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Bulk Photovoltaic Effect: A Modern view and Possible Applications
Masao Nakamura, Masashi Kawasaki
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DOI: 10.22661/AAPPSBL.2020.30.4.22

Bulk Photovoltaic Effect:
A Modern view and Possible Applications

Masao Nakamura1,2 and Masashi Kawasaki1,3
1 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
2 PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, 332-0012, Japan
3 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC),
University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan


Upon photoexcitation, a bulk material lacking inversion symmetry generates an electric current. This phenomenon, referred to as the bulk photovoltaic effect (BPVE), has long been known, but the theories regarding its mechanism remained controversial. Shift current, which is a photocurrent driven by the geometric phase of the electron wave function associated with a nonlinear optical process, recently has been revealed to be BPVE's principal mechanism. We have experimentally demonstrated distinct features of shift current, such as robustness against carrier scattering, high voltage far exceeding the bandgap, and ultrafast response to pulsed light. These features are of great advantage for optoelectronic applications, as exemplified by solar cells and high-speed photodetectors.


The photovoltaic effect, the generation of electric current and/or voltage in a material by light irradiation, has been utilized in various light-to-electricity conversion devices, including solar cells and photodetectors. Most of the present photovoltaic devices employ a semiconductor p-n junction, in which the emergent internal electric field at the junction interface promotes the spatial separation of photogenerated electron-hole pairs. In contrast to such an interfacial photovoltaic effect, materials lacking inversion symmetry exhibit a photovoltaic effect without the junction structure, which is called the bulk photovoltaic effect (BPVE). BPVE has been reported in various ferroelectric and polar compounds from the 1950s [1]. While the extremely high output photovoltage (of even over 1000 V) of BPVE initially attracted attention [2, 3], there has been a recent revival of interest in BPVE due to the theoretically-revealed topological nature of the photocurrent as well as materials development, which could be useful in practical devices [4-6].

Several mechanisms have been proposed to be the origin of BPVE, such as a built-in electric field, shift current, and ballistic current [7, 8]. Among the proposed mechanisms, the shift current mechanism has been recognized as one of the most predominant origins. Shift current is closely related to the geometric Berry phase of the Bloch wavefunction. To see it, we first touch on the quantum-mechanical theory for electronic polarization. In a system having a periodic lattice, the Berry connection in the momentum space given by a = -i <uk│∇kuk>, which represents the real-space displacement of the center of mass of an electron cloud in a unit cell measured from the symmetric position, where uk is the periodic part of the Bloch wavefunction [9, 10]. Thus, the electronic polarization is expressed with the Berry connection of the occupied band av(k) as


On the other hand, shift current is a steady-state photocurrent arising from the second-order nonlinear optical response as expressed by


where E(ω) is the electric field of light, subscripts v and c refer to the valence band and conduction band, Pcv(k) is the transition matrix element, 𝜙cv(k) is the phase of Pcv(k), and εc - εv is the bandgap energy. Equation 2 implies that the position of the electron wave packet shifts in real space by a so-called shift vector Rshift = av(k) - ac(k)+∇k𝜙cv(k) simultaneously with the absorption of light [11, 12]. Figure 1 shows an intuitive picture of the shift current generation process. In compound semiconductors, the local density of state is more concentrated around anion (cation) atoms in the valence band (conduction band). The spatial deviation in the electron density between the two bands corresponds to the difference in the Berry connection av(k) - ac(k). The optical transition induces the relocation of an electron wave packet according to this distance, resulting in an anisotropic charge transfer yielding a finite current in noncentrosymmetric materials.


Fig. 1: Schematic of shift current generation in a one-dimensional chain of alternating anions and cations with polar distortion. ac (av) are Berry connections for the Bloch wavefunction of conduction (valence) bands.

As can be seen in the expression for Rshift, shift current is an inherently quantum-mechanical process and shift current directly reflects the topology of the electronic band structure. The topological nature has been further clarified by formalism based on the Froquet theory that describes a non-equilibrium state under periodic excitation [13]. Also, the first-principles calculation of shift current has been developed and succeeded in explaining the complicated BPVE observed in BaTiO3, which has led to the wide acceptance of shift current as a predominant origin of BPVE [14]. The technique has been applied to various ferroelectric and polar materials and has predicted candidate materials showing large shift current [15-19]. In contrast to these recent and significant advancements on the theoretical side, most of the experimental studies have continued using a classical view of BPVE, with photocurrent generation associated with a built-in electric field. We have experimentally reexamined BPVE based on the concept of the quantum-mechanical shift current and revealed the characteristics stemming from the topological nature of shift current, such as dissipation-less photocurrent generation and ultrafast responsivity.


Fig. 2: (a) Crystal structure of SbSI. (b) A schematic of the configuration for measurement. Light from a solar simulator is on the entire area between the electrodes (0.45 mm). (c) Temperature dependence of a zero-bias photocurrent for SbSI samples with different electrode materials. The current is normalized by the sample width that has a typical value of 0.3 mm. (d) Relation between the magnitude of a zero-bias photocurrent at 200 K and the work function of contact metals. The inset shows the band diagram of SbSI and the Fermi levels of all the contact metals. VL, CBM, VBM, and EF denote vacuum level, conduction band minimum, valence band maximum, and Fermi level, respectively. (e) Current-Voltage (I-V) characteristics for a Pr electrode sample measured at various temperatures under photoirradiation. The intercept points of the I-V curves with the vertical and horizontal axes indicate a zero-bias photocurrent and open-circuit photovoltage, respectively. The inset shows a schematic of the measured sample. (f) Temperature dependence of a zero-bias photocurrent and open-circuit voltage measured with increasing temperature. (Reproduced from Ref. [22])


We experimentally investigated the fundamental characteristics of shift current in a prototypical ferroelectric semiconductor, antimony sulfoiodide (SbSI). SbSI has a quasi-one-dimensional structure as depicted in Fig. 2(a). The ferroelectric transition temperature (TC) is 292 K, and the polarization appears along the c-axis with a sizable saturation polarization value of 30 μCcm-2 comparable to that of BaTiO3 [20]. Furthermore, SbSI has strong absorption in the visible-light range due to the rather narrow bandgap (~2 eV) [21]. Because of the superior ferroelectric property along with the strong visible-light response, SbSI is considered to be a potential candidate for future materials for solar cells [6].

First, we demonstrated the impact of electrodes on shift current using single crystals of SbSI in the configuration depicted in Fig. 2(b) [22]. We chose various electrode materials whose work functions could be distributed throughout a wide energy range. Figure 2(c) shows the temperature dependence of a zero-bias photocurrent measured in warming processes after the poling process. The sharp photocurrent peaks seen at around TC indicate the output of a pyroelectric current upon the ferroelectric transition. Below TC, we observed a zero-bias photocurrent whose temperature dependence and magnitude strongly depended on the electrode materials. The samples with large-work-function electrodes, e.g., Pt and Au, show a sizable zero-bias photocurrent persisting down to low temperatures. On the contrary, in the samples with small-work-function electrodes, the zero-bias photocurrent is small and rapidly decreases as the temperature lowers. A zero-bias photocurrent monotonously increases as the work function of the electrodes increases, as shown in Fig. 2(d). SbSI is known to be a p-type semiconductor with a large Fermi energy (EF). The electrode dependence implies that the closer to EF the work function of the electrode is, the larger the zero-bias photocurrent (inset of Fig. 2(d)). This fact reveals that majority carriers predominantly contribute to the zero-bias photocurrent, which is in stark contrast to photocurrents in conventional p-n junctions that operate as minority-carrier devices. The majority carrier operation is a prominent feature of the shift current.

Figure 2(e) shows current(I)-voltage (V) characteristics for an optimum electrode (Pt) sample measured under photoirradiation at varying temperatures. The zero-bias photocurrent is almost independent of temperature, whereas the slope of the I-V curve, which corresponds to the photoconductance, rapidly decreases as the temperature lowers: the change is as large as four orders of magnitude between 300 K and 40 K. Considering that the lifetime of a photocarrier (~10-9 s) is much larger than the scattering time (<10-14 s) in SbSI, the decrease of the photoconductance at low temperatures is mainly caused by the decrease of carrier mobility. While the mobility shows significant temperature variation, the zero-bias photocurrent barely changes. The mobility-insensitive feature of the observed current indicates its robustness against scattering from defects/impurities, which is a manifestation of the topological nature of the current and can be regarded as a hallmark of the shift current [23]. While the zero-bias current is almost constant, open-circuit voltage increases in inverse proportion to the photoconductance. It becomes as large as over 70 V, much larger than the bandgap at 40 K (Fig. 2(f)), which is a distinctive feature of BPVE.


Fig. 3: (a) Schematic of a non-local photocurrent measurement using a 4-terminal sample. (b) Voltages of three electrodes (V10, V20, and V30), measured at 250 K while feeding a current between electrodes 3 and 0 (I30), as shown in (a). (c) Profile of the voltage under short-circuit conditions (V30 = 0 V), represented by the closed circles in (b). (Reproduced from Ref. [24])

We also investigated photocurrents under local photoexcitation using a SbSI single crystal with four electrodes along the polar axis [24]. As depicted in Fig. 3(a), the sample area between the internal electrodes (electrodes 1 and 2) were uniformly irradiated, and the voltage of each electrode was measured with a feeding current between the external electrodes (electrodes 0 and 3), as shown in Fig. 3(b). In Fig. 3(c) the voltage at each terminal in the short-circuit condition is shown. The voltage drop (V10 and V32) emerges in the unirradiated part and their polarity is opposite to that of the irradiated part (V21). Notably, the photocurrent is flowing against the voltage gradient in the irradiated part, clearly indicating that the observed photocurrent is not driven by the internal electric field, but presumably by shift current. The result is understood to be equivalent to a series circuit composed of dark-resistances for the unirradiated parts and the parallel circuit of a current source and photo-resistance for the irradiated part. The simple equivalent circuit established here is applicable to simulate the device performance of bulk photovoltaic devices non-uniformly exposed to light.


Fig. 4: (a) Schematic of the emission of THz electromagnetic waves induced by ultra-short pulsed laser excitation. (b) Temperature dependence of THz waveforms. (c) Retrieved current dynamics for shift current and in-gap optical rectification. (Reproduced from Ref. [26])


Shift current generation is associated with the coherent evolution of the geometric phase of the wavefunction during the photo-absorption process. Unlike conventional photocurrents driven by drift and diffusion processes, shift current does not involve carrier transport, and is expected to emerge in ultrafast timescales [25]. We have examined the dynamics of shift current by employing time-resolved terahertz (THz) emission spectroscopy [26, 27]. As shown in Fig. 4(a), excitation of SbSI by sub-picosecond pulsed laser induced a pulsed photocurrent, leading to the generation of electromagnetic waves in the THz-frequency range, and the temporal/spectral dynamics of the emitted THz waves were analyzed. Figure 4(b) shows the temperature dependence of THz waveforms, indicating the THz emission below TC = 292 K. We also measured the THz emission spectra by scanning the excitation photon energy from 0.5 to 2.6 eV. It revealed that the predominant origin of the THz emission is shift current for excitation above the bandgap energy (Eg = 2.0 eV), while optical rectification, which is the modulation of polarization by the electric field of light, is predominant below Eg. The current response converted from the THz waveform as shown in Fig. 4(c) indicates that the response time of the shift current is comparable to the pulse width of the incident light. In contrast, the response of a conventional photocurrent exhibits a t-linear nature and, therefore, its decay time should be much longer than the incident light. Note that the opposite current flow observed after the initial instantaneous response probably indicates the swing over of charges in the relaxation process. THz spectroscopy unveiled the ultrafast charge dynamics associated with the shift current mechanism.


A key requirement for shift current to be used in device applications is the improved efficiency of current generation. However, there were no clear guiding principles for finding materials that would enable the enlargement of shift current. We searched for possible candidates based on the following considerations. There are two origins for spontaneous polarization in ferroelectrics: one is ionic polarization (Pion) arising from the displacement of charged ions, and the other is electronic polarization (Pele) arising from the asymmetric distribution of electron clouds. The former is given by the classical point charge model, whereas the latter is expressed with the Berry connection of occupied state (av(k)) as described in Eq. 1 and is closely related to the shift current that is proportional to av(k) - ac(k). Thus, we theorized that materials with large Pele would be potential candidates for enhancing shift current. However, Pion is predominant in most conventional ferroelectrics.


Fig. 5: (a) Molecular structure of tetrathiafulvalene (TTF) and p-chloranil (CA). TTF is an electron donor (D) and CA is an electron acceptor (A). (b) Schematic electronic structures of TTF-CA in the ionic phase. The polarization has ionic and electronic contributions (P = Pion + Pele). The former originates from the displacement of charged molecules, while the latter originates from the charge transfer between D-A molecules. In TTF-CA, Pele is much larger than Pion and their directions are opposite. (c) Temperature dependence of the spontaneous polarization determined from the pyroelectric current measured after the sample was cooled under poling fields (Epole) of ±2 kVcm-1 and without the poling procedure (Epole = 0). (d) Temperature dependence of a zero-bias photocurrent measured under photoirradiation. The measurements were performed in directions parallel and perpendicular to the a-axis. (e) The upper panel shows the polarized optical conductivity spectra of TTF-CA measured in the ferroelectric phase (T = 79 K). ECT denotes the energy of the CT excitons. The lower panel shows the photocurrent action spectra for light polarizations parallel and perpendicular to the a-axis obtained at the same temperature. The onset photon energy of the photocurrent is 0.6 eV, which is slightly higher than ECT. (Reproduced from Ref. [28])

We chose tetrathiafulvalene-p-chloranil (TTF-CA), which is a ferroelectric organic charge-transfer (C-T) complex, as the target material [28]. TTF-CA has a quasi-one-dimensional structure with alternative stacking of the donor molecules (TTF) and the acceptor molecules (CA) (Fig. 5(a)). TTF-CA undergoes a ferroelectric transition at TC = 81 K, below which charge transfer occurs, and simultaneously, dimers are formed associated with the molecular displacement between adjacent molecules (Figs. 5(b) and 5(c)). Both the charge transfer and the molecular displacement causes the emergence of spontaneous polarization, the former (the latter) corresponds to Pele (Pion). TTF-CA shows a much larger Pele (~6 μCcm-2) compared to Pion (0.3 μCcm-2), and thus, it is called electronic ferroelectric [29].

The temperature dependence of a zero-bias photocurrent measured for a single crystal of TTF-CA under the irradiation of light from a solar simulator (0.1 W/cm2) is shown in Fig. 5(d) [28]. It rises sharply at TC along the polarization axis. The current at the peak, 650 pA, corresponding to 1.6 μA/cm2, is more than three orders of magnitude larger than that in a representative visible-light-responsive ferroelectric BiFeO3 (1 nA/cm2 normalized at the light intensity of 0.1 W/cm2) [30]. Figure 5(e) shows the action spectra of shift current (lower panel) as well as the optical conductivity spectra of TTF-CA (upper panel). The peak structure at 0.5 eV observed in the optical conductivity indicates the formation of C-T excitons, which corresponds to the bandgap energy for conventional semiconductors. The spectra of shift current appear from slightly higher than this energy and are spread across a wide photon energy range from the near-infrared to ultraviolet region. The shift current's generation ability is quantified by the Glass coefficient G given by


where σshift is the nonlinear conductivity of shift current, α the absorption coefficient, d the thickness of the sample, and w the width of the sample. The value of G in TTF-CA, estimated from the action spectra, is 1×10-6 cm/V, which is several orders of magnitude larger than those in other typical ferroelectric compounds, e.g., 2×10-8 cm/V in SbSI and 1×10-9 cm/V in BiFeO3 [31, 32]. The results indicate that organic C-T complexes have great potential to increase the magnitude of shift current.


We experimentally demonstrated the unique features of BPVE that principally originates from quantum-mechanical shift current, such as dissipation-less carrier transport and ultrafast dynamics. Dissipation-less photocurrents as well as the extremely high photovoltages are expected to contribute to substantially increasing the performance of energy harvesters. Indeed, it is suggested that BPVE could exceed the maximum power conversion efficiency in a p-n junction structure, i.e., the Shockley-Queisser limit [33]. As demonstrated in TTF-CA, organic ferroelectrics have considerable potential to generate a large shift current and to be useful in energy harvesting applications. We have been exploring other organic ferroelectrics, including supramolecular liquid crystals [34]. Recently, it has been reported that topological materials like Weyl semimetals have a large shift current response in the middle-to-far-infrared region [32, 35, 36]. Such materials are useful for infrared sensors with high-speed responsivity. We have also started thin film fabrication toward such device applications, and succeeded in growing thin films of SbSI with an ordered polarization axis by molecular beam epitaxy [37]. Although BPVE has been long known, its quantum-mechanical qualities have opened a door to new insights and possible device applications.

Acknowledgments: We thank H. Hatada, M. Sotome, N. Ogawa, Y. Kaneko, S. Horiuchi, F. Kagawa, T. Kurumaji, T. Morimoto, N. Nagaosa, and Y. Tokura for their respective collaborations and discussions. This work was supported by the Precursory Research for Embryonic Science and Technology (PRESTO, JPMJPR16R5) program of the Japan Science and Technology Agency (JST), and by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI, 20H02626).


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Masao Nakamura is a senior researcher at the Center for Emergent Mater Science (CEMS) at Riken. He received his Dr. Eng. from the University of Tokyo, Japan in 2005. His research fields are optoelectronic functionalities in oxide and halide thin films.

Masashi Kawasaki is a professor at the Quantum-Phase Electronics Center (QPEC) and the Department of Applied Physics at the University of Tokyo, Japan. He has a joint appointment as a deputy director at Center for Emergent Mater Science (CEMS) in RIKEN. He received his Dr. Eng. from the University of Tokyo in 1989. His research fields are oxide electronics and quantum transport phenomena in topological materials.

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