Molecularly Thin Polyaramid Nanomechanical Resonators

Abstract

Two-dimensional polyaramids exhibit strong hydrogen bonding to create molecularly thin nanosheets analogous to graphene. Here, we report the first nanomechanical resonators made out of a two-dimensional polyaramid, 2DPA-1, with thicknesses as small as 8 nm. To fabricate these molecular-scale resonators, we transferred nanofilms of 2DPA-1 onto chips with previously etched arrays of circular microwells. We then characterized the thermal resonances of these resonators under different conditions. When there is no residual gas inside the 2DPA-1-covered microwells, the eigenfrequencies are well-described by a tensioned plate theory, providing the Young's modulus and tension of the 2DPA-1 nanofilms. With gas present, the nanofilms bulge up and mechanical resonances are modified due to the adhesion, bulging and slack present in the system. The fabrication and mechanical characterization of these first 2DPA-1 nanomechanical resonators represent a convincing path toward molecular-scale polymeric NEMS with high mechanical strength, low density, and synthetic processability.

Figures (3)

• Figure 1: (a) Illustration of an ideal 2DPA-1 monolayer with the molecular structure shown in the inset. (b) Optical microscope image of a typical sample showing the edge of the 2DPA-1 film. Microwells are etched into the $\rm SiO_2$ layer on top of a Si substrate. A 2DPA-1 film is then transferred onto the chip through a wet process to create suspended membranes. The eight microwells on the left are not covered by the film. The scale bar is $20~\rm\upmu m$. The top right inset shows an illustration of the sample. The bottom right inset shows an AFM line scan across the edge of a 35-nm-thick film, along the white line in the corresponding image. (c) SEM images of an intact (top) and a ruptured (bottom) 35-nm-thick membrane. The suspended region is false-colored in orange, and the rest is colored in blue. The scale bar is $2~\rm\upmu m$. (d) AFM line scans through the center of 35-nm-thick circular membranes of radius $4.25~\rm\upmu m$ at atmospheric pressure. The data were taken within one hour after the membranes were removed from a high pressure chamber filled with nitrogen at $50~\rm kPa$ (red) and $100~\rm kPa$ (blue) above atmospheric pressure. Note the region adhered on the wall in the red curve.
• Figure 2: (a) PSD of displacement fluctuations of the first four modes of a membrane with $R=4.25~\rm \upmu m$ and $h=35~\rm nm$. (b) Resonance frequencies $f_{mn}$ for membranes with indicated $R$ and $h$. The lines show the theoretical frequencies of the first four modes calculated using Eq. (\ref{['eq:f_plate_tension']}). (c) Young's modulus $E$ and (d) tension $S$ of the membranes shown in (b) as a function of thickness $h$. The dashed line and the shading respectively indicate the mean and spread of data with the Young's modulus being $E=11.2 \pm 8.8~\rm GPa$. (e) Dissipation constants $f_{mn}\over Q_{mn}$ as a function of frequency for all measured modes. The shading highlights that ${f_{mn}\over Q_{mn}}\propto f_{mn}$, and the dashed line is a linear fit through the origin. (f) Quality factors $Q_{mn}$ of all measured modes as a function of 2DPA-1 thickness.
• Figure 3: (a) Illustration of a membrane at different stages of bulging. Note the time coordinate of our experiments. When $\Delta p=0$ (right), the membrane is flat at $z=0$ and stretched. For $\Delta p>0$ (middle), the membrane is adhered to the wall to position $z>0$ and bulges up by $\delta_c-z$. For $z>z_1$ (left), slack is introduced. Note that the illustration is not to scale; in the experiments, $z \ll \delta_c$. (b) Measured center deflection $\delta_c$ for a 35-nm-thick membrane with $R=4.25~\rm\upmu m$ over time. The $\delta_c=0$ line corresponds to the flat membrane at $z=0$. The inset shows interferograms at wavelengths of $440~\rm nm$ (blue), 540 nm (green), and 600 nm (red) for different $\delta_c$ as indicated by the arrows. (c) Time-dependent $\delta_c$, $f_{01}$, $z$, and tension $S$ for a 35-nm thick membrane. The shown values for $z$ are calculated from measurements. The fit for $z$ is an exponential function with two time constants, which is used to calculate the continuous curve in the frequency plot. The dashed line corresponds to the delamination length $z_1$ below which there is no slack. The total tension $S$ (blue line) is comprised of a component due to bulging (black dashed line) and one due to wall adhesion (black solid line). The shading indicates the region of slack in the membrane. (d) Experimental data (symbols) and fits (lines) for $f_{01}$ as a function of $\delta_c$ for twelve 35-nm-thick membranes, including the one in (c). The shaded regions indicate the range where slack exists in the membrane. (e) Tension components caused by bulging and wall adhesion as a function of $\delta_c$, with the symbols representing the calculated tension at $z=0$. (f) Quality factors $Q_{01}$ as a function of $\delta_c$. (g) Pressure $\Delta p$ in the regime without slack ($z\leq z_1$) as a function of $\delta_c$.