Comments on the size effect on the microcantilever quality factor in free air space

This study presents a numerical approach to investigate the size effect on the quality factor associated with the first mode of microcantilever vibration in 1 atm air. The numerical simulation results are verified by experiments and compared with the approximate analytical solutions. Bulk micromachined cantilever arrays are employed as the test vehicles. Based on the experimental and numerical results, this paper proposes a modification to the existing approximate models for air damping analysis by taking into account the geometry effects of the microcantilevers. The arrived semi-empirical equation suggests that the quality factors of the microcantilevers are approximately proportional to L−1.62 and b0.62 at a low kinetic Reynolds number. Thus, the quality factor of the microcantilever resulting from the free space air can be precisely predicted for design purposes.

[1]  I. Aksay,et al.  Simultaneous liquid viscosity and density determination with piezoelectric unimorph cantilevers , 2001 .

[2]  M. Sepaniak,et al.  Cantilever transducers as a platform for chemical and biological sensors , 2004 .

[3]  Patricia M. Nieva,et al.  Air viscous damping effects in vibrating microbeams , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[4]  K. Bathe,et al.  Finite element developments for general fluid flows with structural interactions , 2004 .

[5]  Shivprasad Patil,et al.  Investigation of the electrostatic forces in scanning probe microscopy at low bias voltages , 2002 .

[6]  Gus Gurley,et al.  Short cantilevers for atomic force microscopy , 1996 .

[7]  W. Newell.  Miniaturization of tuning forks. , 1968, Science.

[8]  A. Kristensen,et al.  A micro-cavity fluidic dye laser , 2003 .

[9]  M. M. Athavale,et al.  Coupled Fluid-Thermal-Structural Simulations In Microvalves And Microchannels , 1999 .

[10]  Thomas Thundat,et al.  RESONANCE RESPONSE OF SCANNING FORCE MICROSCOPY CANTILEVERS , 1994 .

[11]  K. Najafi,et al.  An electromagnetic micro power generator for low-frequency environmental vibrations , 2004, 17th IEEE International Conference on Micro Electro Mechanical Systems. Maastricht MEMS 2004 Technical Digest.

[12]  Stefano Bianco,et al.  Silicon resonant microcantilevers for absolute pressure measurement , 2006 .

[13]  Christiane Ziegler,et al.  Cantilever-based biosensors , 2004, Analytical and bioanalytical chemistry.

[14]  M. Athavale,et al.  MULTI-DISCIPLINARY CAD SYSTEM FOR MEMS , 2001 .

[15]  H. Hosaka,et al.  DAMPING CHARACTERISTICS OF BEAM-SHAPED MICRO-OSCILLATORS , 1995 .

[16]  Hiroshi Hosaka,et al.  Theoretical and Experimental Study on Airflow Damping of Vibrating Microcantilevers , 1999 .

[17]  M. Brandl,et al.  High performance accelerometer based on CMOS technologies with low cost add-ons , 2001, Technical Digest. MEMS 2001. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090).

[18]  Derek G. Chetwynd,et al.  Investigation of a resonance microgenerator , 2003 .

[19]  Brian H. Houston,et al.  Effect of viscous loss on mechanical resonators designed for mass detection , 2006 .

[20]  J. Fluitman,et al.  Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry , 1992 .

[21]  W. Thomson.  Theory of vibration with applications , 1965 .