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

TL;DR

This paper presents a comprehensive method for calibrating nano/micro-mechanical resonators through thermal motion analysis, including derivations of equations and effective mass calculations for various geometries.

Contribution

It introduces a general calibration procedure combining theoretical derivations and FEM modeling for different resonator geometries.

Findings

Derivation of PSD functions for resonator calibration

Effective mass calculations for multiple geometries

A unified approach for thermomechanical calibration

Abstract

We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal 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. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.