Memristive devices are popular among neuromorphic engineers for their ability to emulate forms of spike-driven synaptic plasticity by applying specific voltage and current waveforms at their two terminals. In this paper, we investigate spike-timing dependent plasticity (STDP) with a single pairing of one presynaptic voltage spike and one post-synaptic voltage spike in a BiFeO₃ memristive device. In most memristive materials the learning window is primarily a function of the material characteristics and not of the applied waveform. In contrast, we show that the analog resistive switching of the developed artificial synapses allows to adjust the learning time constant of the STDP function from 25 ms to 125 μs via the duration of applied voltage spikes. Also, as the induced weight change may degrade, we investigate the remanence of the resistance change for several hours after analog resistive switching, thus emulating the processes expected in biological synapses. As the power consumption is a major constraint in neuromorphic circuits, we show methods to reduce the consumed energy per setting pulse to only 4.5 pJ in the developed artificial synapses.

We investigate the hopping transport of positively charged mobile oxygen vacancies $V_{\mathrm{o}}^{+}$ in electroforming-free bipolar memristive ${\mathrm{Bi}\mathrm{Fe}\mathrm{O}}_3$ switches by conducting impedance spectroscopy and quasistatic state-test measurements. We demonstrate that ${\mathrm{Bi}\mathrm{Fe}\mathrm{O}}_3$ switches with mobile oxygen vacancies ($V_{\mathrm{o}}^{+}$) and fixed substitutional ${\mathrm{Ti}}^{\mathrm{4+}}$ donors on ${\mathrm{Fe}}^{\mathrm{3+}}$ lattice sites close to the bottom electrode have a rectifying top electrode with an unflexible barrier height and a rectifying and/or nonrectifying bottom electrode with a flexible barrier height. The field-driven hopping transport of the oxygen vacancies determines the reconfiguration of the flexible barrier and the dynamics of the resistive switching. Average activation energies of 0.53 eV for trapping and of 0.31 eV for the release of oxygen vacancies by the ${\mathrm{Ti}}^{\mathrm{4+}}$ donors during application of the SET and RESET excitation pulses are extracted, respectively. The larger activation energy during SET is experimentally verified by impedance spectroscopy measurements and evidences the local enhancement of the electrostatic potential profile at the bottom electrode due to the ${\mathrm{Ti}}^{\mathrm{4+}}$ donors on ${\mathrm{Fe}}^{\mathrm{3+}}$ lattice sites.

Chua [IEEE Trans. Circuit Theory 18, 507–519 (1971)] predicted rather simple charge-flux curves for active and passive memristors (short for memory resistors) and presented active memristor circuit realizations already in the 1970 s. The first passive memristor has been presented in 2008 [D. B. Strukov, G. S. Snider, and D. R. Williams, Nature (London) 453, 80–83 (2008)]. Typically, memristors are traced in complicated hysteretic current-voltage curves. Therefore, the true essence of many new memristive devices has not been discovered so far. Here, we give a practical guide on how to use normalized charge-flux curves for the prediction of hysteretic current-voltage characteristics of memristors. In the case of memristive BiFeO₃ thin film capacitor structures, the normalized charge-flux curves superimpose for different numbers of measurement points N_s and a different measurement time per measurement point T_s. Such normalized charge-flux curves can be used for the prediction of current-voltage characteristics for input signals with arbitrarily chosen N_s and T_s.

BiFeO₃ based MIM structures with Ti-implanted Pt bottom electrodes and Au top electrodes have been fabricated on Sapphire substrates. The resulting metal-insulator-metal (MIM) structures show bipolar resistive switching without an electroforming process. It is evidenced that during the BiFeO₃ thin film growth Ti diffuses into the BiFeO₃ layer. The diffused Ti effectively traps and releases oxygen vacancies and consequently stabilizes the resistive switching in BiFeO₃ MIM structures. Therefore, using Ti implantation of the bottom electrode, the retention performance can be greatly improved with increasing Ti fluence. For the used raster-scanned Ti implantation the lateral Ti distribution is not homogeneous enough and endurance slightly degrades with Ti fluence. The local resistive switching investigated by current sensing atomic force microscopy suggests the capability of down-scaling the resistive switching cell to one BiFeO₃ grain size by local Ti implantation of the bottom electrode.