Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomic-scale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scale.

Figure 1

$3\times 3{\mathrm{nm}}^2$ NC AFM simultaneously acquired images on $\mathrm{G}/\mathrm{Pt}(111)$. (a),(b) show topography images at $\mathrm{\Delta }f=-72\mathrm{Hz}$ and $\mathrm{\Delta }f=-62\mathrm{Hz}$. The $3\times 3$ moiré pattern is marked in (a). The corresponding dissipation images are shown in (c) and (d). Parameters: $A=20\mathrm{nm}$; $V_{\text{bias}}=0\mathrm{V}$. All data were acquired with WSxM [38].

Figure 2

(a) $3\times 3{\mathrm{nm}}^2$ topographic image acquired at $\mathrm{\Delta }f=-73\mathrm{Hz}$, $A=20\mathrm{nm}$, $V_{\text{bias}}=0\mathrm{V}$. Two-dimensional plots of (b) $\mathrm{\Delta }f$ and (c) energy dissipation measured along the mapping line shown in (a) while varying the tip-sample distance are displayed. Maximum (red) and minimum (blue) in the 2D mapping correspond to maximum and minimum in the topographic image.

Figure 3

(a) DFT relaxed $\mathrm{G}/\mathrm{Pt}(111)$ structure highlighting the low and high moiré areas and the small corrugation. (b) Force vs distance curves in the attractive regime for the four sites marked in (a): top low (solid blue), top high (solid red), hollow low (dashed blue), and hollow high (dashed red). The plot shows atomic contrast on G and contrast inversion. (c) Different repulsive forces between the top-low and top-high sites for $z_t<2.25\AA$ explain the moiré contrast. Calculations on the bare Pt(111) surface for these sites (dashed lines and triangles) do not show any force difference thus signaling that the contrast is due to the sensing of the Pt substrate through the displaced C atoms [insets in panel (c)].

Figure 4

(a) A scheme of the theoretical model which includes a macroscopic and nanoscopic Pt tip, the G surface divided into a local and global area, and the Pt substrate. For different tip heights, $z_t$, (b) 2D minimization of the potential with respect to the local and global deformation and (c) energy profile versus the reaction coordinate. Heights are referenced to the equilibrium position of the G on Pt. (d) Calculated force vs distance curves for the tip approach (solid) and retraction (dashed) in moiré top-high (red) and top-low (blue) sites.