Nature of the Band Gap of In2O3 Revealed by First-Principles Calculations
and X-Ray Spectroscopy

Aron Walsh,1,* Juarez L. F. Da Silva,1 Su-Huai Wei,1 C. Körber,2 A. Klein,2 L. F. J. Piper,3 Alex DeMasi,3 Kevin E. Smith,3

G. Panaccione,4 P. Torelli,5 D. J. Payne,6 A. Bourlange,6 and R. G. Egdell6
1National Renewable Energy Laboratory, Golden, Colorado 80401, USA

2Darmstadt University of Technology, 64287 Darmstadt, Germany
3Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

4Laboratorio TASC, INFM-CNR, Area Science Park, S.S. 14, Km 163.5, 34012 Trieste, Italy
5CNR-INFM-S3, Via Campi 213/A, I-41100 Modena, Italy

6Chemistry Research Laboratory, Mansfield Road, Oxford OX1 3TA, United Kingdom
(Received 5 November 2007; published 25 April 2008)

Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the
valence band edge for In2O3 is found significantly closer to the bottom of the conduction band than
expected on the basis of the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the
upper valence bands of In2O3 exhibit a small dispersion and the conduction band minimum is positioned
at �. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence
band maximum. The results set an upper limit on the fundamental band gap of 2.9 eV.

DOI: 10.1103/PhysRevLett.100.167402 PACS numbers: 78.70.En, 73.20.At, 78.20.Bh

Despite the widespread use of In2O3 as a transparent
contact in photovoltaic devices, liquid crystal displays, and
light emitting diodes [1,2], the nature of the band gap in
this material remains contentious [3–6]. Early measure-
ments on In2O3 single crystals showed that the onset of
strong optical absorption is found to be 3.75 eV, but with
indications of a much weaker absorption onset at 2.62 eV
attributed to indirect electronic transitions [7]. Nonetheless
the ‘‘band gap’’ of In2O3 is widely quoted as 3.75 eV [8] or
thereabouts [9]. However, the top of the valence band in x-
ray photoemission spectra of lightly doped n-type In2O3 is
found to be less than 3 eV below the Fermi level (which is
situated just above the bottom of the conduction band),
adding further weight to the hypothesis that In2O3 may
have an indirect band gap [10]. It has been argued [5] that
an indirect gap could arise from mixing of shallow core In
4d states with O 2p states away from the � point within the
centrosymmetric crystal structure of In2O3: a similar situ-
ation pertains in rocksalt CdO where the lowest energy gap
is undoubtedly indirect [5,11]. However, band structure
calculations [3] on In2O3 have consistently failed to find
upward dispersion of the topmost valence band by the 1 eV
required by the indirect gap hypothesis. It has therefore
been argued that the onset of valence band photoemission
intensity is reduced from the value expected on the basis of
the bulk band gap by upward band bending at the surface
and that the weak optical absorption around 2.6 eV is
associated with defects [4,6].

In this Letter we compare the positions of valence band
edges in conventional x-ray photoemission spectra with
those measured with the very much less surface sensitive
techniques of hard x-ray photoemission and x-ray emission
spectroscopies (XPS and XES): while the valence electron
inelastic mean free path length in Al K� XPS is probably
of the order of 25 Å, under 6000 eV excitation the path

length increases to values around 60 Å [12]. XES is a
photon-in photon-out technique with an effective sampling
depth of order 1000 Å. We find that there is no significant
shift in spectral features between the different experimen-
tal techniques, which argues strongly against the band
bending model. Moreover we further demonstrate, through
symmetry analysis of the band structure, that direct optical
transitions at � from the valence band maximum (VBM) to
the conduction band minimum (CBM) are parity forbidden
and that the first strong transitions occur from valence
bands 0.81 eV below the VBM. This new insight solves
the long-standing ‘‘band gap discrepancy’’ and calls for a
reinterpretation of all experimental and theoretical studies
of In2O3 that require knowledge of the fundamental gap.

In2O3 and Sn-doped In2O3 (2% and 10 weight % Sn)
were deposited by radio frequency magnetron sputtering
onto doped Si substrates to a thickness of 400–500 nm
using pure Ar as the sputter gas and a 400 �C substrate
temperature. Carrier concentrations were estimated from
conductivity values using a mobility of 30 cm2 V�1 s�1

and from measured energies of plasmon satellites on In
3d core lines [10]. For the most highly doped sample the
carrier concentration reaches a value of 1:2� 1021 cm�3.
Conventional x-ray photoemission spectra were measured
in situ in the deposition system with a Physical Electronics
Phi 5700 spectrometer and ex situ with monochromatic Al
K� radiation (h� � 1486:6 eV) in both a Scienta XPS
system (incorporating a rotating anode Al K� x-ray source
and a 300 mm mean radius electron energy analyzer) with
an overall energy resolution of 0.35 eV and a VG
ESCALAB 250. Energies were referenced relative to
Fermi level onsets of Ag samples used to calibrate the
spectrometers. The silver Fermi level was found to coin-
cide with weak but well-defined Fermi edges found for the
doped In2O3 samples. Further Al K� measurements were

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performed on (001) oriented single crystal thin film
samples grown by O-plasma assisted molecular beam epi-
taxy on Y-doped ZrO2 substrates. The positions of the
valence band onsets were consistent between all the differ-
ent data sets. Hard x-ray photoemission spectra (HXPS) at
h� � 6000 eV were measured on beam line 16 at the
ESRF [12] again with an overall energy resolution of
0.35 eV. Here spectra were referenced to the Fermi ener-
gies of the Sn-doped samples. Finally x-ray emission spec-
tra at the O K edge were measured at the soft x-ray
undulator beam line X1B at the National Synchrotron
Light Source (NSLS), Brookhaven National Laboratory.
The emission spectra were obtained using a Nordgren-type
grazing incidence spherical grating spectrometer with an
energy resolution set to 0.35 eV at the O K edge [13]. The
incident photon energy was set far above the absorption
threshold at 567 eV. The emission energy axes were cali-
brated to the second order L edge of a zinc metal, for the
same settings.

The experimental data are shown in Fig. 1. In both Al
K�XPS and HXPS well-defined structure is found close to
the Fermi energy which grows in intensity with increasing
doping and extends down to about 1.5 eV binding energy in
the most highly doped sample. This is associated with
occupied conduction band states. The intensity of the
conduction band feature increases dramatically relative to
the intensity of the valence band edge in switching from
excitation at h� � 1486:6 eV to h� � 6000 eV due to the
pronounced In 5s character of the conduction band states
and the increasing value of the cross section for In 5s states
relative to that for O 2p states with increasing photon
energy [14]. The valence band edge is seen to lie 2.9 eV
below the Fermi level in both Al K� XPS and HXPS for
the nominally undoped sample and moves to higher bind-
ing energies of 3.2 and 3.5 eV, respectively, for 2% and
10% doped samples. All binding energies are referenced to
the Fermi level and the shift arises from the upward move-
ment of the Fermi level within the conduction band with
increasing doping partially offset by band gap shrinkage
with doping. Conduction band occupancy produces the
well known Burstein-Moss shift in optical absorption [8].
The magnitudes of the observed band edge shifts are con-
sistent with the known free carrier concentrations [8]. The
valence band onset energy of 2.9 eV for the nominally
undoped sample sets an upper limit for the fundamental
band gap of In2O3 assuming little or no surface band
bending: this value is further reduced by the occupation
of conduction band states arising from adventitious donor
defects.

A distinct Fermi edge onset was also observed in the x-
ray emission spectrum (which is determined by the bulk
occupied O 2p like partial density of states) of the 10% Sn-
doped sample at h� � 530:06 eV with a sigmoidal width
matching the spectrometer resolution of 0.35 eV. This
feature was absent in the spectrum of the nominally un-
doped sample and allows the x-ray emission data to be
transposed onto the same binding energy scale as the

photoemission data. Although strong band tailing prevents
accurate determination of the valence band onset in this
spectrum, the valence band peak maximum relative to the
Fermi energy is seen to coincide with that in Al K� XPS.
Thus the binding energy scales for all three techniques
coincide, a fact which argues strongly against the band
bending model.

Similar to Tl2O3 [15], In2O3 adopts the body centered
cubic bixbyite (FeMnO3) structure (space group Ia�3, T7

h
symmetry) with 8 f.u. per primitive cell [16]. Each In atom
is coordinated by six oxygen atoms in a distorted octahe-
dron, with In-O interatomic distances ranging from 2.13–
2.23 Å and a lattice constant of 10.12 Å [16]. The equilib-
rium geometric and electronic structure of In2O3 were
calculated using density functional theory [17] within the
generalized-gradient approximation [18] (GGA-PBE) and
the all electron projector-augmented-wave method [19] as
implemented in VASP [20,21]. A plane wave cutoff of

FIG. 1 (color online). (a) Al K� XPS (h� � 1486:6 eV) of
nominally undoped and 2% and 10% Sn-doped In2O3 thin films.
(b) HXPS (h� � 6000 eV) of the same films. (c) Al K� XPS
and O K shell XES of 10% Sn-doped In2O3 aligned using the
Fermi edge (0 eV) visible in both spectra.

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400 eV and a 4� 4� 4 k-point mesh were found to give
sufficient convergence.

The calculated band structure along two high symmetry
linesH�1=2;�1=2; 1=2�-��0; 0; 0�-N�0; 0; 1=2� is shown in
Fig. 2. The highest occupied band exhibits very little
dispersion, e.g., 19 meV along the �-N line. This is clearly
inconsistent with the existence of a strongly indirect fun-
damental gap in the order of 1 eV. The effect of electron
correlation on the In 4d states was investigated by using
GGA�U (U� J � 5 eV). The effect is small, resulting
in a change of �-N band width of less than 50 meV.

The VBM state at � is threefold degenerate and is
derived from O 2p and In 4d character (�4, Tg symmetry),
while the CBM state is a mixture of In 5s and O 2s orbitals
(�1, Ag symmetry). As bixbyite contains an inversion
center and the electric-dipole operator is of odd parity,
strong optical transitions are only permitted between
two states of opposing parity. These symmetry require-
ments result in a zero optical transition matrix element
for direct VBM to CBM absorption at �, confirming that
this �4-�1 transition is formally forbidden and can only
make a very weak contribution to photon absorption under
the influence of lattice vibrations. It is only from 0.81 eV
below the VBM that strong transitions are observed. Here,
the wave function character at � becomes sufficiently p
like (�8, Tu symmetry) and strong optical transitions can
occur, with a transition matrix element of 0.74 a.u. for
�8-�1 absorption. Five sets of bands lie in the range
between 0–0.81 eV, of which three are of even parity,
while two are of odd parity; however, while transitions
from the odd parity bands at 0.25 and 0.50 eV are nonzero,

they result in very small matrix elements on the order of
100 times weaker than the strong �8-�1 absorption at
0.81 eV. This is because these states are derived from the
‘‘fold-in’’ bands of the ideal In2O3 primitive cell, so they
are only pseudodirect. Therefore, both the computed opti-
cal matrix elements and the resulting absorption coefficient
(Fig. 3) are consistent with a fundamental gap 0.81 eV
lower in energy than the optical band gap. While the
absorption spectrum, summed over all possible direct tran-
sitions from a dense sampling of the Brillouin zone, is
calculated with a VBM-CBM separation of 2.89 eV [22],
the onset of optical absorption is only observed at 3.70 eV,
after which the intensity rises with increasing photon en-
ergy. This demonstrates that the valence band states within
0.81 eV of the VBM make no significant contribution to
low energy photon absorption in the frozen bulk crystal;
weak transitions can result experimentally through local
symmetry breaking.

In2O3 is the prototypical n-type transparent conducting
oxide [1]. Occupation of the conduction band through
n-type doping, as observed from the increased Fermi en-
ergy–VBM separation in the experimental spectra on in-
troduction of Sn (Fig. 1), can induce transitions away from
the � point due to a Burstein-Moss shift. To take this effect
into account theoretically, we have examined the magni-
tude of the direct optical transitions along the H-�-N lines.
The lowest energy �4-�1 transition is parity forbidden, and
moving away from the zone center is found to result in no
significant increase in the strength of optical transitions.
Therefore, n-type doping will not induce strong absorption
below the intrinsic optical gap, which is consistent with the
high visible transparency maintained even in heavily doped
In2O3. As the �8 valence band at 0.81 eV below the VBM,
which determines the optical gap, exhibits almost no dis-
persion and the CBM is close to parabolic, there will be a
pronounced movement of the absorption onset to higher
energies as the conduction band becomes more occupied;
this strong shift of the optical gap is well established

-1.0

0.0

1.0

2.0

3.0

4.0

E
ne

rg
y 

(e
V

)

NH

1

4

8

(A )g

(T )g

g

(T )u

FIG. 2 (color online). Band structure of In2O3 (along the
H-�-N lines). The highest energy valence bands resulting in
strong optical absorption to the conduction band are light gray. A
rigid shift of the conduction band is applied to offset the density-
functional theory band gap underestimation [22].

0 2 4 6 8
Energy (eV)

30

60

90

A
bs

or
pt

io
n 

co
ef

fic
ie

nt
 (

10
4  c

m
-1

)

Eg

FIG. 3. Calculated absorption spectrum of bulk In2O3. Note
that the onset of optical absorption is 0.81 eV higher in energy
than the fundamental band gap [22].

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experimentally [1,2]. It is also worth noting that in order to
preserve simultaneous transparency and conductivity, tran-
sitions between the CBM band and other conduction band
states near the � point must be inhibited. For In2O3, this is
well obeyed as the CBM� 1 band (�5) lies 5 eV above the
CBM; i.e., the transitions are well outside the visible
wavelength range.

We have demonstrated experimentally, using a range of
x-ray spectroscopies, that the separation between the VBM
and CBM is much less than the previously quoted band gap
of 3.75 eV, and is not related to surface band bending; the
measurements set an upper limit of 2.9 eV for the funda-
mental gap. These results are supported by theoretical
calculations which conclude that In2O3 is a ‘‘forbidden’’
gap material with a fundamental band gap 0.81 eV lower in
energy than the onset of strong optical absorption. We
therefore propose that the weak absorption observed below
the optical gap of In2O3 is a property of the bulk solid,
resulting from the formally forbidden transitions at the top
of the valence band. Similar symmetry forbidden direct
fundamental gaps have been established in other conduct-
ing oxide systems including spinel SnZn2O4, SnCd2O4 and
CdIn2O4 [23], CuInO2 [24], cuprite Cu2O [25], and rutile
SnO2, TiO2, and GeO2 [26,27].

These results have wide consequences relating to both
the basic understanding of In2O3 and its applications. For
example, the recently observed unusual �1:2 eV redshift
in the onset of optical absorption in nitrogen-doped In2O3

[28] (for the purposes of p-type doping) could be explained
in terms of the introduction of N 2p levels above the VBM
of In2O3, breaking the local symmetry and producing a
parity allowed transition much higher in energy than the
initial optical gap which originates from below the valence
band edge. Furthermore, band offsets are generally mea-
sured relative to the conduction band or valence band
edges, but not both, and thus rely on prior knowledge of
the band gap to determine the overall offset. Past estima-
tions of In2O3 therefore need to be revised; e.g., for
In2O3=Si the reported valence band offset of 1.62 eV
[29] will be reduced to less than 1 eV.

We are grateful to both G. W. Watson and P. J. Dobson
for useful discussions. The work at Golden was supported
by the U.S. Department of Energy (DOE) under Contract
No. DE-AC36-99GO10337. Work in Darmstadt was sup-
ported by DFG Grants No. SFB 595-D3 and No. KL1225/4
and the European Network of Excellence FAME. The
Boston University (BU) program was supported in part
by DOE under No. DE-FG02-98ER45680 and in part by
the donors of the American Chemical Society Petroleum
Research Fund. The BU XES/RIXS spectrometer system
was funded by the U.S. Army Research Office under
No. DAAD19-01-1-0364 and No. DAAH04-95-0014.
The NSLS, Brookhaven National Laboratory, is supported
by DOE under Contract No. DE-AC02-98CH10886. The
Oxford program was supported by EPSRC Grant No. GR/
S94148 and the Scienta XPS facility by EPSRC Grant
No. EP/E025722/1.

*aron_walsh@nrel.gov
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