Electro–opto–mechano driven reversible multi-state memory devices based on photocurrent in Bi0.9Eu0.1FeO3/La0.67Sr0.33MnO3/PMN-PT heterostructures

A single device with extensive new functionality is highly attractive for the increasing demands for complex and multifunctional optoelectronics. Multi-field coupling has been drawing considerable attention because it leads to materials that can be simultaneously operated under several external stimuli (e.g. magnetic field, electric field, electric current, light, strain, etc.), which allows each unit to store multiple bits of information and thus enhance the memory density. In this work, we report an electro–opto–mechano-driven reversible multi-state memory device based on photocurrent in Bi0.9Eu0.1FeO3 (BEFO)/La0.67Sr0.33MnO3 (LSMO)/0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-PT) heterostructures. It is found that the short-circuit current density (Jsc) can be switched by the variation of the potential barrier height and depletion region width at the Pt/BEFO interface modulated by light illumination, external strain, and ferroelectric polarization reversal. This work opens up pathways toward the emergence of novel device design features with dynamic control for developing high-performance electric–optical–mechanism integrated devices based on the BiFeO3-based heterostructures.


Introduction
Facing the challenge of the limitation of Moore's law, 1,2 a single device that integrates extensive new functionality is highly desired for the ever-increasing demands for devices with faster, higher density, high energy efficiency data processing/storage with reversible and nonvolatile manipulation. [3][4][5] Very recently, multiferroic materials and heterostructures have been reported as two of the most promising candidates for realizing such an integration of different functions. [6][7][8][9][10][11][12] However, most of the studies mainly focus on the functional controllability using an external electric or magnetic eld, rarely paying attention to exploration of other external control parameters. In the quest for multifunctional materials, interactions arising from different media or dimensions are highly desirable. Nowadays, light control has become a novel manner with nondestructive program/erase process compared with electrical tuning, and can enhance the device performance remarkably. 2,13 These processes can be achieved through transforming light signal to electric response so as to achieve multi-bit and encryption storage. More particularly, light could also solve sneak path currents that plague ultralow cost electronics, 4,14 which endows new functionality for memory devices and may open possibilities of remote control for advanced optoelectronic applications. BiFeO 3 (BFO) is a multiferroic materials with robust ferroelectric and magnetic orders above room temperature [15][16][17] and a narrow optical bandgap ($2.5 eV) 18,19 than traditional ferroelectric photo-voltaic materials (such as LiNbO 3 , 20 BaTiO 3 , 21 (Pb,Zr)TiO 3 , 22 with quite large bandgap E g > 3.0 eV). It offers considerable light absorption capability and endows with novel physics and new degrees of freedom for multifunctional devices. However, many efforts have been devoted to enhancing the photovoltaic (PV) of BFO, 18,23-28 but unfortunately the power conversion efficiency is still poor (<0.2%) compared with other types of solar cells. 28 Thus, until recently ferroelectric photovoltaic (FE-PV) effect is still in its infancy rather than any real application. Alternatively, not just limited in the power conversion efficiency, the signal of photovoltaic effect can allow for information transfer and storage applications. 29,30 A unique characteristic of FE-PV devices is that the photocurrent direction can be switched by reversing the spontaneous polarization direction of a FE material with electric eld. 18 This feature is compatible and of central importance for the development of on-chip optical communication technology.
More signicantly, since Choi et al. rst reported the switchable ferroelectric diode and visible light-induced photovoltaic effects in BFO single crystals, 23 the coupling of ferroelectric polarization with optical properties in photo-active ferroelectrics has received a renewed attention, triggered notably by low bandgap ferroelectrics and original photovoltaic effects. [31][32][33][34] Interestingly, experimental and theoretical investigations have evidenced that the bandgap and polarization of a perovskite-type ferroelectric thin lm can be tuned by substrate-induced strain. [31][32][33][34] Fu et al. realized a maximum bandgap shi of 0.7 eV by growing BFO lms on SrTiO 3 substrates with various in-plane compressive strain. 33 Sando et al. reported that BFO lms deposited on different substrates can accommodate different kinds of strains from compressive one to tensile one. 34 However, these strain control schemes cannot rule out the effects of other extrinsic factors (oxygen nonstoichiometry, defects, dead layer, disorder, etc.) on the photovoltaic effects.
Alternatively, ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) single crystals are well known for their ultrahigh piezoelectric coefficient, large electromechanical coupling, and excellent ferroelectric and pyroelectric responses. 35 Numerous experimental works have demonstrated that the in-plane strain of oxide lms epitaxially grown on (1 À x)Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (0.28 $ x $ 0.33) ferroelectric substrates can be in situ and dynamically manipulated by applying an electric eld to the PMN-PT substrates, and thus the aforementioned various inuences can be avoided to a great degree. [10][11][12][35][36][37][38][39] Along this line, an emergent scheme is to fabricate multifunctional devices that can be achieved by combining a series of monofunctional components into a tight space. 40 However, as monofunctional devices mature and approach their fundamental limits, a pivotal question now is how to develop technologies enabled with increasing functionalities and reduced product size. A better and highly concerned scheme is to integrate multiple functionalities into one material for multiparametric detection. If it applies, the device structure would be signicantly simplied, beneting to the fabrication complexity reduction, integration level boosting, and possible application expansion.
So far, a comprehensive understanding of the combined electric-eld, light, and mechanical control of FE-PV and the resultant functionalities, both in situ and dynamically, are still limited for BFO thin lms. Moreover, there is an urgent demand for optoelectronics devices with a multifunctional integration and minimal size, which can satisfy the demand for fast, high density, high energy efficiency data processing/storage. There is no doubt that a systematic investigation of multi-eld tuned physical properties of BFO thin lms is highly expected. In this work, we report an electro-opto-mechano-driven reversible and multi-state memory device, based on photocurrent effect in Bi 0.9 Eu 0.1 FeO 3 (BEFO)/La 0.67 Sr 0.33 MnO 3 (LSMO)/PMN-PT heterostructures. The main property to be targeted for such a multi-eld tuning is the photo-induced electronic conduction. For a high-performance consideration, we focus on BEFO thin lms rather than BFO simply due to the fact that a slight Eu substitution at the Bi site would benet to the ionic defect and leakage suppression.
Our comprehensive investigation suggests that the photocurrent J sc of our heterostructures can be effectively switched by modulating the potential barrier height and depletion layer width at the Pt/BEFO interface, by means of various stimuli such as light illumination, strain, and ferroelectric polarization. More importantly, the device can produce photocurrent that allows us to read out the state in a self-powered manner. This discovery provides the means for engineering tunable single memory unit but enabling multi-functionalities such as switching between the volatile and nonvolatile modes by electric-optical-mechanical combination mode. This mode and associated functionalities open the door to novel multifunctional storage devices.
Herein, we propose a memory micro-array based on the Pt/ BEFO/LSMO/PMN-PT heterostructures to demonstrate our idea. In this prototype, "0" state and "1" state represents the P up state and P down state of the BEFO lm layer, respectively. The writing of "0" or "1" state in each cell can be easily realized by reversing the spontaneous polarization direction of the BEFO lm with electric eld. During reading the data, an incident light is irradiated to the whole micro-array, meanwhile, the induced J sc is directly detected for each cell at a zero-bias. Moreover, different polarization state produces different J sc , the data state in each cell is thus read out. This data storage mode can be called as "electrical writing and optical reading", which consumes fewer power than conventional modes. We can also develop a logical switching device that a unit cell with P up (or P down ) state, its logic state will be alternately switched to ON or OFF state when the incident light is on or off, then be read out by detecting the corresponding J sc . What's more, this kind of electronic device has much room to improvement when the light was turned on and off with and without a certain strain applied to the unit cell, which could get more reliable, larger/ smaller, and switchable J sc .

Experimental
The LSMO and BEFO thin lms were epitaxially grown on the (011)-oriented but non-poled PMN-PT substrates using the pulsed laser deposition (PLD) technique. First, the LSMO layer with thickness of 60 nm was deposited on the substrate with a deposition rate of 4 nm min À1 , where the temperature and laser repetition ratio were kept at 700 C and 3 Hz under an oxygen pressure of 40 Pa. Aer the deposition, the oxygen was lled into the chamber at maximal ow rate and the as-grown LSMO was annealed in situ for 30 min at 700 C and then cooled down to room temperature at 4 C min À1 . Subsequently, the BEFO layer with thickness of 120 nm was deposited on the LSMO thin lm at a deposition rate of 2 nm min À1 , where the temperature and laser repetition ratio were kept at 660 C and 3 Hz under an oxygen ambient pressure of 15 Pa. Aerwards, the oxygen was lled into the chamber at maximal ow rate right aer the deposition, while the sample was cooling at a rate of 2 C min À1 . When the chamber pressure reached 1.0 atm, the thin lm was annealed at 400 C for 30 min and then cooled to room temperature at 4 C min À1 . In the case of precise control of above parameters, the lm thickness is controlled by the number of laser pulses.
The structure of the as-prepared BEFO/LSMO/PMN-PT heterostructure was characterized by X-ray diffraction (XRD, Bruker D8 Advance). The ferroelectric domain structures were probed by the piezoresponse force microscopy (PFM, Bruker Multimode 8) using the Pt-coated Si cantilevers. For the strain control, we applied electric eld across the piezoelectric PMN-PT substrate and induced the in-planar lattice distortion (strain) which was transferred into the BEFO thin lm above the LSMO bottom electrode. A voltage source was employed to supply an electric eld across the PMN-PT substrate through the LSMO bottom electrode and the In back-electrode on the back side of PMN-PT substrate (as shown in Fig. 1(a)). It is noted that the positive bias was applied to the In electrode and the ground was applied to the LSMO electrode in our measurement.
For the transport behaviors of the as-prepared BEFO thin lm, the current-voltage (J-V) curve was measured across the BEFO lm using the Keithley 4200 characterization system with the voltage sweeping mode. Here, the top Pt electrode with a 0.5 mm Â 0.5 mm square shadow mask was deposited on the BEFO lm surface using the magnetron sputtering technique. The positive (negative) voltage was dened as the positive (negative) bias applied to the top Pt electrodes.
For the light illumination, a diode laser with a wavelength of 405 nm (hv ¼ 3.06 eV) and power density of 200 mW cm À2 was used as the illumination source. The measurement setup schematic is shown in Fig. 1(a), where photo-current J sc was obtained using the following mode. First, the sample was poled by a voltage pulse V P of 100 ms in width in the dark or light illumination condition. Second, the sample was submitted to a low voltage sweeping from À0.5 V to 0.5 V during which the J-V curve was obtained, noting that a voltage of AE0.5 V is insuf-cient to change the initial polarization state. Third, the value of J sc was extracted from the J-V curve at V ¼ 0. Certainly, J sc can be also directly probed in the illumination ON/OFF testing (J sc ¼ 0 in the OFF case). Fig. 1(b) shows the q-2q scan XRD pattern of the as-prepared heterostructure grown on PMN-PT (011) substrates, in which only strong (0ll) (l ¼ 1, 2) diffractions from the BEFO and LSMO thin lms and substrate appear. It is suggested that both the BEFO and LSMO lms are single phase and highly (011)oriented. The expanded view near the BEFO (011) diffraction peak is shown in the inset (up) while the inset (down) exhibits the 4 scan of the (001) plane. The two-fold symmetrical diffraction peaks from the BEFO and LSMO lms can be clearly identied and they occur at the same 4 angles as those of the PMN-PT substrates, conrming a cube-on-cube epitaxial growth of the BEFO/LSMO lms on PMN-PT substrates. From the XRD spectra, the out-of-plane (OP) lattice constants of the BEFO, LSMO, and PMN-PT, as calculated from the (011) diffraction peak are 2.797, 2.724, and 2.842 A, respectively.

Structural characterizations
A further discussion on the strain state in the BEFO thin lm begins by looking at the lattice mismatch of 1.58% between the lm and substrate. The BEFO lm has smaller OP lattice constant than that of bulk BFO ($2.80 A), 41 revealing that the BEFO lm is subjected to an OP compressive strain ($À0.11%). Similarly, the OP lattice constant of the LSMO lm is smaller than that of bulk LSMO ($2.736 A), 42 revealing that the LSMO lm is subjected to an OP compressive strain ($À0.44%). According to the Poisson equation, the OP strain can be deduced as respectively. Thus, the estimated IP tensile strains for the BEFO and LSMO lms are $0.10% and $0.37%, respectively. These data suggest that the lattice strain in the PMN-PT substrate could largely be coherently transferred into the BEFO lm.

Ferroelectric behaviors
To characterize the ferroelectric properties of the as-prepared BEFO thin lm, vertical piezoresponse force microscopy (V- PFM) was performed and the results are highlighted in Fig. 2. The atomic force microscopy on the BEFO lm shows the small surface roughness of 2.16 nm (Fig. 2(a)). Using the PFM mode, a region of the BEFO lm can be electrically switched to create a "box-in-box" pattern, as shown in Fig. 2(b) for the phase contrast and Fig. 2(c) for the amplitude contrast. The outer region with a scan size of 1.0 mm Â 1.0 mm corresponds to the up-polarization (up-state) under a tip voltage of À10 V, while the internal region with a scan size of 0.6 mm Â 0.6 mm corresponds to the down-polarization (down-state) state under a tip voltage of +10 V. Furthermore, the typical phase and buttery-like amplitude loops are shown in Fig. 2(d) with the coercive voltages of about À1.3 V and 1.2 V, revealing the good ferroelectric property of the BEFO lm.
The PFM phase imaging also clearly identied that the selfpolarization of the fresh state is oriented upwards, which can be seen from the indistinct colour contrast between the AE10 V switching zone and the non-switching zone. This preference is believed to originate from the lattice mismatch induced residual stress in the thin lm. It is noted that the fresh BEFO lm was in the OP compressive state, leaving the positive and negative polarization charges to be created at the Pt/BEFO and BEFO/LSMO interfaces, as evidenced by earlier reports. 45

Polarization control
The photovoltaic responses of the BEFO lm were characterized by measuring the J-V curves under the light illumination (l ¼ 405 nm) onto the unpoled BEFO thin lm with remnant polarization P r 0 , positively poled lm with remnant polarization P r + , and negatively poled lm with remnant polarization P r À , respectively. It is noted that in this experiment, the PMN-PT substrate was in the unpoled state and thus no substrate polarization induced strain is available. The measured data are plotted in Fig. 3(a), from which several features deserve highlighting.
First, at zero bias, no open-circuit voltage V oc and no shortcircuit current J sc can be observed in the dark, as shown in Fig. 3(a). However, the BEFO lm under the light illumination shows signicant photovoltaic responses with V oc ¼ À0.7 mV and J sc ¼ 24.4 mA cm À2 , suggesting that the built-in electric eld can be affected by the illumination due to the photo-generated charges. Such an effect shows good retention, supported by the modulated photocurrent J sc as a function of time t by the light ON/OFF operation with an interval of 20 s, as shown in Fig. 3(b).
Second, to investigate the polarization-modulated photovoltaic effect, the BEFO layer in the heterostructure was prepoled using a pulse of V P ¼ 10 V and À10 V (pulse width 100 ms) so that the BEFO lm had the down-and uppolarization states, respectively, noting that the PMN-PT substrate remained to be unpoled. Here, the positive (negative) voltage is dened as the positive (negative) bias applied to the top Pt electrodes, and the positively and negatively poled states represent the up-and down-states, respectively. As shown in Fig. 3(a), the V oc and J sc values for the up-state increase up to À0.9 mV (by À28%) and 82.8 mA cm À2 (by 2390%), respectively. For the down-state with remnant polarization P r À , the measured V oc and J sc changed their signs and became 0.6 mV (by 186%) and À70.1 mA cm À2 (by À3870%), respectively. Third, the measured J sc shows the opposite responses for the thin lm in the up-state and down-state, as more directly seen in Fig. 3(c), by turning the light ON/OFF with an interval of 20 s, respectively. Here, it is possible to determine the polarization direction (stored information) by sensing the value of J sc , and this process is non-destructive. Subsequently, we performed a series of measurements in which different pulse voltages (V P ) to pole the BEFO thin lm were set and the measured J sc -V P hysteresis loop is plotted in Fig. 3(d). This loop exhibits hysteretic behaviors similar to the P-V loop shown in Fig. 2(d),  indicating that the ferroelectric polarization of the BEFO thin lm plays a key role in the switchable photovoltaic effect. The asymmetric J sc -V P curves also suggest that the photovoltaic response was dominated by the polarization modulated interfacial barriers rather than the bulk photovoltaic effect (BPE), 46 noting that the bulk effect dominated effect would produce a symmetric J sc -V P curve.

Strain control
The previous subsections have been devoted to the modulation of photovoltaic effect by external electric eld and ferroelectric polarization from the BEFO lm. This section is devoted to the intrinsic effect of electric-eld-induced PMN-PT piezoelectric strain on the photocurrent. To achieve it, a large dc electric eld E $ 10 kV cm À1 across the PMN-PT substrate was applied for 30 min to ensure a full polarization state (i.e. the pole state) of the substrate, noting that the positive bias was applied to the In back-electrode and the negative bias to the LSMO electrode. Fig. 4(a) shows the in situ XRD data from the heterostructure, given the unpoled and poled states of the PMN-PT substrate. An expansion along the OP direction associated with an effective IP lattice contraction can be identied. It is thus revealed that the BEFO lm is subjected to an OP compressive strain ($À0.04%) and an IP tensile strain (0.03%), noting that the initial OP and IP strains of the BEFO thin lm are À0.11% and 0.10%. The application of an electric eld with the same direction as the poling direction would induce an IP compressive strain in the PMN-PT via the well-known converse piezoelectric effect. 47 The induced strain is expected to be transferred to the BEFO lm via the LSMO layer.
As a result of the substrate piezoelectric strain, the photovoltaic properties can be modied due to the variation of strain state inside the BEFO lm. Fig. 4(b) shows the measured J-V curves of the BEFO lm in the dark and under light illumination (l ¼ 405 nm), given that the PMN-PT substrate was in the unpoled and poled states respectively for a comparison. In this experiment, the BEFO lm was in the unpoled state with remnant polarization P r 0 in this measurement. Obviously, the J-V curve of the fresh BEFO lm does not exactly pass through the origin in the dark, as shown in the inset of Fig. 3(a), indicating a built-in electric eld in the heterostructure. Under the light illumination, the fresh BEFO lm showed signicant photovoltaic response, also an indirect evidence for the built-in electric eld. 48 The measured J sc $ À1.6 mA cm À2 and V oc $ 0.1 mV were obtained, respectively, and the sign changes of V oc and J sc suggest that the built-in electric eld can be affected by the illumination due to the photo-generated charges. 30,49 The observed zero-bias photocurrent density was À1.6 mA cm À2 , which is superior to most active ferroelectric oxide BiFeO 3 ($0.4 mA cm À2 ). 50 Moreover, the M À H loops at different poling states have shown (Fig. S1 †) that the magnetization of the heterostructure can be manipulated by the electric eld induced piezo-strain, which could be used as evidence for magnetoelectric coupling effect at room temperature. However, we may need further research to understand this effect in depth. Now we come to see the consequence of applying an electric eld of +10 kV cm À1 to the PMN-PT substrate. The measured V oc and J sc signicantly increased up to 1.8 mV and À7.2 mA cm À2 , resulting in an enhancement by 1700% and 350%, respectively. These effects are much larger than earlier reported data for Fe 3 O 4 /PMN-0.29 PT (011) heterostructure where the modulation magnitude for magnetization is only <3% at 300 K and that for resistance is also only <3% at 300 K. 51 Certainly, it is highly desirable to achieve a sufficiently large modulation of the concerned properties in a reversible and nonvolatile manner at room temperature, and thus the present work represents a substantial step to practical applications.
To check the stability and reliability of this piezoelectric strain induced effect, we measured J sc as a function of time by turning the light ON and OFF, given that the PMN-PT substrate was under zero electric eld and non-zero eld E ¼ +10 kV cm À1 . The results are plotted in Fig. 4(c). It is seen that the measured J sc under E ¼ +10 kV cm À1 was much larger than that under E ¼ 0. The magnitude of J sc under E ¼ +10 kV cm À1 is even more stable than the case under E ¼ 0, upon turning the light on and off. These effects can be further demonstrated by turning ON/OFF the electric eld applied to the PMN-PT substrate between E ¼ +10 kV cm À1 and E ¼ 0, given the on-state of the light illumination. As seen in Fig. 4(d), the sequence of E ¼ +10 kV cm À1 and E ¼ 0 did make the response of J sc sharply and repeatedly. All these results demonstrate that the piezoelectric strain from the substrate can be used to modulate the photovoltaic effects in the present heterostructure.

Multi-eld control
Given the photocurrent modulation using the ferroelectric polarization of the BEFO thin lm and the piezoelectric strain from the substrate, it is time to investigate the multi-eld control sequence. It is proposed that the control parameters include the polarization states (P r + or [, P r À or Y) of the BEFO thin lm and the piezoelectric strain states (1 @ E ¼ 10 kV cm À1 , 0 @ E ¼ 0) of the PMN-PT substrate. The memory state of the Pt/BEFO/LSMO/PMN-PT heterostructure is characterized by the photocurrent J sc stimulated by the light illumination on/ off switching. Surely, we can reach at least eight photocurrent states that can be denoted by J sc ([, 0,  However, it should be mentioned that the difference in J sc among the four light illumination off states is technically indistinguishable, and therefore usually the four states are treated as one high-resistance state (J sc $ 0). In consequence, we can access the ve states rather than eight states: J sc ([, 0, on), J sc (Y, 0, on), J sc ([, 1, on), J sc (Y, 1, on), J sc (off). Fig. 5 presents one set of measured data for multi-eld control.
From Fig. 5(a and b), it is clearly shown that the ve states can be easily accessed by simply switching on/off the lightillustration, the electric eld applied to the PMN-PT substrate, and the [Y ferroelectric polarization states. For a quantitative estimation of the photocurrent switching performance, one may dene the equivalence-of-merit (EOM) as: ; onÞ À J sc ðoffÞÞ=J sc ðoffÞ; EOM Y ¼ ðJ sc ðY; 1; onÞ À J sc ðoffÞÞ=J sc ðoffÞ; (1) First, it is interesting to note that the EOM [ and EOM Y can be as large as $1130% and 1200%, respectively, representing the largest values so far reported in literature. Second, it is further demonstrated that the photocurrent switching on/off can be safely and reliably realized by either switching on/off the electric eld applied to the PMN-PT substrate (piezoelectric switching on/off), or switching the ferroelectric polarization of the BEFO thin lm between P r + and P r À , or even switching both simultaneously. Whether with or without the application of E ¼ +10 kV cm À1 to the PMN-PT, the signs of J sc are always positive for P r + and negative for P r À , respectively (as shown in Fig. 5 (a and b)). Moreover, when applying an electrical eld of E ¼ +10 kV cm À1 to the PMN-PT, the value of J sc are reduced for P r + and enhanced for P r À , respectively. Just looking at the data in Fig. 5 indicates that the light turn-on can make the magnitude of J sc to rapidly rise up to 0.124 mA cm À2 and À0.088 mA cm À2 for the [ and Y states respectively, from the black state with J sc $ 8.0 mA cm À2 . Furthermore, sharp response to the on/off switching of the substrate piezoelectric strain is also clearly identied.

Discussion
In this section, we focus on the possible mechanisms underlying such multi-eld control processes, and a comprehensive microscopic scenario would be very helpful for designing and fabricating advanced devices. Obviously, once the piezoelectric strain is applied, the negative photocurrent (for P r À ) will be enhanced, the positive photocurrent (for P r + ) will be reduced. The underlying mechanism is dominated by the enhanced (or reduced) the barrier of the Pt/BEFO lm by the piezoelectric potential, and this enhanced (or reduced) the barrier does suppress (or enhanced) the photovoltaic effect of the heterostructure. Such a stable and distinct electric-eld-and light-driven ferroelectric photovoltaic effect in the heterostructures may provide a pathway toward multistate memory and electro-optical devices.
To understand this behavior, it is noted that Fu et al. systematically investigated the relationship between the bandgap (E g ) and the in-plane stress (s xx ) for the BFO lm, and it was found that the E g as a function of s xx can be described by the following relation: 33 From eqn (2), the electric-eld-induced shi in bandgap DE g can be written as: where s xx (0) and s xx (E) are the in-plane stress of the BFO lm under zero and nonzero electric eld (E) applied to the PMN-PT substrate. For the BEFO lm, the in-plane stress can be estimated using the biaxial strain model: 47 where Y is the Young's modulus of the BEFO lm, d eff is the effective piezoelectric coefficient. We have: where c ij denotes the elastic stiffness constants and one can choose c 11 ¼ 302 GPa and c 12 ¼ 162 GPa. 52 Assuming a plane stress condition, one can have d eff as To further understand the electro-and mechano-driven photovoltaic effect, we sketch a schematic of the multi-eld coupling and interfacial band diagrams in Fig. 6. In order to determine the energy band alignment of BEFO, we carried out ultraviolet photoelectron spectroscopy (UPS) measurement (the results are shown in Fig. S2 †). The band-gap and electron affinity of BFO are 2.8 eV and 3.39 eV respectively. 53 The work function of LSMO and Pt are 4.7 eV and 5.3 eV. 54 Thus, a Schottky barrier can be developed at the Pt/BEFO interface, while the BEFO/LSMO interfacial band is nearly at. On the other hand, due to lattice mismatch-induced residual stress, the fresh BEFO lm is in the compressive strain state. This results in the positive and negative polarization charges created at the Pt/BEFO and BEFO/LSMO barriers. It is the reason why the selfpolarization of the fresh BEFO lm was oriented upwards.
The piezoelectric potential can be generated, which can modulate effectively the carrier transport and subsequently the energy band at the interface. The so-called piezo-phototronic effect, which causes the interfacial band bending via piezoelectric strain, can also modulate the interfacial carrier transport behavior. Under the light illumination, the photogenerated carriers are excited from the BEFO layer, and then separated by the net built-in electric eld (E bi ) which is the summation of the built-in eld (E in ) based on the Pt/BEFO Schottky barrier, the piezoelectric eld E piez induced by piezoelectric polarization charges, and the depolarization eld E dp caused by ferroelectric polarization.
It is well known that the ferroelectric polarization plays a dominant role in the transport of the metal/ferroelectrics/ metal structure. For the BEFO with the downward polarization, the depletion region at the Pt/BEFO interface becomes wider and the band bending goes up. The direction of E bi is upward aligned, generating a negative photocurrent and a positive photovoltage. On the other hand, for the BEFO lm with the upward polarization, due to the positive polarization charges, the depletion region at the Pt/BEFO interface becomes narrower and the band bending goes down. The direction of E bi is downward aligned, generating a positive photocurrent and negative photovoltage.
If the polarization is reversed, the direction of built-in eld in the Pt/BEFO interface can be reversed. Therefore, the signs of J sc and V oc are opposite for the two different polarization states in the Pt/BEFO/LSMO/PMN-PT heterostructure (as shown in Fig. 3(b)). Moreover, the higher Schottky barrier at the Pt/BEFO interface provides a larger built-in eld as a driving force to separate the photo-generated electron-hole pairs more efficiently. Therefore, the larger magnitudes of V oc and J sc in the Pt/ BEFO/LSMO/PMN-PT heterostructure with the upward polarization were observed experimentally.
The modulation of the photocurrent by strain can be also discussed following this scheme. If a strain is applied, a certain amount of negative or positive piezo-charges will gather at the Pt/BEFO and BEFO/LSMO barriers, respectively. These piezocharges can adjust the height and width of the Pt/BEFO barriers. When the direction of E piez is parallel to E dp , the transport of photon-generated holes to the bottom of the BEFO layer will be enhanced. If the direction of E piez is anti-parallel to E dp , the mobility of photon-generated holes would be suppressed.
Meanwhile, if the BEFO thin lm is submitted to a compressive strain, the reduced E g in BEFO will result in the release of more electrons from oxygen vacancies to the conduction band under the UV light illumination, leading to the enhanced carrier density. Conversely, if the BEFO lm is in the tensile strain state, the enlarged E g in BEFO reduces the carrier density. Given that tensile and compressive strains result in opposite electric eld in a piezoelectric material, as negative and positive piezo-potential is applied to the BEFO lm. Consequently, a permanent and controllable internal electric eld can be introduced to reversibly modulate the height of potential barrier and width of depletion region at the Pt/BEFO interface by piezo-phototronic effect and ferroelectric polarization effect. Such an electric-optical-mechano driven photocurrent in a single device with diverse functionalities may provide a pathway toward multi-state memory and electrooptical devices.

Conclusions
In summary, we have successfully achieved an electro-optomechano-driven reversible multi-state memory based on photocurrent in the BEFO/LSMO/PMN-PT heterostructures.
Here the key mechanism is that the competition between the built-in eld (E in ) based on the Pt/BEFO Schottky barrier, the piezoelectric eld E piez induced by piezoelectric polarization charges, and the depolarization eld E dp caused by ferroelectric polarization plays a key role in determining the modulation of the photovoltaic process. By electrically switching the polarization state between P up and P down , the polarization direction can be detected non-destructively via J sc at a zero-bias. Moreover, if a unit cell in P up (or P down ) state, its logic state will be alternately switched to On or OFF state when the incident light is on or off, and can be read out by detecting the corresponding J sc . Further, the piezoelectric potential can be generated when the BEFO in a compressive or tensile state, which can modulate effectively the carrier transport and subsequently the energy band at the interface. Based on the ferroelectric photovoltaic effect and piezo-phototronic effect, we achieved a ve J sc states in a unit cell, which is more benecial for the multi-bit data storage and data readout. Meanwhile, it is interesting to note that the EOM [ and EOM Y can be as large as $1130% and 1200%, respectively, representing the largest values so far reported in literature. Our ndings offer a new insight for integrated with much new functionality into one single device, which provide a pathway toward multi-state memory and electro-optical devices.

Conflicts of interest
There are no conicts to declare.