Physics-Based Solution for Electrical Resistance of Graphene Under Self-Heating Effect

In this brief, we present a physics-based solution for the temperature-dependent electrical resistance of a suspended metallic single-layer graphene (SLG) sheet under Joule self-heating. The effect of in-plane and flexural phonons on the electron scattering rates for a doped SLG layer has been considered, which particularly demonstrates the variation of the electrical resistance with increasing temperature at different current levels using the solution of the self-heating equation. The present solution agrees well with the available experimental data done with back-gate electrostatic method over a wide range of temperatures.

I. Introduction

In recent years, metallic graphene materials have demonstrated withstanding and possessing a reportedly very high breakdown current density and thermal conductivity (on the order of [1]–[3] and 600–7000 [4], respectively, at 300 K), which makes them fit to emerge as potential candidates for next-generation interconnect materials in integrated circuits. However, applications near the limiting breakdown current have also resulted in Joule heating over the metallic single-layer graphene (SLG) surface [5]–[7], which initiates our motivation to study the temperature-dependent electrical resistance through the solution of the Joule-heating equation containing a temperature-dependent thermal conductivity .