Modelling Resistive and Phase Change Memory with Passive Selector Arrays -- A Matlab Tool

Abstract—Memristor devices are crucial for developing neuromorphic computers and next-generation memory technologies. In this work, we provide a comprehensive modelling tool for simulating static DC reading operations of memristor crossbar arrays that use passive selectors with matrix algebra in MATLAB. The software tool was parallel coded and optimized to run with personal computers and distributed computer clusters with minimized CPU and memory consumption. Using the tool, we demonstrate the effect of changing the line resistance, array size, voltage selection scheme, selector diode’s ideality factor, reverse saturation current, temperature and sense resistance on the electrical behavior and expected sense margin of one-diode-one-resistor crossbar arrays. We then investigate the effect of single and dual side array biasing and grounding on the dissipated current throughout the array cells. The tool we offer to the memristor community and the studies we present enables the design of larger and more practical memristor arrays for application in data storage and neuromorphic computing.
Index Terms — memristor, phase change memory, neuromorphic computing, neural networks, crossbar array, line resistance, word line, bit line, Lambert-W function, selector device, ideality factor, reverse saturation current, sense resistor, sense margin, GeSbTe, GeSe, GeTe. I. INTRODUCTION EMRISTOR hardware is being extensively developed as artificial synapses, inspired by the brain intelligence and the efficient information processing it is capable of [1]–[3]. This has the potential to achieve major breakthroughs in pattern recognition and machine learning. In addition, CMOS based resistive RAMs (ReRAM) and non-volatile phase-change memories (PCM) are being developed by major industrial players, such as Intel and Micron Technology, for applications in the memory-storage space, motivated by their scalable device footprint and high switching speed [4]–[7]. The roadmap of phase change memories anticipates the technology to bridge the gap between the fast but low bit density dynamic random access memory (DRAM) and the slow but relatively higher bit density flash technology in a hybrid memory system [8]–[10].
Memristor architectures have been primarily based around the simple crossbar array structure. The simplicity of crossbar arrays can allow the realization of high device density in two

Manuscript received June 20, 2019. This work was funded by the EPSRC programme grant ADEPT – Advanced Devices by ElectroPlaTing, EPSRC reference: EP/N035437/1. The authors would like to thank Ruomeng Huang for suggesting this research direction. The authors are affiliated with the school of Electronics and Computer Science, The University of Southampton, Southampton, SO17 1BJ, UK. (Corresponding author: Yasir J. Noori, y.j.noori@southampton.ac.uk).

and three-dimensions whilst enabling low fabrication and production costs [11]–[14]. However, designing memristive crossbar arrays require rigorous quantitative electrical analysis of the system to assess its performance. While there have been considerable efforts to model crossbar arrays in the past, in most attempts, the selector device parameters and line resistances were not included in the models. Most of these crossbar array modellings have been done using the SPICE modelling tool [15]–[17]. However, modelling large memory arrays above a Megabit requires extensive computational power with SPICE [18]. Although SPICE is a compact tool that is highly optimized for modelling complicated electronic circuits, the nature of node analysis makes it slow for modelling very large memory arrays. Therefore, a highly parallelized MATLAB tool that can perform the array simulation with matrix algebra utilizing large supercomputer clusters, makes modelling future high-density memory arrays much more practical for research and commercial purposes [19]. There are two aspects to the novelty of this work. Firstly, we are providing a parallelized open-access software tool for the memristor scientific community that can be used to model memristor crossbar arrays with passive selector devices. This work follows from the theoretical work of An Chen which proposes a comprehensive crossbar array model that incorporates both line resistance and nonlinear device characteristics [20]. Secondly, we extend his work by utilizing the Lambert-W function for simulating reading operations of diode-memristor crossbar arrays. The function allows incorporating the selector diode’s ideality factor, reverse saturation current and temperature as simulatable parameters in the algorithm of the tool. Compared to previous works, this is the first work that shows a simulation of a comprehensive list of all the input parameters of an ar

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