Deep neural networks (DNNs) have shown great promise in various applications, but their computational intensity poses challenges for on-chip implementation within the von Neumann architecture due to the separation of memory and processing units. The shift towards memory-centric architectures, such as neuromorphic computing, offers a solution. Emerging memory technologies, including resistive random-access memory (RRAM), are considered strong candidates for neuromorphic computing due to their high density, fast switching speed, low power consumption, CMOS compatibility, and excellent endurance and retention properties. Recent work has shown that quantizing 32-bit floating weights to 1-bit binary or even 1-bit ternary precision (−1, 0, +1) significantly reduces model size and improves energy efficiency without substantial accuracy loss. This simplification allows for the replacement of vector-matrix multiplication with simpler addition/subtraction operations, further optimized to XNOR and bit-counting operations in XNOR-Net. However, conventional cross-point architectures for RRAM have limitations in scaling and density. 3D vertical stacking technologies like VRRAM offer a solution to these limitations, but the use of conventional metal materials as word-plane electrodes can restrict array size and performance. Graphene, with its excellent electronic and thermal conductivity, presents a potential replacement for metal interconnects in 3D VRRAM, promising improved device characteristics and array performance. This study aims to investigate the potential of a graphene-based VRRAM array as a neuromorphic computing platform, integrating considerations of device design, circuit architecture, and algorithmic optimization.

The paper reviews existing literature on neural network quantization, showing that reducing weight precision to 1-bit binary or ternary improves accuracy, computation rate, and architecture size. It also discusses the advantages of 3D VRRAM arrays for high density and low energy consumption. Existing work on RRAM devices, including their materials, characteristics, and applications in neuromorphic computing is reviewed. The limitations of conventional metal-based VRRAM word planes are highlighted, motivating the exploration of graphene as a superior alternative. Previous research on graphene's properties and its potential use in memory devices is also summarized.

The study involved both experimental and simulation work. Experimentally, TiN/HfO/Pt (Pt-RRAM) and TiN/HfO/graphene (Gr-RRAM) devices were fabricated and characterized. High-resolution transmission electron microscopy (TEM) was used to image the devices. DC I-V characteristics were measured to study the switching behavior of both Pt-RRAM and Gr-RRAM devices, revealing differences in switching polarity attributed to graphene's role as an oxygen reservoir. The stochasticity of device response was analyzed, and safe write and read protocols were established based on experimental results. A Verilog-A compact model was developed to accurately represent the VRRAM resistive switching behavior, incorporating programming variations and read noise. A virtual 3D VRRAM array was simulated using HSPICE, using the 2x2x2 sub-circuit as a building block. The impact of graphene, both pristine and doped (DGr-RRAM), was investigated in terms of array programming, reading, and weighted-sum (WS) operations. The simulation considered different array sizes and evaluated parameters like write access voltage, read margin, programming energy, and read inaccuracy. Finally, a 2-layer Multilayer Perceptron (MLP) neural network was simulated in MATLAB, using MNIST data for training and testing. The effect of weight precision (32-bit floating-point, 6-bit, and 1-bit ternary) and read noise on recognition accuracy was studied. The XNOR operation-inspired architecture was implemented for the 1-bit ternary VRRAM array.

The experimental results showed that Gr-RRAM devices exhibited lower switching voltages and currents compared to Pt-RRAM devices, resulting in significantly reduced programming energy. Gr-RRAM also showed better uniformity and a larger memory window. The simulation results revealed that the graphene-based VRRAM arrays outperformed the Pt-based VRRAM arrays in terms of write access voltage, read margin, and energy consumption. Specifically, Gr-RRAM and DGr-RRAM arrays showed significantly lower energy consumption (262x lower for RESET and 8x lower for SET) and higher tolerance to read inaccuracy during weighted-sum operations. The graphene-based VRRAMs maintained satisfactory performance even at large array sizes (416x224), while the Pt-based VRRAMs failed to meet the minimum access voltage requirement beyond 128x128. The 1-bit ternary precision neural network with XNOR operations implemented on the Gr-RRAM array achieved ~94.1% recognition accuracy on the MNIST dataset, demonstrating the effectiveness of the proposed architecture. The study also showed that the read inaccuracy increased with the number of parallel bit-lines used for inference, suggesting an optimal number of 8 BLs for this architecture.

The findings demonstrate the significant advantages of using graphene as a word-plane electrode in 3D VRRAM arrays for neuromorphic computing. The improved device characteristics, lower energy consumption, and higher tolerance to read inaccuracy contribute to a substantial performance enhancement. The successful implementation of the XNOR architecture with 1-bit ternary precision showcases the potential for energy-efficient and high-accuracy neuromorphic computing. This holistic approach, integrating material and device engineering, circuit design, and algorithm development, is crucial for realizing the potential of memory-centric computing architectures. The results strongly support the use of graphene in next-generation computing systems.

This study highlights the significant potential of graphene-based 3D VRRAM arrays for neuromorphic computing. The use of graphene leads to improved device characteristics, reduced energy consumption, and enhanced accuracy in large-scale arrays. The XNOR-based architecture with 1-bit ternary precision is shown to be highly effective. Future research could focus on optimizing the graphene synthesis and transfer processes for better integration with current semiconductor technologies and exploring other 2D materials for further performance enhancements.

The study is based on simulations of a virtual 3D VRRAM array, and the actual performance of a physically implemented array may differ due to fabrication imperfections and other unforeseen factors. The study used a specific neural network architecture and dataset (MNIST); further research is needed to explore the generalizability of the findings to other networks and datasets. The dry transfer method of graphene remains a challenge in current manufacturing processes which may have been under-considered here.