Supplemental Material for “Doped, porous iron oxide films and their optical functions and anodic
photocurrents for solar water splitting”
Coleman X. Kronawitter1,2, Samuel S. Mao1,2, and Bonnie R. Antoun3
1Department
of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
2Environmental
3Sandia
Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
National Laboratories, Livermore, CA 94551, USA
Determination of optical functions
The optical properties of films were analyzed by measurement and modeling of spectral normal transmission and normal and
70 degree specular reflection data using a thin film metrology system and its multi-layer film analysis software (FilmTek 3000
PAR SE).
As described below, the optical functions of a film deposited at 300 °C onto SiO2 were determined by simulation
of the dielectric functions of a substrate-film-surface roughness structure as indicated in Figure S1. The regression analysis
software attempts to minimize a root mean square error function associated with the simulated quantities over the entire
spectral range of collected data.
Statistical analysis of the accepted final simulation yielded a correlation coefficient of 0.995
and standard errors as tabulated below.
It is noted that a compensator in the 70 degree light source beam path polarized
Since α-Fe2O3 crystals are known to be birefringent, it was necessary to check for polarization effects in the
incident light.
reflection measurement.
This was accomplished by adjusting the angular positions of the analyzer and polarizer so that they
are crossed by 90 degrees, and monitoring the signal at the detector.
No signal beyond the system noise was detected; the
sample did not depolarize incident light to any measurable degree.
This is further confirmed by the observed correlation
between experimental and simulated values.
FIG S1.
Multi-layer structure used as model for simulation of optical functions, with final determined values for layer thickness included.
The complex index of refraction of the 0.5 mm-thick SiO2 substrate was modeled with the Cauchy dispersion relations1:
n  An 
Bn
k   Ak 
Bk


2
2

Cn
(1)

Ck
(2)
4
4
Coefficient data used were literature-derived values included in the commercial software package, displayed in Table S1.
Supplemental Material: Kronawitter et al. 1
Cauchy
Table S1.
Parameter
Value
An
Bn
Cn
Ak
Bk
Ck
1.44785
3.4134 x 10-3
2.0470 x 10-5
2.8619 x 10-19
1.2274 x 10-19
6.5623 x 10-21
Coefficients for the Cauchy dispersion relations used for substrate characterization
The optical functions of the photoactive Fe2O3:TiO2 films were simulated using the Tauc-Lorentz parameterization, formulated
by Jellison and Modine in 1996.2
m
 2 (E)  
j
The software performs the regression with the parameterization:
A 2j ( E center ) j  ( E  E g ) 2 1

2
E
E 2  ( E center ) 2j


 2 (E)  0
1 (E)    
2


P
Eg
E  Eg
(3)
E  Eg
(4)
 2 ( )
d
 2  E2
(5)
The fitted values for a single oscillator and their associated standard errors are presented in Table S2.
Tauc-Lorentz
Parameter
Value
Standard Error

2.042
0.025
Eg
1.894
2.265 x 10-3
A
11.091
0.158
Ecenter
2.652
0.032
3.622
0.076

Table S2.
Coefficients for the Tauc-Lorentz dispersion relations used for film characterization.
The thickness of the Fe2O3:TiO2 layer at the probe location was determined to be 303.5 nm.
The surface roughness was modeled with the Bruggeman3 Effective Medium Approximation, which in this case assumes an
isotropic mixture of the dielectric functions of void space and film.
m
 fi
i 1
 i   eff
0
 i  2 eff
m
f
i 1
i
1
(6)
Where f represents the volume fraction of constituent phases.
The regression analysis determined a composition of 87 % void and 13% film (volume percent), with a total layer thickness of
34.7 nm.
Supplemental Material: Kronawitter et al. 2
Deposition geometry
The off-angle deposition geometry, as described in the main text, is represented schematically over a photograph of a typical
ablation plume in Fig. S2.
FIG S2. Schematic of the deposition geometry overlayed onto a photograph of an ablation plasma and its optical emission (d = 7.9 cm, β =
49° for all depositions).
Effect of post-deposition heat treatment on structure morphology
SEM imaging was performed for both as-deposited and heat-treated films.
effect of the heat treatment process.
The SEM images shown in Fig. S2 indicate the
The 23 °C sample shows the most dramatic morphology change upon annealing.
This
result suggests the as-deposited sample may contain significant void space, unresolved in the SEM imaging, which grows
upon annealing as particles coalesce.
FIG S3.
SEM images indicating the effect of annealing on film morphology: (a) 300 °C sample as deposited. (b) 23 °C sample as
deposited. (c) 300 °C sample after heat treatment at 450 °C. (d) 23 °C sample after heat treatment at 450 °C.
References
1
H. Fujiwara, in: Spectroscopic Ellipsometry: Principles and Applications, (Wiley, West Sussex, UK, 2007).
2
G. E. Jellison, and F. A. Modine, Appl. Phys. Lett. 69, 371 (1996).
3
D. A. G. Bruggeman, Ann. Phys. Leipzig 24, 636 (1935).
Supplemental Material: Kronawitter et al. 3
All scale bars indicate 1 m.