Surrogate Models for Forward and Inverse Problems and Uncertainty Quantification of High-Speed Devices and Circuits.

Abstract

Electronic design automation (EDA) tools play a critical role in forward and inverse modeling by enabling preliminary performance assessments and reducing reliance on costly and timeconsuming direct measurements. Modern design tools support accurate modeling, but uncertainties from fabrication process variations, manufacturing tolerances, approximation errors due to simulations, human error, and operating conditions make deterministic analysis insufficient. As a result, effective uncertainty quantification (UQ) algorithms for forward and inverse modeling must capture these uncertainties to ensure reliable performance predictions for high-speed devices and circuits. This thesis presents advanced surrogate modeling and inverse modeling techniques for uncertainty quantification (UQ) and parameter extraction in high-speed electronic devices and circuits. The work addresses critical challenges in handling mixed epistemic-aleatory uncertainties and non-unique inverse problems, with applications in Aluminum Gallium Nitride/Gallium Nitride (AlGaN/GaN) high electron mobility transistors (HEMTs) and multilayer graphene nanoribbon (MLGNR) interconnects. The first contribution of this thesis is the development of a polymorphic polynomial chaos (PPC) surrogate model to overcome the curse of dimensionality in traditional polynomial chaos (PC) methods for mixed uncertainty quantification. The PPC formulation develops novel polymorphic variables that can capture the combined effect of epistemic and aleatory uncertainty embedded in circuit parameters. The proposed PPC framework reduces computational complexity while without involving any approximations. This enables scalable UQ for highfrequency circuit simulations. The second contribution of this thesis is the development of machine learning (ML) enhanced artificial neural network (ANN) models for trap-related UQ in AlGaN/GaN HEMTs, eliminating the need for explicit RC networks and their repeated tuning for UQ while preserving physical fidelity. This approach enhances industry-standard models like ASM-HEMT, facilitating efficient UQ in practical circuit design.