1) A model was developed to understand the sharp transition between copper oxide phases observed during CVD. The model considers oxygen transport and the single degree of freedom in the Cu2O-O2-CuO system. 2) 1D and 2D models were used to predict spatial oxygen profiles and examine the effects of temperature, oxygen flow, and surface/gas phase reaction rates on the transition location. 3) Comparisons to experimental film measurements suggest surface reactions play a primary role in the transition, though gas phase reactions may also contribute. Further work aims to estimate adsorption rates and refine surface/gas phase reaction mechanisms.

1. Introduction Methodology Results Conclusion
Modeling Spatial Variations In Thin-Film
Processing of Copper Oxide Films for Solar Energy
Applications and Hydrogen Production
David Arana-Chavez and Raymond A. Adomaitis
Department of Chemical & Biomolecular Engineering
Institute for Systems Research
University of Maryland
January 5, 2012
Support: NSF CBET-0828410

2. Introduction Methodology Results Conclusion
1 Introduction
Film growth by chemical vapor deposition
The sharp transition
2 Methodology
Estimating the cuprous oxide to cupric oxide ratio
Design of experiments - temperature and oxygen flow
3 Results
Oxygen partial pressure profiles
Limiting cases: gas phase reaction vs surface deposition
Comparison with experiments
4 Conclusion
Summary

3. Introduction Methodology Results Conclusion
Solar photoelectrochemical H2 production from water
Hydrogen
O2 H2
Tremendous interest and hv
research focused on
counter electrode (anode)
transparent conductor
2e- + 2H2O 2OH- + H2 e- h+
hydrogen production at
p-type semicond
photo-cathode
this meeting (ICE 2011) OH-
Substantial discussion of
2OH- H2O + 1/2 O2 + 2e-
mass production,
manufacturability issues e-
PEC
Goal: direct solar conversion of water to H2
PEC system components: a semiconductor (metal oxide) in
contact with an electrolyte inside an electrochemical cell

4. 0.5
Introduction Methodology Results Conclusion
dark
light
Copper oxide
current (mA/cm2)
2
0
PEC (p-type) semiconductors
we investigate: Cu2 O, CuO
Precursors available for a −0.5
−1 −0.5 0 0.5 1
relatively benign CVD process bias (V)
Measured band gap: 2.06 eV 11 NaOH
0.5
for Cu2 O, 1.8 eV for CuO dark
light
CVD films are stable in high pH
current (mA/cm2)
2
electrolytes, physically robust
0
Photoactivity has been
established for both CVD films
by collaborators
Cu2 O is a promising catalyst for −0.5
−1 −0.5 0 0.5 1
various reactions as well as for bias (V)
arsenic removal from Cu2 O sample
contaminated water

5. Introduction Methodology Results Conclusion
Copper oxide CVD reactions/reactor
2CuI(g) + 1/2 O2 (g)
→ Cu2 O(s) + I2 (g) O2
Ar
2CuI(g) + O2 (g)
CuI Substrate
→ 2CuO(s) + I2 (g)
Tubular CVD reactor
elements: gas flow
controllers (left), the
process tube and furnace
(center), and gas
scrubbing system (right).

6. Introduction Methodology Results Conclusion
Initial experimental results
Experimental conditions: 0.1g CuI; total P = 1atm; T = 775o C ;
Ar flow O2 flow; dep time = 5min; quartz substrate.
(Red) Cu2 O at substrate
leading edge and O2 feed
tube; decrease in (black) CuO
film thickness in the direction
of gas flow

7. Introduction Methodology Results Conclusion
Dependence on total O2 flow
Modeling motivation:
Understand the unique CVD behavior exhibited (e.g.,
unusually sharp and stable composition transitions);
Control the deposition behavior, including film thickness,
composition, and morphology;
Assess potential effects of substrate and previous deposition
layers.

8. Introduction Methodology Results Conclusion
Why is the Cu2 O/CuO transition so sharp?
Consider a system of O2 (g) and D.o.F . = c − π + 2 − r
crystalline CuO(s) and Cu2 O(s): = 3−3+2−1=1
1 Both phases can only coexist at
Cu2 O(s) + O2 (g ) ↔ CuO(s)
2
eq 2
PO2 = Po /Keq
= 24Pa at 750o C
24 Pa
PO2 < < PO2
The white bar corresponds to 1 mm

9. Introduction Methodology Results Conclusion
Cuprous to cupric oxide ratio from substrate images
Photos were converted to RGB images in
MATLAB.
Two major color modes detected with
separation around gray scale 70.
This representation allows for calculation of
the percentage of the area of the films
covered by Cu2 O.

10. Introduction Methodology Results Conclusion
Effects of temperature and pressure
Design of experiments Response surface model
Cu2 O Area
m = -1,0,1 → qO2 = 4.3, y= Total Area × 100
6.4, 8.5 sccm
t = -1,0,1 → T = 725, 750, y = 52.4 − 18.6 · m + 8.3 · t
775 o C

11. Introduction Methodology Results Conclusion
1D oxygen partial pressure profile
L1 L2
O2
substrate exhaust
Ar
CuI boat
dCO2
JO2 ,z = −DO2 ,Ar + vCO2
dz
JO2 ,z constant within each
segment, [0, L1 ) and
(L1 , L1 + L2 ];
Flux discontinuity at the feed
point L1 .
max
PO2 exp (v (z − L1 − δshift )/D) z ≤ L1
PO2 = max
PO2 z > L1

12. Introduction Methodology Results Conclusion
Comparison with DoE
Initially the 1D
profile shows
c
PO2 off the
substrate.
An estimated
displacement
due to radial
diffusion added
(δshift ).
After the spatial
shift, 1D
calculations
agree with
response surface
model.

13. Introduction Methodology Results Conclusion
2D oxygen partial pressure profile model
Axial and radial O2 diffusion;
Initially investigate limiting case of no O2 consumption by rxn:
1 ∂ ∂CO2 ∂ 2 CO2 v ∂CO2 fO2
r + 2
− =
r ∂r ∂r ∂z DO2 ,Ar ∂z DO2 ,Ar
∂CO2
with BCs JO2 = −DO2 ,Ar ∂z + vCO2 = 0 @ z =0
∂CO2
−DO2 ,Ar ∂z =0 z =L
∂CO2
JO2 = −DO2 ,Ar ∂r =0 r = Ro
∂CO2
∂r =0 r =0
δ (r )
where fO2 = qO2 δ (r , z − L1 ) = qO2 δ (z − L1 )
2πr

14. Introduction Methodology Results Conclusion
2D oxygen partial pressure profile model solution
m n
CO2 = αi,j ψi (r ) θj (z)
i j
Solved through the projection of the concentration on a set of
eigenfunctions.
Eigenfunctions ψi (r ) and θj (z) based on 1D Sturm-Liouville
similar problems with eigenvalues λi and ωj , respectively.
where
v
ψi (r ) = J0 (λi r /Ro ) , φj (z) = Dωj sin (ωj z) + cos (ωj z)
Oxygen feed modeled as a point source at feed tube exit
location:
m n
fO2 = βi,j ψi (r ) θj (z)
i j

15. Introduction Methodology Results Conclusion
2D model solution: eigenfunctions
r -direction z-direction
Eigenfunction equation Eigenfunction equation
1d dψ d 2θ
r = λ2 ψ = ω2θ
r dr dr dz 2
BCs BCs
dψ(r )
dr = 0 at r =0 −D dθ(z) + v θ(z) = 0
dz z =0
dψ(r ) dθ(z)
dr =0 r = Ro dz = 0 z = L1 + L2
Eigenvalue equation Eigenvalue equation
J1 (λj ) = 0 (D/vL)ωi = tan (ωi L)

16. Introduction Methodology Results Conclusion
Computed O2 pressure profile
O2 pressure profile estimated by solving the 2D governing equation with
a parabolic velocity profile v (r ). The units in the color bar are [Pa].

17. Introduction Methodology Results Conclusion
O2 Convergence test
Mass balance equation
Ro /L
qO2 − 0 (v (r )CO2 (m, n, r , z = L)2πr ) dr
MB(m, n) = × 100
qO2

18. Introduction Methodology Results Conclusion
O2 Profile - COMSOL Model
Newtonian incompressible
fluid
Axial symmetry
Velocity profile results
parabolic and is develop
soon after the oxygen feed
point.

19. Introduction Methodology Results Conclusion
O2 Comparison with COMSOL Model
Comparison of the
oxygen partial
pressure profile at
the wall of the
reactor
Model with 100
eigenfunctions in
both the r and z
directions

20. Introduction Methodology Results Conclusion
Limiting Case - O2 consumption in the gas phase
1 ∂ ∂CO2 ∂ 2 CO2 v ∂CO2 kG fO2
r + 2
− − CO2 =
r ∂r ∂r ∂z DO2 ,Ar ∂z DO2 ,Ar DO2 ,Ar
Oxygen is only consumed by reactions in the gas phase;
1st-order reaction constant kG for the consumption of oxygen.

21. Introduction Methodology Results Conclusion
Limiting Case - O2 consumption by deposition
B.C. at r = Ro
∂CO2
kpO2 · PO2 = kadsO2 CO2 = −DO2 ,Ar
∂r
The eigenvalues λ are obtained from the following equation
DO2 ,Ar λ
kads J0 (λRo /L) = J1 (λRo /L)
L
Oxygen is consumed only by deposition on the walls and the
substrate. The governing equation does not change, only the
boundary condition at the walls.

22. Introduction Methodology Results Conclusion
Limiting Cases Comparison
Representative
experimental film profiles:
Da = Damk¨hler
o
number
DaG = kG L/vavg

23. Introduction Methodology Results Conclusion
Limiting cases comparison
Representative
experimental film profiles:
DaS = kadsO2 Ro 2 /DO2 ,Ar
DaS (750o C) = 464
max
kads related to kPO2 :
max RT
kadsO (T ) =
2 2πMwO2 RT

24. Introduction Methodology Results Conclusion
Conclusions
We account for a spatially sharp film composition transition by the
single degree of freedom in the Cu2 O-O2 -CuO system. Transition
location can be estimated from the O2 partial pressure profile in the
reactor.
Transport models in 1 and 2 dimensions were created to predict the
O2 spatial profiles to probe the effect of T and O2 flow on
transition position. Transition location positions as a function of
surface and homogeneous gas phase O2 consumption rates were
examined over a range of rate constants.
Qualitative comparisons to observed film measurements tend to
support the likelihood of the primary role of surface reactions,
although gas-phase reactions cannot be ruled out.
Current work focuses on estimating dissociative O2 adsorption rates
and more detailed surface- and gas-phase reaction mechanisms.