1. 1 Numerical ElectroMagnetics & Semiconductor Industrial Applications Ke-Ying Su Ph.D. National Central University Department of Mathematics 01. Introduction

2. 2 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. I. What are Numerical ElectroMagnetics Cellphone RF circuit Automobile Tank Airplane Warship PS: Figures are from Google search.

3. 3 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. This course will focus on the application of integrated circuit (IC) Basic electromagnetic theory A transistor model including passive components 3D libraries of passive RC components Design layout & EM simulation Whole chip RC extraction PS: Figures are from Google search.

4. 4 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. II. When to use Numerical ElectroMagnetics Schematic Pre-Layout Simulation Place & Route Layout Design Rule Check (DRC) Layout vs Schematic (LVS) RC Extraction (RC) Post-Layout Simulation Spec. Tape out Yes No Design House Foundry foundry support AMD, nVidia, Qualcomm, Broadcom, MTK, etc. TSMC, UMC, etc. EDA Synopsys, Cadence, Mentor, Magma, etc.

5. 5 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. III. Where to use Numerical ElectroMagnetics Pre-Layout Simulation Place & Route Design Rule Check (DRC) Layout vs Schematic (LVS) RC Extraction (RC) Post-Layout Simulation Spec. Tape out Yes No Design House Foundry Schematic Passive device models: inductor & capacitor Interconnect: RCLK extraction Real silicon Related math: logic operation, topology, etc. Related math: optimization, graphic theory, etc.

6. 6 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. IV. How to implement Numerical ElectroMagnetics integral equation in frequency domain Galerkin’s procedure 3D EMX 3D EMX 2D & 3D Raphael 2D & 3D Raphael Boundary element method (BEM) Finite difference Method (FD) 3D QuickCap 3D QuickCap Laplace’s equation Floating random walk method 3D Lorentz 3D Lorentz Mixed potential integral equation Partial Element Equivalent Circuit (PEEC) 3D Momentum 3D Momentum Method of moment microwave full wave mode faster RF quasi-static mode QRC RLC extractor QRC RLC extractor Partial Element Equivalent Circuit (PEEC) for RLCK extraction

7. 7 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. V. Who works with Numerical ElectroMagnetics Foundry Design House EDA company TSMC UMC GlobalFoundries Intel, Apple AMD, nVidia, Qualcomm, MTK, etc. Synopsys, Cadence, Mentor, Magma, etc.

8. 8 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. VI. Learn from this course Contents 1.Electromagnetic problems & solutions40% 2.Mathematical theory & methods20% 3.Numerical method & coding20% 4.Semiconductor industrial cases20% Theory (1) Quasi-static-analyses (C extraction) corss-section profile, Green's function & method of moment (2) PEEC (RLK extraction) Partial-Element-Equivalent-Circuit (PEEC) (3) Full-wave analyses (S-parameter extraction) Maxwell's equations

9. 9 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. VII. Score Purpose of this course 1.Concepts for semiconductor industry 2.Realistic mathematical applications 3.Inspiration & Innovation Score 1.Midterm homework50% (a) A report of mathematical derivation and/or programming (b) Reference: papers and source code 2. Research30% (a) IEEE (EM) topic with math method (b) A presentation & open discussion in the course 3. Innovation20% (a) Possible new math method for the topic or new topic for the math method (b) A presentation & open discussion in the course

10. 10 Ke-Ying Su Ph.D. The material is for NCU/MATH course only. Thank You