Giant photovoltaic response in band engineered ferroelectric perovskite

Recently the solar energy, an inevitable part of green energy source, has become a mandatory topics in frontier research areas. In this respect, non-centrosymmetric ferroelectric perovskites with open circuit voltage (VOC) higher than the bandgap, gain tremendous importance as next generation photovoltaic materials. Here a non-toxic co-doped Ba1−x(Bi0.5Li0.5)xTiO3 ferroelectric system is designed where the dopants influence the band topology in order to enhance the photovoltaic effect. In particular, at the optimal doping concentration (xopt ~ 0.125) the sample reveals a remarkably high photogenerated field EOC = 320 V/cm (VOC = 16 V), highest ever reported in any bulk polycrystalline non-centrosymmetric systems. The band structure, examined through DFT calculations, suggests that the shift current mechanism is key to explain the large enhancement in photovoltaic effect in this family.


Results and Discussion
The Ba 1−x (Bi 0. 5 Li 0.5 ) x TiO 3 (BBLT) samples, x = 0.0, 0.05, 0.075, 0.1, 0.125 and 0.15, are synthesized by solid-state method. X-ray diffraction (XRD) patterns for x = 0.125 ( Fig. 1(a)), 0.0, 0.05, 0.075, 0.1, and 0.15 (Supplementary Information Fig. 1(a) to (e)) show pure tetragonal phase with P4mm space group as confirmed by Rietveld refinements. For large doping concentration (x > 0.125) the tetragonality is reduced which is illustrated through merging of peaks ( Fig. 1(b)) and is further reaffirmed by the ratio of lattice parameters, c/a, approaching towards unity ( Fig. 1(c)). However, the c/a ratio shows a subtle increment for x = 0.05 and thereafter decreasing trend with x ( Fig. 1(c)) which can be correlated with tilting of oxygen octahedra associated with expansion of the lattice constant a in the region of 0.075 ≤ x ≤ 0.15 24 . The decrease in cell-volume with x ( Fig. 1(c)) is due to the smaller ionic radii of the dopants. The temperature variation of real part of permittivity (ε′) and loss factor (tanδ) at 1 kHz from 0 to 200 °C ( Fig. 1(e),(f)) unveil the ferroelectric to paraelectric transition (T C ) which is at 124 °C for BTO; increased to 137 °C for x = 0.05 and thereafter decreased to 129, 108, 79, and 55 °C for x = 0.075, 0.10, 0.125, and 0.15, respectively. The change in T C with composition is in accordance with change in c/a ratio ( Fig. 1(c)) as reported in several A-site doped BTO samples [24][25][26] . Additionally, we find that x = 0.15 composition exhibits relaxor behaviour as evidenced from the shift in T C with frequency ( Supplementary Information Fig. 2).
The polarization versus electric field hysteresis loops measured at 4 Hz ( Fig. 2(a)) reiterates the prevailing ferroelectric state of all samples. The remnant polarization (2P r ) is enhanced compared to BTO value for each doping   Fig. 2(b)). Notably, x = 0.10 composition exhibits 2P r = 19.5 μC/cm 2 which is nearly 100% more than BTO. In fact, our first principle calculations demonstrate that the total ionic dipole moments p i follow similar trend with composition ( Fig. 2(b)). The samples show nearly invariant optical bandgap of around 3.2 eV, as deduced from Kubelka-Munk plot based on diffused reflectance spectrum ( Fig. 2(c)) 27,28 . The optical absorption spectra measured from DFT calculations further confirms the invariance (Fig. 2(c), inset).
To examine the photovoltaic response of the BBLT samples, the adopted capacitor includes a finger geometry as top electrode ( Fig. 3(a)) and the current density (J) versus bias voltage (V) is measured under dark and 160 mW/ cm 2 light illumination ( Fig. 3(b)). Upon co-doping, there is a remarkable enhancement in V OC ( Supplementary  Information Fig. 3). In fact, x = 0.125 composition ( Fig. 3(b)) exhibits the maximum V OC of 16 V (E OC = 320 V/ cm) with J SC = 9.18 nA/cm 2 . To the best of our knowledge the displayed V OC of the present polycrystalline sample (x = 0.125) brings 2 fold increase in the earlier reported value on single crystalline BTO 8 . According to the comparison histogram (Fig. 3(c)) it is indeed the largest ever reported V OC for any bulk polycrystalline ferroelectric oxides including few single crystalline compounds 6,7,16,18,29,30 . Surprisingly, even though x = 0.15 composition has polarization the PV response almost ceases to exist (Supplementary Information Fig. 4(d)). It suggests that there is a simultaneous effect of lattice polarization and conduction band topology to create an optimum composition (x ~ 0.125) for which the PV response is maximum as will be understood from the DFT calculations.
The photocurrent response under zero bias measured in light ON and OFF states for x = 0.125 (Fig. 3b), 0.05, 0.075, 0.10 and 0.15 (Supplementary Information Fig. 4(a) to (d)) samples confirm a quick photocurrent response. The spikes observed are due to the pyroelectric response 6 . Notably, the PV response of x = 0.125 sample illustrates a systematic increase in J SC with light intensity while V OC remains constant ( Fig. 3(d)). Although the light polarization dependent PV response could provide direct evidence for bulk photovoltaic effect (BPVE), the V OC being independent of light intensity can also indicate the signature of BPVE 8,11,31,32 . To investigate the photovoltaic response on polarization state, J-V measurements and time dependent photocurrent responses are carried out on samples subjected to positive and negative poling fields. The respective plots for x = 0.125 are shown in Fig. 4(a),(b). The plots reveal a sign change on V OC and J SC with change in poling state. The observed switchable PV response elucidates the major role of polarization than the electrode contribution.
Since BPVE is largely influenced by the band structure in the vicinity of the Fermi level, we have carried out band structure calculations using DFT (see computational method) to examine the role of the dopants in enhancing the PV response. Bader charge of the ions ( Table 1) and deviation of this from the ideal charge state provides a measure of covalency. As the table shows, Ti 4+ and O 2− exhibit a significant deviation of ~1.9 e and 0.8 e  Fig. 5), we find that the CBM is again dominated by the xy states while CBM-2 is by the other t 2g characters. Beside Ti-O polarization, the doping brings an additional Bi-O polarization along the z-axis and it breaks the three fold degeneracy of Bi-p states. As seen from the Bi-p DOS and charge densities (Fig. 5), the contribution of the p z state in CBM-1 gradually increases with doping. Additionally, the shape of the charge densities highlights the Bi-O covalent interaction. A larger doping concentration strengthens both Bi-O polarization and Bi-O interaction. As a consequence the antibonding Bi-p states lie above the CBE and do not contribute to PV response. Also we find that large Bi-O polarization decreases the Ti-O bond length along z leaving the xy states lower in energy to form the CBE which further decreases the PV response supporting the experimental results.
According to shift current theory, if the CBE is more occupied by z-axis oriented orbitals (e.g. p z , xz, yz, z 2 −1) and is very delocalized, resulting from stronger covalent interaction along the polarization direction, the shift current response is high and a large BPVE is observed 12 . As discussed above, in the case of BBLT, the following trends are observed. (I) Initially the polarization increases with x and peaks around x = x opt (~0.125) and decreases afterwards. (II) The covalency increases with x and it is attributed to Bi-p -O-p interactions. (III) The conduction band edge is more occupied by the z-axis oriented orbitals (Bi-p z , Ti-xz and yz) and the contribution become maximum around x = x opt . Therefore, based on shift current theory, the BPVE should increase with x and become maximum at x opt . We may note that since the calculations are carried out for some discrete values of x, exact value of x opt cannot be determined theoretically. However, experimentally we find that the BPVE is maximum at x = 0.125.

Conclusion
In summary, we have demonstrated a unique way to tailor the bands via A-site doping to create giant photovoltaic response in polycrystalline perovskite ferroelectric oxides. In the present work, this has been achieved by co-doping Bi and Li in BaTiO 3 . This work opens up an opportunity to design new family of ferroelectric  compounds for photovoltaic studies by carefully choosing the dopants in such a way that it will lead to simultaneous increase in lattice polarization and delocalization of the conduction band edge state.

Materials and Methods
Experimental section. as measuring unit. The values of current density, J SC , were arrived by considering the entire top surface area (7 × 7 mm 2 ) in the calculation.

Computational method. Present DFT calculations are performed using Pseudopotential (PP) based
Vienna ab-initio Simulation Package (VASP) 34 . PPs are based on projected augmented wave (PAW) method with exchange and correlation effects described using Generalised Gradient Approximation (GGA) and Perdew-Burke-Ernzerhof (PBE) functional 35,36 . For the elements present in our model, the following valance electrons were explicitly considered in the PP: Ba 4 s 2 4p 6 5 s 2 , Li 1 s 2 2s 1 , Bi 5d 10 6 s 2 6p 3 , Ti 3p 6 3d 2 4 s 2 and O 2 s 2 2p 4 . In order to account for relativistic effects arising from heavy Bi element, spin orbit coupling (SOC) has been included in our calculations. SOC calculations were performed as implemented in PAW methodology in VASP package 37,38 . Since SOC is predominantly act in the immediate vicinity of nuclei, the SOC Hamiltonian λL.S is solved self consistently along with PAW Hamiltonian within the PAW sphere. The plane wave cut-off energy was chosen as 500 eV. To simulate experimental doping concentrations we adopted supercell approach with periodic boundary conditions and performed our calculations using 3 × 3 × 3, 3 × 3 × 2, 2 × 2 × 4 and 2 × 2 × 2 supercells corresponding to x = 0.07, 0.11, 0.125, and 0.25 respectively. In each of these supercells, two Ba ions are replaced by single Bi and Li ions. We performed our calculations with Li 6.94 Å respectively. The total energy and band structure of these configurations are found to be nearly identical. Therefore, in the present work only one of them [001] is presented in detail. For structural optimization, we chose a convergence criterion of 10 −6 eV for self-consistent field (SCF) electronic energy and 10 −3 eV/Å for Hellmann-Feynman forces on each atom. A 8 × 8 × 8 Monkhorst-Pack grid is used for the Brillouin Zone integration of bulk BaTiO 3 39 . Proportionate k-grids are used for the supercells. The total ionic charges were calculated using the Bader Atom Molecule (AIM) approach as implemented in the program by Arnaldsson et al. 39,40 .