High-Fidelity Conformation of Graphene to ${\mathrm{SiO}}_2$ Topographic Features

High-resolution noncontact atomic force microscopy of ${\mathrm{SiO}}_2$ reveals previously unresolved roughness at the few-nm length scale, and scanning tunneling microscopy of graphene on ${\mathrm{SiO}}_2$ shows graphene to be slightly smoother than the supporting ${\mathrm{SiO}}_2$ substrate. A quantitative energetic analysis explains the observed roughness of graphene on ${\mathrm{SiO}}_2$ as extrinsic, and a natural result of highly conformal adhesion. Graphene conforms to the substrate down to the smallest features with nearly 99% fidelity, indicating conformal adhesion can be highly effective for strain engineering of graphene.

Figure 1

(a) STM of ${\mathrm{SiO}}_2$-supported graphene monolayer ($195\times 178\mathrm{nm}$, $-305\mathrm{mV}$, 41 pA). (b) High-resolution NC-AFM of ${\mathrm{SiO}}_2$ ($195\times 178\mathrm{nm}$, $A=5\mathrm{nm}$, $\Delta f=-20\mathrm{Hz}$).

Figure 2

Fourier amplitude spectra of: ${\mathrm{SiO}}_2$ NC-AFM (red squares), monolayer graphene/${\mathrm{SiO}}_2$ STM (blue triangles), and under-resolved ${\mathrm{SiO}}_2$ (black dots). Spectras 1 and 2 were obtained from an averaged data set to establish statistical uncertainty, as discussed in the supporting information. Wave number is defined as ${\mathrm{\text{wavelength}}}^{-1}$.

Figure 3

Curvature histograms, normalized to unit area, for graphene (narrower distribution) and ${\mathrm{SiO}}_2$ (broader distribution).