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. 2013:4:1771.
doi: 10.1038/ncomms2784.

Nanobatteries in redox-based resistive switches require extension of memristor theory

I Valov  1 , E Linn, S Tappertzhofen, S Schmelzer, J van den Hurk, F Lentz, R Waser
Affiliations
Free PMC article

Nanobatteries in redox-based resistive switches require extension of memristor theory

I Valov et al. Nat Commun. 2013.
Free PMC article

Abstract

Redox-based nanoionic resistive memory cells are one of the most promising emerging nanodevices for future information technology with applications for memory, logic and neuromorphic computing. Recently, the serendipitous discovery of the link between redox-based nanoionic-resistive memory cells and memristors and memristive devices has further intensified the research in this field. Here we show on both a theoretical and an experimental level that nanoionic-type memristive elements are inherently controlled by non-equilibrium states resulting in a nanobattery. As a result, the memristor theory must be extended to fit the observed non-zero-crossing I-V characteristics. The initial electromotive force of the nanobattery depends on the chemistry and the transport properties of the materials system but can also be introduced during redox-based nanoionic-resistive memory cell operations. The emf has a strong impact on the dynamic behaviour of nanoscale memories, and thus, its control is one of the key factors for future device development and accurate modelling.

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Figures

Figure 1
Figure 1. Origins of emf in nanoscale cells.
These sketches show situations for SiO2-based cells in which one of the three basis origins of emf dominates. (a) A Nernst potential VN of a Ag/SiO2/Pt cell arising from the difference of the chemical potential of Ag metal at the interfaces Ag/electrolyte and Pt/electrolyte ΔμAg=μ′Ag−μ″Ag. The Nernst potential VN according to equation (11) has a negative value and it is given by the difference of the electrical potentials at both electrodes formula image generated to keep the condition formula image (formula image is the electrochemical potential given by formula image). Depending on the specific chemical redox system and the chemical potential gradients, the sign of the Vemf can also be positive. (b) A diffusion potential Vd is generated in a Pt/SiO2/Pt cell by gradients of the chemical potentials of the Ag+ and OH− ions, that is, ΔμAg+=μ′Ag+−μ″Ag+ and ΔμOH−=μ′OH−−μ″OH− inhomogeneously distributed in the thin film as given by equation (5). (c) In the case of a nanosize filament, the chemical potential of Ag contains an additional surface energy term generating a chemical potential gradient ΔμAg=μAg-micro−μAg-nano in accordance with equation (6) (Gibbs–Thomson Potential VGT). (d) In the case of a fully metallic contact or a highly conducting tunnel junction, the emf is Vcell=0. The potential of the right electrode is used as a reference throughout the text. Please note that profiles of the electrostatic potential φ is sketched without zooming into the space charge layers.
Figure 2
Figure 2. Steady-state emf measurements for Ag/SiO2/Pt ECM cells.
(a) Simplified equivalent circuit model of a ReRAM device. (b) Vcell for a Ag/SiO2/Pt cell measured under open circuit conditions. The red line curve (1) depicts Vcell in the OFF state after a SET/RESET cycle. For the other curves, the ion concentration cion (that is, the sum of the Ag+ and OH− ion concentrations, averaged over the thickness) was controlled and preset using different sweep rates. Curve (2) corresponds to cion=1.4 × 10−4 M cm−3, (3) to cion=9.2 × 10−5 M cm−3, (4) to cion=2 × 10−5 M cm−3 and curve (5) to cion=1.7 × 10−5 M cm−3, respectively. Details of the measurements are depicted in Supplementary Fig. S2. Further voltage sweeps in the negative voltage regime result in further decrease of the ion concentration (Supplementary Fig. S3). (c) The slope of the line provides the pre-exponential term and we were thus able to determine the ionic transference number formula image by using equations (10) and z=+1 (for Ag+). (d) The time evolution of the discharge current (for V=0 V) of the cell (diameter d=100 μm) after SET and subsequent RESET operation is shown. Inset: the same plot for an extended time and a log current scale. The integration reveals the charge (5 nC) of the nanobattery.
Figure 3
Figure 3. Time-dependent emf measurements for Ag/Ge0.3Se0.7/Pt ECM cells.
After a SET/RESET cycle (initial state), a negative voltage is applied to the Ag electrode resulting in a dendrite formation. At t1=0 s the voltage measurement is started. Fading of the diffusion potential contribution from t1 to t2 leads to a highly negative Vcell owing to a significant Nernst potential between the electrodes. In parallel to the dissolution of the dendrites (t2), the emf increases to positive values again with a diffusion potential as the remaining component of the emf owing to the different activity of Ag+ ions at the both s′, s″ surfaces (t>t3). The scale bar in the inset corresponds to 20 μm.
Figure 4
Figure 4. Emf for different types of ReRAM cells.
All tested cells showed an emf varying from some hundreds of microvolts to some hundreds of millivolts (a). The specific steady-state emf depends on the type of cell and the device operation (for example, sweep rate or voltage amplitude before the (open cell) emf measurement). For the sake of completeness, the internal resistance Ri normalized by the total resistance Rtot is given (for details: see Supplementary Table S1). The influence of the emf on the current–voltage sweeps, resulting in non-zero-crossing characteristics (b), is given for the Cu/SiO2/Pt system (red curve) as an example (electrode area Acell=2 × 10−4 cm2, sweep rate ν=400 mV s−1). The I–V characteristics in grey are provided for statistical verification. For the sake of clarity, the currents of the OFF state (A) and (C) and the ON state (B) are labelled, respectively. The formed valence change memory (VCM)-type cells (Ti/SrTiO3/Pt and Ta/Ta2O5/Pt) show lower emf for the OFF state owing to the higher electronic partial conductivity, that is, higher currents, but lower ion transference number. Emfs for VCM cells are depicted in Supplementary Figs S7,S8, respectively. The I–V characteristics for Ag/SiO2/Pt and Ti/SrTiO3/Pt cells are shown in Supplementary Figs S9,S10.
Figure 5
Figure 5. Classification of mem devices.
(a) Memristive, memcapacitive and meminductive devices are assumed to offer pinched characteristics at the origin in general. In the case of memcapacitive and meminductive devices, a spontaneous polarization of a ferroelectric and ferromagnetic material, respectively, leads for example, to non-zero-crossing characteristics. Similarly, a non-zero-crossing I–V characteristic of a memristive device indicates the presence of an inherent nanobattery, that is, this device is active. Therefore, we introduce the generic terms extended memristive device, extended memcapacitive device and extended meminductive device to account for both zero-crossing and non-zero-crossing I–V characteristics. Note that the origin of non-zero-crossing behaviour in memcapacitive and meminductive devices is of completely different nature than in memristive devices, thus require specific modifications of the concept. Interestingly, spin-transfer torque (STT) MRAM cells offer zero-crossing in contrast to ReRAM cells, thus can be considered as conventional memristive device. (b) Equivalent circuit of the extended memristive element. The ionic current is defined by the nanobattery, which controls the state-dependent resistor representing the electronic current path. The capacitance of the device is neglected as its influence is not significant. The partial electronic conductivity in the electrolyte induces a state-independent resistance Rleak due to a leakage current in parallel. (c) Simulated I–V characteristic of the extended memristor. The zoom shows the non-zero-crossing behaviour. Further considerations on the simulation are described in Supplementary Note 4.
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