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.

@article{
  author = {Hauer, B. D. and Doolin, C. and Beach, K. S. D. and Davis, J. P.},
  title = {A general procedure for thermomechanical calibration of nano/micro-mechanical resonators},
  journal = {Annals of Physics},
  volume = {339},
  numpages = {27},
  pages = {181--207},
  year = {2013},
  keywords = {Thermomechanical calibration; MEMS; NEMS; Classical resonator; Damped Brownian motion}
  issn = {0003-4916},
  doi = {10.1016/j.aop.2013.08.003},
  url = {https://www.sciencedirect.com/science/article/abs/pii/S0003491613001723}
}