A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

• Model micro- and nanomechanical resonators displaced by their own thermal motion.
• Review the theoretical framework for describing thermomechanical systems.
• Present a recipe for measurement calibration on devices of arbitrary shape.
• Point out and correct inconsistencies in the existing literature.
• Provide an authoritative guide and reference for practitioners in this area.

We describe a general procedure to calibrate the detection of a nano/micro-mechanical resonator’s displacement as it undergoes thermal Brownian motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function, which is identical in all situations aside from a system-dependent effective mass value. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.