Analysis and minimization of practical energy in 45nm subthreshold logic circuits

Over the last decade, the design of ultra-low-power digital circuits in subthreshold regime has been driven by the quest for minimum energy per operation. In this contribution, we observe that operating at minimum-energy point is not straightforward as design constraints from real-life applications have an important impact on energy. Therefore, we introduce the alternative concept of practical energy, taking functional-yield and throughput constraints on minimum Vdd into account. In this context, we demonstrate for the first time the detrimental impact of DIBL on minimum Vdd. Practical energy gives a useful analysis framework of circuit optimization to reach minimum-energy point, while considering the throughput as an input variable dictated by the application. From simulation of a benchmark multiplier in 45 nm technology, we find out that practical energy can be far higher than minimum energy point, in the case of low-throughput applications (ap 10-100 kOp/s) because of static leakage energy and robustness-limited minimum Vdd. With the proposed framework, we investigate the capability of conventional optimization techniques to make practical energy meet minimum energy point. Amongst these techniques, channel length upsize is shown to be more efficient than MTCMOS power gating, body biasing, Vt selection or device width upsize, as it increases robustness while simultaneously reducing static leakage energy. A small length upsize with low area overhead is shown to reduce practical energy at low throughput to less than 2.1 times the minimum energy level. At medium throughput, it even brings practical energy 30% lower than minimum energy level without optimization techniques.