REACTION FACTORIZATION FOR DISTRIBUTED DEPOSITION SYSTEMS: APPLICATION TO COPPER FILM GROWTH

Abstract

A model reduction methodology based on a Gauss-Jordan reaction factoriza-

tion for thin-film deposition reaction systems is developed in this thesis. The fac-

torization generates a transformation matrix that is used to create a new coordinate

system that guides the separation of the deposition process time scales by decoupling

the net-forward reaction rates to the greatest extent possible. The new coordinate

space enables recasting the original model as a singular perturbation problem and

consequently as a semi-explicit system of differential-algebraic equations (DAE) for

the dominant dynamics in the pseudo-equilibrium limit. Additionally, the factor-

ization reveals conserved quantities in the new reaction coordinate system as well

as potential structural problems with the deposition reaction network.

The reaction factorization methodology is formulated to be suitable for appli-

cation to dynamic, spatially distributed reaction systems. The factorization provides

a rigorous pathway to decouple the time evolution and the spatial distributions of

deposition systems when the dynamics of reactor-scale gas-phase transport are fastrelative to the deposition process. Moreover, the factorization approach provides a

solution to the problem of formulating Danckwerts-type boundary conditions where

gas-phase equilibrium reactions are important.

The reaction factorization is used to study the chemical vapor deposition of

copper on a tubular hot-wall reactor using copper iodide as the Cu precursor. A

film-growth mechanism is proposed from experimental observations that the copper

films deposited on quartz substrates suggest a Volmer-Weber growth mode. A model

based on this mechanism is used to track spatial distribution of the average Cu island

size in the reactor.

The rate expressions used in the Cu deposition model are determined using

absolute rate theory. To carry out these calculations in an organized manner, a

library of object-oriented classes are created in the Python programming language.