282102 First Principles Modeling of Atomic Layer Deposition (ALD) Surface Reaction and Process Dynamics Using Absolute Reaction Rate Theory
First principles modeling of atomic layer deposition (ALD) surface reaction and process dynamics using absolute reaction rate theory
Curtisha D. Travis* and Raymond A. Adomaitis
Department of Chemical and Biomolecular Engineering
Institute for Systems Research
University of Maryland
College Park, MD 20742 USA
*Presenting author: firstname.lastname@example.org
Submitted to the 2012 AIChE Annual Meeting, Pittsburgh, PA
A physically based model of atomic layer deposition reaction kinetics is developed and applied to alumina ALD using water and trimethylaluminum precursors . The modeling strategy is based on computing the adsorbed adduct surface concentrations during each half reaction and the subsequent rate of the ligand exchange reactions using transition state theory. Upon precursor adsorption, barrierless formation of a stable Lewis acid-base adduct is facilitated through electron interactions between the aluminum and oxygen atoms . An equilibrium is established between the adduct and transition states which is evaluated through a first principles analysis using statistical thermodynamics. Our derivations of the partition functions determining the reaction equilibrium relationships governing adsorbed surface species concentrations and reaction rates will be shown to produce tractable reaction kinetics models from which quantitative rate information can be extracted.
To complete the model, the resulting rate expressions are incorporated into time-dependent reaction material balance expressions accounting for the temporal evolution of the surface states during each exposure period. The key assumption in our model is that the adsorption, desorption, and processes responsible for formation of the two transition states instantly reach their equilibrium values relative to the changes that take place on the reaction surface due to the final irreversible ligand-exchange reaction. Elliott and Greer  demonstrate the TMA reaction takes place whether or not surface hydroxyl groups are present, and so the overall deposition process will be modulated by the extent to which the surface is covered by -CH3 ligands acting as an inert species or steric factor.
The ALD surface reaction models are treated as true dynamic systems, with continuous ALD reactor operation described by limit-cycle solutions, numerically computed using a polynomial collocation technique (see figure below). The linear nature of the water exposure dynamics is attributable to the ligand exchange reaction where one reacting water precursor molecule results directly in the production of one CH4 molecule desorbing to the gas phase. The curved nature of the TMA portion of the curve is due to the slower accumulation of -CH3 groups when the growth surface has a higher density of -OH groups, switching to a more rapid accumulation as -CH3 ligands are left by the TMA surface reactions. To illustrate the dependency of growth-per-cycle (GPC) as a function of both precursor exposure levels for a fixed precursor pressure of 1 Torr, a GPC map generated by the limit cycle solutions is shown. Under saturating conditions, we find GPCmax=0.925 A/cycle. While this value is less than the nominally observed value of 1.1 A/cycle GPC for the TMA/water ALD system, the prediction is significant given that the only limit to GPC in our model is the close-packing limit of -CH3 groups on the growth surface.
This work was motivated by the predictive capabilities of physically based models to decouple the effects of precursor pressure, exposure time, reactor temperature, and the dynamics of each exposure period on growth-per-cycle . As such, our model demonstrates a good match between its predictions and observed GPC behavior in experimental alumina ALD studies. We note that the model has no adjustable parameters, eliminating the need for sticking coefficients. Model predictions indicating optimal operating conditions for most efficient ALD operation will be discussed. Work to couple these surface rate expressions to models of precursor transport in reactor-scale environments will also be discussed.
Figure 1: Surface -CH3 and -OH limit-cycle coverage dynamics (left) for a representative set of alumina ALD operating conditions. The red curve corresponds to the TMA dose, the blue to water. Alumina GPC (A/cycle) map (right) as a function of each precursor exposure level, with limit-cycle conditions marked as +.
 Adomaitis, R. A. ``A Ballistic Transport and Surface Reaction Model for Simulating Atomic Layer Deposition Processes in High Aspect-Ratio Nanopores,'' Chemical Vapor Deposition, 17 353-365 (2011).
 Deminski, M., A. Knizhnik, I. Belov, S. Umanskii, E. Rykova, A. Bagatur'yant, B. Potapkin, M. Stoker, and A. Korkin, ``Mechanism and kinetics of thin zirconium and hafnium oxide film growth in an ALD reactor,'' Surf. Sci. 549 67-86 (2004).
 Elliott, S. D. and J. C. Greer, ``Simulating the atomic layer deposition of alumina from first principles,'' J. Mater. Chem. 14 3246-3250 (2004).
 Puurunen, R. L., ``Surface chemistry of atomic later deposition: A case study of the trimethylaluminum/water system,'' Appl. Phys. Rev. 97 121301 (2005).
 Widjaja, Y. and C. B. Musgrave, ``Quantum chemical study of the mechanism of aluminum oxide atomic layer deposition,'' Appl. Phys. Lett. 80 3304-3306 (2002).