Analysis and mitigation of variability in subthreshold design

Subthreshold circuit design is a compelling method for ultra-low power applications. However, subthreshold designs show dramatically increased sensitivity to process variations due to the exponential relationship of subthreshold drive current with V_th variation. In this paper, we present an analysis of subthreshold energy efficiency considering process variation, and propose methods to mitigate its impact. We show that, unlike superthreshold circuits, random dopant fluctuation is the dominant component of variation in subthreshold operation. We investigate how this variability can be ameliorated with proper circuit sizing and choice of circuit logic depth. We then present a statistical analysis of the energy efficiency of subthreshold circuits considering process variations. We show that the energy optimal supply voltage increases due to process variations and study its dependence on circuit parameters. We verify our analytical models against Monte Carlo SPICE simulations and show that they accurately predict the minimum energy and energy optimal supply voltage. Finally, we use the developed statistical energy model to determine the optimal pipelining depth in subthreshold designs.