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Conventional yield optimization algorithms try to maximize the success rate of a circuit under process variations. These methods often obtain a high yield but reach a design performance that is far from the optimal value. This article investigates an alternative yield-aware optimization for photonic ICs: we will optimize the circuit design performance while ensuring a high yield requirement. This problem was recently formulated as a chance-constrained optimization, and the chance constraint was converted to a stronger constraint with statistical moments. Such a conversion reduces the feasible set and sometimes leads to an over-conservative design. To address this fundamental challenge, this article proposes a carefully designed polynomial function, called optimal polynomial kinship function, to bound the chance constraint more accurately. We modify existing kinship functions via relaxing the independence and convexity requirements, which fits our more general uncertainty modeling and tightens the bounding functions. The proposed method enables a global optimum search for the design variables via polynomial optimization. We validate this method with a synthetic function and two photonic IC design benchmarks, showing that our method can obtain better design performance while meeting a prespecified yield requirement. Many other advanced problems of yield-aware optimization and more general safety-critical design/control can be solved based on this work in the future.

PoBO: A Polynomial Bounding Method for Chance-Constrained Yield-Aware Optimization of Photonic ICs