Predictions of the Compressible Fluid Model and its Comparison to Experimental Measurements of Factors and Flexural Resonance Frequencies for Microcantilevers

Jason Jensen,Martin Hegner

doi:10.1155/2012/258381

Abstract

The qualitative agreement between experimental measurements of the factors and flexural resonance frequencies in air of microcantilevers and calculations based on the compressible fluid model of Van Eysden and Sader (2009) is presented. The factors and resonance frequencies observed on two sets of cantilever arrays were slightly lower than those predicted by the model. This is attributed to the individual design and geometry of the microfabricated hinged end of the cantilever beams in the array.

Highlights

The introduction of the atomic force microscope [1] and the improvement of silicon fabrication technologies resulted in the ready availability of high-quality, reproducible, and inexpensive silicon cantilevers
Van Eysden and Sader’s extended viscous [18] and compressible fluid models [20] were used to predict the resonance frequency and Q factor of modes of the 7 μm thick cantilevers which were below 2 MHz and the modes of the 2 μm thick cantilevers below 1 MHz
It is clear that the experimental data agrees qualitatively with the predictions of the compressible fluid model of Van Eysden and Sader, but that absolute quantitative agreement is not demonstrated here

Summary

Introduction

The introduction of the atomic force microscope [1] and the improvement of silicon fabrication technologies resulted in the ready availability of high-quality, reproducible, and inexpensive silicon cantilevers. Applications for micron-scale cantilevers as a sensing tool have been found in the fields of genomics [2,3,4,5,6], proteomics [7,8,9], microbiology [10,11,12,13,14], and many others. Many of these applications make use of the microcantilever as a sensitive mass detector. It has been shown that operating the cantilever at higher resonance modes increases the mass sensitivity of the device [15]. Models indicating the dynamics of the cantilever are useful when planning such experiments and determining the expected minimum response required for successful detection of the target

Methods

Results

Conclusion