We investigate a design strategy for subthreshold circuits focusing on energy-consumption minimization and yield maximization under process variations. The design strategy is based on the following findings related to the operation of low-power CMOS circuits: (1) The minimum operation voltage (VDDmin) of a circuit is dominated by flip-flops (FFs), and VDDmin of an FF can be improved by upsizing a few key transistors, (2) VDDmin of an FF is stochastically modeled by a log-normal distribution, (3) VDDmin of a large circuit can be efficiently estimated by using the above model, which eliminates extensive Monte Carlo simulations, and (4) improving VDDmin may substantially contribute to decreasing energy consumption. The effectiveness of the proposed design strategy has been verified through circuit simulations on various circuits, which clearly show the design tradeoff between voltage scaling and transistor sizing.

A delay-compensation circuit for low-power subthreshold digital circuits is proposed. Delay in digital circuits operating in the subthreshold region of MOSFETs changes exponentially with process and temperature variations. Threshold-voltage monitoring and supply-voltage scaling techniques are adopted to mitigate such variations. The variation in the delay can be significantly reduced by monitoring the threshold voltage of a MOSFET in each LSI chip and exploiting the voltage as the supply voltage for subthreshold digital circuits. The supply voltage generated by the threshold voltage monitoring circuit can be regarded as the minimum supply voltage to meet the delay constraint. Monte Carlo SPICE simulations demonstrated that a delay-time variation can be improved from having a log-normal to having a normal distribution. A prototype in a 0.35-µm standard CMOS process showed that the exponential delay variation with temperature of the ring-oscillator frequency in the range from 0.321 to 212 kHz can remain by using compensation in the range from 5.26 to 19.2 kHz.