Engineering Mechanical Engg Design and … and Simulation of a... · Engineering Mechanical Engg...

VFSTR Journal of STEM Vol. 01, No. 01 (2015) xxxx-xxxx

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Engineering Mechanical Engg

Design and Simulation of a Capacitive Micro Bridge Type Accelerometer for μg Applications S. S. A. Hasanth Pulavarthy1, B. Ramamoorthy2,* 1Ashok Leyland, Chennai, M.Tech IIT-M, India. 2Rector, Vignan’s Foundation for Science, Technology and Research University (VFSTR Univ. VIGNAN UNIVERSITY), Vadlamudi, Guntur 522 213 Andhra Pradesh, INDIA.

*Corresponding Author: Tel.: +91-863-234-4700 Ext.: 401 Fax: +91-863-253-4468 E-mail: [email protected]

ARTICLE HISTORY

Received 1 August 2015

Revised 20 September 2015

Accepted 25 September 2015

Available online 1 October 2015

GRAPHICAL ABSTRACT

ABSTRACT The objective of this work is to simulate the mechanical behaviour of two different types of precision μg micro electromechanical systems (MEMS) accelerometers and determine the optimal design of capacitive micro bridge type accelerometer by comparing their performance as a function of their respective displacements and stresses. The structure of the accelerometer consists of a proof mass which is suspended by tether beams between fixed rigid electrodes to provide differential capacitance measurements. The analysis of displacement and stress of the accelerometers have been performed in FEM simulation software COMSOLTM. The limitations of one of the models, i.e., the two beam accelerometer have been discussed and one of the possible solutions, i.e., the four beam accelerometer has been discussed in detail. Sensitivity analysis has been presented for the aforementioned accelerometers. The process flow diagrams for the fabrication of the final model of the accelerometer have been simulated in IntellisuiteTM . Results of the simulation and analysis show that the two beam accelerometer proved to be more sensitive than its four beam counterpart. However, the four beam accelerometer proved to be mechanically stable. The four beam accelerometer is also subjected to lower stresses and it has linearity over the entire operational range where as the two beam accelerometer is subjected to higher stresses and also has non linearity when the entire operational range is considered.

Keywords: MEMS; Capacitive Accelerometer; Displacement; Stress; Sensitivity; COMSOL TM; IntellisuiteTM .

© 2015 VFSTR Press. All rights reserved XXXX-XXX | http://dx.doi.org/xx.xxx/xxx.xxx.xxx |


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1. INTRODUCTION

Micro electromechanical Systems (MEMS) is the integration of mechanical elements, sensors, actuators, and electronics on a common silicon substrate through micro fabrication technology. MEMS technology can be implemented using a number of different materials and manufacturing techniques; the choice of which will depend on the device being created and the market sector in which it has to operate. These devices generally integrate signals from one physical domain to another, such as mechanical to electrical, electrical to mechanical, electrical to chemical (Stephen Beeby et al, 2004). A key contribution of the development of MEMS technology is that it has enabled the integration of sensors, actuators and signal processing on a single chip (Eddy et al, 1998), and their integration has positive effects upon performance, reliability and cost. The ability to integrate actuators on chip leads to the possibility of new distributed control systems (Frank et al, 2000). The performance of MEMS sensors being superior to macro sensors in terms of resolution and maximum frequency, make them viable for their usage as a variety of commercial MEMS sensors, such as accelerometers and pressure sensors. The low manufacturing costs and small package size also play a major role in the success of these devices (Bell et al, 2005). Single-crystal silicon is being increasingly employed in a variety of new commercial products not because of its well established electronic properties, but rather because of its excellent mechanical properties (Petersen, 1982). It is mechanically stable and it can be integrated into electronics on the same substrate. Silicon is almost an ideal structural material. It has about the same Young’s modulus as steel (about 2 x 105 MPa), but is as light as aluminum, with a mass density of about 2.3 g/cm3. Materials with a high Young’s modulus can better maintain a linear relationship between applied load and the induced deformations. In Microsystems or MEMS, silicon needs to withstand severe

mechanical and thermal loads. It is thus important to have a good understanding of the mechanical characteristics of silicon as a structural material. 2. Design of accelerometer

Design of the sensor Acceleration is a physical quantity gaining increasing interest in many systems with regard to monitoring, control or measurement applications. In the past there have been two distinct fields of accelerometry, vibration measurement and inertial guidance and navigation. For vibration measurement, requiring low sensitivity and large bandwidth, the piezoelectric approach is optimum and there are many commercially available sensors On the other hand, accelerometers for inertial guidance and navigation, are characterized by high precision, small bandwidth and low working ranges. Two silicon based approaches are presently in a well-advanced state of development; one is of the capacitive type (Rudolf et al, 1983) and the other of the piezo resistive type. While the fabrication costs of the two approaches are very similar, the capacitive approach has the advantage of higher stability, high reliability, lower power consumption, lower non-linearity, lower noise, lower temperature coefficients, higher overload resistance and gives a much higher sensitivity and resolution, reliability as well as low drift (Boser, 1996). Capacitive MEMS sensors are widely preferred in consumer applications due to their high performance and low cost. In this paper two different models of accelerometers are analyzed. The structure of either of the two accelerometers consists of three-layers, i.e., a bottom silicon layer (bottom electrode) adhering to the substrate, a top silicon layer (top electrode) also adhering to the substrate, and a middle layer of silicon suspended by tether beams (proof mass supported by tether beams). The middle layer, with the top and bottom layers respectively, forms two capacitors. When subjected to acceleration, the middle layer is deflected. This


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motion results in change in capacitance for both capacitors, generating a differential output signal. Two Beam Accelerometer A two beam accelerometer is shown in Fig.1. It consists of a proof mass suspended by two tether beams, along with a top electrode and a bottom electrode. The dimensions of the accelerometer are given in Table 1. Fig.1. Model of the two beam accelerometer

Geometry dimension / Properties

Two beam model

Width of the beam (μm) 250

Length of the beam (μm) 700

Thickness of the beam (μm)

50

Width of the mass (μm) 2500

Length of the mass (μm) 2500

Thickness of the mass (μm)

500

Distance between electrodes (μm)

50

Free space permittivity (F/m)

8.8541878 x 10-12

Young modulus (Pa) 1.7 x 1011

Specific mass of material (kg/m3)

2230

Table.1. Parameters used for the two beam accelerometer

Fig.2. Meshed model of the two beam accelerometer The accelerometer is meshed fine in COMSOL as shown in Fig.2 and a point load equal to the magnitude of the subjected acceleration is applied at the midpoint of the top face of the proof mass. The two tether beams are fixed in all degrees of freedom. A voltage of 5V is applied to the top electrode while maintaining the bottom electrode as ground. The behaviour of the accelerometer is studied in the vibration range of 10μg - 60μg and the results are presented in Tables 3 – 6. The graphs are plotted and are shown in Figs. 26 – 29. Four beam accelerometer A four beam accelerometer is shown in Fig.3. It consists of a proof mass suspended by four tether beams, along with a top electrode and a bottom electrode. The dimensions of the accelerometer are given in Table 2.

Fig.3. Model of the four beam accelerometer


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Geometry dimension / Properties

Two beam model

Width of the beam (μm) 250

Length of the beam (μm) 700

Thickness of the beam (μm)

50

Width of the mass (μm) 2500

Length of the mass (μm) 2500

Thickness of the mass (μm)

500

Distance between electrodes (μm)

10

Free space permittivity (F/m)

8.854 x 10-

12

Young modulus (Pa) 1.7 x 1011

Specific mass of material (kg/m3)

2230

Table.2. Parameters used for the four beam accelerometer Fig.4. Meshed model of the four beam accelerometer The accelerometer is meshed fine in COMSOL as shown in Fig.4 and a point load equal to the magnitude of the subjected acceleration is applied at the midpoint of the top face of the proof mass. The four tether beams are fixed in all degrees of freedom. A voltage of 5V is applied to the top electrode while maintaining the bottom electrode as ground. The behaviour of the accelerometer is studied in the vibration

range of 10μg - 60μg and the results are tabulated in Tables 7 – 10. The graphs are plotted and are shown in Figs. 30 – 33. Simulation of fabrication of the accelerometer

(a) (b) (c) Fig.5 (a) Mask 1 (b) Mask 2 (c)Mask 3, modeled in Intellisuite Surface micromachining is used for realization of the proof mass where as bulk micromachining is used for realization of the tether beams. The masks required for realization of the accelerometer have been modeled in IntellisuiteTM as shown in Fig. 5, and the process steps required for realization for the fabrication of the accelerometer are shown in Fig. 6.

Fig.6 Process flow steps followed for realization of the four beam accelerometer

Signal Processing of the accelerometer The differential capacitance accelerometer works on the principle of complementary changes of two capacitors with acceleration. For the two beam accelerometer shown in Fig.1, these changes are above and below the nominal


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capacitance whose typical value is 13.17 pF. The maximum capacitance change with full-scale excitation is about 8.83 pF. For the two beam accelerometer shown in Fig.3, these changes are above and below the nominal capacitance whose typical value is 32.93 pF. The maximum capacitance change with full-scale excitation is about 25.7 pF. These small values of capacitance are critical for capacitance to voltage conversion schemes as the parasitics are introduced while integration with signal conversion electronics and packaging. A high input impedance inverting operational amplifier with feedback capacitor configured as charge amplifier can be used for capacitance to voltage conversion. The circuit is as shown in Fig. 7. The output voltage is made proportional to the total change in the differential capacitance. The common plate/ electrode connected to inverting input of the Op-amp and the other two terminals of the sensor are applied with square wave out of phase with each other. The feedback capacitor value determines the sensitivity of the unit (Boser, 1996). Fig.7. Signal condition circuit for four beam accelerometer 3. Results and Discussion

Two beam accelerometer

Displacement Analysis

Fig.8. Displacement of proof mass when subjected to an acceleration of 10μg along Z axis When the two beam accelerometer is subjected to an acceleration of 10 μg the maximum displacement of the proof mass is obtained as 7.604 μm as shown in fig. 9. The nominal value of the capacitance can be calculated as given below (Beeby, 2004): Hence the differential change in capacitance can be obtained as: When the proof mass deflects by a displacement of ‘x’ (μm), the capacitance changes as given below: Now the differential change in capacitance can be obtained as: In this case, x = 7.604 μm, d= 50 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 4.10 pF. The ratio

(12)

(2)

(1)

(3)

(4)


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∆C/C is about 0.311. The sensitivity of the accelerometer is about 31123.77. Fig.9. Displacement of proof mass when subjected to an acceleration of 20μg along Z axis When the two beam accelerometer subjected to an acceleration of 20 μg the maximum displacement of the proof mass is obtained as 15.21 μm as shown in fig. 9. In this case, x = 15.21 μm, d= 50 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 8.33 pF. The ratio ∆C/C is about 0.670. The sensitivity of the accelerometer is about 33523.16. Fig.10. Displacement of proof mass when subjected to an acceleration of 30μg along Z axis When the two beam accelerometer subjected to an acceleration of 30 μg the maximum displacement of the proof mass is obtained as

22.81 μm as shown in fig. 10. Ideally this should be one-third of the nominal gap between the electrodes (i.e., atmost 16.67 μm). Since this condition has been violated, the capacitance values obtained are not considered since it leads to non linear behavior of the accelerometer. Thus the operational range of the two beam accelerometer is confined to 10 μg – 20 μg. Stress Analysis Stress analysis has been carried out in the finite element simulation software COMSOLTM by giving acceleration as input within the aforementioned range as an input and the results are presented in Figs. 11 -13. Fig.11. Stress on sensor when subjected to an acceleration of 10μg along Z axis Fig.12. Stress on proof mass when subjected to an acceleration of 20μg along Z axis


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Fig.13. Stress on proof mass when subjected to an acceleration of 30μg along Z axis Four beam accelerometer

Displacement Analysis

Fig.14. Displacement of proof mass when subjected to an acceleration of 10μg along Z axis When the four beam accelerometer is subjected to an acceleration of 10 μg the maximum displacement of the proof mass is obtained as 1.147 μm as shown in fig. 14. The nominal value of the capacitance and the value of differential change in capacitance are calculated using the equations (1) to (4) mentioned earlier. In this case, x = 1.147 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 3.79 pF. The ratio ∆C/C is about 0.115. The sensitivity of the accelerometer is about 11510.16.

Fig.15. Displacement of proof mass when subjected to an acceleration of 20μg along Z axis When the four beam accelerometer is subjected to an acceleration of 20 μg the maximum displacement of the proof mass is obtained as 2.294 μm as shown in fig. 15. In this case, x = 2.294 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 8.46 pF. The ratio ∆C/C is about 0.257. The sensitivity of the accelerometer is about 12846.99. Fig.16. Displacement of proof mass when subjected to an acceleration of 30μg along Z axis When the four beam accelerometer is subjected to an acceleration of 30 μg the maximum displacement of the proof mass is obtained as 3.441 μm as shown in fig. 16. In this case, x = 3.441 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 11.68 pF. The ratio ∆C/C is about 0.355.


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The sensitivity of the accelerometer is about 11824.50. Fig.17. Displacement of proof mass when subjected to an acceleration of 40μg along Z axis When the four beam accelerometer is subjected to an acceleration of 40 μg the maximum displacement of the proof mass is obtained as 5.735 μm as shown in fig. 17. In this case, x = 5.735 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 15.95 pF. The ratio ∆C/C is about 0.625. The sensitivity of the accelerometer is about 12110.49. Fig.18. Displacement of proof mass when subjected to an acceleration of 50μg along Z axis When the four beam accelerometer is subjected to an acceleration of 50 μg the maximum displacement of the proof mass is obtained as 5.735 μm as shown in fig. 18. In this case, x = 5.735 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is

about 25.7 pF. The ratio ∆C/C is about 0.781. The sensitivity of the accelerometer is about 12494.69. Fig.19. Displacement of proof mass when subjected to an acceleration of 60μg along Z axis When the four beam accelerometer is subjected to an acceleration of 60 μg the maximum displacement of the proof mass is obtained as 6.883 μm as shown in fig. 19. In this case, x = 6.883 μm, d= 20 μm and A = 2500 μm x 2500 μm. Thus the differential capacitance obtained is about 15.95 pF. The ratio ∆C/C is about 0.484. The sensitivity of the accelerometer is about 13008.97.

Stress Analysis

Fig.20. Stress on sensor when subjected to an acceleration of 10μg along Z axis Stress analysis has been carried out in the finite element simulation software COMSOLTM by giving acceleration as input within the


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aforementioned range as an input and the results are presented in Figs. 20 - 33.

Fig.21. Stress on sensor when subjected to an acceleration of 20μg along Z axis Fig.22. Stress on sensor when subjected to an acceleration of 30μg along Z axis

Fig.23. Stress on sensor when subjected to an acceleration of 40μg along Z axis

Fig.24. Stress on sensor when subjected to an acceleration of 50μg along Z axis Fig.25. Stress on sensor when subjected to an acceleration of 60μg along Z axis Two Beam Accelerometer

Acceleration (µg)

Total deflection (µm)

10 7.604

20 15.21

30 22.81

40 30.42

50 38.02

60 45.62

Table 3. Variation of displacement with respect to applied acceleration


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Fig.26. Variation of displacement with respect to applied acceleration

Acceleration (µg) ∆C (pF)

10 0.3446

20 0.7419

30 1.2754

40 2.1376

50 3.9906

60 12.067

Table 4. Variation of change in capacitance with respect to applied acceleration

Change in capacitance Vs. Acceleration

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70

Acceleration (µg)

Chan

ge in

cap

acit

ance

(pF)

Fig.27. Variation of change in capacitance with respect to applied acceleration

Acceleration (µg) ∆C/C

10 0.31135

20 0.67031

30 1.15233

40 1.93133

50 3.60553

60 10.90260

Table 5. Variation of change in capacitance per unit capacitance with respect to applied acceleration

∆C/C Vs. Acceleration

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Acceleration (µg)

∆C

/C

Fig. 28. Variation of change in capacitance per unit capacitance with respect to applied acceleration


10 31134.803

20 33515.540

30 38411.035

40 48283.339

50 72110.589

60 181710.035

Table 6. Variation of sensitivity with respect to applied acceleration

Sensitivity Vs. Acceleration

0

50000

100000

150000

200000

0 10 20 30 40 50 60 70

Acceleration (µg)

Se

nsi

tiv

ity

Fig. 29. Variation of sensitivity with respect to applied acceleration


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Four beam accelerometer

Acceleration (µg)

Total deflection (µm)

10 1.147

20 2.294

30 3.441

40 4.588

50 5.735

60 6.882

Table 7. Variation of displacement with respect to applied acceleration

Table 8. Variation of change in capacitance with respect to applied acceleration

Fig.30. Variation of displacement with respect to applied acceleration

Acceleration (µg) ∆C (pF)

10 3.79

20 7.65

30 11.68

40 15.95

50 20.57

60 25.7

Table 9. Variation of change in capacitance per unit capacitance with respect to applied acceleration

Fig.31. Variation of change in capacitance with respect to applied acceleration

∆C/C Vs. Acceleration

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60 70

Acceleration (µg)

∆C/

C

Fig.32. Change in capacitance per unit capacitance with respect to applied acceleration


10 11510.66

20 11616.96

30 11824.5

40 12110.49

50 12494.69

60 13008.97

Table 10. Variation of sensitivity with respect to applied acceleration


10 0.115

20 0.232

30 0.355

40 0.484

50 0.625

60 0.781


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Sensitivity Vs. Acceleration

11400

11600

11800

12000

12200

12400

12600

12800

13000

13200

0 20 40 60 80

Acceleration (µg)

Sens

itiv

ity

Fig.33. Variation of sensitivity with respect to applied acceleration 4. Conclusion In the present work, simulation of a two beam capacitive accelerometer and a four beam capacitive accelerometer has been carried out. The process flow steps involved in fabrication of the accelerometers have been indicated. Based on the simulation carried out and the analysis made by subjecting the accelerometers to acceleration in the aforementioned range, the following conclusions are drawn:

The two beam capacitive micro bridge type accelerometer has 4-8 % higher differential capacitance change

The two beam capacitive micro bridge type accelerometer has 60 -70 % higher ratio of differential capacitance change to unit capacitance

The two beam capacitive micro bridge type accelerometer has 61 – 64 % higher sensitivity than its four beam counterpart.

But the four beam capacitive micro bridge type accelerometer has many advantages such as

The mechanical stability of the four beam capacitive micro bridge type accelerometer is higher compared with its two beam counterpart.

The size of the four beam capacitive micro bridge type accelerometer is 10 % smaller than its two beam counterpart.

The four beam capacitive micro bridge type accelerometer is subjected to 60 % lower stresses than its two beam counterpart.

The four beam capacitive micro bridge type accelerometer exhibits linearity in the operational range.

Thus it is observed that behaviour of the four beam capacitive micro bridge type accelerometer is better that its two beam counterpart. Hence, the four beam capacitive micro bridge type accelerometer is suggested for the detection of vibration in the aforementioned range.

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