Ultrahigh Bulk Photovoltaic Effect Responsivity in Thin Films: Unexpected Behavior in a Classic Ferroelectric Material

The bulk photovoltaic effect (BPE) has drawn considerable attention due to its ability to generate photovoltages above the bandgap and reports of highly enhanced photovoltaic current when using nanoscale absorbers or nanoscale electrodes, which, however, do not lend themselves to practical, scalable implementation. Herein, it is shown that a strikingly high BPE photoresponse can be achieved in an ordinary thin‐film configuration merely by tuning fundamental ferroelectric properties. Nonmonotonic dependence of the responsivity (RSC) on the ferroelectric polarization is observed and at the optimal value of the film polarization, a more than three orders of magnitude increase in the RSC from the bulk BaTiO3 value is obtained, reaching RSC close to 10−2 A W−1, the highest value reported to date for the archetypical ferroelectric BaTiO3 films. Results challenge the applicability of standard first‐principles‐based descriptions of BPE to thin films and the inherent weakness of BPE in ferroelectric thin films.


Introduction
[3][4][5][6] Since the excited carrier separation occurs within the bulk of the material, the open-circuit voltage of a BPE-based device can be higher than E g , eliminating a major constraint on the PCE that leads to the Shockley-Queisser limit.Despite its promise to overcome this long-standing limit on the PCE of photovoltaic (PV) devices, BPE has been considered to be purely of academic interest for several decades following its discovery due to the high E g of typical ferroelectrics (>3.0 eV) and due to the very small photocurrents generated under illumination.The last decade has seen a resurgence of interest in the BPE with advances in its theoretical understanding and in the design of BPE materials that have led to progress toward its use in practical devices.  Firstinciples-based descriptions of shift current and ballistic mechanisms of BPE showed [15][16][17] that the BPE effect is impractically weak, and the generated photocurrent is very small for both mechanisms (Table S1, Supporting Information).This is in agreement with the BPE currents observed in ceramic samples in the horizontal configuration where the sample is illuminated on the side and its top and bottom electrodes are separated by a large (%1 mm) distance.][35] For example, PCE above the Shockley-Queisser limit was obtained for BaTiO 3 with nanoscale electrodes. [7]Similarly, a high R SC was obtained for strained MoS 2 and WS 2 nanotubes, with an R SC % 1 A W À1 . [34,35]This R SC value is orders of magnitudes higher than for planar films and ceramics (Figure 1a) (We note that due to the use of different illumination intensities in experiments, R SC values rather than J SC values should be used when comparing the BPE photocurrents obtained in different systems).These results suggest that while standard BPE may be unsuitable for practical use, high BPE photocurrent can be obtained through special nanoscale effects present in novel 1D and 2D nanoscale systems and in thin films with precisely engineered nanoscale electrodes.However, the mechanism of these effects is currently unknown, and a path to achieving scalable BPE, that is, practical-area PV devices using such nanoscale systems or nanoscale electrodes, remains elusive.
Here, we show a more than three orders of magnitude enhancement in the BPE photocurrent responsivity in thin-film ferroelectrics compared to bulk in the classic BaTiO 3 ferroelectric, contrary to standard first-principles predictions and measurements of weak BPE.We propose that photoresponse in thin-film ferroelectrics is governed by an interplay between the generation of asymmetric distributions of excited-carrier electrons that increases with increased cation displacement and the collection of these carriers by the electrode that decreases exponentially with increasing cation displacement. [36]Measured responsivity R SC in a simple planar-electroded ferroelectric BaTiO 3 thin film can be enhanced by more than 30-fold, to at least 10 À2 -10 À1 A W À1 , comparable to that achieved in recent nanoscale ferroelectric systems but in a configuration that points to even higher R SC and permits facile use of larger-area absorbers and electrodes and therefore practical, scalable implementation.
The strain and film orientation imposed by the substrate has a strong effect on the out-of-plane polarization of the grown BaTiO 3 films, allowing us to obtain a series of BaTiO 3 systems that are similar chemically but differ in the degree of polarization and structural asymmetry.Reciprocal space mapping and highangle out-of-plane X-ray diffraction measurements were used to confirm the perovskite structure of the films and evaluate the lattice parameters of BaTiO 3 .Then, we evaluated the PV response of the films under the illumination wavelengths of 365, 375, 395, and 405 nm.The obtained V OC , J SC , and R SC are presented in Table 1 for 365 nm and in Table S2, Supporting Information for the other wavelengths.To obtain the Ti off-center displacement D, polarization P, and absorption coefficients (α) of the grown BaTiO 3 films, we use density functional theory (DFT) calculations for BaTiO 3 at the experimental lattice parameters of each film.
Examination of the experimental J-V curves (Figure 1b and S1, Supporting Information) of the (001)-oriented films shows several features characteristic of BPE, rather than the conventional junction-based effect (Section SI, Supporting Information).First, we find that the photocurrent under linearly polarized illumination shows a sinusoidal variation with the rotation of the film that is expected for BPE (Figure S2 and Section SI, Supporting Information), indicating the presence of BPE contribution.Second, experiments using BaTiO 3 doped on the B-site to become paraelectric at room temperature found a short-circuit current ( J SC ) of essentially zero (Section SII, Supporting Information), strongly suggesting that the photocurrent is generated due to the presence of asymmetry in the material that gives rise to BPE.
We then analyze the J SC values extracted from the J-V curves.We first normalize J SC by dividing by the illumination power density to obtain the R SC and plot the obtained R SC values versus Figure 1.a) Comparison of R SC as a function of incident energy above the corresponding E g , for bulk materials (BaTiO 3 (BTO), [6] GaP [51,52] and BiFeO 3 (BFO) [53] ), films (BTO, [23] BFO, [54] and Mn-doped BFO (BFO: Mn) [54] ), nanostructures (MoS 2 , [34] WS 2 nanotubes [33] ), and tip-enhanced materials (BTO [7] and BFO [12] ), adapted from Jiang et al. [34] The compared values are the R SC for all materials, except for bulk BTO and bulk BFO, which are the β 31 and β 22 BPE coefficients, respectively.The R SC of all samples was measured in a vertical configuration, except for BFO:Mn and WS 2 which were studied using a lateral configuration.The R SC for the BaTiO 3 films studied in this work are indicated by the shaded region with triangles marking the measurement results at the boundaries of the region.
Predicted responsivity of the BaTiO 3 (111)/KTaO 3 (111) film at illumination 1 eV above the gap according to the variation of its absorption coefficient is shown by the red triangle connected to the shaded region by the dashed line.b) Measured photovoltaic current-voltage traces for selected 50 nmthick BaTiO 3 /KTaO 3 , BaTiO 3 /GdScO 3 and BaTiO 3 /SrTiO 3 films under 365 nm-wavelength illumination.
the photon energy in a log-scale plot (Figure 2a).It is observed that the R SC data for the different BaTiO 3 films show two different regimes, with a linear rise in R SC on log scale with photon energy observed for 405, 375, and 395 nm followed by a strong jump to much higher R SC values at 365 nm.The decrease in BaTiO 3 R SC values from 365 to 405 nm is quite strong (factor of 40-100).Since the E g of BaTiO 3 is in the 3.1-3.3eV range, we assign the difference in the response observed at 365 nm and the response at 375, 395, and 405 nm to the difference in the light absorption properties of BaTiO 3 between these wavelengths, with the response at 365 nm due to interband transitions and the response observed at 375, 395, and 405 nm to the excitations from impurity states corresponding to the long tail in the BaTiO 3 absorption spectrum.
Comparison of the R SC data for the (001)-oriented films shows that for all wavelengths the R SC decreases strongly (by a factor of more than 4) from the BaTiO 3 (001)/KTaO 3 (001) and BaTiO 3 (001)/KTaO 3 (001) (2) films to the BaTiO 3 (001)/ GdScO 3 (110), BaTiO 3 (001)/GdScO 3 (110) (2), BaTiO 3 (001)/ DyScO 3 (110), and BaTiO 3 (001)/SrTiO 3 (001) films, despite their higher c/a ratio, out-of-plane P, and out-of-plane titanium displacement D (Figure 2a, Table 1 and S2, Supporting Information).Meanwhile, R SC is zero for the nonpolar-doped BaTiO 3 sample (Section SII, Supporting Information).Comparison of the calculated E g values for the different films shows only small E g variations among the films (Table 1).Thus, unlike in the previous works that observed a similar trend of increasing R SC with decreasing P, [24,37] for our systems, the changes in R SC cannot be explained by the variation in E g .Additionally, as discussed above, a drastic drop in R SC is observed experimentally from 365 to 375 nm for all films, indicating that for all films, the E g is between these two wavelengths, in agreement with the DFT calculations.Comparison of the calculated α shows that the small changes in the E g due to the changes in the c/a of the different films lead to only small changes in absorption that cannot account for the observed large variation in the experimental R SC values with strain, c/a, and outof-plane P (Figure 2a, Table 1 and S2, Supporting Information).For example, while the R SC of the BaTiO 3 (001)/KTaO 3 (001) is almost an order of magnitude larger than that of BaTiO 3 (001)/GdScO 3 (110) (2), the absorbance coefficient of BaTiO 3 (001)/GdScO 3 (110) (2) at 365 nm is %70% of that of BaTiO 3 (001)/KTaO 3 (001).Therefore, we conclude that the variation in the R SC is due to the effect of the structural variations among the films as manifested by the changes in the c/a, out-of-plane D, and P of the films.Thus, the results for the (001)-oriented films show a nonmonotonic dependence of R SC on the out-of-plane P.
Comparison of the R SC values to the results in the literature shows that the R SC values of our (001)-oriented films are higher than those for ceramics and are consistent with the R SC values previously obtained for thin films in vertical configurations (Figure 1).The observed trend of increasing R SC with decreasing out-of-plane P and D suggests that even higher R SC values will be observed for smaller out-of-plane P and D values, with peak values reached between D = 0.0 Å and 0.2 Å.
To decrease the out-of-plane P and D further and examine the R SC values in the D = 0.0-0.2Å range, we grew BaTiO 3 films on KTaO 3 (110) and (111) substrates, forming the BaTiO 3 (101)/ KTaO 3 (110) and BaTiO 3 (111)/KTaO 3 (111) heterostructures.As expected, we obtained much higher J SC that corresponds to R SC of 10 À2 A W À1 , which is close to the values obtained for Exponential fit of the R SC is plotted (solid lines) for each sample and is continued by an interpolation for the higher energy (dashed lines).The films systems are abbreviated and labeled as KTO, GSO, STO, and DSO for the films grown on KTaO 3 , GdScO 3 , SrTiO 3 , and DyScO 3 substrates, respectively.b) R SC variation with D of the sample for different incident wavelengths.Plotted lines are a fitting of the values for the function of a 0 D 3 e Àa 1 D for 365 nm and a 0 D 2 e Àa 1 D for the other wavelengths, fitted for all of the samples.Table 1.Experimental lattice parameters, DFT-calculated D, P, E g , and α of each studied film, alongside their experimentally measured R SC , V OC , J SC , and fill factor (FF) at 365 nm.Rigid shift of 1.1 eV [55] is applied to E g to account for the underestimation of DFT.nanoscale systems and is the largest value reported to date for BaTiO 3 films (to the best of our knowledge).The nonmonotonic dependence of R SC on the out-of-plane P suggests that the magnitude of the photoresponse is controlled by more than one effect.A log-scale plot of the R SC values versus the out-of-plane D (which determines the out-of-plane P) as shown in Figure 2b reveals an exponential dependence of R SC on the out-of-plane D (and therefore on the out-of-plane P) in the high-D region (D > 0.2 Å).Therefore, for simplicity, we empirically characterize the nonmonotonic R SC dependence on D as where a 0 and a 1 are constants and n is an integer.We fit the R SC data to Equation (1) for n = 1, 2, and 3 (Figure S3, Supporting Information).We find that n = 2 and 3 give the best fit, with clearly poor matching between the fit and the experimental data obtained for n = 1.The fitting suggests that the BaTiO 3 (111)/ KTaO 3 (111) film obtains close to the maximum possible R SC values at 365 nm for BaTiO 3 films.Similarly, good agreement is obtained between the R SC values for illumination at 375 and 395 nm and the D 2 e Àa 1 D scaling of R SC .For 405 nm, the fit is more poor, most likely due to the large relative error (scatter) of the R SC values due to the small absolute magnitude of the response to illumination at 405 nm.
Our results demonstrate, remarkably, that a larger PV response can be obtained in BaTiO 3 films by appropriately decreasing the out-of-plane polarization to P % 0.18 Cm À2 , which corresponds to an out-of-plane D % 0.1 Å.Furthermore, since BaTiO 3 has a low absorption coefficient at 365 nm, a further increase in R SC can be obtained by simply using a higher photon energy of light, reaching the R SC magnitudes observed for the WS 2 and MoS 2 nanoscale systems.In fact, examination of R SC of different ferroelectric systems reported in the literature plotted versus the difference between the photon energy (E hν ) and the E g of the ferroelectric material in Figure 1 shows that our films achieve values comparable to those of the nanoscale MoS 2 systems for the same E g -E hν difference values.Thus, it is clear that even planar-electroded BaTiO 3 films can show strong photocurrent response that is much larger than that predicted by the firstprinciples calculations for the BPE photocurrent in BaTiO 3 . [16,17]

Interpretation and Mechanism
We now seek to identify a mechanism that would explain the empirically observed nonmonotonic dependence of R SC on the out-of-plane P given by Equation (1).Since the observed R SC -P relationship cannot be explained either by the standard heterojunction effect, or by the model of the BPE focusing solely on the absorber, such as the first-principles approaches for calculations of the shift-current and ballistic current and the phenomenological ballistic current model, we attribute the nonmonotonic variation of R SC with out-of-plane P to the combination of the effect of the asymmetry of the film leading to BPE and the effect of the Schottky barriers at the absorber-electrode interfaces.
According to the classic phenomenological theory of the ballistic BPE taking into account the FE absorber only, the short-circuit current is given by where q is the electron charge, l 0 is the thermalization length, ξ is a parameter characterizing the asymmetry of the current generated by the excitation, ϕ is the quantum yield, and φ opt is the photon flux.The photocurrent described by Equation (2) assumes a mechanism in which the excited electrons are sufficiently energetic to be transported over the Schottky barrier at the absorber-electrode interface. [38]This assumption is not necessarily reasonable for the interband transitions generated by 365 nm (3.4 eV) illumination with energy that is only slightly larger than the E g .For such illumination, the changes in the Schottky barrier height (Φ) will have a strong effect on the photocurrent collected by the electrode due to the exponential dependence of the photocurrent on the changes in the excited electron energy.For a ferroelectric-electrode interface, Φ increases with increasing out-of-plane P, [13,39,40] so that higher Schottky barriers and lower photocurrent can be expected for BaTiO 3 films with higher c/a, out-of-plane P, and D. On the other hand, for a non-polar material, there is no BPE so that no photocurrent is generated (In principle, a nonzero photoresponse due to the Schottky junction alone is possible.However, our experiments show an essentially zero photoresponse for the doped nonpolar BaTiO 3 film and we therefore consider the Schottky junction photoresponse to be negligible for our systems.For films where such response is significant, Equation ( 3) should be modified by adding a term that reflects the contribution of the Schottky junction photocurrent).Therefore, we assign the observed decrease in the photocurrent for films with greater out-of-plane P to the higher Schottky barriers of the more strongly polar films, with the observed photocurrent described by a modification of Equation (2) as where k is an empirical parameter and Φ is linearly proportional to the out-of-plane P (an ionic displacement) of the BaTiO 3 film.Phenomenologically, for the ballistic current generated by the phonon mechanism, ξ is proportional to D 3 and for the impurity mechanisms it is proportional to D 2 (Section SIII and SIV, Supporting Information).Therefore, according to Equation (3), for 365 nm illumination, J SC can be expected to scale as D n e ÀkΦ where n = 2 and 3, matching the empirically fit nonmonotonic dependence of R SC on out-of-plane D (Figure 2a).For excitation at below-the-gap photon energies, the asymmetry parameter ξ of the ballistic current mechanism should scale as D 2 (Section SV, Supporting Information), so that J SC will scale as D n e ÀkΦ where n = 1 and 2. Thus, R SC will first increase and then decrease with increasing out-of-plane D, matching the experimentally observed trend in the R SC values (Figure 2b).Using the DFT calculated values for the absorption coefficient α (Figure S4, Supporting Information) and assuming that ξ is proportional to either D 2 or D 3 we obtain excellent fits to Equation (3) for the experimentally obtained R SC under illumination at 365 nm (Figure 3b) and the other illumination wavelengths (Figure S5 and S6, Supporting Information).Thus, the proposed mechanism is consistent with our R SC data.
As discussed earlier, recent studies of 1D and 2D systems found high J SC and R SC values that were ascribed to BPE.
Similarly, extremely high J SC values and R SC values were obtained for BaTiO 3 with nanostructured electrodes. [7]In these studies the J-V relationship was linear.This suggests that the low gap (for the 1D and 2D systems) and the strong band bending due to nanostructured electrodes (for BaTiO 3 [7]   ) eliminate the Schottky barrier in these systems, obtaining an Ohmic contact and the corresponding high PV response.Thus, it is likely that the high performance of these system is at least in part not due to a nanoscale electrode effect per se but rather simply due to the creation of favorable Ohmic contact that allows the full collection of excited hot carriers.The consideration of the effect of the Schottky barrier can also explain the nonlinear J-V plots and the differences between these plots for the different BaTiO 3 systems studied in our work.
While for bulk BPE systems, a linear J-V dependence is always observed, the recently studied FE films in some cases show fairly nonlinear dependence of J on V, [13] while in other cases bulk-like linear or almost linear dependence of J on V has been observed. [13,14]For our films, the BaTiO 3 (100)/GdScO 3 (110) film has a close to linear J-V dependence, while as the out-of-plane P values decrease and the J SC increases, the J-V dependence becomes more nonlinear (Figure 1b and S1, Supporting Information).However, in all cases, the V OC is independent of the light intensity.We suggest that the observed variation in J-V curvature is due to the Schottky barrier effect.If the effects of Schottky barriers at the top and bottom of the film are taken into account, J(V ) is given by where σ ph is the conductivity contribution by the excited carriers, V is the applied bias, d is the thickness of the absorber (Section SV, Supporting Information), and t and b denote the top and bottom electrode, respectively.In this case, only some fraction of the excited hot carriers traveling toward the top interface (comprising J BPE ) and the bottom interface (comprising J opposite ) are actually extracted into the electrode.Furthermore, the polarization of a thin film will be affected by the applied bias field and this in turn will affect the Schottky barrier height.The dependence of P on V is given by where d is the thickness of the film and epsilon is the dielectric constant.Assuming a linear dependence of Φ on P, Φ is given by where γ t and γ b are constants.Thus, an applied bias that decreases P will lead to smaller Φ at both the top and bottom interfaces.Additionally, due to the proportionality between P and ξ, an applied bias that decreases P will, in turn, decrease ξ.It can be shown that Equation ( 4) predicts that more strongly nonlinear J-V curves will be obtained for films with smaller polarization, greater sensitivity of polarization to electric field, and lower thickness.In contrast, very thick films and strongly polar films will show a lower J-V curvature (Figure S7, Supporting Information).This is in agreement with the results obtained for our films.The strongly polar BaTiO 3 (100)/ GdScO 3 (110) film with high out-of-plane D, out-of-plane P, and c/a show almost linear dependence of J SC on V, while the curvature of the J-V dependence increases strongly as the outof-plane out-of-plane P and D decrease.We fit the J-V curves obtained for our films to Equation ( 4) and find that a good match with the experimental data is obtained (Figure 4a, using the fitting parameters specified in Table S3, Supporting Information).Thus, Equation ( 4) accurately describes the J-V curves of our BaTiO 3 films.Equation ( 4) also explains the obtained V OC values which are governed by the complex interplay of intrinsic 4. a) R SC -V experimental data for illumination at 365 nm for our BaTiO 3 films (symbols) with fits of R SC to the suggested model equation (solid lines), alongside an extrapolation of the initial linear response at low voltages for the BaTiO 3 (111)/KTaO 3 (111) sample.Fitting was done for the positive R SC range.b) I-V curves of films with different thicknesses (nm) studied by Tan et al. [13] together with fits to the model suggested in this work (solid lines).c) J-V curves of PZT films under different illumination intensity (mW cm À2 ) studied by Tan et al. [13] together with fits to the suggested model (solid lines).ferroelectric properties, such as P and ε, and the characteristics of the ferroelectric-electrode interface described by the parameters k and Φ (Section SVI, Supporting Information) (It is important to point out here that in contrast to the standard PV materials, a higher FF value is actually unfavorable for the ferroelectric systems that follow the BPE-Schottky barrier mechanism.In the absence of the Schottky barrier effect, a linear J-V relationship would be obtained, whereas due to the Schottky barrier effect, J(V ) decreases more rapidly (Figure S7, Supporting Information) and a lower V OC is obtained.However, due to the nonlinearity of the J-V relationship, such a curve will exhibit a higher FF.Nevertheless, it is clear that the extracted power density is larger for the linear J-V relationship with a FF of 0.25 than for the nonlinearity of the J-V relationship with FF larger than 0.25 (Table S2, Supporting Information)).
An examination of the results reported in a previous study by Tan et al. [13] suggests that they can be explained by the proposed mechanism of the joint effects of BPE and Schottky barriers expressed by Equation ( 4).Tan et al. [13] studied the dependence of J SC , V OC , and the PCE on the film thickness in ultrathin Pb(Zr 0.2 Ti 0.8 )O 3 (PZT) films.They found that J SC and PCE increased with lower film thickness, reaching high values of %2 mA cm À2 and 2.49%, respectively, for a 12 nm-thick film.Interestingly, the V OC did not show a strong increase for lower film thickness and increasingly nonlinear J-V curves were observed as the film thickness changed from 300 (almost linear) to 120 nm (very curved).Tan et al. [13] ascribed their results to the interplay between the film thickness and the Schottky barrier that creates an electric field that separates the excited charge carriers (see Section SV, Supplemental Material).However, the obtained J-V curves can be also fit well by Equation ( 4), as shown in Figure 4b,c (fitting parameters are presented in Table S4 and S5, Supporting Information), showing that their results are consistent with the BPE-Schottky barrier mechanism that predicts stronger J-V nonlinearity for thinner films.[43] While in several cases, these effects were ascribed to heterojunctions; in light of our results for the BaTiO 3 films here, it is likely that in fact they are also due to the BPE-Schottky barrier mechanism.

Possible Origin of the Strong BPE in Planar Films
We now discuss the origin of the high-BPE R SC that is much higher (even in the presence of the Schottky barrier effect) than the values predicted by first-principles calculations.In a bulk ferroelectric material, ballistic photocurrent arises either from the scattering of the hot carriers from asymmetric impurities or from phonons, both of which generate a asymmetric potential that affects the Bloch states of the system.As shown by firstprinciples calculations, [17] both of these effects are weak.
However, in a thin ferroelectric film, an additional source of asymmetric scattering is present that has not been considered in first-principles calculations, namely, the deviation of the film structure from periodicity near the ferroelectric-electrode interface.While ferroelectric-electrode systems are often idealized as a simple combination of ferroelectric and electrode, in practice, the presence of the electrode affects the structure of the ferroelectric film in the vicinity of the interface, generating deviation from the bulk structure.For example, band bending and a curved electrostatic potential in the vicinity of the interface (Figure S8, Supporting Information) will lead to an aperiodic asymmetric structure close to the electrode, in contrast to the periodic asymmetric structure obtained in the presence of a linearly changing V arising from the presence of the depolarizing field.Such deviation from periodicity will act as an impurity and give rise to a ballistic photocurrent for the electrons excited in the vicinity of the ferroelectric-electrode interface.In contrast to the impurities such as defects that typically have a very low concentration, the deviation from the bulk periodic structure occurs in every unit cell of the top layers of the ferroelectric films.Thus, the asymmetric scattering that gives rise to ballistic photocurrent should be much stronger in the thin film in the vicinity of the electrode than that arising from the presence of impurities in the bulk system.We suggest that this impurity-like scattering is the origin of the extremely high R SC values observed in our films and in other recent experiments on ferroelectric BPE devices.This hypothesis suggests that engineering of greater deviation from periodicity either through the modification of the ferroelectricelectrode interface or by targeted growth of impurity layers can be used to further increase the R SC and PCE of ferroelectric PV devices.

Conclusion
Our results show that the electrode-absorber interface, the orientation of the out-of-plane P relative to the crystal axis, and the local structure can be used to enhance the photocurrent of BPE-based devices so that simple changes of the film orientation and strain conditions result in up to a factor of 20 difference in the R SC and the generated photocurrent.Significantly, at the optimal value of the film polarization, a more than three orders of magnitude increase in the R SC from the bulk BaTiO 3 value is obtained.Specifically, for the BaTiO 3 (111)/KTaO 3 (111) film, R SC reaches %10 À2 A W À1 in a planar-electroded device due to the weaker Φ effect that allows collection of a greater fraction of the generated bulk photocurrent.Considering the weak absorption of BaTiO 3 at 365 nm, R SC can be increased to 10 À1 simply by enhancing absorption using higher photon energies.Such high values of R SC are comparable to those obtained for devices based on ferroelectric WS 2 and MoS 2 nanotubes and for devices based on the tip enhancement effect (Figure 1).This suggests that the high responsivities observed in these nanoengineered systems may not be due to a nanoscale electrode effect per se or to the changes to the bulk carrier separation mechanism, but rather to the reduction of the Schottky barrier.The good fit of the experimental data obtained for our BaTiO 3 films to Equation (4) suggests that even for the BaTiO 3 (111)/ KTaO 3 (111) film, a Schottky barrier still exists and prevents some fraction of excited carriers from being collected by the electrodes.This suggests that a realization of an Ohmic contact should enable an even higher R SC , perhaps reaching as high as 1 A W À1 .Thus, our results demonstrate that BPE is in fact a strong effect for thin-film systems that is often masked by the weak light absorption due to the large gap of the absorber and by the poor carrier collection due to the Schottky barrier at the absorber-electrode interface.
With regard to applications, consideration of our results suggests the following research directions for achieving high R SC and PCE in ferroelectric PV thin-film devices.First, it is vital to increase the amount of the light absorbed by the film.Second, it is necessary to eliminate the deleterious effect of the Schottky barrier to obtain a high J SC , which will also tend to increase V OC and PCE.Finally, to obtain a high V OC , the P of the film should be stable in the presence of the applied V, allowing the favorable linear J-V relationship to be obtained.Furthermore, our results suggest that a film with a polarization gradient through the entire film thickness may exhibit a high PCE.In such a film, deviation from periodicity is obtained throughout the film rather than only in the vicinity of the FEelectrode interface, so that the ultrahigh-BPE hot-carrier scattering effect will enable photocurrent generation even in the region far from the film-electrode interface, allowing the use of thick films, which can achieve higher-than-bandgap V OC simply by increasing the film thickness due to the linear dependence of V OC on d.Aditionally, even with a V OC under the E g , PV devices based on BPE can be used for wavelength-sensitive photodetection [44] and for low-intensity light harvesting, due to the lack of dependence of PCE on light intensity.In theoretical research, further efforts are necessary to develop a microscopic, first-principles-based description of the strong BPE effect in thin films that incorporates the effect of the interface and enables first-principles calculations to provide guidance for further BPE device design efforts.

Experimental Section
The studied BaTiO 3 thin films were deposited by pulsed laser deposition (MTI and CrysTech GmbH) from solid-state SrRuO 3 and BaTiO 3 ceramic targets using a 248 nm wavelength KrF excimer laser under fluences ranging from 1.3 to 1.75 mJ cm À2 , background O 2 (g) pressures ranging from 20-75 mTorr, and a substrate temperature controller setting of 700 °C.The substrates were maintained at a distance of 6.0 cm away from the target.Reciprocal space mapping and high-angle out-of-plane X-ray diffraction measurements were performed on film heterostructures using Panalytical Empyrean 3 Rigaku SmartLab, Bruker Discovery D8 or Panalytical X'Pert 3 MRD X-ray diffractometers.Shown in Figure S9, Supporting Information, are results for the (001)-oriented heterostructured BaTiO 3 /SrRuO 3 films on SrTiO 3 (001), DyScO 3 (101), GdScO 3 (101), KTaO 3 (001), KTaO 3 (101), and KTaO 3 (111) substrates.The reciprocal space mapping studies about the 103, (222), and (321) diffraction conditions of BaTiO 3 and pseudocubic orthorhombic SrRuO 3 layers confirmed that the deposited films were coherently strained with the GdScO 3 , DyScO 3 and KTaO 3 substrates and compressively strained, not unexpectedly, whereas that for the SrTiO 3 showed a purely horizontal shift and broadening compared with the bulk value, [45] consistent with (partial) strain relaxation and mosaicity of the film (Figure S9, Supporting Information).The c/a of each film was calculated from the reciprocal space mapping through a modified Bragg equation for a tetragonal unit cell (Table 1 and Section SI, Supporting Information).SrRuO 3 films and BaTiO 3 /SrRuO 3 heterostructures were measured by topographic height scanning probe microscopy and determined to have root mean squared values of 0.83 nm and between 1.01 and 1.38 nm for the SrRuO 3 and BaTiO 3 /SrRuO 3 heterostructures, respectively.Four-point probe resistivity measurements of the as-deposited %15 nm-thick SrRuO 3 films yielded values ≤1.7 mΩ cm.The films were single domain as shown by piezoelectric force microscopy measurements.Film heterostructures were photolithographically patterned with square DCsputtered (Denton Explorer 14) indium tin oxide (90 wt% In 2 O 3 , 10 wt % SnO 2 ) transparent top electrodes with a side length of 90 μm.The PV response of the films was studied under selected illumination wavelengths of 365, 375, 395, and 405 nm.The obtained V OC , J SC , and R SC are presented in Table 1 for 365 nm and in Table S2, Supporting Information for the other wavelengths.Data were collected under atmosphere and at room temperature using a Keithley semiconductor parameter analyzer (SCS-4200) in a Lakeshore model TTP4 probe station using narrow-spectral-linewidth LED illuminations at 365, 375, 395, and 405 nm (Thorlabs models M365LP1, M375L4, M395L4 and M405LP1, respectively) under irradiances ranging from %1 to 30 mW cm À2 using neutral density filters.Photovoltaic current data were collected on 5-7 electrode test structures for each heterostructure thin film/substrate combination using voltage sweeps from 0.1 to À1.0 V.
We used DFT calculations to obtain the D, P, and absorption coefficients (α) of BaTiO 3 at the lattice parameters of the experimental films.The D, P, and α under different c/a ratios calculations were carried out using five-atom BaTiO 3 unit cells.In each case, we imposed the experimental lattice parameters of the studied film and performed the relaxation of the internal coordinates.All of the relaxations, Schottky barrier, and bulk properties calculations were performed using the Quantum ESPRESSO package [46] with the Perdew-Burke-Ernzerhof functional. [47]The optical properties were calculated using the ABINIT package. [48]In all calculations, norm-conserving psuedopotnetials from the Pseudo-Dojo database were used. [49]The calculated D, P, E g , and α at 365 nm are presented in Table 1.The α at the other wavelengths can be found and Table S2, Supporting Information, alongside the absorption coefficient plot in Figure S4, Supporting Information.For the parameters optimization and curve fitting, basin-hopping optimization was used as implemented in the SciPy package. [50]

Figure 2 .
Figure 2. Different scalings of the R SC for the studied samples in (001), (101), and (111) orientation marked with circle, square, and triangle, respectively.a) R SC variation as a function of incident energy.Exponential fit of the R SC is plotted (solid lines) for each sample and is continued by an interpolation for the higher energy (dashed lines).The films systems are abbreviated and labeled as KTO, GSO, STO, and DSO for the films grown on KTaO 3 , GdScO 3 , SrTiO 3 , and DyScO 3 substrates, respectively.b) R SC variation with D of the sample for different incident wavelengths.Plotted lines are a fitting of the values for the function of a 0 D 3 e Àa 1 D for 365 nm and a 0 D 2 e Àa 1 D for the other wavelengths, fitted for all of the samples.

Figure 3 .
Figure 3. a) Illustration of the proposed BPE mechanism.Asymmetric momentum distribution of hot electrons in the direction of polarization is generated by BPE.The nonthermalized electrons travel ballistically toward the interface and then only a fraction of these electrons are transmitted through the Schottky barrier.b) Variation of the R SC at 365 nm illumination as a function of out-of-plane D for the different samples in the (001), (101), and (111) orientations (circles, square, and triangle, respectively), together with a fit of R to a 0 l 0 αD 3 e Àa 1 D (dashed line).