Photovoltaic conversion and quantum efficiency in perovskite multiferroic ceramics Authors: Chi-Shun Tun, Pin-Yi Chen, Cheng-Sao Chen, R. R. Chien, V. Hugo Schmidt, and Chun-Yen Lin NOTICE: this is the author’s version of a work that was accepted for publication in Acta Materialia. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Acta Materialia, vol. 149, May 2018, DOI# 10.1016/j.actamat.2018.02.043 Tu, Chi-Shun, Pin-Yi Chen, Cheng-Sao Chen, R. R. Chien, Hugo V. Schmidt, and Chun-Yen Lin. "Photovoltaic conversion and quantum efficiency in perovskite multiferroic ceramics." Acta Materialia 149 (May 2018): 248-255. DOI: 10.1016/j.actamat.2018.02.043. Made available through Montana State University’s ScholarWorks scholarworks.montana.edu http://scholarworks.montana.edu/ http://scholarworks.montana.edu/ https://dx.doi.org/10.1016/j.actamat.2018.02.043 https://www.sciencedirect.com/science/journal/13596454 Photovoltaic conversion and quantum efficiency in perovskite multiferroic ceramics Chi-Shun Tu a, Pin-Yi Chen b, Cheng-Sao Chen c, R.R. Chien d, V. Hugo Schmidt d, Chun-Yen Lin a a Department of Physics, Fu Jen Catholic University, New Taipei City 24205, Taiwan b Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City 24301, Taiwan c Department of Mechanical Engineering, Hwa Hsia University of Technology, New Taipei City 23567, Taiwan d Department of Physics, Montana State University, Bozeman, MT 59717, USA a b s t r a c t Junction-driven photovoltaic effects in lead-free perovskite BiFeO3 multiferroic materials have demon- strated promising applications in energy harvesting and optical sensors. This study highlights remark- able photon-to-electron external quantum efficiency (EQE) of ~9% and light-to-electric power-conversion efficiency (PCE) of ~0.8% in the heterostructure consisting of A-site neodymium-doped BiFeO3 ceramic and indium-tin-oxide (ITO) thin film under irradiation of wavelength l¼ 405 nm. A theoretical p-n- junction model based on the photo-generated carriers was employed to quantitatively describe open- circuit voltage (Voc) and short-circuit current density (Jsc) as functions of irradiation intensity, and to widths stimat elations calculate junction defect state) were e Tauc and Urbach r and carrier densities. The direct band gap and the degree of local disorder (or ed using the photon-energy-dependent optical attenuation coefficient with the . 1. Introduction Photovoltaic (PV) effects in non-centrosymmetric polar perov- skite oxides have attracted much attention in recent years for po- tential applications of solar energy harvesting [1e4]. The bulk photovoltaic effect (BPVE) has been observed in perovskite ferro- electric (FE)/piezoelectric oxides which lack a center of inversion symmetry, such as LiNbO3 [5,6], BaTiO3 [7], Pb(Zr,Ti)O3 (PZT) [8e14], (Pb,La)(Zr,Ti)O3 [15e17], KNbO3-Ba(Ni1/2Nb1/2)O3 [18], and tungsten-doped Pb(Mg1/3Nb2/3)1-xTixO3 (PMN-PT) crystals [19]. Two mechanisms have been proposed to account for the BPVE phenomena, including ballistic and shift mechanisms [3,4,20]. The ballistic mechanism is associated with the asymmetric momentum distribution of non-thermalized carriers [20]. The shift mechanism is attributed to the non-diagonal elements of the density matrix, in which the BPVE is caused by the shift (R) in the material following the band-band transition [2]. The linear BPVE current density is expressed by the relation jiBPVE ¼ agijlejelIo, where a is the ab- sorption coefficient, ej and el are the components of light polarization, gijl is the third-rank piezoelectric tensor, and Io is the light intensity [4]. The photocurrent densities of most FE materials are however only of order 10�2-10�5 A/m2 due to wide optical band gaps (typically 3e4 eV) [5e19]. Enhanced PV power-conversion effi- ciencies (from 10�4 to ~0.5%) have been achieved recently by tailoring layer thickness, poling electric field, domain structures, electrode-ferroelectric interface, and band gap [16e19,21]. For example, the (La0.7Sr0.3)MnO3/(Pb0.97La0.03)(Zr0.52Ti0.48)O3/Nb- SrTiO3 heterostructure exhibited a maximal power-conversion ef- ficiency (PCE) of 0.28% under ultraviolet irradiation (photon en- ergy¼ 3.5 eV) [16]. A first-principles calculation proposed that the band gap (Eg) depends on structure in perovskite ferroelectrics, for instance Eg¼ 2.3 eV and Eg¼ 1.74 eV in BaTiO3 for rhombohedral and tetragonal phases, respectively [22]. A high PCE (~4.8%) at nanoscale distances was obtained recently from a (001) BaTiO3 single crystal under 1 sun (1000W/m2) AM1.5G irradiance by using an atomic force microscope (AFM) tip [4]. It has been demonstrated that the high PCE can be achieved within a free path (lo), which is estimated to be from tens to hundreds of nanometers [4]. Photovoltaic phenomena in lead-free multiferroic BiFeO3 (BFO) with various electrodes have been explored intensively in recent years [23e44]. Several mechanisms have been proposed for the PV mailto:chishun.tu@gmail.com https://doi.org/10.1016/j.actamat.2018.02.043 Fig. 1. (a) Optical transmission, (b) ln(a), and (c) (ahn)2 vs. photon energy. The inset in (a) is an illustration of the specimen used for transmission measurement. effects, including the asymmetric ferroelectric PV effect (or BPVE) [11,29], the domain-wall model [30], and the p-n junction model [39,40]. The Pt/BFO single crystal/Pt heterostructure showed an open-circuit voltage Voc~13 V and a short-circuit current density Jsc~0.01 A/m2 under irradiation of l¼ 405 nm [35]. The open-circuit voltage in Pt/BFO/TbScO3 thin films can reach Voc~50 V under irradiation of l¼ 405 nm by controlling the conductivities along domain walls [37]. An external quantum efficiency (EQE) of 10% under irradiation of l¼ 340 nm was reported in ITO/BFO/SrRuO3 thin films [39]. Substantial PV effects have been reported recently in a heterostructure consisting of a p-type rare-earth (RE) substituted BiFeO3 and an n-type ITO thin film (top electrode) [41e44]. An ITO/BFO5Sm ceramic/Au heterostructure exhibited a maximal PCE of ~0.37% and an EQE of ~4.1% respectively under irradiation of l¼ 405 nm [42]. A theoretical p-n-junction-like model based on photo-generated current in the depletion region between the BFO ceramics and the ITO thin film was developed to describe Voc and Jsc as functions of irradiation intensity [40,42]. The direct band gaps of (Bi1-xSmx)FeO3 ceramics vary from 2.24 eV in BFO to 2.15 eV in (Bi0.9Sm0.1)FeO3 (BFO10Sm) [42]. This is consistent with the first-principles-calculated band gap of ~2.25 eV in BFO ceramic [41]. It was suggested that microstructures and atomic orbital hybridizations (between O 2p and Fe 3d/Bi 6sp orbital states) play important roles for the PV responses as photo-generated car- riers travel through ceramic matrix [42]. A structural transition from a ferroelectric rhombohedral R3c to a nonpolar orthorhombic Pnma structure was proposed upon heating in (Bi1-xREx)FeO3 based on average A-site ionic radii [45]. The XRD and TEM studies revealed a rhombohedral R3c phase in (Bi1-xNdx)FeO3 ceramics for 0� x� 0.1 [46,47]. Our previous study in (Bi1-xNdx)FeO3 (0� x� 0.10) ceramics suggests that A-site Nd substitution decreases hybridizations of the O 2p-Fe 3d and the O 2p-Bi 6sp orbitals [47]. In this work, we focus on effects of A-site Nd substitution on PV properties in ITO/BF100xNd ceramics/Au het- erostructures under near-ultraviolet irradiation (l¼ 405 nm). The influences of optical band gap and microstructure in PV responses are explored as functions of Nd concentration. A p-n-junction model based on the photo-generated carriers was employed to quantitatively describe the open-circuit voltage (Voc) and short- circuit current density (Jsc) as functions of irradiation intensity. 2. Experimental procedure (Bi1-xNdx)FeO3 (x¼ 0.03e0.10) ceramics were prepared by the solid state reaction, in which Bi2O3, Nd2O3, and Fe2O3 powders (purity� 99.0%) were weighed in the stoichiometric ratios. Here- after, BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd represent compo- sitions of x¼ 0.03, 0.05, 0.07, and 0.10, respectively. The powders were mixed in an agate mortar with alcohol as milling medium for more than 72 h and then were calcined at 800 �C for 3 h. The sin- tering temperatures are respectively 850, 870, 890, and 890 �C (dwell time¼ 3 h) for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd. Average grain sizes are respectively 5.4, 4.5, 4.3, and 4.2 mm for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd [47]. The optical trans- mission spectra were measured by using a Cary 5E UV-Vis-NIR spectrometer. A high-resolution transmission electron microscope (HRTEM, JEOL JEM-2100 LaB6) with an accelerating voltage of 200 kV was used to analyze microstructures and diffraction patterns. For photovoltaic effects, indium tin oxide (ITO) and Au thin films were deposited on the ceramic surfaces as top and bottom elec- trodes respectively by sputtering depositions. The irradiated area (also electrodes area) of as-sintered specimens is about 0.15 cm2. The ceramic samples were not poled by a dc electric field before the photovoltaic measurements. A diode laser beam of wavelength l¼ 405 nm was used as the irradiation source and was incident perpendicularly on the ITO surface. The optical transmission of ITO thin film is about 80% at wavelength l¼ 405 nm [41]. For power- conversion efficiency (PCE), an adjustable load resistance (RL) was used to obtain curves of load current density (JL) vs. load voltage (VL) under irradiation. The light-to-electric power-conversion effi- ciency (PCE) is calculated by using the equation, PCE ¼ Pout/Pin, where Pout¼ JL$VL is the output electric power density (W/m2) across the load and Pin is the irradiation intensity (W/m2) measured on the ITO surface. 3. Results and discussion Fig. 1 shows curves of optical transmission (T), ln(a), and (ahn)2 vs. photon energy (hv). a, h, and n are absorption coefficient, Planck's constant, and photon frequency, respectively. The speci- mens for optical transmission measurements were polished to a fewmicrometers as illustrated in the inset of Fig.1(a). The specimen thicknesses were determined by using a Hitachi S-3400N scanning electronmicroscope (SEM) and are about 9.3, 7.4, 7.3, and 7.4 mm for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd, respectively. The correlation between the optical transmission T and absorption co- efficient a can be expressed by Ref. [48], T ¼ � 1� R2 � e�ad (1) where R and d are the optical reflectivity and specimen thickness, respectively. In this study, we assume the reflectivity to be negli- gible, i.e. a ¼ � lnðTÞ=d. To analyze the effects of defects and degree of local disorder on the optical absorption behavior, the curves of ln(a) vs. photon en- ergy are plotted in Fig. 1(b). The linear regions near the band edges can be described by the Urbach relation [48], i.e. a ¼ aoehv=EU (2) where ao and EU are the characteristic parameter and Urbach en- ergy. The solid lines in Fig. 1(b) are fits of Eq. (2) with parameters in Fig. 1(b). BFO10Nd has an apparently larger Urbach energy than the other three compositions. The EU corresponds to the width of tail states near the absorption-band edge and is associated with the structural defects and disordering in thematerials, which can result in sub-band defect states between conduction and valence bands. Fig. 1(c) shows the plots of (ahn)2 vs. photon energy (hv). The direct optical band gap (Eg) can be estimated using the Tauc relation [48], ðahvÞ2 ¼ Aðhv� EgÞ, by extrapolating the straight lines as indicated by the dashed lines in Fig. 1(c). The optical band gaps (Eg) decrease from 2.19 eV in BFO3Nd to 2.12 eV in BFO10Nd. The significant reduction of band gap in BFO10Nd can result from intrinsic defects and is consistent with the larger Urbach energy (EU) in BFO10Nd as shown in Fig. 1(b). It was reported that the optical band gap also depends on electronic bond, grain size, and impurity phase [48,49]. To studymicrostructure and lattice defects, high-resolution TEM was used to obtain nanoscale lattice structures and diffraction patterns. Fig. 2(a) shows TEM bright-field images (BFI) in BFO5Nd. Fig. 2(b) is the enlargement from the red rectangle indicated in Fig. 2(a) and reveals some high-strain regions with local lattice distortion. Fig. 2(c)-(f) are selected area diffraction patterns (SADPs) along the [100], [110], [111], and [112]-zone axes with 1 =2 ðoooÞ superlattice diffractions from a number of grains in the BFO5Nd Fig. 2. (a) TEM bright-field image (BFI), (b) high-resolution lattice image from the red rectangle in (a), and (c)e(f) SADPs from a number of grains in the BFO5Nd ceramic matrix. (g) Bi2Fe4O9 impurity phase as indicated by the circle and (h) its SADP. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) ceramic matrix, indicating a rhombohedral R3c symmetry [50e52]. A minor orthorhombic Pbam impurity phase (Bi2Fe4O9) was iden- tified in the ceramic matrix as indicated by the circle in Fig. 2(g) with its SADP in Fig. 2(h). Fig. 3(a) and (b) show the TEM BFIs and SADPs in BFON10Nd. As evidenced in Fig. 3(a’) and (a”), the SADPs confirm a dominant rhombohedral R3c phase [50e52] with aminor orthorhombic Pbam phase (Bi2Fe4O9) in the ceramic matrix as revealed by the Rietveld refinement [47]. These results are consis- tent with the previous XRD and TEM studies in (Bi1-xNdx)FeO3 (0� x� 0.2) ceramics, which indicated a rhombohedral R3c phase for 0� x� 0.1 [46,47]. As shown in Fig. 3(b), a complicated micro- structure with different contrast fringes suggests structural mod- ulation defects resulting from composition fluctuations in the lattice, which can be attributed to inhomogeneous distributions of A-site ions. The SADPs along the [100]-zone axis in Fig. 3(b’) and (b”) reveal respectively a normal R3c symmetry and a R3c sym- metry with coherent reflections resulting from a lattice fluctuation region. The TEM results confirm more structural defects in BFO10Nd than in BFO5Nd. This is consistent with the larger Urbach energy (EU) in BFO10Nd as shown in Fig. 1(b). For photovoltaic measurements, a top electrode of n-type ITO thin film was deposited on ceramic surface as shown in Fig. 4(a), which demonstrates a cross section between the ITO thin film (thickness~100 nm) and the BFO5Nd ceramic observed by bright- field TEM. The X-ray diffraction (XRD) pattern of the ITO thin film in Fig. 4(b) indicates a preferred (222) crystallographic orientation [53]. Fig. 4(c) is the photovoltaic experimental configuration for open-circuit voltage (Voc) and short-circuit current density (Jsc) measurements. The 1 =2 ðoooÞ superlattice diffraction pattern along the [110]-zone axis in Fig. 4(d) confirms a R3c phase in BFO5Nd [50,51]. Fig. 5(a) and (b) show open-circuit voltages (Voc) and short- circuit current densities (Jsc) measured from the heterostructures of ITO/BFO100xNd ceramics/Au as the laser irradiation (l¼ 405 nm) was switched on and off in sequencewith increasing intensity (I) by steps. Curves of Voc and Jsc vs. irradiation intensity are plotted in Fig. 6(a) and (b), which show rapid increases for lower irradiation Fig. 3. TEM bright-field images and selected area diffraction patterns (SADPs) in BFO10Nd. Fig. 4. (a) TEM bright-field image of cross section between the ITO thin film and BFO5Nd ceramic. (b) XRD pattern of ITO thin film (on the BK7 glass). (c) Photovoltaic experimental configuration for open-circuit voltage and short-circuit current. (d) SADP along the [110]-zone axis. Fig. 5. (a) Open-circuit voltage (Voc) and (b) short-circuit current density (Jsc) with increasing intensity. “ON” and “OFF” indicate with and without irradiation. The labeled numbers are irradiation intensities in W/m2. Fig. 6. Irradiation intensity-dependent (a) Voc, (b) Jsc, and (c) EQE. The ceramic thickness is 0.15mm for all samples. Solid lines in (a) and (b) are fits of Eqs. (6) and (7) with parameters in (a). Dashed lines in (c) are guides for the eye. Fig. 7. Characteristic curves of current vs. bias voltage without irradiation. Solid lines are fits of Eq. (3) with parameters in the Figure. The ceramic thickness is 0.15mm. intensities (<~200W/m2). Fig. 6(c) shows the external quantum efficiencies (EQE ¼ hvJsc=qI; q ¼ 1:6� 10�19C), which is a conver- sion from incident photons to conduction electrons in the photo- voltaic process [40]. BFO5Nd and BFO7Nd show respectively maximal EQEs of ~9% and ~8%, which are remarkably larger than EQE~1.11 reported in BaTiO3 single crystal measured by the AFM tip under irradiation of l¼ 405 nm [4]. Fig. 8. Curves of power-conversion efficiency vs. load voltage (VL) for various irradi- ation intensities. The ceramic thickness is 0.15mm. Solid lines are guides for the eye. To characterize the correlation between PV effects and irradia- tion intensity, we use a previously developed p-n-junction model to describe the irradiation intensity-dependent Voc and Jsc [40,54]. The photodiode current id under a bias voltage V without irradia- tion can be expressed by the implicit relation [55]. id ¼ iofexp½qðV � idRsÞ=xkBT� � 1g (3) where io, Rs, and x are respectively dark current, source resistance, and diode-quality factor. Fig. 7 shows characteristic curves of cur- rent vs. voltage without irradiation. The solid lines are fits of Eq. (3) with parameters as listed in the Figure. The electron charge q¼ 1.6� 10�19 C and T¼ 300 K were chosen for simplicity though irradiation may increase temperature at the junction. According to Eq. (3), the current i under irradiation can be written as [40]. id ¼ iofexp½qðV � idRsÞ=xkBT� � 1g: (4) Table 1 Comparison of photovoltaic parameters in some conventional ferroelectric oxides and BiF conversion efficiency and external quantum efficiency, respectively. STO, SRO, and LSMO Heterostructures Voc (V) Jsc (A/m2) Maxima PCE (%) BaTiO3 crystal (AFM tip electrode) 363 doped LiNbO3 crystal (transparent electrode) ~1600 ~10e5 doped BaTiO3 ceramic (Au electrode) ~70 ~10e6 Pt/PZT(52/48)/Ni thin films 0.8 6� 10�4 Pt/PZT(20/80)/Pt thin films 0.08 ITO/PZT(53/47)/ITO thin films 0.25 5� 10�5 0.22 LSMO/PLZT(3/52/48)/Nb:STO thin films ~0.7 ~0.7 ~0.02 ~0.01 ~0.05 ~0.28 KNbO3-Ba(Ni1/2Nb1/2)O3 ceramic (ITO electrode) ~7� 10�4 ~10e3 ITO/doped PMN-PT crystal/ITO <0.2 Au/BFO crystal/Au 0.075 ITO/BFO/SRO thin films 0.3 4� 10�3 Pt/BFO crystal/Pt (AFM tip electrode) 13 0.01 ITO/BFO ceramic/Au 0.58 0.05 0.005 ITO/BFO5Sm ceramic/Au 0.7 0.94 0.25 Pt/BFO/Pt thin films 20 0.5 ITO/Bi2FeCrO6/Nb:STO thin films ~0.6 ~1.1/9.9 ITO/BFO3Nd ceramic/Au (d¼ 0.15mm) 0.77 0.45 0.08 ITO/BFO5Nd ceramic/Au (d¼ 0.15mm) 0.72 1.27 0.24 ITO/BFO7Nd ceramic/Au (d¼ 0.15mm) 0.73 1.39 0.32 ITO/BFO10Nd ceramic/Au (d¼ 0.15mm) 0.71 0.67 0.09 where ip, id, and V are the photovoltaic (or photo-generated) cur- rent, diode current, and measured voltage. For no irradiation, the open-circuit voltage Voc is cancelled by the built-in voltage Uo from the ohmic contacts to the n-type ITO thin film and p-type BFO100xNd ceramics. In the depletion region, there exists a small density of thermally generated carriers (elec- trons and holes) with no net current. The photo-generated carriers will decrease the depletion regionwidth and the retarding voltage, which limits the diffusion currents. The reduced depletion region width indicates a decrease in the downward voltage step (Uoc) in the depletion region. Therefore, the open-circuit voltage Voc can be expressed as [40,54]. VocðIÞ ¼ Uo � UocðIÞ (5) where I is irradiation intensity. As derived in the previous work [40,54], the irradiation intensity-dependent open-circuit voltage (Voc) and short-circuit current (isc) can be expressed by the following Equations [40]; Voc ¼ Uo � Bb2i2o ½expðVocq=xkTÞ � 1�2 . ðqSlI=hcÞ2 (6) isc ¼ ðUo=RsÞ � Bb2fisc þ io½expðiscRsq=xkTÞ � 1�g2 . � h RsðqSlI=hcÞ2 i (7) B ¼ � qnp � 2εoεp �þ � 1þ npεp � εnnn � (8) where S, l, h, and c are irradiated area, irradiation wavelength, Planck constant, and light speed. b is the optical attenuation length and can be determined from the transmission curve in Fig. 1(a), i.e. b¼�d/ln(T). The optical attenuation lengths are respectively about 1.4, 1.1, 1.1, and 1.2 mmat l¼ 405 nm for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd. np and nn in Eq. (8) are the carrier densities of p-type BFO100xNd ceramics and n-type ITO thin film, respectively. εp and εn are the real parts of the dielectric permittivities. The room- temperature dielectric permittivities (εp) are respectively 192, 177, 130, and 180 for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd at measuring frequency f¼ 1MHz. We used a Hall-effect measure- ment to determine carrier density of the n-type ITO thin film, which eO3materials under ultraviolet and visible irradiation. PCE and EQE represent power- represent SrTiO3, SrRuO3, and (La0.7Sr0.3)MnO3, respectively. l EQE (%) Irradiation l (nm)/intensity (W/m2) References (mechanism) 1.11 405/1000 [4] (BPVE) 514.5/1500 [6] (BPVE) mercury arc lamp/100 [7] (internal field) 300-390/10 [12] (barrier PV effects) 350-450/100 [13] (Schottky barrier) 632/4.5 [14] 365/~8.5 365/~0.59 [16] halogen lamp/40 [18] (ferroelectric-metal interface) 406/2600 [19] 532 [23] (diode effect) 435/7.5 [24] (BPVE) 3� 10�5 405 [35] 0.16 405/100 [42] (p-n junction) 3 405/100 [42] (p-n junction) 375/1000 [60] (domain walls) ~0.8/6 635/15 [61] 1.4 405/~100 This work (p-n junction) 4.0 405/~100 This work (p-n junction) 4.4 405/~100 This work (p-n junction) 2.1 405/~100 This work (p-n junction) is nn~6� 1026m�3 and is consistent with the reported value of ~1027m�3 [56]. The permittivity 2n of ITO at low frequency as needed in Eq. (8) has not been measured because of the high conductivity of bulk ITO. However, Eq. (8) applies to the depletion region of ITO which is almost free of charge carriers. Accordingly, the relevant permittivity is expected to be near that of a material with structure close to that of ITO (indium tin oxide) but without the high conductivity of ITO. Indium oxide (In2O3) thin film at 300 K and 1 kHz has 20 � 37 [57]. If the depletion region of ITO has 2n near this value, the 2pnp=2nnn term in Eq. (8) is much smaller than 1 and so is negligible. Thus, fromEq. (8) the carrier densities np can be calculated by the approximate relation, np~ 2Bεoεp/q. The estimated carrier densities np are about 2� 1024, 1� 1024, 7� 1023, and 2� 1024m�3 for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd, respectively. These carrier densities are comparable with np~1023m�3 reported for epitaxial BFO thin film [39]. The slightly larger carrier densities in BFO3Nd and BFO10Nd may be associated with local structural defects as revealed by TEM (Fig. 3) and Urbach energy (Fig. 1), which may indicate increased charge carrier con- centrations. The p-n junction width do (without irradiation) be- tween the ceramic layer and the ITO thin film can be estimated by Fig. 9. (aec) Voc and Jsc vs. irradiation intensity for various ceramic thicknesses (d using the relation, do~(Uo/B)1/2 [40]. The calculated p-n-junction widths do are respectively about 94, 109, 130, and 91 nm for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd and are fairly consistent with the depletion layer width between the ITO and BFO thin films, which was estimated to be a few hundred nanometers [39]. The solid lines in Fig. 6(a) and (b) are theoretical fits of Voc and Jsc (¼isc/S) by using Eqs. (6) and (7) respectively with parameters in Fig. 6(a). The calculated curves agree well quantitatively with experimental data at the lower irradiation intensities. The dis- crepancies between the experimental and calculated Voc at higher irradiation intensities mainly result from increase of the intrinsic carrier density. As irradiation intensity increases, the fermi level can be pushed higher due to increasing thermal energy. The built-in potential barrier (Uo) in a p-n junction is mainly caused by the difference in fermi levels between the p-type and n-type regions. Thus, the built-in voltage (Uo) is expected to decrease as the band gap of the fermi levels decreases with increasing irradiation intensity. The experimental Jsc exhibits a rapid deviation from the theo- retical curves with increasing irradiation intensity as shown in Fig. 6(b). The reduction of photo-generated current can be ). (def) Plots of PCE vs. VL at I¼ 24W/m2. Solid lines are guides for the eye. Table 2 Comparison of photovoltaic parameters (Voc, Jsc, EQE, and maximal PCE) for different ceramic thicknesses. Heterostructures Voc (V) at I~910W/m2 Jsc (A/m2) at I~910W/m2 EQE (%) at I~910W/m2 Maximal PCE (%) at I~24W/m2 ITO/BFO3Nd/Au d¼ 0.10mm 0.87 0.98 0.33 0.25 0.15mm 0.86 0.76 0.26 0.23 0.20mm 0.89 0.67 0.23 0.23 ITO/BFO5Nd/Au d¼ 0.10mm 0.78 3.88 1.31 0.82 0.15mm 0.80 3.17 1.07 0.70 0.20mm 0.76 2.96 1.00 0.28 ITO/BFO7Nd/Au d¼ 0.10mm 0.90 3.44 1.16 0.76 0.15mm 0.82 3.50 1.18 0.75 0.20mm 0.87 1.86 0.63 0.59 attributed mainly to the carrier recombination, which can occur both at the surface and in the bulk of the cell. The carrier recom- bination is also responsible for the rapid decay in the EQE with increasing irradiation intensity as shown in Fig. 6(c). The p-n- junction model used in this study only considers the electron-hole generation by irradiation [40]. The smaller Jsc in BFO3Nd and BFO10Nd may be associated with oxygen vacancies, because oxy- gen vacancies can increase charge recombination rate at the interface [58]. It was reported that local domain structure, polari- zation, and electronic states may also affect the PV responses [25,59]. Fig. 8 shows plots of power-conversion efficiency (PCE) vs. load voltage (VL) for various irradiation intensities. The maximal power- conversion efficiencies (PCEs) occur at lower intensities and are respectively about 0.26, 0.70, 0.75, and 0.22% for BFO3Nd, BFO5Nd, BFO7Nd, and BFO10Nd. The decrease of PCEs for higher irradiation intensities can be mainly due to the recombination of charge car- riers as discussed above. A brief summary of experimental PV pa- rameters under ultravioletevisible irradiations is given in Table 1, including previous PV results in some conventional perovskite ferroelectric/piezoelectric oxides and BFO materials with various electrodes [4,6,7,12e14,16,18,19,23,24,35,42,60,61]. The maximal photovoltaic PCEs obtained in this work are comparable or larger than those in most conventional ferroelectric oxides and BiFeO3 materials under ultraviolet or visible irradiation. Fig. 9(aec) show curves of Voc and Jsc for three different ceramic thicknesses (d) of 0.1, 0.15, and 0.2mm for BFO3Nd, BFO5Nd, and BFO7Nd. A brief list of PV parameters (Voc, Jsc, EQE, and maximal PCE) for different ceramic thicknesses is given in Table 2 at irradi- ation intensities of 24 and 910W/m2. Thickness-dependent plots of power-conversion efficiency (PCE) vs. load voltage (VL) at irradia- tion intensity I¼ 24W/m2 are given in Fig. 9(def). The maximal PCEs at d¼ 0.1mm for BFO3Nd, BFO5Nd, and BFO7Nd can respec- tively reach ~0.25, ~0.82, and ~0.76%, which are respectively larger than ~0.23, ~0.28, and ~0.59% at d¼ 0.2mm. As shown in Table 2, Jsc, EQE, and PCE decrease with increasing ceramic thickness, but Voc does not show consistent thickness dependence. Thickness- dependent PV effects were also reported in ITO/BFO/SRO [39] and Au/BFO/Pt [62] thin film heterostructures, in which Voc shows a rapid decrease with decreasing thin film thickness below a few hundreds of nanometers and was correlated to ferroelectric po- larization at the junction layer. However, BiFeO3 ceramics do not exhibit macroscale saturated ferroelectric polarization hysteresis loop mainly due to current leakage [63,64]. In our previous study for (Bi1-xNdx)FeO3 (0� x� 0.10) ceramics [47], the local domain switching as found from piezoresponse force microscopy revealed coexistence of polar ferroelectric rhombohedral and minor nonpolar orthorhombic phases in the ceramic matrix. The decreased Jsc, EQE, and PCE with increasing ceramic thickness in Fig. 9 and Table 2 can be mainly attributed to recombination of photo-generated carriers while they travel through ceramic matrix from the p-n junction to the bottom electrode. Local domain walls [37], nano-to-micro domain structures [42], and atomic orbital hybridizations [42] are also suggested to contribute to the PV re- sponses. The stronger PCEs and EQEs in BFO5Nd and BFO7Nd are likely associated with less structural defects as revealed by high- resolution TEM observations in Figs. 2 and 3. 4. Conclusions This study demonstrated extraordinary junction-driven photo- voltaic effects in the heterostructure consisting of lead-free (Bi1- xNdx)FeO3 multiferroic ceramics and ITO thin film (top electrode) under irradiation (l¼ 405 nm). The maximal power-conversion efficiency (PCE) and external quantum efficiency (EQE) can respectively reach ~0.8% and ~9% at lower irradiation intensity. The photovoltaic effects show strong dependences on irradiation in- tensity, ceramic thickness, and Nd concentration. The photo- generated open-circuit voltage (Voc) and short-circuit current density (Jsc) can be quantitatively described by a p-n-junction model as functions of irradiation intensity. Microstructure defects are likely responsible for the decrease of direct optical band gaps from 2.19 eV in BFO3Nd to 2.12 eV in BFO10Nd. Acknowledgement This project is supported by the Ministry of Science and Tech- nology of Taiwan under Project Nos. 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http://refhub.elsevier.com/S1359-6454(18)30151-4/sref64 Photovoltaic conversion and quantum efficiency in perovskite multiferroic ceramics 1. Introduction 2. Experimental procedure 3. Results and discussion 4. Conclusions Acknowledgement References