Introduction

Innovative strategies have recently been introduced into photovoltaics for efficient solar energy conversion1,2,3,4. To absorb light over a broad spectral range and convert the incident energy into electricity, intermediate band (IB) solar cells are designed in which the IB provides electronic states that are partially filled with electrons within the bandgap of a host semiconductor. The IB acts as a stepping stone to generate an electron–hole pair under illumination with below bandgap energy, thereby delivering a large photocurrent5,6,7. In spite of extensive studies on IB solar cells, the present devices suffer from a reduction in open-circuit voltage compared with the reference cells without IBs8.

The photovoltaic (PV) effect in polar materials9,10,11 has allowed researchers to develop novel methods of light energy conversion, generating voltages beyond the bandgap limit of semiconductor p–n junctions12, 13. Because ferroelectrics have multiple polar states14 that can be selectively stabilized by electric and/or stress fields and exhibit a photoresponse arising from spatial inversion symmetry breaking15, 16, advanced functionalities based on the coupling between the PV effect and the switchable polarization17, 18 have stimulated renewed interest in photoferroelectrics19, 20.

The ferroelectric PV effect has been extensively studied for LiNbO3 9, 21, 22, BaTiO3 23,24,25,26,27, PbTiO3-based perovskites28,29,30 and BiFeO3 (BFO)12, 13, 31, 32. Recent studies have demonstrated that control of domain architecture can enhance the photoresponse due to the domain-wall-driven effect12, 27. However, these conventional ferroelectrics suffer from poor absorption of visible light because of their bandgap energy (E g) of ∼3–4 eV33,34,35. Even for BFO with its relatively small E g of 2.7 eV36, 37, photons with wavelengths of λ>460 nm, constituting >80 % of the sunlight, cannot be utilized, raising the question of how to activate the PV effect under visible light.

In ferroelectric oxides, their electronic structure with a wide bandgap is characterized by an O-2p-derived valence band (VB) and a transition metal (TM)-d-derived conduction band (CB) that are accompanied by the orbital interactions of cations and oxygen atoms38, 39. The TM-d and O-2p hybridization is enhanced upon atomic displacements40, and the hybridization of Pb- or Bi-6s(p) with O-2p induces strong covalent bonding associated with polar lattice distortions14, 41. Both of these cation–oxygen interactions favour coherent off-centre displacements of the cations in their oxygen polyhedra, delivering substantially large spontaneous polarization (P s)42.

Considerable effort has been devoted to narrowing the bandgap of ferroelectrics by rational modification of their compositions. Bandgap tuning has produced narrow-bandgap materials such as KBiFe2O5 43 with FeO4 tetrahedra, site-specific LaCoO3-substituted Bi4Ti3O12 44, heavily Co- and Fe-doped Bi3.25La0.75Ti3O12 45, KNbO3-based solid solution of [KNbO3]1−x [BaNi0.5Nb0.5O3−δ ] x 46, and cation-ordered Bi(Fe,Cr)O3 47, exhibiting enhanced PV responses under visible light. This bandgap tuning is based on a solid solution or structural formation composed of wide-gap ferroelectrics and non-polar counterparts and is, in principle, accompanied by a substantial reduction in P s. Meanwhile, the strongly distorted polar lattice yields a robust photoresponse15, 16, called the bulk PV (BPV) effect9,10,11, and the high photovoltages relies on the large magnitude of P s. The tradeoff between narrow gap and large polarization motivates us to explore an alternative route to the material design of photoferroelectrics that exhibit a response to low-energy light without sacrificing P s.

Here, we report an approach, ‘gap-state’ engineering, to produce visible-light-active ferroelectrics. Our approach is based on the creation of defect states within the bandgap, i.e., gap states, half of which are filled with electrons. Under illumination with below-bandgap energy, photon absorption via the half-filled states enables the empty states to receive electrons from the VB and the filled states to supply them to the CB, generating electron–hole pairs. We choose BFO as a model material to investigate the impact on the BPV effect. Our theoretical and experimental investigations demonstrate that the gap states enhance both photocurrents and photovoltages over a broad spectral range. This approach opens a promising route to the development of visible-light-active ferroelectrics with little or no loss of P s.

Results

Electronic structure calculations

Figure 1 shows the schematic band structures of the TM-doped BFO. The E g of BFO is calculated to be 2.8 eV, consistent with experiments (2.7 eV36, 37). The TM doping does not change significantly in either the E g or in the electronic character of the VB maximum (VBM) constructed by the O-2p orbitals and the CB minimum (CBM) formed by the Fe-3d orbitals (Supplementary Fig. 1).

Fig. 1
figure 1

Wave functions and schematic electronic structures of transition metal (TM=Cr, Mn, Co, Ni and Cu)-doped BFO obtained from DFT calculations. The bandgap (E g) of BiFeO3 (BFO) is calculated to be 2.8 eV. The valence band maximum (VBM) is primarily formed by O-2p, and the conduction band minimum (CBM) is formed by Fe-3d. Filled and open rectangles indicate electron-filled and electron-unoccupied states, respectively. The e states of Cr, Mn and Co are half-filled with electrons, while the e state of Cu is empty. The blue arrows designate spin-polarized electrons in the gap states. Except for TM=Ni, the gap states are derived from the 3d orbitals of TMs hybridized with the surrounding O-2p. For TM=Ni, the 3d-derived filled states are present below the VBM, and the unoccupied O-2p state appears just above the VBM, showing Ni2+ with a ligand hole in the O-2p state (see text). The wave functions of each gap state are visualized. The wave functions coloured in blue feature orbitals filled with electrons, and those in yellow present empty orbitals, where the iso-surface level remains constant for displaying the wave functions. The 3d orbitals of TMs are hybridized with the O-2p of the surroundings in different manners reflecting their interactions. The 1e state of TM=Cr and Co shows π * bonding having d xy and d x2−y2 characters, while the 2e state of TM=Mn and Cu exhibits σ* bonding featuring d yz and d zx characters

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According to group theory, the 3d orbitals of the TMs in rhombohedral BFO (C 3v symmetry) are split into a 1, 1e and 2e, where 1e and 2e denote lower-lying and higher-lying e states, respectively. As shown in Fig. 1, the TMs of Cr, Mn, Co and Cu produce e states within the bandgap. Especially, Cr, Mn and Co yield the gap states, half of which are filled with electrons (half-filled). Relative to the VBM, the gap state is located at 1.9 eV for Cr and 0.9 eV for Mn, while that of Co is in the vicinity of the VBM.

Figure 2 displays the detailed electronic structure of Mn (6%)-doped BFO with the optimized structure, the density of states and the band structure. A partial density of states analysis reveals that the gap state arises from the hybridized orbital of the Mn-2e and the adjacent O-2p with a significant contribution of Fe-3d, as shown in its wave function (Fig. 1). The 2e state is composed of the d yz - and d zx -derived orbitals (Fig. 2c) and their spin-polarized electron occupancies are in the range of 0.4–0.6 over the entire Brillouin zone. We can therefore regard the 2e as a half-filled state (see Supplementary Note 2).

Fig. 2
figure 2

Crystal and electronic structures of Mn-doped BFO. a Optimized crystal structure of Mn-doped BFO [Bi16(Fe15Mn)O48] in rhombohedral R3 symmetry, b total density of states (DOS) and partial DOS (PDOS) of Mn-3d, Fe-3d and O-2p and c electronic band structure. In b, the nearest neighbour Fe and O atoms of Mn are selected, and majority- and minority-spin bands are described in the right (↑) and left (↓) panels, respectively. The Mn-3d orbitals are split into up-spin a 1, 1e and 2e and down-spin a 1, 1e and 2e. Taking the d 4 electron configuration of Mn3+ into account, we can regard it as up-spin a 1 1, 1e 2 and 2e 1 and down-spin a 1 0, 1e 0 and 2e 0. In c, red and blue lines represent majority- and minority-spin states, respectively, and the blue arrow indicates a spin-polarized electron in the gap state, exhibiting that Mn provides the half-filled gap (2e) state. For the 2e state, the d yz - and d zx -derived orbitals are degenerate at the Γ and Z points in the Brillouin zone, while the degeneracy is lifted once the k-point is away from these high-symmetry points; its energy difference is 0.03 eV at the L point

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We found that Ni on the Fe site has a d 8 electron configuration, representing the Ni2+ valence state. The d-derived state of Ni2+ does not construct a gap state, while an unoccupied O-2p state appears just above the VBM. This result indicates that one hole is transferred from Ni to the ligand oxygen in the NiO6 octahedron, as reported in ref. 48. This electronic state is expressed as Ni2+ Ḻ(d8 Ḻ), where Ḻ denotes a ligand hole.

Under illumination with hv (photon energy) >E g, photons pump electrons from the VB to the CB and generate electron–hole pairs that are spatially separated in the polar lattice. The optical transition associated with this charge separation delivers a PV current. Given that electronic states within the bandgap, so-called ‘gap’ states, are present, the absorption of light at hv<E g is capable of inducing a PV response. For gap states filled with electrons, pumping electrons from the gap states to the CB injects carriers leaving behind empty traps, and the continuous illumination yields a PV current arising from a sequential trapping and detrapping of photogenerated electrons21, 22, 49. When gap states are empty, pumping electrons from the VB to the gap states creates holes, and this illumination also brings a PV current via trapping and detrapping of photogenerated holes26.

Provided that the gap states are partially filled with electrons, we expect that the absorption of two sub-bandgap photons generates electron–hole pairs by pumping electrons from the VB to the CB via the gap states, as is seen for IB solar cells3, 8. This two-photon absorption has a high probability when its state is half-filled50. Moreover, its energy level is preferred in or near the middle of the bandgap. Compared with the filled or empty gap states, where the majority photocarrier is either electron or hole, respectively, we anticipate that the half-filled mid-gap state acts as a scaffold for a robust PV response under illumination with below-bandgap light.

The material design strategy described above leads us to hypothesize that the TMs of Cr and Mn are promising candidates for enhancing the PV effect. Because of a small solubility limit of Cr (several percentage51), we think that Mn is attractive as the TM dopant for two reasons: there is practically no solubility limit, and its doping does not deteriorate P s up to 50%52. Here, we choose Mn as a dopant for testing the hypothesis of the half-filled gap state and, for comparison, Ni as an example of how the empty state plays a role in the BPV effect.

Photocurrent properties

In Fig. 3a, we illustrate the single-domain (SD) structure associated with the pseudocubic [hkl] directions showing the crystallographic orientations (also see Supplementary Fig. 2). For a precise description of the 4° vicinal angle from the pseudocubic axes owing to the miscut of the substrate, we employ the lab-coordinate (xyz) system exhibiting the PV measurement configuration (Fig. 3b). Figure 3c presents the J–V bias properties in the y direction under illumination (hν = 2.4 eV) at ω = 90° (ω denotes light polarization angle). The Mn-BFO film shows a V y of −3.1 V and a J y of −15 μA cm−2 that are much higher than those of the BFO film (V y  = −0.6 V, J y  = −1.3 μA cm−2).

Fig. 3
figure 3

Measurement configuration and photovoltaic (PV) properties of the Mn-BFO film. a Schematic of the single-domain (SD) structure associated with the pseudocubic [hkl] directions exhibiting the crystallographic orientations with respect to the lab-coordinate (xyz) system. The x axis lies along \([1\bar 10]\), and the y and z axes are 4° away from [110] and [001], respectively. b PV measurement configuration in which polarized light with photon energy hv propagates along the z axis and is incident on the sample surface. The incident light has a polarization angle (ω) from the y axis in the xy plane. The short-circuit current density (J sc) and open-circuit voltage (V oc) along the m direction are expressed as J m and V m , respectively. A positive J m indicates that the photocurrent flows in the m direction. The bias voltage (V bias) at which the current density (J) becomes zero is denoted by −V m . c Current density–bias voltage (J–V bias) properties along the y direction under dark and illuminated (hv=2.4 eV) conditions, where the polarization angle ω is aligned so that the PV response becomes maximum for both the BFO and Mn-BFO (Mn 5%) films. Light polarization angle ω dependences of short-circuit currents d J y and e J −x in the Mn-BFO film

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In Fig. 3d, e, we exhibit the J y and J −x data, respectively, as a function of ω at hν = 2.4 eV for the Mn-BFO film. We found that J −x (Fig. 3e) shows a sinusoidal dependence on ω without offset, while J y (Fig. 3d) has an offset of \({J_{y,{\rm{off}}.}}\) in addition to a sinusoidal oscillation with an amplitude\({J_{y,{\rm{amp}}.}}\)(the data of the BFO film are presented in Supplementary Fig. 4c, d). Even at hν=1.9 eV, the Mn-BFO film clearly shows similar sinusoidal behaviour in J y and J −x (Supplementary Fig. 5c, d, whereas we cannot observe a PV response for the BFO film.

Photon energy dependence

In Fig. 4a, b, we show the hv dependences of |V y | and |J y |, respectively. Under illumination at hν=3.1 eV, the BFO film generates a |V y | of 4.3 V. However, |V y | decreases to 0.6 V at hν=2.4 eV and below the detection limit at hν=1.9 eV (Fig. 4a). A similar reduction in |J y | is also detected in the low-hv range (Fig. 4b). We note that both the |V y | and |J y | of the Mn-BFO film are much larger than those of the BFO film at hv above E g in addition to below E g. The Mn-BFO film exhibits a |V y | exceeding the bandgap voltage under illumination at hν=2.4 eV. The Mn-BFO film clearly exhibits a substantial PV response at 1.9 eV and no detectable signal at 1.5 eV (Supplementary Fig. 11).The overall tendency of the PV response with respect to hv agrees qualitatively with the results of the absorption spectra (Supplementary Fig. 3). (An estimation procedure of α is presented in Supplementary Note 4 and Supplementary Fig. 10.)

Fig. 4
figure 4

Photogenerated current and voltage as a function of photon energy (hv). a |V y | and b |J y |, where the polarization angle ω is aligned so that the PV response becomes maximum: ω = 90 ° in the BFO film (regardless of hv); ω = 0 ° at hν = 3.1 eV, and ω = 90 ° at hν = 2.4 eV and 1.9 eV in the Mn-BFO (Mn 5 %) film. The horizontal line in b indicates the detection limit in our measurements. The J–V bias properties of the films of BFO (hν=3.1 eV) and Mn-BFO (hν=3.1 eV, 1.9 eV and 1.5 eV) in the y direction are shown in Supplementary Fig. 6a, b 11, respectively

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The Ni-BFO film displays a relatively high |J y | whereas the |V y | is lower than 0.1 V at 2.4 eV (Supplementary Fig. 8). The small |V y | is attributed to its high conductivity (Supplementary Table 3), and the resultant photogenerated power |J y ×V y |/4 becomes much smaller.We note that its high conductivity and density functional theory (DFT) calculation results of Ni-doped BFO confirm Ni2+ Ḻ(d8 Ḻ) state in the Ni-BFO film (see Supplementary Note 3 and Supplementary Fig. 9).

Discussion

We estimate the BPV tensor elements (β 15, β 22, β 31 and β 33) from the ω dependences of J y and J −x by taking into account the 4° deviation of the measurement directions from the pseudocubic axes, the details of which are described in ref. 32. In Fig. 5a, we present the BPV tensor elements at hν=2.4 eV obtained by fitting the experimental data with the analytic equations. We found that the absolute values of the Mn-BFO film are 2–10 times as large as those of the BFO film. This result clearly demonstrates that the Mn doping dramatically enhances the BPV effect under illumination with below-bandgap light. The apparent ω-dependent photocurrents of the Mn-BFO film at hν=1.9 eV (Supplementary Fig. 5c, d) enable us to obtain the BPV tensor elements (Supplementary Fig. 7).

Fig. 5
figure 5

Bulk photovoltaic (BPV) tensor elements (β ij ). Under illumination at a hν=2.4 eV and b hν=3.1 eV estimated from light polarization angle ω dependences of short-circuit currents. The data of the BFO film are shown in Supplementary Fig. 4 and that of the Mn-BFO film are exhibited in Supplementary Fig. 5

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Figure 5b exhibits the BPV tensor elements at hν=3.1 eV in a similar manner. The Mn doping decreases |β 15| and |β 31| but increases |β 33| markedly. This result indicates that the larger values of |V y | and |J y | at hν=3.1 eV achieved by the Mn doping (Fig. 4a, b) originate from the enhanced β 33. The BPV tensor elements are listed in Supplementary Table 1.

Here, we discuss why the Mn doping markedly enhances the BPV effect at hν<E g. The BFO film shows the BPV effect at hν=3.1 eV because photons with hν≥E g (2.7 eV) can generate electron–hole pairs that are subsequently separated in the polar lattice. A small but significant photoresponse of the BFO film at hν=2.4 eV is attributed to a dipole-forbidden p-d charge transfer transition53.

The robust response of the Mn-BFO film at hν<E g enables us to consider that the optical transitions via the half-filled gap state enhances the BPV effect. The Mn-BFO film at hν=2.4 eV exhibits the comparable or large BPV tensor elements compared with the BFO film at hν=3.1 eV (hν>E g), supposing that the PV effect observed at hν=2.4 eV stems from electron–hole pair generation. The details of the photogenerated carriers are described in Supplementary Note 5. In principle, visible light with hv higher than the sub-bandgap energies can create electron–hole pairs via the gap state by the following two-photon absorption. A sub-bandgap transition pumps an electron from the gap state to the CB (a charge transfer from Mn to its adjacent Fe) and does so from the VB to the gap state (a charge transfer from O to Mn), where these processes are accompanied by the changes in the valence state of Mn. Even when the optical transitions occur successively, electron–hole pairs are generated, because once an electron or hole is pumped the carrier is directed away from Mn in the polar lattice.

The Mn-BFO film exhibits an apparent PV response at hν=1.9 eV but no detectable short-circuit photocurrent at hν=1.5 eV (Supplementary Fig. 11). These results combined with the optical transition processes (Supplementary Note 5 and Supplementary Fig. 12) suggest that the majority photocarrier at hν=1.9 eV is electron–hole pair. In contrast, we found that photogenerated holes can induce the BPV effect in the Ni-BFO film at hv=1.9 eV (Supplementary Fig. 8). The Ni doping provides the empty state in the vicinity of the VBM. This shallow state gives rise to the high conductivities under dark and illumination (Supplementary Table 3), leading to the high currents with sacrificing the voltages. The much higher photogenerated power of the Mn-BFO film compared with the Ni-BFO film shows that the half-filled gap state is effective for the BPV effect.

Next, we discuss the origin of the enhanced β in Mn-BFO at hν<E g. The BPV tensor element β ij can be written as β ij =αG ij 21, where α denotes the absorption coefficient and G ij indicates the Glass coefficient determined by the shift vector representing the average distance travelled by the coherent carriers during their lifetimes15. Though anisotropy in α 54 may cause variations in the photocurrents, the experimental data of the ω-dependent J y and J −x are well fitted by the analytical equations adopting an isotropic α, showing that the anisotropy in α does not have a significant influence on our PV results.

One possible origin of the enhancement in β by the Mn doping is an increase in α. We found, however, that the Mn doping yields only a 22% increase in α at hν = 2.4 eV (Supplementary Fig. 3) while the β of the Mn-BFO film is 2–10 times as large as that of the BFO film, demonstrating that the enhanced β cannot be explained solely by its slightly larger α.

We now estimate G ij representing photogeneration strength in the BPV effect. The one-photon transition of the VB to CB has a contribution of β ij,1 (=α 1 G ij,1) to the BPV effect, as observed for the BFO film. The two-photon absorption via the gap (2e) state delivers an additional β ij,2=α 2 G ij,2 for the Mn-BFO film, where α 1 and α 2 denote their respective absorption coefficients. Because the Mn doping does not change the fundamental feature of the VB and the CB, β ij representing the net BPV response of Mn-BFO is expressed as β ij =β ij,1+β ij,2. As a result, G ij,2 arising from the Mn-derived gap state can be expressed as

$${G_{ij,2}} = \frac{{{\beta _{ij,2}}}}{{{\alpha _2}}}{\rm{ = }}\frac{1}{{{\alpha _2}}}\left( {\beta _{ij}^{{\rm{Mn}} - {\rm{BFO}}} - \beta _{ij}^{{\rm{BFO}}}} \right),$$
(1)

where \(\beta _{ij}^{{\rm{BFO}}}\) and \(\beta _{ij}^{{\rm{Mn}} - {\rm{BFO}}}\) are their respective experimental β ij values.

Using the relations of α 1 = α BFO and α 1 + α 2 ≈ α Mn−BFO and the experimental result of α Mn−BFO=1.22α BFO (hν=2.4 eV, see Supplementary Fig. 3), we obtain α 2=0.22α BFO. From the experimentally determined \(\beta _{ij}^{{\rm{BFO}}}\) and \(\beta _{ij}^{{\rm{Mn}} - {\rm{BFO}}}\) values (Fig. 5a), \({G_{ij,1}}\left( {{\rm{ = }}\frac{{{\beta _{ij,1}}}}{{{\alpha _1}}}{\rm{ = }}\frac{{\beta _{ij}^{{\rm{BFO}}}}}{{{\alpha ^{{\rm{BFO}}}}}}} \right)\) and G ij,2 at hν=2.4 eV are estimated as displayed in Fig. 6a, b, respectively. The G ij,1 and G ij,2 values at hν=3.1 eV, 2.4 eV and 1.9 eV are summarized in Supplementary Table 2, where the data at 3.1 eV and 1.9 eV are estimated in a similar manner at 2.4 eV. The above estimation reveals that |G ij,2| is much larger than |G ij,1|: |G 31,2| is ∼50 times as large as |G 31,1| at hν=2.4 eV. These results lead to the conclusion that the major origin of the enhanced PV response achieved by the Mn doping is not the increase in α but the large Glass coefficients.

Fig. 6
figure 6

Glass coefficients of G ij,1 and G ij,2 at hν=2.4 eV. a G ij,1 represents the photogenerated strength arising from the one-photon optical transition of the VB to the CB in the BFO film, while b G ij,2 reflects what is attributed to the charge transfer transition via the Mn-3d-derived gap (2e) state

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Finally, we address how the half-filled gap states in ferroelectrics are different from IBs in semiconductor solar cells. For bulk IB solar cells, such as V2In14S24 55 and ZnTe:O[7], extended IBs are situated in or near the middle of the bandgap. The IBs act as a stepping stone for generating electron–hole pairs by absorbing sub-bandgap photons and thereby photocurrents are enhanced by an increase in α at hν<E g 8. The crucial problem to be overcome is a reduction in V oc with respect to the reference cells without IBs at room temperature8, where the Shockley–Read–Hall (SRH) recombination56 influences their V oc to some extent. In contrast, the gap-state engineering in ferroelectrics can not only increase α but also enhance V oc. In fact, the Mn doping leads to larger values of both V oc and J sc (Fig. 4). Although the SRH recombination is suggested to reduce the carrier lifetimes, the gap state increases the Glass coefficients by over one order of magnitude at hν=2.4 eV (hν<E g). This experimental fact shows that the average drift velocity of photogenerated electrons and holes is higher in the presence of the gap state, and thereby delivering the robust BPV effect.

Our experimental and theoretical investigations demonstrate that the mid-gap half-filled state acts as a scaffold for the BPV effect over a broad hv range. Gap-state engineering is revealed to enhance not only photocurrents but also photovoltages, and therefore providing a promising route to the material design of visible-light-active photoferroelectrics.

Methods

DFT calculations

First-principles calculations based on DFT57 were performed within the generalized gradient approximation (GGA)58 in the projector-augmented-wave method59, as implemented in the Vienna ab initio simulation package60. We employed the gradient corrected exchange–correlation functional of the PBEsol (Perdew–Burke–Ernzerhof revised for solids)61 for structural optimization. To obtain insight into the role of the defect states arising from TM elements, accurate information on bandgaps is an essential foundation for investigating their influence on the bulk PV effect. We therefore adopted the density functional MBJLDA (modified Becke–Johnson exchange plus local density approximation)62 to calculate the electronic band structures and density of states. Within the simplified GGA+U approach63, on-site Coulomb interaction parameters of U−J=4 eV were added to all the d elements of the TMs, including Fe. The Monkhorst–Pack k-point mesh of 3 × 3 × 3 was adopted for the supercell of Bi16 (Fe15TM)O48 in rhombohedral R3 symmetry (TM=Cr, Mn, Co, Ni and Cu) (see Supplementary Note 1). All results were obtained by explicitly treating 15 valence electrons for Bi (5d 106s 26p 3), 8 for Fe (3d 64s 2), 6 for Cr (3d 44s 2), 7 for Mn (3d 54s 2), 9 for Co (3d 74s 2), 10 for Ni (3d 84s 2), 11 for Cu (3d 104s 1) and 6 for O (2s 22p 4). The plane-wave cutoff energy was set at 520 eV, and the electronic energy was converged to less than 10−5 eV in all calculations.

Film fabrication and characterization

Thin films of BFO, Mn (5%)-doped BFO (Mn-BFO) and Ni (5%)-doped BFO (Ni-BFO) with a thickness of 300 nm were deposited on vicinal SrTiO3 (STO) (100) single-crystal substrates with a miscut angle of 4° along the [110] direction by pulsed-laser deposition with a KrF excimer laser (λ=248 nm). We set the following parameters for the film preparation: a substrate temperature of 630 °C, an oxygen pressure of 11 Pa, a laser energy of 1.2 J cm−2 and a laser repetition rate of 7 Hz. Domain structures were investigated by piezoresponse force microscopy (PFM) and X-ray diffraction measurements. For the PFM observations, in-plane and out-of-plane phase and amplitude images were measured.

PV measurements

The PV properties of the SD films along the y and –x directions were measured under illumination with light at wavelengths of 405 nm (hν=3.1 eV), 515 nm (hν=2.4 eV) and 639 nm (hν=1.9 eV). The light propagated along the z axis and was incident on the sample surface. The power of the incident light was set at 2.5 W cm−2. The incident light was adjusted to have a polarization angle (ω) from the y axis in the xy plane using a polarizing plate and a half-wave plate. Pseudocubic notation is adopted throughout this article to express the crystallographic directions.

The BPV tensor elements (β 15, β 22, β 31 and β 33) were estimated from the ω dependences of J y and J −x . When linearly polarized light is incident on a ferroelectric crystal, the photocurrent density J derived from the BPV effect is expressed by the equation

$${{\bf{J}}_i}={I_{{\rm{opt}}}}{{\bf{\beta }}_{ijk}}{{\bf{e}}_j}{{\bf{e}}_k},$$
(2)

where β ijk is a third-rank BPV tensor, I opt is the incident light intensity, and e j and e k are the components of the unit vectors along the j and k directions in the crystallographic coordinate system, respectively. For ferroelectrics in C 3v symmetry, β ijk in matrix notation is expressed as

$${{\bf{\beta }}_{ijk}} = \left( {\begin{array}{*{20}{c}}\\ 0 & 0 & 0 & 0 & {{\beta _{15}}} & { - {\beta _{22}}} \\ \\ { - {\beta _{22}}} & {{\beta _{22}}} & 0 & {{\beta _{15}}} & 0 & 0 \\ \\ {{\beta _{31}}} & {{\beta _{31}}} & {{\beta _{33}}} & 0 & 0 & 0 \\ \end{array}} \right).$$
(3)

We obtain J [110] and \({J_{[\bar 110]}}\) as follows:

$$\begin{array}{ccccc}\hskip-7pc {J_{[110]}} = \frac{{{I_{{\rm{opt}}}}}}{{3\sqrt 3 }}\left( {\sqrt 2 {\beta _{15}} + {\beta _{22}} + 2\sqrt 2 {\beta _{31}} + \sqrt 2 {\beta _{33}}} \right)\\ {\rm{ + }}\frac{{{I_{{\rm{opt}}}}}}{{3\sqrt 3 }}\left( {\sqrt 2 {\beta _{15}} - 2{\beta _{22}} - \sqrt 2 {\beta _{31}} + \sqrt 2 {\beta _{33}}} \right)\sin \left[ {2\left( {\omega + \frac{\pi }{4}} \right)} \right]. \end{array}$$
(4)
$${J_{[\bar 110]}} = {I_{{\rm{opt}}}}\left[ {\frac{2}{{\sqrt 6 }}{\beta _{15}} + \frac{1}{{\sqrt 3 }}{\beta _{22}}} \right]\sin \left( {2\omega } \right)$$
(5)

When we neglect the deviation of the measurement directions from the crystallographic orientations and the decay of light in the ferroelectric layer by absorption, we can regard J [110] as J y and \({J_{[\bar 110]}}\) as J −x . The details of the accurate descriptions of J y and J −x taking into account the light absorption and the vicinal angle are described in ref. 32. For the calculations of the PV tensor elements, we adopted the relation β 22=1/10β 33 that has been proven for LiNbO3 in C 3v symmetry.

Data Availability

The data that support the findings of this study are available from the corresponding author on reasonable request.