Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

Abstract

Uncertainty quantification has become an efficient tool for yield prediction, but its power in yield-aware optimization has not been well explored from either theoretical or application perspectives. Yield optimization is a much more challenging task. On one side, optimizing the generally non-convex probability measure of performance metrics is difficult. On the other side, evaluating the probability measure in each optimization iteration requires massive simulation data, especially when the process variations are non-Gaussian correlated. This paper proposes a data-efficient framework for the yield-aware optimization of the photonic IC. This framework optimizes design performance with a yield guarantee, and it consists of two modules: a modeling module that builds stochastic surrogate models for design objectives and chance constraints with a few simulation samples, and a novel yield optimization module that handles probabilistic objectives and chance constraints in an efficient deterministic way. This deterministic treatment avoids repeatedly evaluating probability measures at each iteration, thus it only requires a few simulations in the whole optimization flow. We validate the accuracy and efficiency of the whole framework by a synthetic example and two photonic ICs. Our optimization method can achieve more than 30× reduction of simulation cost and better design performance on the test cases compared with a recent Bayesian yield optimization approach.

Yield-Constrained Optimization Design Using Polynomial Chaos for Microwave Filters

“…Since it is difficult to calculate prob(I (x, ξ ) = 1|x) directly [27], yield estimation is used to obtain the approximate solution of (2). Two classical methods, namely yield estimation using the Monte Carlo sampling (MCS) method and yield estimation using the PC model, are introduced in Section II.A and Section II.B, respectively.…”

“…x Prob(I (x, ξ ) = 1 | x) (10) where x * is the optimal design. Another method adopts the yield as the constraint [27] and employs other performances as the objective function f obj (x, ξ ). This method considers both the yield function and objective function and we call this method yield-constrained optimization.…”

“…where 1-ε is the desired yield by users (or called chance), and ε [0,1] is the risk level that users can accept. Formula ( 21) is also known as the chance constraint [27], [33]- [36] used for obtaining the optimal solution in different yield levels.…”

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

“…While most existing yield optimization approaches try to maximize the yield of a circuit, the obtained design performance (e.g., signal gain, power dissipation) may be far from the achievable optimal solution. Recently, an alternative approach was proposed in [48] to achieve both excellent yield and design performance. Instead of simply maximizing the yield, the work [48] optimizes a design performance metric while enforcing a high yield requirement.…”

“…Recently, an alternative approach was proposed in [48] to achieve both excellent yield and design performance. Instead of simply maximizing the yield, the work [48] optimizes a design performance metric while enforcing a high yield requirement. Specifically, the yield requirement is formulated as some chance constraints [49], which are further transformed to tractable constraints of the first and second statistical moments.…”