Abstract
Recently, graphene has gained a lot of attention in the electronic industry due to its unique properties and has paved the way for realizing novel devices in the field of electronics. For the development of new device applications, it is necessary to grow large wafer-sized monolayer graphene samples. Among the methods to synthesize large graphene films, chemical vapor deposition (CVD) is one of the promising and common techniques. However, during the growth and transfer of the CVD graphene monolayer, defects such as wrinkles, cracks, and holes appear on the graphene surface. These defects can influence the electrical properties and it is of interest to know the quality of graphene samples non-destructively. Electrical impedance tomography (EIT) can be applied as an alternate method to determine conductivity distribution non-destructively. The EIT inverse problem of reconstructing conductivity is highly non-linear and is heavily dependent on measurement accuracy and modeling errors related to an accurate knowledge of electrode location, contact resistances, the exact outer boundary of the graphene wafer, etc. In practical situations, it is difficult to eliminate these modeling errors as complete knowledge of the electrode contact impedance and outer domain boundary is not fully available, and this leads to an undesirable solution. In this paper, a difference imaging approach is proposed to estimate the conductivity change of graphene with respect to the reference distribution from the data sets collected before and after the change. The estimated conductivity change can be used to locate the defects on the graphene surface caused due to the CVD transfer process or environment interaction. Numerical and experimental results with graphene sample of size 2.5 × 2.5 cm are performed to determine the change in conductivity distribution and the results show that the proposed difference imaging approach handles the modeling errors and estimates the conductivity distribution with good accuracy.
Highlights
Graphene, which is an allotrope of carbon, is a two-dimensional (2D) material made of a single atomic layer with carbon atoms arranged in a hexagonal honeycomb lattice and has special unique properties [1]
Numerical simulations are carried out using a graphene sample that is square-shaped and has the same geometry as the graphene sample used for the experiment
Fine mesh with 20,440 triangular elements is used to generate true data and coarse mesh with 5110 elements is used to estimate the conductivity distribution across the graphene (Figure 2)
Summary
Graphene, which is an allotrope of carbon, is a two-dimensional (2D) material made of a single atomic layer with carbon atoms arranged in a hexagonal honeycomb lattice and has special unique properties [1]. Microscopic techniques such as Kelvin probe force microscopy [19,20,21], and conductive atomic force microscopy (AFM) [22], scanning tunneling microscopy (STM) [23,24] are used for studying the electrical properties of graphene locally at the nanoscale spatial resolution They provide accurate characterization locally, to have the mapping of conductivity over a large area of graphene it is cumbersome and difficult to evaluate the sample quality in a given time frame. Electrical impedance tomography (EIT) is applied as an alternate nondestructive method to map the conductivity distribution of graphene assuming point electrodes [39]. Numerical and experimental studies are performed using the proposed method on large-area graphene of size 2.5 cm × 2.5 cm for conductivity estimation and the results are compared with the absolute imaging approach
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