Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters.
Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters.
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具有相关和非高斯随机参数的硅光子器件的不确定性量化。
作者：
Tsui;Zheng Zhang;Z. Su;Y. Marzouk;A. Melloni;L. Daniel
工艺变化会显著降低硅光电子的器件性能和芯片成品率。为了降低设计和制造成本，在最终制造之前预测器件的统计行为是非常必要的。蒙特卡罗是用于估计工艺变化引起的不确定性的主流计算方法。然而，由于收敛速度较慢，它往往过于昂贵。近年来，基于多项式混沌展开的随机谱方法已经成为一种很有前途的替代方法，它们在许多工程问题上表现出了比蒙特卡罗方法显著的加速比。现有文献大多假定随机参数是相互独立的。然而，在实际应用中，这样的假设并不一定准确。在本文中，我们发展了一种基于随机配置的有效数值技术来模拟具有相关和非高斯随机参数的硅光子学。通过对一个基于绝缘体上硅的定向耦合器实例的仿真，验证了该方法的有效性。由于本文中的数学公式非常通用，我们提出的算法可以应用于一大类光子设计案例以及许多其他工程问题。
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.