  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 paper
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 paper 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 pre-specified 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.
