Method of Moment Analysis of Carbon Nanotubes Embedded in a Lossy Dielectric Slab Using a Multilayer Dyadic Green’s Function

Abstract

Modeling the electromagnetic response of carbon nanotube (CNT) reinforced composites is inherently a threedimensional (3D) multi-scale problem that is challenging to solve in real-time for nondestructive evaluation applications. This article presents a fast and accurate full-wave electromagnetic solver based on a multi-layer dyadic Green's function approach. In this approach, we account for the effects of the dielectric slab, where the CNTs are embedded, without explicitly discretizing its interfaces. Due to their large aspect ratios, the CNTs are modeled as arbitrary thin wires (ATWs), and the method of moment (MoM) formulation with distributed line impedance is used to solve for their coupled currents. The accuracy of the inhouse solver is validated against commercial method of moment (MoM) and finite element method (FEM) solvers over a broad range of frequencies (from 1 GHz to 10 THz) and for a wide range of dielectric slab properties. Examples of 100 nm long vertical and horizontal CNTs embedded in a 1 µm thick lossy dielectric substrate are presented. The in-house solver provides more than 50 × speed up while solving the vertical CNT, and more than 570 × speed up while solving the horizontal CNT than a commercial MoM solver over the GHz to THz frequency range.Index Terms-Arbitrary thin wire (ATW), carbon nanotubes (CNTs), electric field integral equation (EFIE), method of moment (MoM), multilayer dyadic Green's function, Sommerfeld integrals (SI). I. INTRODUCTIONO VER the past decade, carbon nanotube (CNT) reinforced composites have been used in a wide range of applications including automotive and aerospace materials, electro-mechanical actuation and sensing, packaging, adhesives, conductive ink, coatings, electromagnetic interference (EMI) shielding and many more [1]-[5]. The unique carbon atom arrangements of metallic CNTs provides them with a unique high electrical conductivity [1], [2]. The inclusion of a small volume fraction of CNT fillers This paragraph of the first footnote will contain the date on which you submitted your paper for review.