Intrinsic and extrinsic corrugation of monolayer graphene deposited on ${\mathrm{SiO}}_2$

Using scanning tunneling microscopy in an ultrahigh vacuum and atomic force microscopy, we investigate the corrugation of graphene flakes deposited by exfoliation on a $\mathrm{Si}/{\mathrm{SiO}}_2$ (300 nm) surface. While the corrugation on ${\mathrm{SiO}}_2$ is long range with a correlation length of about 25 nm, some of the graphene monolayers exhibit an additional corrugation with a preferential wavelength of about 15 nm. A detailed analysis shows that the long-range corrugation of the substrate is also visible on graphene, but with a reduced amplitude, leading to the conclusion that the graphene is partly freely suspended between hills of the substrate. Thus, the intrinsic rippling observed previously on artificially suspended graphene can exist as well, if graphene is deposited on ${\mathrm{SiO}}_2$.

Figure 1

(a) Raman spectra using laser light of wavelength 532.1 nm. The spectra are recorded on different areas of the graphene flake and the attribution to monolayer, bilayer, and multilayer is marked. (b) Optical image of the graphene sample with gold contacts. The different areas of monolayer (1L), bilayer (2L), and multilayer (MuL) as identified by Raman spectroscopy are indicated. Insets show two STM images acquired at the edge of the gold contact, which are used for orientation. (c) Microscopic image of the STM tip in tunneling contact with the graphene in UHV recorded with a long-range optical microscope.

Figure 2

(a) Constant current STM image of multilayer graphene (0.4 V, 258 pA) (raw data). (b) Higher resolution STM image of the same area as in (a) with triangular atomic structure indicated (0.4 V, 198 pA). (c) High resolution STM image of graphene monolayer area with hexagonal atomic structure indicated (1 V, 394 pA). (d) Lower resolution STM image of monolayer graphene (0.5 V, 292 pA) (raw data). (e) Line section along the lines depicted in (a)(MuL) and (d)(1L). (f) Normalized $dI/dV$ spectrum of monolayer graphene: $V_{\mathrm{stab}}=0.7\mathrm{V}$, $I_{\mathrm{stab}}=300\mathrm{pA}$, $V_{\mathrm{mod}}=20\mathrm{mV}$.

Figure 3

(a), (b) 3D and 2D constant current STM image of monolayer graphene (1 V, 207 pA). (c) 3D tapping mode AFM image of the ${\mathrm{SiO}}_2$ substrate (resonance frequency 326.4 kHz, force constant $47\mathrm{N}/\mathrm{m}$, excitation frequency 326.5 kHz, oscillation amplitude 18 nm, constant amplitude feedback, set point 90%). Note the identical scale of both images.

Figure 4

(a) 2D autocorrelation function of the drift corrected STM image of monolayer graphene as shown in Fig. 3a. (b) 2D autocorrelation function of the AFM image of the ${\mathrm{SiO}}_2$ surface as shown in Fig. 3c, same color scale as in (a). (c) Fast Fourier transform high pass filtered image (1 order Butterworth, 20 nm) of the 2D autocorrelation function shown in (a). (d) Radial line sections of the unfiltered autocorrelation image (b) (black line), of the high pass filtered autocorrelation image (c) (gray line), and of the high pass filtered autocorrelation image to Fig. 3c, which is not shown (dotted line). The inset shows a larger view of the area marked by the dashed line. The black and gray graphs are offset vertically for clarity.