Selective body biasing for post-silicon tuning of sub-threshold designs: A semi-infinite programming approach with Incremental Hypercubic Sampling

Sub-threshold designs have become a popular option in many energy constrained applications. However, a major bottleneck for these designs is the challenge in attaining timing closure. Most of the paths in sub-threshold designs can become critical paths due to the purely random process variation on threshold voltage, which exponentially impacts the gate delay. In order to address timing violations caused by process variation, post-silicon tuning is widely used through body biasing technology, which incurs heavy power and area overhead. Therefore, it is imperative to select only a small group of the gates with body biasing for post-silicon-tuning. In this paper, we first formulate this problem as a linear semi-infinite programming (LSIP). Then an efficient algorithm based on the novel concept of Incremental Hypercubic Sampling (IHCS), specially tailored to the problem structure, is proposed along with the convergence analysis. Compared with the state-of-the-art approach based on adaptive filtering, experimental results on industrial designs using 65 nm sub-threshold library demonstrate that our proposed IHCS approach can improve the pass rate by up to 7.3× with a speed up to 4.1×, using the same number of body biasing gates with about the same power consumption.