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[Hina Kitano](https://orcid.org/0009-0008-9132-0275), [Daiki Nishioka](https://orcid.org/0000-0002-3369-7700), [Kazuya Terabe](https://orcid.org/0000-0003-3988-3456), [Takashi Tsuchiya](https://orcid.org/0000-0002-6950-6160)

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[Physical reservoir computing with graphene-based solid electric double layer transistor and the information processing capacity analysis](https://mdr.nims.go.jp/datasets/1c555c29-4898-4edd-b872-e7ebacdfadf2)

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Physical reservoir computing with graphene-based solid electric double layer transistor and the information processing capacity analysisApplied PhysicsExpress      LETTER • OPEN ACCESSPhysical reservoir computing with graphene-basedsolid electric double layer transistor and theinformation processing capacity analysisTo cite this article: Hina Kitano et al 2025 Appl. Phys. Express 18 024501 View the article online for updates and enhancements.You may also likeThermal conductivity of BaZrO3 andKTaO3 single crystalsMakoto Tachibana, Cédric Bourgès andTakao Mori-Surface and interface physics driven byquantum materialsShuji Hasegawa-A time-delayed physical reservoir withvarious time constantsYutaro Yamazaki and Kentaro Kinoshita-This content was downloaded from IP address 144.213.253.16 on 23/02/2025 at 01:06https://doi.org/10.35848/1882-0786/adb19b/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad5c26/article/10.35848/1882-0786/ad4468/article/10.35848/1882-0786/ad4468/article/10.35848/1882-0786/ad2782/article/10.35848/1882-0786/ad2782https://pagead2.googlesyndication.com/pcs/click?xai=AKAOjss1o9qbrdk1fAA4oC2X_FYcMp8GXqkS7YNtEnk9VuQBY_sv6o04EoKQgkSvj47VKsNllOEs4z71O8xXoYkD7CKxmDUL3ngrikF7_qCCQ9t71y0wp8HOctwrDErazYq-W52lDqhwNwEHlsjV9rMF_7FetLirzYQ5wm-UUtb-c3u0HMr2LM-NKnhWeoHXbeC0t_27agJingTPe7fKUj6theUoSYcsmRZ1stP2AwR5I_T06_6XA-K7PTRquRRM46MydD_QN-5QzVOZE-iZHKpunoI328pVwPLJv5HrCBWGv6vxlRJ929fEsDRiQN92IySODr2eJ28Vtdsv0bPbixWRE0yhjhaSL7fqTHYaeKbPG46_Qw&sig=Cg0ArKJSzNjAI1MAhUeq&fbs_aeid=%5Bgw_fbsaeid%5D&adurl=https://ecs.confex.com/ecs/248/cfp.cgi%3Futm_source%3DIOP%26utm_medium%3Dbanner%26utm_campaign%3DIOP_248_abstract_submission%26utm_id%3DIOP%2B248%2BAbstract%2BSubmissionPhysical reservoir computing with graphene-based solid electric double layertransistor and the information processing capacity analysisHina Kitano1,2 , Daiki Nishioka1,3 , Kazuya Terabe1 , and Takashi Tsuchiya1,2*1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044,Japan2Department of Applied Physics, Faculty of Advanced Engineering, Tokyo University of Science, Katsushika, Tokyo 125-8585, Japan3International Center for Young Scientists (ICYS), NIMS, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan*E-mail: TSUCHIYA.Takashi@nims.go.jpReceived December 22, 2024; revised January 26, 2025; accepted February 2, 2025; published online February 13, 2025Physical reservoir computing (PRC) is helpful for power reduction in machine learning technology, although the challenge is to improvecomputational performance. In this study, we developed a PRC device utilizing ion-electron coupled dynamics in an electric double layer transistor(EDLT) consisting of monolayer graphene channels and a Li+ conducting inorganic oxide thin film. The ambipolar transfer characteristics ofgraphene channels in the EDLT obtained complex and diverse drain current responses, providing high information processing capacity and highPRC performance in the nonlinear autoregressive moving average (NARMA) task. © 2025 The Author(s). Published on behalf of The JapanSociety of Applied Physics by IOP Publishing LtdSupplementary material for this article is available onlineRecently, the research and development of brain-inspired computing, or neuromorphic computing,has been progressing in order to reduce the powerconsumption of machine learning, which has been increasingexponentially with the advent of deep learning and generativeAI in the past decade.1) In particular, physical reservoircomputing (PRC), which uses the nonlinear phenomenaexhibited by physical devices as dynamical systems toperform information processing, has been attractingattention,2) and material-based PRC or in-materio reservoircomputing, which uses the nonlinear phenomena that occurinside materials, is particularly promising due to its excellentversatility.3–17) For example, Usami et al. showed that it ispossible to solve short-term memory tasks and speechrecognition tasks with high accuracy using the electricalresponse of the organic electrochemical network formed bysulfonated polyaniline, strongly suggesting that the intrinsicproperties of materials can be used as computationalresources.4) Many researchers have been working on ex-ploring various material systems for application to PRC, suchas soft bodies, atomic switches, nanowire networks, ferro-electrics, and spintronics materials, and the movement isshowing remarkable development.3–17) The present authorsreported that the interaction between ion and electrontransport in electric double layer transistors (EDLTs) fabri-cated using ion-conducting inorganic oxide thin films andhydrogen-terminated diamond single crystals produced com-plex electrical responses and that it was possible to performvarious time series data processing.18–21) However, unlikesimulation-based machine learning, which can freely sethyperparameters and optimize performance, the correlationbetween the properties of the EDLTs and the computationperformance, and the degree of this correlation were unclear,making it challenging to obtain design guidelines forachieving higher performance.In this study, we developed an EDLT consisting ofgraphene and a lithium ion-conducting inorganic solidelectrolyte thin film and evaluated its physical reservoircomputing performance. Graphene has a Dirac cone-typeelectronic structure, and is a semi-metal that exhibits both n-type and p-type ambipolar transport by controlling the Fermilevel.22) Its I-V characteristics differ significantly from thoseof the hydrogen-terminated diamond, which was used in theprevious reports and is a wide-gap semiconductor,18–21) so itis possible to investigate how the I-V characteristics of thechannel material affect the computation performance. Inaddition to the nonlinear autoregressive moving-average(NARMA) task, which is a typical benchmark task forPRC,17,18,21,23–26) we analyzed the information processingcapacity (IPC), which is an index of computation perfor-mance that is independent of the type of task, for theevaluation of PRC performance.27–29) By controlling thevoltage width and pulse period of the gate voltage pulsestreams used for information input as hyperparameters andevaluating them, we investigated how the I-V characteristicsof the EDLT correlate with computation performance toobtain guidelines for improving the performance of the PRCdevice.Figure 1(a) shows the schematic of the fabricated EDLTconsisting of a Li+ conducting amorphous oxide thin filmand monolayer graphene. A chemical vapor deposition(CVD) grown monolayer graphene on SiO2/Si substratewas used as the channel. Au/Cr thin films were depositedas source and drain electrodes using photolithography andelectron-beam evaporation. Li+ conducting amorphous Li-Nb-O (a-LN) and Li+-hole mixed conducting LiCoO2 thinfilms were then deposited by pulsed laser deposition. Pt wasalso deposited on top of the LiCoO2 layer as a currentcollector [Fig. 1(b)]. The number of graphene layers wasconfirmed to be one from the Raman spectrum of thechannel, consisting of G band (1582 cm−1) and D band(2685 cm−1) [Fig. 1(b) inset].30) Six channels with differentchannel lengths (channel length: 5∼ 100 μm) were fabricatedto obtain diverse output from the EDLT, as shown in anoptical microscopy image of the actual graphene channels[Fig. 1(c)]. Please refer to the supplementary information forContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of thiswork must maintain attribution to the author(s) and the title of the work, journal citation and DOI.024501-1© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 18, 024501 (2025) LETTERhttps://doi.org/10.35848/1882-0786/adb19bhttps://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/adb19b&domain=pdf&date_stamp=2025-02-13https://orcid.org/0009-0008-9132-0275https://orcid.org/0009-0008-9132-0275https://orcid.org/0000-0002-3369-7700https://orcid.org/0000-0002-3369-7700https://orcid.org/0000-0003-3988-3456https://orcid.org/0000-0003-3988-3456https://orcid.org/0000-0002-6950-6160https://orcid.org/0000-0002-6950-6160mailto:TSUCHIYA.Takashi@nims.go.jphttps://doi.org/10.35848/1882-0786/adb19bhttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/adb19bdetails on device fabrication. Figure 1(d) shows the transfercurve of the EDLT for a channel length of 100 mm, measuredat a drain voltage (VD) of −0.1 V. As positive gate voltage(VG) is applied to the EDLT, Li+ ions move towards thechannel side and electrons accumulate in the graphenechannel (an EDL charging), reducing the channel resistanceand increasing drain current (ID), and vice versa. Theambipolar (V-shaped) transfer characteristic observed inFig. 1(d) is a typical behavior of the graphene-based fieldeffect transistors.22,31–34) It corresponds to the Dirac-cone-like band structure of the monolayer graphene. The hysteresisobserved in the transfer curve is due to the relatively slowrelaxation of Li+ near the a-LN/graphene interface, which isbeneficial for enhancing short-term memory. Figure 1(e)shows a typical ID response of the EDLT against a singleVG pulse. From the ID response, the time constant (τ) of theEDL charging/discharging is derived to be approximately1.10 ms by assuming the condition, where, at t = τ, IDreduces to 1/e of the initial value A [i.e., 37% of A(decrement is 63% of A)].19)Such ID responses of the EDLT were utilized as computa-tion resources in the PRC scheme, as shown in Fig. 1(f). Itsperformance was evaluated based on a second-order non-linear autoregressive moving-average (NARMA2) task, atypical benchmark task for PRCs (details of the task arediscussed later). Time-series data u(k) is inputted in the inputlayer, where k is the time step. In the present case, u(k) isinput as VG pulse streams. Subsequently, u(k) is mapped into(a)(b)(c)(d)(e) (f)Fig. 1. (a) Schematic illustration of the EDL-based IGR consisting of graphene and a-LN. (b) Schematic of the EDL mechanism in the IGR. The inset showsthe Raman spectrum of the graphene channel. (c) Optical microscope image of graphene channels. (d) The ID -VG characteristic of the EDLT. (e) A typical IDresponse of the EDLT against VG pulse. (f) Schematic of the NARMA2 task in the study.024501-2© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 18, 024501 (2025) H. Kitano et al.a nonlinear high-dimensional space through the ion-electroncoupling dynamics within the EDLT serving as the reservoirlayer. These are represented as various ID responses (spatialstate evolution) and time-multiplexing (temporal state evolu-tion), yielding the reservoir state Xi(k) at each node i (i= 1, 2,…, N). The reservoir output y(k) is obtained as a linearcombination of Xi(k) and the readout weights wi, as follows,( ) ( ) ( )y k w X k b 1iNi i1å= +=where N and b are the numbers of the reservoir state and bias,respectively. The readout weights were trained using ridgeregression. The primary role of the EDLT as a physicalreservoir, as mentioned above, is to serve as a mappingfunction into a high-dimensional space for the input.Therefore, the nonlinearity of the device’s transfer curvesignificantly affects this mapping, while the ID relaxationbehavior strongly influences the effectiveness of the time-multiplexing method, namely, the high-dimensionality of thereservoir.As mentioned above, we investigated the effect of thegraphene’s ID-VG characteristics on the information proces-sing performance using the NARMA2 task, that predicts theNARMA2 model shown in Eq. (2).35)( ) ( )( ) ( ) ( ) ( )y k y ky k y k u k1 0.40.4 1 0.6 0.1 2t tt t3+ =+ - + +Here, u(k) is a random sequence with a uniform distribu-tion taking values between 0 and 0.5. Equation (2) describesthe state evolution yt of the NARMA2 model, where themodel output consists of terms such as cross-products of itsown output with a two-step time lag and cubic terms of pastinputs. Therefore, to accurately reproduce the NARMA2model using the on-gating reservoir (IGR), the IGR mustpossess sufficient expressive power (i.e., nonlinearity andmemory capacity) to represent these elements. As shown inFig. 2(a), the input data was converted into a VG pulse streamin the VG range between the base VG (Vbase), which was fixedto −1.5 V, and the maximum VG (Vmax), which was variedfrom −1.2 to +2.0 V in each case. By varying Vmax, theimpact of the ID-VG characteristics of graphene on IDresponses and computational performance was investigated.For instance, when Vmax=−0.8 V (indicated by the bluearrow), it is below the Dirac point, resulting in a monotonicID-VG characteristic and a simple ID response. In contrast,when Vmax exceeds the Dirac point (indicated by the greenarrow), the ID-VG characteristic exhibits a V-shaped transfercurve, suggesting a more complex ID response. To explorethe relationship between ID relaxation properties and compu-tational performance, the pulse period T of the VG pulsestream was set between 0.5 and 300 ms. The VD were set to+0.1 V for all channels. To enhance the performance, weused the inverted input method.20) A VG pulse stream wasapplied to the common gate, and the output current wasmeasured from six drain terminals with different channellengths and one gate terminal. In overall, there were a total ofseven physical nodes: six ID and one IG. From each currentwaveform, 10 virtual nodes were extracted (time-multi-plexing). Thus, under N= 140, the reservoir output y wasobtained as described in Eq. (1). The computational(a)(d)(b) (c)(e) (f)(g)Fig. 2. (a) Relationship between VG parameters (Vmax, Vbase) and the corresponding ID response. (b) ID responses under the two Vmax conditions [(I) and (II)].(c) The fast Fourier transform (FFT) spectrum of (I) and (II). (d) The target and prediction waveforms under conditions (I) and (II). (e) The pulse period T andVmax dependence of NMSEs. The optimal condition is indicated by *. (f) NMSE dependence on Vmax (T = 160 ms). (g) NMSE dependence on T (Vmax= +1.2 V).024501-3© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 18, 024501 (2025) H. Kitano et al.performance was evaluated using the normalized meansquare error (NMSE) defined as follows:[ ( ) ( )][ ( )]( )My k y ky kNMSE13kMtt122ås=-=where M is the data length (M= 2000 for the training phaseand M=700 for the test phase); s2(·) is the variance.Figure 2(b) compares the ID responses of channel 3 (ch3)to VG pulse streams for representative Vmax values: (Ⅰ)Vmax=−0.8 V (T= 160 ms) and (Ⅱ) Vmax=+2.0 V(T= 160 ms). Please refer to Fig. S1 for the other represen-tative results. Under the condition (Ⅰ) with Vmax=−0.8 V, IDresponse to the VG variation from one to another appears tobe simple in which ID monotonously increases or decreasesduring VG is constant. However, under the condition (Ⅱ) withVmax=+2.0 V, ID shows a complex response in which thedirection of ID variation (increases or decreases) changeseven during VG is constant. This unique ID transient behaviororiginates from including the Dirac point in the measured VGrange and the resultant switching between n- and p-conduc-tion during the EDL charging. Such behavior generatesquasi-second harmonic waves, as shown in Fig. S2,demonstrating the excellent nonlinearity of the device.Power spectra derived by the Fourier transform help obtainan intuitive distribution of the higher-order terms ofnonlinearity.4) Figure 2(c) shows the fast Fourier transform(FFT) spectra of the VG input and the corresponding ID outputunder conditions (I) and (II). All three FFT spectra include astrong peak at 6.29 Hz and odd harmonics, which are causedby the VG input in the form of a square wave with a duty ratioof 50%. Whereas the spectrum for condition (I) is similar tothe one for the VG input, even harmonics (indicated by the redarrows) are prominent only in the spectrum for condition (II),which indicates that the inclusion of Dirac point in the VGrange enhances the higher-order terms of nonlinearity. Targetand predicted waveforms for the conditions (Ⅰ) and (Ⅱ) arecompared in Fig. 2(d). Under condition (I), the predictionerror is relatively large (NMSE= 0.14), whereas undercondition (II), the predicted waveform closely matches thetarget waveform, and the prediction error during the testingphase is nearly an order of magnitude lower compared to thatof condition (I) (NMSE= 0.019). This result indicates thatstrong nonlinearity in the device’s transport characteristicssignificantly enhances computational performance in PRC.Figure 2(e) illustrates the dependence of NMSE on Vmaxand T during the testing phase. As indicated by the asterisk inthe figure, the optimal condition was achieved atVmax=+1.2 V and T= 160 ms, with a general trend ofimproved performance as Vmax and T increased. Figure 2(f)shows the Vmax dependence of NMSE at T= 160 ms [high-lighted by the white square in Fig. 2(e)]. The NMSEdecreases with increasing Vmax up to +1.2 V and saturatesbeyond this value, reflecting performance improvement dueto enhanced nonlinearity. Figure 2(g) presents the T depen-dence of NMSE at Vmax=+1.2 V [highlighted by the greensquare in Fig. 2(e)]. NMSE decreases with increasingT, saturating around T= 100 ms. The broad operationalrange with high performance from T= 100 ms to 300 msis particularly advantageous for processing time-series dataacross various time scales. Moreover, as shown in Fig. 2(e),increasing Vmax to around 2 V achieves high performanceeven in a high-speed region with T= 2∼ 3 ms. This demon-strates the potential for optimizing operational speed bytuning Vmax. These results highlight the wide operationalrange and tunability of the device, underscoring its suitabilityas an integrated edge AI device for processing diverse time-series data.To elucidate the relationship between the device’s oper-ating conditions (Vmax) and the key RC characteristics(nonlinearity and memory capacity), the information proces-sing capacity (IPC) of the IGR was evaluated, linking thetunable nonlinearity under different operating conditions tothe device’s nonlinear mapping capability in informationprocessing. IPC is an index of the reservoir’s computationalpower independent of tasks, quantitatively characterizing thereservoir’s short-term memory and nonlinearity. The IPC iscalculated based on the accuracy of regression tasks, wherethe reservoir generates outputs for targets transformed by n-degree polynomials of the input (and its delays).27–29) Thetotal capacity Ctot is defined as the sum of the sub-capacitiesCn for each degree n.( )C C 4nntot å=Generally, a reservoir with a high Ctot can perform wellacross various tasks, exhibiting high computational perfor-mance. We performed the IPC analysis with n up to nine inthis study: C1 is the linear component corresponding to short-term memory, and C2∼C9 are the nonlinear components.Figure 3(a) shows the Vmax dependence of Ctot and NMSE.Whereas Ctot monotonically increases as Vmax rises in apositive direction, NMSE falls up to Vmax of +1.2 V and thensaturates. Related to the behavior, the Vmax dependence of the(a) (b) (c)Fig. 3. (a) Vmax dependence of Ctot and NMSE. (b) Vmax dependence of IPC. (c) The relationship between the linear component (C1) and the nonlinearcomponent (Ctotal-C1).024501-4© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 18, 024501 (2025) H. Kitano et al.sub-capacities C1 to C9 in Fig. 3(b) includes contrastingtendencies for C1 (linear component) and C2 to C9 (nonlinearcomponents). While C2 to C9 monotonically increases withreference to Vmax, C1 peaks at Vmax=+0.4 V, indicating atrade-off relationship between C1 and C2 to C9 in the highVmax region. Figure 3(c) shows the relationship between thelinear component (C1) and the nonlinear component(Ctotal-C1), which are obtained with a variety of Vmax. Asexpected from Fig. 3(b), the nonlinear component mono-tonically increases in the whole range, but the linearcomponent peaks at Vmax=+0.4 V. Therefore, it was con-cluded that the decrease in C1 (the short-term memory) aboveVmax=+0.4 V compensates for the benefit of the increase inthe nonlinear component (Ctotal-C1) and thus restricts thefurther improvement of computation performance. A similartrade-off relationship between linear and nonlinear compo-nents was observed in both theory and experiments.36) Theprecise control of the relationship is thus of great importancein achieving high-performance PRC.In this study, we developed PRC utilizing an EDLT-basedIGR consisting of graphene and a-LN thin film and evaluatedits PRC performance. Thanks to the ambipolar characteristicof graphene due to the Dirac cone-type electronic structure,which differs from previously reported diamond-basedEDLT, the ID-VG characteristic takes V-shaped transfercurve. This provides complex and diverse ID responses,which are under the strong influence of Vmax and T, leadingto the strong dependence of computation performance for theNARMA2 task on the parameters. By optimizing the opera-tion condition, the lowest NMSE in the study was 0.015,which is 25% lower than the diamond-based EDL-IGR(NMSE= 0.020) in the previous report.18) The computationperformance dependence on Vmax and T was further inves-tigated by IPC analysis. While the nonlinear components C2to C9 monotonically increase as the VG range expands in apositive direction, the linear component C1 peaks atVmax=+0.4 V. The decrease in C1 (i.e., the short-termmemory) above Vmax=+0.4 V compensates for the benefitof the increase in the nonlinear components (Ctotal-C1, or C2to C9), limiting the further improvement of computationperformance. The result indicates that obtaining a highcompatibility of linear and nonlinear IPC components inthe output dynamics is vital for PRC devices. The optimiza-tion of hyperparameters, not only by the tuning of operationconditions of PRC devices, but also by the tuning ofmaterials characteristics as dynamical systems based onmaterials science and technology can offer a reliable wayto achieve high-performance PRC.Acknowledgments This research was supported by the JFE 21st CenturyFoundation, JST PRESTO under Grant No. JPMJPR23H4, and JSPS KAKENHIunder Grant No. JP24KJ0229 (Grant-in-Aid for JSPS Fellows). A part of thiswork was supported by ‘Advanced Research Infrastructure for Materials andNanotechnology in Japan (ARIM)’ of the Ministry of Education, Culture, Sports,Science and Technology (MEXT) under Grant Nos. JPMXP1224NM5236 andJPMXP1224NM5357.ORCID iDs Hina Kitano https://orcid.org/0009-0008-9132-0275Daiki Nishioka https://orcid.org/0000-0002-3369-7700Kazuya Terabe https://orcid.org/0000-0003-3988-3456Takashi Tsuchiya https://orcid.org/0000-0002-6950-61601) D. Kramer, Phys. Today 77, 28 (2024).2) W. Maass, T. 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