Measurement of optical functions of highly oriented pyrolytic graphite in the visible

The spectroscopic dielectric functions of highly oriented pyrolytic graphite (HOPG) are determined at nine different wavelengths from $405\text{to}750\mathrm{nm}$ $(3.06–1.65\mathrm{eV})$. This determination is made on the basis of two ellipsometry measurements: (1) Standard ellipsometry measurements are performed on HOPG with the $c$ axis perpendicular to the sample surface, and (2) two-modulator generalized ellipsometry microscope (2-MGEM) measurements are performed on HOPG cut and polished such that the $c$ axis is parallel to the sample surface. Both the ordinary and extraordinary complex dielectric functions show nonzero absorption throughout the observed spectral range, while the ordinary dielectric function shows Drude-like behavior at longer wavelengths. From this, it can be concluded that graphite is metallic for visible light polarized parallel to the graphene planes, but acts more as a semiconductor or semimetal for visible light polarized perpendicular to the graphene planes. The 2-MGEM technique can also be used to generate images of the diattenuation, retardation, and direction of the principal axis.

Figure 1

Pseudodielectric functions of $c\perp$ HOPG, where the angles of incidence are listed in the figure. The before and x-ray samples were not cleaned, while the A and B samples were cleaned using the tape cleave technique described in the text.

Figure 2

(Color online) Polarized microscope picture of HOPG (a) and an AFM contacting mode image of the $20\times 20\mu {\mathrm{m}}^2$ region indicated (b). The rms roughness from the AFM image was $5.5\mathrm{nm}$ and the $z$-height scale was $0–20\mathrm{nm}$.

Figure 3

(Color online) 2-MGEM data for the same sample shown in Fig. 2. The images show the diattenuation $N$, the absolute retardation $\mid \delta \mid$, and the direction of the fast axis $\gamma$. The pictures to the left and right show two selected regions at higher magnification. The black mark in the lower right corner of the center images indicates $100\mu \mathrm{m}$. The color scale for the maximum and minimum values is shown to the right. The optical resolution is $4\mu \mathrm{m}$ and the pixel size is $2.5\mu \mathrm{m}$.

Figure 4

Diattenuation $N$ and retardation $\delta$ for HOPG $c\parallel$ averaged over 1599 points. The error limits show the standard deviation of the measurements.

Figure 5

The calculated values of the complex refractive index for light polarized perpendicular to the optic axis (ordinary, $n_o$, $k_o$) and for light polarized parallel to the optic axis (extraordinary, $n_e$, $k_e$) as a function of the thickness of the surface roughness. The wavelength was $577\mathrm{nm}$.

Figure 6

The real and imaginary parts of the complex dielectric function for light polarized perpendicular $\left(o\right)$ and parallel $\left(e\right)$ to the optic axis. The line shows the best fit obtained using the Drude-like expression in Eqs. (7) (see text).