# Fileset [nn5c06174_si_001.pdf](https://mdr.nims.go.jp/filesets/1fe36db9-94c2-4b74-a70c-2698b7331654/download) ## Creator [Daiki Nishioka](https://orcid.org/0000-0002-3369-7700), [Hina Kitano](https://orcid.org/0009-0008-9132-0275), [Wataru Namiki](https://orcid.org/0000-0003-4053-7366), Satofumi Souma, [Kazuya Terabe](https://orcid.org/0000-0003-3988-3456), [Takashi Tsuchiya](https://orcid.org/0000-0002-6950-6160) ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Two Orders of Magnitude Reduction in Computational Load Achieved by Ultrawideband Responses of an Ion-Gating Reservoir](https://mdr.nims.go.jp/datasets/470dca15-9f14-4adc-b3cf-8f5554a9ac93) ## Fulltext 1 Supporting information Two Orders of Magnitude Reduction in Computational Load Achieved by Ultra-wideband Responses of Ion-Gating Reservoir Daiki Nishioka1*, Hina Kitano2,3, Wataru Namiki2, Satofumi Souma4, Kazuya Terabe2 and Takashi Tsuchiya2,3* 1International Center for Young Scientists (ICYS), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, 305-0044, Japan. 2Research Center for Materials Nanoarchitectonics (MANA), NIMS, 1-1 Namiki, Tsukuba, Ibaraki, 305-0044, Japan. 3Department of Applied Physics, Faculty of Advanced Engineering, Tokyo University of Science, Katsushika, Tokyo 125-8585, Japan 4Department of Electrical and Electronic Engineering, Kobe University, Kobe 657-8501, Japan *Email: TSUCHIYA.Takashi@nims.go.jp, NISHIOKA.Daiki@nims.go.jp 2 Note S1: Effect of Channel Length on the Modulation Range of Drain Current (On/Off Ratio) In this section, we examine how the channel length of the device affects the modulation range of the drain current, i.e., the on/off ratio. Figure S1(a) shows normalized transport characteristics obtained from the devices presented in Fig. 1c, corresponding to Drain0 through Drain2. These devices share a channel width of 30 µm and have channel lengths of 5 µm, 20 µm, and 100 µm, respectively. To focus on the on/off ratio of each channel, the horizontal axis represents the relative gate voltage with respect to the Dirac point, defined as VG' = VG - VDirac, and the vertical axis shows the normalized increase in drain current relative to the value at VG' = 0 V. As a result, we observed that shorter channels tend to exhibit a suppressed increase in drain current in response to gate voltage. For instance, the on/off ratio z at a given gate voltage (VG' = -1.35 V) was found to increase with the channel length L, as shown in Figure S1(b). To explain this behavior, we describe the drain current ID using a composite resistance model, as illustrated in Figure S1(c). The total channel resistance Rtot is expressed as the sum of the VG'-independent lead resistance RL (primarily due to contact and lead electrodes) and the VG'-dependent channel resistance RC: 𝑅!"!(𝑉#) = 𝑅$ + 𝑅%(𝑉#) (S1) In this model, for shorter channels, RC becomes smaller, making the contribution of RL relatively larger. Therefore, even if RC decreases under gate bias, the overall increase in ID is limited as long as RL remains dominant. Let RC,off and RC,on be the channel resistances in the off-state (VG' = 0 V) and on-state (VG' = -1.35 V), respectively. The channel-length dependence of the on/off ratio z(L) can then be expressed as: 𝑧(𝐿) =𝑅$ + 𝑅%,"''𝑅$ + 𝑅%,"( (S2) The channel resistances can further be expressed using their respective resistivities: 𝑧(𝐿) =𝑅$ +𝜌%,"''𝑊 𝐿𝑅$ +𝜌%,"(𝑊 𝐿 (S3) Here, rC,off and rC,on are the resistivities of the channel in the off and on states, respectively. The red line in Figure S1(b) shows the fitting result of the experimental data (gray dots) using the above model (Equation S3), indicating that the model accurately captures the channel-length dependence of the on/off ratio. Here, RL was treated as a length-independent constant, and the parameters RL, rC,off and rC,on were numerically determined to be 128.1 Ω, 1842 Ω, and 203.2 Ω, respectively. 3 Figure S1: (a) Normalized transfer characteristics for devices with a fixed channel width of 30 µm and channel lengths of 5 µm, 20 µm, and 100 µm (Drain0–Drain2), plotted against the relative gate voltage VG’ =VG−VDirac. The vertical axis shows the increase in drain current relative to VG’ =0 V. The dashed line indicates VG’ =-1.35 V where on/off ratios were calculated. (b) Channel-length dependence of the on/off ratio z evaluated at a fixed VG’, showing a monotonic increase with increasing channel length. The red dashed curve represents the fitting based on the composite resistance model (Eq. S3). (c) Schematic illustration of the composite resistance model, where the total channel resistance Rtot is composed of the gate-independent lead resistance RL and the gate-dependent channel resistance RC(VG). Next, we used the obtained RL to model the gate-voltage dependence of the drain current and validate the model. Using the composite conductance Gtot = 1/ Rtot, the drain current is expressed as: 𝐼) (𝑉#) = 𝐺!"!(𝑉#)𝑉) =𝐺$𝐺%(𝑉#)𝐺$ + 𝐺%(𝑉#) 𝑉) (S4) where GL = 1/ RL is the lead conductance, and GC = 1/ RC is the channel conductance. Ideally, GC = a|VG'|, showing linear dependence on gate voltage. However, due to the voltage drop along the channel induced by the source–drain bias VD, the potential distribution varies within the channel. In particular, near VG' ~ 0 V, both n-type and p-type regions may coexist, leading to a broadening of the conductance profile and preventing the emergence of a sharp V-shaped response. To account for this behavior, we constructed a segmented channel model in which the channel is divided into N = L/l sub-regions of length l = 20 nm, as illustrated in Figure S2. Let VC,i be the local channel potential in the i-th segment (i=1,2,…,N). The effective gate voltage applied to that segment is V’G,eff = VG' - VC,i, and the partial conductance Gi is defined as: 𝐺* = 𝑎 ⋅ 5𝑉#,+'', 5 + 𝑏 = 𝑎 ⋅ 5𝑉#, − 𝑉%,*5 + 𝑏 (S5) Here, 𝑎 = (𝑊 𝑙⁄ ) ∙ 𝜇𝐶-)$ is the slope of conductance change with effective gate voltage, and b is the minimum conductance at V’G,eff = 0 V. Due to thermally excited carriers at room temperature, b > 0. Assuming experimental condition of VD = 0.5 V, the local channel potential VC,i was defined using a linear profile: 𝑉%,* =𝑉)𝑁⋅ ?𝑖 −12A −𝑉)2(S6) 87654321Normalized drain current-1.5 -1.0 -0.5 0.0 0.5VG' = VG - VDirac /V L = 5 µm L = 20 µm L = 100 µmRL RC(VG)VDID(VG) = VD / Rtot(VG)Lead Channel87654321On/off ratio z12080400Chanel length L /µm Experiment Modela b c 4 It should be noted that this definition ensures VC,i = 0V at the center of the channel (i=N/2), thereby preventing an artificial shift of the Dirac point caused by the introduction of VD. This is consistent with the use of the relative gate voltage VG’, which already compensates for the Dirac point shift. The total channel conductance GC is then given by the series combination of the segment conductances: 𝐺% = CD1𝐺*.*/0E10= CD1 𝑎 ⋅ 5𝑉#, − 𝑉%,*5 + 𝑏.*/0E10(S7) Substituting into Equation S4, the drain current response becomes: 𝐼)(𝑉#,) =𝐺2 ⋅ G∑1 𝑎 ⋅ 5𝑉#, − 𝑉%,*5 + 𝑏.*/0 I10𝐺$ + G∑1 𝑎 ⋅ 5𝑉#, − 𝑉%,*5 + 𝑏.*/0 I10 𝑉) (S8) Using this model, we performed fitting to the measured data. The value of RL was taken from the previous model (Equation S3), while a and b were treated as fitting parameters. Here, b corresponds to the minimum conductance near the Dirac point, and a is a coefficient related to the channel geometry, carrier mobility, and EDL capacitance as described above. Theoretically, based on a carrier mobility of ~3000 cm2/V·s (from Hall measurements) and an EDL capacitance of ~1 µF/cm2, the estimated value of a is approximately 4.5, which is consistent with the fitting results shown in Table S1. Figure S2: Segmented channel model used to describe the broadened conductance behavior near the Dirac point. The channel is divided into N=L/l segments of length l=20 nm, with each segment assigned a local potential VC,i defined by a linear voltage drop under VD=0.5 V. The effective gate voltage in each segment is VG’−VC,i, and the local conductance is given by Gi=a∣VG’−VC,i ∣+b. The red curves in Figures S3(a–c) illustrate the transport characteristics reproduced using Equation S8 and RL = 128.1 Ω. The comparison with the experimental data (gray dots) shows that the model successfully captures the saturation behavior of ID caused by the lead resistance. In contrast, the ElectrolytePositionPotentialVG’V ’G,effGDS0 LChannelVC,iii-1 i+1 ……20 nm……Gi Gi+1Gi-1 V ’G,effGiba 5 simplified model without RL (i.e., ID = GC·VD) fails to match the experimental results, particularly under large negative VG'. This discrepancy becomes more pronounced in short-channel devices, where the contribution of RL is relatively significant. These results strongly support the validity of our model and indicate that the observed channel-length dependence of the on/off ratio in the devices arises from the relative contribution of the lead resistance. Figure S3: Comparison of the modeled (red curves) and experimental (gray dots) drain current characteristics for devices with different channel lengths of (a) 5 µm, (b) 20 µm and (c) 100 µm. The model incorporates the lead resistance RL and the segmented channel conductance to reproduce the observed saturation behavior. Dashed curves represent the simplified model without RL, which fails to capture the measured response, especially under large negative VG’. Table S1: Fitting parameters a and b for the segmented conductance model. Channel Parameter a Parameter b L = 5 µm 7.54 0.135 L = 20 µm 5.61 0.294 L = 100 µm 3.76 0.206 43210Drain current /mA-1.2 -0.8 -0.4 0.0VG' /VL = 5 µm Experiment Model Model (w/o- RL)2.52.01.51.00.50.0Drain current /mA-1.2 -0.8 -0.4 0.0VG' /VL = 20 µm Experiment Model Model (w/o- RL)8006004002000Drain current /µA-1.2 -0.8 -0.4 0.0VG' /VL = 100 µm Experiment Model Model (w/o- RL)a b c 6 Figure S4: Optical microscope image of the Hall bar-type graphene channel. The Hall measurements shown in Figure 1e were performed using an EDLT fabricated by placing ion-gel and Au foil on this Hall bar-type channel. I+ and I- are the current terminals, V+ and V- are the voltage terminals, and VH is the terminal for Hall voltage measurements. 50 µmGrapheneCr/AuI+ I-V+ V-VH 7 Note S2: Simulation-Based Reproduction and Interpretation of 100~ns Switching Behavior The experimentally observed switching response on the order of 99 ns can be quantitatively explained by incorporating electrostatic screening effects into numerical simulations based on the Nernst-Planck-Poisson (NPP) equations as follows. In this framework, the NPP equations are solved to obtain the time evolution of ionic concentrations (both anions and cations), fluxes, and electrostatic potential within the ion gel, where the presence of the graphene channel is taken into account by calculating the charge distribution using a tight-binding (TB) method combined with a quantum capacitance model. The electrostatic potential is obtained by solving the Poisson equation over the entire simulation domain, including the graphene layer, under the boundary condition that a gate voltage is applied to the opposite side of the ion gel. Then the channel current in graphene is calculated using the Boltzmann transport theory. The detailed methodology has been reported previously[1]. In the present study, we explicitly consider the electrostatic screening within the ion gel, which acts as the gate dielectric. Given the relatively high ionic conductivity of the gel, s = 6 mS/cm, it is reasonable to assume that the electric field inside the electrolyte is dynamically suppressed via ionic motion, which is captured by solving the time-dependent NPP equations. That is, we consider a Debye-length-dependent additional term in the Poisson equation as 𝑑3𝜙(𝑧)𝑑𝑧3= −𝜌(𝑧)𝜀+(𝜙(𝑧) − 𝜙4567)𝜆)3 (S9) along the ion-gel thickness direction (normal to the graphene plane), where the second term on the right-hand side effectively accounts for the electrostatic screening arising from mobile ions under the assumption of linearized Boltzmann statistics, with the Debye screening length 𝜆) = Q𝜀𝑘8𝑇/2𝑛𝑒3 estimated based on the ion density n. In the above Poisson’s equation, 𝜙4567 denotes the bulk electrostatic potential determined by the charge neutrality condition, and is assumed to be moderately shifted toward the graphene channel potential near the graphene interface (within a few nanometers) due to asymmetric electrostatic coupling and incomplete ionic screening. In the actual simulation, we assume the ion density 𝑛 = 3.23 × 1039 m1: and the diffusion constant 𝐷 = 1.5 × 10100 m3/s for both anion and cation. These parameter choices are consistent with the experimentally observed conductivity s ≈ 6 mS/cm through the Nernst-Einstein relation: 𝜎 =2𝑒3𝑛𝐷/𝑘;𝑇 at the room temperature. The permittivity is assumed as 𝜀 = 10𝜀<. Figure S5 shows the time evolution of the normalized graphene channel current in response to a pulsed gate voltage applied to a graphene FET with a 500 μm-thick ion gel as the gate dielectric. The pulse width is 5 μs, with the base (off-state) gate voltage set to Vb = -0.1 V and the input (on-state) gate voltage set to Vin = -0.55 V. As can be seen from the result, a switching response on the order of 100 ns, comparable to the experimental observation, is successfully reproduced. The agreement between the experimental and simulation results suggests that the relaxation time on the order of 100 ns can be interpreted as 𝜏 = 𝑑-)$3 /𝐷, where the typical width of the electric double layer is assumed to be dEDL =1.2 nm and the diffusion constant is taken as 𝐷 = 1.5 × 10100 m3/s as mentioned above, yielding t ≈ 100 ns. 8 Figure S5: Time evolution of the normalized graphene channel current in response to a pulsed gate voltage applied to a graphene FET with a 500 μm-thick ion gel as the gate dielectric. The inset shows a magnified view of the time window from 0 to 0.5 μs, highlighting the fast switching response on the order of 100 ns. 9 Note S3: CEDL Evaluation The electric double-layer capacitance CEDL of the ion-gel/graphene EDLT was 0.91 µF/cm2 in the p-type region and 0.88 µF/cm2 in the n-type region. These values were calculated by applying the widely used relationship =>=?!= 𝐶-)$ (the differential capacitance of the EDL) to the changes in Hall density and electron density obtained from Hall measurements as a function of VG2-4). Figure S6 shows the carrier density dependence obtained from Hall measurements, with linear fitting performed over the p-type region (from VG-VDirac=-1.525 V to -0.425 V) and the n-type region (from VG-VDirac=0.375 V to 1.275 V). From these fittings, CEDL was calculated, and as shown in Figure S6, the fitting lines match well across a wide VG range. This result indicates that CEDL has little dependence on the applied VG. The CEDL values calculated here are consistent with experimentally and theoretically estimated values for graphene EDLTs using ionic liquids3-5). The relatively low CEDL<1 µF/cm2, compared to the typical ~10 µF/cm2 for ionic liquid-based EDLs6), arises from the limitation imposed by the series quantum capacitance Cq5). Figure S6: Carrier density changes in the graphene channel as a function of the applied gate voltage obtained from Hall measurements. The red and blue lines represent linear fittings in the p-type and n-type regions, respectively, and the slopes of these fittings were used to calculate the electric double-layer capacitance CEDL. 86420Carrier density / ×1012 cm-2-1.0 0.0 1.0VG−VDirac / V!"!#!= 0.91 µF cm"⁄!"!#!= 0.88 µF cm"⁄ 10 Figure S7: Conceptual design of vertically stacked ion-gating transistors with multi-timescale responses. (a) Schematic illustration of a vertical organic electrochemical transistor (vOECT) composed of stacked channel materials with different ion diffusion coefficients Dion, enabling engineered temporal dynamics across layers. (b) Vertically integrated graphene-based architecture, where varying the channel area and using multilayer graphene allows integration of multiple timescales. Ion trapping in multilayers may further enhance tunability. DSubstrateSDElectrolyteGHigh Dion ChannelLow Dion Channel…Mobile ionFastSlow DSubstrateSDElectrolyteGSmall ChannelLarge Channel…Mobile ionFastSlowLayered Graphenea b 11 Figure S8: Influence of channel geometry on relaxation time. (a)–(h) Optical microscope images of graphene channels and source/drain electrodes for individually fabricated devices. The channel width is fixed at 30 µm, and the channel lengths L are 5 µm, 10 µm, 20 µm, 50 µm, 100 µm, 200 µm, 500 µm, and 1000 µm, respectively. The white boxes in the images indicate a scale bar of 500 µm. (i) Channel resistance of graphene as a function of channel length. (j) Overview and (k) magnified view of the normalized drain current responses to pulsed gate voltages for each device. (l) Relaxation time as a function of channel length. 1.20.80.40.0Normalized drain current1.51.00.50.0-0.5Time /ms Channel length 5 µm 10 µm 20 µm 50 µm 100 µm 200 µm 500 µm 1000 µm 2.01.61.20.8VG /V2.01.61.20.8VG /VL :1000 µmL :500 µmL :200 µmL :100 µmL :50 µmL :20 µmL :10 µmL :5 µm1.20.80.40.0Normalized drain current40200Time /µs10-6246810-524Relaxation time /s2 4102 41002 410002Channel length /µm2520151050Chennel resistance /kΩ10008006004002000Channel length /µm1-1/ea b c de f g hij kl 12 Note S4: Detailed calculation method for information processing capacity Here, we describe the detailed procedure for calculating the information processing capacity (IPC). The IPC is evaluated based on the reservoir's ability to reconstruct a target signal ym, which is defined as follows, from a random input sequence u(k): 𝑦@(𝑘) =h𝑃A",$[𝑢(𝑘 − 𝑑)]B=/< (S10) In this expression, m is the index representing a specific polynomial term; d is the delay; D is the maximum delay; and nm,d denotes the polynomial order associated with a given index and delay. The polynomial Pn' represents the n'-th order orthogonal polynomial generated via the Gram-Schmidt process, and is defined as: 𝑃A%[𝑢(𝑘 − 𝑑)] = 𝑢A%(𝑘 − 𝑑) −D𝑐*CA%D𝑃*[𝑢(𝑘 − 𝑑)]A10*/< (S11) 𝑐*CA%D =∑ 𝑃*[𝑢(𝑘 − 𝑑)]𝑢A%(𝑘)E&'('F/0∑ 𝑃*[𝑢(𝑘 − 𝑑)]3E&'('F/0 (S12) with P0 = 1. For example, the first- and second-order polynomials are given by: 𝑃0[𝑢(𝑘 − 𝑑)] = 𝑢(𝑘 − 𝑑) − 𝑢n (S13) 𝑃3[𝑢(𝑘 − 𝑑)] = 𝑢3(𝑘 − 𝑑) +𝑢n𝑢3nnn − 𝑢:nnn𝑢3nnn − 𝑢n3𝑢(𝑘 − 𝑑) +𝑢n𝑢:nnn − 𝑢3nnn3𝑢3nnn − 𝑢n3 (S14) where 𝑢A,nnnn = 0E&'('∑ 𝑢A%(𝑘)E&'('F/0 (n’=1,2,…). Higher-order polynomials such as P3 and beyond can be defined recursively using the above relation. Next, for each index m (corresponding to a specific combination of delay and polynomial order), we perform a regression task in which the reservoir is trained to reconstruct the target signal ym defined above. Since ym is a product of multiple polynomials of degree nm,d, the total degree n of the target function can be written as: 𝑛 =D 𝑛@,=B=/< (S15) Let y(k) denote the output of the reservoir. The accuracy of this reconstruction task is evaluated based on the error between ym(k) and y(k), and is defined as the component-wise capacity Cm: 𝐶@ = 1 −∑ [𝑦@(𝑘) − 𝑦(𝑘)]3E&'('F/0∑ [𝑦@(𝑘)]3E&'('F/0 (S16) By performing the above reconstruction task for all index values m, the overall IPC can be obtained. In addition, by focusing only on the components with a specific polynomial degree n, the sum of Cm over the corresponding indices m(n) is defined as the degree-specific capacity Cn. The total IPC, Ctot, 13 is then given by the sum of Cm over all indices: 𝐶A = D 𝐶@@∈@(A) (S17) 𝐶!"! =D𝐶@@ (S18) As an illustrative example, we describe the step-by-step calculation of the first-order capacity C1 under the optimal condition for the NARMA2 task (T = 100 µs). For n = 1, the target signal ym(k) is given by Eq. (S10) as: 𝑦@(𝑘) = 𝑃<[𝑢(𝑘 − 0)] × 𝑃<[𝑢(𝑘 − 1)] × 𝑃<[𝑢(𝑘 − 2)] × … × 𝑃