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Intrinsically stretchable neuromorphic devices for on-body processing of health data with artificial intelligence

神经形态工程学 计算机科学 人工智能 人机交互 纳米技术 神经科学 人工神经网络 材料科学 心理学
作者
Shilei Dai,Yahao Dai,Zixuan Zhao,Fangfang Xia,Yang Li,Youdi Liu,Ping Cheng,Joseph Strzalka,Songsong Li,Nan Li,Qi Su,Shinya Wai,Wei Liu,Cheng Zhang,Ruoyu Zhao,Yunqiao Zhou,Rick Stevens,Jie Xu,Huang Jia,S. Wang
出处
期刊:Matter [Elsevier]
卷期号:5 (10): 3375-3390 被引量:12
标识
DOI:10.1016/j.matt.2022.07.016
摘要

•An intrinsically stretchable electrochemical neuromorphic transistor is developed•The neuromorphic device shows highly stable computing performance under stretching•Vector-matrix multiplication has been demonstrated on the prototype device array•Implementation of AI processing of health data shows stability against stretching The combination of wearable electronics and artificial intelligence (AI) technology can benefit many application domains, such as precision medicine. Despite the rapid development of wearable electronics with skin-like form factors and the paralleled progress of AI technology, AI computing has not been brought into such a futuristic type of wearable electronics for achieving the highly desired near-sensor data processing. The major gap is the lack of devices that can efficiently implement AI algorithms with skin-like stretchability. Here, we report an intrinsically stretchable neuromorphic device that provides all the desired computational and mechanical characteristics. Further integration into a prototype array successfully realized the implementation of vector-matrix multiplication even at 100% strain. The intrinsically stretchable neuromorphic device developed in this work opens up a new research direction for bridging wearable electronics and AI computing at the hardware level. For leveraging wearable technologies to advance precision medicine, personalized and learning-based analysis of continuously acquired health data is indispensable, for which neuromorphic computing provides the most efficient implementation of artificial intelligence (AI) data processing. For realizing on-body neuromorphic computing, skin-like stretchability is required but has yet to be combined with the desired neuromorphic metrics, including linear symmetric weight update and sufficient state retention, for achieving high computing efficiency. Here, we report an intrinsically stretchable electrochemical transistor-based neuromorphic device, which provides a large number (>800) of states, linear/symmetric weight update, excellent switching endurance (>100 million), and good state retention (>104 s) together with the high stretchability of 100% strain. We further demonstrate a prototype neuromorphic array that can perform vector-matrix multiplication even at 100% strain and also the feasibility of implementing AI-based classification of health signals with a high accuracy that is minimally influenced by the stretched state of the neuromorphic hardware. For leveraging wearable technologies to advance precision medicine, personalized and learning-based analysis of continuously acquired health data is indispensable, for which neuromorphic computing provides the most efficient implementation of artificial intelligence (AI) data processing. For realizing on-body neuromorphic computing, skin-like stretchability is required but has yet to be combined with the desired neuromorphic metrics, including linear symmetric weight update and sufficient state retention, for achieving high computing efficiency. Here, we report an intrinsically stretchable electrochemical transistor-based neuromorphic device, which provides a large number (>800) of states, linear/symmetric weight update, excellent switching endurance (>100 million), and good state retention (>104 s) together with the high stretchability of 100% strain. We further demonstrate a prototype neuromorphic array that can perform vector-matrix multiplication even at 100% strain and also the feasibility of implementing AI-based classification of health signals with a high accuracy that is minimally influenced by the stretched state of the neuromorphic hardware. Precision medicine, the future landscape of healthcare, can provide personalized diagnosis and treatments to each individual by taking into account the underlying differences in people’s genes, ages, health histories, and living environments.1Mesko B. The role of artificial intelligence in precision medicine.Expert Rev. Precis. Med. Drug Dev. 2017; 2: 239-241https://doi.org/10.1080/23808993.2017.1380516Crossref Scopus (99) Google Scholar On the technological level, this futuristic vision for healthcare requires the development of two major capabilities: (1) the effective and continuous acquisition of multi-modal health data during long-term daily activities outside of clinics, for which wearable electronics emerge as the ideal solution,2Gao W. Emaminejad S. Nyein H.Y.Y. Challa S. Chen K. Peck A. Fahad H.M. Ota H. Shiraki H. Kiriya D. et al.Fully integrated wearable sensor arrays for multiplexed in situ perspiration analysis.Nature. 2016; 529: 509-514https://doi.org/10.1038/nature16521Crossref PubMed Scopus (2935) Google Scholar and (2) the high-throughput and intelligent analysis of such complicated and large-quantity datasets for extracting the underlying personalized health patterns, which is becoming one of the main application directions of artificial intelligence (AI).3Yu K.-H. Beam A.L. Kohane I.S. 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Electron. 2021; 4: 143-150https://doi.org/10.1038/s41928-020-00525-1Crossref Scopus (107) Google Scholar that can adhere seamlessly to the human skin to provide on-body and high-fidelity measurements of various types of health data. However, to further incorporate AI data analysis, a major gap still exists on the hardware level. The efficient and secure processing of such continuously generated health data demands AI computation (Figure 1A ) to happen physically next to the data-acquisition sites (i.e., sensors) to minimize the need for wireless, long-distance data transfer that typically comes with the problems of latency, insecurity, and extra power consumption.10Zhou F. Chai Y. Near-sensor and in-sensor computing.Nat. Electron. 2020; 3: 664-671https://doi.org/10.1038/s41928-020-00501-9Crossref Scopus (202) Google Scholar,11Covi E. Donati E. Liang X. Kappel D. Heidari H. Payvand M. Wang W. Adaptive extreme edge computing for wearable devices.Front. Neurosci. 2021; 15: 611300https://doi.org/10.3389/fnins.2021.611300Crossref PubMed Scopus (39) Google Scholar For such close-proximity integrations with on-skin sensors, the computing units for implementing AI data processing also need to have soft and stretchable properties, without incorporating rigid circuits, so as to achieve good wearing comfort and avoid unreliable but potentially numerous interconnections between soft and rigid parts. In particular, intrinsically stretchable designs are the most ideal choice for achieving the highest possible skin conformability and high device integration density.8Wang S. Xu J. Wang W. Wang G.J.N. Rastak R. Molina-Lopez F. Chung J.W. Niu S. Feig V.R. Lopez J. et al.Skin electronics from scalable fabrication of an intrinsically stretchable transistor array.Nature. 2018; 555: 83-88https://doi.org/10.1038/nature25494Crossref PubMed Scopus (1322) Google Scholar,9Wang W. Wang S. Rastak R. Ochiai Y. Niu S. Jiang Y. Arunachala P.K. Zheng Y. Xu J. Matsuhisa N. et al.Strain-insensitive intrinsically stretchable transistors and circuits.Nat. Electron. 2021; 4: 143-150https://doi.org/10.1038/s41928-020-00525-1Crossref Scopus (107) Google Scholar,12Zheng Y.Q. Liu Y. Zhong D. Nikzad S. Liu S. Yu Z. Liu D. Wu H.-C. Zhu C. Li J. et al.Monolithic optical microlithography of high-density elastic circuits.Science. 2021; 373: 88-94https://doi.org/10.1126/science.abh3551Crossref PubMed Scopus (86) Google Scholar Recently, a new computing paradigm—neuromorphic computing—that mimics brain operation has been created and developed as a more suitable platform for AI, offering much lower system complexity, lower energy consumption, and faster speed. Remarkable progress has been made in neuromorphic computing based on a variety of device types, such as phase-change memory,13Tuma T. Pantazi A. Le Gallo M. Sebastian A. Eleftheriou E. Stochastic phase-change neurons.Nat. 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Training and operation of an integrated neuromorphic network based on metal-oxide memristors.Nature. 2015; 521: 61-64https://doi.org/10.1038/nature14441Crossref PubMed Scopus (1845) Google Scholar,17Zidan M.A. Strachan J.P. Lu W.D. The future of electronics based on memristive systems.Nat. Electron. 2018; 1: 22-29https://doi.org/10.1038/s41928-017-0006-8Crossref Scopus (1025) Google Scholar and electrolyte-gated transistors.18Gkoupidenis P. Koutsouras D.A. Malliaras G.G. Neuromorphic device architectures with global connectivity through electrolyte gating.Nat. Commun. 2017; 8: 15448https://doi.org/10.1038/ncomms15448Crossref PubMed Scopus (210) Google Scholar,19Kim Y. Chortos A. Xu W. Liu Y. Oh J.Y. Son D. Kang J. Foudeh A.M. Zhu C. Lee Y. et al.A bioinspired flexible organic artificial afferent nerve.Science. 2018; 360: 998-1003https://doi.org/10.1126/science.aao0098Crossref PubMed Scopus (767) Google Scholar However, there has not been any report of intrinsically stretchable neuromorphic devices that possess the set of neuromorphic performance metrics needed for the on-body processing of health data,20van de Burgt Y. Melianas A. Keene S.T. Malliaras G. Salleo A. Organic electronics for neuromorphic computing.Nat. Electron. 2018; 1: 386-397https://doi.org/10.1038/s41928-018-0103-3Crossref Scopus (476) Google Scholar, 21Lee Y. Oh J.Y. Xu W. Kim O. Kim T.R. Kang J. Kim Y. Son D. Tok J.B.-H. Park M.J. et al.Stretchable organic optoelectronic sensorimotor synapse.Sci. Adv. 2018; 4: eaat7387https://doi.org/10.1126/sciadv.aat7387Crossref PubMed Scopus (269) Google Scholar, 22Shim H. Sim K. Ershad F. Yang P. Thukral A. Rao Z. Kim H.-J. Liu Y. Wang X. Gu G. et al.Stretchable elastic synaptic transistors for neurologically integrated soft engineering systems.Sci. Adv. 2019; 5: eaax4961https://doi.org/10.1126/sciadv.aax4961Crossref PubMed Scopus (142) Google Scholar, 23Kim S.H. Baek G.W. Yoon J. Seo S. Park J. Hahm D. Chang J.H. Seong D. Seo H. Oh S. et al.A bioinspired stretchable sensory-neuromorphic system.Adv. Mater. 2021; 33: 2104690https://doi.org/10.1002/adma.202104690Crossref Scopus (32) Google Scholar which include (1) a wide range of linear and symmetric weight updates, (2) sufficient state-retention time (>1,000 s) for learning and inference, (3) excellent write endurance, (4) low variation in weight update, and (5) over 100 separable memory states. For providing all these performance characteristics, organic electrochemical transistors (OECTs) have been recently demonstrated as the most promising device platform.24van de Burgt Y. Lubberman E. Fuller E.J. Keene S.T. Faria G.C. Agarwal S. Marinella M.J. Alec Talin A. Salleo A. A non-volatile organic electrochemical device as a low-voltage artificial synapse for neuromorphic computing.Nat. Mater. 2017; 16: 414-418https://doi.org/10.1038/nmat4856Crossref PubMed Google Scholar, 25Fuller E.J. Keene S.T. Melianas A. Wang Z. Agarwal S. Li Y. Tuchman Y. James C.D. Marinella M.J. Yang J.J. et al.Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing.Science. 2019; 364: 570-574https://doi.org/10.1126/science.aaw5581Crossref PubMed Scopus (357) Google Scholar, 26Fuller E.J. Li Y. Bennet C. Keene S.T. Melianas A. Agarwal S. Marinella M.J. Salleo A. Talin A.A. Redox transistors for neuromorphic computing.IBM J. Res. Dev. 2019; 63: 1-9https://doi.org/10.1147/JRD.2019.2942285Crossref Scopus (15) Google Scholar Toward the incorporation of stretchability onto OECTs, despite some demonstrations based on strain-engineering (i.e., rigid-island or buckling) designs,27Lee W. Kobayashi S. Nagase M. Jimbo Y. Saito I. Inoue Y. Yambe T. Sekino M. Malliaras G.G. Yokota T. et al.Nonthrombogenic, stretchable, active multielectrode array for electroanatomical mapping.Sci. Adv. 2018; 4: eaau2426https://doi.org/10.1126/sciadv.aau2426Crossref PubMed Scopus (113) Google Scholar,28Matsuhisa N. Jiang Y. Liu Z. Chen G. Wan C. Kim Y. Kang J. Tran H. Wu H. You I. et al.High-transconductance stretchable transistors achieved by controlled gold microcrack morphology.Adv. Electron. Mater. 2019; 5: 1900347https://doi.org/10.1002/aelm.201900347Crossref Scopus (50) Google Scholar intrinsic stretchability has been rarely achieved.29Zhang S. Li Y. Tomasello G. Anthonisen M. Li X. Mazzeo M. Genco A. Grutter P. Cicoira F. Tuning the electromechanical properties of PEDOT:PSS films for stretchable transistors and pressure sensors.Adv. Electron. Mater. 2019; 5: 1900191https://doi.org/10.1002/aelm.201900191Crossref Scopus (45) Google Scholar,30Li Y. Zhang S. Li X. Unnava V.R.N. Cicoira F. Highly stretchable polystyrene sulfonate organic electrochemical transistors achieved via polyethylene glycol addition.Flex. Print. Electron. 2019; 4: 044004https://doi.org/10.1088/2058-8585/ab5202Crossref Scopus (30) Google Scholar The very few reports up to date share two major limitations (Table S1): incomplete OECT device structures (i.e., without incorporating stretchable solid/gel-state electrolyte and stretchable gate electrode), which is not compatible for circuit-level integration, and inferior stretchable OECT performance from the use of engineered poly(3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS). The combination of full-device stretchability and desirable neuromorphic performance for on-body AI computation has been hindered by the lack of stretchable materials across the board (including semiconductors, conductors, and dielectrics) with suitable properties for high-performance OECTs. Moreover, toward coupling mechanical stretching onto this new paradigm of analog computing and on-body AI analysis, a major challenge also lies in the lack of knowledge on the mechanical strain’s influence on the implementation of artificial neural network (ANN) algorithms, which is pivotal for the further co-design of suitable AI algorithms for stretchable neuromorphic chips. Here, through a holistic innovation in material and device designs, we report the first intrinsically stretchable neuromorphic device (Figures 1B–1F) that provides all the desired computational and mechanical characteristics, including a large number (>800) of memory states, quasi-linear/symmetric weight update, excellent switching endurance (>108), low variation in weight update, good state retention (>104 s), and high stretchability (100% strain). These computational properties are either comparable to or even better than those of the state-of-the-art non-stretchable neuromorphic transistors (Table S2). The further integration of this device into a neuromorphic array has demonstrated the ideal implementation of the basic computation in ANN algorithms—vector-matrix multiplication (VMM)—under stretching to 100% strain. We also implemented different types of neural-network simulations on a large-scale array built from our stretchable neuromorphic devices, from which the training-based classifications of a representative type of health data—electrocardiogram (ECG)—were realized. With the training and inference processes carried out on the neuromorphic device operating under different strain levels from 0% to 100%, we show that the computation outcome based on 1-layer convolutional neural network (CNN) is not influenced by stretching. As a whole, these results from the device level to the algorithm-implementation level demonstrate the promise and the possible pathway for realizing skin-like, on-body AI computation. Our stretchable neuromorphic device is designed with an extended-gate structure (Figure 1B) that consists of four components: a redox-active semiconducting layer, an electrolyte-type dielectric, source/drain (S/D) electrodes, and a redox-active gate electrode. We successfully incorporated the stretchability of 100% strain to each of the component materials that provide desired properties for OECT operations. For the semiconductor layer, stretchability is achieved on redox-active semiconducting polymers based on the polythiophene backbone and tri-ethylene-glycol (TEG) side chain, namely poly-[3,3′-bis(2-(2-(2-methoxyethoxy)ethoxy)ethoxy)-2,2′-bithiophene] (p(gT2)) (Figures 1C, S1, and S2). It provides an OECT performance close to the state of the art.31Tan S.T.M. Giovannitti A. Melianas A. Moser M. Cotts B.L. Singh D. McCulloch I. Salleo A. High-gain chemically gated organic electrochemical transistor.Adv. Funct. Mater. 2021; 31: 2010868https://doi.org/10.1002/adfm.202010868Crossref Scopus (26) Google Scholar, 32Dai Y. Dai S. Li N. Li Y. Moser M. Strzalka J. Prominski A. Liu Y. Zhang Q. Li S. et al.Stretchable redox-active semiconducting polymers for high-performance organic electrochemical transistors.Adv. Mater. 2022; 34: 2201178https://doi.org/10.1002/adma.202201178Crossref Scopus (18) Google Scholar, 33Paulsen B.D. Tybrandt K. Stavrinidou E. Rivnay J. Organic mixed ionic–electronic conductors.Nat. Mater. 2020; 19: 13-26https://doi.org/10.1038/s41563-019-0435-zCrossref PubMed Scopus (312) Google Scholar For the electrolyte-type dielectric layer that can form a continuous ion-transport pathway between the semiconductor layer and gate electrode, we realized the stretchability by creating a hybrid organo-hydrogel, based on a polyacrylamide network swelled by a water-glycerol binary solvent (Figures 1D and S3). The added NaCl inside the gel can be solvated by water and can penetrate the semiconductor layer to dope the polymer semiconductor. Glycerol, which can form strong hydrogen bonding with water, is added to achieve the long-term stability of the gel dielectric by preventing dehydration and lowering the freezing point.34Han L. Liu K. Wang M. Wang K. Fang L. Chen H. Zhou J. Lu X. Mussel-inspired adhesive and conductive hydrogel with long-lasting moisture and extreme temperature tolerance.Adv. Funct. Mater. 2018; 28: 1704195https://doi.org/10.1002/adfm.201704195Crossref Scopus (651) Google Scholar,35Lane L.B. Freezing points of glycerol and its aqueous solutions.Ind. Eng. Chem. 1925; 17: 924https://doi.org/10.1021/ie50189a017Crossref Scopus (131) Google Scholar The stretchable S/D electrodes in such OECT devices need to have electrochemical stability under the doping condition of p(gT2) and high conductivity, which precludes the commonly used options of stretchable conductors made from carbon-nanotube assemblies, Ag nanowire assemblies, liquid metal, and stretchable PEDOT:PSS. We fulfilled such stability and conductivity requirements through a unique stretchable design for Au, which is a vertically grown nanowire array36Zhu B. Gong S. Lin F. Wang Y. Ling Y. An T. Cheng W. Patterning Vertically grown gold nanowire electrodes for intrinsically stretchable organic transistors.Adv. Electron. Mater. 2019; 5: 1800509https://doi.org/10.1002/aelm.201800509Crossref Scopus (48) Google Scholar embedded in a poly(dimethylsiloxane) (PDMS) substrate (Figures S4–S9) that can be stretched to 100% strain while maintaining a low sheet resistance of ∼30 Ω/sq (Figure S9). A commercially available Ag/AgCl paste was used as the stretchable redox-active gate electrode (Figure S10), which functions as a reference electrode for providing a stable electrode potential. This paste is formulated to be screen printed but can also be syringe dispensed, dipped, and sprayed. Also, this paste is very resistant to flexing, creasing, and stretching. The device built by the above set of materials enables voltage-driving redox reactions between the p(gT2) layer and the Ag/AgCl gate (AgCl + [p(gT2)] ⇌ Ag + [p(gT2)]+Cl−), which provides analog and non-volatile modulation of the channel’s conductivity (Figure 1E). This stretchable device enabled the first realization of a skin-like neuromorphic “chip” with multiple devices (Figure 1F) that can function on the body with deformable and conformable properties. Among all the materials, p(gT2) is the key enabler for both the high stretchability and high computing performance of the neuromorphic device. As shown in Figures 2A , S11, and S12, a p(gT2) film can be stretched to 100% strain without any cracks, which should be mainly rendered by the relatively flexible polythiophene backbone. We used the transfer-lamination method to measure the OECT performance of p(gT2) under different strains (Figure S13). Starting from an ideal OECT performance (Figure 2B) with an on/off ratio over 103 and a normalized transconductance (Gm) of (81 ± 14) S/cm, the stretching processes in parallel, and perpendicular, to the channel-length direction, respectively, lead to a slight increase and a slight decrease in Gm (Figure 2C). Upon releasing to 0% strain, Gm mostly reverts to the original value. These trends agree very well with the changes of the mobility under these stretching processes (Figures 2C, S14, and S15), with the onset voltage of oxidation (Vox, onset), volumetric capacitance (C∗), and the threshold voltage (VTh) remaining stable (Figures S16 and S17). Such anisotropic response to stretching mainly comes from the strain-induced chain alignment on this highly stretchable polymer, as confirmed by the cross-polarized optical microscopy images (Figure S18), the increase of the dichroic ratio from the polarized UV-visible (vis) spectroscopy (Figure S19), and the change in the grazing-incidence X-ray diffraction (GIXD) with incident beams in parallel and perpendicular to the strain (Figures 2D and S20).The GIXD results also show moderate crystallinity of the p(gT2) polymer, which should serve as a morphological basis for the high stretchability. We can also observe the strain-induced change of mixed face-on and edge-on packing to edge-on-dominated packing. With an ideal transistor-type transfer behavior (Figure S21) obtained from the fabricated fully stretchable neuromorphic device, we tested its neuromorphic computing performance through the two core neuromorphic properties—analog weight update and state retention. Under an optimized pulsing condition, as many as 800 distinct conductance states can be obtained (Figure 2E), which is the highest number of states reported so far for neuromorphic devices (Table S2). This is enabled by the high C∗ of the p(gT2) semiconductor (227 ± 26 F/cm3). Following the weight update (i.e., the “writing” process), the retention for both the fully potentiated and fully depressed states in the “reading” condition (i.e., with disconnected source and gate electrodes) can last for over 10,000 s (Figure 2F), which is sufficient for on-device training applications.20van de Burgt Y. Melianas A. Keene S.T. Malliaras G. Salleo A. Organic electronics for neuromorphic computing.Nat. Electron. 2018; 1: 386-397https://doi.org/10.1038/s41928-018-0103-3Crossref Scopus (476) Google Scholar When the “reading” period is further increased to 105 s, the accumulated decay of the states should just come from the unavoidable self-discharging behaviors of any electrochemical cells. In long-term potentiation-depression (LTP-LTD) cycles, a dynamic range (Gmax/Gmin) value greater than 100 was achieved under the optimized pulse conditions (i.e., VLTP and VLTD) (Figures 2G and S22). Very high linearity and symmetricity are also obtained at the same time, which, for accurate and efficient online training of ANN algorithms, could be even more important performance characteristics than the dynamic range. To examine the switching endurance of our device, we applied more than 108 pulses during repeated LTP-LTD cycles, and no significant degradation of the device performance can be observed (Figure 2H). We also investigated the switching speed of our device, and a decent response under the pulse with a width of 500 μs was observed (Figure S23). The switching speed can be future improved by optimizing device geometry, reducing the ionic resistance of the electrolyte, etc.25Fuller E.J. Keene S.T. Melianas A. Wang Z. Agarwal S. Li Y. Tuchman Y. James C.D. Marinella M.J. Yang J.J. et al.Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing.Science. 2019; 364: 570-574https://doi.org/10.1126/science.aaw5581Crossref PubMed Scopus (357) Google Scholar Moreover, with PDMS packaging, the on-shelf stability of our device is demonstrated for more than 4 months (Figure S24). We then proceeded to characterize the stretchability of the device by measuring the LTP-LTD cycles when the device is stretched stepwise from 0% to 100% strain and then released, in both parallel and perpendicular directions to the channels. As shown in Figures 3A, 3B , and S25, the most obvious influence of the strain is the moderate decreases of the conductance level of each updated weight, which should come from the combined effects of the device’s geometry change and the strain-induced chain alignment in the semiconducting layer, as described above. Upon releasing to 0% strain, these changes are mostly reversible. The further 100 cycles of stretching to 100% strain caused negligible changes to the LTP-LTD performance. On the other hand, the high degrees of linearity and symmetricity are well maintained during these stretching processes. This is quantitatively analyzed using two extracted parameters: the non-linearity index (β) and the symmetricity index (Figures S26 and S27). As shown in Figures 3C, 3D, and S28, the stretching leads to minimal changes to the initial β around 0.2 and 1.2 (indicating high linearity) for LTP and LTD and to the initial symmetricity index around 70 (indicating high symmetricity). In addition, the state retention of the device at 100% strain is largely unaltered (Figure S29). These behaviors indicate the device’s well-maintained capability for implementing ANN computation under large strains. We further analyze the linearity in detail from 50 repeated LTP-LTD cycles (Figures 3E and 3F) under both 0% and 100% strain. At each conductance state (G) during repeated LTP-LTD cycles (Figure S30), the weight updates (ΔG) from a single write pulse are extracted and analyzed using the cumulative distribution function (CDF), asCDFG(ΔGx)=∫−15ΔGxpG(ΔG)dΔGx,in which pG (ΔG) is the probability distribution for ΔG under a certain conductance state G. As shown by the heat plots of CDF for the ΔG distribution (Figures 3G–3J), our device maintains high linearity and repeatability (i.e., low weight-update distribution) under both pristine and stretched conditions. Next, toward using our stretchable neuromorphic device to achieve integrated neuromorphic chips capable of implementing ANN algorithms, an important step is to integrate the single device into an array (Figure 4A ) that can carry out the VMM operation (Figure 4B), which is the basic computational step in most ANN algorithms. To demonstrate this capability of our device, we fabricated a 3-by-3 prototype array (Figures 4C and 1F) by patterning all the components: the p(gT2) semiconductor, the organo-hydrogel, the stretchable Au nanowire electrodes, and the stretchable Ag/AgCl reference gate (see experimental procedures and Figure S31). In our design, the source electrodes from the three neuromorphic devices in each row are connected as three output lines. The measured LTP-LTD cycles from each of the 9 devices in the array all show similar performances (Figure S32) to the single device reported above. To demonstrate VMM operations, we first mapped a random set of conductance states {Gij} (Figures 4
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