Two-dimensional (2-D) nanomechanical resonators are interesting for the tunability of their resonant frequencies over wide frequency ranges using electrical means. These resonators are often made by transferring thin membranes of layered materials onto cavities fabricated in oxidized silicon wafers. The resonant frequency of vibrational modes is tuned by applying a dc voltage between the membrane and the silicon substrate acting as a global gate, which creates an electrostatic force that pulls the membrane towards the global gate and changes the strain within the membrane. Here, we measure the frequency response of 2-D resonators based on few-layer graphene transferred onto cavities milled in silicon oxide using focused ion beam (FIB) lithography. In response to a step in gate voltage, we find that resonant frequencies of vibrational modes decay in time. To explain this phenomenon, we propose that residual gallium ions from the ion beam form a floating gate at the bottom of the cavity and create a weak link between this floating gate and the graphene membrane. Leakage of charges between graphene and the floating gate lowers the strain induced by the voltage applied between graphene and the gate electrode, making the resonant frequency of the graphene membrane decay. We present a model based on a floating gate structure to effectively explain the decay of graphene resonant frequency in our device.
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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.