Micromechanical Characterization of Polysilicon Films through On-Chip Tests
<p>SEM picture of (<b>a</b>) the testing device; and close-ups of (<b>b</b>) the beam and of (<b>c</b>) the bottom-right corner of the plate.</p> "> Figure 2
<p>Rotational actuation through <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>R</mi> </msub> </semantics> </math>: experimentally-measured capacitance change with (<b>a</b>) rotational sensing and (<b>b</b>) lateral sensing.</p> "> Figure 3
<p>Lateral actuation through <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>L</mi> </msub> </semantics> </math>: experimentally-measured capacitance change with (<b>a</b>) rotational sensing and (<b>b</b>) lateral sensing.</p> "> Figure 4
<p>(<b>a</b>) Schematic of the behavior of the whole test structure in the case of lateral actuation and (<b>b</b>) close-up of the deflected micro-beam.</p> "> Figure 5
<p>Sensitivity of the pull-in voltages <math display="inline"> <semantics> <msubsup> <mi>V</mi> <mi>R</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>l</mi> <mi>l</mi> </mrow> </msubsup> </semantics> </math> and <math display="inline"> <semantics> <msubsup> <mi>V</mi> <mi>L</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>l</mi> <mi>l</mi> </mrow> </msubsup> </semantics> </math> to a variation of (<b>left</b>) over-etch <span class="html-italic">O</span> or (<b>right</b>) the polysilicon Young’s modulus <span class="html-italic">E</span>.</p> "> Figure 6
<p>Comparison between the electro-mechanical responses of two devices respectively featuring <math display="inline"> <semantics> <mrow> <msub> <mi>O</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>0</mn> <mo>.</mo> <mn>15</mn> </mrow> </semantics> </math> <math display="inline"> <semantics> <mi mathvariant="sans-serif">μ</mi> </semantics> </math>m (solid line) and <math display="inline"> <semantics> <mrow> <msub> <mi>O</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>15</mn> </mrow> </semantics> </math> <math display="inline"> <semantics> <mi mathvariant="sans-serif">μ</mi> </semantics> </math>m (dashed line), with <math display="inline"> <semantics> <mrow> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>=</mo> <mover accent="true"> <mi>E</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics> </math>.</p> "> Figure 7
<p>Evolution of the estimates of (<b>top</b>) <span class="html-italic">O</span> and (<b>bottom</b>) <span class="html-italic">E</span>, at varying filter initialization. Blue dashed lines: rotational actuation through <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>R</mi> </msub> </semantics> </math>; orange solid lines: lateral actuation through <math display="inline"> <semantics> <msub> <mi>V</mi> <mi>L</mi> </msub> </semantics> </math>. (<b>a</b>) Specimen #2, leading to consistent final estimates, and (<b>b</b>) Specimen #5, leading instead to non-consistent results.</p> "> Figure 8
<p>Specimen #2, rotational actuation case, <math display="inline"> <semantics> <mrow> <msub> <mi>ξ</mi> <mi>O</mi> </msub> <mo>=</mo> <msub> <mi>ξ</mi> <mi>E</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>75</mn> </mrow> </semantics> </math>: evolution of the PDFs of (<b>a</b>) <span class="html-italic">O</span> and (<b>b</b>) <span class="html-italic">E</span> corresponding to the evolution of estimates represented by blue curves in <a href="#sensors-16-01191-f007" class="html-fig">Figure 7</a>a.</p> "> Figure 9
<p>Specimen #2, lateral actuation case, <math display="inline"> <semantics> <mrow> <msub> <mi>ξ</mi> <mi>O</mi> </msub> <mo>=</mo> <msub> <mi>ξ</mi> <mi>E</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>75</mn> </mrow> </semantics> </math>: evolution of the PDFs of (<b>a</b>) <span class="html-italic">O</span> and (<b>b</b>) <span class="html-italic">E</span> corresponding to the evolution of estimates represented by orange curves in <a href="#sensors-16-01191-f007" class="html-fig">Figure 7</a>a.</p> "> Figure 9 Cont.
<p>Specimen #2, lateral actuation case, <math display="inline"> <semantics> <mrow> <msub> <mi>ξ</mi> <mi>O</mi> </msub> <mo>=</mo> <msub> <mi>ξ</mi> <mi>E</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>75</mn> </mrow> </semantics> </math>: evolution of the PDFs of (<b>a</b>) <span class="html-italic">O</span> and (<b>b</b>) <span class="html-italic">E</span> corresponding to the evolution of estimates represented by orange curves in <a href="#sensors-16-01191-f007" class="html-fig">Figure 7</a>a.</p> "> Figure 10
<p>Specimen #5, rotational actuation case, <math display="inline"> <semantics> <mrow> <msub> <mi>ξ</mi> <mi>O</mi> </msub> <mo>=</mo> <msub> <mi>ξ</mi> <mi>E</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>75</mn> </mrow> </semantics> </math>: evolution of the PDFs of (<b>a</b>) <span class="html-italic">O</span> and (<b>b</b>) <span class="html-italic">E</span> corresponding to the evolution of estimates represented by blue curves in <a href="#sensors-16-01191-f007" class="html-fig">Figure 7</a>b.</p> "> Figure 11
<p>Specimen #5, lateral actuation case, <math display="inline"> <semantics> <mrow> <msub> <mi>ξ</mi> <mi>O</mi> </msub> <mo>=</mo> <msub> <mi>ξ</mi> <mi>E</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>75</mn> </mrow> </semantics> </math>: evolution of the PDFs of (<b>a</b>) <span class="html-italic">O</span> and (<b>b</b>) <span class="html-italic">E</span> corresponding to the evolution of estimates represented by orange curves in <a href="#sensors-16-01191-f007" class="html-fig">Figure 7</a>b.</p> ">
Abstract
:1. Introduction
2. On-Chip Test Device: Operational Principles and Experimental Results
3. Analytical Modeling of the Test Structure
3.1. Rotational Actuation
3.2. Lateral Actuation
3.3. Sensing
4. Statistical Effects and Particle Filtering
5. Results and Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Parameter | Value | Parameter | Value |
---|---|---|---|
beam length (l) | 20 m | initial gap at capacitors () | 2 m |
beam width (h) | 2 m | a | 17 m |
out-of-plane film thickness (w) | 22 m | plate sidelength (L) | 200 m |
O (m) | E (GPa) | ||||
---|---|---|---|---|---|
Specimen # | Through | Through | Through | Through | |
1 | −0.13 | −0.13 | 138.4 | 131.8 | |
2 | −0.04 | 0.02 | 137.4 | 135.3 | |
3 | 0.03 | −0.09 | 134.3 | 151.9 | |
4 | −0.12 | −0.07 | 145.7 | 132.1 | |
5 | 0.06 | −0.13 | 130.5 | 164.2 | |
6 | 0.01 | 0.00 | 144.5 | 166.3 | |
7 | −0.14 | −0.15 | 136.5 | 130.4 | |
8 | −0.14 | −0.15 | 140.1 | 130.1 | |
9 | −0.15 | −0.15 | 159.1 | 130.1 | |
10 | −0.15 | −0.15 | 152.8 | 130.2 |
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Mirzazadeh, R.; Eftekhar Azam, S.; Mariani, S. Micromechanical Characterization of Polysilicon Films through On-Chip Tests. Sensors 2016, 16, 1191. https://doi.org/10.3390/s16081191
Mirzazadeh R, Eftekhar Azam S, Mariani S. Micromechanical Characterization of Polysilicon Films through On-Chip Tests. Sensors. 2016; 16(8):1191. https://doi.org/10.3390/s16081191
Chicago/Turabian StyleMirzazadeh, Ramin, Saeed Eftekhar Azam, and Stefano Mariani. 2016. "Micromechanical Characterization of Polysilicon Films through On-Chip Tests" Sensors 16, no. 8: 1191. https://doi.org/10.3390/s16081191