(343b) Reaction Network Structure and Flux Analysis for Thin-Film Deposition Processes

Reaction network structure and flux
analysis for thin-film deposition processes.

Hossein Salami, Raymond A. Adomaitis

Chemical Vapor Deposition (CVD) and Atomic Layer
Deposition (ALD) are vapor-based processes for production of thin solid films in
which heterogeneous and homogenous reactions with widely ranging time scales
are involved. Proposing an accurate reaction mechanism consisting of
adsorption/desorption and reactions within various phases that results in a
well-posed species balance is among the first steps in studying these processes.
A valid reaction network (RN) combined with accurate kinetic data is vital for
process modeling and optimization and forms the backbone of further engineering
analysis.

In this contribution, we will introduce an analysis approach
based on RN graphs and linear algebra methods which provides a mechanistic framework
for answering four critical questions regarding the validity of a proposed
reaction RN prior to the often time-consuming step of calculating individual
reaction rates and any attempt to solve the system of differential equations produced
by species balances:

1.     
Can the equilibrium and finite-rate
reaction time scales be decoupled and independently measured?

2.      What
is the physical origin of time-independent modes in the system’s dynamic
behavior and how they can be used to validate the proposed RN?

3.      Does
the proposed RN result in a unique film stoichiometry that is independent of reaction
rates?

4.     
Does the RN pose a self-limiting
mechanism essential to a true ALD process?

The
first question can be answered by finding a transformation which essentially
separates the effect of different reaction rates and defines new variables in
the form of reaction variants and invariants that are linear combination of
original concentrations [1]. However, this approach does not provide answers to
the remaining questions and additional analysis is required. The approach we
will describe is based on the species-reaction graphs introduced by Craciun and
Feinebrg [2] and provides a set of rules which can be used to answer
above questions using the graph constructed from the RN under study without
requiring any knowledge regarding individual reaction rates.

Furthermore,
we demonstrate the application of our RN graphs in material flux analysis and in
studying the sensitivity of the RN to the process parameters such as the reactor
temperature and precursor partial pressure. We also will assess its potential
for extension to other areas in chemical engineering research, such as
metabolic engineering or polymerization reactions.

In
this talk, we use the RN associated with the titania ALD process based on titanium
isopropoxide (Ti(iPrO)4 or TTIP) / water precursors as a representative case to
show the applicability of the proposed approach. This process has been shown to
deviate from an ideal self-limiting ALD at temperatures greater than 250 ^oC
where the rate of hydrolysis reactions begins to decrease while pyrolysis
reactions are activated [3,4]. The relative contribution of ALD versus CVD
growth mode to TiO2 film deposition will be assessed using our flux analysis
method and the results will be presented in the context of the RN graphs.

Figure 1. The sub-graph associated with the initial
adsorption of TTIP molecule on a hydroxylated surface in titania ALD process.
The blue color highlights the path which can be used to derive the formula for
the time-independent mode associated with conservation of titanium atoms in the
reactor. (g) and (b) refer to bulk and gas phases, others are surface species.

[1] D.
Rodrigues, S. Srinivasan, J. Billeter, D. Bonvin, Comput. Chem. Eng., 2015,
73, 23.

[2] G.
Craciun, M. Feinberg, SIAM J. Appl. Math., 2006, 66(4), 1321.

[3]
A. Rahtu, M. Ritala, Chem. Vap. Deposition, 2002, 8, 21.

[4]
M. Reinke, Y. Kuzminykh, P. Ho_mann, J. Phys. Chem., 2016, 120(8), 4337.