Photonic Physical Reservoir Computing with Tunable Relaxation Time Constant

Abstract Recent years have witnessed a rising demand for edge computing, and there is a need for methods to decrease the computational cost while maintaining a high learning performance when processing information at arbitrary edges. Reservoir computing using physical dynamics has attracted significant attention. However, currently, the timescale of the input signals that can be processed by physical reservoirs is limited by the transient characteristics inherent to the selected physical system. This study used an Sn‐doped In2O3/Nb‐doped SrTiO3 junction to fabricate a memristor that could respond to both electrical and optical stimuli. The results show that the timescale of the transient current response of the device could be controlled over several orders of magnitude simply by applying a small voltage. The computational performance of the device as a physical reservoir is evaluated in an image classification task, demonstrating that the learning accuracy could be optimized by tuning the device to exhibit appropriate transient characteristics according to the timescale of the input signals. These results are expected to provide deeper insights into the photoconductive properties of strontium titanate, as well as support the physical implementation of computing systems.


Figure S3
shows the measured current retention characteristics after switching the device to LRS by applying a positive bias (+ 3 V).The V read was +0.3 V.The current value gradually relaxes over approximately 10 3 s.This forgetting characteristic is similar to those observed in memristors with the structure of metal (Pt)/Nb:STO junction [1,2].In recent years, this property has been found to be suitable for neuromorphic computing [3,4,5].Figure S4 shows the area dependence of the initial resistance of the ITO/Nb:STO junction device.The initial resistance (R) is inversely proportional to the device area (S), R ∝ 1/S (see Figure S5).This result suggests that the resistive switching takes place over the entire interface area.After the initial switching cycle, we continued to switch the device further and investigated the area dependence of resistances in HRS and LRS.  Figure S6 shows the area dependence of resistances in HRS and in LRS.The resistances in both HRS and LRS are inversely proportional to the device area, R ∝ 1/S (see Figure S7 and Figure S8) similarly to that was confirmed for the initial resistance.Therefore, it was suggested that the resistive switching takes place over the entire interface area even after repeating resistance switching.This result, which was observed in, is similar to that of Pt/Nb:STO junction memristors reported by Sim et al [6], and consistent with the report that the resistive switching of memristors with the structure of metal (Pt, Ni)/Nb:STO junction occur in the entire interface area [6,7,8,9].Figure S8.The relationship between resistance and the inverse of device area (LRS).The resistance value used for fitting was the median resistance value for each device area in Figure S6.
We performed peak fitting of the obtained photoluminescence (PL) spectra in order to discuss the recombination centers attributed to the luminescence.For all the PL spectra shown in Figures 4a-c in the main text, optimal fitting results were obtained by assuming the addition of the three Gaussian functions.The Gaussian used in the fitting is given by Equation S1, where I is the intensity of the PL spectrum, S i is the intensity parameter in each Gaussian, E is the energy, E peak i is the peak energy in each Gaussian, Γ i is the broadening parameter in each Gaussian, and A is the background intensity.Tables S1-S3 show the peak fitting results for Figures 4a-c in the main text, respectively, while A's were determined to be 81.6,65.1, and 96.7, respectively.
Table S1.Peak fitting results in Figure 4a.           Figure S17 shows the reproducibility of the output current (I out ) at V read = −0.3V, which is the best performance shown in the main text.The measurement was repeated three times, the plotted points represent the average values, and the error bars represent the maximum and minimum values.The reproducibility is good for the same 4-bit pattern.On the other hand, the difference in I out between "0110," "0001," and "1010" and between "1001" and "0101" is small.This tendency is undesirable in a task that requires accurate classification of 4-bit patterns.However, when processing time-series signals, this randomness can have a positive effect.The addition of another heterogeneity or randomness to the reservoir components improves performance, as shown for example in the following references [10,11].

Figure 3 GND
Figure S1 shows a schematic of the Sn-doped In 2 O 3 (ITO)/Nb-doped SrTiO 3 (Nb:STO) junction with a structure to avoid the direct contact of the probe with the area of the ITO/Nb:STO interface.Adopting this structure made it possible to prevent light from being reflected by the measurement probe during light irradiation and ensured that the ultraviolet (UV) light was incident on the ITO/Nb:STO interface.

FigureFigure S2 .
FigureS2shows cyclic endurance of the ITO/Nb:STO junction until 200 switching cycles, where the readout voltage (V read ) was +0.3 V.The transitions from a high-resistance state (HRS) to a low-resistance state (LRS) and vice versa are called SET and RESET, respectively.The one cycle consists of a set of SET and RESET switching.A memory window, the resistance ratio of HRS to LRS, was retained more than 10 3 through 200 switching cycles.

Figure S3 .
Figure S3.Current retention characteristics of the device.

Figure S4 .
Figure S4.Device area dependence of initial resistance.

Figure S5 .
Figure S5.The relationship between resistance and the inverse of device area.The resistance value used for fitting was the median resistance value for each device area in FigureS4.

Figure S6 .
Figure S6.Device area dependence of resistance after switching.

Figure S7 .
Figure S7.The relationship between resistance and the inverse of device area (HRS).The resistance value used for fitting was the median resistance value for each device area in FigureS6.

Figure S9 and
FigureS9and FigureS10show the time dependence of the current (I-t characteristics) when +0.5 V or −0.5 V was applied to the device for 3000 s, respectively.

Figures S11 -
Figures S11-S15 show the photo-induced current characteristics of the device when irradiated with of UV pulse train of 4-bit signals of 16 patterns.

FigureFigure S16 .
FigureS16shows the results of an analysis of the effect of the threshold used to binarize the input patterns on the accuracy of the system.

Figure S17 .
Figure S17.Reproducibility of device output current when 4-bit encoded UV pulses were input to the ITO/Nb:STO junction.Measurements were repeated three times.

Table S2 .
Peak fitting results in Figure4b.

Table S3 .
Peak fitting results in Figure4c.