The role of Schottky barrier in the resistive switching of SrTiO₃: direct experimental evidence

Abstract

Single crystalline SrTiO₃ doped with 0.1 wt% Nb was used as a model system to evaluate the role of the Schottky barrier in the resistive switching of perovskites. The Ti bottom electrode formed an ohmic contact in the Ni/Nb:SrTiO₃/Ti stack, whereas the Ni top electrode created a strong Schottky barrier, which was reflected in a huge semi-circle in the impedance spectrum of the stack. Bipolar switching was achieved in the voltage range of −4 to 4 V for the stack, two clear resistance states were created by electric pulses, and the Schottky barrier heights corresponding to the high/low resistance states were experimentally determined. A direct relationship between the resistance state and the Schottky barrier height was thus established.

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The phenomenon of resistive switching has been extensively observed in various perovskite oxides, such as Pr_1−xCaMnO₃,¹ SrZrO₃,² SrTiO₃,³ and BaTi_0.95Co_0.05O₃,⁴ and Pb(Zr_0.2Ti_0.8)O₃.⁵ Among perovskite oxides, SrTiO₃ has been thoroughly investigated;^6–12 the knowledge about SrTiO₃ helps understanding the switching behaviours of other perovskite oxides. Therefore, SrTiO₃ is addressed in this work as a model system.

Quite different mechanisms have been proposed to explain the switching behaviours of SrTiO₃, and the most relevant switching mechanisms have been reviewed by Waser et al.^13,14 and Sawa.¹⁵ Usually the work on acceptor-(e.g. Cr) doped SrTiO₃ (ref. 6 and 9) emphasizes the property change in the crystal bulk, in which, oxygen vacancies (or oxygen ions) play a key role: either the fast transport of oxygen vacancies along dislocations¹⁰ or the formation of an oxygen-vacancy array under high electrical stress¹¹ was suggested to be responsible for the switching. Guo¹⁶ performed the electroforming of acceptor-doped SrTiO₃ single crystals at 200 °C and realized bipolar switching at room temperature. Since oxygen vacancies (or oxygen ions) are sufficiently mobile at 200 °C, this work established a clear relationship between the migration of oxygen vacancies and the resistive switching. In a very recent work,¹⁷ the concentration variation of oxygen ions at different resistance states was directly measured.

A Schottky barrier is formed at the metallic electrode/SrTiO₃ contact, therefore, for donor-(e.g. Nb) doped SrTiO₃ the role of the Schottky barrier is emphasized:^7,8,14,15 the change in the Schottky barrier height under voltages of different polarities is responsible for the different resistance states. The important experimental results for the Schottky barrier model are:¹⁵ (1) the on/off resistance of Nb-doped SrTiO₃ is inversely proportional to the electrode/SrTiO₃ interface area, suggesting that the resistive switching takes place over the entire interface area, and (2) Nb-doped SrTiO₃ with ohmic contact does not show any switching behaviour, whereas Nb-doped SrTiO₃ with Schottky-type contact shows resistive switching, and the switching behaviour can be alternated by modifying the electrode/SrTiO₃ interface.

However, the effect of the Schottky barrier was not separated from that of the bulk of donor-doped SrTiO₃ in many cases. For example, the stack (interface plus bulk) capacitance was measured without differentiating the contribution of the crystal bulk from that of the interface;¹⁸ as a result, one could not conclude that the different capacitances in the low and high resistance states were only due to the interface effect. Also the direct link between the Schottky barrier height and the resistance state is still lacking.

An obvious advantage of the impedance spectroscopy technique is that the interface effect and the bulk contribution can be readily separated.¹⁹ Impedance spectroscopy has been popularly used to investigate the switching of Fe-doped SrTiO₃,¹⁹ Nb-doped SrTiO₃,²⁰ (Ba,Sr)(Zr,Ti)O₃,²¹ NiO and TiO₂,²² SrZrO₃,²³ and graphene oxide;²⁴ in most of these cases, impedance spectroscopy was used to characterize the bulk properties of thin films, and in all the cases, the Schottky barrier height was not determined.

In this work, the impedance responses of the Schottky barrier in the high resistance state (HRS) and the low resistance state (LRS) were measured, and the bias-dependent response of the Schottky barrier unambiguously demonstrated that one could change the stack resistance by orders of magnitude only by manipulating the Schottky barrier height. More importantly, the Schottky barrier heights of the HRS and the LRS were derived from the I–V and 1/C²–V curves, and a direct relationship between HRS/LRS and a larger/smaller barrier height was established.

Ni/Nb:SrTiO₃/Ti stacks were fabricated in this work. The sample configuration is illustrated in Fig. 1(a). (100)-oriented SrTiO₃ single crystals (5 × 5 × 0.5 mm³) doped with 0.1 wt% Nb (CrysTec, Germany) were used. The top Ni electrode (diameter: 0.4 mm, thickness: 200 nm) and the bottom Ti electrode (area: 5 × 5 mm², thickness: 200 nm) were prepared by sputtering with shadow masks. The Ti electrode was further capped with a 100 nm thick Ag layer to prevent oxidation.

Fig. 1 (a) Configuration of the Ni/Nb:SrTiO₃/Ti stack, and the inset is the optical image of the top Ni electrodes, and (b) bias-dependence of the Ni/Nb:SrTiO₃/Ti stack. Insets (upper) show the magnified impedance spectrum under 0.2 V bias (left), and the equivalent circuit for fitting the impedance spectrum (right).

Nb-doped SrTiO₃ (Nb:SrTiO₃) is a n-type semiconductor with a wide band gap of 3.3 eV,²⁵ and a Ti electrode usually forms an ohmic contact at the Ti/Nb:SrTiO₃ junction.²⁶ However, owing to the large work function of Ni (ϕ_M = 5.15 eV), a Ni electrode forms a Schottky barrier at the Ni/Nb:SrTiO₃ junction; a Schottky barrier is composed of a depletion layer of electrons at the Ni/Nb:SrTiO₃ interface. According to the Schottky–Mott relation:²⁷ϕ_B = ϕ_M − χ_S (where χ_S is the electron affinity, ∼3.9 eV for SrTiO₃ (Ref. 25)), the ideal Schottky barrier height ϕ_B for the Ni/Nb:SrTiO₃ junction is ∼1.25 eV.

The properties of the Nb:SrTiO₃ single crystal and the Schottky barrier at the Ni/Nb:SrTiO₃ junction can be investigated by impedance spectroscopy, and the impedance spectroscopy investigations were carried out using a 1260 Frequency Response Analyzer, in conjunction with a 1296 Dielectric Interface (Solartron Instruments, Farnborough, U.K.) in the frequency range of 1 to 10⁶ Hz at an amplitude of 50 mV in air and at ambient temperature. Fig. 1(b) shows the impedance spectra of the Ni/Nb:SrTiO₃/Ti stack under different dc bias voltages; all the spectra are characterized by semi-circles. The bulk resistance of the Nb:SrTiO₃ single crystal was measured to be ∼170 Ω, while the resistance of the Ni/Nb:SrTiO₃/Ti stack, as determined from the intersect of the impedance semi-circle on the real axis, was ∼1.68 × 10⁸ Ω under 0 V bias; therefore, the huge semi-circle can only be due to the impedance response of the Schottky barrier. Very interestingly, the semi-circle could be depressed by applying dc biases, as shown in Fig. 1(b). Such a phenomenon further demonstrates that the semi-circle is due to the Schottky barrier, because the bulk resistance of the Nb:SrTiO₃ single crystal could not be modified by the biases ≤0.2 V.

The current I–voltage V characteristics of the Ni/Nb:SrTiO₃/Ti stack were investigated using the Keithley 4200 semiconductor characterization system in air and at ambient temperature. The voltage sweep was set to 0 → +V_max → 0 → −V_max → 0 V. The hysteretic semi-logarithmic current density J–voltage V curve is depicted in Fig. 2; the stack could be set from the HRS to the LRS by applying positive forward voltages, and reset from the LRS back to the HRS by applying negative reverse voltages. However, when Ti was applied for both the top and bottom electrodes, only ohmic contact was achieved, as evidenced by the right inset in Fig. 2.

Fig. 2 Hysteric current density J–voltage V curve of the Ni/Nb:SrTiO₃/Ti stack. Voltage sweeping was set to 0 → +4 → 0 → −4 → 0 V. The left inset shows the corresponding I–V curve on a linear scale, and the right one is the I–V curve of the Ti/Nb:SrTiO₃/Ti stack, demonstrating the ohmic contact between Ti and Nb:SrTiO₃.

The HRS and the LRS could also be created by applying electric pulses; a sequence of electric pulses with the amplitudes between −12 and +12 V and the width of 1 ms were applied to the Ni/Nb:SrTiO₃/Ti stack, and the stack resistance was recorded under a voltage of −0.1 V after each pulse. The results are given in Fig. 3(a). By applying pulses of +12, −12, −10, −8, −6 V, LRS with the resistance of ∼10 KΩ and different HRSs with the resistances of ∼1600, ∼780, ∼260, ∼50 KΩ were obtained. A relaxation of the resistance states could be observed, which was especially noticeable for LRS. The variation of low resistance R with time is shown in Fig. 3(b), and it follows the Curie-Von Schweidler law R ∞ t^β, here β is a constant less than 1. This equation describes a charge trapping effect in high-κ dielectrics.²⁸ It was suggested that this resistance relaxation could be understood by the defects near the interface.²⁹

Fig. 3 (a) Pulses with amplitudes of +12, −12, −10, −8 and −6 V (upper) and corresponding resistance responses (lower). Pulse width was fixed at 1 ms. Read voltage was –0.1 V. (b) Relaxation of low resistance with time. R_nomalized = R/R_time=1000s.

To demonstrate the I–V characteristics more clearly, the I–V curve of the Ni/Nb:SrTiO₃/Ti stack is replotted on a linear scale in Fig. 2 (the left inset). At room temperature, the thermal voltage (V_T = k_BT/q) is approximately 26 mV; when the applied voltage is higher than the thermal voltage, the current increases exponentially, and such behaviour can be described using eqn (1),²⁷

J = A**T² exp(−ϕ_B/k_BT)exp(qV/nk_BT) (1)

where A** is the effective Richardson constant (156 A cm⁻² K⁻² for Nb:SrTiO₃ (ref. 30)), T the absolute temperature, k_B the Boltzmann constant, q the electron charge, ϕ_B the Schottky barrier height and n the ideality factor. The ideality factor n describes the deviation from the ideal thermionic emission. By fitting the linear log J–V sections in Fig. 2 according to eqn (1), one can determine the n and ϕ_B values; the Schottky barrier heights ϕ_B thus deduced are 0.72 eV for the HRS and 0.50 eV for the LRS, and the ideality factors n are 2.12 for the HRS and 2.54 for the LRS. The deviation of the Schottky barrier height ϕ_B and ideality factor n of the HRS from the expected value (ϕ_B = 1.25 eV and n = 1) could be attributed to the presence of the interface layer and/or interface states.^26,28

To further understand the Ni/Nb:SrTiO₃ interface, the capacitance C–voltage V characteristic was measured at 1 MHz with a signal of 50 mV, and the 1/C²–V curves at the HRS and the LRS are given in Fig. 4. The carbon contamination or the atomic rearrangement when a metal electrode is deposited on the SrTiO₃ surface causes an interface layer at the electrode/SrTiO₃ junction.^28,30 Taking the interfacial layer into consideration, the junction capacitance is described using³¹

where V_bi, N_d, ε₀, and ε_r are the built-in potential, dopant concentration, vacuum permittivity, and relative dielectric constant, respectively. Fitting the experimental results given in Fig. 4 according to eqn (2), the built-in potentials were deduced to be 1.16 eV and 0.78 eV for the HRS and the LRS, respectively. For Nb:SrTiO₃, V_bi − ϕ_B ≈ 0.1 eV,³² therefore, the Schottky barrier heights could thus be determined to be 1.06 eV and 0.68 eV for the HRS and the LRS, respectively. These values are larger than those deduced from the J–V fitting, but the Schottky barrier height at the HRS is quite close to the ideal height value.

Fig. 4 1/C²–V curves of the Ni/Nb:SrTiO₃/Ti stack at the HRS and the LRS. The dotted lines are fitting results.

Now it is clear that the LRS and the HRS are due to different Schottky barrier heights. To make the relation more visible, the impedance spectroscopy investigation of the Ni/Nb:SrTiO₃/Ti stack was conducted again, and the spectra in the HRS and the LRS are presented in Fig. 5. Immediately after the voltage sweep of 0 → −4 → 0 V, the impedance spectrum at the HRS [Fig. 5(a)] was recorded; and after the voltage sweep of 0 → +4 → 0 V, the impedance spectrum at LRS [Fig. 5(b)] was recorded. The diameter of the impedance semi-circle can be regarded as a visual measure of the Schottky barrier; it is obvious from Fig. 5 that the HRS is due to a larger Schottky barrier height, and that LRS due to a smaller Schottky barrier height.

Fig. 5 Impedance spectra of the Ni/Nb:SrTiO₃/Ti stack in (a) the HRS and (b) the LRS.

In the Schottky contact model, the value of the contact resistance is related to the height of the Schottky barrier and the width of the depletion layer. Considering all the experimental results presented in the above, we come up with a plausible switching mechanism. Different defects (e.g. oxygen vacancies) act as interface states in the interface.^18,30 An interfacial layer inevitably exists on the Ni/Nb:SrTiO₃ interface,²⁸ and forms a potential drop Δ across the interfacial layer. The Schottky barrier height can be written as: ϕ_B = ϕ_M − χ_S − Δ. When a forward voltage is applied to the Ni/Nb:SrTiO₃ interface, a large amount of electrons is extracted from the interface states, leading to an increase of Δ. This discharge effect decreases the Schottky barrier height and results in LRS. When a reverse voltage is applied, electrons are trapped in the interface states, and the Schottky barrier height increases, leading to the HRS. The amount of trapped/detrapped electrons in the interface states can be modified by controlling the magnitude of voltage or pulse,²⁸ which induces different Schottky barrier heights, and thus different resistance states are obtained.

Conclusion

An unambiguous relationship between the resistance state and the Schottky barrier height is established, and the impedance spectroscopy investigations make such a relationship clearly visible. The variation of the Schottky barrier height can be attributed to charge trapping/detrapping in the interface states.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51372094).

Notes and references

1. S. Q. Liu, N. J. Wu and A. Ignatiev, Appl. Phys. Lett., 2000, 76, 2749–2751.
2. X. Chen, N. Wu, J. Strozier and A. Ignatiev, Appl. Phys. Lett., 2006, 89, 063507.
3. A. Beck, J. G. Bednorz, C. Gerber, C. Rossel and D. Widmer, Appl. Phys. Lett., 2000, 77, 139–141.
4. Z. B. Yan, Y. Y. Guo, G. Q. Zhang and J. M. Liu, Adv. Mater., 2011, 23, 1351–1355.
5. D. Pantel, S. Goetze, D. Hesse and M. Alexe, ACS Nano, 2011, 5, 6032–6038.
6. Y. Watanabe, J. G. Bednorz, A. Bietsch, C. Gerber, D. Widmer, A. Beck and S. J. Wind, Appl. Phys. Lett., 2001, 78, 3738–3740.
7. T. Fuji, M. Kawasaki, A. Sawa, H. Akoh, Y. Kawazoe and Y. Tokura, Appl. Phys. Lett., 2005, 86, 012107.
8. D. Choi, D. Lee, H. Sim, M. Chang and H. Hwang, Appl. Phys. Lett., 2006, 88, 082904.
9. S. Karg, G. I. Meijer, D. Widmer and J. G. Bednorz, Appl. Phys. Lett., 2006, 89, 072106.
10. K. Szot, W. Speier, G. Bihlmayer and R. Waser, Nat. Mater., 2006, 5, 312–320.
11. M. Janousch, G. I. Meijer, U. Staub, B. Delley, S. F. Karg and B. P. Andreasson, Adv. Mater., 2007, 19, 2232–2235.
12. F. La Mattina, J. G. Bednorz, S. F. Alvarado, A. Shengelaya and H. Keller, Appl. Phys. Lett., 2008, 93, 022102.
13. R. Waser and M. Aono, Nat. Mater., 2007, 6, 833–840.
14. R. Waser, R. Dittmann, G. Staikov and K. Szot, Adv. Mater., 2009, 21, 2632–2663.
15. A. Sawa, Mater. Today, 2008, 11, 28–36.
16. X. Guo, Appl. Phys. Lett., 2012, 101, 152903.
17. Y. Aoki, C. Wiemann, V. Feyer, H. S. Kim, C. M. Schneider, H. I. Yoo and M. Martin, Nat. Commun., 2014, 5, 3473.
18. A. Sawa, T. Fujii, M. Kawasaki and Y. Tokura, Proc. SPIE, 2005, 5932, 59322C.
19. T. Menke, P. Meuffels, R. Dittmann, K. Szot and R. Waser, J. Appl. Phys., 2009, 105, 066104.
20. J. Lee, E. M. Bourim, D. Shin, J. S. Lee, D. J. Seong, J. Park, W. Lee, M. Chang, S. Jung, J. Shin and H. Hwang, Curr. Appl. Phys., 2010, 10, e68–e70.
21. Y. D. Xia, Z. G. Liu, W. Yang, L. Shi, L. Chen, J. Yin and X. K. Meng, Appl. Phys. Lett., 2007, 91, 102904.
22. X. L. Jiang, Y. G. Zhao, Y. S. Chen, D. Li, Y. X. Luo, D. Y. Zhao, Z. Sun, J. R. Sun and W. H. Zhao, Appl. Phys. Lett., 2013, 102, 253507.
23. C. H. Lai and C. Y. Liu, Appl. Phys. Lett., 2013, 103, 263505.
24. N. T. Ho, V. Senthilkumar and Y. S. Kim, Solid-State Electron., 2014, 94, 61–65.
25. J. Robertson and C. W. Chen, Appl. Phys. Lett., 1999, 74, 1168–1170.
26. C. Park, Y. Seo, J. Jung and D. W. Kim, J. Appl. Phys., 2008, 103, 054106.
27. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, Wiley, New Jersey, 3rd edn, 2007.
28. E. Mikheev, B. D. Hoskins, D. B. Strukov and S. Stemmer, Nat. Commun., 2014, 5, 3990.
29. M. C. Ni, S. M. Guo, H. F. Tian, Y. G. Zhao and J. Q. Li, Appl. Phys. Lett., 2014, 91, 183502.
30. T. Shimizu and H. Okushi, J. Appl. Phys., 1999, 85, 7244–7251.
31. M. Yang, L. Z. Ren, Y. J. Wang, F. M. Yu, M. Meng, W. Q. Zhou, S. X. Wu and S. W. Li, J. Appl. Phys., 2014, 115, 134505.
32. Y. Hikita, Y. Kozuka, K. Susaki, H. Takagi and H. Y. Wang, Appl. Phys. Lett., 2007, 90, 143507.

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