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Analysis and analytical modeling of static pull-In with application to MEMS-based voltage reference and process monitoring

Publication Type:

Journal Article


(IEEE) Journal of Microelectromechanical Systems, Number 2, p.342 - 354 (2004)



hysteresis micromechanical devices modelling numerical analysis process monitoring reference circuits 100 hours 2-DOF asymmetrically operated device 5 to 10 V MEMS-based voltage reference analytical modeling analytically simulation asymmetrically driven s


The pull-in voltage of one- and two-degrees-of-freedom (DOF) structures
has been symbolically and numerically analyzed with respect to drive
mode dependence and hysteresis. Moreover, the time and temperature
stability has been investigated and tested. Modeling results have
been applied in the design of both folded-spring-suspended 1-DOF
structures and single-side-clamped 2-DOF beams with a nominal pull-in
voltage in the 5-10 V range and fabricated in an epi-poly process.
Asymmetrically driven structures reveal pull-in close to the value
predicted by the model (V/sub pi/ 1-DOF is 4.65 V analytically simulated
and 4.56 V measured; V/sub pi/ 2-DOF is 9.24 V analytically simulated,
9.30 V in FEM and 9.34 V measured). Also the hysteresis is in close
agreement (release voltage, V/sub r/, 1-DOF is 1.41 V analytically
simulated and 1.45 V measured; V/sub r/ 2-DOF is 9.17 V analytically
simulated, 9.15 V in FEM and 9.27 V measured). In symmetrically operated
devices the differences between the computed and measured V/sub pi/
and V/sub r/ are much larger and are due to process dependencies,
which make these devices very suitable for process monitoring. The
2-DOF asymmetrically operated device is the most suitable for MEMS-based
voltage reference. The stability in time is limited by charge build-up
and calls for a 100-hour initial burn-in. Temperature dependence
is -100 /spl mu/V/K at V/sub pi//spl ap/5 V, however, is calculable
and thus can be corrected or compensated.

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Research Area(s): 
Sensors and Actuators