Imaging vibrations of locally gated, electromechanical few layer graphene resonators with a moving vacuum enclosure

TL;DR

This paper introduces a robust optical system for imaging vibrations of few-layer graphene resonators at room temperature in vacuum, providing detailed mode shape information and insights into their mechanical properties.

Contribution

It presents a simple, stable setup for room-temperature vibration imaging of 2D graphene resonators with high precision, including electrical actuation and local gating techniques.

Findings

Measured mode shapes and frequency responses of graphene resonators.

Estimated thermal expansion to conductivity ratio of the membrane.

Identified local suppression of vibrations due to membrane folds.

Abstract

Imaging the vibrations of nanomechanical resonators means measuring their flexural mode shapes from the dependence of their frequency response on in-plane position. Applied to two-dimensional resonators, this technique provides a wealth of information on the mechanical properties of atomically-thin membranes. We present a simple and robust system to image the vibrations of few layer graphene (FLG) resonators at room temperature and in vacuum with an in-plane displacement precision of $\approx0.20$ $\mu$m. It consists of a sturdy vacuum enclosure mounted on a three-axis micropositioning stage and designed for free space optical measurements of vibrations. The system is equipped with ultra-flexible radio frequency waveguides to electrically actuate resonators. With it we characterize the lowest frequency mode of a FLG resonator by measuring its frequency response as a function of position on the membrane. The resonator is suspended over a nanofabricated local gate electrode acting both as a mirror and as a capacitor plate to actuate vibrations at radio frequencies. From these measurements, we estimate the ratio of thermal expansion coefficient to thermal conductivity of the membrane, and we measure the effective mass of the lowest frequency mode. We complement our study with a globally gated resonator and image its first three vibration modes. There, we find that folds in the membrane locally suppress vibrations.