The origin of photovoltaic responses in 
BiFeO3 multiferroic ceramics
Authors: C.-S. Tu, C.-M. Hung, V. Hugo Schmidt, R. 
R. Chien, M.-D. Jiang, and J. Anthoninappen
This is an author-created, un-copyedited version of an article published in Journal of Physics: 
Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this 
version of the manuscript or any version derived from it. The Version of Record is available online 
at http://dx.doi.org/10.1088/0953-8984/24/49/495902.
C.-S. Tu, C.-M. Hung, V.H. Schmidt, R.R. Chien, M.-D. Jiang, and J. Anthoninappen, “The origin 
of photovoltaic responses in BiFeO3 multiferroic ceramics,” Journal of Physics: Condensed Matter 
24, 495902 (5 pp.) (2012). doi: 10.1088/0953-8984/24/49/495902.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
The origin of photovoltaic responses in
BiFeO3 multiferroic ceramics
C-S Tu1,2, C-M Hung1, V H Schmidt3, R R Chien3, M-D Jiang2 and
J Anthoninappen1
1 Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, Taipei 24205,
Taiwan
2 Department of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan
3 Department of Physics, Montana State University, Bozeman, MT 59717, USA
Abstract
Multiferroic BiFeO3 (BFO) ceramics with electrodes of indium tin oxide (ITO) and Au thin
films exhibit significant photovoltaic effects under near-ultraviolet illumination (λ = 405 nm)
and show strong dependences on light wavelength, illumination intensity, and sample
thickness. The correlation between photovoltaic responses and illumination intensity can be
attributed to photo-excited and thermally generated charge carriers in the interface depletion
region between BFO ceramic and ITO thin film. A theoretical model is developed to describe
the open-circuit photovoltage and short-circuit photocurrent density as a function of
illumination intensity. This model can be applied to the photovoltaic effects in p–n junction
type BFO thin films and other systems. The BFO ceramic exhibits stronger photovoltaic
responses than the ferroelectric Pb1−xLax(ZryTi1−y)1−x/4O3 (PLZT) ceramics under
near-ultraviolet illumination. Comparisons are made with other systems and models for the
photovoltaic effect.
(Some figures may appear in colour only in the online journal)
A p-type semiconductivity was found in BFO film with
impurity density of np ∼ 1023 m−3 [13]. The photovoltaic
responses were attributed to a p–n junction layer at
the ITO–BFO interface. ITO film has been reported as
being a n-type semiconductor with carrier concentration
of nn ∼ 1026–1027 m−3 [15, 16]. Photovoltaic responses
were also observed in the p–n depletion layer of a
LaMnO3/Nb-doped SrTiO3 structure, in which LaMnO3 plays
the role of p-type semiconductor [17]. The photovoltaic
responses of ferroelectric/piezoelectric PLZT ceramics and
Pb(Mg1/3Nb2/3)1−xTixO3 (PMN–PT) crystals are sensitive to
thickness and grain size [18–21]. A photovoltaic mechanism
associated with charge distributions (polarization charge,
Schottky space charge, and screening charge) was proposed
for PLZT thin films and its efficiency can be improved with
reduced thickness [22].
Most photovoltaic studies and proposed mechanisms
in BFO films have been focusing on the current–voltage
correlation under a constant light intensity. In this work,
1. Introduction
Photovoltaic and photostrictive effects have been extensively 
investigated in antiferromagnetic/ferroelectric BiFeO3 (BFO) 
thin films a nd c rystals [ 1–13]. S everal m echanisms were 
proposed for the photovoltaic responses in BFO thin films 
and crystals, including asymmetric ferroelectric photovoltaic 
effect (bulk photovoltaic effect) [7, 14], domain-wall 
model [8], and semiconductor-like p–n junction model [13]. 
The domain walls in rhombohedral BFO thin films exhibit a 
p–n junction-like potential step, whose value is theoretically 
higher in the 109◦ domain walls (∼0.15 V) compared to 
the 71◦ domain walls (∼0.02 V) [9]. The effects of electric 
(E)-field poling [2], illumination wavelength and intensity [2, 
5], substrate [4], and electrode [5, 6] on photovoltaic 
responses and optical properties of BFO films have also been 
explored. In addition, the photostrictive effect in BFO crystal 
can reach 10−5 with response time less than 0.1 s, which 
depends on light polarization and magnetic field [11].
Figure 1. Open-circuit photovoltage (Voc) as light was switched on
and off with increasing light intensity. The intensity is labeled on
the top of each illumination.
a theoretical model was first proposed to describe the
correlation between photovoltaic responses and illumination
intensity in the ITO film/BFO ceramics/Au film capacitor
configuration.
2. Experimental details
The BiFeO3 (BFO) ceramics were prepared by the solid state
reaction method. In the synthesis, Bi2O3 and Fe2O3 powders
(purity ≥ 99.0%) were weighed in 1.1:1 ratio to compensate
the loss of Bi during the sintering process. The powders were
mixed in an agate mortar for more than 24 h using alcohol as a
medium. The mixture was dried before calcining at 800 ◦C for
3 h. The calcined powder was then pressed into a disk before
sintering at 830 ◦C for 10 h. ITO and Au films were deposited
on the BFO ceramic as electrodes by dc sputtering. Two
intensity-adjustable diode lasers of λ = 405 and 532 nm were
used for photovoltaic effects. The laser beam was incident
perpendicular to the sample surface with ITO film.
3. Results and discussion
Figures 1 and 2 show open-circuit photovoltage (Voc) and
short-circuit photocurrent density (Jsc) as light was switched
on and off under illuminations of λ = 405 and 532 nm for
thicknesses of t = 0.2, 0.3, and 0.5 mm. Both Voc and Jsc
exhibits strong and nonlinear dependences on light intensity
(I) and wavelength (λ). The intensity-dependent Voc and Jsc
are plotted in figures 3 and 4. Compared with λ = 532 nm,
the illumination of λ= 405 nm (Eph ∼ 3.06 eV) induces much
stronger photovoltaic responses. These results agree with the
optical band gap of ∼2.74 eV in BFO [2, 12]. The Jsc for
Figure 2. Short-circuit photocurrent density (Jsc) with increasing
light intensity.
t = 0.2 mm can reach∼0.23 A m−2 for I ∼ 1.9×103 W m−2
under illumination of λ = 405 nm. This Jsc is much stronger
than in the poled PLZT(3/52/48) ceramics, whose Jsc (t =
50µm) shows a linear increase with I and is∼0.2 mA m−2 for
I ∼ 2× 103 W m−2 under illumination of λ = 366 nm [18].
To understand the light intensity-dependent Voc and Jsc, a
theoretical model is derived as follows. We consider a p-type
BFO slab on the right and an n-type ITO slab on the left.
Electrons will diffuse right, and holes diffuse left, annihilating
each other and leaving a depletion region. The first task is
to find the open-circuit voltage step −Uo going from left to
right across the p–n junction under no illumination. For no
illumination, this voltage is cancelled by a voltage Uo from
the contacts to the ITO and BFO. In the depletion region, there
will be a small thermally generated electron–hole creation
rate, and in this region the holes will go right and the electrons
left, giving a small current to the right. For no illumination
there can be no net current. The compensating current is from
holes from the non-depleted p-type BFO diffusing ‘uphill’ in
electrostatic energy to the non-depleted n-type ITO and from
electrons from the non-depleted n-type ITO diffusing ‘uphill’
in electrostatic energy to the non-depleted BFO.
In addition to the thermally generated charges, many
electron–hole pairs will be generated optically under
illumination. These additional holes will flow right, and the
electrons left, thereby decreasing the depletion-region width.
However, the decreased width will lower the retarding voltage
that limits the leftward hole and electron diffusion currents,
thus increasing these currents. The decreased width decreases
the downward voltage step from the depletion region,
to magnitude U < Uo, and so the measured open-circuit
Figure 3. The experimental open-circuit photovoltage and
theoretical fits versus intensity. The inset is the ratio doc/do (=Doc)
as a function of light intensity for λ = 405 nm.
voltage is
Voc(I) = Uo − Uoc(I). (1)
There are three contributions to the total current density
J. The first contribution Jt is from thermally stimulated
electron–hole pairs created in the depletion region. The
number density nv of electrons close enough to the top of the
valence band so that they have a chance to be excited to the
conduction band is assumed to be nv = NkT/Evn, where N is
the density of electrons in the valence band, k is Boltzmann’s
constant, T = 300 K is chosen as room temperature, and
Evn is the top energy of the valence band. The thermal
excitation probability pv per unit time per electron is pv =
v exp(−Ecn/kT), where v is the attempt frequency and Ecn
is the bottom energy in the conduction band. Considering
both the n- and p-type regions, we multiply nvpv by the
depletion-region width d and by the carrier charge q to find Jt,
Jt = qkTv[(dnNn/Evn)e−Ecn/kT + (dpNp/Evp)e−Ecp/kT ]. (2)
The second contribution to J is the Je from existing
carriers that are close to the depletion region and have enough
thermal energy to jump across it against the coulomb force.
The dopant concentration n is assumed to be independent of
position. The holes (or electrons) that are close enough to
the depletion region so that when thermally excited they do
not lose much energy to other carriers, are assumed to come
from a plane of thickness corresponding to the mean spacing
between acceptors (or donors). The number density per unit
area of these potentially excited carriers accordingly is n2/3p
(or n2/3n ). The probability per unit time per carrier that such a
carrier obtains enough energy to cross the depletion region is
Figure 4. The experimental short-circuit photocurrent density and
theoretical fits versus intensity. The inset is the ratio dsc/do (=Dsc)
as a function of light intensity for λ = 405 nm.
v exp(−qU/kT). The hole and electron contributions to Je are
negative, so Je is given by
Je = −qv(n2/3n + n2/3p )e−qU/kT . (3)
The third contribution is the photo-excited current density
Jp. The light intensity is assumed to decay exponential in
the BFO-side depletion region with a general form of I(z) =
I exp(−z/β), where β is the attenuation length. The ITO layer
absorbs little light because its optical band gap is larger than
the photon energy. The absorbed intensity Ia in the depletion
region can be estimated by Ia = Id/β. The creation rate of
electron–hole pairs can be estimated to be Ia/(hc/λ), then Jp
is given by
Jp = qdIλ/(hcβ). (4)
We now find an expression for the p–n junction voltage
step –U in terms of the depletion-region widths dp and
dn, which are parameters of light intensity. Let position
coordinate x be zero at the interface of the p–n junction.
In the depletion region of −dn < x < 0, ρn = qnn comes
from the ionized donors each of which has donated one
electron to the conduction band. Similarly, in the depletion
region of 0 < x < dp, ρp = qnp comes from the acceptors
each of which has accepted one electron from the valence
band. Using Gauss’ law for the region −dn < x < 0, the
position-dependent E-field is,
E(x) =
∫ x
−dn
(ρn/εoεn) dx′ = (ρn/εoεn)(x+ dn). (5)
Then the contribution from the n-type material to −U is,
−Un = −
∫ 0
−dn
E(x) dx = −(ρn/εoεn)d2n/2. (6)
Table 1. The fitting parameters for the solid lines in figures 3 and 4.
λ = 405 nm Uo (V) C α (W m−2)−1 RAO ( m2) η (W m−2)−1
t = 0.2 mm 0.78 28 2.2× 108 9.4 0.001
t = 0.3 mm 0.59 23 1.0× 107 12 0.0008
t = 0.5 mm 0.57 23 1.0× 107 23 0.0004
Similarly, −Up = (ρp/εoεp)d2p/2 is from the p-type
material. The total contributions for –U are
−U = (ρp/εoεp)d2p/2− (ρn/εoεn)d2n/2
= (−q/2εo)(npd2p/εp + nnd2n/εn) (7)
εp and εn are the dielectric permittivities of p- and n-type
materials. dn and dp are not independent, but are related by the
requirement that there is no net charge in the junction region.
This requirement gives dn = (np/nn)dp. We designate dp as
simply d. Then equation (7) yields
−U = −(qd2np/2εoεp)(1+ npεp/εnnn) = −Bd2;
B = (qnp/2εoεp)(1+ npεp/εnnn). (8)
We use the condition of no illumination to solve for Uo,
and designate d as do. For no illumination we have Jto+Jeo =
0, i.e.
qkTvdo[(Nnnp/nnEvn)e−Ecn/kT + (Np/Evp)e−Ecp/kT ]
− qv(n2/3n + n2/3p )e−qBd2o/kT = 0. (9)
Before solving do and Uo, it is worthwhile to know how
Jto is related to the diode reverse saturation current Io. We
rewrite equation (9), still for no illumination, but now with an
applied voltage Va given by Va = Uo−U. From equation (8),
we have d = [(Uo − Va)/B]1/2. Inserting this d value in place
of do in equation (9) gives the current density Ja resulting from
Va:
Ja = Jto[(1− Va/Uo)1/2 − exp(Va/Vc)], (10)
where Vc ≡ kT/q. The diode current–voltage characteristic as
given by Shockley et al [23] is
Ja = (I0/A)[1− exp(Va/Vc)], (11)
where A is junction area. As increasingly negative voltage is
applied, the exponential term quickly approaches zero, before
the square root term in equation (10) changes appreciably
from unity, so Ja becomes Jto in equation (10) and I0/A in
equation (11).
Now we use equation (9) to solve do. We can use
equations (2), (3), and (8) to find Uo, Jto, and Jeo. To find Voc,
we start by finding the d that gives Jt + Je + Jp = 0. Then we
find U corresponding to this d, and use V = Uo − U. We set
D = d/do, α = qdoλ/(hcβJto), and C = qBd2o/kT = qUo/kT .
For the open-circuit case, the illumination intensity-dependent
Doc = doc/do can be obtained by
Jt + Jp + Je = JtoDoc + JtoDocαI
− Jto exp[C(1− D2oc)] = 0. (12)
Then the Voc can be obtained by using equation (8), i.e.
Voc = Uo − BD2ocd2o = Uo(1− D2oc). (13)
Now we investigate the total short-circuit current density
Jsc and area-specific resistance RA = RS, where R = Rs + Rl
(source plus load resistance) and S is the illuminated area
of the p–n junction. Note that Rl is zero in the short-circuit
case. The resistivity of semiconductors typically decreases
as temperature is increased. If the temperature due to laser
illumination does not vary too much, a linear approximation
between resistance and intensity can be used, i.e. RA =
RAO(1 − ηI). η is the intensity coefficient of resistance. The
emf driving the Jsc through the source area-specific RA is
Uo − Usc. Here, the Jsc is,
Jsc = (Uo − Usc)/RA = Uo(1− D2sc)/RA. (14)
From equation (12), modified for the short-circuit case,
we have
Jsc = Jto{Dsc(1+ αI)− exp[C(1− D2sc)]}. (15)
We subtract equation (14) from equation (15) and use F ≡
Uo/RAJto. We then obtain
Dsc(1+ αI)− exp[C(1− D2sc)] − F(1− D2sc) = 0. (16)
The short-circuit Dsc = dsc/do as a function of I can
be obtained from equation (16). Then, the Jsc can then
be obtained from equation (15). In the fitting, a weak
intensity-dependent resistance was used in F, i.e. F ∼= Uo(1+
ηI)/RAOJto.
The solid lines in figures 3 and 4 are fits of Voc and Jsc
as a function of intensity (I) by using equations (12)–(16)
with parameters given in table 1. The experimental results and
theoretical fits agree reasonably well. The insets of figures
3 and 4 show the correlation between the ratio d/do and
light intensity for the open-circuit and short-circuit cases. The
measured Voc are comparable with the BFO thin films, whose
Voc varies in the range of 0.3–0.5 V [2, 6]. The measured Voc
was predicted by our model if values for Evn, Evp, Ecn and Ecp
from the literature are used in equations (8), (9), and (12) to
find do, doc and Uo, and then equation (13) is used to find Voc.
In fact, our model using these parameters predicts Voc in the
0.3–0.5 V range found in BFO thin-film-based structures as
well as in common photovoltaic junction materials like Si and
Ge.
In choosing the fit parameters, we note that the carrier
concentration nn in the n-type ITO films is larger than np in
the p-type BFO films [13, 15, 16]. Thus, from equation (8)
we have B = Uo/d2o ∼= qnp/(2εoεp). The room-temperature
dielectric permittivity εp in BFO ceramic is ∼102 [24]. We
use the carrier density np ∼= 1023 m−3 as reported for BFO
film [13]. For the case of t = 0.2 mm, do ∼= (2εoεpUo/qnp)1/2
was estimated to be ∼330 nm, which is consistent with the
depletion layer in ITO–BFO films [13]. The parameters C and
Uo are related by the carrier charge q (=CkT/Uo), where we
chose q as the electron charge ∼1.6× 10−19 C.
Finally, we consider three related questions. First, how
do the shapes of our Voc and Jsc curves versus I compare
with those for other p–n-junction-based photovoltaic systems?
Second, how can our model account for the similarities and
differences between those systems and ours? Third, how does
our model for these intensity dependences compare with other
models?
Other reports [25, 26] show curves for Voc versus I
with convex shape similar to ours. However [25], shows
linear dependence of Jsc on I, unlike our convex curves.
Our model is able to account for this difference in Jsc
behavior, by analyzing the differences in the ratios Doc and
Dsc shown in the insets of figures 3 and 4. Mathematically,
from equations (12) and (16), one can think of F as being
a function of D, and we find that ∂F/∂D > 0 and so also
∂D/∂F > 0. This means that Dsc > Doc. The crucial factor
in F ≡ Uo/RAJto is the area-specific source resistance RA. As
RA becomes infinite, Dsc and Doc become equal. If RA = 0,
Dsc = 1. Physically, this means that there is no hindrance
for photo-generated electron–hole pairs to travel around the
circuit until they recombine, whereas for nonzero RA this
hindrance narrows the depletion-region width. For RA small
but nonzero, the parameter 1 − D2sc becomes small. If we
expand equation (15) in this small parameter, we arrive at the
relation
Jsc (small RA) ∼= JtoαI. (17)
This relation that is linear in I can account for the linear
dependence of Jsc on I observed by Cusano [25] if RA is small.
Cusano [25] has no expressions for Voc or Jsc. Rose [26]
does not provide an expression for Jsc. Reference [26] shows
a linear dependence in Voc at low intensity, followed by a
convex curve that saturates into a horizontal line. If we take
the low and high intensity limits for Doc in equation (12) and
insert these values into equation (13), we obtain
Voc (low I) ∼= αUoI/(C + 1/2);
Voc (high I) ∼= Uo. (18)
Accordingly, our model predicts the same linear, convex
curve, constant I dependence sequence that is presented by
Rose [26].
4. Conclusions
The ITO film/BFO ceramic/Au film configuration exhibits
significant photovoltaic effects under illumination of λ =
405 nm, which strongly depend on light wavelength,
illumination intensity, and thickness. The proposed model
which includes both thermally generated and photo-excited
electron–hole pairs, can reasonably describe the photovoltaic
responses as a function of illumination intensity. This physical
model can be applied to the photovoltaic effects in p–n
junction type BFO thin films and pother systems.
Acknowledgment
This work was supported by National Science Council of
Taiwan Grant No. 100-2112-M-030-002-MY3.
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