N. Mahmoodi 1 , C. J. Anthony 1 1 University of Birmingham, School of Mechanical Engineering, Edgbaston, Birmingham, B15 2TT, UK Air Damping Simulation of MEMS Torsional Paddle Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge A MEMS torsional paddle (Figure 1) can be considered as a potential device for bio/chemical sensing [1]. The Quality Factor (QF) is inversely proportional to energy loss of the resonator and can determine the sensitivity. The effect of geometrical parameters on the behavior of the MEMS torsional resonator was investigated. It was shown that by changing these parameters the quality factor could be enhanced which consequently could have significant results on the sensitivity of the sensor. The fabrication of the resonator by Focused ion beam would be the next step to verify these results. [1] Boonliang, B. , et al. , "A focused-ion-beam-fabricated micro-paddle resonator for mass detection." Journal of Micromechanics and Microengineering 18(1), (2008) device thickness) on air damping and Quality factor of the torsional paddle are investigated using COMSOL Multiphysics® 4.4. The Fluid-Structure Interaction interface was used. 2-D model was developed. Angular displacement () = 0 sin is applied on opposite sides to produce the moment (Figure 3). Fluid is in continuum regime and classified as a laminar and incompressible fluid. Time domain analysis was performed. Figure 3. Applying angular displacement Power loss • = ( . ) Energy loss • = () 0 Quality factor • = 2 = 2 Figure 2. Steps to calculate the Quality factor ρ = . [− + µ + + . =0 −. = Figure 4. Eigenfrequency and air flow distribution around the paddle (length×width ×thickness=10×8×0.2μm 3 ),(a,b) anchors at the centre, (c,d) anchors offset from the centre. (b) (d) Q=127 Q=95 f=1.37 (MHz) f=2.01 (MHz) (a) (c) Figure 5. (a) phase difference between the damping torque and angular velocity, (b) sine and cosine components of damping torque Figure 6. (a) Damping coefficient versus angular velocity, (b) damping torque versus angular velocity 0 5E-16 1E-15 1.5E-15 2E-15 2.5E-15 0 10000 20000 30000 40000 Damping drag torque (N.m) Angular velocity (rad/s) 2.E-20 3.E-20 4.E-20 5.E-20 6.E-20 0 20000 40000 60000 Damping coefficient (N.m.s) Angular velocity (rad/s) (a) (b) L (μm) t (nm) f (MHz) T(max) (N.m) D (N.m.s) QF 1 200 2.86 8.03E-16 4.47E-20 170 2.5 200 2.01 5.31E-16 4.21E-20 127 5 200 1.47 3.48E-16 3.75E-20 105 1 500 6.33 2.36E-15 5.92E-20 712 2.5 500 4.50 1.47E-15 5.19E-20 578 5 500 3.34 9.57E-16 4.56E-20 488 Table 1. Summarized simulation results (L=anchors’ length, t=thickness, f=resonance frequency, T(max)=damping torque, D=damping ratio, Q=quality factor L (μm) t (nm) Sensitivity (Hz/fg) 2.5 (asymmetric) 200 5.58 2.5 200 8.17 2.5 500 10.88 0 1000 2000 3000 4000 5000 6000 0.E+0 2.E+6 4.E+6 6.E+6 Maximum displacement (pm) Frequency (Hz) Unloaded resonator Resonator with added mass (100 pg) Q=578 Table 2. Summarized sensitivity value for paddle Figure 7. Response curve for loaded and unloaded micro paddle -4.E-15 -3.E-15 -2.E-15 -1.E-15 0.E+00 1.E-15 2.E-15 3.E-15 4.E-15 2.22E-07 3.22E-07 4.22E-07 Damping torque(N.m) Time(s) Cos component Sin component Total damping torque -4E-15 -3E-15 -2E-15 -1E-15 0 1E-15 2E-15 3E-15 4E-15 2.22E-07 5.22E-07 8.22E-07 1.12E-06 Time (s) Angular velocity*10^-15 (rad/s) Total damping torque (N.m) (a) (b) Prediction of the QF is important for optimization and precise dynamic performance analysis of such a sensor. In this study the geometrical effect (anchors’ length, position and Introduction Figure 1. MEMS Torsional paddle Results Computational method Refrence Conclusion () −()