A Body Bias Clustering Method for Low Test-Cost Post-Silicon Tuning

Post-silicon tuning is attracting a lot of attention for coping with increasing process variation. However, its tuning cost via testing is still a crucial problem. In this paper, we propose tuning-friendly body bias clustering with multiple bias voltages. The proposed method provides a small set of compensation levels so that the speed and leakage current vary monotonically according to the level. Thanks to this monotonic leveling and limitation of the number of levels, the test-cost of post-silicon tuning is significantly reduced. During the body bias clustering, the proposed method explicitly estimates and minimizes the average leakage after the post-silicon tuning. Experimental results demonstrate that the proposed method reduces the average leakage by 25.3 to 51.9% compared to non clustering case. In a test case of four clusters, the number of necessary tests is reduced by 83% compared to the conventional exhaustive test approach. We reveal that two bias voltages are sufficient when only a small number of compensation levels are allowed for test-cost reduction. We also give an implication on how to synthesize a circuit to which post-silicon tuning will be applied. key words: post-silicon tuning, body bias clustering, process variation, body biasing, statistical static timing analysis