Raman scattering and electrical resistance of highly disordered graphene

Raman scattering (RS) spectra and current-voltage characteristics at room temperature were measured in six series of small samples fabricated by means of electron-beam lithography on the surface of a large size $(5\times 5\text{mm)}$ industrial monolayer graphene film. Samples were irradiated by different doses of $\mathrm{C}{}^{+}$ ion beam up to ${10}^{15}$ $\mathrm{cm}{}^{-2}$. It was observed that at the utmost degree of disorder, the Raman spectra lines disappear which is accompanied by the exponential increase of resistance and change in the current-voltage characteristics. These effects are explained by suggestion that highly disordered graphene film ceases to be continuous and splits into separate fragments. The relationship between structure (intensity of RS lines) and sample resistance is defined. It is shown that the maximal resistance of the continuous film is of the order of reciprocal value of the minimal graphene conductivity $\pi h/4e^2\approx 20$ kOhm.

Figure 1

Microphotograph of the graphene monolayer specimen.

Figure 2

RS spectra: (a) initial sample “0” and sample 1 (after EBL, nonirradiated); (b) samples 1–6. $\Phi ,\mathrm{cm}{}^{-2}$: (1) 0, (2) $0.5\times {10}^{14}$, (3) $1\times {10}^{14}$, (4) $2\times {10}^{14}$, (5) $4\times {10}^{14}$, and (6) $1\times {10}^{15}$. The lines are shifted for clarity.

Figure 3

Ratio $I_D/I_G$ as a function of the mean distance between defects LD. Solid line represents Eq. (3) with $C_A=5.4,C_S=0,r_S=1.55$ nm, and $r_A=4.1$ nm.

Figure 4

RS line ratio $I_D/I_G$ and the sample resistance $R$ at 300 K plotted as a function of the defect concentration $N_D$.

Figure 5

Static resistance $R=V/I$ at $T=300$ K as a function of current $I$ for samples 2–6.