A low pressure meter based on a capacitive micro sensor

Transcription

1 Available online at Physics Physics Procedia Procedia (9) (9) Proceedings of the JMSM 8 Conference A low pressure meter based on a capacitive micro sensor L. Kaabi a, *, J. Sakly a, M. Saafi b a Laboratoire Matériaux, Mesures et Application, Institut National des Sciences Appliquées et de Technologie. Centre Urbain Nord, BP : 676, Cédex 18, Tunis Cedex, Tunisia. b Department of Construction Engineering and Management, North Dakota State University, Fargo, ND, USA Received 1 January Elsevier9; use only: received Received in revised date here; form revised 31date Julyhere; 9; accepted date 31 hereaugust 9 Abstract An implementation of a low pressure meter based on a capacitive micro sensor is exposed in this paper. In the first part, we presented the analysed sensor s structure and the developed theoretical model that permits to simulate the variation of its capacitance under applied absolute pressure. Keeping in mind that the variation of the sensor s capacitance is non linear and to allow for a direct measure of applied absolute pressures in a specified range and with a specified resolution, we proposed geometrical sizes for the design of the studied sensor. From the theoretical study, we deduced a suitable model for low pressure measurement. Considering this model, we developed in the second part an electronic associated conditioner using a differential sensing procedure that permits the direct display of low pressures with a desired resolution. An experimental setup with some results was shown by the end to confirm the validity of the proposed model. 9 Elsevier B.V. Open access under CC BY-NC-ND license. PACS: Type pacs here, separated by semicolons ; Keywords: MEMS, capacitive sensor, low pressure, conditioner. 1. Introduction Microelectronics has known very important development. Specific manufacturing techniques have been developed to reduce the cost of objects using this technology [1, ]. In particular, Micro Electromechanical Systems, called by the acronym MEMS, which combine mechanical, optical, electromagnetic, thermal and fluidic in electronic semiconductor substrates drivers, have benefits widely of this development [3, 4, 5, 6]. In the area of pressure measurement, research efforts have been directed to the sensors based on a capacitive architecture. In fact, capacitive sensors, compared to piezoresistive sensors, may have characteristics almost independent of temperature. The result is an improved reliability and a reduction in the cost of the sensor [7, 8, 9, 1]. * Corresponding author. Tel.: ; fax: address: lanouarkaabi@yahoo.fr. doi:1.116/j.phpro

2 1496 L. L. Kaabi Kaabiet al. / PhysicsProcedia Procedia (9) (9) In the first part of this paper, a theoretical model including the edge effects of the studied structure of a capacitive low pressure sensor is presented. A study and a parametric characterization of the capacitive pressure sensor is conducted [11, 1]. In the second part, it was proposed a simplified model suitable for low pressure range. Based on this model, we developed an absolute pressure meter that allows a direct display of the sensed low pressure. To verify the validity of this model, an experimental setup was realized and some experimental results are exposed.. Presentation of the studied sensor The capacitive sensor object of this study is composed of two circular frames with a parabolic cavity. The bottom frame is fixed, while the upper frame is deformed under the applied absolute pressure P. Figure 1 shows a schematic diagram of the studied sensor. Fig. 1. Schematic representation of the capacitive sensor at rest Under an applied pressure, the upper deformable frame undergoes a deflection w(x,y) at any point (Figure ) and produces a change in the capacity of the sensor. The geometry will be modeled by a circular area and two areas that form an arch. The new term binding capacity to the applied pressure can be approximated by the sum of capacity resulting from these two areas. The overall capacity of the sensor is given by: ds C (P) = ε ε + C (1) r br d w(x, y) S where w (x, y) is the deflection of the upper frame under the applied pressure P, C br is the resulting capacitance the arc-shaped sides, ds is the surface element, d is the distance between the two frames.

3 L. Kaabi L. Kaabi et al. et / Physics al. / Physics Procedia Procedia (9) (9) y x Fig.. Schematic representation of the sensor under applied pressure In what follows, we assume that the constraints are weak which means that the deflection is small. The expression of w under variation of ρ is given by [11,1,] : 4 P R w ( ρ ) = 64 D ρ 1 R with 3 E e = and ρr. () 1(1 ) D where E is Young's modulus, e is the thickness of the membrane and is the poisson coefficient. By stimulating the expression of the deflection in the equation (1), we obtain : R ε ε ρ r C ( P ) = d d C br d π ϕ ρ + (3) w ( ) ρ 1 1 d R 3(1 ν ) S Where w( ) = P is the deflection at the centre of the moving frame (ρ =). 3 16π E e To calculate the integral, we consider x given as : w ( ) ρ ( ) 1 R 1 x d = (4)

4 14984 L. L. Kaabi Kaabiet al. / PhysicsProcedia Procedia (9) (9) After development, equation (3) leads to following equation: w() 1+ ε ε d r d C (P) = ln + Cbr d w() w() 1 d (5) Based on the range variation of the pressure, the term 1 x ln + 1- x in equation (5) can be written as a Taylor series as showninequation(6): n w() w () w () C (P) = C... C repos n br 3d 5d (n 1)d (6) Within the quasi-linear regime (w() << d ) and considering only the first order term, the previous expression of C (P) can be written as : 4 ( ) ( 1 ν ) R P C P Crepos C 3 br 16 E e d (7) 3. Operating principle of the low pressure sensor conditioner The proposed sensor is a capacitive sensor whose variation of capacitance is a function of applied pressure field asshowninequation(7) E e d By assuming that P =, the previous relationship becomes: M 4 1- ν R P C (P) = C 1 + C + br P (8) M For low pressure (P << PM) and neglecting momently the correction term Cbr, equation (8) can be written as: C(P) C P 1 P (9) M where C : the capacitance of the sensor at P =. P M appears as the pression for which the fixed and the deformable frames shows a capacitance C( P) C.It depends on the geometry of the sensor and the material s properties of the membrane. To obtain, for example, a pressure sensor which limits P M equals 1 Pa, we adopt the following geometrical sizes: diaphragm radius R = 4 mm, diaphragm thickness e = 15 μm, distance between frames d = 3.5 μm, Young modulus of the used material which is the silicon E = 13 GPa and Poisson ratio of silicon =.8. To measure low absolute pressures, a conditioner is associated to the sensor. This conditioner provides a complete digital readout and performs the measuring function with a resolution P of 1 Pascal. The schematic diagram of the proposed conditioner is shown in Figure 3.

5 L. Kaabi L. Kaabi et al. et / Physics al. / Physics Procedia Procedia (9) (9) C(P) Oscillator Oscillator with a Fixed frequency f f DOWN UP Counter BCD Control Logic nbits RAZ UP/ DOWN Hold Numeric data Decoder/ Driver Fig. 3. Functional block diagram of the proposed conditioner The reference logic signal whose frequency is f is generated by a TTL clock oscillator. Our sensor capacity C (P) will be integrated in a second oscillator that provides a clock output signal with frequency f (P). f is the frequency reflecting the change of pressure. These two respective signals supply an UP/down BCD counter as showninfigure3. An additional control logic was associated to ensure at each measurement cycle: the reset the up/down counter, the pulse counting at a fixed-frequency f for a duration, the count-down of pulses at frequency f during the same period, the hold of the generated numerical code at the output of the counter in order to allow the display of the measured pressure value. To calculate the number n of output bits of the up-down counter and the count-up / down duration τ, we choose to fix f at 1 khz. k Knowing that f = with k a constant characteristic of the two clock oscillators, we obtain f = f for C =. From the simplified C relationship given by equation (9), it can be shown that : C k P f 1 (1) C PM The number of pulses counted during the counting duration τ is given by : N = τ (11) f The down-counting pulses during the same period τ is given by : N 1 = τ f (1) he equality between the two expressions of τ given respectively by equations (11) and (1) gives : P N N 1 (13) 1 PM

6 156 L. L. Kaabi Kaabiet al. / PhysicsProcedia Procedia (9) (9) ThedifferencebetweenN and N 1 gives a number N which is proportional to the applied absolute pressure. The number N is given by : τ f N = N N.P 1 (14) PM From this latter equation, we deduce: PM P N (15) N P If we manage to have M = 1 N, the decimal value of the numeric code N obtained at the output of the counter during the hold phase, equals the pressure P expressed in Pascal. With chosen pressure P M = 1 Pa, a measuring range set at 4 Pa and a resolution P = 1 Pa, calculations of the duration τ of the count-up and count-down phases in addition to the number of bits n of the up/down BCD counter will be conducted as follows. τ f Keeping in mind that: N P and by differentiating this equation we obtain : P M τ f Δ N ΔP (16) PM From the latter equation, we obtain: ΔN. PM τ = (17) f. ΔP Since the resolution P = 1 Pa, we obtain N = 1 and we deduce τ = 1 ms. Keeping in mind that number N of pulses counted during the count up phase can be expressed as a function of n the number n of bits of the counter as shown in equation: N = 1 = τ f. Consequently, the number n of bits will be: ( τ f 1) ln + n = (18) ln By calculation, we obtain n 7 bits. Figure 4 shows the timing of the different logic control signals applied to BCD counter in order to achieve the exposed measuring procedure. UP/ DOWN HOLD Reset Fig. 4. Timing diagram

7 L. Kaabi L. Kaabi et al. et / Physics al. / Physics Procedia Procedia (9) (9) To allow for the display of pressure value, the resulting number N must be holded at the BCD counter outputs. This is done by activation of the Hold input. 4. Experimental setup and validation In order to test the functionality of the conditioner module and to allow for its calibration, an experimental workbench was made. The calibration procedure of the conditioner module is performed by varying the capacitance of a precision capacitor connected to the input of the conditioner. The variation of its capacitance simulates the variation of the sensor capacitance under applied pressure. The experimental results show good agreement between the theoretical and experimental values as shown in figure 6. Fig. 5. Photography of the experimental setup

8 158 L. L. Kaabi Kaabiet al. / PhysicsProcedia Procedia (9) (9) C(nF) P (Pa) Fig. 6. Experimental capacitance variation versus applied pressure 5. Conclusion An analytical study was conducted on a capacitive micro sensor dedicated for absolute pressure measurement and led to a model that takes into account the capacitance of boards. From this study, we obtained a theoretical model giving the variation of its capacitance under applied pressure. To exploit the micro sensor in low pressure measurement, we developed a simplified model and we proposed geometrical sizes for its achievement. Based on this model, we designed an associate conditioner using a differential measurement technique and allows a direct read out of the applied pressure with a defined resolution of 1 Pa. A calibration setup of the conditioner was made using precision capacitances, simulating the sensor s response to the pressure. It shows a good agreement with the obtained theoretical results. References [1] W.P. Eaton, J.H. Smith, IOP 6 (1997) 53. [] H.H. Beau, N.F. de Rooij, B. Kloeck, Mechanical Sensors, VCH verlagsgesellshaft, Germany, 1994 [3] B. Claudia, F. Luigi, G. Pietro, G. Salvatore, Sensors and Actuators A13 14 (5) 146 [4] N. Maluf, K. Williams, Introduction Microelectromechanical Systems Engineering, Artech House, 4 [5] H. MUNZEL, Application of etching technologies MICROSYSTEM Technologies, 1994 [6] S. M. Sze, Semiconductor sensors, Wiley- Interscience Publication, 1994 [7] S. K. Clark, K.D. Wise, IEEE trans. Electron Dev. 6 (1979) 1886 [8] C. Sung-Pil, G.A. Mark, J. Micromech. Microeng. 14 (4) 61

9 L. Kaabi L. Kaabi et al. et / Physics al. / Physics Procedia Procedia (9) (9) [9]W.Qiang,H.K.Wen,SensorsandActuators75(1999)3 [1] M. Al Bahri, Influence de la température sur le comportement statique et dynamique des capteurs de pression capacitifs au silicium, thèse de doctorat, INSA Toulouse, 5 [11] L. Kaabi, A. Kaabi, J. Sakly, F. Abdelmalek, Materials Science and Engineering C7 (7) 691 [1] A. Ettouhami, N. Zahid, M. Elbelkacemi, C. R. Mecanique 33 (4) 141