electronics Article VO2 Carbon Nanotube Composite Memristor-Based Cellular Neural Network Pattern Formation Yiran Shen and Guangyi Wang * Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China; [email protected] * Correspondence: [email protected] Abstract: A cellular neural network (CNN) based on a VO2 carbon nanotube memristor is proposed in this paper. The device is modeled by SPICE at first, and then the cell dynamic characteristics based on the device are analyzed. It is pointed out that only when the cell is at the sharp edge of chaos can the cell be successfully awakened after the CNN is formed. In this paper, we give the example of a 5 × 5 CNN, set specific initial conditions and observe the formed pattern. Because the generated patterns are affected by the initial conditions, the cell power supply can be pre-programmed to obtain specific patterns, which can be applied to the future information processing system based on complex space–time patterns, especially in the field of computer vision. Keywords: VO2 carbon nanotube composite memristor; cellular neural network (CNN); von Neu- mann structure; local activity; edge of chaos 1. Introduction Citation: Shen, Y.; Wang, G. VO2 The traditional processor uses the von Neumann structure, in which the storage unit Carbon Nanotube Composite and the processing unit are separated and connected by bus. In recent years, with the Memristor-Based Cellular Neural development of semiconductor technology, the speed of processing units has been greatly Network Pattern Formation. improved. However, due to the limitation of bus bandwidth, the operation speed of the Electronics 2021, 10, 1198. https:// whole processor is limited, which is called the “von Neumann bottleneck problem” [1,2]. In doi.org/10.3390/electronics10101198 order to solve this problem, inspired by the biological way of processing information, many pieces of literature have proposed various non-von Neumann processor solutions [3–5]. Academic Editor: Kris Campbell Typical bio-inspired computing relies on nonlinear networks that contain the same cells; each cell has a relatively simple structure and interacts with the surrounding cells. This Received: 10 April 2021 structure, called a CNN, a cellular neural network, has been applied in fields such as Accepted: 11 May 2021 Published: 18 May 2021 computer vision [6–8]. The concept of a CNN can be traced back to two articles by Chua in 1988 [9,10], which Publisher’s Note: MDPI stays neutral respectively give the theory and application of CNNs. Recently, Itoh [11] summarized with regard to jurisdictional claims in some characteristics of CNNs in a long paper. Weiher et al. [12] discussed the pattern published maps and institutional affil- formation of CNNs based on the NbO2 memristor. iations. Recently, brain-like computing has become a hot topic in research [13–15], and the key is to find devices that can produce spike signals like neurons and that have very low power consumption. The VO2 carbon nanotube (CNT) composite device is a Mott memristor recently proposed [16]. It can generate periodic peak pulses with a pulse width of less than 20 ns, it is driven by a DC current or voltage, and it does not need additional Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. capacitance. It uses metal–carbon nanotubes as heaters, and, compared with the pure Mott This article is an open access article VO2 proposed earlier, adding CNTs can greatly reduce the transient duration and pulse distributed under the terms and energy and increase the frequency of a peak pulse by three orders of magnitude. conditions of the Creative Commons The VO2 nano crossbar device does not need the process of electric forming and has Attribution (CC BY) license (https:// low device size dispersion. For devices with a critical size between 50 and 600 nm, the creativecommons.org/licenses/by/ change coefficient of the switch threshold voltage is less than 13%, the switch durability 4.0/). is more than 26.6 million cycles, and the IV characteristics of the device are not changed Electronics 2021, 10, 1198. https://doi.org/10.3390/electronics10101198 https://www.mdpi.com/journal/electronics Electronics 2021, 10, x FOR PEER REVIEW 2 of 14 Electronics 2021, 10, 1198 2 of 13 change coefficient of the switch threshold voltage is less than 13%, the switch durability is more than 26.6 million cycles, and the IV characteristics of the device are not changed significantly. The VO2 device technology in the process of non-electric formation acceler- significantly.ates the development The VO2 device of an technologyactive memristor in the process neuron of circuit. non-electric It ca formationn simulate accelerates the most theknown development neuron dynamics of an active and memristorclear the way neuron for the circuit. realization It can simulateof a large-scale the most integrated known neuron dynamics and clear the way for the realization of a large-scale integrated circuit circuit (IC). In addition, the VO2 memristor is superior to its NbO2 counterpart in both (IC). In addition, the VO2 memristor is superior to its NbO2 counterpart in both switch switch speed and switching energy. The simulated Mott transition in the VO2 is 100 times speed and switching energy. The simulated Mott transition in the VO2 is 100 times faster faster than in the NbO2 and consumes only about one-sixth (16%) of the energy [17]. than in the NbO2 and consumes only about one-sixth (16%) of the energy [17]. In this paper, a cellular neural network based on a VO2 CNT is proposed. As a cell In this paper, a cellular neural network based on a VO2 CNT is proposed. As a cell itself, a VO2 CNT is set to be stable and static, that is, in “sleep”. If the memristor is on the itself, a VO CNT is set to be stable and static, that is, in “sleep”. If the memristor is “edge of chaos”,2 two or more cells are connected by the RC coupling, which will make it on the “edge of chaos”, two or more cells are connected by the RC coupling, which will in the state of “wake-up”, namely, in the dynamic oscillation mode. The second part of make it in the state of “wake-up”, namely, in the dynamic oscillation mode. The second this paper is the modeling of VO2 CNT composite devices, providing the SPICE model. part of this paper is the modeling of VO CNT composite devices, providing the SPICE The third part is the cell circuit, which gives2 the analysis process of the decoupled circuit. model. The third part is the cell circuit, which gives the analysis process of the decoupled circuit.The response The response of the memristor of the memristor is expanded is expanded near the near operating the operating point and point the and small-signal the small- signalequivalent equivalent circuit circuitis given. is Based given. on Based this, on the this, influence the influence of coupling of coupling R and CR deviceand C param-device parameterseters on the oninput the impedance input impedance of one port of one is analyzed. port is analyzed. The fourth The part fourth is the part CNN is the simula- CNN simulation,tion, which describes which describes the pattern the patternformation formation characteristics characteristics of a CNN of composed a CNN composed of memris- of memristor-basedtor-based cells. cells. Compared with the traditional CMOS realization of CNN, the memristor counterpart can largely save power and chipchip area,area, andand provideprovide ultra-highultra-high processingprocessing speeds.speeds. 2. VO 2 CarbonCarbon Nanotube Nanotube Compos Compositeite Device Device Modeling The structure of of the the VO VO22 carboncarbon nanotube nanotube composite composite device device is isshown shown in inFigure Figure 1.1 It. Itcontains contains a transverse a transverse active active region, region, which which is defined is defined by a byVO a2 VOthin2 metalthin metal strip with strip a with thick- a thicknessness of about of about 5 nm 5(as nm shown (as shown in the in red the region red region of the of figure), the figure), and its and two its ends two endsare con- are connectednected with with Pd electrodes Pd electrodes (as shown (as shown in the in blue the blueregion region of the of figure). the figure). This is This a planar is a planar Mott Mottmetal-insulator metal-insulator transition transition device. device. The aligned The aligned carbon carbon nanotubes nanotubes (as shown (as shown in the inblack the blackline) were line) first were grown first grown on quartz on quartz substrate, substrate, and then and thentransferred transferred to the to surface the surface of a VO of a2 VOthin2 metalthin metal strip stripbefore before the whole the whole device device was formed. was formed. Figure 1. A VO 2 carboncarbon nanotube composite device structure. The redred partpart isis thethe VOVO22 and the black lineblack over line it over represents it represents the carbon the carbon nanotube. nanotube. As a Mott metal-insulator transition device, it satisfiessatisfies thethe followingfollowing equationequation [[16]:16]: p βφvdb− vm/d−f 2 m( ) i = ATekT kT iATe=m 2 m i v +v2 /R T−T (1) dT = m m m CNT − amb (1) dt ivC+−th v2 RC Tth R Tth dT =−mm m CNT amb dtC CR The first formula of Equation (1) is the currentth emission th th equation of the Schottky diode, and the second formula is Newton’s cooling law, where, im and νm are the current and voltageThe through first formula the memristor of Equation NDR (1) device, is the cu respectively;rrent emissionT is equation the absolute of the temperature Schottky di- of theode, device; and theT ambsecondis the formula ambient is temperature;Newton's coolingA and law,b are where, scaling ݅m constants;and ݒm ared theis thecurrent effective and devicevoltage length;throughk theis Boltzmann memristor constant;NDR device,f is respectively; the energy barrier;T is the absoluteCth is the temperature heat capacity of (effectivethe device; thermal Tamb is the mass); ambientRth is temperature; the thermal A resistance; and ߚ areR scalingCNT is theconstants; resistance d is valuethe effective of the CNT (carbon nanotube), taking 600 kW.