Experimental Adhesion Energy in van der Waals Crystals and Heterostructures from Atomically Thin Bubbles

The formation of gas-filled bubbles on the surface of van der Waals crystals provides an ideal platform whereby the interplay of the elastic parameters and interlayer forces can be suitably investigated. Here, we combine experimental and numerical efforts to study the morphology of the bubbles at equilibrium and highlight unexpected behaviors that contrast with the common assumptions. We exploit such observations to develop an accurate analytical model to describe the shape and strain of the bubbles and exploit it to measure the adhesion energy between a variety of van der Waals crystals, showing sizable material-dependent trends.

Figure 1

(a) Sketch of the top-down approach: A 2D material is deposited onto another crystal and contaminants remain trapped in between; the contaminants coalesce to form a bubble. (b) Sketch of the bottom-up approach: A bulk crystal is irradiated with H ions that penetrate through it; molecular hydrogen forms and coalesces. Two exemplifying AFM images of ${\mathrm{MoS}}_2/\text{hBN}$ heterostructured bubbles (a) and ${\mathrm{WS}}_2/{\mathrm{WS}}_2$ homostructured bubbles (b) are shown.

Figure 2

(a) Experimental profiles of three bubbles (1, ${\mathrm{WS}}_2$; 2, ${\mathrm{WSe}}_2$; 3, ${\mathrm{MoTe}}_2$), fitted by Eq. (1) (orange lines). (b) Numerical calculations of the constant $q$ in Eq. (1) vs $h_0/R$. The black dots concern ${\mathrm{MoS}}_2$, while the gray-shaded area embeds other 2D materials (${\mathrm{MoSe}}_2$, ${\mathrm{MoTe}}_2$, ${\mathrm{WS}}_2$, ${\mathrm{WSe}}_2$, ${\mathrm{WTe}}_2$, hBN, and graphite). The orange-shaded areas highlight the range of aspect ratios measured experimentally in 2D-material bubbles. (c) Radial dependence of the circumferential (${ϵ}_{\theta }$) and radial (${ϵ}_r$) in-plane strain components (sketched as insets), derived by the Raman data, calculated by FEM-numerical calculations and calculated via Eqs. (2). All the strain values were normalized to the numerical strain at the center (${ϵ}_c^{\mathrm{num}}$).

Figure 3

(a) Histograms of the aspect ratios (left) and corresponding $h_0$ vs $R$ values (right) measured in homostructured bubbles. (b) $h_0/R$ values (top; the lines are average values) and corresponding $h_0$ vs $R$ plots (bottom) obtained for heterostructured bubbles. (c) Adhesion energies obtained via Eq. (12), as listed in Supplemental Note 7. The open symbols refer to aspect ratios measured in other works.