Simulation of RF and Optical Components with Uncertainty Quantification

• Applicants: Professor Dr.-Ing. Ulrich Römer; Professor Dr. Rolf Schuhmann
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 398356058

Numerical electromagnetic simulations are nowadays a key part of the design and analysis of electromagnetic devices. Commonly, input parameters such as parameters describing the geometry and the material of a device, are assumed to be known. However, in practice this is not the case as parameter variability due to the manufacturing process occurs which can only be described statistically. Additionally, input parameters cannot be fully determined due to measurement errors. In view of these uncertainties, properties of the real device may violate design specifications. This often leads to an over-design of the system and the choice of unnecessarily high safety factors. Moreover, difficulties arise in view of smaller and smaller structure sizes and tighter design specifications, e.g., in nanotechnological applications.In recent years, many new algorithms for uncertainty quantification have been developed. Relying on powerful computational resources, an important aim is a more realistic prediction of the behaviour of a technical system in the presence of uncertainties. Adopting a probabilistic approach, both input and output parameters of mathematical models are described as random variables. Given a probabilistic characterization of the inputs, the goal is to compute probabilities, or a few statistical moments, of the outputs. A key step is the solution of stochastic differential equations, e.g., the Helmholtz or wave equation. To this end, polynomial spectral methods have been established as an alternative to Monte Carlo simulation and perturbation methods.This project aims at developing methods for the quantification of uncertainties in radio frequency devices and optical components. A major part is devoted to the extension and application of polynomial spectral methods. The numerical approximation of stochastic wave problems is more difficult compared to low-frequency applications in general, as convergence rates may be significantly reduced. Additionally, for complex applications, time-domain simulations may be computationally demanding and handling additional parametric dependencies is numerically challenging. The development of general and efficient solution strategies for stochastic time-domain, frequency-domain and eigenvalue problems is the primary aim of the project. From an application point of view, emphasis is put on periodic meta-materials and plasmonic structures, which can exhibit large parameter variations due to nanotechnological manufacturing.

• DFG Programme: Research Grants