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Optical contrast and clarity of graphene on an arbitrary substrate
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View: Figures


Image of FIG. 1.
FIG. 1.

The reflection coefficient of a Bragg-stack substrate is determined by all interfaces, calculated by the transfer matrix method derived from Fresnel’s law. When a film is on the substrate, the film plus substrate has a reflection . The new is explicitly determined by the original and by the optical properties of the film and requires no explicit structure of substrate. Note that both and are calculated with the same reference plane which is the surface of the substrate.

Image of FIG. 2.
FIG. 2.

(a) Contrast map of graphene on the complex plane defined by the complex . This map shows the contrast of graphene on an arbitrary substrate with reflection coefficient at the wavelength 532 nm and at normal incidence. The for , , and SiC/Si (from outer ring to inner ring) substrates evolves in circles as the thickness of the supporting layer increases with periods of 183, 132, and 101 nm, respectively. The white dots on the circles indicate the oxide thickness that maximizes the absolute value of the contrast. (b) The contrast of graphene on a 285 nm substrate was measured to be −0.06 under light. The red dot on the circle in (a) indicates a contrast −0.063 for graphene on a 285 nm substrate.

Image of FIG. 3.
FIG. 3.

Clarity map of graphene on the complex plane for . Taking the CCD noise into account, clarity [defined in Eq. (6)] is more appropriate than contrast to describe the quality of a graphene image. Clarity depends on , which is the square of the ratio of CCD static noise to shot noise. ranges from 1:0 to 1:100 in many practical situations and typically . Clarity is optimized on a substrate with .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Optical contrast and clarity of graphene on an arbitrary substrate