Experimental Section/Methods

The film thickness of the device was measured using a profiler (DektakXT-A, Bruker). The electrical characteristics of the devices were measured using a semiconductor parameter analyzer (4200-SCS, Keithley) combined with an ultrafast IV module (4225-PMU, Keithley), in an ambient condition with a relative humidity of 30 %, at 27 °C. In the electrical measurements, the inert electrode (gold or indium tin oxide) was grounded, and the active electrode of silver was used for the scanning voltage. The active area of the lateral-type memristor was investivated using a field-emission scanning electron microscope (S-4800, Hitachi).
To fabricate an organic memristor with a planar structure, a glass substrate was cleaned under ultrasonication in acetone, isopropyl alcohol, and deionized water in sequence for 10 min. For the inert electrode, a 50-nm-thick gold layer was thermally deposited on the substrate at 1 Å/s under 10–6 Torr. The inert electrode was patterned using a photoresist (PR) (AZ 1512, AZ electronic materials) through conventional photolithography and a wet-etching process using an etchant (TFA, Transene) for gold. Then, the active electrode of 50-nm-thick silver was thermally evaporated on the PR patterned film at 1 Å/s under 10–6 Torr. Through the lift-off process for removing the PR, the active electrode was patterned. The width of each electrode and the gap distance between the electrodes were about 300 and 5 μm, respectively. As the polymer medium, a poly (vinyl alcohol) (PVA) powder with molecular weight (Mw) of 10000, 23000, or 130000 gmol-1, dissolved in deionized water in 5, 4, or 2wt%, respectively, was spin-coated on the substrate with the electrode patterns, at a rate of 2000 rpm for 30 s. The PVA layer was soft-baked at 100 °C for 1 hour to remove the residual solvent after spin-coating.
To fabricate an organic memristor with a vertical structure, an indium tin oxide (ITO)-patterned substrate (glass for a rigid device and polyethylene naphthalate for a flexible device) was cleaned under ultrasonication in acetone, isopropyl alcohol, and deionized water sequentially for 10 min. Note that the ITO patterns on the substrate acted as inert electrodes of the memristors. Regarding the polymer medium of the devices, PVA, with Mw = 10000 gmol-1 (or 13000 gmol-1), dissolved in deionized water in 5 wt% (or 4 wt%) was spin-coated on the substrate at a rate of 2000 rpm for 30 s. The PVA layer was then annealed at 100 °C for 1 hour. The thickness of the PVA film was about 300 nm. For producing the active electrode, a 50-nm-thick silver layer was thermally evaporated at 1 Å/s under 10−6 Torr. The active area of the devices was 0.5 × 0.5 mm2.

Results

We first analyzed the ECM phenomenon for the metallic CF growth in the PVA medium. Three types of planar-structured memristors consisting of PVA insulator with the different Mws (10000, 23000, and 130000 gmol-1) were fabricated as shown in Figure 1b. Active and inert electrodes were prepared using silver and gold, respectively, and the gap distance between the electrodes was about 5 μm. As shown in Figure S1, in the device with the high Mw of 130000 gmol-1, the resistive switching behaviors were not observed, which is consistent with the previous study \cite{Krishnan_2018}. However, the devices with the low Mw of 10000 and 23000 gmol-1 clearly showed the resistive switching characteristics (see Figures S2 and S4). In the organic memristors, the ECM phenomenon for resistive switching can be promoted as Mw decreased, because of an increase in the free volumes for ion migration and metallization \cite{Lee_2019}. We measured the current–voltage (IV) characteristics at six different compliance currents (CCs) (10−7, 5 × 10−7, 10−6, 5 × 10−6, 10−5, and 3 × 10−5 A) to explore the ECM phenomenon for resistive switching in the device with Mw = 10000 gmol-1 (see Figure S2). During the successive voltage sweeps, the CC value was set to be increased sequentially. In all the conditions, the device showed the resistive switching characteristics, and the conductance at the low resistance state (LRS) was larger at higher CCs. However, the LRS of the device was maintained only at relatively high CC conditions (10−5 and 3×10−5 A). As the CC value increased, the retention performance was enhanced, and the device exhibited a nonvolatile memory behavior in the case when the CC was larger than 10−5 A. When the device was operated as a nonvolatile memory, the reversible resistive switching characteristics were also observed (see Figure S3). In typical ECM memristors, the conductance and memory volatility are highly dependent on the CC which governs the CF thickness \cite{Lee_2019,Hsiung_2010}, following the results in Figure S2. Moreover, in the resistive switching device with Mw = 23000 gmol-1, the nonvolatile memory characteristics were achieved at the relatively low CC conditions, compared to the device with Mw = 10000 gmol-1. For the organic ECM devices, the lateral diffusion of the CF is governed by the polymer Mw related with the free volume distributions in the medium, and thus, the memory stability is enhanced when Mw is higher \cite{Lee_2020,Lee_2019}.
Let us discuss the operating principle for the resistive switching in the PVA based memristors. Figure S5 shows the temperature effect on the conductance of the device with Mw = 10000 gmol-1. The LRS conductance of the device was decreased with the increase in temperature (see Figure S5), which is consistent with the characteristics of the memristors based on the ECM phenomenon \cite{Jang_2016}. To clearly elucidate the physical mechanism for the resistive switching in the device, the IV curves of the device investigated via voltage sweeps with a CC of 10−5 A (dark blue curves in Figure S2a) were replotted in a log−log scale, as shown in Figure S6. During the sweeping process, the current flow followed the space charge-limited conduction composed of the regions for the Ohmic, Child's law, and abrupt conductance increase, consistent with the electrical characteristics of the ECM based nonvolatile memory \cite{Kim_2021,Sun_2017}. This means that the resistive switching behaviors in the device may be governed by the ECM mechanism.
For directly verifying the ECM phenomenon in the device, we carried out the observation of the active surface according to the resistance state, utilizing the field emission electron scanning microscopy (see Figure 1c). With the transition from the high resistance state (HRS) to the LRS, the CFs comprising several branches were formed in the active area of the device. In addition, after the erasing process, the CFs were partially ruptured. The morphology of the CFs in the device at each resistance state was similar to that of other organic ECM memristors\cite{Park_2020c}\cite{Park_2020b,Park_2021a}, indicating that the resistive switching characteristics of the PVA based memristors originated from the ECM phenomenon consisting of the electrochemical redox reaction and the ion migration along the polymer medium.