Optimal switching time to minimize store energy in MTJ-based flip-flops under process and temperature variations

Introducing a magnetic tunneling junction (MTJ) into a flip-flop enables non-volatile power gating but large store energy to MTJ is a critical concern. A two-step store (TSS) to first perform a short store for all non-volatile flip-flops and then perform a long store only at the failed ones is an effective approach to reduce energy under switching time variation. However, properties of the optimal short-store time Tshort_opt to minimize the total store energy in TSS and physical/statistical parameters affecting T
short_opt
have not been studied yet. In this paper, we propose an analytical expression for T
short_opt
,assuming that the switching time variation follows a normal distribution. The derived expression revealed that T
short_opt
is affected only by µ and σ of the distribution and the long store time. Results with fabricated chips in a 40nm CMOS/MTJ hybrid process demonstrated that the analytical T
short_opt
shows a good agreement with the measured value (within 8% difference) under process and temperature variations. The TSS with T
short_opt
reduced energy for the store operation to 0.32X of that of the conventional long-store-only technique.