Unconventional approaches to combine optical transparency with electrical
conductivity
J. E. Medvedeva∗
Department of Physics, University of Missouri–Rolla, Rolla, MO 65409
Combination of electrical conductivity and optical transparency in the same material – known
to be a prerogative of only a few oxides of post-transition metals, such as In, Sn, Zn and Cd –
manifests itself in a distinctive band structure of the transparent conductor host. While the oxides
of other elements with s2 electronic configuration, for example, Mg, Ca, Sc and Al, also exhibit the
desired optical and electronic features, they have not been considered as candidates for achieving
good electrical conductivity because of the challenges of efficient carrier generation in these wide-
bandgap materials. Here we demonstrate that alternative approaches to the problem not only
allow attaining the transport and optical properties which compete with those in currently utilized
transparent conducting oxides (TCO), but also significantly broaden the range of materials with a
potential of being developed into novel functional transparent conductors.
The key attribute of any conventional n-type TCO host
is a highly dispersed single free-electron-like conduction
band [1, 2, 3, 4, 5, 6, 7, 8]. Upon proper doping, it
provides both (i) high mobility of extra carriers (elec-
trons) due to their small effective mass, and (ii) low op-
tical absorption in the visible part of the spectrum due
to high-energy inter-band transitions, e.g., Fig. 1. For
the complete transparency in the visible range, the tran-
sitions from the valence band, Ev, and from the partially
filled conduction band, Ec, should be larger than 3.1 eV,
while the intra-band transitions as well as the plasma fre-
quency should be smaller than 1.8 eV. The high energy
dispersion also ensures a pronounced Fermi energy dis-
placement, so-called Burstein-Moss (BM) shift, so that
the optical transparency can be achieved in a material
with a relatively small bandgap, for example, in CdO
where the optical (direct) band gap is 2.3 eV.
Figures 1(a) and 1(b) illustrate the typical conduction
band of a conventional n-type transparent conductor and
how doping alters the electronic band structure of the
TCO host affecting the optical transitions. It is seen that
upon introduction of extra carriers into the host, a large
BM shift which facilitates higher-energy transitions from
the valence band (Ev), leads to a reduced energy of the
transitions from the Fermi level up into the conduction
band (Ec), i.e., Ev and Ec are interconnected [9]. In
other words, large carrier concentrations desired for a
good conductivity, may result in an increase of the optical
absorption because the Ec transitions become smaller in
energy. In addition, the transitions within the partially
filled band as well as plasma frequency may lead to the
absorption in the long-wavelength range.
The mutual exclusiveness of the optical transmittance
and electrical conductivity (see Refs. [5, 10, 11]) makes
it challenging to achieve the optimal performance in a
transparent conductor. Below we outline novel, uncon-
ventional ways to balance the optical and transport prop-
erties and to improve one without making a sacrifice of
the other.
 (a) 
 Γ  N  P  Γ  H  N 
        
 (b) 
 N  H  Γ  P  N  Γ 
 (c) 
 N  H  Γ  P  N  Γ 
 N  H  Γ  P  N  Γ 
 (d) 
        
FIG. 1: Electronic band structure of pure (a), 6.25% Sn-doped
(b), and 6.25% Mo-doped In2O3 for the majority (c) and the
minority (d) spin channels.
Magnetically mediated transparent conductors
One of the possible routes to avoid compromising the
optical transparency is to enhance conductivity via mo-
bility of the carriers rather than their concentration [11].
Recently, the mobility with more than twice the value
of the commercial Sn-doped indium oxide (ITO) was ob-
served in Mo-doped In2O3 (IMO), and it was shown that
the conductivity can be significantly increased with no
changes in the spectral transmittance upon doping with
Mo [12, 13, 14, 15]. Surprisingly, introduction of the
http://arxiv.org/abs/0704.1494v1
Complex M Eg(0) k
[110]
[111]
[010]
Mo•••In(1) 1.85 1.38 0.152 0.148 0.157 1.63
Mo•••In(2) 1.32 1.18 0.194 0.187 0.201 2.05
[Mo•••In O
• 0.50 1.26 0.125 0.123 0.132 1.27
Sn•In(1) — 0.98 0.201 0.203 0.205 2.29
In2O3+e
— 1.16 0.206 0.204 0.213 2.38
TABLE I: Calculated magnetic moments on the Mo atoms,
M, in µB ; the fundamental band gap values Eg(0), in eV; the
Fermi wave vectors kF , in atomic units; and the plasma fre-
quency ωp, in eV, for the different substitutional complexes
with 6.25% Mo doping level. Calculated values for pure (rigid-
band model) and 6.25% Sn-doped In2O3 are given for com-
parison.
transition metal Mo which donates two more carriers per
substitution compared to Sn, does not lead to the ex-
pected increase of the optical absorption or a decrease of
the mobility due to the scattering on the localized Mo
d-states.
Our electronic band structure investigations of IMO
revealed [8] that the magnetic interactions which have
never been considered to play a role in combining opti-
cal transparency with electrical conductivity, ensure both
high carrier mobility and low optical absorption in the
visible range. As one can see from Figs. 1(c) and 1(d),
strong exchange interactions split the Mo d-states located
in the vicinity of the Fermi level. These d-states are res-
onant states, while the conductivity is due to the delo-
calized In s-states which form the highly dispersed free-
electron-like conduction band. In other words, the free
carriers in the system flow in a background of the Mo
defects which serve as strong scattering centers. Because
of the exchange splitting of the Mo d-states, the carriers
of one spin is affected by only a half of the scattering
centers, i.e., only by the Mo d-states of the same spin.
Therefore, the concentration of the Mo scattering cen-
ters is effectively lowered by half compared to the Mo
doping level.
Figs. 1(b) and 1(c,d) show that the BM shift is less
pronounced in the IMO case – despite the fact that Mo6+
donates two extra carriers as compared to Sn4+ at the
same doping level. Such a low sensitivity to doping ap-
pears from the resonant Mo d-states located at the Fermi
level that facilitates the d-band filling (pinning) and thus
hinders further displacement of the Fermi level deep into
the conduction band. Smaller BM shift in IMO leads to
the following advantageous features to be compared to
those of ITO:
(i) Smaller increase in the effective mass is expected
upon Mo doping. In addition, the resonant Mo d-states
do not hybridize with the s-states of indium and so do
not affect the dispersion of the conduction band. There-
fore, the effective mass remains similar to the one of pure
indium oxide. This is borne out in experimental observa-
tions [14] showing that the effective mass does not vary
with doping (up to 12 % of Mo) and/or carrier concen-
tration.
(ii) Larger (in energy) optical transitions from the par-
tially occupied band (cf., Figs. 1(b) and 1(c,d)) along
with the fact that transitions from d- to s-states are for-
bidden ensure lower short-wavelength optical absorption.
(iii) The calculated plasma frequency, ωp, in IMO is be-
low the visible range and significantly smaller than that
of ITO (Table I). This finding suggests a possibility to in-
troduce larger carrier concentrations without sacrificing
the optical transmittance in the long wavelength range.
(iv) Smaller BM shift does not lead to the appear-
ance of the intense inter-band transitions from the va-
lence band, Ev, in the visible range due to the large op-
tical band gap in pure indium oxide, namely, 3.6 eV [16].
Furthermore, in contrast to ITO where the bandgap nar-
rowing has been demonstrated both experimentally [16]
and theoretically [2], doping with Mo shows an opposite
(beneficial) trend: the fundamental band gap increases
upon introduction of Mo, Table I, because the asymmet-
ric d-orbitals of Mo rotate the p-orbitals of the neighbor-
ing oxygen atoms leading to an increase of the overlap
between the latter and the In s-states.
It is important to note that the optical and transport
properties in IMO are sensitive to specific growth condi-
tions, namely, the ambient oxygen pressure. It is found
[8] that an increased oxygen content facilitates the forma-
tion of the oxygen compensated complexes which reduces
the number of free carriers – from 3 to 1 per Mo substitu-
tion – but, at the same time, improves the carrier mobil-
ity due to smaller ionized impurity scattering and hence
longer relaxation times. On the other hand, the inter-
stitial oxygen significantly supresses the magnetic inter-
actions, Table I, which should be strong enough to split
the transition metal d-states in order to provide good
conductivity in one (or both) spin channels.
Thus, the transition metal dopants can be highly ben-
eficial in providing the transport and optical properties
which compete with those of commercially utilized ITO.
Similar behavior is expected upon doping with other
transition metal elements and other hosts – provided that
the magnetic interactions are small enough to keep the
d↑-d↓ transitions out of the visible range.
Multicomponent TCO with layered structure
Complex transparent conductors consisting of struc-
turally and/or chemically distinct layers, such as
InGaO3(ZnO)m, m=integer, offer a way to increase con-
ductivity by spatially separating the carrier donors (tra-
ditionally, oxygen vacancies or aliovalent substitutional
dopants) and conducting layers which transfer the carri-
ers effectively, i.e., without charge scattering on the im-
purities [17, 18, 19].
1.2 1.6 2 2.4 2.8
Energy, eV
0.005
0.01  
     
    0
0.005
     
    0
0.005
InGaZnO4
In s−states
Ga s−states
Zn s−states
O1 s, p−states
O2 s, p−states
0.4 0.8 1.2 1.6 2
Energy, eV
     
    0
0.005
0.01 
     
0.005
0.01 
     
InAlMgO4
In s−states
Al s−states
Mg s−states
O1 s, p−states
O2 s, p−states
FIG. 2: Partial density of states for InGaZnO4 and
InAlMgO4.
The homologous series InGaO3(ZnO)m and
In2O3(ZnO)m, also known for their promising ther-
moelectric properties [20], have been extensively studied
experimentally [1, 18, 19, 21, 22, 23, 24, 25]. In these
materials, octahedrally coordinated In layers alternate
with (m + 1) layers of oxygen tetrahedrons around Zn
(and Ga) [26, 27, 28]. Because the octahedral oxygen co-
ordination of cations was long believed to be essential for
a good transparent conductor [1, 4, 17, 29, 30, 31, 32],
it has been suggested that the charge is transfered
within the InO1.5 layers while Ga and Zn atoms were
proposed as candidates for efficient substitutional doping
[1, 18, 19].
However, accurate electronic band structure investiga-
tions for InGaZnO4, m=1, showed [33] that the atoms
from both InO1.5 and GaZnO2.5 layers give compara-
ble contributions to the conduction band, Fig. 2(a).
This resulted in a three-dimensional distribution of the
charge density: the interatomic (or “background”) elec-
tron density is similar in and across the [0001] layers.
The isotropy of the electronic properties in this layered
compound manifests itself in the electron effective masses
being nearly the same in all crystallographic directions
(Table II).
Most strikingly, we found that the effective mass re-
mains isotropic when the cation(s) in InGaZnO4 are re-
placed by other elements with s2 electronic configuration,
for example, Sc, Al and/or Mg. This finding may seem
to be counterintuitive, since the s-states of Sc, Al and
Mg are expected to be located deeper in the conduc-
tion band due to significantly larger band gaps in Sc2O3,
Al2O3 and MgO as compared to those in In2O3, Ga2O3
and ZnO. Analysis of the partial density of states shows
that although the contributions from the Sc, Al and Mg
atoms to the bottom of the conduction band are notably
reduced, cf., Fig. 2 and Table II, the states of these
Compound N1 N2 Eg(0) m[100] m[010] m[001] mab mz
InGaZnO4 48% 52% 1.30 0.23 0.22 0.20 0.23 0.23
InGaMgO4 58% 42% 2.15 0.27 0.27 0.24 0.28 0.29
ScGaZnO4 26% 74% 2.48 0.33 0.33 0.34 0.33 0.53
InAlMgO4 72% 28% 2.78 0.32 0.31 0.35 0.31 0.34
TABLE II: Net contributions to the conduction band at the
Γ point from the states of the atoms that belong to the
In(Sc)O1.5, N1, or Ga(Al)Zn(Mg)O2.5, N2, layers, in per
cent; the LDA fundamental bandgap values Eg(0), in eV; the
electron effective masses m, in me, along the specified crys-
tallographic directions; and the components of the electron
effective-mass tensor, ma,b and mz, calculated via simple av-
eraging of those of the corresponding single-cation oxides.
atoms are still available for the electron transport. Con-
sequently, the interatomic charge density distribution is
three-dimensional for all these layered multi-cation ox-
ides – in accord with the isotropic electron effective mass.
Moreover, we found [33] that the electron effective mass
in these complex materials can be predicted via simple
averaging over those of the corresponding single-cation
oxides (Table II).
It is important to stress that the isotropic character of
the intrinsic transport properties in the TCO hosts with
layered structure may not be maintained when extra car-
riers are introduced. Different valence states (In3+ and
Ga3+ vs Zn2+) and oxygen coordination (octahedral for
In vs tetrahedral for Ga and Zn) are likely to result in
preferential (non-uniform) arrangement of aliovalent sub-
stitutional dopants or oxygen vacancies. We believe that
the observed anisotropic conductivity [20, 21] as well as
its dependence on the octahedral site density [1, 32] in
the layered TCO’s is a manifestation of a specific carrier
generation mechanism. While proper doping can help
make either or both structurally distinct layers conduct-
ing, leading to a highly anisotropic or three-dimensional
electron mobility, respectively, amorphous complex ox-
ides [22, 24, 25] readily offer a way to maintain isotropic
transport properties.
Thus, we believe that other cations with s2 electronic
configuration, beyond the traditional In, Sn, Zn and Cd,
can be effectively incorporated into novel complex mul-
ticomponent TCO hosts – such as the layered materi-
als decribed above, ordered ternary oxides [32, 34, 35],
solid solutions [1] as well as their amorphous counterparts
[22, 35], important for flexible electronics technologies
[24]. Significantly, the sensitivity of the bandgap value
to the composition of a multicomponent oxide (Table II)
offers a possibility to manipulate the optical properties
as well as the band offsets (work functions) via proper
composition of an application-specific TCO.
Finally, it should be mentioned, that the efficient dop-
ing of the wide-bandgap oxides is known to be a chal-
lenge [36, 37, 38]. Alternative carrier generation mech-
anisms, for example, magnetic dopants discussed above,
FIG. 3: Crystal structure of H-doped 12CaO·7Al2O3. On the
left, only three of the 12 cages in the unit cell are shown. The
cube (right) represent the unit cell. Only the atoms that par-
ticipate in hopping transport are shown: Ca (yellow), OH−
(blue) and H− (green spheres). Red line represent the elec-
tron hopping path.
introduction of hydrogen [39] or ultraviolet irradiation in
nanoporous calcium aluminate [5, 40, 41], are being ac-
tively sought and have already yielded promising results
– as outlined in the following section.
Novel UV-activated transparent conductors
Cage-structured insulating calcium-aluminum oxide,
12CaO·7Al2O3, or mayenite, differs essentially from the
conventional TCO’s not only by its chemical and struc-
tural properties but also by the carrier generation mecha-
nism: a persistent conductivity (with a ten-order of mag-
nitude change) has been achieved upon doping with hy-
drogen followed by UV irradiation [40, 41].
Mayenite belongs to the CaO-Al2O3 family of Portland
cements which are known for their superior refractory
properties. The unique structural features of mayenite,
Fig. 3, namely, the encaged “excess” oxygen ions, al-
low incorporation of hydrogen according to the chem-
ical reaction: O2−(cage) + H2(atm.) → OH
−(cage)
+ H−(another cage). While the H-doped mayenite re-
mains insulating (Fig. 4(a)), the conductivity results
from the electrons excited by UV irradiation off the H−
ions into the conduction band formed from Ca d-states.
The charge transport occurs by electron hopping through
the encaged “defects” – the H0 and OH− located inside
the large (more than 5.6 Å in diameter) structural cavi-
ties. Understanding of the conduction mechanism on the
microscopic level [41, 42] resulted in prediction of ways
to control the conductivity by targeting the particular
atoms that participate in the hopping. These predictions
have been confirmed experimentally [41, 43].
The low conductivity in H-doped UV-irradiated
mayenite (∼1 S/cm, Ref. [40, 41]) was attributed to
the strong Coulomb interactions between the UV released
electrons which migrate along a narrow conducting chan-
(a) (b)
 N  H  Γ  P  N  Γ 
FIG. 4: Electronic band structure of (a) H-doped
and (b) H-doped UV-irradiated Ca12Al14O33 and (c)
[Ca12Al14O32]
2+(2e−).
nel – the hopping path, Fig. 3. Alleviation of the elec-
tronic repulsion [42] resulted in the observed [44] 100-fold
enhancement of the conductivity in the mayenite-based
oxide, [Ca12Al14O32]
2+(2e−), although the carrier con-
centration was only two times larger than that in the H-
doped UV-irradiated Ca12Al14O33. The improved con-
ductivity, however, came at the cost of greatly increased
absorption [42, 44] due to an increased density of states
at the Fermi level, making this oxide unsuitable for prac-
tical use as a transparent conducting material.
Despite the failure to combine effectively the opti-
cal transparency and with useful electrical conductiv-
ity in Ca12Al14O33, the band structure analysis of the
mayenite-based oxides suggests that these materials be-
long to a conceptually new class of transparent conduc-
tors where a significant correlation between their struc-
tural peculiarities and electronic and optical properties
allows achieving good conductivity without compromis-
ing their optical properties. In striking contrast to the
conventional TCO’s, where there is a trade-off between
optical absorption and conductivity, as discussed above,
nanoporous materials allow a possibility to combine 100%
optical transparency with high electrical conductivity.
The schematic band structure of such an “ideal” TCO
is shown in Fig. 5. Introduction of a deep impurity band
in the bandgap of an insulating material would help to
keep intense interband transitions (from the valence band
to the impurity band and from the impurity band to the
conduction band) above the visible range. This requires
the band gap of a host material to be more than 6.2
eV. Furthermore, the impurity band should be narrow
enough (less than 1.8 eV) to keep intraband transitions
(as well as the plasma frequency) below the visible range.
In order to achieve high conductivity, the concentra-
tion of impurities should be large enough so that their
electronic wavefunctions overlap and form an impurity
band. The formation of the band would lead to a high
carrier mobility due to the extended nature of these states
resulting in a relatively low scattering. For this, a ma-
terial with a close-packed structure should not be used,
because large concentration of impurities would result
in (i) an increase of ionized impurity scattering which
Conduction band
Valence band
FIG. 5: Schematic band structure of conventional (left) and
“ideal” (right) transparent conductor.
limits electron transport; and (ii) a large relaxation of
the host material, affecting its electronic structure and,
most likely, decreasing the desired optical transparency.
Therefore, an introduction of a deep impurity band into a
wide-band insulator with a close-packed structure would
make the material neither conducting nor transparent.
Alternatively, materials with a nanoporous structure may
offer a way to incorporate a large concentration of impuri-
ties without any significant changes in the band structure
of the host material. Zeolites have been proposed [5] as
potential candidates for the “ideal” TCO’s because they
possess the desired structural and optical features, i.e.,
spacious interconnected pores and large bandgaps, and
also exhibit the ability to trap functional “guest” atoms
inside the nanometersized cavities which would govern
the transport properties of the material.
Thus, understanding the principles of the conventional
transparent conductors provide a solid base for further
search of novel TCO host materials as well as efficient car-
rier generation mechanisms. Ab-initio density-functional
band structure investigations [45] are valuable not only
in providing a thorough insight into the TCO basics but
also in predicting hidden capabilities of the materials be-
yond the traditionally employed.
∗ E-mail:juliaem@umr.edu
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earized augmented plane wave (FLAPW) method [46, 47]
with the local density approximation for the electronic
band structure investigations of Mo-doped In2O3, mul-
ticomponent XY2O4 compounds, H-doped Ca12Al14O33
and oxygen deficient [Ca12Al14O32]
2+(2e−). Each struc-
ture has been optimized via the total energy and atomic
forces minimization. During the optimization, all atoms
were allowed to move along x, y, and z directions while
the lattice parameters were fixed at the correspond-
ing experimental values. The UV-irradiated H-bearing
Ca12Al14O33 was investigated within the linear muffin-
tin orbital method (LMTO) in the atomic sphere approx-
imation [48].
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  Combination of electrical conductivity and optical transparency in the same
material -- known to be a prerogative of only a few oxides of post-transition
metals, such as In, Sn, Zn and Cd -- manifests itself in a distinctive band
structure of the transparent conductor host. While the oxides of other elements
with $s^2$ electronic configuration, for example, Mg, Ca, Sc and Al, also
exhibit the desired optical and electronic features, they have not been
considered as candidates for achieving good electrical conductivity because of
the challenges of efficient carrier generation in these wide-bandgap materials.
Here we demonstrate that alternative approaches to the problem not only allow
attaining the transport and optical properties which compete with those in
currently utilized transparent conducting oxides (TCO), but also significantly
broaden the range of materials with a potential of being developed into novel
functional transparent conductors.

Introduction of a deep impurity band
in the bandgap of an insulating material would help to
keep intense interband transitions (from the valence band
to the impurity band and from the impurity band to the
conduction band) above the visible range. This requires
the band gap of a host material to be more than 6.2
eV. Furthermore, the impurity band should be narrow
enough (less than 1.8 eV) to keep intraband transitions
(as well as the plasma frequency) below the visible range.
In order to achieve high conductivity, the concentra-
tion of impurities should be large enough so that their
electronic wavefunctions overlap and form an impurity
band. The formation of the band would lead to a high
carrier mobility due to the extended nature of these states
resulting in a relatively low scattering. For this, a ma-
terial with a close-packed structure should not be used,
because large concentration of impurities would result
in (i) an increase of ionized impurity scattering which
Conduction band
Valence band
FIG. 5: Schematic band structure of conventional (left) and
“ideal” (right) transparent conductor.
limits electron transport; and (ii) a large relaxation of
the host material, affecting its electronic structure and,
most likely, decreasing the desired optical transparency.
Therefore, an introduction of a deep impurity band into a
wide-band insulator with a close-packed structure would
make the material neither conducting nor transparent.
Alternatively, materials with a nanoporous structure may
offer a way to incorporate a large concentration of impuri-
ties without any significant changes in the band structure
of the host material. Zeolites have been proposed [5] as
potential candidates for the “ideal” TCO’s because they
possess the desired structural and optical features, i.e.,
spacious interconnected pores and large bandgaps, and
also exhibit the ability to trap functional “guest” atoms
inside the nanometersized cavities which would govern
the transport properties of the material.
Thus, understanding the principles of the conventional
transparent conductors provide a solid base for further
search of novel TCO host materials as well as efficient car-
rier generation mechanisms. Ab-initio density-functional
band structure investigations [45] are valuable not only
in providing a thorough insight into the TCO basics but
also in predicting hidden capabilities of the materials be-
yond the traditionally employed.
∗ E-mail:juliaem@umr.edu
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