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Help solve to plot ellipsometry data for Bilayer Graphene with CaF2 substrates

The refractive index of the transparent substrate is described by the Sellmeier equation, whose coefficients are obtained from measurements of bare substrates.

 

The monolayer graphene is from Bluestone Global Tech (Gratom-M-Cu); Bilayer CVD graphene

 

Graphene samples are transferred onto CaF2 substrates, which are transparent from ultraviolet to mid-infrared. Because the substrates have no absorption at the wavelengths of interest, Del from the bare substrates is either 0 or pi.

 

The substrates are wedged by 2 degree to avoid backside reflection.

 

We use two ellipsometers, Woollam M-2000 and Woollam IR-VASE, for wavelengths of 0.23 to 1.64 um and 1.8 to 7 um, respectively. The longest wavelength is limited by the choice of CaF2 substrates

 

The angles of incidence used in the experiment are 47deg, 57deg, and 67deg. The spot size of M-2000 is about 3mm by 5.5mm at 57deg. We mask the samples for IRVASE measurement because its spot size (8mm by 20mm at 57deg) is larger than the graphene sample area (~10mm by 10 mm). Bare CaF2 substrates are measured and fitted by the Sellmeier equation to obtain the refractive index of CaF2. Fig. 1(a) shows the optical conductivity of monolayer CVD graphene extracted by our technique. The quality of the fit can be quantified by the MSE defined by Eq. (2). The MSEs of the M-2000 and the IR-VASE measurements of the data shown in Fig. 1(a) are 0.88 and 4.65, respectively

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