MEMS finals needs answer
yuanhouwang
mems_sp20_final1.pdf
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EE 446 MEMS Spring 2020: Final Exam Name:______________________________________ Student ID: _________________ Please use very brief answer for each question. Please note that the grade is decided by the accuracy instead of the length of your answer. 1.(25’) A capacitive silicon bulk-micromachined MEMS accelerometer is shown in Figure 1. It has a symmetrical Glass-Silicon-Glass sandwich structure with the four beams located in the middle. The device can sense the acceleration perpendicular to the device plane. 1). Briefly explain the working principle of the device. How does it sense acceleration? Compared to traditional design with beams located along the top surface of the silicon wafer, what is the advantage of having the beams located in the middle of the silicon wafer? 3). Assume double-side photolithography is available. That is, we can pattern and etch both sides of the device simultaneously with proper alignment. Sketch the fabrication flow chart (cross-sectional view) of the complete device (including both the silicon part and glass parts) step by step. 4). How many photolithography and etching processes do we need to fabricate the device? Assume positive photoresist is used, can you roughly sketch the patterns of four photolithography masks to be used?
Figure 1. Structure diagram of symmetrical bulk-micromachined accelerometer with beams in the
middle (a) Bulk-micromachined capacitive accelerometer. (b) Cross-section view (A–A ). 2. (25’) Research paper reading: A poly-silicon dual-axis MEMS micromirror is shown in Figure 2. It is reported in IEEE paper - Jie Wen, et al, "Analysis of the Performance of a MEMS Micromirror", IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 2, MARCH 2004 (see attached PDF file for full paper). Read the full paper carefully.
(a). View of the micromirror system
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(b). Micromirror dimensions (unit: µm). (c). Torque against angle for increasing E–W voltage
Figure 2. A poly-silicon dual-axis MEMS micromirror The electrostatic forces rotate the mirror while a restoring torque is generated by the twisting of the rectangular beams (torsion springs) which support the mirror structure. The restoring torque generated by twisting a rectangular cross-section beam is: Tmech=Kαα where Tmech is the mechanical torque at an angle α and Kα is the spring constant. For two torsional beams connected in parallel, each has length l, width w, and thickness t, the total spring constant is
3
5
192 2 1 tanh
3 2
Gwt t w K
l w t
and G is given by 2(1 )
E G
where ν (Poisson’s ratio)=0.28 for polysilicon and E (Young’s modulus) is 1.35×1011Pa for polysilicon. 1). Briefly explain the working principle of the device. How would it allow dual-axis rotation of the micromirror? What’s the name of actuation technique being used in this micromirror? 2). Based on the dimensions of micromirror design, the width, length and thickness of inner torsional beam is: w=6µm, l=20µm, t=2µm, Young’s modulus of poly-Si is E=1.35×1011Pa, Poisson’s ratio of poly-Si is ν=0.28. Based on the equations listed in the paper, calculate the torsional spring constant of the beams Kα=? If defection angle α=0.006rad, what is the restoring torque of the torsional beams Tmech=? 3). Based on result in Figure 2(c), to achieve stable deflection angle of α=0.006rad, what is the approximate E-W driving voltage Vd required? For this driving voltage, there is another deflection angle where electrical torque can balance the restoring torque. What is that deflection angle α=? Is it stable equilibrium? If driving voltage Vd=30V, is there any stable defection angle? 3.(25’) The working principle of Sanger method for DNA sequencing is explained in Figure 3. Assume original DNA sequence is X1X2X3X4TACGTTCAGCA (NOT the example sequence shown in Figure 3), where X1, X2, X3, X4 are based on the last 4 digits of your student ID. If the digit of your ID is 0, 1, 2: Xi=A; If the digit of your ID is 3, 4, 5: Xi=T; If the digit of your ID is 6, 7: Xi=C; If the digit of your ID is 8, 9: Xi=G. For example, if your student ID is 1234567, then X1X2X3X4=4567=TTCC.
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If we make the complementary copies and randomly stop at A, what are the resulted copies obtained? Please also list the different copies obtained when we make the complementary copies and randomly stop at T, C and G respectively. If we do electrophoresis for all these different DNA segments starting from the left side, please roughly sketch the bars we expect to obtain for the electrophoresis spectrum in Figure 3, and mark the corresponding DNA segment for each bar (We already show two example bars in the figure). If we read from the right-most bar, what is the sequence of the complement copy of DNA? What is the sequence of the original DNA sample inferred from the result?
Figure 3. Sanger method for DNA sequencing (example sequence used to explain the concept only)
4. (25’) An isolated RF tunable capacitor is shown in Figure 4. In the figure, the shaded and gray areas are anchored to substrate. The left driving portion and right capacitance output portion are connected by a connector, which forms an isolation bridge through a thin film oxide layer. Four folded beams support the movable mass of the device. The device is fabricated with poly-silicon surface micromachining technology. 1). Why is the connector designed in this way (i.e. SiO2 connecting two poly-Si parts together)? List the two functions of this connector. 2). Assume there are totally Nc fixed fingers in the right portion (capacitance output portion), the capacitance output would be:
d
tLN C ovc
2
In it, ε is dielectric constant of air, ε=8.85×10-12F/m, t is device thickness, Lov is the overlap length between movable and fixed fingers, d is the capacitance gap. Assume we have Nc=160, t=3µm, d=2µm, Lov=100µm in static mode when there is no displacement of the movable mass, what is the static capacitance output C0? 3). Assume for each section of the folded beam, the beam width Wb=2μm, length Lb=2XYμm, (where XY is the last two digits of your student ID. For example, if your student ID is 1234567, then Lb=267µm), thickness tb=3μm. The Young’s modulus of poly-Si: E=1.70×1011Pa. Find out the total spring constant Ktot of the whole device. 4). If we apply variable driving voltage V0 on movable driving fingers, but set the voltages on left and right fixed driving fingers as –VA and VA (constant voltages) separately. The electrostatic driving forces F1 (F2) along left (right) directions can be calculated as:
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d
VVtN F Ad
2
)(2 1
2 0
,
d
VVtN F Ad
2
)(2 2
2 0
.
In them, Nd is the number of left/right fixed driving fingers, t is device thickness, d is capacitance gap. Prove that the capacitance change ΔC will be in linear (instead of quadratic) relationship (with the driving voltage V0. If for driving part, Nd=200, t=3µm, d=2µm, VA=20V, in order to have output capacitance change ΔC=(1/3)C0, what should be the driving voltage V0 applied?
(a). MEMS variable capacitor (b). SEM photo of connector
Figure 4. MEMS variable capacitor device
