TWO SEGMENTS CANTILEVER BEAM MASS SENSOR WITH CAPACITIVE ACTUATION AND READOUT
Gabriel Vidal Álvarez
NiPS Workshop: Noise in dynamical systems at the micro and nanoscale, August 6‐8, 2010
MEMS Applications 2
Sensors (Pressure, acceleration, mass, etc.) Actuators (DLP, inkjet printers, etc.) RF Applications (Oscillators, filters, etc.) Energy harvesting
Mass Sensing 3
Dynamic mass sensing is based on the measure of the frequency shifts in the resonant frequencies of a mechanical structure due an added mass.
Mass Sensing
Responsivity
Sensitivity
Dynamic Range
4
Frequency resolution
Mass resolution
Mass Sensing 5
State of the art
Quartz crystals microbalances have very good noise performance
MEMS mass sensors have ultrasmall mass sensitivities
6
State of the art
Mass of a gold atom ≈ 0.327 zg Mass of an hydrogen atom ≈ 0.00166 zg
7
Mass Sensor Type of Mass Sensor and Experimental
Condi6ons Mass Resolu6on (zg)
Jensen 2008 Double-‐walled carbon nanotube can0lever beam in ultra high vacuum and at room temperature
0.13
Yang 2006 Magnetomo0ve driven and detected cc-‐beam
opera0ng in high vacuum and at 4.7 K 7
Ekinci 2004 Magnetomo0ve driven and detected cc-‐beam opera0ng in ultra high vacuum and at 17 K
2530
Verd 2008 Capaci0ve driven and detected CMOS metal
can0lever beam in air and at room temperature 24000
Lavrik 2003 Photothermal actuated and interferometric readout silicon can0lever opera0ng in air at room temperature and atmospheric pressure
5500000
The idea
First segment as transducing part
8
Second segment as sensing part
Euler-Bernoulli Beam Theory 9
Energetic approach to model beam-like structures
Euler-Bernoulli equation
Two Segments Cantilever Beam Mass Sensor Mechanical Behaviour
10
Two Segments Cantilever Beam Mass Sensor Mechanical Behaviour
11
Two Segments Cantilever Beam Mass Sensor Mechanical Behaviour
12
Two Segments Cantilever Beam Mass Sensor Mechanical Behaviour
13
Two Segments Cantilever Beam Mass Sensor Mechanical Behaviour
14
Choosing the appropriate ratio between segments, the two segments cantilever beam improves the sensitivity of the first segment standalone.
The maximum attainable sensitivity is a little bit lower than the attainable with the second segment acting independently.
MEMS Modeling 15
MEMS Modeling 16
Capacitive Transduction 17
Capacitive Transduction 18
Two-Port configuration
Noise in MEMS 19
Thermomechanical noise is related to the Brownian motion of the molecules surrounding the mechanical structure of the MEMS device
Noise in MEMS 20
Phase noise
Two Segments Cantilever Beam Mass Sensor
21
Mass Sensor Mechanical Sensi6vity
(zg/Hz) Two-‐Port Sensi6vity (zg/
Hz) Frequency Resolu6on (Hz) Mass Resolu6on (zg)
Two Segments Can?lever Beam
1.15 6.07 0.01 0.05
First Segment Standalone Can?lever Beam
1687.52 8881.7 0.0002 1.54
Second Segment Standalone Can?lever
Beam 1.095 5.76 0.71 4.08
Conclusions 22
With a two segments cantilever beam we can obtain very good mass sensitivities.
Thermomechanical noise has less importance for big devices than for smaller ones. The frequency resolution is better for a “big” two segments cantilever beam than for small simple cantilever beam.
In conclusion, we can attain better mass resolutions with capacitive transduction with a two segments cantilever beam than with other structures.