Power minimization under variability is formulated as a rigorous statistical robust optimization program with a guarantee of power and timing yields. Both power and timing metrics are treated probabilistically. Power reduction is performed by simultaneous sizing and dual threshold voltage assignment. An extremely fast run-time is achieved by casting the problem as a second-order conic problem and solving it using efficient interior-point optimization methods. When compared to the deterministic optimization, the new algorithm, on average, reduces static power by 31 % and total power by 17 % without the loss of parametric yield. The run time on a variety of public and industrial benchmarks is 30X faster than other known statistical power minimization algorithms.

We describe an optimization strategy for minimizing total power consumption using dual threshold voltage (Vth) technology. Significant power savings are possible by simultaneous assignment of Vth with gate sizing. We propose an efficient algorithm based on linear programming that jointly performs Vth assignment and gate sizing to minimize total power under delay constraints. First, linear programming assigns the optimal amounts of slack to gates based on power-delay sensitivity. Then, an optimal gate configuration, in terms of Vth and transistor sizes, is selected by an exhaustive local search. Benchmark results for the algorithm show 32 % reduction in power consumption on average, compared to sizing only power minimization. There is up to a 57 % reduction for some circuits. The flow can be extended to dual supply voltage libraries to yield further power savings.

We describe various design automation solutions for design migration to a dual-Vt process technology. We include the results of a Lagrangian Relaxation based tool, iSTATS, and a heuristic iterative optimization flow. Joint dual-Vt allocation and sizing reduces total power by 10+% compared with Vt allocation alone, and by 25+% compared with pure sizing methods. The heuristic flow requires 5x larger computation runtime than iSTATS due to its iterative nature.

Low-power circuits are especially sensitive to the increasing levels of process variability and uncertainty. In this paper we study the problem of leakage power minimization through dual Vth design techniques in the presence of significant Vth variation. For the first time we consider the optimal selection of Vth under a statistical model of threshold variation. Probabilistic analytical models are introduced to account for the impact of Vth uncertainty on leakage power and timing slack. Using this model, we show that the non-probabilistic analysis significantly (by 3x) underestimates the leakage power. We also show that in the presence of variability the optimal value of the second Vth must be about 30mV higher compared to the variation-free scenario. In addition, this model provides a way to compute the optimal value of the second Vth for a variety of process conditions.

Energy-efficient design of integrated circuits requires specialized tools and technologies. This chapter surveys some of the most important contributions in logic synthesis for achieving low-power consumption, by means of gate-level and register-transfer level restructuring. It presents also specialized techniques that leverage specific low-power silicon technologies.