Unified theory of gas damping of flexible microcantilevers at low ambient pressures

Author

• Rahul Bidkar, Purdue University - Main CampusFollow
• Ryan C. Tung, Purdue University - Main CampusFollow
• Alina A. Alexeenko, Purdue University - Main CampusFollow
• Hartono Sumali, Sandia Natl Labs
• Arvind Raman, Birck Nanotechnology Center and School of Mechanical Engineering, Purdue UniversityFollow

Abstract

Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.

Keywords

Boltzmann equation; cantilevers; damping; elemental semiconductors; Knudsen flow; microfluidics; microsensors; silicon; slip flow

Citation

APPLIED PHYSICS LETTERS 94, 163117 (2009)

Date of this Version

4-20-2009

Recommended Citation

Bidkar, Rahul; Tung, Ryan C.; Alexeenko, Alina A.; Sumali, Hartono; and Raman, Arvind, "Unified theory of gas damping of flexible microcantilevers at low ambient pressures" (2009). Birck and NCN Publications. Paper 357.
https://docs.lib.purdue.edu/nanopub/357