Nonlinear Difference Imaging to Image Local Conductivity of Single-Layer Graphene Using Electrical Impedance Tomography

Abstract

Single-layer graphene synthesized using the chemical vapor deposition (CVD) technique contains defects on the graphene surface that are formed during the growth and transfer process. These defects influence the graphene electrical characteristics, especially the conductivity distribution. Nondestructive characterization of graphene samples is therefore essential for developing single-layer graphene devices. Electrical impedance tomography (EIT), a low-cost nondestructive method with high temporal resolution characteristics, can be applied to obtain the local conductivity distribution. Due to the very high conductivity of the background and inaccurate knowledge of contact impedances, the conventional absolute imaging methods do not give desired conductivity reconstruction for graphene. This study uses a nonlinear difference imaging (NDI) approach to estimate the local conductivity changes across the graphene surface quantitatively. In NDI, the conductivity after the change is parameterized as a linear combination of initial and the conductivity change. The conductivity change restricted to the region of interest (ROI) is determined using the Otsu method. The NDI with Otsu method (NDIWO) estimates the initial distribution and conductivity changes simultaneously from the two datasets measured at different time intervals. NDIWO tolerates modeling errors to some extent and quantitively provides more accurate local conductivity changes. The feasibility of NDIWO is tested with numerical simulations and experiments with graphene wafer of size 2.5 cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times2.5$ </tex-math></inline-formula> cm, and results show that the proposed method is successful in estimating the conductivity changes with better accuracy than conventional absolute and linear difference imaging.