Gordon, R. G., D. Hausmann, E. Kim, and J. Shepard, A kinetic model for step coverage by ALD in narrow holes or trenches, Chem. Vap. Deposition 9 (2) 73-78 (2003).
[6] Granneman, E., P. Fischer, D. Pierreux, H. Terhorst, and P. Zagwijn, Batch ALD: Characteristics, comparison with single wafer ALD, and examples, Surface & Coatings Tech. 201 8899-8907 (2007).
[7] Perez, I. E. Robertson, P. Banerjee, L. Henn-Lecordier, S. J. Son, S. B. Lee, and G. W. Rubloff, TEM-based metrology for HfO2 layers and nanotubes formed in anodic aluminum oxide nanopore structures, Small 4 1223-1232 (2008).