Modelling the dynamics of a MEMS resonator : simulations and experiments

Nonlinearities in MEMS silicon resonators are caused by different effects. Depending on the resonator layout, different nonlinearities may be dominant in the resonator response. Based on experimental results, a modelling approach is proposed to arrive at a nonlinear dynamic model that potentially captures the observed behaviour. Apart from the model, consisting of a mechanical and an electrical (measurement) part, the effect of thermal noise is also estimated. With the proposed model, a quantitative match between the simulation and experimental results is established such that a good starting point is achieved for a more thorough modelling procedure.

[1]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[2]  J. Johnson.  Thermal Agitation of Electricity in Conductors , 1927, Nature.

[3]  Rhb Rob Fey,et al.  Long term structural dynamics of mechanical systems with local nonlinearities , 1996 .

[4]  Jon Juel Thomsen,et al.  Vibrations and Stability , 2003 .

[5]  H. Nyquist.  Thermal Agitation of Electric Charge in Conductors , 1928 .

[6]  Tomi Mattila,et al.  A 12 MHz micromechanical bulk acoustic mode oscillator , 2002 .

[7]  H. Nijmeijer,et al.  Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .

[8]  Thomas F. Fairgrieve,et al.  AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) , 1997 .

[9]  Wolfgang Sachse,et al.  Nonlinear elastic equation of state of solids subjected to uniaxial homogeneous loading , 2000 .

[10]  A. Nayfeh,et al.  Secondary resonances of electrically actuated resonant microsensors , 2003 .

[11]  Tomi Mattila,et al.  Nonlinear mechanical effects in silicon longitudinal mode beam resonators , 2005 .

[12]  Ali H. Nayfeh,et al.  Dynamics of MEMS resonators under superharmonic and subharmonic excitations , 2005 .

[13]  14 MHz micromechanical oscillator , 2002 .

[14]  Henk Nijmeijer,et al.  Nonlinear oscillations in MEMS resonators , 2006 .

[15]  H. Seppa,et al.  Nonlinear limits for single-crystal silicon microresonators , 2004, Journal of Microelectromechanical Systems.

[16]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .