Fabrication of graphene nanomechanical resonators using focused ions beam lithography

Two-dimensional (2-D) nanomechanical resonators are based on thin layers of graphene, black phosphorus, transition metal dichalcogenides and van der Waals heterostructures. Detection of nanomechanical vibrations can be done using optical reflectometry, whereby vibrations modulate the optical reflectance of the resonator. For this type of detection to work, it is essential to fabricate cavities with a precise depth. Here we report on the fabrication of 2-D nanomechanical resonators in which the cavity is made using focused ion beam (FIB) lithography. We mill down an array of cylindrical cavities with the same diameter but different depths. We drive vibrations electrically and detect vibrations optically. At the resonant frequency of vibrations, we observe that the measured signal, which is proportional to the vibrational amplitude and to a transduction factor, is different for different cavity depths. Since all resonators have the same diameter, are made of the same graphene flake and are actuated the same way, our observation implies that the transduction factor changes with cavity depth. Using principles of thin film optics, we show that each estimated transduction factor is indeed consistent with the dimensions of the resonator, including the cavity depth, the thickness of the patterned substrate, and the number of graphene layers. This result supports the idea of using FIB to fabricate cavities for 2-D nanomechanical resonators, instead of using standard wet etching or reactive ion etching which require additional lithography steps and cannot easily be used to pattern cavities with different depths on the same substrate.