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Spectroscopic imaging ellipsometry and Fano resonance modeling of graphene
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10.1063/1.4771875
/content/aip/journal/jap/112/12/10.1063/1.4771875
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/12/10.1063/1.4771875
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Figures

Image of FIG. 1.
FIG. 1.

(a) Optical (left) and ellipsometric contrast (right) microscope images of the measured graphene sample on a 90 nm layer. The spot in the microscope image marks the area of Raman measurements. In the ellipsometric contrast microscope image, regions 0 and 1 indicate ROI used for the spectroscopic measurements of the single-layer graphene and the substrate, respectively. (b) Optical (left) and ellipsometric contrast (right) microscope images of the measured graphene sample on a 300 nm layer. Spots in the microscope image mark areas used for Raman measurements of single- and bi-layer graphene. In the ellipsometric contrast microscope image, regions 0, 1, and 2 indicate ROI used for the spectroscopic measurements of single-layer, substrate, and bi-layer graphene, respectively. Scale bar is 20 μm. (c) and (d) Raman spectra of the samples shown in (a) and (b), respectively. Areas measured with Raman spectroscopy are chosen to match ROI used for ellipsometric measurements.

Image of FIG. 2.
FIG. 2.

(a) Schematic representation of the ellipsometric setup; in the polarizer, compensator, sample, analyzer setup (PCSA). Also shown is the state of polarization during null ellipsometry. (b) Optical model of the sample, also showing p- and s-polarizations of the light.

Image of FIG. 3.
FIG. 3.

Ellipsometric data of the sample on a 90 nm layer used for retrieval of graphene's optical properties. (a) Measured spectra of the sample (circles) and substrate (triangles) with fitted sample (solid line) and substrate (dotted-dashed line) data. (b) Measured and fitted spectra. Measurements were carried out with same ROI used under two different angles of incidence: and . Image of the sample and ROI used are shown in Fig.1(a).

Image of FIG. 4.
FIG. 4.

(a) Complex refractive index of graphene, obtained by inversion (circles), parameterized by the Fano profile (solid lines) and extrapolated Fano model data (dotted-dashed lines); (b) simulated absorption of a free-standing graphene sheet, based on the data from (a). Circles represent absorption calculated from the refractive index obtained by inversion, while solid line represents extrapolated data based on the Fano model. Absorption is compared with the results obtained by other groups7,13–17 (dashed and dotted-dashed lines). In the data taken from Ref. 17, abbreviations (n) and (i) stand for non-interacting and interacting model, respectively.

Image of FIG. 5.
FIG. 5.

Ellipsometric data of the sample on a 300 nm layer. (a) Measured spectra of the single-layer (circles), bi-layer (squares) sample, and substrate (triangles) with fitted single-layer (solid line), bi-layer (dashed line) sample, and substrate (dotted-dashed line) data. (b) Measured and fitted spectra. Vertical lines at 430 nm, 470 nm, and 501 nm indicate wavelengths used for ellipsometric mapping of the sample. Image of the sample and ROI used are shown in Fig. 1(b).

Image of FIG. 6.
FIG. 6.

(a) and (b) maps of the graphene sample at a fixed wavelength of 430 nm and under incident angle. (c) Graphene and (d) water layer thickness maps calculated from all spectral maps. Numbers “1” and “2” indicate cross sections for single- and bi-layer regions, respectively. (e) Thickness cross section of the single-layer region, and (f) thickness cross sections of the bi-layer region. Solid line represents graphene layer thickness, while dashed line represents water layer thickness.

Image of FIG. 7.
FIG. 7.

The relation between the AFM and imaging ellipsometry of the single-layer graphene/substrate step. Dashed lines in the maps indicate corresponding cross sections, shown underneath their maps. (a) AFM image of the sample, graphene/substrate step is estimated to be 0.98 nm. (b) Calculated water layer thickness map, step height is estimated to be 0.85 nm. (c) Calculated graphene thickness map, step height is estimated to be 0.35 nm.

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/content/aip/journal/jap/112/12/10.1063/1.4771875
2012-12-27
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spectroscopic imaging ellipsometry and Fano resonance modeling of graphene
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/12/10.1063/1.4771875
10.1063/1.4771875
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