Design and Optimization of Non-Volatile Capacitive Crossbar Array for In-Memory Computing
Yuan-Chun Luo, Anni Lu, Jae Hur, Shaolan Li, Shimeng Yu
Abstract
Resistive crossbar array for in-memory computing suffers from high static power and sneak-path current. To address these issues, we proposed a ferroelectric Hf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1−x</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (HZO) based capacitive crossbar array for in-memory computing. The non-volatile capacitive synapse allows the minimization of both sneak-path current and steady-state power consumption. Furthermore, since the capacitive synapse is read at DC 0V, we claim that this architecture allows read-disturbance-free and energy-efficient in-memory computing. In this brief, we first introduce the device properties of the non-volatile capacitor and their underlying physical mechanism. Moving to array-level analysis, we obtain the optimal ratios between reference and ferroelectric capacitors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{C}_{\mathrm{ ref}}/\text{C}_{\mathrm{ FE}}$ </tex-math></inline-formula> ) for the maximum output swing to occur. Subsequently, the tradeoff between output swing and delay has been explored. We show that a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$128\mathrm {\times }128$ </tex-math></inline-formula> non-volatile capacitive crossbar array can be designed with >75 mV swing and <30 ns delay. Under transient noise simulation, capacitive array is compatible with 3-bit partial sum quantization. Without steady-state energy consumption, the optimized capacitive array can achieve 3.8 pJ per vector-matrix multiplication, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$14.3\mathrm {\times }\mathrm {\sim } 57.3\mathrm {\times }$ </tex-math></inline-formula> lower compared to those of the representative resistive crossbar arrays. Furthermore, we propose a charge-cancelling technique and a guideline with on/off ratio projection for a system with arbitrary ENOB requirements to address the issues caused by limited on/off ratios. Finally, we suggest a 1/3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{V}_{\mathrm{ w}}$ </tex-math></inline-formula> scheme with little write disturbance.