Zeptogram sensing from gigahertz vibration: Graphene based nanosensor

We develop the mathematical framework for using single layer graphene sheet as nanoscale label-free mass sensors. Graphene resonators are assumed to be in the cantilevered configuration. Four types of mass loadings are considered and closed-form equations are derived for the frequency shift due to the added mass. Using the potential and kinetic energy of the mass loaded graphene sheets, generalised non-dimensional calibration constants are proposed for an explicit relationship between the added mass and the frequency shift. These equations in turn are used for sensing the added mass. Numerical results illustrate that the sensitivity of graphene sensors is in the order of gigahertz/zeptogram. We show that the performance of the sensor depends on the spatial distribution of the attached mass on the graphene sheet.