Spatially resolved spectroscopy of monolayer graphene on ${\text{SiO}}_2$

We carried out scanning tunneling spectroscopy measurements on exfoliated monolayer graphene on ${\text{SiO}}_2$ to probe the correlation between its electronic and structural properties. Maps of the local density of states are characterized by electron and hole puddles that arise due to long-range intravalley scattering from intrinsic ripples in graphene and random-charged impurities. At low energy, we observe short-range intervalley scattering which we attribute to lattice defects. Our results demonstrate that the electronic properties of graphene are influenced by intrinsic ripples, defects, and the underlying ${\text{SiO}}_2$ substrate.

Figure 1

(Color online) (a) Schematic of a mechanically exfoliated monolayer graphene flake (gray) with gold electrodes on a ${\text{SiO}}_2$ substrate. (b) STM topographic image of monolayer graphene showing the hexagonal lattice as well as the underlying surface corrugations. The scale bar is 2 nm. The imaging parameters are sample voltage $V_s=0.25\text{V}$ and tunneling current $I_s=100\text{pA}$.

Figure 2

(Color online) $dI/dV$ point spectroscopy shows a linear relationship between the tunneling conductance and the sample voltage $V_s$. The inset shows the region near the Fermi level; no gap is seen.

Figure 3

(Color online) (a) STM topography showing the lattice and surface corrugations. The scale bar is 8 nm. The topography is recorded with $V_s=0.4\text{V}$ and $I_s=100\text{pA}$. [(b)–(e)] $dI/dV$ maps at sample voltages $-0.2$, 0.0, 0.2, and 0.4 V, respectively, showing electron and hole puddles. For all the images, the current was stabilized at the parameters of (a) and the feedback was then switched off. The maps were recorded using lock-in detection. (f) Spatially averaged $dI/dV$ curves at five different regions of the graphene indicated in (a). The curves show a crossover near 0.2 V as a result of the shifting Dirac point.

Figure 4

(Color online) (a) Illustration of effecting of shifting Dirac point on $dI/dV$ curves. The shift in the Dirac point causes the slopes of the $dI/dV$ curves to change leading to a crossover at $V_s/2$. Furthermore, the value of $dI/dV$ at $V_s$ gives information about the amount of the shift in the Dirac point $\Delta$. (b) Standard deviation of $dI/dV$ for three different locations and values of $V_s$. The setpoint voltage $V_s$ is 0.4 (blue squares), 0.25 (green triangles), and 0.15 V (yellow circles). The minimum occurs at $V_s/2$ for each of the curves.

Figure 5

(Color online) (a) STM topographic image of $30\times 30{\text{nm}}^2$ area taken with $V_s=0.15\text{V}$ and $I_s=50\text{pA}$. (b) Shift in local electrochemical potential calculated from the curvature of the topographic image shown in (a). (c) LDOS map recorded at $V_s=0.15\text{V}$ with the tip height determined using the imaging parameters from the topography measurement in (a). Scale bar in all images is 3 nm.

Figure 6

(Color online) (a) STM image of graphene, the scale bar is 6 nm. Inset is a 4-nm region within the image showing the hexagonal lattice. (b) LDOS map at the Fermi energy (0 V) taken simultaneously. Inset corresponds to the same $4\times 4{\text{nm}}^2$ area as in the topography image showing a different pattern due to scattering from defects. (c) 2D Fourier transform of (a) showing the reciprocal lattice (red circles) and components due to the $\text{C}\text{–}\text{C}$ bonds (brown squares). The scale bar is $4{\text{nm}}^{-1}$. (d) Fourier transform of (b). The inner hexagon (blue triangles) represents the interference pattern due to intervalley scattering. The outer hexagon (red circles) is due to the reciprocal lattice.

Figure 7

(Color online) (a) 2D Fourier transform of a LDOS map recorded at the Fermi energy. The traces represent the contours corresponding to a 2D Lorentzian fit. The scale bar is $3{\text{nm}}^{-1}$. (b) Line scan across one of the peaks in the Fourier transform (blue trace) and the corresponding Lorentzian fit [red (smooth) trace]. (c) Amount of intervalley scattering as a function of sample voltage. Each curve is from a different region of the graphene flake. The blue squares correspond to the area shown in Fig. 3 and are taken with $V_s=0.4\text{V}$. The green triangles and the yellow circles are from different $\left(30\times 30{\text{nm}}^2\right)$ areas taken with $V_s=0.25$ and 0.15 V, respectively.