Tutorial I

Integral equation methods for the electromagnetic analysis of interconnect networks: state of art and recent advancements

Shashwat Sharma and Piero Triverio, University of Toronto

Abstract - Electromagnetic solvers are an essential tool for signal and power integrity engineers working at the chip, package and board level. The need for full-wave simulations is rapidly increasing, driven by emerging technologies (3D integration, 400 Gigabit Ethernet) and applications (cloud computing, IoT, quantum computing. As industrial needs in terms of computational electromagnetism soar well beyond the state of the art, new ideas and development become necessary to sustain technological progress.

This tutorial will first review the state of the art on integral equation methods for Maxwell's equations, that are often advocated for interconnect analysis. A comprehensive overview of their mathematical foundations will be presented, with an emphasis on: wideband modeling of skin effect, accounting for layered substrates, and acceleration with iterative solvers and far-field approximations. Finally, we will survey recent advancements in the field including the parallelization of integral equation solvers across thousands of processing cores. Examples related to interconnect networks and integrated passive components will be presented.

Shashwat Sharma received the B.A.Sc. degree in Engineering Physics and the M.A.Sc. degree in Electrical Engineering from the University of Toronto, Canada, in 2014 and 2016, respectively. From September 2016 to March 2017 he worked as a Research Intern in the computational science group at Autodesk Research, Toronto. Since 2017 he has been working towards the Ph.D. degree in electrical engineering at the University of Toronto. His research focuses on computational electromagnetics, with an emphasis on fast and robust boundary element techniques for multiscale electromagnetic modeling. His interests include all aspects of numerical methods, computational science and high-performance computing in the context of electromagnetics.

Mr. Sharma received the Piergiorgio Uslenghi Letters Prize Paper Award (2021) and placed second at the CNC/USNC-URSI Student Paper Competition of the 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (AP-S/URSI). He was also a finalist for the Best Student Paper Award at the 2018 IEEE Conference on Electrical Performance of Electronic Packaging and Systems. Mr. Sharma received honorable mentions for his contributions to the AP-S/URSI symposia in 2019 and 2020, and a TICRA-EurAAP Grant at the 2021 European Conference on Antennas and Propagation. He is currently serving as Vice Chair for the University of Toronto student chapter of the IEEE Antennas and Propagation Society.

Piero Triverio received the Ph.D. degree in Electronic Engineering from Politecnico di Torino, Italy, in 2009. He is an Associate Professor in The Edward S. Rogers Sr. Department of Electrical & Computer Engineering (ECE) at the University of Toronto, and in the Institute of Biomaterials and Biomedical Engineering (IBBME). He holds the Canada Research Chair in Computational Electromagnetics. His research interests include signal integrity, computational electromagnetism, model order reduction, and computational fluid dynamics applied to cardiovascular diseases.

Prof. Triverio and his students received the Piergiorgio Uslenghi Letters Prize Paper Award (2021), the Best Paper Award of the IEEE Transactions on Advanced Packaging (2007), the EuMIC Young Engineer Prize (2010), and the Ontario Early Researcher Award (2016). From 2013 to 2018, Triverio held the Canada Research Chair in Modeling of Electrical Interconnects. Triverio and his students were awarded the Best Paper Award of the IEEE Conference on Electrical Performance of Electronic Packaging and Systems (2008, 2017), and several Best Student Paper Awards at international symposia. He serves as an Associate Editor for the IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY. He is a member of the Technical Program Committee of the IEEE Workshop on Signal and Power Integrity, and of the IEEE Conference on Electrical Performance of Electronic Packaging and Systems.