Ferroelectric synapses

We work with purely electronic memristors based on ferroelectric tunnel junctions (FTJs), in which an ultrathin ferroelectric film is sandwiched between two electrodes23,24. In such devices, sketched in Fig. 1b, the junction resistance sensitively depends on the relative fraction of ferroelectric domains with polarization pointing towards one or the other electrode25. Applying voltage pulses to the device modifies the domain population, thereby inducing resistance changes25. Furthermore, supertetragonal BiFeO 3 (BFO) tunnel barriers combined with (Ca,Ce)MnO 3 (CCMO) bottom and Co top electrodes give rise to OFF/ON resistance ratios up to 104 (ref. 26) paired with high endurance and operation speed27.

Figure 1c shows the dependence of the junction resistance with the amplitude of 100 ns voltage pulses in a Co/BFO/CCMO junction (Methods). In this hysteresis cycle, one clearly notes the existence of voltage thresholds beyond which switching between low- and high- (high- and low-) resistance states occurs. The existence of such well-defined voltage thresholds (associated with the coercivity of the ferroelectric) makes it possible to implement STDP28 in these FTJs. According to STDP, if the pre-neuron spikes just before the post-neuron—indicating a ‘causal’ relationship—the synapse should be strengthened whereas if the pre-neuron spikes just after the post-neuron—indicating an ‘anticausal’ relationship—the synapse should be weakened. We emulate the spikes from pre- and post-neurons (sketched in Fig. 1a) by the waveforms shown in Fig. 1b: rectangular voltage pulses followed by smooth slopes of opposite polarity. Importantly, the voltage never exceeds V th , so that a single spike cannot induce a change in resistance.

When both pre- and post-neuron spikes reach the memristor with a delay Δt, their superposition produces the waveforms (V pre −V post ) displayed in the inset of Fig. 1d. The resulting combined waveform transitorily exceeds the threshold voltage, leading to an increase (ΔG>0, synapse strengthening) or a decrease (ΔG<0, synapse weakening) of the FTJ conductance (G), depending on the sign of Δt. As can be seen from the experimental STDP curve in Fig. 1d, only closely timed spikes produce a conductance change whereas long delays leave the device unchanged.

Domain dynamics probed by tunnelling

Modelling the shape of the STDP curve requires understanding the physical process underlying the time-dependent variation of the FTJ conductance while the waveform is applied. For this purpose, we image the pseudo real-time evolution of the ferroelectric domain configuration by means of stroboscopic piezoresponse force microscopy (PFM)29, while simultaneously measuring the electrical properties of the device. Figure 2a shows the PFM phase and amplitude signals after cumulative pulses of constant amplitude (1 V) from the ON to the OFF state. The evolution of the phase images in stroboscopic PFM reveals the gradual reversal of the polarization from up (dark domains) to down (bright domains) and is reminiscent of the polarization reversal with increasing voltages previously observed by PFM26. The weak amplitude signal during reversal (for example, stages 2 and 3) indicates that the ferroelectric system is split into many small (≲10 nm) domains and that polarization switching is governed by the inhomogeneous nucleation of new domains rather than by the expansion of existing ones. We complemented these experiments by molecular dynamics (MD) simulations (Methods) on defect-free supertetragonal BFO films. These computations also yield an inhomogeneous character for polarization switching (Supplementary Fig. 1), therefore implying that this process is intrinsic in nature, that is, one does not require the presence of defects to obtain an inhomogeneous switching in supertetragonal BFO. Such findings contrast with the case of bulk-like BFO (rhombohedral phase) for which a homogeneous switching was recently predicted30 as a result of large oxygen octahedra tilts that provide a specific homogeneous path for polarization reversal.

Figure 2: A memristor governed by nucleation-limited ferroelectric domain switching. (a) Evolution of the PFM phase and amplitude signals of a ferroelectric memristor under cumulated pulses of 1 V and 100 ns. Cumulative pulses induce a progressive switching with multiple nucleation areas and limited propagation of ferroelectric domains from up (dark phase) to down (bright phase) polarization. The scale bar is 50 nm. (b, top) Normalized switched area as a function of cumulated pulse time calculated from time-dependent transport measurements of a ferroelectric memristor. The black squares indicate the normalized switched area obtained from the PFM measurements in a. (bottom) Corresponding conductance (G) evolution measured as a function of cumulated pulse time. (c) Normalized switched area as a function of cumulated pulse time calculated from time-dependent transport measurements of a ferroelectric memristor at different pulse amplitudes. The black lines are fit results from the nucleation-limited switching model. (d) Examples of Lorentzian distributions of switching times extracted from the fits in c at different pulse amplitudes and (inset) from the MD simulations (Supplementary Fig. 2). (e) Evolution of the switching time (t mean ) as a function of the inverse of the electric field (1/E) obtained from fits of the transport data in c and (inset) from MD simulations. Full size image

We extract the normalized reversed area S from the phase images and plot it as a function of the cumulated pulse duration in Fig. 2b (black squares). Owing to the direct link between the junction resistance R and this normalized reversed area S (well described by a simple model of parallel resistances, , ref. 25), one can also extract S from measurements of the junction resistance after consecutive pulses of 1 V (green squares in Fig. 2b; note the excellent agreement between the PFM and transport data). Figure 2c shows transport data sets at different pulse amplitudes. They follow a systematic trend where, for a given cumulated pulse duration, the switched area is larger under higher voltages.

In ferroelectrics, inhomogeneous polarization switching can be described by a nucleation-limited model, which considers that the ferroelectric film is composed of different zones with independent switching kinetics31,32. Assuming for each voltage V a broad Lorentzian distribution of the logarithm of nucleation times—with width Γ(V) and centred at log(t mean (V))—the normalized reversed area S can be approximated as a function of time t and applied voltage V (ref. 31):

where the index relates to the sign of the applied voltage. Fits obtained with this expression accurately reproduce the experimental data of ferroelectric switching as a function of time and voltage (black lines in Fig. 2c). Figure 2d displays several representative distributions of switching times and illustrates the main trends. For larger voltages, switching occurs earlier and in a narrower time window (decrease of t mean and Γ), in agreement with previous results obtained on thick ferroelectric capacitors32. As shown in the inset of Fig. 2d, MD simulations performed at 10 K confirm the relevance of equation (1) (Methods and Supplementary Fig. 2) to characterize the switching process as well as the measured trends of t mean and Γ with the magnitude of the electric field. Figure 2e shows that the evolution of the switching time (t mean ) as a function of the inverse electric field, extracted from transport measurements (Fig. 2c), follows the characteristic Merz’s law32 for ferroelectric switching (t mean ∝exp(α/E)) where the activation field α is of the order of 3.0 V nm−1. Due to the idealized nature of BFO during MD simulations (no interface, no defects, no tunnel current), the timescale for polarization switching is much shorter than in experiments, while the electric field is larger. Nevertheless, Merz’s law can be applied to the MD simulation results (inset of Fig. 2e) and indicates an activation field of 2.4 V nm−1, that is, in the same range as for experimental results. These simulation results strongly suggest that the experimentally observed inhomogeneous polarization switching in ultrathin films of BFO has an intrinsic origin.

Predictive modelling of synaptic learning

Because of the direct relationship between S and R in these devices, the accurate description of ferroelectric switching by the nucleation-limited model can be further extended to the modelling of resistance changes as a function of voltage amplitude. Figure 3a shows nested resistance hysteresis loops as a function of voltage pulse amplitude, characteristic of memristors. The STDP curve of the same device is displayed in Fig. 3b. Using equation (1) in combination with the parallel resistance model (Methods and Supplementary Fig. 3), we simultaneously fit the resistance versus voltage cycles and the STDP curve. Both resistance changes can be accurately replicated (solid lines in Fig. 3a,b) using the same set of parameters t mean (V) and Γ(V).

Figure 3: Predicting STDP learning with ferroelectric synapses. (a) Multiple hysteresis loops of a ferroelectric memristor showing a clear dependence of resistance switching with the maximum pulse amplitudes. (b–d) Examples of STDP learning curves of different shapes. The pre- and post-synaptic spikes and conductance variations are shown in the top and bottom panels, respectively. For each device, simultaneous fits of data in a,b (solid lines) using equation (1) allow the prediction of new learning curves in c,d (orange lines). Full size image

This full description for each memristor device makes it possible to predict the conductance changes driving STDP learning in ferroelectric synapses. In Fig. 3b–d, we apply different voltage waveforms to our memristors to emulate various types of pre- and post-neuron activities3. This procedure allows the generation of biologically realistic2, though accelerated (Fig. 3b,c), or artificially designed (Fig. 3d) STDP learning curves. Using our model with the parameters extracted previously, we can now predict the conductance changes for these specific types of STDP. Figure 3c,d shows the excellent agreement between these predictions and the measured conductance variations associated with different STDP waveforms.