Theoretical current-voltage characteristics of ferroelectric tunnel junctions

H. Kohlstedt, N. A. Pertsev, J. Rodríguez Contreras, and R. Waser

Phys. Rev. B 72, 125341 – Published 29 September 2005

Abstract

We present the concept of ferroelectric tunnel junctions (FTJs). These junctions consist of two metal electrodes separated by a nanometer-thick ferroelectric barrier. The current-voltage characteristics of FTJs are analyzed under the assumption that the direct electron tunneling represents the dominant conduction mechanism. First, the influence of converse piezoelectric effect inherent in ferroelectric materials on the tunnel current is described. The calculations show that the lattice strains of piezoelectric origin modify the current-voltage relationship owing to strain-induced changes of the barrier thickness, electron effective mass, and position of the conduction-band edge. Remarkably, the conductance minimum becomes shifted from zero voltage due to the piezoelectric effect, and a strain-related resistive switching takes place after the polarization reversal in a ferroelectric barrier. Second, we analyze the influence of an internal electric field arising due to imperfect screening of polarization charges by electrons in metal electrodes. It is shown that, for asymmetric FTJs, this depolarizing-field effect also leads to a considerable change of the barrier resistance after the polarization reversal. However, the symmetry of the resulting current-voltage loop is different from that characteristic of the strain-related resistive switching. The crossover from one to another type of the hysteretic curve, which accompanies the increase of FTJ asymmetry, is described taking into account both the strain and depolarizing-field effects. It is noted that asymmetric FTJs with dissimilar top and bottom electrodes are preferable for the nonvolatile memory applications because of a larger resistance on/off ratio.

Received 18 May 2004

DOI:https://doi.org/10.1103/PhysRevB.72.125341

Authors & Affiliations

H. Kohlstedt^1,4,*, N. A. Pertsev^1,2, J. Rodríguez Contreras¹, and R. Waser^1,3

¹Institut für Festkörperforschung and CNI, Forschungszentrum Jülich, D-52425 Jülich, Germany
²A. F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
³Institut für Werkstoffe der Elektrotechnik, RWTH Aachen University of Technology, D-52056 Aachen, Germany
⁴Department of Material Science and Engineering and Department of Physics, University of California, Berkeley, California 94720, USA

^*Electronic address: h.h.kohlstedt@fz-juelich.de

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Vol. 72, Iss. 12 — 15 September 2005

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Images

Figure 1
Simplified band diagram of a ferroelectric tunnel junction. $E_{F}$ is the Fermi energy, $χ$ is the electron affinity of the ferroelectric, $E_{c}$ is the bottom of the barrier conduction band, $E_{v}$ is the top of the valence band, $t_{0}$ is the barrier thickness, and $ϕ_{1}, ϕ_{2}$ are the barrier heights at the bottom and top electrode, respectively. The inserted sketch shows the structure of a unit cell of $Ba Ti O_{3}$ , which represents the ferroelectric barrier. Two equilibrium positions of the ${Ti}^{4 +}$ ion are labeled with numbers (1) and (2).Reuse & Permissions
Figure 2
Influence of converse piezoelectric effect on the current-voltage (a) and conductance-voltage (b) characteristics of tunnel junctions. Theoretical calculations of the current density $J$ and conductance $G$ per unit area were performed using the following values of the junction: parameters $ϕ_{0} = 0.5 eV$ , $t_{0} = 2 nm$ , $m_{3}^{* 0} = 0.2 m$ , $d_{33}^{*} = 50 pm ∕ V$ , $κ_{3} = - 4.5 eV$ , and $μ = 10$ . The conductance is normalized by its value at zero voltage, $G_{0} = G (V = 0)$ . The resistive switching at voltages $\pm V_{c}$ and the resulting hysteretic behavior correspond to the case of a ferroelectric tunnel junction, where the polarization reversal takes place in the barrier at the coercive voltage $V_{c}$ . The panel (c) shows schematically the dependence of the out-of-plane lattice strain $Δ S_{3}$ in an epitaxial ferroelectric film on the applied voltage $V$ .Reuse & Permissions
Figure 3
Internal electric fields $E_{dep}$ and $E_{el}$ in a short-circuited symmetric FTJ (a) and the model distribution of an electrostatic potential across this junction (b). Two possible polarization states and the corresponding potential profiles are shown by solid and dotted arrows and lines. The penetration of electric field into the electrodes is determined by the screening length of electrode material.Reuse & Permissions
Figure 4
Internal electric fields $E_{dep}$ and $E_{int}$ in a short-circuited asymmetric FTJ (a) and the model distribution of an electrostatic potential across this junction (b). The junction contains an effective (or real) interfacial layer of thickness $Δ t$ at the left film/electrode interface. The model corresponds to a junction involving two different electrodes (e.g., Pt and SRO). The screening abilities of electrodes are assumed to be very different, but their work functions are taken to be the same. Two possible polarization states and the corresponding potential profiles are shown by solid and dotted arrows and lines. The screening charges in the electrodes are not depicted.Reuse & Permissions
Figure 5
Combined effect of piezoelectric strain and depolarizing field on the current-voltage characteristics of asymmetric FTJs. The strength $Δ \bar{ϕ}$ of the depolarizing-field effect is assumed to be $0.02 eV$ (a), $0.03 eV$ (b), and $0.04 eV$ (c). Other junction parameters are taken to be $ϕ_{0} = 0.5 eV$ , $t_{0} = 2 nm$ , $m_{3}^{* 0} = 0.2 m$ , $d_{33}^{*} = 50 pm ∕ V$ , $κ_{3} = - 4.5 eV$ , and $μ = 10$ . The source of depolarizing field is situated at the biased electrode (another electrode is grounded).Reuse & Permissions
Figure 6
Current-voltage curves of “strongly” asymmetric ferroelectric tunnel junctions $(Δ \bar{ϕ} = 0.1 eV)$ . Two curves here show the characteristics of FTJs with the source of depolarizing field situated at the biased electrode (1) or at the grounded electrode (2).Reuse & Permissions

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