A Statistical Framework for Post-Silicon Tuning through Body Bias Clustering

Adaptive body biasing (ABB) is a powerful technique that allows post-silicon tuning of individual manufactured dies such that each die optimally meets the delay and power constraints. Assigning individual bias control to each gate leads to severe overhead, rendering the method impractical. However, assigning a single bias control to all gates in the circuit prevents the method from compensating for intra-die variation and greatly reduces its effectiveness. In this paper, we propose a new variability-aware method that clusters gates at design time into a handful of carefully chosen independent body bias groups, which are then individually tuned post-silicon for each die. We show that this allows us to obtain near-optimal performance and power characteristics with minimal overhead. For each gate, we generate the probability distribution of its post-silicon ideal body bias voltage using an efficient sampling method. We then use these distributions and their correlations to drive a statistically-aware clustering technique. We study the physical design constraints and show how the area and wirelength overhead can be significantly limited using the proposed method. Compared to a fixed design time based dual threshold voltage assignment method, we improve leakage power by 38-71% while simultaneously reducing the standard deviation of delay by 2-9times