Statistical mixed $V_t$ allocation of body-biased circuits for reduced leakage variation

Abstract

Leakage current is susceptible to variation of transistor parameters and environment such as temperature, which results in wide spread in leakage distribution. The spread can be reduced by employing body biasing: reverse body bias for too leaky dies and forward body bias for too slow dies. We investigate body biasing of mixed $V_t$ circuits. It is shown that the conventional body biasing has limitation in reducing leakage variation of mixed $V_t$ circuits. This is because low- and high-$V_t$ devices do not track each other and their body biasing sensitivities are different. We present alternative body biasing scheme that targets compensating die-to-die variation of low $V_t$. Under this body biasing scheme, within-die profiles of low- and high-$V_t$, which we need for statistical allocation of mixed $V_t$, get wider thus become different from the original ones. We present an analytical procedure to derive new within-die profiles. Experiments with 45-nm predictive model show that the spread in leakage distribution (ratio of maximum and minimum leakage) can be reduced to 4.4 as opposed to 10.0 from conventional body biasing on mixed $V_t$ circuits for circuit implementation. In this work, we also consider on-chip body bias controller. Adequate body controller is revised for our approach and conventional approach. The operation of revised body bias controller is verified. Additionally, the efficiency of our approach with body bias controller is still valid for reducing leakage variation from 3.22 -- 8.17 to 1.4 in this work.