(362d) 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: cdtravis@umd.edu

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 [4]. 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 [5]. 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 [3] 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 [2].
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 +.

References

[1] 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).

[2] 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).

[3] Elliott, S. D. and J. C. Greer, ``Simulating the atomic layer deposition
of alumina from first principles,'' J. Mater. Chem. 14 3246-3250 (2004).

[4] Puurunen, R. L., ``Surface chemistry of atomic later deposition: A case
study of the trimethylaluminum/water system,'' Appl. Phys. Rev. 97 121301 (2005).

[5] 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).