the vacu um test ch amber at vario us pressu re levels u sing room air. At each p ressure l evel,  measurement s were p erformed to determine the  resonant frequ ency, the Q-factor, and th e drive voltag e  requi red to a chieve an end mass displacement of ±8 µm a s measured by the blur envelop e on the scale   fabricated at the tip of the beam.  

All six oscillator geomet ries were operated over the  pressure ran ge from 1  atmosph ere to  < 1.33 P a (0.01   Torr). Results of thi s testing a re summarized in Fi gure 4  (from 4). Fo r these te sts, the system was started at   atmosp heric pressure and  pumpe d down furth er between   each set of measurement s. The botto m panel of Fi gure 4   shows that the re sonant freque ncy remain s un change d  with p ressure, as expe cted. In co ntrast, the  require d  operating v oltage d ecreases substantially at lower  pressures fro m near 7 0 V at atmosp heric pressu re to less  than 5 V at around 5 Pa  (0.04 To rr). T he Q -facto r exhibits  some  int eresting characteristics with pressure. As  expecte d, the Q levels off at low pre ssures, h oweve r, this  does not occur u ntil ~1 3 Pa (0.1 Torr). Assu ming that gasdynamic dam ping would be the mai n damping  force , we  expecte d tha t almost all of the variati on with p ressure  would occur above ~130 Pa (10  Torr), whe re almo st 99%   of the air has alrea dy bee n remove d. An other surprise was  the inflection in Q-factor at ~130 Pa (10 Torr), suggesting  that some chang e in the physi cal mech anism of the   dampin g process occu rs around thi s pressure.  Figure 3.  Photogr aph of a mediu msized type oscillator dev ice. 

Based  on the results foun d in Fi gure 4,  we decided to rerun this test with on e device (P2S1 ) in order to  determi ne if it mattered  wheth er the MEMS we re bein g furth er pumped down or let up in p ressure  (vented ) between th e measurem ents. Our thin king was that  there might be  some  surfa ce friction, owing to  residual g as layers b etween the MEMS parts, in ad dition to the gas-dynami c damping. If so, we expe cted  to see some hystere sis in the Q-fa ctor as a fun ction of partial pressure, with highe r Q-val ues expe cted  durin g time s when the p ressure was being let u p compa red to when it wa s being pump ed down to a   particula r pre ssure l evel. Thus, we m ade ou r mea sureme nts in an increa sing pressu re regim e after  holdin g the MEMS pa rts und er mu ch lo wer pressure fo r an extended  period. T he increasing and  decrea sing pressure point s coin cided very well, sho wing no hyste resis. 

Other i nteresting ph enom ena were observe d on all devic es tested at pressures below 13 Pa (0.1  Torr).  The freq uency resp onse of  a given device be came a symmetri cal, with the oscill ation amplitu de falling off  much fa ster on the high fre quen cy sid e of the re sonance peak. Fu rtherm ore, very low d amping lead s to a  slow ramp -up an d ramp -down of th e displa ceme nt amplitud e when th e drive signal  is appli ed and  remove d. A d evice ta kes nearly a second to sta bilize at maximum amplitude wh en turned on.  Additionally,  if the d evice was ove rdriven such th at “pull-in ” to the fixed co mb fi ngers o ccurre d, the device  contin ued to  resonate, merely bo uncing off the fixed  fingers. T he low drive  amplitude was not sufficie nt to sho rt and  hold the m oving mass (as seen whe n overd riving normally at atmosp heric pre ssure) u ntil the drive   voltage am plitude was increased to  ~15 volts. Thi s feature could  be imp ortant for space applicatio ns of  MEMS as it is harde r to get  the device s to lock up at  the lower d riving voltage s, makin g them more robu st. 

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