Studies on effect of geometry of a silicon based diaphragm on the sensitivity of a MEMS PARALLEL Plate Capacitive sensor used in pressure measurement

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International Journal of Electrical, Electronics and Computer Systems (IJEECS)

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ISSN (Online): 2347-2820, Volume -3, Issue-6 2015 24

Studies on effect of geometry of a silicon based diaphragm on the sensitivity of a MEMS PARALLEL Plate Capacitive sensor used in

pressure measurement

1M. Srinagesh, ²K. Durga Aparna & ³D.V.Ramakoti Reddy Instrument Technology Department, Andhra University, Vizag.

Abstract - In this paper the effect of the geometry of the silicon diaphragm used as moving plates in a Micro- electromechanical systems pressure sensor operating in harsh environments is studied. The principle of the paper is to propose a most ideally suitable geometry of the moving plate and bottom plate of parallel plate MEMS parallel plate capacitor which will have a better sensitivity when compared to the other geometric shapes of the moving plate diaphragm having the same area of cross section and thickness. The theoretical mathematical results are compared with the simulation using MEMS SOLVER software where the deflection dependency on the shape and size of the diaphragm is clearly visualized. As the sensitivity of the pressure sensor is dependent on the deflection of the moving diaphragm through the gap between the plates and the amount of deflection depends on the shape and size of the diaphragm the geometry of the diaphragm plays important role in the design of the sensor.

The proposed pressure sensor parameters are radius of the diaphragm150µm², and the thickness is 6µm and the gap between the plates is 10µm. The range of the sensor is 0- 1MPa.

Keywords- MEMS, capacitive pressure sensor, harsh environment, MEMS Solver, and diaphragm geometry.

I. INTRODUCTION

Mems pressure sensors have advantages of low cost, small size, low power consumption and high resolution.

Diaphragms are the most important parts for many mems sensors. A thin membrane serves as the sensing element in Mems pressure sensors. Pressure applied on the diaphragm deflects the membrane and this deflection is limited until the elastic force is balanced by pressure.

In order to get high sensitivity the diaphragm thickness should be thin to maximize the load deflection response.

On the other hand thin deflection under high pressure may result in large deflection and nonlinear effects that are not desirable.

The different shapes of diaphragms (square, rectangle, circular) play a significant role in operation in different applications. The purpose of this paper is to show which type of diaphragm can be chosen for specific Mems devices.

II. CIRCULAR DIAPHRAGM:

The circular diaphragm has lowest stress on its edges when applying the pressure. Largest centre deflection can be seen in the diaphragm. So, in applications where maximum deflection plays the major role circular diaphragm is suggested

For a circular shaped pressure sensor the change in capacitance due to deflection is given by

∆C = 3 1 − v² R⁴∗∈0 ∈rAsense

16ET³g² ∗ P

Where ∆c is change in capacitance, P is the pressure difference across the diaphragm, R and T are the radius and thickness of the diaphragm, E and ʋ are the Youngs modulus and Poissons ratio of the diaphragm material, A_sense is the area of the moving plates, and g is the sensing gap between the moving plate and fixed plate.

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So, here for the circular diaphragm the radius is 150µm, poissons ratio is 0.22,youngs modulus is 170Gpa,thickness is 6µm,gap between the plates is 10µm and the pressure range is from 0 to 1Mpa.

Table 1: circular diaphragm Pressure (Mpa) Sensitivity

0.1 1.5387×10^-6 0.2 3.0775×10^-6 0.3 4.6162×10^-6 0.4 6.1550×10^-6 0.5 7.6937×10^-6 0.6 9.2325×10^-6 0.7 1.0771×10^-5 0.8 1.2310×10^-5 0.9 1.3848×10^-5

No. of Vertical Elements : 8 No. of Edge Elements : 152 No of Boundary Elements : 1400 No . of Elements : 1891 Minimum Element Quality : 0.3483

MEMS TOOL USED: COMSOLMULTIPHYSICS 4.0 Courtesy: ANDHRA UNIVERSITY NPMASS CENTER, Vizag, AP

SQUARE DIAPHRAGM:

As far as the induced stress for a given pressure is concerned the square diaphragm has the highest induced stress and hence it is the preferred geometry for the pressure sensors.

For a square shaped pressure sensor the change in capacitance due to deflection is given by [2],[3]

∆c = [0.01512(1-ν²⁾ PL⁴/Eh³] [εoεrA/d²]]

Where ∆c is change in capacitance, ε is permittivity, ʋ is poisons ratio, a is area, E is youngs modulus, h is the thickness, d is the gap between the plates and P is the pressure.

So, here for the square diaphragm the poisons ratio is 0.22,youngs modulus is 170Gpa,distance between the

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plate is 10µm,thickness is 6µm and the pressure range is from 0 to 1Mpa and L is the length of the side

=266.80µm.

Pressure (Mpa) Sensitivity 0.1 1.223×10^-6 0.2 2.446×10^-6 0.3 3.670×10^-6 0.4 4.893×10^-6 0.5 6.117×10^-6 0.6 7.340×10^-6 0.7 8.563×10^-6 0.8 9.787×10^-5 0.9 0.0531x10^-5

III. RECTANGLE DIAPHRAGM:

The rectangle diaphragm is commonly used in applications as it occupy lesser area and enable easier fabrication and lithography.

For a rectangle shaped diaphragm the change in the capacitance is given by [2], [3]

∆c = [ἀ(1-ν²) Pb⁴/Eh³] [εoεrA/d²]]

Where ∆c is change in capacitance is permittivity is poisons ratio, A is area of moving plate, E is youngs modulus, h is the thickness, d is the gap between the plates and P is the pressure and b is the smaller side (width) of the diaphragm and α is the ratio of length to width of the diaphragm.

So, here for the rectangular diaphragm the poisons ratio is 0.22,youngs modulus is 170Gpa,distance between the plate is 10µm,thickness is 6µm,ἀ is 1.46 and the pressure range is from 0 to 1Mpa.

Pressure (Mpa) Sensitivity 0.1 5.534×10^-11 0.2 1.106×10^-10 0.3 1.660×10^-10 0.4 2.213×10^-10 0.5 2.767×10^-10 0.6 3.320×10^-10 0.7 3.873×10^-10 0.8 4.427×10^-10 0.9 4.980×10^-10

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No. of Vertical Elements : 8 No. of Edge Elements : 152 No of Boundary Elements : 1400

No .of Elements : 1891

Minimum Element Quality :0.3483

MEMS TOOL USED: COMSOLMULTIPHYSICS 4.0 Courtesy: ANDHRA UNIVERSITY NPMASS CENTER, Vizag, AP

l =321.21µm, b = 220µm

IV. CONCLUSION:

We have designed, simulated and analyzed the capacitive pressure sensor diaphragm with three shapes i.e circular, rectangle and square diaphragms. Among the three shapes the circular diaphragm has got the best senstivity due to ease of fabrication and low cost due to symettry and widely used for large diflections and more suitable for bio medical applications and automotive.

Square diaphragm can be used upto some extent in aeronatical applications and rectangular diaphragm can be used in biomedical applications. But from the senstivity point of view the circualr diaphragm can be used in the mems pressure applications.

REFERENCES:

[1] F. He, Q. –A. Huang, and M. Qin, “A silicon directly bonded capacitive absolute pressure sensor,” Sensors and Actuators A vol. 135, pp.

507–514, 2007.

[2] S. Timoshenko and S. Woinowsky- Krieger,

“Theory of Plates and Shells,” New York, McGraw-Hill., 1959.

[3] Y. Zhang, R. Howver, B. Gogoi* and N. Yazdi Evigia Systems, Inc., Ann Arbor, Michigan, USA “A High-Sensitive Ultra-Thin MEMS Capacitive Pressure Sensor”

[4] Prasad N Acharya Sujata Naduvinamani “Design and Simulation of MEMS based Micro Pressure Sensor”

[5] Y. Hezarjaribi, M.N. Hamidon and et.al

“Analytical and Simulation Evaluation for Diaphragm’s Deflection and its Applications to Touch Mode MEMS Capacitive Pressure Sensors”

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