Shift current bulk photovoltaic effect in polar materials—hybrid and oxide perovskites and beyond
Shift current bulk photovoltaic effect in polar materials-hybrid and oxide perovskites and beyond
Liang Z Tan 0 3
Fan Zheng 0 3
Steve M Young 1 3
Fenggong Wang 0 3
Shi Liu 2 3
Andrew M Rappe 0 3
0 The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania , Philadelphia, PA , USA
1 Center for Computational Materials Science, United States Naval Research Laboratory , Washington, DC , USA
2 Geophysical Laboratory, Carnegie Institution of Science , Washington, DC , USA
3 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
REVIEW ARTICLE The bulk photovoltaic effect (BPVE) refers to the generation of a steady photocurrent and above-bandgap photovoltage in a single-phase homogeneous material lacking inversion symmetry. The mechanism of BPVE is decidedly different from the typical p-n junction-based photovoltaic mechanism in heterogeneous materials. Recently, there has been renewed interest in ferroelectric materials for solar energy conversion, inspired by the discovery of above-bandgap photovoltages in ferroelectrics, the invention of low bandgap ferroelectric materials and the rapidly improving power conversion efficiency of metal halide perovskites. However, as long as the nature of the BPVE and its dependence on composition and structure remain poorly understood, materials engineering and the realisation of its true potential will be hampered. In this review article, we survey the history, development and recent progress in understanding the mechanisms of BPVE, with a focus on the shift current mechanism, an intrinsic BPVE that is universal to all materials lacking inversion symmetry. In addition to explaining the theory of shift current, materials design opportunities and challenges will be discussed for future applications of the BPVE.
? ? JscVocPin:
Here Voc is the open-circuit voltage, Jsc is the short-circuit current,
FF is the fill factor and Pin is the power of the incident radiation on
the solar cell. These quantities can be measured from the current?
voltage (I?V) curve, as shown in Figure 1. In traditional solar cells,
the mechanism for separation of the photoexcited carriers
(electrons and holes) is the built-in electric field inside p?n
junctions. Hot carriers typically relax to the bandedges via inelastic
scattering events before being collected at the electrodes. These
energy losses hamper the improvement of the PCE and limit the
Voc to the bandgap of light-absorbing semiconductors. In addition,
the requirement of p?n junctions for carrier separation demands
careful interface engineering and sophisticated fabrication
In this review article, we discuss the bulk photovoltaic effect
(BPVE), in particular, the shift current mechanism, which has a
number of advantages over traditional p?n junction-based solar
cells. In the shift current mechanism, the driving force for carrier
separation is not the built-in electric field, but the coherent
evolution of electron and hole wavefunctions. Although the
carriers in p?n junctions travel to the electrodes via drift-diffusive
transport, shift current carriers instead rapidly propagate to the
electrodes, minimising the opportunity for energy losses. Because
this is a hot carrier effect, carrier separation does not depend
on any internal electric fields (see the ?Polarisation? section),
above-bandgap photovoltages can be generated, and the
Shockley?Queisser limit could be surpassed. Because the shift
current mechanism relies only on bulk inversion asymmetry, it can
be realized in single-phase materials. The lack of p?n interface
ensures that the entire PV material is active for current generation
and allows for a simple and robust fabrication process.
In general, the symmetry requirement to produce a current
from unpolarised light is to have a structure that allows for the
definition of a unique spatial vector (i.e., a polar material).
Therefore, materials with bulk inversion symmetry cannot
generate photocurrents in the bulk. Materials that have broken
bulk inversion symmetry but are non-polar (e.g., GaAs) can
generate bulk photocurrents, but only in response to polarised
light.1 Ferroelectric materials, which have a switchable polarisation
direction, satisfy the symmetry requirements for the generation of
bulk photocurrents, and have historically been among the most
studied BPVE materials.2?4 However, the switchable aspect is not a
necessity for the observation of BPVE. In addition, we will show
below (see the section ?Polarisation?) that the BPVE response is not
simply a measure of the strength of this polarisation field.
There are a number of BPVEs closely related to the shift current.
Photocurrents can be generated in the bulk when scattering sites
or absorption centres possess some amount of asymmetry.4?6
Such processes rely on the generation of an asymmetric
distribution of nonthermalised carriers, in contrast to the coherent
evolution in the shift current mechanism. These ballistic
photocurrents have been discussed in ref. 7. In gyrotropic crystals, the
switching of photocurrent directions with the helicity of circularly
polarised light is known as the circular photogalvanic effect. In
metals and semiconductors, under the assumptions of low
frequencies and short relaxation times, this effect is controlled
by the anomalous velocity that arises from orbital Berry
phases.8?10 The circular photogalvanic effect has been
experimentally observed in quantum wells.11?14 It has also been
observed in tellurium crystals with significant spin?orbit valence
The shift current BPVE has been observed in many materials
systems, including ferroelectrics,2,3,16 quantum wells,17 organic
crystals18 and two-dimensional interfaces.19 The shift current
theory was proposed as an explanation for the BPVE in BaTiO3 by
von Baltz and Kraut,1 and was later derived within the framework
of Green?s functions20 and nonlinear optics.21 Young and Rappe
reformulated the shift current theory to enable efficient
calculation from first-principles,22 and provided the first comparison of
experimental BPVE data with shift current theory.22 In subsequent
first-principles studies of the shift current in ferroelectric materials,
it was shown that the shift current is the main contributor to the
BPVE.23?30 As such, we will focus on the shift current.
In this review article, we provide an introduction to the basic
theory and phenomenology of the shift current BPVE, with the aim
of reviewing recent major developments in the field. In particular,
there have been many recent efforts to increase shift current
densities and efficiencies, and this will be the main focus of this
review. We begin with a theoretical review of the shift current
response, developed within the framework of a time-dependent
perturbation theory, in the section ?Theory of the shift current
response?. In the section ?Material properties conducive to shift
current response?, we will discuss intrinsic material properties
conducive to shift current response with a tight-binding model.
After a review of recent experimental studies of ferroelectric and
polar materials for solar energy conversion in the section ?Review
of experiments?, we present first-principles studies of the shift
current response in various real materials, with an emphasis on
oxide and halide perovskites, in the section ?Modern materials
design for shift current?. The review concludes with a
consideration of new directions for realising BPVE-based solar cells.
THEORY OF THE SHIFT CURRENT RESPONSE
In the shift current mechanism, the behaviour of carriers
immediately after excitation by light is governed by coherent
excitation instead of inelastic scattering. The time-dependent
perturbation theory should therefore provide a good description
of the electronic behaviour at these timescales. We first present a
simplified derivation of the shift current in a three-level system:
the energy level n = 0 is initially occupied, whereas the levels n = 1
and n = 2 are initially unoccupied. In the presence of an electric
field E oscillating at frequency ?, the electron at n = 0 evolves into
a linear combination of n = 0, 1 and 2. Within a first-order
timedependent perturbation theory, this state is
j??t?i ? ??0??t?E ? ??1??t?E ? j0i ?
Xe - iontdn?t?jni
n ? 0
with the coefficients
i ei?on0?o?t ei?on0 - o?t
dn?t? ? - _ Vn0 i?on0 ? o? ? i?on0 - o?
Here Vn0 and ?n0 are the dipole matrix element and energy
difference between the levels n and 0. The current carried by the
state ?(t) is given by J ? me ??t?9P9??t? , where P is the
momentum operator and contains both oscillatory and constant
components. The contribution to the constant current from the
first-order wavefunction is
e D??1??t?jPj??1??t?E ? m n;n0
e Xeion0 tdn0 e - iontdnPn0n
? m n;n0
where gn0n are phases derived from equation (
). The constant
component of the current depends quadratically on the optical field and
is a nonlinear optical effect. We note that the shift current also
contains contributions from the momentum matrix elements
between zeroth- and second-order wavefunctions in a
timedependent perturbation theory (SMY and AMR, unpublished data).
2, 3, 4
) describe the picture of electrons in a
coherent, current-carrying excited state ?(t) that arises in an
oscillating light field. Equivalently, these equations imply that an
electron can be excited from the ground state 0 to a higher state n
by a photon of frequency +?, or it can be excited to a higher state
n0 by a photon of frequency ? ?. These two different excitation
amplitudes interfere, giving a d.c. response, provided that the
amplitudes interfere asymmetrically. That is, the matrix element
describing the interference, Vn00Vn0Pn0n in equation (
not vanish by symmetry. In real materials, this asymmetry is
manifested in the different spatial character of conduction and
valence bands.31 Heuristically, this causes the electrons (and holes)
to ?shift? on excitation by light.
In general, the shift current J is related to the electric field via
the frequency- and material-dependent response function ?.
Jq ? ?rsqEr Es
) shows that ?rsq is a second-order response function.
The direction of the shift current is not necessarily the same as the
applied electric field, as can be seen from the tensorial property of
?rsq. The second-order nature of the shift current response already
imposes certain symmetry constraints on the classes of materials
that can exhibit nonzero shift current response. In a material with
inversion symmetry, the response function ? is left unchanged by
an inversion operation, whereas the current and electric field,
being vector quantities, each pick up a negative sign.
?rsq0 ? ?rsq
q ? - Jq
Eq0 ? - Eq
Using equation (
) in the constitutive equation (equation (
implies that Jq = 0 in such an inversion symmetric system. The shift
current response can only be observed in materials with broken
inversion symmetry. In the following sections, we will elaborate on
the microscopic interpretation of this observation.
In crystalline materials, the response function can be written as
an integral over the Brillouin zone.24
?rsq?o? ? 2?e
ReX Z dkhvkjPr jckihckjPsjvkiRq?c; v; k?
? ??oc - ov - o?
where c and v are conduction and valence bands, respectively. The
derivation of this integral is provided in ref. 21 using nonlinear
susceptibilities and in ref. 20 using Green?s functions. Like linear
absorption, the shift current response depends on the momentum
matrix elements on a constant energy difference manifold given
by ?c ? ?v = ?. There is an additional factor Rq(c, v, k) that has
dimensions of length and is known as the shift vector.20,21 In terms
of the conduction and valence band wavefunction,
If we assume that the photoconductivity is proportional to the
number of carriers excited, then we may take it to be ?ph = c??I,
where ? is the mobility, and we have
? ? 0:25 ?SC2I ? 0:25 ?SCIG:
direction (Figure 1c). In the former case, AI = AJ and d = L, so that
Rq?c; v; k? ? - ??vc?k? - ?cq?k? - ?vq?k? :
Here ?vc(k) is the phase of the transition dipole?vk9Pr 9ck?, and
?cq?k? ? ?uc?k?9i?k?q9uc?k?i is the Berry connection for band c, in
terms of the Bloch functions uc(k). Although each of the individual
terms in equation (
) depends on the arbitrary gauge of the
wavefunctions, their sum is gauge-independent and is a
welldefined physical quantity.22 Furthermore, by expressing the
electric field in terms of the light intensity, the shift current
response susceptibility can be shown to be proportional to light
intensity. Although the shift current expression in equation (
appropriate for thin samples without significant attenuation of the
incident light, corrections have to be made for bulk crystals where
the light intensity is inhomogeneous. In the latter, where the light
intensity is fully attenuated by the sample, the shift current is
related to the incident light intensity by the Glass coefficient3
?rrq Er2w ? GrrqIr w;
Jq ? ?rr
where w is the width of the crystal surface exposed to illumination
and ?rr is the absorption coefficient and Ir the light intensity along
the direction of incident light polarisation. We will study both the
shift current response function and the Glass coefficient in the
The PCE of the shift current mechanism we have described in
this section is not the subject to the same limitations as ordinary
photocurrent.32 As the shift current is generated by the incident
illumination and does not depend on an external voltage, the
photovoltage is not limited by the bandgap. In addition, the shift
current is generally found to be insensitive to photovoltage,
so that that total current is
where V is the photovoltage, JSC is the short-circuit shift current
density, L is the distance between electrodes, and ?d and ?ph are
the dark and photoconductivities, respecitively. Thus, the
relationship between photovoltage and photocurrent is linear,33 implying
a maximum fill factor of 0.25 (Figure 1a). The open-circuit
photovoltage VOC is then achieved when the shift current is fully
cancelled by the backflow of conventional current that occurs due
to thermalised carriers driven by the photovoltage. Thus, in the
limit of a thin sample, and assuming that dark conductivity is
JSC ? VLOC ?ph
VOC ? J?SpChL
The maximum power that may be drawn is Pmax ?
0:25JSCVOCAJ ? 0:25 JSC2LAJ where AJ is the area through which
JSC flows. The total power absorbed by the sample is IAI?d, where I
is the intensity, AI is the area illuminated, ? is the absorption
coefficient and d is the sample depth. The efficiency is then
? ? 0:25 ?ASI?C2dL?ApJhI. At this point, we must recognise that there are at
least two possible cell geometries. In the first, the electrode faces
are normal to the illumination direction (Figure 1b), whereas in the
second the electrode normal is perpendicular to the illumination
The same result may be obtained in the thin-film limit for the
second geometry. From this, it is clear that high efficiency requires
maximising the Glass coefficient and minimising the mobility. The
latter may be accomplished by creating heterostructures that
feature regions with low mobility that the shift current is
nonetheless able to flow through. An example of such a strategy
was presented in ref. 34, where the authors show that domain
walls of BFO possess very low photoconductivity, preventing
carriers leaking back through the sample.
In this discussion of shift current efficiency, we have neglected
the recombination current. In principle, geminate recombination
of an electron?hole pair, which occurs before the electron and
hole have separated, can result in a recombination current
opposing the shift current, reducing the magnitude of the total
photocurrent. However, in the usual setting of the BPVE, where
the photocurrent arises primarily in the bulk of a strongly bonded
material, the recombination current is likely to be negligible. This
is because momentum scattering rates are many orders of
magnitude faster than recombination rates in most
semiconductors and insulators,20 and the momenta of electrons and holes are
likely to be randomised before recombination occurs. In isolated
or weakly bonded systems far from the bulk limit, this assumption
may not apply. For instance, in an isolated polar diatomic
molecule, only geminate recombination is present. However, as
we show below (see the section ?Delocalised electronic states?),
we are often interested in the opposite limit of strongly
delocalised electronic states, as these tend to give the largest
shift current density. We note that momentum relaxation has the
effect of homogeneous broadening; ?-functions are replaced by
Lorentzians in equation (
), but the shift current magnitude is not
expected to change.
MATERIAL PROPERTIES CONDUCIVE TO SHIFT CURRENT
As we have seen above, the breaking of inversion symmetry is
necessary for the shift current response. Materials with broken
inversion symmetry can either be polar or non-polar, and this
has implications for the type of shift current response in
these materials. As an example, consider the non-polar
noncentrosymmetric material hexagonal boron nitride (h-BN).
Unpolarised light with wavevector incident normal to the h-BN
plane does not break the threefold symmetry of the h-BN lattice.
In this situation, there is zero net shift current in the h-BN plane.35
Therefore, to exhibit shift current under unpolarised light, polar
non-centrosymmetric materials are required. Kr?l has proposed
removing the threefold symmetry of h-BN by rolling a flat h-BN
sheet into a cylindrical nanotube.35 Such a structure can host a
nonzero shift current in the presence of unpolarised light.
Depending on the chirality of the nanotube, the shift current
can have components along the length of the nanotube, as well as
around the circumference of the nanotube. It is possible to study
the relationship between the magnitude of the polarisation and
the strength of the shift current response in this system by tuning
the on-site potential difference between the boron and nitrogen
sites in a tight-binding model. At small values of polarisation,
the magnitude of the shift vector scales linearly with the
polarisation, but the dependence becomes sublinear at higher
values of polarisation.
The relationship between shift current response and
polarisation is less straightforward in more complex materials. The shift
current response of PbTiO3 was calculated using first-principles
methods in ref. 22. The polarisation can be changed in the
calculation by rigidly displacing the oxygen ions along a single
Cartesian axis. The results reveal a complex relationship between
the oxygen ion displacement and the shift current (Figure 2).
At certain frequencies, an increase of the polarisation causes the
shift current to first decrease in the magnitude and then reverse in
the direction, whereas at other frequencies, the shift current
response is relatively insensitive to the polarisation. Furthermore,
a comparison with a related oxide perovskite BaTiO3 shows that
despite PbTiO3 having more than twice the polarisation of BaTiO3,
both materials exhibit a similar shift current response.22 Therefore,
although polarisation is necessary for the shift current response
under unpolarised light, a larger polarisation does not always
imply a larger shift current response. In equation (
), there is
not an explicit dependence of the shift current on material
polarisation. Rather, the correlations between shift current and
material polarisation arise from how each depends on the
breaking of inversion symmetry.
Bonding character In addition to polarisation, the type of bonding in a system can also affect the magnitude of the shift current response.
To understand these effects, we construct a simple
onedimensional tight-binding model36 based on the Su?Shrieffer?
Heeger model used in the study of conducting polymers.37 The
tight-binding Hamiltonian is
X ?? - 1?jcjycj ? ?t ? ? - 1?j??cjycj?1 ? h:c:
This Hamiltonian describes a one-dimensional chain of orbitals
(Figure 3) with alternating on-site energies +? and ? ?. In
addition, the bonds between the two inequivalent orbitals are
alternating with strengths t+? and t ? ?. The parameter ? controls
the site asymmetry of the model, whereas the parameter
? controls the bonding character.
We have calculated the shift current response of this
tightbinding model, and the results are displayed in Figure 3b. In the
(?, ?) parameter space, the lines ? = 0 and ? = 0 describe systems
with no bond asymmetry and with no on-site energy asymmetry,
respectively. The model has inversion symmetry in either of these
cases, and the shift current vanishes at these lines. Away from
these lines of high symmetry, a change in the sign of either ? or ?
changes the direction of the shift current. This is because
changing the sign of ? applies a bond-centred inversion operation
to the system, while changing the sign of ? applies a site-centred
inversion operation. At a given value of ? and ?, the direction of
the shift current is dictated by the movement of electrons
between sites A and B upon excitation. In ref. 38, explicit formulas
are given for the bandedge shift current response of this
one-dimensional inversion-breaking model.
When t is set to 0, adjacent bonds have hopping integrals of
different sign. In the context of the Slater?Koster tight-binding
scheme, this can be interpreted as the orbitals A and B having
different orbital characters. For example, if the A and B sites were s
and p orbitals respectively, the sp? bonds between them would
have hopping integrals of alternating sign. An increase in the
magnitude of ? increases the magnitude of the shift current
(Figure 3). This suggests that larger bond asymmetries tend to
result in higher shift current responses. On the other hand, the site
asymmetry parameter ? is not well correlated with the shift
current magnitude (Figure 3b). This is consistent with the general
observation made in the previous section that there does not
seem to be a simple relationship between polarisation and shift
Delocalised electronic states
In this section, and in ref. 36 (SMY and AMR, unpublished data),
the tight-binding model of the section ?Bonding character? is
extended by introducing hopping beyond nearest neighbours. We
let the higher-order hopping amplitudes decay exponentially with
distance by parameterising them as e - Rl=? , with ?40 and Rl a
lattice vector. We have found that the magnitude of the shift
vector is enhanced significantly by the presence of higher-order
hopping, particularly near the ? point of the Brillouin zone
(Figure 4). As the higher-order hopping increases, the bandwidth
and band dispersion increase also, particularly at the ? point. As
the wavefunctions therefore become more delocalised with
higher-order hopping, this implies a correlation between
delocalised electronic states and large shift current. Away from ?, the
wavefunctions pick up a phase that varies rapidly in space,
resulting in destructive interference and diminishing the effects of
These observations are supported by our density functional
theory (DFT) calculation of shift current in PbTiO3.22 We find that
large shift current occurs when the states involved in the
transition have a strong bonding or anti-bonding character along
the Ti?O chains collinear with the direction of polarisation. On the
other hand, non-bonding states, such as those comprising only
oxygen or titanium orbitals, have a weaker shift current response.
Heuristically, current-carrying excited states are more likely to be
constructed from a superposition of delocalised orbitals rather
than heavily localised orbitals.
We have therefore identified two factors that contribute to large
shift current response. Promising candidate materials are those
with strong covalent bonds that imply highly delocalised states.
Wavefunction asymmetry, due either to large atomic
displacements from high-symmetry structures or to atomic species with
varied orbital characters, will generally increase the shift current
REVIEW OF EXPERIMENTS
The BPVE in ferroelectric materials has been explored
experimentally for 450 years. In many of the older papers on BPVE
(e.g., refs 39?41), the measured photocurrents were given
different names (optical damage, anomalous PV effect,
photogalvanic effect, above-bandgap optical rectification and resonant
nonlinear susceptibility), and were only re-interpreted as the shift
current42 and referred to as such after the development of the
shift current theory. In ferroelectrics, the application of an external
electric field is not necessary for the generation of photocurrent,
as demonstrated in early work on the prototypical ferroelectric
BaTiO3,43 where the photocurrent was attributed to surface
spacecharge layers. This was followed by studies3,44?47 showing the
presence of photocurrents and photovoltages in many other
ferroelectrics. The authors of refs 3,47 were the first to propose
that the generation of photocarriers in the bulk of a ferroelectric
was the direct consequence of the unique axis of polarisation.
Further developments include the strong dependence of
photocurrent on light polarisation direction in BaTiO3,39 and a giant
BPVE in LiNbO3 (ref. 48) scaling linearly with light intensity.
Following the development of the shift current theory,1,21,35
there appeared experiments that discussed the shift current,
and in particular, its relation to other nonlinear optical effects.
Above-bandgap optical rectification, which was later understood
to be dominated by the shift current,42 was measured in GaAs40
and modelled from the perspective of the nonlinear optical
susceptibility.41 Experiments on semiconductor quantum wells
have distinguished between shift currents and circular
photogalvanic currents.49,50 An estimate of the shift vector was
extracted by comparing a phenomenological model for shift
currents with the experiments on wurtzite semiconductors,51
while a shift current model was used to understand the ultrafast
optical response of GaAs.52 In ferroelectrics, a direct comparison of
ab initio shift current calculations with experiment has provided
support for the shift current theory.22,53 Recently, shift current
effects have been studied in the high-field, low-frequency
regime,16 whereas the effect of Coulombic interactions on the
shift current have also been studied experimentally.17
Shift currents have also been measured in systems other than
bulk ferroelectrics, such as GaAs quantum wells and surfaces.
Due to the Td symmetry of GaAs, only xyz, zxy, yzx, yxz, zyx and yzx
tensor elements are nonzero. Bieler et al.17,54 reported additional
nonzero tensor elements of the shift current in semiconductor
quantum wells because of symmetry reduction of the quantum
well structure. Furthermore, this quantum confinement-induced
BPVE is also observed recently in ferroelectric heterojunctions.
Nakamura et al.19 have measured the photocurrent in
LaFeO3/SrTiO3 heterojunctions with varying LaFeO3 thickness.
This work illustrates the co-existence of the shift current and the
drift current (induced by internal electric field) with opposite
directions. By manipulating the LaFeO3 layer thickness, the
polarisation magnitude can be changed, introducing sign change
of the total photocurrent due to the competing contributions of
the shift current and the drift current. With the decrease of the
system dimensions, the BPVE is also observed in one-dimensional
molecules and organic crystals. Ogden and Gookin18 measured
the BPVE in a prototypical organic polymer with net electric
dipole moment 430 years ago. Recently, Vijayaraghavan et al.55
observed the BPVE of 1,4-diphenylbutadiene crystal with
?-conjugated molecules, providing experimental evidence for the
BPVE in polar organic crystals.
It was found that BPVE is enhanced in nanostructures.56 For
example, (Pb,La)(Zr,Ti)O3 (PLZT) and its solid solutions in a
thinfilm form can have high photocurrent magnitude. Ichiki et al.57
observed higher BPVE in a crystallographically oriented PZT film
than in a randomly oriented film. Qin et al.58 reported that
decreasing film thickness is an effective way to engineer BPVE and
increase the efficiency markedly, which is further supported by the
giant BPVE observed in BaTiO3 thin films.56 Pintilie et al. have
measured the short-circuit photocurrent of Pb(Zr,Ti)O3 (PZT)
polycrystalline layers and epitaxial films under different light
frequencies. The direction of the photocurrent flips when the
polarisation of the film is reversed by applying voltage.59,60
Materials with low bandgaps and high polarisations have
attracted considerable attention in PV material design. There have
been many studies on understanding and optimising the BPVE in
BiFeO3 (BFO)34,61?65, because of its relatively low bandgap
(2.3?2.8 eV), high polarisation (90 ?C/cm2)66 and functional optical
properties.67 In particular, the observed large open-circuit
voltage34,61,62 suggests its use as a potential PV material.
Choi et al.68 reported a diode-like effect in a single-domain BFO
crystal, and the direction of the diode is determined by the
polarisation of the crystal and can be switched by larger external
fields. This ability to switch the BPVE direction in BFO is also
supported by measurements of Ji et al.69 on an epitaxial BFO thin
film. The photocurrent was observed to flow in the opposite direction
of the BFO polarisation, and the current is switchable by switching
the polarisation direction. Recently, [KNbO3]1 ? x [BaNi1/2Nb1/2O3 ? ?]x
(KBNNO) with large bandgap tunability (Eg = 1.1?3.8 eV) and
spontaneous polarisation was found to generate BPVE
photocurrent ~ 50 times larger than that of the ferroelectric PLZT,
suggesting potential applications in PV solar cells.70
As mentioned above, the excellent PV properties of BFO are
likely related to its large polarisation and low bandgap compared
with other ferroelectrics. However, there are many other factors
that affect the BPVE in BFO. Seidel et al.62 observed that domain
walls have a critical role in carrier generation and recombination.
Including more domain walls gives rise to higher open-circuit
photovoltage61 and enhances the photoconductivity of BFO.35 On
the other hand, Alexe et al.71 suggested that shallow defect levels
in the bandgap of BFO are important. Interestingly, in ref. 69,
nonzero BPVE was observed in single-domain BFO perpendicular
to the polarisation direction, showing that for various space
groups, BPVE need not be along the ferroelectric polarisation
The role of defects in the BPVE is also emphasised, showing that
oxygen vacancies are important for the electric-field-induced
switching PV diode effect74,75 and the photoconductivity.76?78
Furthermore, the BPVE and photo-refractive effect in iron-doped
LiNbO3 have been studied for a long time,79?83 demonstrating the
significant role of Fe in enhancing the performance. The
photorefractive effect, or ?optical damage?, is caused by the BPVE
without electrodes, leading to a space-charge field that changes
the refractive index via the electro-optic effect.80 Recently,
Cr-doped BFO (including BFO and BiCrO3 solid solutions) has
attracted great interest. Nechache et al.84 have observed 6% PCE
in Bi2FeCrO6 epitaxial thin films. Moreover, this material shows
strong bandgap tunability (as high as 1 eV) by varying the B-site
cation ordering and ordered domain size, and ?8% PCE was
reported in a multilayer configuration of this material.85 In these
complex materials with dopants and defects, inelastic scattering
may have a role in PV response, and other theories besides the
shift current may be necessary in these cases.7
MODERN MATERIALS DESIGN FOR SHIFT CURRENT
In this section, we apply shift current design principles to a wide
variety of real materials, and study their shift current responses,
calculated within the first-principles formalism introduced in the
section ?Theory of the shift current response?.
Polar order engineering
The starting point of shift current materials design is the breaking
of inversion symmetry, which is essential for the shift current
response. The ferroelectric oxides, with their switchable polar
order, are a natural class of materials to consider.
First, we consider the well-known room temperature
multiferroic material BFO. In the following, the polarisation direction is
taken to be the z direction. The R3c space group of BFO only
allows a few nonzero tensor elements for its BPVE responses,
which can be computed from first principles using the shift
current theory outlined in the section ?Theory of the shift current
response?. To calculate the shift current response, the electronic
structure of BFO must first be computed. Young et al. used the
DFT+U method along with a semi-core pseudopotential for Fe to
improve the description of the 3d electrons and correctly describe
the antiferromagnetic physics in this material, giving Eg = 2.58 eV.
Shown in Figure 5c,b are the yyY components of the Glass
coefficient and shift current response tensor ? as a function of
light frequency.24 The response occurs at photon energies higher
than the bandgap of the bulk. As shown in the spectra, the
experimentally measured shift current and Glass coefficient
perpendicular to the polarisation63 are in good agreement
with calculations. Current in directions perpendicular to the
polarisation should not contain contributions directly generated
by the polarisation, such as the depolarisation field photocurrent.
Therefore, these results establish that the shift current mechanism
has a significant role in the BPVE of BFO.
Besides explaining the BPVE in BFO, the first-principles
approach to computing shift current has also successfully
explained the BPVE in the prototypical ferroelectrics BaTiO3
(BTO) and PbTiO3 (PTO), and provides further guidelines for
designing materials with large BPVE. Shown in Figure 6 is
the comparison between experimentally measured I(?)39 and
computed shift current response spectrum for BTO.22 The shaded
region indicates the experimental error bars using parameters
from the original experiment. The calculated short-circuit
photocurrents agree with the measurements very well in terms of both
direction and magnitude.
Although materials that are almost non-polar tend to have small
shift current responses (see the discussion of hybrid perovskites in
the section ?Wavefunction engineering?), a larger polarisation does
not always lead to larger shift currents. To understand the
relationship of shift vector and shift current to polarisation, these
quantities are calculated while manually moving the atoms to vary
the polarisation magnitude. As illustrated in Figure 2a, the
dependence of shift vectors on polarisation can be nonlinear.
Even the direction of the shift current may not be related to the
direction of the bulk polarisation, and the current direction can
change as a function of light frequency (Figure 6).
These observations suggest that the material polarisation does
not determine the shift current magnitude and direction. Instead,
there are other factors related to the electronic structure of the
materials which strongly affect shift current magnitudes. These
will be analysed in the following sections.
Electronic structure engineering
In this section, we examine electronic structure design principles
for high shift current responses: (
) engineering delocalised orbital
characters using s and p orbitals; (
) the need for an appropriate
bandgap in the visible light region; (
) attaining high density of
states using materials with low-dimensional components.
Wavefunction engineering. The tight-binding results of the
section ?Delocalised electronic states? suggest that delocalised
electronic states are beneficial for large shift currents, as they are
more likely to support current-carrying excited states. In PTO, DFT
calculations22 show that states with delocalised character tend
to give high shift current responses (Figure 2b), whereas
nonbonding or strongly localised states tend to give low shift current.
Transitions involving bands with strong contributions from
transition metals with localised d orbitals tend to have small shift
A family of materials with strong s and p orbital characters in
the valence and conduction bands is the organometal-halide
perovskites (OMHPs). They have attracted huge interest due to
their rapidly increasing PCE. Appropriate bandgaps within the
visible light range,86 long carrier lifetime,87 and strong light
absorption88 make these materials promising for PV solar cells. To
illustrate the above ideas about wavefunction delocalisation, we
consider the most studied OMHP?CH3NH3PbI3 (MAPbI3), which
has a dipolar molecular cation at each A-site.89 We consider
configurations of MAPbI3 that break inversion symmetry and
thereby allow BPVE.
The valence bands MAPbI3 are primarily of Pb 6s and I 5p
characters,90 which is reminiscent of the simplified tight-binding
model introduced in the section ?Bonding character?. The shift
current response in MAPbI3 has been computed,27 including
spin?orbit coupling,90?92 in two types of structures: one with all
the molecular dipole moments aligned (M1) and another in which
all the molecular dipole moments nearly cancel with neighboruing
molecules (M2). The nearly non-polar M2 structure has a much
smaller shift current response than M1 (Figure 7). The importance
of the strongly delocalised states involved in the photo-transitions
in MAPbI3 is demonstrated by the fact that MAPbI3 has a shift
current magnitude comparable to that of BFO, despite having a
much smaller polarisation (? 5 ?C/cm2 in the z direction) than BFO
(? 100 ?C/cm2).
The delocalised nature of the conduction and valance band
states in MAPbI3 can be further increased by Cl doping. It was
shown that doping Cl at the equatorial positions increases the
shift current of the M1 structure, giving an approximately three
times larger shift current response than BFO. The equatorial Cl
doping results in structural distortions and hybridisation of the
conduction band Pb 6px/y orbitals with the halide p orbitals,
leaving the Pb 6pz orbitals as the dominant orbital character of the
conduction band. As pz is more delocalised in the direction of
current (z) than px/y, this results in an enhanced shift current.
Experimentally, Cl doping enhances the ordinary PV effect in
MAPbI3 greatly, although the origin of this effect is still under
Another materials design strategy in the OMHPs is the
substitution of A- and B-site members of the perovskite structure.
By introducing Ge on the B-site and having both Cs and organic
molecules as A-site in OMHPs, the resulting materials show
spontaneous polarisation as a consequence of the Ge2+ lone pair,
and they exhibit large second-harmonic generation.96 Such a
strategy might also hold promise for the shift current response,
which, like second-harmonic generation, is a nonlinear optical
Bandgap engineering. It is desirable for the bandgap of a shift
current material to lie in the visible spectrum, if it is to be used in
solar power light-harvesting devices. In this section, we focus on
ways to control the onset of light absorption and shift
current generation, using the recently synthesised low bandgap
ferroelectric material (K,Ba)(Ni,Nb)O3 ? ? (KBNNO)70,97,98 as an
One method of controlling the bandgap is by introducing
site-specific aliovalent substitutions99 and vacancies into the
parent material KNbO3.100,101 Oxygen vacancies may have both
positive and negative effects on the functional properties of
materials. For example, oxygen vacancies are one of the most
important providers of n-type carriers, making them beneficial for
n-type semiconductors, but O vacancies remove p-type carriers,
making them detrimental for p-type semiconductors. For PV
and photocatalytic materials, oxygen vacancies are generally
detrimental, because they can enhance the charge recombination
rate and reduce the mean free path of the charge carriers.
Nevertheless, oxygen vacancies can also be incorporated
purposefully to reduce conventional mobility (which enhances
Voc, equation (
)), to compensate charge, and to induce desired
structural changes, as we show here in KBNNO.
In this material, the substitutional defects involve Ni2+ ions
replacing Nb5+ ions, Ba2+ ions replacing K+ ions and charge
compensation by O vacancies. We consider two structural
configurations of (2/3)KNbO3-(1/3)Ba(Ni1/2Nb1/2)O11/4 with two
Ni2+ substitutions each. In one configuration (C1 configuration),
the two Ni ions are distributed along the body diagonal direction
with the O vacancy adjacent to only one Ni2+ ion (NiO6 and NiO5),
whereas in the other (C2 configuration), the two Ni ions are
aligned along the Cartesian z axis with one O vacancy in between,
leaving both Ni2+ an environment of O5 (two NiO5).
Compared with the C2 configuration, the C1 configuration
exhibits a larger Glass coefficient and a lower onset photon energy
(Figure 8). These two arrangements have very different electronic
structure properties. In the C1 arrangement, Nb and Ni
orbitaldominated gap states are induced, leading to a smaller bandgap.
In the C2 arrangement, these states move deeper into the valence
band, and O 2p orbitals dominate the top of the valence band.
This difference in the electronic properties is ascribed to their
different structural properties. The larger lattice asymmetry
corresponding to the NiO5 complex induces a much bigger
splitting between the dz2 and dx2 - y2 orbitals and a much lower
energy of the dz2 orbital than those for the NiO6 complex. As a
result, gap states are induced for the C1 arrangement because it
also contains NiO6 complexes, but in the C2 arrangement these
states do not contribute to the bandedge electronic transitions, as
only NiO5 complexes are involved. Therefore, by moving O
vacancies away from Ni, the shift current is significantly enhanced
and this effect is accomplished through the change of structural
and electronic orbital character properties.
Strain is another method of controlling the bandgap. It is widely
applied via epitaxial growth of thin films in order to achieve
desired functional properties, as it can substantially affect the
octahedral cage distortions, rotate the polarisation and change
the electronic structure of perovskites.102?104 We consider
applying in-plane compressive strain to the (2/3)KNbO3-(1/3)
Ba(Ni1/2Nb1/2)O11/4 solid solution. The configuration we adopt
here includes two Ni atoms at the body diagonal positions (C1).
Our results show that compressive strains increase the shift
current onset photon energy (Figure 8). A detailed electronic
structure and wavefunction analysis indicates that the applied
compressive strains drive the original dz2 orbital-dominated gap
states to shift downwards in energy and finally merge into the
valence band.28 This gives rise to a larger band gap and also
reduces the magnitude of the shift current response.
To make use of the beneficial effect of in-plane compressive
strains, materials must have delocalised electronic orbitals that can
be shifted to bandedges by these strains.
Apart from defects and strain, other methods are available for
tuning the properties of KBNNO. Recently, manipulation of local
polar order (potential gradients) has been proposed as a way to
control shift current response in solid solutions in this material.30
Density of states engineering. Another approach for increasing
shift currents is designing materials with large density of states
near the bandedges.38 The shift current responses at frequencies
close to the bandgap energy are often the most relevant for large
bandgap semiconductors, as they fall in the visible light spectrum.
Furthermore, first-principles calculations show that the shift vector
is often large near the bandgap. One-dimensional structures have
increased joint densities of states near the bandgap energy,
magnifying the shift current at this energy. This suggests that
low-dimensional materials such as chain- and layer-like structures
may be promising materials with large BPVE.
The alkali-metal chalcogenides are a class of materials with this
property. Many members of the class, such as KPSe6, K2P2Se6,
LiAsSe2, LiAsS2 and NaAsSe2 show bandgaps in visible
light region.105 It was also found that some of them show
spontaneous polarisation and strong second-harmonic generation
responses.105,106 We consider the shift current responses of
LiAsSe2, LiAsS2 and NaAsSe2. All three materials have been
synthesised in polar monoclinic space group, with Cc for LiAsSe2
and LiAsS2, and Pc for NaAsSe2. Figure 9 shows that these three
compounds have one-dimensional As-X chain (X = Se, S) motifs.
The orbitals of the states near the bandgap are mainly s and p
orbitals coming from P, As or Se, with a strong covalent character.
Shown in Figure 9 is the shift current response spectrum of
LiAsSe2, with the dashed line indicating the shift current response
of BFO (with a magnitude of ? ?3 ? 10 ? 4 (A/m2)/(W/m2)). Due to
the well-known issue of underestimation of band gaps in DFT, the
LiAsSe2 spectrum has been shifted to have the experimental
bandgap (1.11 eV).24 The zzZ component of LiAsSe2 shift current
shows broad and high magnitude, displaying around 50 times
larger response than BFO, making it a potential candidate for solar
cell materials. LiAsS2 shows similar spectrum line shape to LiAsSe2
but with smaller magnitude. This may be because the bonds
between As and S are not as covalent as between As and Se.
These results for the alkali-metal chalcogenides suggest that
materials with a strong degree of anisotropy and one-dimensional
conducting channels can potentially have large shift current
CONCLUSIONS AND OUTLOOK
In this review, we have examined the factors contributing to the
shift current response arising from exciting a current-carrying
coherent state. The breaking of inversion symmetry is necessary,
but there are many other electronic structure factors affecting the
shift current magnitude. We have seen that it is desirable to have a
bandgap in the visible spectrum, as well as a large density of
states at the bandedges to efficiently capture incident light.
Once excited, the shift current carriers rapidly propagate to the
electrodes via coherent evolution of the current-carrying state. For
this purpose, it is beneficial to have highly delocalised conduction
or valence band states, to aid in the coherent evolution of the
carriers from the bulk of the material to the electrodes. There are
many specific materials design approaches that can be used to
achieve these requirements, such as substitutional doping, the
introduction of vacancies, the application of strain and the use of
low-dimensional materials. In addition, it has recently been
suggested that the tuning of topological phase transitions29 can
enhance the shift current response.
A remaining open question is the calculation of the PCE of a
shift current material. The formalism developed in the section
?Theory of the shift current response? is useful for calculating the
short-circuit current, but the open-circuit voltage, one of the
important factors contributing to the PCE, is less amenable to
calculation using periodic boundary conditions. Furthermore, the
open-circuit voltage depends on factors external to the shift
current theory, such as the total conductivity, which is not
generally a bulk quantity. A related issue is the effect of electrodes
on the measured photocurrent. Careful selection of electrode
materials has improved PCE in the linear response regime, and it is
likely that a similar effect exists for shift current materials. The
study of the temporal shift current response beyond the
continuous wave limit,53,107 the topological aspects of nonlinear
optics29,108 and the effect of excitons109 have also become
interesting directions of research in recent years. It is expected
that shift current is preserved in the presence of excitons.109
In summary, the nascent applications of polar materials in PV
applications call for a clear understanding of the origin of the
BVPE. Understanding and quantifying the interplay between bulk
photocurrent, material compositions, nanostructures, strains and
structural defects will help to realise the true potential of BVPE.
Distinguishing the truly bulk effect from the interfacial effect in
ferroelectrics will inspire device engineering guidelines to apply
both mechanisms for solar energy conversion. The shift current
theory provides a valuable tool to discover, design and optimise
materials for BVPE-based devices with first-principles methods. We
believe that with concerted experimental and theoretical efforts,
the BVPE will find its applications in the PV industry.
L.Z.T., F.Z., F.W. and A.M.R. were supported by the US Department of Energy (DOE),
under grant DE-FG02-07ER46431. S.M.Y. was supported by a National Research
Council Research Associateship Award at the US Naval Research Laboratory. S.L.
acknowledges the support from the Carnegie Institution for Science. We
acknowledge computational support from the NERSC of the DOE.
The authors declare no conflict of interest.
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