Creating One-Dimensional Nanoscale Periodic Ripples in a Continuous Mosaic Graphene Monolayer

In previous studies, it has proved difficult to realize periodic graphene ripples with wavelengths of a few nanometers. Here we show that one-dimensional (1D) periodic graphene ripples with wavelengths from 2 nm to tens of nanometers can be implemented in the intrinsic areas of a continuous mosaic (locally N-doped) graphene monolayer by simultaneously using both the thermal strain engineering and the anisotropic surface stress of the Cu substrate. Our result indicates that the constraint imposed at the boundaries between the intrinsic and the N-doped regions play a vital role in creating these 1D ripples. We also demonstrate that the observed rippling modes are beyond the descriptions of continuum mechanics due to the decoupling of graphene’s bending and tensional deformations. Scanning tunneling spectroscopy measurements indicate that the nanorippling generates a periodic electronic superlattice and opens a zero-energy gap of about 130 meV in graphene. This result may pave a facile way for tailoring the structures and electronic properties of graphene.

Figure 1

Morphology of modulation-doped graphene. (a) A SEM image of a mosaic graphene on Cu foils. Intrinsic ($i$) and N-doped ($n$) portions can be identified by the contrast. (b) A scanning tunneling microscopy image of a mosaic graphene measured at atmosphere. The white dotted curves indicate the boundaries between the intrinsic and N-doped portions of the mosaic graphene. (c) A SEM image of mosaic graphene transferred onto a 300 nm ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate. The light blue arrow indicates the bilayer or multilayer graphene. (d) Typical Raman spectra of intrinsic and N-doped portions of mosaic graphene collected with a 514 nm incident laser. The black curve exhibited sharp $G$ and 2D Raman bands, with the ratio of $I_{2\mathrm{D}}/I_G>2$, and was identified as the intrinsic graphene. The absence of the $D$ Raman band indicates the high quality of graphene with few of the defects. In contrast, the red curve exhibited strong $D$ and $D^{\prime }$ bands with the broadening and shift of both the $G$ and 2D bands, and was recognized as the N-doped portion, indicating the lower quality of the direct growth of N-doped graphene.

Figure 2

Atomic-resolution STM images of graphene nanoripples. (a) A STM topography of a graphene sheet with nanoscale graphene ripples crossing over a copper step ($V_{\text{sample}}=0.62\mathrm{V}$ and $I=19.2\mathrm{pA}$). (b) Zoom-in topography of the white frame in panel (a) ($V_{\text{sample}}=0.62\mathrm{V}$ and $I=28.6\mathrm{pA}$). The inset is the fast Fourier transform showing the reciprocal lattice of the periodic ripples. The scale bar is $3{\mathrm{Gm}}^{-1}$. (c) Upper panel: the height profile along the dashed line in (a), lower panel: the height profile along the dashed line in (b). (d) Atomic-resolution STM image of the white frame in panel (b) ($V_{\text{sample}}=0.79\mathrm{V}$ and $I=35.8\mathrm{pA}$) exhibiting the honeycomb lattice of graphene. The atomic structure of graphene is overlaid onto the STM image.

Figure 3

(a) The theoretical length ($L_{\text{th}}$) as a function of wavelength for $A=0.2\pm 0.02\mathrm{nm}$. The $L_{\text{th}}$ is calculated according to Eq. (1) with $t=0.08\mathrm{nm}$ (red bars) and $t=0.335\mathrm{nm}$ (blue bars), respectively. (b) The theoretical lengths, experimental wavelengths, and experimental amplitudes of all the graphene nanoripples observed in our experiments. The wavelength $\lambda$ and the amplitude $A$ of the nanoscale ripples are determined from STM images in the experiments.

Figure 4

The STM image and STS of graphene nanoripples. (a) A STM topography of a periodic rippled graphene on a Cu foil ($V_{\text{sample}}=0.67\mathrm{V}$ and $I=69.4\mathrm{pA}$). (b) Tunneling spectra, i.e., $dI/dV-V$ curves, recorded at different positions, as marked by the dots with different colors in panel (a), of the graphene ripples. The spectra were vertically offset for clarity. A spectrum recorded on a flat graphene area (black curve) grown on the Cu foil is also shown for comparison.