Optimized Two-Step Store Control for MTJ-Based Nonvolatile Flip-Flops to Minimize Store Energy Under Process and Temperature Variations
Kimiyoshi Usami, Daiki Yokoyama, Aika Kamei, Hideharu Amano, Kenta Suzuki, Keizo Hiraga, Kazuhiro Bessho
Abstract
Introducing a magnetic tunneling junction (MTJ) into a flip-flop enables nonvolatile power gating (PG) but large store energy to MTJ is a critical concern. We propose an optimized two-step store (TSS) control to first perform a short store with an optimal time for all nonvolatile flip-flops (NVFFs) and then perform a long store only at the failed ones for reducing the store energy. As the key technologies to realize this, we present a verify-and-retryable NVFF (VR-NVFF) circuit enabling the TSS control and an analytical expression for the optimal short-store time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{\text {short}{\_}\text{opt}}$ </tex-math></inline-formula> ) minimizing the store energy. To examine the effectiveness of the optimized TSS control and the validity of analytically derived <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{\text {short}{\_}\text{opt}}$ </tex-math></inline-formula> , we implemented the TSS control on a coarse-grained reconfigurable array (CGRA)-based accelerator chip and fabricated it in a 40-nm CMOS/MTJ hybrid process technology. Results demonstrated that analytical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{\text {short}{\_}\text{opt}}$ </tex-math></inline-formula> showed a good agreement with the measured value (within 8% difference) under process and temperature variations. The TSS control with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{\text {short}{\_}\text{opt}}$ </tex-math></inline-formula> reduced the store energy to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.32\times $ </tex-math></inline-formula> of that of the conventional long-store-only technique. The break-even time (BET), which is the minimum power-gating time to get the gain in energy savings, was shortened to 0.51– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.7\times $ </tex-math></inline-formula> by the TSS control, achieving the BET of 50– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$923 \mu \text{s}$ </tex-math></inline-formula> in the range of 0 °C–80 °C.