Chapter 5. Optimization
5.3. Definition of Sensitivity Function
5.3.2. Structure Dimension Arrangement and Mechanical Sensitivity ….51
In this work, the concerned output signal OS, the signal variation ΔOS, and the external application P shown in Eq. (14) are respectively the natural frequency f0 of microbeam, the frequency shift due to one G variation, i.e. Δf(G), and the acceleration G.
The connection between f0 and Δf(G) is shown in Eq. (15), and Eq. (14) can be represented as Eq. (16).
In order to realize how the sensitivity is related to the dimension arrangement for the proof mass and microbeam, some illustrated microaccelerometers with thickness h of 20 μm and confined by the dimension arrangement of W=L+2l=6000 μm are evaluated using Eq. (16).
Δf
(
G,L,l,w)
= f(
G,L,l,w)
− f0(
L,l,w)
(15) S(
L,l,w)
≡ Δf (16)Figure 36(a) displays the result of using Eq. (16) to evaluate the sensitivity function S(L,l,w) for the illustrated microaccelerometers. It shows that, for the same length, a narrower width induces a more sensitive microbeam. However, the most important result is that, when the length l of microbeam (1500 μm) is equal to one half of the width L of proof mass (3000 μm), the microaccelerometer is most sensitive.
Figure 36(b) is a part of Figure 36(a), which shows that for microbeams having wider width w, the maximum sensitivity will decrease. It indicates that there is an inverse proportional relation between the beam width and the sensitivity.
Figurer 36 (a). Sensitivity evaluation for the illustrated microaccelerometers.
Figure 36(b). Magnifies of Figure 36(a), for microbeams with thickness ranged from 5μm to 10μm.
Figure 36. The sensitivity evaluation of microaccelerometers with thickness h of 20 μm, confined by W=L+2l=6000 μm.
0.0
In contrast to Figure 36, Figure 37 describes the maximum detectable acceleration, which is limited by the compression of Eq. (11) applied on the microbeam, and the maximum compression has to be less than the buckling loading of the microbeam in Eq.
(12). For the same length, although the wider microbeam the dopy is to respond to a small acceleration, it is able to measure a larger acceleration before buckle. In other words, when the sensitivity increases, the maximum measurable acceleration decreases.
max max M2 a
T ≅ (11) (Repeat)
2
In addition to the sensitivity consideration, it is necessary to design a proper separation between the movable proof mass and the underneath substrate to prevent the proof mass and microbeam from contacting the substrate during operation.
FEA is used to estimate the vertical displacement of proof mass due to Z-directional gravitation or acceleration. Figure 38 shows that, the displacement variation tendency of the proof mass is similar with that of the sensitivity distribution depicted in Figure 36(a), and the maximum vertical displacement of the proof mass also appeared when l equals to L/2.
0
Figure 37. The distribution of the vertical displacement of proof mass due to Z-directional gravitation or acceleration.
Figure 38. The maximum detectable acceleration for the illustrated
Vertical Displacement of Proof Mass
t
Figure 39. The dimension of the separation v is to be optimized to maximize the capacitance change ratio for the capacitor under a voltage application.
5.4. Optimization for Capacitor Dimension
When a voltage V is applied across the microbeam and the electrode pad, an electrostatic field is established, as shown in Figure 40(a), and an electrostatic force fe
[31] is generated using the hypothesis of the parallel-plate capacitor:
2
Where ε0 is the permittivity constant and Ac is the area of capacitor plate.
By static analysis, the released and movable microbeam, as shown in Figure 40(b), is attracted by the electrostatic force of per unit length qe, where
02 2
2 V
d qe ε h
= (17b)
The deflection curve y(x) of the microbeam, deflected toward to the electro pad is
( ) ( ) ( ) ( ) ( ) ( )
where two distinct separations v shown in Figure 40(b) are respectively used to separate the electrode pad from the proof mass, and from the anchor.
The original gap do between the microbeam and the electrode pad decrease to d due to the deflection y(x) caused by the electro static force qe, and accordingly the original capacitance C0 is increased to C
Where
(
l v hAccording to Eq. (17b), when the microbeam deflects toward to the electrode pad, the unit electrostatic force qe is increased corresponding to the decreasing gap d between the electrode pad and the microbeam. However, according to Eqs. (17b) and (18), under the application of a constant voltage, there should be a transformation between strain energy stored in the deflected microbeam and the work done by the electrostatic force qe. That is, an initial qe not only decrease gap between the microbeam and the electrode pad from d0 to d but also increase qe itself and the strain energy in the bent microbeam, thereby the interaction of further decreasing gap d and the increasing qe are finally equilibrium as more strain energy has been stored. However, for a small deflection, the described complex nonlinear phenomena can be simplified by assuming the unit electrostatic force qe is constant, and varying little as the gap d decreasing.
Thus, the deflection curve y(x) of the microbeam caused by the electrostatic force qe, as shown in Eq. (18), can be estimated by using the classic mechanics of material.
Under the assumption of applying a constant electrostatic force qe, the change ratio of the capacitance S(v) with respect to the separations v is defined below,
( )
From Eqs. (17) to (21), it can be concluded that the change ratio of the capacitance S(v) is not only dominated by the gap d and the applied voltage V, but also the separations v.
Figure 40(a). Voltage V is applied across the microbeam and the electrode pad, and an electrostatic field is established.
Figure 40(b). The electrostatic force qe generates and attracts the released microbeam to deflect along the y-direction toward to the electrode pad and forming a deflection curve y(x).
Figure 40. Dimension optimization for separation v.
Figure 41. The change ratio of the capacitance S(v) of the capacitor of the microaccelerometer under the application of a voltage at 10V. The length l of the microbeam is 1500μm, the separation v and gap d are respectively ranged from 0.1 l to 0.5 l and 2 to 7 μm.
Capacitance Change Ratio S(V) (%)
Ratio of Seperation v to microbeam's length l Capacitor G
ap (μm)
Capacitor Dimension Optimization
Figure 41. Shows the change ratio of the capacitance S(v), for the capacitor form by the electrode pad and the microbeam shown in Figure 40, under the application of a voltage at 10V. In this simulaiton, the length l of the microbeam is 1500 μm, which forms the one plate of the capacitor, and the separation v and the gap d are in the range from 0.1 l to 0.5 l and 2 to 7 μm, respectively. In Figure 41, the maximum change ratio of the capacitance appears around v = 0.15 l to v = 0.2 l for the given gap d. In general, S(v) increases as the gap d decreases.
5.5. Summary
To design a resonant microbeam microaccelerometer structure with highest sensitivity, a sensitivity function of geometry parameters is defined. The analytical model derived in Chapter 3 is used to evaluate the sensitivity for the proposed microaccelerometer confined by a dimension constraint. The sensitivity evaluation result reveals that, when the length l of the microbeam and the width L of the proof mass have been specified, a microbeam having a narrower width w leads to a more sensitive accelerometer, however, in case of the microbeam width w has been specified, the optimum dimension arrangement to achieve a microaccelerometer with highest sensitivity is to assign the length of microbeam equal to one half of the width of the proof mass.
Chapter 6 Discussion
6.1. Modeling and Geometry
The symmetrical and orthogonal characterizations of the structure makes the proposed microaccelerometer is able to decouple a planar acceleration into two independent components and the compactness of the proposed microaccelerometer shown in Figure 1, let a simple analytical model can be derived to represent the response i.e. the natural frequency shift of the microbeam due to the acceleration.
Microbeam with high-aspect-ratio provides itself rigidity to against the gravitation and thereby reduce the deformation due to gravitation. The largest shrinkage of the 1000 µm long microbeam before bulking is about 0.007 µm, and the response of the accelerometer structure induced by the acceleration does not cause any significant geometric deformation but a physical effect, such as the natural frequency variation of the microbeam induced by the axial force, that implies, the little deformation of the structure makes the analytical model always in coincidence with the geometry and the dimension of the microbeam. Therefore the derived model is reliable in acceleration detection.
6.2. Mechanical Sensitivity and Structural Dimension
Typically, the performance of a microaccelerometer is dominated by the designed microstructure [11, 32, 36]. That is, structural geometry, response, electrical reaction region, sensitivity and rigidity of the device are the major factors have to be concerned in designing the microstructure. In design the configuration for the proposed microaccelerometer, the structural geometry is deliberated by qualitatively complying
frequency shift of the microbeams due to the acceleration, is evaluated quantitatively by a derived model and FEA. And the most sensitive structure, the optimal dimension ratio is 1:2 for the microbeam’s length to the width of the proof mass. The maximum capacitance change ratio under a voltage application for the capacitor disposed on the sidewall of the microbeam is about v = 0.15 l to v = 0.2 l for the given gap do. In general, the capacitance change ratio increases as the gap do decreases.
6.3. Fabrication
In addition to the design considerations mentioned above, to verify the capability of manufacturing the microstructure with high-aspect-ratio, a prototype made of nickel is shown in Figures 7 and 8, which is electroplated by using SU-8 mold [10, 11].
Figure 8 demonstrates the degree of freedom of using UV-LIGA process to fabricate the high-aspect-ratio structure. This degree of freedom in fabrication is available to enlarge the capacitor area disposed on the sidewall of the microbeam along the direction of the structural height, and the capacitance is thereby increasable.
Chapter 7
Conclusion and Future works
7.1. Conclusion for Design, Fabrication and Optimization 1. The derived 1D analytical model is verified by FEA.
2. Frequency shift principle is used to get a linear response, and the largest mechanical non-linearity is about 10% FSO (Full Scale Output).
3. Structure with high-aspect ratio is used to enhance the rigidity to resist the vertical acceleration, and the vertical deformation is less than 0.05 μm under gravity.
4. Geometry symmetry can decouple a planar acceleration into two independent components. The cross-axis sensitivity is less than 0.002%, thereby the derived 1D model can be used to evaluate a 2D acceleration.
5. The optimization results show that, when proof mass’ width is twice of beam’s length, the structure is most sensitive.
6. Dimension optimization can increase the sensitivity up to 8%/G..
7. The electroploated Ni microbeam with 4 μm width show that, the adopted UV-LIGA process can meet the dimension requirement for the microbeam with 5 μm width in simultion.
7.2. Future works
1. Design - Complete the accelerometer system consisting of mechanical structure and circuit.
z Design the structure dimension according to a practical spec requirement.
z Dynamics Evaluation and Characterization (Mechanical Plant)
z Capacitance and Electrostatic Force Evaluation (ME interface)
z Design and Implement Phase Lock Loop (PLL) circuit; Controller, Electric Hardware
z Control Algorithm Development; Controller, Software or Firmware
z Test
2. Fabrication - Use SOI and Adopt DRIE with Anodic Bonding Process - NeoStones can offer this process.
0 0.1
0.2 0.3
0.4 0.57 6 5 4 3 2 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14
Capacitance (pF)
Seperation v (l ; l =1500
microns) Gap
(micron)
Original Capacitance C0
Figure 42 (b). The distribution of original capacitance Co when h=20μm.
Figure 42. The estimation of original capacitance Co.
L h l
Figure 42 (a). The dimension arrangement of the microbeam-capacitor configuration.
Figure 43 (a). Schematic diagram of driving and sensing circuit.
Figure 43 (b). Schematic diagram of PLL.
Figure 43. Schematic diagram of driving, sensing circuits and PLL.
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Acknowledgements
This dissertation is dedicated to Prof. Kan-Ping Chin, who was the first author’s adviser and initiated this research. Unfortunately, Dr. Chin passed away on February 8, 2002 (1960-2002) due to pneumonia.
Authors would like to thank Dr. S. C. Chang for his valuable suggestions on this research. Financial supports from the National Science Council of the Republic of China (Contract No. NSC88-2218-E-009-007) and the Materials Research and Development Center of CSIST (Contract No. BV89H14P) are acknowledged. The staffs at the Nano Facility Center of National Chiao Tung University are also appreciated for providing technical assistance.
Publication List Journal Paper:
1. Deng-Huei Hwang, Kan-Ping Chin, Yi-Chung Lo and Wensyang Hsu, “Structure Design of A 2D High-Aspect-Ratio Resonant Microbeam Accelerometer”, Journal of Microlithography, Microfabrication, and Microsystem. In press.
Conference Papers:
1. Deng-Huei Hwang, Kan-Ping Chin and Yi-Chung Lo, “Modeling, Optimum Design and Fabrication for a Biaxial Frequency-Shifted Microaccelerometer”, Micro System Technologies 2001, Düsseldorf, March 27-29, 2001, International Conference & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, pp. 290 ~ 302.
2. Deng-Huei Hwang, Kan-Ping Chin and Yi-Chung Lo, “On A Recipe For SU8-5 Photoresist to Fabricate The Electroplating Micromold of A Biaxial
Microaccelerometer”, Micro System Technologies 2001, Düsseldorf, March 27-29, 2001, International Conference & Exhibition on Micro Electro, Opto, Mechanical Systems and Components, pp. 567~569.
3. Deng-Huei Hwang, Yi-Chung Lo and Kan-Ping Chin, “Design considerations of the biaxial frequency-shifted microaccelerometer”, Proceeding of SPIE, Design,
Characterization, and Packaging for MEMS and Microelectronics II, Vol. 4593-15, pp. 62~71. SPIE Microelectronics and MEMS Conference, 17~19, December 2001, Adelaide, Australia.
4. Deng-Huei Hwang, Yi-Chung Lo and Kan-Ping Chin, “Development of a systematic recipe set for processing SU8-5 photoresist”, Proceeding of SPIE, Device and
Process Technologies for MEMS and Microelectronics II, Vol. 4592-14, pp.
131~139. SPIE Microelectronics and MEMS Conference, 17~19, December 2001, Adelaide, Australia.
Patent:
1. 中華民國發明專利證號：I220667, “液體噴射器製造方法(Method for
manufacturing Liquid Injector)”, 發明人：陳志明，黃鐙輝，陳昭晧，張永欣。
專利核准日期：民國93 年 9 月 1 日。
黃鐙輝之聯絡方式- Email address: