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.
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