All-Optical Blister Test of Suspended Graphene Using Micro-Raman Spectroscopy

We report a comprehensive micro-Raman study of a pressurized suspended graphene membrane that hermetically seals a circular pit, etched in a $\mathrm{Si}/{\mathrm{SiO}}_2$ substrate. Placing the sample under a uniform pressure load results in bulging of the graphene membrane and subsequent softening of the main Raman features, due to tensile strain. In such a microcavity, the intensity of the Raman features depends very sensitively on the distance between the graphene membrane and the Si substrate, which acts as the bottom mirror of the cavity. Thus, a spatially resolved analysis of the intensity of the $G$- and $2D$-mode features as a function of the pressure load permits a direct reconstruction of the blister profile. An average strain is then deduced at each pressure load, and Grüneisen parameters of $1.8\pm 0.2$ and $2.4\pm 0.2$ are determined for the Raman $G$ and $2D$ modes, respectively. In addition, the measured blister height is proportional to the cubic root of the pressure load, as predicted theoretically. The validation of this scaling provides a direct and accurate determination of the Young’s modulus of graphene with a purely optical, hence contactless and minimally invasive, approach. We find a Young’s modulus of $(1.05\pm 0.10)\mathrm{TPa}$ for monolayer graphene, in a perfect match with previous nanoindentation measurements. This all-optical methodology opens avenues for pressure sensing using graphene and could readily be adapted to other emerging two-dimensional materials and to nanoresonators.

Figure 1

Formation of a pressurized graphene blister. (a) Sketch of a suspended graphene membrane at pressure equilibrium (upper part) and under a uniform pressure load (lower part). An optical image of a suspended graphene monolayer sealing a cylindrical pit with a radius $a\approx 4\mu \mathrm{m}$ is shown in the center left part of (a). (b) Micro-Raman spectra recorded at the center of the graphene membrane at different values of $\mathrm{\Delta }p=p_{\text{int}}-p_{\text{ext}}$.

Figure 2

Strain-induced phonon softening. (a),(b) Spatially resolved Raman maps of the $G$- and $2D$-mode frequencies recorded on the sample shown in Fig. 1, under a uniform pressure load of $\mathrm{\Delta }p=74\mathrm{kPa}$. The step size is 250 nm. The upper left part of the sample contains a supported bilayer region, where, as expected, ${\omega }_{2\mathit{D}}$ upshifts significantly. The border of the pit is represented by gray dashed circles. (c) High-resolution radial line scans of the frequencies of the $G$- (black squares) and $2D$-mode (red circles) features, recorded across the pit at $\mathrm{\Delta }p=0\mathrm{kPa}$ (filled symbols) and $\mathrm{\Delta }p=74\mathrm{kPa}$ (open symbols), with a step size of 100 nm. (d) Correlation between ${\omega }_G$ and ${\omega }_{2\mathit{D}}$ plotted for each pressure difference at four different values of $r$, ranging from $r=0\mu \mathrm{m}$ to $r=3\mu \mathrm{m}$. The solid line is a linear fit with a slope $\partial {\omega }_{2\mathit{D}}/\partial {\omega }_G=\mathrm{2.2.}$ (e) $\partial {\omega }_{2\mathit{D}}/\partial {\omega }_G$ as a function of $r$, the distance from the blister center.

Figure 3

Influence of the pressure load on the Raman scattering intensity. Maps of (a) the integrated intensity of the $G$-mode feature $I_G$ and of (b) $I_{2\mathit{D}}/I_G$, the ratio of the integrated intensities of the $2D$- and $G$-mode features recorded on the sample shown in Fig. 1, under a uniform pressure load of $\mathrm{\Delta }p=74\mathrm{kPa}$. The step size is 250 nm. The border of the pit is represented by gray dashed circles. (c) High-resolution radial line scans of $I_G$ (black squares) and $I_{2\mathit{D}}$ (red circles), recorded across the pit at $\mathrm{\Delta }p=0\mathrm{kPa}$ (filled symbols) and $\mathrm{\Delta }p=74\mathrm{kPa}$ (open symbols), with a step size of 100 nm.

Figure 4

Determination of the blister height from the Raman scattering intensity. (a) Evolution of the integrated intensities of the $G$- and $2D$-mode features measured at the center of the sample shown in Fig. 1, as a function of the pressure load $\mathrm{\Delta }p$. (b) Calculated Raman enhancement factors. (c) Raman $G$-mode intensity $I_G$ and (d) blister height $h(r)$, deduced from the data in (c), as a function of the distance from the blister center $r$ and the pressure load $\mathrm{\Delta }p$.

Figure 5

Reconstruction of the blister topography. (a) Reconstructed three-dimensional image of the pressurized blister topography at $\mathrm{\Delta }p=74\mathrm{kPa}$. (b) Blister height profile recorded at various values of $\mathrm{\Delta }p$. The error bars in (b) take into account the fact that it is not possible to give an accurate value of the height when the Raman intensity is approaching a local minimum [see Fig. 4]. The dashed lines are guides to the eye.

Figure 6

Determination of the Grüneisen parameters. Evolution of the $G$-mode (a) and $2D$-mode (b) frequencies measured at the center of the sample shown in Fig. 1, as a function of the tensile strain ${\epsilon }_p$ induced by the uniform pressure load. The straight lines are linear fits.

Figure 7

Determination of the Young’s modulus of graphene. Third power of the height of the graphene blister, $h_{\max }$, measured at its center as a function of the pressure load. Data obtained from the measurement of the $G$- ($2D$-) mode integrated intensity are shown with black squares (red circles). The straight line is a linear fit, which allows one to deduce a Young’s modulus of $E=(1.05\pm 0.1)\mathrm{TPa}$.