Flexo-photovoltaic effect

It is highly desirable to discover photovoltaic mechanisms that enable enhanced efficiency of solar cells. Here we report that the bulk photovoltaic effect, which is free from the thermodynamic Shockley-Queisser limit but usually manifested only in noncentrosymmetric (piezoelectric or ferroelectric) materials, can be realized in any semiconductor, including silicon, by mediation of flexoelectric effect. We used either an atomic force microscope or a micrometer-scale indentation system to introduce strain gradients, thus creating very large photovoltaic currents from centrosymmetric single crystals of strontium titanate, titanium dioxide, and silicon. This strain gradient–induced bulk photovoltaic effect, which we call the flexo-photovoltaic effect, functions in the absence of a p-n junction. This finding may extend present solar cell technologies by boosting the solar energy conversion efficiency from a wide pool of established semiconductors.

Since its first observation in the 19th century, the photovoltaic (PV) effect has been studied intensively for scientific interest and as a sustainable energy source to replace fossil fuels and reduce carbon emissions (1–3). In 1954, the first high-power modern silicon solar cells—in which the photoexcited carriers were separated by a built-in electric field developed at a p-n junction—were invented (4). By virtue of the appropriate bandgap energies of the semiconductors in a p-n junction solar cell, sunlight is efficiently absorbed, resulting in considerable power conversion efficiency. At present, silicon PV cells are the mainstay of the modern solar industry, contributing more than 1% of the global electricity supply. Nevertheless, PV cells based on p-n junctions have a photovoltage limited by the bandgap energy of the constituent semiconductors and an ultimate efficiency constrained by the Shockley-Queisser (S-Q) limit (5).

Ferroelectric materials exhibit a PV effect, called the bulk photovoltaic (BPV) effect (6, 7), that is distinct from that of p-n junctions. Under uniform illumination, a homogeneous ferroelectric material gives rise to a current under zero bias [short-circuit current (ISC)] that depends on the polarization state of the incident light and produces an anomalously large photovoltage well exceeding its bandgap energy. This peculiar PV effect originates from the asymmetric distribution of photoexcited nonequilibrium carriers in momentum space, caused by the absence of centrosymmetry in the material (7). Owing to its distinctive charge separation mechanism, solar cells based on the BPV effect can, in principle, exceed the S-Q limit (8). However, a substantial BPV effect is generally found in wide-bandgap noncentrosymmetric materials such as ferroelectric BaTiO3 (8) and BiFeO3 (9), leading to an overall extremely low device efficiency under solar illumination. Hence, one way to enhance the efficiency may be to realize the BPV effect in semiconductors with more favorable bandgaps, regardless of their crystalline symmetry.

Flexoelectricity is an electromechanical property that reflects a coupling between an electric polarization and a strain gradient (10, 11). In centrosymmetric materials, a strain gradient breaks its inversion symmetry, resulting in a polarization with a preferred direction and enabling a piezoelectric composite containing no piezoelectric elements (11, 12). Likewise, one can hypothesize that a strain gradient allows the manifestation of the BPV effect in materials that were originally centrosymmetric. In this study, we propose and demonstrate that the BPV effect can be induced in any semiconductor by mediation of the flexoelectric effect. Given that flexoelectricity is a universal property of all materials, ranging from biomaterials (13) to semiconductors and dielectrics (14) to two-dimensional materials such as graphene (15), this strain gradient–induced BPV effect, termed here the flexo-photovoltaic (FPV) effect, is possible for all symmetry classes. Thus, devices designed on the basis of the FPV effect can be fabricated with silicon or any other semiconductors.

To demonstrate our idea, we explored the PV effect induced by a point force exerted onto the surface of centrosymmetric materials, including a SrTiO3 single crystal and a rutile TiO2 single crystal [section S1 of (16)]. The point force was exerted by the tip of an atomic force microscope (AFM), inducing local inhomogeneous strain at the tip-surface contact area and, therefore, a local breaking of centrosymmetry (17, 18). In our experiments, we used a custom-made photoelectric atomic force microscope (Ph-AFM) consisting of an AFM-based system equipped with a customized current amplifier-filter system and an optical system (19). The optical system allowed us to illuminate a sample surface with a 405-nm laser properly polarized by a halfwavelength plate. A conductive AFM tip applied a local force on a sample surface and simultaneously collected the resultant PV current. A brief schematic of the Ph-AFM setup is shown in Fig. 1, A and B.

SrTiO3 single crystals are ideal for studying the flexoelectric effect, owing to their simple cubic centrosymmetric lattices and large dielectric permittivities (14, 20). Unlike its sister material BaTiO3, ordinary crystals of SrTiO3 do not exhibit the BPV effect because they have a center of inversion symmetry. However, with illumination around the contact area on a (001) face of a SrTiO3 crystal, we observed that ISC exhibits a large transient peak as the loading force is increased from 1 to 18 mN (Fig. 1C). This peak is reproducible, proven by repeated exertion and withdrawal of the loading force.

To show that the pronounced enhancement of ISC by the point force is not confined to SrTiO3 crystals or a cubic structure, we investigated the force-induced PV current in a single crystal of rutile TiO2, which is well known for its photoelectric applications such as dye-sensitized PV cells and photocatalysis. As in the case of SrTiO3, large negative ISC appears once a large force is exerted on a TiO2 (100) face. Figure 1D shows a stable current under the 15-mN force, confirming that the force-induced PV effect is not a transient effect in this material. Although it depends on contact conditions and locations, the point force exerted by the AFM tip gives rise to a substantial current density (up to ~1 A/cm2) at the nanoscale contact area. This current density is more than three orders of magnitude higher than the ISC value (0.3 mA/cm2) obtained from a Schottky junction between TiO2 and Pt under the same illumination condition [section S6 of (16)].

The current density increases by more than a factor of 100 when the loading force is increased from 1 to 15 mN (Fig. 1E). This phenomenon cannot be explained by expansion of the contact area with the loading force, because a contact area increases by, at most, a factor of ~6 with a 15-fold increase in loading force in a simple elastic sphere contact model [section S2 of (16)]. Moreover, a 100-fold increase in contact area as a result of force applied by an AFM tip is not realistic. Notably, ISC has a negative value on a (100) face of the TiO2 crystal but becomes positive when the conductive AFM tip is loaded on a (001) face (Fig. 1F). The fact that the direction of the PV current depends on the crystallographic orientation of the TiO2 crystal indicates that the observed PV effect cannot merely be attributed to a probable Schottky contact formed by the TiO2 surface and the Pt coating of the AFM tip.

The BPV effect is a potential origin of this PV current enhancement. As hypothesized, it is likely that a point force exerted on a crystal surface generates a local strain gradient, resulting in local centrosymmetry breaking and, thus, a local BPV current under illumination—i.e., the FPV effect—in the absence of a p-n junction and an appropriate band alignment. Given that both the flexoelectric response and the BPV effect depend on the crystallographic orientation (19–21), our results suggest that the strain gradient and the resultant FPV effect have a predominant role in the enhanced local PV current.

The strain gradient induced by a sphere contact has a complex spatial distribution with very large strain gradient values in an elastic material, as described in section S2 of (16). An AFM tip apex can be approximated as a hemisphere, and the distribution of strain gradient induced by the AFM tip can be calculated analytically with the Hertzian model and the Boussinesq’s calculation (22). Figure 2 shows the spatial distributions of the z component of the calculated strain and its derivative with respect to z under ~15.7 mN of force with a 10-nm–radius contact area at the origin. The strain gradient is as large as 107 m−1. We found that the ISC density and the volume beneath the AFM tip, which is subject to a strain gradient larger than 1 × 106 m−1, show a similar dependence on the exerted force [(Fig. 1E); the detailed process to obtain the relative volume can be found in fig. S9]. It is expected that the very large strain gradients induced by the AFM tip will break local symmetry, thus leading to the manifestation of the BPV effect locally under illumination. However, deep theoretical considerations are required to understand the intricate relationship between the complex distribution of the strain gradient and the BPV properties.

The main characteristic of the BPV effect is a periodic dependence on the angle between the PV current and the light polarization, stemming from its tensorial nature (21). For the present case, this dependence is predicted to be

Where IFPV is the PV current, I0 is a light intensity, Az and Bz are effective BPV coefficients of the locally deformed crystal, and a is the polarization angle of the incident light with respect to the top surface edge as described in section S3 of (16). The FPV effect should inherit the distinctive feature of the BPV effect and exhibit a sinusoidal dependence on the incident light polarization angle with a period of 180°. Indeed, ISC measured by a conductive AFM tip in the configuration illustrated in Fig. 1B on the SrTiO3 (010) and TiO2 (001) surfaces exhibits a light polarization dependence in accord with Eq. 1, as seen in Fig. 3. The sinusoidal behavior upon rotating the light polarization provides strong evidence that the underlying mechanism of the force-induced PV effect is the BPV effect generated by local symmetry breaking due to inhomogeneous strain—namely, the FPV effect.

The FPV effect should be neither confined to ionic crystals nor restricted to nanoscale geometries. First, we performed the same experiment (as depicted in Fig. 1) on an HF-passivated surface of a commercial p-type Si (001) crystal. As in our initial experiment, ISC increased by two orders of magnitude from ~5 pA with the 1-mN loading force to ~0.5 nA with the 15-mN loading force [Fig. 4A and section S7 of (16)]. Second, we demonstrated the FPV effect by using a homebuilt indentation system that deforms a semiconductor by means of a conductive tungsten probe needle with a radius of ~10 mm (fig. S1). Figure 4B shows crystallographic orientation– dependent photocurrent-voltage (I-V) characteristics of the SrTiO3 crystal acquired under 4 N of mechanical force exerted by the probe needle and 405-nm laser illumination directly to the probe contact area, as in Fig. 1A. These linear I-V characteristics are similar to those of ferroelectrics under illumination (23). The oscillating PV current with the rotating light polarization, which is well fitted to Eq. 1 (Fig. 4C), demonstrates the FPV effect under the indentation force on the micrometer scale. The crystallographic orientation–dependent PV current is also observed when the TiO2 crystal is deformed by the indentation system (fig. S2). The persistence of the FPV effect from the nanoscale (AFM) to the micrometer level is promising for future device design and potential applications. The FPV effect is not related to a plasmonic effect found in the tip-enhanced Raman scattering: Only an atomically sharp tip coated with Ag or Au shows the plasmonic enhancement in the visible range (24), whereas we used platinum or tungsten probes ranging from the nanoscale to the micrometer scale. Likewise, a potential cubic-to-tetragonal phase transition induced in a SrTiO3 single crystal under a large hydrostatic pressure (>6 GPa) should not play a large role because of the centrosymmetric nature of the induced tetragonal phase (25).

We emphasize here four main features of the FPV effect. First, the separation of the photoexcited carriers in the FPV effect is controlled by the local symmetry and the resultant local BPV effect, in which the power conversion efficiency can, in principle, exceed the S-Q limit (8). Second, to obtain a high photocurrent from any semiconductor, only a strain gradient generator, such as a sharp probe with a sufficient loading force is necessary. This should be distinguished from the previous reports that a strain gradient modifies a bandgap, but the charge separation in the photoelectric process still requires a proper band alignment (26) or a nanostructure (27, 28). Third, whereas the BPV effect is possible only in noncentrosymmetric materials, the FPV effect is universal. It is allowed by symmetry in all materials, owing to the universal nature of the strain gradient– induced centrosymmetry breaking. The FPV effect can be realized in ionic crystals (SrTiO3 and TiO2) and covalent crystals (Si) but is also relevant to any semiconductors, ranging from organic-inorganic hybrid perovskites to semiconducting polymers and even topological insulators. For instance, the topological insulator Bi2Te3 with a centrosymmetric structure exhibits the BPV effect by means of the flexoelectric effect (29). Finally, given that the BPV effect consists of asymmetric quantum mechanical processes such as photoexcitation, relaxation, recombination, and scattering, we demonstrate that one can readily control the quantum mechanical processes by macroscopic tools such as an AFM tip and a probe needle.

The configuration of our PV indentation system is very simple, and the FPV effect can be increasingly substantial with material dimensions decreasing into the nanoscale where flexoelectricity is more important (11). Thus, an valuable strain engineering route for improving the performance of solar cells and optoelectronic devices is now open. For example, a tandem solar cell can be easily fabricated by combining an array of indenters and a conventional p-n junction, enabling a higher efficiency because the FPV effect can be designed to boost the existing PV current generated by the buried p-n junction. Given that the lattice mismatch at the interfaces and crystallographic disorders in epitaxial and polycrystalline thin film solar cells produce substantial strain gradients (30–32), the associated FPV effect would considerably enhance the performance of these solar cells; however, this topic remains largely unexplored. In addition to inorganic solar cells, the FPV effect is also likely to play an important role in flexible and stretchable electronics based on organic and polymeric semiconductors. Both the bending of flexible organic devices at the macroscopic level (33) and the folding and entanglement of the polymeric chains at the nanoscale would generate sizable strain gradients (34), which redistribute the electron cloud of p molecular orbits, modifying electronic transport and inducing the FPV effect under illumination (15, 35). But the details of how strain gradient and FPV effects influence nanoscale electronic properties remain a matter of debate.

ACKNOWLEDGMENTS

We thank J. Lloyd-Hughes for grammatical revision of the manuscript and B. Tao for assistance with schematic drawing. Funding: M.-M.Y. acknowledges the University of Warwick for a Chancellor’s International Scholarship. M.A. acknowledges the Wolfson Research Merit and Theo Murphy Blue Skies awards from The Royal Society. This work was partly supported by the EPSRC (UK) through grants EP/M022706/1, EP/P031544/1, and EP/P025803/1. Author contributions: D.J.K. initiated the project. M.-M.Y., D.J.K., and M.A. conceived of and developed the ideas. M.-M.Y. and D.J.K. designed and conducted the experiments, analyzed the data, and wrote the manuscript. All authors contributed to the discussion of the results and the manuscript revision. M.A. supervised the project. Competing interests: M.-M.Y., D.J.K., and M.A. are authors of British Patent Application GB1702466.2 filed in the UK by the University of Warwick on 15 February 2017 that covers PV devices based on strain gradient inducers. Data and materials availability: All scientific data related to this paper are available at the University of Warwick open access research repository (http://wrap.warwick.ac.uk/100429).

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/360/6391/904/suppl/DC1 Supplementary Text Figs. S1 to S15 References (36–43) 28 March 2017; accepted 6 April 2018 Published online 19 April 2018 10.1126/science.aan3256

GRAPH: Fig. 3. Light polarization dependence of the force-induced photocurrent. (A and B) Sinusoidal dependence of the photocurrent measured on (A) a SrTiO3 (010) face and (B) a TiO2 (001) face under 405-nm laser illumination. The red lines are fits to Eq. 1. Error bars indicate the SD of the PV current measured 25 times.

GRAPH: Fig. 4. FPV effect extended to covalent crystals and to the micrometer scale. (A) Force-induced photocurrent on a (001) Si crystal, as measured by Ph-AFM under illumination of the top indented surface. (B) Current-voltage characteristics measured on (001) and (111) faces of a SrTiO3 crystal by the microindenter applying a 4-N force under illumination of the top indented surface. (C) Light polarization dependence of the photocurrent on a SrTiO3 (010) face measured by the microindenter under illumination on the side surface. The red line is the fit of experimental data to Eq. 1. Because the polarization angle origin of the microindenter is not coincident with the Ph-AFM setup, the oscillating ISC has a phase shift compared with that depicted in Fig. 3B. Error bars indicate the SD of the PV current measured 50 times.

GRAPH: Fig. 1. Force-induced PV effect in centrosymmetric SrTiO3 and TiO2 single crystals. (A) Setup for illumination around the contact area. The tip loading force is controlled by the feedback loop of an AFM. (B) Setup for illumination on the side surface. This illumination geometry was chosen to avoid the effect of Fresnel reflection and to ensure that light absorption would be independent of the light polarization. (C and D) Evolution of the photocurrent induced and collected by a conductive AFM tip with a high loading force on (C) a SrTiO3 (001) face and (D) a TiO2 (100) face. (E) Loading force dependence of the induced photocurrent density and the relative volume subject to a strain gradient higher than 1 × 106 m−1 (fig. S9). a.u., arbitrary units. (F) Positive photocurrent measured on a TiO2 (001) face with a 15-mN force applied by the AFM tip.

GRAPH: Fig. 2. Spatial distributions of strain and strain gradient induced by an ideal spherical indenter. (A) The z component of strain (e) and (B) its partial derivative with respect to z are shown. The contact area with a radius (r) of 10 nm is centered at the origin, and the force is pointing upward. The positive (or negative) value of the strain means a tensile (or compressive) strain along the z axis.

PHOTO (BLACK & WHITE)