Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters

Abstract

Abstract:Process variations can significantly degrade device performance and chip yield in silicon photonics. In order to reduce the design and production costs, it is highly desirable to predict the statistical behavior of a device before the final fabrication. Monte Carlo is the mainstream computational technique used to estimate the uncertainties caused by process variations. However, it is very often too expensive due to its slow convergence rate. Recently, stochastic spectral methods based on polynomial chaos expansions have emerged as a promising alternative, and they have shown significant speedup over Monte Carlo in many engineering problems. The existing literature mostly assumes that the random parameters are mutually independent. However, in practical applications such assumption may not be necessarily accurate. In this paper, we develop an efficient numerical technique based on stochastic collocation to simulate silicon photonics with correlated and non-Gaussian random parameters. The effectiveness of our proposed technique is demonstrated by the simulation results of a silicon-on-insulator based directional coupler example. Since the mathematic formulation in this paper is very generic, our proposed algorithm can be applied to a large class of photonic design cases as well as to many other engineering problems.

Silicon Photonics Circuit Design: Methods, Tools and Challenges

“…In polynomial chaos expansion (PCE), the system model is replaced with a higher‐order model where the distribution of the low‐level parameters is directly mapped onto the distribution of the performance metrics of the system . This technique has already been applied to map geometric parameter variations onto device performance statistics . These techniques can make yield assessment more practical, to a point where the sensitivity of circuits to stochastic variations can be efficiently assessed and circuits can be optimized for yield …”

“…[136,137] This technique has already been applied to map geometric parameter variations onto device performance statistics. [138,139] These techniques can make yield assessment more practical, to a point where the sensitivity of circuits to stochastic variations can be efficiently assessed [140] and circuits can be optimized for yield. [141] There remains significant effort needed to improve yield estimation simulations, in particular, to combine the efficient simulation techniques mentioned above, with the necessary locationdependant or distance-aware approaches that take correlations of parameters into account.…”

Stochastic collocation for device-level variability analysis in integrated photonics

“…The generalized polynomial chaos (gPC) expansion has been applied in several domains as an efficient alternative to the classic MC method [6][7][8] and, recently, * Corresponding author: wim.bogaerts@ugent.be it has been proposed for the variability analysis of photonic devices [9,10].…”

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

“…In the domain of electrical engineering, intrusive methods are already successfully applied in the variability analysis of on-chip interconnects [3,4] and scattering problems [5][6][7]. Recently, in the domain of photonics, the non-intrusive SCM method has been applied for the UQ of a silicon-on-insulator based directional coupler [8]. In this paper, the focus is on the UQ of large optical lens systems.…”