Nanomechanical resonators based on two-dimensional materials offer opportunities to study the mechanical properties of atomically thin membranes and to develop sensitive detection schemes. However, these applications are limited by problems with nanofabrication. In addition, graphene is a pure surface that is sensitive to contamination. It is challenging to keep graphene clean during fabrication. Here we present our graphene resonator fabrication process. We control the geometry of the cavity over which graphene is suspended to prevent the membrane from collapsing. Then we minimize the occurrence of fabrication residues on the supporting substrate and optimize the cleanliness and flatness of the interface between graphene and electrodes used for electrostatic actuation. After optimizing the fabrication of the graphene resonator, we measure the frequency response of our resonators using an optical interferometry setup. We control the resonant frequency of vibrational modes by applying a dc voltage between the membrane and an electrode patterned at the bottom of the cavity and verify that the response of our resonators is tunable over a wide frequency range.
We present a simple method to measure the width of a focused laser beam, where we define the width as the radius of the beam at which the intensity is 1/e2 of its on-axis value. Our method is based on measuring the power of light reflected off a metallized microstructure patterned on a oxidized silicon substrate that is placed on a tri-dimensional positioner. As the boundary between the microstructure and the substrate is scanned across the beam, changes in reflected power provide a quantitative measurement of the width of the beam. Our method is a useful alternative to the knife edge technique if optical measurements in transmission are not possible.
Mechanical resonators based on two-dimensional materials have gained attention for their interesting optical and mechanical properties, which translate into versatile applications such as ultrasensitive force detection and pressure sensing. Optical reflectometry is a technique of choice to measure the flexural vibrations of these resonators. The latter consists in sending normally incident monochromatic light on the resonator and measuring the intensity of reflected light, which varies as the distance d between the resonator and a nearby mirror varies. In this work we consider resonators based on suspended membranes of graphene, molybdenum disulfide and tungsten diselenide, and theoretically investigate the dependence of the reflectance R(d) of the resonator on the angle of incidence θ of the probing light. The optical response of these membranes is accounted for by their complex refractive indices. For s-polarized light, we find that R oscillates as a function of d with an amplitude that increases as theta increases. These results may help enhance the optical readout accuracy of these two-dimensional resonators.
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