Impulse voltage control of continuously tunable bipolar resistive switching in Pt/Bi
0.9Eu
0.1FeO
3/Nb-doped SrTiO
3heterostructures
Maocai Wei1 · Meifeng Liu1 · Xiuzhang Wang1 · Meiya Li2 · Yongdan Zhu2 · Meng Zhao2 · Feng Zhang2 · Shuai Xie2 · Zhongqiang Hu3 · Jun-Ming Liu4
Received: 19 December 2016 / Accepted: 6 February 2017 / Published online: 1 March 2017
© Springer-Verlag Berlin Heidelberg 2017
1 Introduction
With the fast development of information storage tech- nology, high-density, fast, and nonvolatile random access memory with low energy consumption has attracted exten- sive research interest [1–5]. Resistive switching (RS) devices [1, 4], usually consisting of an insulating or semi- conducting layer sandwiched by two electrodes, is one of the most promising candidates for non-volatile memories, in which the resistance can be reversibly switched between a high resistance state (HRS) and a low resistance state (LRS) by applying a voltage pulse while the read out is non- destructive. The RS effect has been evidenced in a num- ber of materials, including binary transition metal oxides [2, 6–8], ternary and multicomponent perovskite-type oxides [9–11], and some others [12]. Several mechanisms underlying the RS behaviors have been proposed, includ- ing the conductive filament mechanism [7], cation valence changes [10], and ferroelectric polarization modulation of the Schottky barrier [13, 14]. However, both the conductive filament mechanism and the cation valence change mecha- nism involve the local chemical or valence changes, which may result in the degeneration of data retention and endur- ance [15, 16]. In the ferroelectric polarization modulation of the Schottky barrier, a Schottky junction or a p-n junc- tion could be formed at the metal/ferroelectric interface or the ferroelectric/n-type semiconductor interface, in which the height of potential barrier and width of depletion region can be modulated by the ferroelectric polarization, conse- quently inducing the RS behaviors. Furthermore, since the ferroelectric polarization reversal does not induce a chemi- cal change and is an intrinsically fast process, the ferroe- lectric RS effect has attracted increasing attention in recent years [13, 14, 16].
Abstract Epitaxial Bi0.9Eu0.1FeO3 (BEFO) thin films are deposited on Nb-doped SrTiO3 (NSTO) substrates by pulsed laser deposition to fabricate the Pt/BEFO/NSTO (001) heterostructures. These heterostructures possess bipolar resistive switching, where the resistances versus writing voltage exhibits a distinct hysteresis loop and a memristive behavior with good retention and anti-fatigue characteristics. The local resistive switching is confirmed by the conductive atomic force microscopy (C-AFM), sug- gesting the possibility to scale down the memory cell size.
The observed memristive behavior could be attributed to the ferroelectric polarization effect, which modulates the height of potential barrier and width of depletion region at the BEFO/NSTO interface. The continuously tunable resis- tive switching behavior could be useful to achieve non-vol- atile, high-density, multilevel random access memory with low energy consumption.
* Meiya Li [email protected]
1 Institute for Advanced Materials, and School of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China
2 School of Physics and Technology, and Key Laboratory of Artificial Micro/Nano Structures of the Ministry of Education, Wuhan University, Wuhan 430072, China
3 Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA
4 Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
BiFeO3 (BFO) is one of the most studied single-phase multiferroic materials at room temperature [17–21]. Its fas- cinating physical properties provide extensive possibilities for multifunction device applications [18–21], such as fer- roelectric/multiferroic tunnel junctions [19, 20], switchable photo-voltaics [21], and ferroelectric memristors [13, 16].
The bipolar RS effect was observed in BFO thin films with metal-ferroelectric-metal structure [13, 16, 21–23]; how- ever, its memristive behavior has not yet attracted enough attention until recently [13, 24]. When the sweeping volt- age is removed, the device retains its last resistance state and this resistance depends on the applied pulse voltage.
Therefore, BFO heterostructures can act as nonvolatile and multilevel memory elements, which offer the potential applications in high-density multilevel nonvolatile memo- ries and adaptive networks that require synapse-like func- tions [24]. In the high-quality epitaxial films, the observed ferroelectric RS behaviors have been attributed to the ferro- electric polarization modulation on the height of potential barrier and width of depletion region under applied elec- tric field [13, 22, 23]. Even though the films are grown epi- taxially, conductive filaments may readily form in the films due to the possible charged defects and domain boundaries [25]. Doping with rare-earth oxides could reduce impu- rity phases and suppress the generation of oxygen vacan- cies and other charge defects, which may greatly modify the conductive behavior of BFO-based heterostructures [26–28]. Nevertheless, study on the RS properties in doped BFO has been limited in the literature.
In this paper, we report the bipolar RS behaviors of a 10.0 at% Eu-doped BFO (BEFO) in the Pt/BEFO/NSTO heterostructures, in which the possibility of conductive fila- ments formation can be maximally reduced [28]. We find that the resistance states vary with the writing pulse volt- ages, and the states are reversible and continuously tuna- ble. Each state exhibits the good retention and anti-fatigue characteristics. The observed memristive behaviors can be attributed to the ferroelectric modulation on the height of potential barrier and width of depletion region at the BEFO/NSTO interface.
2 Experimental details
The Bi0.9Eu0.1FeO3 (BEFO) thin films were epitaxially grown on one-side-polished (001) oriented 0.7 wt% Nb- doped SrTiO3 (NSTO) single crystal substrates (with size of 3 × 3 × 0.5mm3) by pulsed laser deposition using a KrF excimer laser (248 nm, Lambda Physik COMPex 205). Due to the volatility of bismuth during deposition, BiEu0.1FeO3 ceramic target with 10% excess bismuth was used to fabri- cate the BEFO films. During the deposition, the substrate temperature and laser repetition ration were, respectively,
kept at 660 °C and 3 Hz under an oxygen ambient pres- sure of 15 Pa. The thickness of BEFO thin films is about 180 nm. After deposition, the samples were firstly cooled to 400 °C at 2 °C/min in an oxygen pressure of 1 atm and then cooled to room temperature at 4 °C/min. The Pt top elec- trodes with diameter of 200 µm were deposited by magne- tron sputtering with a shadow mask. The bottom electrode was fabricated by welding In pad on the back side of NSTO substrates.
The surface morphology of the BEFO films was observed using an atomic force microscope (AFM). The crystallographic orientation and phase purity of the BEFO films and epitaxial relationship between the BEFO film and NSTO substrate were characterized by X-ray diffraction (XRD, Bruker D8 Advance) θ − 2θ and ϕ-scans, respec- tively, equipped with Cu Kα1 radiation (λ = 1.5406 Å).
The current–voltage (I–V) measurements were carried out using a Keithley 4200 semiconductor characterization sys- tem with the voltage sweeping mode at room temperature, in which the top Pt electrode was connected to the posi- tive and the bottom In electrode to the ground. The maxi- mum current was limited by a compliance current (CC) to avoid permanent hard breakdown during the HRS to LRS switching. The local conductive properties were character- ized by the conductive atomic force microscope (C-AFM, Bruker Multimode8 SPM) with Pt-coated Si probes (SCM- PIT). For the electrical measurements, the bias voltage was applied to the sample and the conductive tip was grounded and directly contacted the BEFO films.
3 Results and discussion
Figure 1a shows the XRD θ-2θ scan of the BEFO films grown on NSTO (001) substrates. The strong BEFO (00l) (l = 1, 2) diffraction peaks appear in the XRD pattern, sug- gesting a single phase and highly (00l) oriented BEFO film.
Additionally, the in-plane epitaxial relationship between the BEFO film and the NSTO substrate was confirmed by the ϕ-scan of the BEFO (011) and NSTO (011) plane, as shown in the inset (top) of Fig. 1a. The fourfold sym- metrical diffraction peaks from the BEFO film appear at every 90°, occurring at the same ϕ-angles as those from the NSTO substrate, revealing good epitaxy of the BEFO film on the NSTO substrate.
The square average roughness of the BEFO film meas- ured by an AFM in a scan size of 5 μm × 5 μm is about 2.72 nm, indicating a smooth surface of the film, as shown in the inset (bottom) of Fig. 1a. The I–V characteristics of the Pt/BEFO/NSTO heterostructures obtained at room tem- perature are shown in Fig. 1b. It is noted that a fresh sample was always in the HRS which can be switched to an LRS by applying a high positive voltage pulse, without forming
process, and then it can be switched back to the HRS by applying a negative voltage pulse. The I–V curve exhibits a hysteresis behavior, indicating a RS characteristic of the heterostructures. In addition, a distinct diode-like current rectification [29] can be identified as shown in the inset of Fig. 1b. This is understandable since the BEFO is a p-type semiconductor and it can form a p–n junction barrier at the BEFO/NSTO interface after connecting with an n-type NSTO, resulting in the forward current rectification behav- ior. Although the Pt/BEFO interface is also a Schottky junction, the p–n junction across the BEFO/NSTO inter- face plays a dominate role in the RS behavior, which can be seen from the direction of current rectification, consistent with earlier reports [13, 30].
To investigate the bistable RS behavior in the hetero- structures, we applied the positive (+2.5 V) and negative (−4 V) voltage pulses (with pulse width of 1.0 ms) to polarize the BEFO film downward and upward, respec- tively, and then measured the I–V curves in a low voltage range, respectively, as shown in the Fig. 2a. Obviously, the current after applying the positive voltage is larger than that after applying the negative one, which means that the resistance switches from LRS to HRS when the polarization is reversed from downward direction to upward one. This suggests that the polarization reversal is closely related to the RS in the Pt/BEFO/NSTO het- erostructures, similar to previous reports [13, 16, 23].
We chose −0.3 V as the reading voltage and recorded the resistance of the heterostructure after applying writ- ing voltage pulses, as shown in Fig. 2b. We noted that the resistance–voltage (R–V) loop is asymmetric, indi- cating a bipolar RS behavior. If the device is set to HRS by applying a pulse of −4 V, the resistance will gradu- ally reduce with increasing positive writing pulse volt- age. Conversely, if the heterostructure is set to LRS by
applying a pulse of +2.5 V, the resistance will gradually increase with increasing negative writing pulse voltage.
These results indicate a memristive behavior that can be continuously tuned by the voltage pulse, which benefits to the multilevel memories with low energy consumption.
Furthermore, the retention capability of the device in HRS and LRS was investigated, and no significant decrease in resistance magnitudes was observed within 50000s, revealing the good retention characteristics of the resist- ance in the heterostructures, as shown in Fig. 2c. Figure 2d presents the anti-fatigue test, and the resistance can be switched between the HRS and LRS, thus achieving the nonvolatile bipolar electric field control of resistances.
These good retention and anti-fatigue characteristics are highly desired for the non-volatile random access mem- ory devices. For our Pt/BEFO/NSTO heterostructures, the resistance ratio is comparable with those data reported ear- lier for the BFO devices [13, 30, 31] and the writing volt- age is smaller, which show advantages for the application in the nonvolatile memories.
The local C-AFM current images (with size of 1 µm × 1 µm) were obtained by scanning at bias of +4 V and −4 V, as shown in Fig. 3a, b, respectively. The dark area in Fig. 3a or bright area in Fig. 3b is the area with high conductive current. For the scanning bias of +4 V, some conductive locations corresponding to the LRS are of sizes up to a few hundred nanometers, obviously larger than the size of filaments with tens of nanometers [6]. For the scan- ning at −4 V, most of the conductive locations disappear, so the resistance switches to HRS. The local variations in the obtained current image are similar to that previously reported in BFO [13, 32]. Even though the distribution of the conductive regions is inhomogeneous, it is quite differ- ent from the images arising from the formation and rupture of filaments. Furthermore, this observed local RS suggests
Fig. 1 a XRD θ − 2θ scan of BEFO/NSTO heterostructures, inset (top) is ϕ-scan of the BEFO (011) and NSTO (011) planes, inset (bottom) is the AFM image of the BEFO film within a scan size of
5 μm × 5 μm. b Measured I–V curve of the Pt/BEFO/NSTO hetero- structures, the inset shows the rectifying I–V characteristics
Fig. 2 The RS characteristic of the Pt/BEFO/NSTO heterostructures: a I–V curves at the LRS and HRS; b Resistances as a function of writing pulse voltages at Vread = −0.3 V. c The retention time at both the HRS and LRS; d the anti-fatigue test of the Pt/BEFO/NSTO heterostructures
Fig. 3 a and b show the local area C-AFM current images scanned by applying a bias of +4 V and −4 V, respectively
the possibility to scale down the RS cell size, which is promising for high-density storage devices.
Figure 4a presents a schematic equilibrium energy band structure of the Pt/BEFO/NSTO heterojunctions, where NSTO has an energy band gap of 3.2 eV and an electron affinity of 4 eV [33], while the energy band gap and elec- tron affinity of BFO are 2.8 eV and 3.3 eV [34], respec- tively. Noting that the work function of Pt is 5.65 eV [35], the built-in voltage Vbi can be deduced as the difference between the two work-functions Vbi(Pt/BEFO) = 5.65 − (4.7 + y) ~ 0.95 V and Vbi(BEFO/NSTO) = (4.7 + y) − (4.08 + x) ~ 0.6 2 V, where x and y are small values. The two built-in volt- ages are aligned along the same direction, leading to a big total built-in voltage of ~1.57 V, which is the reason for the asymmetry in R-V loop curve in Fig. 2b.
Since the barrier heights of electrons and holes are 1.32 eV and 1.72 eV, respectively, the conductive behav- iors are mainly dominated by the major charge carrier (electrons), corresponding to a turn-on voltage of ~1.32 V for an ideal p-n junction. The turn-on voltages for the HRS and LRS are 1.5 V and 1.0 V, respectively. These values are more or less deviated from the ideal turn-on voltage of 1.32 V, which is most likely due to the band modulation
by the ferroelectric polarization of the BEFO. The forward current rectification observed in the Pt/BFO/NSTO het- erostructures suggests that the p–n junction at the BEFO/
NSTO interface plays a dominate role [13, 30], as shown in Fig. 4b, c. The RS behavior in the Pt/BFO/NSTO het- erostructures can be explained by considering the ferroelec- tric polarization modulation on both the width of depletion region and height of potential barrier at the BEFO/NSTO interface [32]. The depletion region with a certain width will form across the BEFO/NSTO interface after reach- ing the dynamic equilibrium state. When the polarization is downward upon the positive bias voltage imposing, the negative majority carriers (electrons) in the n-type NSTO are attracted by the positive bound charges and migrate to the interface, resulting in a decrease in the depletion width, as shown in Fig. 4b. In contrast, when the polari- zation is upward upon the negative bias voltage applying, the electrons in the n-type NSTO are repelled by the nega- tive bound charges at the BEFO/NSTO interface, which increases the depletion width, as shown in Fig. 4c.
Furthermore, since the screening of the bound charges is usually incomplete, a depolarization field with opposite direction to the polarization is developed in the ferroelectric
Fig. 4 Energy band diagrams for the Pt/BEFO/NSTO heterojunction a at original as grown state, b with polarization downward (at LRS) and c with polarization upward (at HRS)
layer, which induces energy band bending at the interface, leading to the variation of the potential barrier height and, consequently, a larger negative pulse voltage than the posi- tive pulse voltage is needed. Moreover, since the ferroelec- tric polarization reversal is driven by the applied voltage, the depletion width and potential barrier height would vary continuously with the applied voltage, and accordingly induce a gradually change in resistance. Therefore, the memristive behavior of the Pt/BEFO/NSTO heterostructure could be attributed to the modulation effect of ferroelectric polarization on both the depletion width and the potential barrier height of the BEFO/NSTO interface.
4 Conclusions
In summary, the epitaxial BEFO thin films have been suc- cessfully prepared on NSTO substrates by pulsed laser dep- osition to form the Pt/BEFO/NSTO heterostructures. The heterostructures exhibit the significant memristive behav- iors with a continuously tunable RS behavior, and good retention and anti-fatigue characteristics. By simply apply- ing voltage impulses, a robust, non-volatile, and reversible modification of resistance states is demonstrated due to the remnant polarization in the ferroelectric layer. The local RS observed by C-AFM suggests the possibility to scale down the memory cell size. Our results provide a pathway towards ferroelectric memristor that could be useful for compact, reconfigurable, and energy-efficient adaptive net- works and memory devices.
Acknowledgements This work was supported by the National Nat- ural Science Foundation of China (Grant Nos. 51372174, 51132001, 11364018, J1210061 and 11504101), the Natural Science Founda- tion of Hubei Province (Grant No.: 2014CFB610), and the Excel- lent Young Innovation Team Project of Hubei Province (Grant No.
T201429).
References
1. R. Waser, R. Dittmann, G. Staikov, K. Szot, Redox-based resis- tive switching memories—nanoionic mechanisms, prospects, and challenges. Adv. Mater 21, 2632 (2009)
2. M.J. Lee, C.B. Lee, D. Lee, S.R. Lee, M. Chang, J.H. Hur, Y.B.
Kim, C.J. Kim, D.H. Seo, S. Seo, A fast, high-endurance and scalable non-volatile memory device made from asymmetric Ta2O5-x/TaO2-x bilayer structures. Nat. Mater 10, 625–630 (2011) 3. J.M. Hu, Z. Li, L. Chen, C.W. Nan, High-density magnetoresist- ive random access memory operating at ultralow voltage at room temperature. Nat. Commun 2, 533 (2011)
4. D.S. Jeong, R. Thomas, R.S. Katiyar, J.F. Scott, H. Kohlstedt, A. Petraru, C.S. Hwang, Emerging memories: resistive switch- ing mechanisms and current status. Rep. Prog. Phys 75, 076502 (2012)
5. P. Jain, A. Stroppa, D. Nabok, A. Marino, A. Rubano, D. Pap- aro, M. Matsubara, H. Nakotte, M. Fiebig, S. Picozzi, E.S. Choi,
A.K. Cheetham, C. Drax, N.S. Dalal, V.S. Zapf, Switchable elec- tric polarization and ferroelectric domains in a metal-organic- framework. npj Quantum Mater 1, 16012 (2016)
6. D.H. Kwon, K.M. Kim, J.H. Jang, J.M. Jeon, M.H. Lee, G.H.
Kim, X.S. Li, G.S. Park, B. Lee, S. Han, Atomic structure of conducting nanofilaments in TiO2 resistive switching memory.
Nat. Nanotech 5, 148–153 (2010)
7. S.H. Chang, J.S. Lee, S.C. Chae, S.B. Lee, C. Liu, B. Kahng, D.W. Kim, T.W. Noh, Occurrence of both unipolar memory and threshold resistance switching in a NiO film. Phys. Rev. Lett.
102, 026801 (2009)
8. G.F. Zhu, S.S. Peng, C.L. He, X.J. Zhu, X.X. Chen, Y.W. Liu, R.W. Li, Improvement of resistive switching in Cu/ZnO/Pt sand- wiches by weakening the randomicity of the formation/rupture of Cu filaments. Nanotechnology 22, 275204 (2011)
9. G. Kim, D. Mazumdar, A. Gupta, Nanoscale electroresistance properties of all-oxide magneto-electric tunnel junction with ultra-thin barium titanate barrier. Appl. Phys. Lett. 102, 052908 (2013)
10. S.W. Chen, J.M. Wu, Unipolar resistive switching behavior of BiFeO3 thin films prepared by chemical solution deposition.
Thin Solid Films 519, 499–504 (2010)
11. Z.T. Xu, K.J. Jin, L. Gu, Y.L. Jin, C. Ge, C. Wang, H.Z. Guo, H.B. Lu, R.Q. Zhao, G.Z. Yang, Evidence for a crucial role played by oxygen vacancies in LaMnO3 resistive switching memories. Small 8, 1279–1284 (2012)
12. T.W. Kim, D.F. Zeigler, O. Acton, H.L. Yip, H. Ma, A.K.Y. Jen, All-organic photopatterned one diode-one resistor cell array for advanced organic nonvolatile memory applications. Adv. Mater 24, 828–833 (2012)
13. Z.Q. Hu, Q. Li, M.Y. Li, Q.W. Wang, Y.D. Zhu, X.L. Liu, X.Z.
Zhao, Y. Liu, S.X. Dong, Ferroelectric memristor based on Pt/
BiFeO3/Nb-doped SrTiO3 heterostructure. Appl. Phys. Lett. 102, 102901 (2013)
14. A.Q. Jiang, C. Wang, K.J. Jin, X.B. Liu, J.F. Scott, C.S. Hwang, T.A. Tang, H.B. Lu, G.Z. Yang, A resistive memory in semicon- ducting BiFeO3 thin-film capacitors. Adv. Mater 23, 1277–1281 (2011)
15. G.I. Meijer, Giant tunnel electroresistance for non-destructive readout of ferroelectric states. Science 319, 1625–1626 (2008) 16. A. Tsurumaki, H. Yamada, A. Sawa, Impact of Bi deficiencies
on ferroelectric resistive switching characteristics observed at p-type Schottky-like Pt/Bi1–δFeO3 interfaces. Adv. Funct. Mater 22, 1040–1047 (2012)
17. W. Ratcliff, J.W. Lynn, V. Kiryukhin, P. Jain, M.R. Fitzsim- mons, Magnetic structures and dynamics of multiferroic systems obtained with neutron scattering. npj Quantum Mater 1, 16003 (2016)
18. S. Dong, J.-M. Liu, S.W. Cheong, Z.F. Ren, Multiferroic materi- als and magnetoelectric physics: symmetry, entanglement, exci- tation, and topology. Adv. Phys 64, 519–626 (2015)
19. V. Garcia, S. Fusil, K. Bouzehouane, S. Enouz-Vedrenne, N.D.
Mathur, A. Barthelemy, M. Bibes, Giant tunnel electroresistance for non-destructive readout of ferroelectric states. Nature 81, 460 (2009)
20. A. Chanthbouala, A. Crassous, V. Garcia, K. Bouzehouane, S.
Fusil, X. Moya, J. Allibe, B. Dlubak, J. Grollier, S. Xavier, C.
Deranlot, A. Moshar, R. Proksch, N.D. Mathur, M. Bibes, A.
Barthelemy, Solid-state memories based on ferroelectric tunnel junctions. Nat. Nanotech 7, 101 (2012)
21. D. Lee, S.H. Baek, T.H. Kim, J.G. Yoon, C.M. Folkman, C.B.
Eom, T.W. Noh, Polarity control of carrier injection at ferroelec- tric/metal interfaces for electrically switchable diode and photo- voltaic effects. Phys. Rev. B 84, 125305 (2011)
22. C. Wang, K.J. Jin, Z. Xu, L. Wang, C. Ge, H. Lu, H. Guo, M.
He, G. Yang, Switchable diode effect and ferroelectric resistive
switching in epitaxial BiFeO3 thin films. Appl. Phys. Lett. 98, 192901 (2011)
23. F. Yan, G.Z. Xing, L. Li, Low temperature dependent ferroelec- tric resistive switching in epitaxial BiFeO3 films. Appl. Phys.
Lett. 104, 132904 (2014)
24. D.J. Kim, H. Lu, S. Ryu, C.W. Bark, C.B. Eom, E.Y. Tsymbal, A. Gruverman, Ferroelectric tunnel memristor. Nano Lett. 12, 5697–5702 (2012)
25. K.B. Yin, M. Li, Y.W. Liu, C.L. He, F. Zhuge, B. Chen, W. Lu, X. Pan, R. Li, Resistance switching in polycrystalline BiFeO3 thin films. Appl. Phys. Lett. 97, 042101 (2010)
26. B.F. Yu, M.Y. Li, Z.Q. Hu, L. Pei, D.Y. Guo, X.Z. Zhao, S.X.
Dong, Enhanced multiferroic properties of the high-valence Pr doped BiFeO3 thin film. Appl. Phys. Lett. 93, 182909 (2008) 27. V.A. Khomchenko, D.A. Kiselev, I.K. Bdikin, V.V. Shvartsman,
P. Borisov, W. Kleemann, J.M. Vieira, A.L. Kholkin, Crystal structure and multiferroic properties of Gd-substituted BiFeO3. Appl. Phys. Lett. 93, 262905 (2008)
28. Z.Q. Hu, M.Y. Li, J. Liu, L. Pei, J. Wang, B.F. Yu, X.Z. Zhao, Structural transition and multiferroic properties of Eu-doped BiFeO3 thin films. J. Am. Ceram. Soc. 93, 2743–2747 (2010) 29. H. Yang, H.M. Luo, H. Wang, I.O. Usov, N.A. Suvorova, M.
Jain, D.M. Feldmann, P.C. Dowden, R.F. DePaula, Q.X. Jia,
Rectifying current-voltage characteristics of BiFeO3/Nb-doped SrTiO3 heterojunction. Appl. Phys. Lett. 92, 102113 (2008) 30. T.L. Qu, Y.G. Zhao, D. Xie, J.P. Shi, Q.P. Chen, T.L. Ren, Resist-
ance switching and white-light photovoltaic effects in BiFeO3/ Nb–SrTiO3 heterojunctions. Appl. Phys. Lett. 98, 173507 (2011) 31. L.N. Zhao, Z.X. Lu, F.Y. Zhang, G. Tian, X. Song, Z.W. Li, K.R.
Huang, Z. Zhang, M.H. Qin, S.J. Wu, X.B. Lu, M. Zeng, X.S.
Gao, J.Y. Dai, J.M. Liu, Current rectifying and resistive switch- ing in high density BiFeO3 nanocapacitor arrays on Nb-SrTiO3 substrates. Sci. Rep 5, 9680 (2014)
32. T.G. You, N. Du, S. Slesazeck, T. Mikolajick, G.D. Li, D.
Burger, I. Skorupa, H. Stocker, B. Abendroth, A. Beyer, K. Volz, O.G. Schmidt, H. Schmidt, Bipolar electric-field enhanced trap- ping and detrapping of mobile donors in BiFeO3 memristors.
ACS Appl. Mater. Interfaces 6, 19758–19765 (2014)
33. Y. Watanabe, Tunneling current through a possible all-perovskite oxide p-n junction. Phys. Rev. B 59, 11257 (1999)
34. S.J. Clark, J. Robertson, Band gap and Schottky barrier heights of multiferroic BiFeO3. Appl. Phys. Lett. 90, 132903 (2007) 35. H.B. Michaelson, The work function of the elements and its peri-
odicity. J. Appl. Phys 48, 4729 (1977)
