Measurement of Young’s modulus via mechanical test of MEMS cantilevers
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Measurement of Young’s modulus via mechanical test of MEMS cantilevers
Tony Hyun KimApril 23, 20096.152: MEMS Presentation
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Topics to be discussed
1. Introduction1. MEMS Cantilevers, Fixed-fixed beams2. Theory of cantilever mechanics: Young’s modulus, etc.
2. Fabrication details3. Experimental setup for mechanical test4. Analysis and results
1. Young’s modulus of SiNx2. Breaking point of the fixed-fixed beam
5. Sources of error6. Conclusions
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MEMS Cantilevers and Fixed-fixed beams
Most ubiquitous structure in MEMS
Starting point for many applications: Sensors Platform for material experiments
It’s easy to build and easy to use (in principle).
Image source: Hayden, Taylor. “MEMS Analysis 2” (On 6.152 Stellar)
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MEMS Cantilevers and Fixed-fixed beams
Most ubiquitous structure in MEMS
Starting point for many applications: Sensors Platform for material experiments
It’s easy to build and easy to use (in principle).
Our experimental goals:
•Build an array of MEMS cantilevers and fixed-fixed (FF) beams.•Perform optical and mechanical verification of the devices.
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Theory of cantilever mechanics
Once the structure is built, we want to test it. i.e. perform consistency checks against literature
Image source: Schwartzman, Alan. “MEMS Analysis 1” (On 6.152 Stellar)
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The deflection of the target point (at distance L from fixed end):
Young’s modulus (E) is a material property measuring stiffness.
Theory of cantilever mechanics
ELWtkF 3
3
max 41/
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Fabrication details (1)
Silicon nitride was deposited on wafer by Scott. Thickness was measured by ellipsometry: mt )01.94.1(
SiNx
Silicon wafer
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Fabrication details (2) Silicon nitride
patterned according to mask on left.
Pattern transferred by contact lithography.
The nitride was etched by SF6/plasma.
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Fabrication details (3)
Finally, an anisotropic etch (KOH) was utilized to etch the Si bulk. Two hour etch in 80ºC KOH bath.
The <111> orientation is stable against KOH Allows for the material below the bridge to be removed first.
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Experimental Setup: Mechanical test
“TriboIndenter” in the NanoLab
Optical microscope: Position target.
Force-displacement transducer: With a blunt tip.
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Experimental Setup: Mechanical test
The spring constant is dependent on the point of application of force, L:
Can deduce Young’s modulus without L, by the above scheme
ELWtkF 3
3
max 41/
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Results: Young’s modulus The Young’s modulus was computed using the following:
“b” is the slope of k-1/3 vs. L Optically measured width (W); thickness (t) from ellipsometry
Our results are within 1 std. of published values.
33
4Wtb
E
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Sources of error in Young’s modulus determination
Geometric complications Sloped cantilevers “Effective” width smaller Undercut below the fixed-end
33
4Wtb
E
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Conclusions
Constructed MEMS cantilevers (and fixed beams) Performed a mechanical experiment using the
cantilevers Provides consistency check:
Also verifies MEMS as useful platform for doing material studies.
GPaEmeas )3183(
GPaElit )9195(
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Fixed-fixed beam analysis Model is:
Young’s modulus is directly related to the cubic coefficient.
33
4
3
340
2
862
LEWt
LEWt
LWtF
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Fixed-fixed beam analysis Young’s modulus through the cubic
coefficient a:
Significant deviation from published values.
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Fixed-fixed beam analysis Possible sources of errors to
consider: Sloped edges have huge effect on width: 6
vs. 9 um. Bridge is slanted
Force-displacement profile prefers quadratic term.
aWtLE 3
4
8