IJE TRANSACTIONS B: Applications Vol. 26, No. 11, (November 2013) International Journal of Engineering

Transcription

1 IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November International Journal o Engineering Journal Homepage: Modeling o apacitance and Sensitivity o a MEMS Pressure Sensor with lamped Square Diaphragm B. A. Ganji*, M. Shams Nateri Department o Electrical & omputer Engineering, Babol University o Technology, Babol, Iran PAPER INFO Paper history: Received 06 December 01 Recivede in revised orm 03 February 013 Accepted 8 February 013 Keywords: MEMS Modeling Displacement apacitance Sensitivity 1. INTRODUTION 1 A B S T R A T The MEMS pressure sensor is one o the best developed devices in use today. The pressure sensors are critical or advanced industrial, automotive, petrochemical, aerospace, deense, marine and water industries, meteorology, control systems and process control. Most pressure sensors rely on the piezoresistive sensing principle. However, in the past years capacitive pressure sensors have received increasing attention due to several advantages when compared to the piezoresistive sensors. The main disadvantage o the piezoresistive principle is the inherent temperature dependence o the piezoresistive coeicients. The capacitive micro machined pressure sensors have good stability, higher pressure sensitivity, and lower power consumption compared to the piezoresistive structures [1-4]. Generally, Micro-electromechanical system (MEMS capacitive pressure sensor consists o a thin, lexible conductive membrane (diaphragm as one o the electrodes that is separated rom a ixed back plate by a small air gap. In capacitive sensors, a thin diaphragm is used as a pressure sensing element [3, 5]. When the diaphragm is exposed to an external uniorm pressure the diaphragm delects causing a decrease in the air gap that results an increase in capacitance * orresponding Author baganji@nit.ac.ir (B. A. Ganji In this paper, or the irst time, the modeling o capacitance and sensitivity or MEMS capacitive pressure sensor with clamped square diaphragm is presented. In capacitive sensor the sensitivity is proportional to delection and capacitance changes with pressure. Thereore, irst the diaphragm displacement, capacitance and sensitivity o sensor with square diaphragm have been modeled and then simulated using inite element method (FEM. It can be seen that the analytical results agree with simulation. The results also show that the high sensitivity can be achieved by decreasing the diaphragm thickness and increasing its size. doi: /idosi.ije b.08 between the diaphragm and the ixed back plate. So, delection o the movable part due to applied pressure is sensed and translated into an electrical capacitance change []. The sensitivity o the capacitive sensors largely depends on the capacitance change. Hence, modeling o capacitance or exact calculation o the capacitance between the deormed diaphragm and the back plate is necessary. Understanding o capacitance changes in the structure requires more knowledge about mechanical delection o an upper electrode [6, 7]. In this paper the diaphragm displacement, capacitance and sensitivity o MEMS pressure sensor with clamped square diaphragm have been modeled. To evaluate analytical results, inite element analysis (FEA is used and compared with the analytical results.. APAITIVE SENSOR STRUTURE In general, the capacitive sensor is made o two parallel plates in between with D voltage The two plates act as electrodes o capacitors. The upper plate is usually moveable (diaphragm and the lower one is ixed (see Figure 1. The upper electrode can move with external pressure, so the capacitor between the plates will be changed. As a result, the capacitor changes are used or pressure sensing. The sensitivity o the sensor is related

2 B. A. Ganji and M. Shams Nateri / IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November to the capacitive changes. Thus, more changes cause the higher sensitivity. As mentioned earlier, the diaphragm displacement should be enhanced so that the changes o capacitor increase. The shape o the diaphragm can be circular or square. These shapes behave similarly to an applied pressure. For clamped circular diaphragm with small delection (less than 30% o its thickness the displacement is given by [9]: 3. MODELING OF APAITANE AND SENSITIVITY In this paper, or the irst time, the modeling o capacitance and sensitivity or MEMS capacitive pressure sensor with clamped square diaphragm is presented. In our previous works in reerences [5-8], two new capacitive sensors (ingerprint and microphone with square diaphragms are presented without modeling o capacitance and sensitivity. But in this work, the new equations have been extracted or calculating the capacitance and sensitivity o the capacitive pressure sensors with square diaphragm and compared with simulation results. As shown in Figure a, the capacitance between two parallel electrodes without external pressure is given by: A 0 ε0 (1 d 0 where ε 0 is permittivity, A is surace o the plate, and d 0 is distance between two plates. From the Figure b, ater applied pressure, Equation (1 cannot be used or calculating the capacitance o pressure sensor with clamped diaphragm. Figure 1. Diaphragm displacement due to applied pressure Figure. Electrodes o sensor, (a without applied pressure, (b with applied pressure pr ( r w( r ( 64D where w, r, R, and P are the delection, radial distance rom the center o the diaphragm, diaphragm radius and applied pressure respectively. D is the lexural rigidity, given by: D 3 Eh 1(1 v (3 where E, h, and ν are the Young's modulus, thickness, and Poisson's ratio o diaphragm, respectively. The central delection, w, o a lat and circular diaphragm with clamped edges and homogeneous pressure, P, can be calculated rom Equation ( with r 0: D W 64 Eh W 5.33 Eh W p R 1(1 ν R (1 ν R h where E, ν, R, and h are the Yong s modulus, the Poison s ratio, the radius and the thickness o the diaphragm, respectively. The mechanical sensitivity o diaphragm is deined as: dw S m dp The mechanical sensitivity or circular diaphragm is obtained as: w R Sm P πh Eh R v [5.33 / π (1 ] The central delection o a lat, clamped square diaphragm is given approximately by [8]. P h w h w (1 ν ˆ a h (1 ν ˆ a h E ( E ( 4 4 (7 For small delection, the mechanical sensitivity o a lat square diaphragm can be expressed as: w ˆ a Sm P πh Eh ˆ a v [4. / π (1 ] (4 (5 (6 (8 The capacitance o pressure sensor with circular diaphragm is given by [9]: 1 ε( rdrdθ (9 d w( r, θ In circular diaphragm, the displacement o the diaphragm is not aected by angle changes, thus w(r,ө in Equation (9 can be replaced with w(r. Using Equation ( in Equation (9 yields: π a ε rdrdθ pr r (10 ( 0 0 d 64D

3 1333 B. A. Ganji and M. Shams Nateri / IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November It can be written as: 1 d π a ε rdrd θ p( r R ( With assuming: r R p 64Dd u (1 8 Dd 1 P du rdr. 4 dd which (13 rdr du.4 dd (14 P and ε dd.4 d p u π R 1 dudθ ( By solving the Equation (15, the capacitance o sensor can be obtained as: D 1 r p 8πε tanh pd 8 Dd (16 By replacing D rom Equation (3 in Equation (16 we have: 3 Eh 1 r 1 p(1 v 8πε tanh 3 1 pd (1 v 8 Edh ( 17 The capacitance versus applied pressure is generally nonlinear due to the nonlinear delection o the diaphragm. The sensitivity o the pressure sensor can be deined and calculated as ollowing: ε1(1 ν r Sc 3 p 49.6Ed h 6 (18 The sensor sensitivity depends on the membrane thickness, h, and electrodes distance, d, under the same pressure. The theory being valid or circular membranes is converted to the square diaphragms assuming equal areas (( aˆ π R [8]. Thus, the delection o a lat square diaphragm can be approximated by replacing R with 4â /π in the above mentioned relation or a moving square diaphragm sensor, the capacitance and sensitivity can be obtained: 4. RESULTS AND DISUSSION First, we examine the appropriate shape or the diaphragm o the pressure sensor. The capacitive structure with various shapes such as circular or square can be designed. A simulation using FEA (Finite Element Analysis method has been done or square shape with dimensions o 50 micrometer and circular diaphragm with a diameter o 50 micrometer. The diaphragm is made o is micrometer thick aluminium oil (see Figure 3. Figure 4 shows the simulation results. It can be seen that the square diaphragm has more delection than the circular one under the same load. From Figure 4, the mechanical sensitivity (dw/dp o the square diaphragm is and the circular one is Since the mechanical sensitivity o the square diaphragm is more than that o the circular one, thus, the circular diaphragm has been chosen or sensor structure. Figures 5 and 6 show the analytical and simulation results o displacement versus pressure or square and circular diaphragms, respectively. Figure 7 shows the simulated and calculated capacitance o sensor versus pressure or square diaphragm. From Figure 7, the calculated sensitivity o sensor (d/dp is , while the simulation result is It can be seen that the analytical result is very close to the simulation result. Figure 3. apacitive sensors with dierent diaphragms D 8πε tanh pd 1 a π 8 p Dd (19 a ε1(1 ν π Sc 3 p 49.6Ed h 6 (0 Figure 4. Diaphragm displacements vs. pressure or square and circular diaphragms

4 B. A. Ganji and M. Shams Nateri / IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November Figure 5. Displacement o square diaphragm vs. pressure Figure 6. Displacement o circular diaphragm vs. pressure Figure 8. Displacement o square diaphragm vs. diaphragm size Figure 9. apacitance vs. diaphragm size Figure 7. apacitance vs. pressure or square diaphragm Figure 8 shows the eect o diaphragm size on displacement. It can be seen that, by increasing the size o the diaphragm, the displacement also increases. Figure 9 shows the capacitance o sensor versus diaphragm size. As shown in Figures 9, by increasing the dimensions o the diaphragm, the capacitance has increased. Figure 10. Mechanical sensitivity o square diaphragm vs. diaphragm size Figure 10 shows the mechanical sensitivity and Figure 11 shows the sensor sensitivity with square diaphragm versus dimension. As shown in Figures 10 and 11, by increasing the dimension o diaphragm, the sensitivity has been increased. Figure 1 shows the displacement o square diaphragm versus diaphragm

5 1335 B. A. Ganji and M. Shams Nateri / IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November thickness. As can be seen in Figure 1, the thinner diaphragm causes more displacement. However, by reducing too much the thickness o diaphragm, maybe has been too bended and broken. Figure 11. Sensor sensitivity vs. diaphragm size Figure 1. Displacement o square diaphragm vs. diaphragm thickness Figure 14. Mechanical sensitivity o square diaphragm vs. diaphragm thickness Figure 15. Sensor sensitivity vs. diaphragm thickness The eect o diaphragm thickness on capacitance is shown in Figure 13. It can be seen that, the high capacitance is related to the thinner diaphragm. The eect o diaphragm thickness on sensitivity are shown in Figures 14 and 15. As shown in Figures 14 and 15, the high sensitivity is related to the thinner diaphragm (0.5 μm. Thus, to have a high sensitivity, the diaphragm size should be increased and thickness decreased. It can be seen that the analytical results is very close to the simulation results. 5. ONLUSION Figure 13. apacitance vs. diaphragm thickness In this paper, the modeling o capacitance and sensitivity o a MEMS pressure sensor with square diaphragm have been presented, or the irst time. The sensor consists o a ixed back plate, air gap and lat square diaphragm. The diaphragm can be delect by external pressure which causes the capacitance to change. In this paper a new equation is suggested or calculating the capacitance o sensor with square clamped diaphragm and its accuracy is veriied with

6 B. A. Ganji and M. Shams Nateri / IJE TRANSATIONS B: Applications Vol. 6, No. 11, (November MEMS simulation tool (Intellisuite using inite element method. The results show that the theoretical results in good agreement with the simulation. The results also show that as the diaphragm size increases or its thickness decreases, the diaphragm delection, and capacitance will be increased under the same load. 6. REFERENES 1. Pedersen, T., Fragiacomo, G., Hansen, O. and Thomsen, E. V., "Highly sensitive micromachined capacitive pressure sensor with reduced hysteresis and low parasitic capacitance", Sensors and Actuators A: Physical, Vol. 154, No. 1, (009, Zhou, M.-X., Huang, Q.-A., Qin, M. and Zhou, W., "A novel capacitive pressure sensor based on sandwich structures", Journal o Microelectromechanical Systems, Vol. 14, No. 6, (005, Zhang, Y., Howver, R., Gogoi, B. and Yazdi, N., "A highsensitive ultra-thin mems capacitive pressure sensor", in Solid- State Sensors, Actuators and Microsystems onerence (TRANSDUERS, 16th International, IEEE. (011, Rahman, M. M. and howdhury, S., "Square diaphragm cmut capacitance calculation using a new delection shape unction", Journal o Sensors, Vol. 011, ( Ganji, B. A. and Majlis, B. Y., "Fabrication and characterization o a new mems capacitive microphone using perorated diaphragm", International journal o Engineering, Vol., No., (009, Ganji, B. A. and Nateri, M., "Fabrication o a novel mems capacitive microphone using lateral slotted diaphragm", International Journal o Engineering-Transactions B: Applications, Vol. 3, No. 3&4, (010, Ganji, B. A. and Nateri, M. S., "A high sensitive mems capacitive ingerprint sensor using slotted membrane", Microsystem Technologies, Vol. 19, No. 1, (013, Ganji, B. A. and Majlis, B. Y., "Analytical analysis o lat and corrugated membranes or mems capacitive sensors", International Journal o Nonlinear Dynamics Engineering Science, Vol. 1, No. 1, (008, Timoshenko, S., Woinowsky-Krieger, S. and Woinowsky, S., "Theory o plates and shells", McGraw-hill New York, Vol., (1959. Modeling o apacitance and Sensitivity o a MEMS Pressure Sensor with lamped Square Diaphragm B. A. Ganji, M. Shams Nateri Department o Electrical & omputer Engineering, Babol University o Technology, Babol, Iran PAPER INFO چکیده Paper history: Received 06 December 01 Recivede in revised orm 03 February 013 Accepted 8 February 013 Keywords: MEMS Modeling Displacement apacitance Sensitivity در این مقاله براي اولین بار مدل سازي خازن و حساسیت حسگرهاي خازنی با دیافراگم مربعی چهار طرف ثابت اراي ه شده است. حسگر خازنی داراي دو الکترود موازي میباشد که معمولا یک الکترود قابلیت جابهجایی بر اثر اعمال فشار را دارد. تغییرات خازنی که پارامتر اصلی در عملکرد این گونه حسگرهاست بر اساس جابهجایی همین الکترود ایجاد میشود. در حسگرهاي خازنی حساسیت متناسب با تغییرات خازن بر حسب فشار است و بنا بر این ابتدا جابهجاي ی دیافراگم ظرفیت خازن و حساسیت حسگر مدل سازي و سپس با استفاده از روش اجزاء محدود شبیه سازي شدهاندکه نتایجشان بسیار نزدیک به هم هستند. نتایج همچنین نشان میدهند که با کاهش ضخامت دیافراگم و افزایش اندازهي آن حساسیت حسگرافزایش مییابد. doi: /idosi.ije b.08