High-precision and linear weight updates by subnanosecond pulses in ferroelectric tunnel junction for neuro-inspired computing

The rapid development of neuro-inspired computing demands synaptic devices with ultrafast speed, low power consumption, and multiple non-volatile states, among other features. Here, a high-performance synaptic device is designed and established based on a Ag/PbZr0.52Ti0.48O3 (PZT, (111)-oriented)/Nb:SrTiO3 ferroelectric tunnel junction (FTJ). The advantages of (111)-oriented PZT (~1.2 nm) include its multiple ferroelectric switching dynamics, ultrafine ferroelectric domains, and small coercive voltage. The FTJ shows high-precision (256 states, 8 bits), reproducible (cycle-to-cycle variation, ~2.06%), linear (nonlinearity <1) and symmetric weight updates, with a good endurance of >109 cycles and an ultralow write energy consumption. In particular, manipulations among 150 states are realized under subnanosecond (~630 ps) pulse voltages ≤5 V, and the fastest resistance switching at 300 ps for the FTJs is achieved by voltages <13 V. Based on the experimental performance, the convolutional neural network simulation achieves a high online learning accuracy of ~94.7% for recognizing fashion product images, close to the calculated result of ~95.6% by floating-point-based convolutional neural network software. Interestingly, the FTJ-based neural network is very robust to input image noise, showing potential for practical applications. This work represents an important improvement in FTJs towards building neuro-inspired computing systems.


S1. Desirable specifications for synaptic devices
summarizes the target specifications of artificial synapse devices. For weight updates during the long term potentiation (LTP) and long term depression (LTD) processes, the conductance (G) evolution with pulse number (P) can be modeled by Equation S1 and S2, respectively 3 . α=1.726/(A+0.162).
Here, Gmax and Gmin are the maximum and minimum conductances of the device, respectively. Pmax is the maximum number of pulses to tune the conductance. Parameter α is the nonlinearity of weight updates. By fitting the conductance versus pulse number with Equation S1 or S2, the parameter A can be obtained, and α is then calculated by Equation S3. The lower α is, the more linear the curve is.

S2. I-V curves and transport mechanism analyses
Fig. S1a shows a typical I-V hysteresis loop of the Ag/PbZr0.52Ti0.48O3 (PZT)/Nb:SrTiO3 (NSTO) FTJ, indicating its memristive characteristic, similar to the earlier report 4 . In addition, the I-V curve clearly shows a rectifying transport character, suggesting the existence of the Schottky barrier for the MFS-type FTJs. To explore the transport and resistive switching mechanisms, the I-V curves at different temperatures from 150 to 270 K were measured at ON and OFF states of the FTJ with (111)-oriented PZT barrier, as shown in Fig. S1b and c, respectively. To semi-quantitatively analyze the ferroelectricity tuned barrier, the thermally assisted tunneling model can be used after simplifying the composite barrier to be a Schottky barrier. The thermally-assisted tunneling current can be described by 5,6 J F =J S (T)exp ( qV/E 0 ). (S4) Through fitting the lnJF vs. V curves using Equation S4, the JS and 1/E0 at different temperatures can be extracted, and their relationship follows Equation S5: where E 0 =nk B T and E 00 = qh 4π [N D /m n * ε r ε 0 ] 1/2 . The temperature dependent relative permittivity ε r (T) of NSTO can be described by Barrett

S3. Ferroelectric switching dynamics in (001)-oriented PZT FTJs
The ferroelectric switching dynamics of FTJs with (001)-oriented PZT were also investigated as a comparison with that of (111)-oriented PZT. Obviously, there is no plateau during switching, as shown in Supplementary Fig. S2, which implies that only one step switching process occurs in FTJs with (001)-oriented PZT. Pulse duration (s) than the slope parameter of Kay-Dunn law 11 may be related to the depleted region at the semiconductor interface which shares the applied voltage.
Besides, it is noted that with increasing PZT thickness, the FTJ resistance increases as a result. As shown in Fig Table S2. With increasing work functions of electrodes from Ag to Pt, the ON/OFF ratio increases, while the coercive voltages increase obviously.

S5. FTJs with different top electrodes
Considering that the ON/OFF ratio of >100 for the FTJ with Ag electrode is sufficient to meet the target performance for an synaptic device (Table S1) 15   In addition, the electrodes also influence switching endurance of FTJ. Fig. S5 shows the switching endurances of FTJs with Pt and Ag electrodes using the same pulse duration td = 1 μs. For the FTJ with Pt top electrode, larger operation voltages of 3.5 V/−4.5 V are required to realize the ON/OFF ratio ~1500 and the corresponding switching endurance is ~2×10 6 . By decreasing applied voltages to 2.7 V/−3.2 V, the ON/OFF ratio decreases to ~200, as shown in Fig. S5b, and the corresponding switching endurance increases to ~10 8 .
While for FTJ with Ag electrode with an ON/OFF ratio of ~200, the switching endurance is as high as 6×10 8 . This should be due to the lower operation voltages of 1.5 V/−2.5 V for the FTJ with Ag electrode.

S6. Excluding the occurrence of Ag migration.
The resistance switching mechanism of our FTJ is closely related to the ferroelectricity-affected band structure instead of Ag migration. There are some experimental evidences to exclude the occurrence of Ag migration.
1) The resistance switching characteristics based on the tunneling across a ferroelectric barrier of FTJs are different from these of Ag migration. For Ag conducting filament based memristors, the current increases abruptly when Ag filament formed 16 . Thus, the I-V curve is typically linear at ON state, and the current would decrease with increasing temperature because the conduction mechanism follows a metallic behavior 17 . While for our FTJs, as shown in Fig. S1, the I-V curves at ON state follow a thermally-assisted tunneling model, suggesting a quantum tunneling mechanism. In addition, as shown in Fig. S3, both ON and OFF states of resistances show exponential dependences on the PZT thickness, also indicating a tunneling effect in FTJs 14 .
2) As shown in Fig. S4, the resistance switching behavior of the FTJ with Ag electrode is similar to these with Cu and Pt electrodes, supporting the same underlying resistance switching mechanism among different electrodes 18 . This is also an evidence to exclude the occurrence of Ag filaments in the samples.
3) The resistive switching of the Ag/BTO/NSTO FTJ is closely correlated with a nucleation-limited-switching (NLS) model of the ferroelectric domain dynamics 19 , as demonstrated in Fig. 3 of the manuscript.
All the above experimental results confirm that the resistance switching of the Ag/BTO/NSTO FTJ is caused by ferroelectric polarization switching rather than the conduction bridge based on Ag filaments. To ensure that sub-nanosecond pulsed voltages are successfully delivered to the FTJ and to measure the current through the FTJ for energy consumption estimation, we conducted a real-time electrical measurement that is similar to the previous literatures 20, 21 .
By applying positive and negative voltage pulses of ~600 ps shown in Fig. S6a and b, respectively, the transmitted current signals through the FTJ are captured by the oscilloscope, as depicted in Fig. S6c and d, respectively. It can be seen that the transmitted positive pulse is extended from 600 ps to 630 ps (defined as full width at half maximum), while the negative signal is deformed in shape with an even smaller pulse width ~470 ps. The different deformed current signals between positive and negative voltage pulses are related to the rectification characteristics of our FTJ (see Fig. S1), and this will lead to the different impedance mismatching conditions. Similar deformed transmitted signals have also been reported in other memristors 22,23 . In addition, under the positive and negative pulses, the write current densities can be estimated to be about 1.0×10 3 and 1.3×10 3 A/cm 2 , respectively, and these lead to the energy consumptions per operating pulse ~440 and ~520 pJ, respectively.

S9. Ultrafast resistance switchings by 300 ps pulsed voltages
By increasing the amplitude of voltage pulses, the resistive switching speed can be further accelerated to 300 ps, which is the highest resistance switching speed among

S11. Summary of conductance manipulations of different types of memristors
The representative performances of different types of memristors including conducting filament modulated memristors, interfacial ionic displacement type memristors, ferroelectric field effect transistor (FeFET) memristors, and FTJ memristors are listed in     Table S4), which is close to that of 95.6% achieved by floating-point-based software. When the CNN was simulated based on the 150 states with 630 ps pulse duration, In addition, the CNN simulations on common MNIST dataset were also carried out.
As shown in Fig. S12a    The pulsed voltages before and after passing through the waveguide were measured by an oscilloscope, as shown in Fig. S13c. The pulse ~600 ps shows little shape deformation after transmitted through the waveguide, which implies that the voltage pulse maintains its shape when it is delivered to the device.

S13. Ultrafast test circuit with a waveguide
The circuit was further characterized after connecting the FTJ onto the waveguide by short copper wires. High frequency scattering (S)-parameter measurements from 0.1 to 3 GHz were performed, as shown in Fig. S14a where Z0 = 50 Ω is the characteristic impedance and ZL is the impedance of the equivalent circuit that was calculated by advanced design system (ADS) software. The results in Fig.   S14a