Structure design of micro touch sensor array

Transcription

1 Sensors and Actuators A 107 (2003) 7 13 Structure design of micro touch sensor array Liqun Du a, Guiryong Kwon a,, Fumihito Arai a, Toshio Fukuda a, Kouichi Itoigawa b, Yasunori Tukahara b a Department of Micro System Engineering, Nagoya University, Furo-cho, Chikusa-ku Nagoya , Japan b Tokai Rika Co. Ltd., Oguchi, Niwa-gun, Aichi , Japan Received 10 April 2002; received in revised form 18 February 2003; accepted 4 July 2003 Abstract The micro touch sensor array is fabricated by Ti substrate and PZT thin-film. PZT thin-film is synthesized by hydrothermal method and used as both micro sensor and micro actuator. Micro touch sensor array is not only simple to suit for miniaturization, but also robust against the disturbance. It will have numerous areas of application instead of conventional switch based on the mechanical contact. In this study, structure design of micro touch sensor array is presented. The main focus of structure design is on improving the sensitivity of micro touch sensor array. A mathematical model, which is used to optimize structure design of micro touch sensor array, is derived. According to cantilever beam theory, the frequency response to electric output of micro touch sensor unit has been discussed. The effects of changing physical parameters such as the location of the electrodes of PZT actuation and sense layer, and the length of the electrodes of PZT layers are studied. Based on the maximum output of micro touch sensor unit, the optimal structure has been obtained from both sides of analysis and experiment Elsevier B.V. All rights reserved. Keywords: Optimal design; Hydrothermal method; Piezoelectric thin-film; Micro touch sensor; Sensitivity 1. Introduction During recent years, the study of micro-electro-mechanical systems (MEMS) has shown significant opportunities for miniaturized mechanical devices based on thin-film materials and silicon technology. Among the various functional materials for MEMS technology, lead zirconate titanium piezoelectric thin-film (PZT) is very attractive. It is high electro-mechanical coupling material (it can undergo mechanical strain when subjected to an applied electric field and generate an electric field in response to mechanical stresses and strains) and the output force of the material is large. Especially, at the resonance operation condition, the output power density and efficiency is high if the load condition is appropriate, too. Its piezoelectricity can be used in sensors, actuators, and transducers; its pyroelectricity is used in infrared detectors. The actuation characteristics of piezoelectric actuators are determined by their position and orientation of PZT thin-film and electrodes with respect to the host structures Corresponding author. Tel.: ; fax: address: kwon@robo.mein.nagoya-u.ac.jp (G. Kwon). [1]. A number of models have been proposed to represent the static and dynamic interaction between PZT and the structures, such as the static pin-force model by Crawley and de Louis [2] that can be used for active beams. The two-dimensional model for plates developed by Dimitriadis et al. [3] and a number of finite-element approaches [4]. We have proposed a micro touch sensor array fabricated by PZT thin-films, which are synthesized by the hydrothermal method on titanium substrates. Its properties have been reported in [5,6]. In this paper, we show a method to improve the sensitivity of micro touch sensor array. In order to improve the efficiency of PZT thin-film sensors and actuators, the mathematical model, which is used to optimize design of micro touch sensor array structure, is derived. The model approach is based on un-damped Euler Bernoulli beam theory. In the course of optimization, the maximum output of micro touch sensor unit is regarded as object function. Simulation and experiment results indicate that the sense characteristics of micro touch sensor are determined by position of PZT sense and actuation layers with respect to the host structures just like piezoelectric actuators structures. By optimal structure design of micro touch sensor unit, the sensitivity of micro touch sensor array can be improved /$ see front matter 2003 Elsevier B.V. All rights reserved. doi: /s (03)

2 8 L. Du et al. / Sensors and Actuators A 107 (2003) 7 13 Fig. 1. Concept scheme of micro touch sensor. 2. Micro touch sensor array 2.1. Principle A micro touch sensor array was fabricated. It can sense mechanical pressure distributed over the array. Fig. 1 shows the basic concept of the micro touch sensor array. One sensor unit is a micro cantilever with two PZT thin-film layers. One layer is used as micro actuator to drive the cantilever into resonant based on converse piezoelectric effect, and another layer is used as micro sensor to detect the change of charge based on direct piezoelectric effect. When pressure acts on the beam, the polarization charge will change. By detecting the change of polarization charge, the contact can be sensed Structure The structure of the parallel touch sensor array is shown in Fig. 2. In this photograph, the parallel touch sensor array is composed by three sensor units A, B and C. Fig. 3 shows one sensor unit of the micro touch sensor. The sensor unit consists of a sense part and an actuation part. The sensor Fig. 2. Photograph of the parallel touch sensor array. Fig. 3. Configuration of one sensor unit. Fig. 4. Concept photo of micro touch sensor application. unit is a cantilever beam with rectangle cross-section. The downside area of the beam is the sense part and the upside area is the actuation part. The sense and actuation parts are PZT thin-films synthesized by hydrothermal method. The surface of actuation and sense parts are deposited with electrodes. The middle of them is Ti substrate Application Micro touch sensor array is not only simple to suit miniaturization, but also robust against the disturbance. Because the conventional switch based on the mechanical contact has difficulty to be miniaturized. The most promising key input device is micro touch sensor pad just like computer touch pad. Fig. 4 shows one of the concepts in numerous areas of application. In this case, micro touch sensor array can be used as the control touch sensor pad of a car instead of the capacitive type touch sensor. 3. Deposition of PZT thin-film Most of the existing coating techniques have been investigated for the deposition of PZT. The early work was carried out by means of physical techniques such as ion beam sputtering, RF planar magnetron sputtering [7] or dc magnetron sputtering [8]. Recently, PZT thin-films have been synthesized by several chemical methods such as sol gel method [9], metal organic chemical vapour deposition (MOCVD) [10], dip-coating, screen-press. By these methods, it is difficult to make PZT thin-film on a three-dimensional structure, and reaction temperature is also higher than 500 C. But by the hydrothermal method, we can avoid the previous mentioned manufacturing difficulties. The hydrothermal method that deposits PZT thin-film on Ti substrate was proposed by Ohba et al. [11 13] and improved by Higuchi et al. [14]. PZT thin-film was fabricated through two reaction steps. The first step is the reaction between titanium substrate and KOH solution containing Pb and Zr ions for nucleation (nucleation process). Ti dissolved from the substrate reacts with Pb and Zr in the solution, and PZT precipitated on the substrate. The second step is the crystal growth of PZT nuclei on the substrate in KOH solution containing Pb, Zr and Ti ions (crystal growth process). The scheme of the process is shown in Fig. 5. In the reaction, KOH is catalyst.

3 L. Du et al. / Sensors and Actuators A 107 (2003) Fig. 5. Schema of the hydrothermal method for PZT thin-film. 4. The analytic model of one sensor unit One sensor unit is a cantilever beam with sense part and actuation part. The composite beam model is shown in Fig. 6. The beam is composed of the substrate, actuation layer, sense layer and intermediate layers. The intermediate layers with low piezoelectric constant [12] are synthesized through nucleation process. Actuation layer and sense layer are PZT growth layers synthesized through crystal growth process The actuating equation In this section, static elastic models, which represent the interaction of PZT layers and substrate, will be presented. The models are based on following assumptions. Pure one-dimensional shear exists in the intermediate layer. Pure extensional and shrinkable strain exists in the PZT growth layers and Ti substrate. The PZT layer on both sides are completely fixed to Ti substrate. The PZT layer is homogeneous in terms of composition. The length of the central axis is fixed. The beam is bent only by the expansion or shrinkage of PZT thin-film. The deformation of PZT thin-film is caused by the piezoelectric effect. Neglect the thickness of intermediate layer. The distribution of strain in every layer is linear along the direction of thickness. Namely, the strains vary linearly with the distance y from the neutral axis. The strain in substrate, actuation layer and sense layer can be written as ε s = yκ, ε a = yκ Λ, ε b = yκ (1) where κ is the curvature of the neutral axis. Λ is free strain of PZT actuation layer. ε a, ε s and ε b are the strain of PZT actuation layer, PZT sense layer and substrate, respectively; y is the displacement above the neutral axis along y-direction. The equation of balance of force along x-direction can be written as D (ta /2) (tb +(t a /2) D) E b κy dy + E s κy dy (t b +(t a /2) D) (t b +(t a /2) D+t s ) D+(ta /2) + E a (κy Λ) dy = 0 (2) D (t a /2) The equation of balance of moment along x-direction can be written as: D (ta /2) (tb E b κy 2 +(t a /2) D) dy + E s κy 2 dy (t b +(t a /2) D) (t b +(t a /2) D+t s ) D+(ta /2) + E a (κy Λ) dy = 0 (3) D (t a /2) where E b, E a, E s are the Young s modulus of substrate, actuation layer, and sense layer, respectively. t b, t a, t s are the thickness of substrate, actuation layer, and sense layer, respectively. D represents the distance from central plate of PZT actuation layer to the neutral axis of composition cantilever beam; and Λ = d 31 V i sin ωt (4) t a where d 31 and V i sin ωt are the piezoelectric constant and input voltage. The bending moment caused by PZT actuation layer can be written as: M(ω, t) = ΛE a t a bd (5) where b is width of substrate, and Fig. 6. A composition cantilever beam model consisting of titanium substrate, actuation layer and sense layer. L: length of beam; x s1, x s2 : left edge coordinate and right edge coordinate of sense layer; x a1, x a2 : left edge coordinate and right edge coordinate of actuation layer; x-axis: neutral axis; y 1, y 2 : the coordinates of sense layer along y-direction. D = E b t 3 b + 6E st s t 2 b + 4E st 3 s + 9E st 2 s t b + E a t 3 a + 3E s t 2 s t a + 3E s t s t b t a 6E b t 2 b + 6E st 2 s + 6E st s t a + 6E b t b t a + 12E s t s t b + t b + t a 2 (6)

4 10 L. Du et al. / Sensors and Actuators A 107 (2003) The vibration equation In this section, the dynamic model for the cantilever beam that is excited and driven by the actuation layer will be derived. The cantilever theory is used to obtain the theoretical expression for the resonant frequency modes of the micro touch sensor. Under the assumption that the structural damp is ignored, the equation of motion governing the vibration of cantilever beam is written in the form [15]: ρ(x)a(x) 2 w t 2 [ ] + 2 x 2 E(x)I(x) 2 w x 2 = M(ω,t)[δ (x x a1 ) δ (x x a2 )] (7) where w is the deflection of the composition beam and l the length; ρ(x), A(x) and E(x) are the mass density, cross-sectional area, and the Young s modulus of the composite beam, respectively. I(x) is the moment of inertia of the composition beam cross-section and δ( ) the Dirac delta function; x a1 and x a2 are the two edges coordinates of the actuation layer. ρ(x)a(x) = ρ b A b + ρ a A a + ρ s A s (8) E(x)I(x) = E b I b + E a I a + E s I s (9) Applying the method of separation of variables to Eq. (7) and multiplying both sides of Eq. (7) by mode function, then integrating from x = 0toL, by virtue of the orthogonality of mode function, Eq. (7) can be rewritten in the form q i (t) + ω 2 i q i(t) = M i (ω, t)[φ i (x a2) Φ i (x a1)] (10) where q i (t) is mode coordinates, Φ i ( ) is the derivative of mode function with respect to x, ω i are the natural frequencies of the beam. ω i = (β i l) 2 E(x)I(x) ρ(x)a(x)l 4 (11) and β 1 l = 1.875, β 2 l = 4.694, β 3 l = 7.855, β 4 l = , β 5 l = , β 6 l = The mode function can be written Φ i (x) = cosh β i x cos β i x C 1 (sinh β i x sin β i x) (12) C 1 = sinh β il sin β i l cosh β i l + cos β i l (13) The solution of force vibration is written ( ) P i w(x, t) = Φ i ωi 2 sin ωt (14) ω2 where i=1 P i = M i (ω, t) [ Φ i (x a2) Φ i (x a1) ] (15) 4.3. The sensing equation For the sensor, the piezoelectric equation based on direct piezoelectric effect can be written as [16]: y D y = e 31 S x = e 31 (16) R where D y is the electric displacement along y-axis, e 31 the piezoelectric stress constant, S x the strain along x-axis, y the displacement above the neutral axis and R the curvature of the neutral axis. R is written as 1 w(x, t) R =± 2 x 2 (17) According to Gauss theory q = D y ds (18) where q is the charge. The total charge in sense layer is the average value of the charge produced in upper and lower surface of sense layer. The total charge can be written as q = 1 ( ) D y1 ds + D y2 ds 2 total [ xs2 = 1 2 b 2 w(x, t) s e 31 y 1 x s1 x 2 dx xs2 2 ] w(x, t) + e 31 y 2 x s1 x 2 dx ( ta = b s e t ) s 2 + t b D [ w (x s2,t) w (x s1,t) ] (19) where x s1, x s2 are the two edge coordinates of sense layer, b s is the width of sense layer, w (x, t) the derivative of the deflection with respect to x, y 1, y 2 are the coordinates of sense layer along y-direction. The output voltage V o can be obtained, total V o = q ( ta = b s d 31 E s C p 2 + t ) s t b D C p [ w (x s2,t) w (x s1,t) ] (20) where C p is the capacity of PZT sense layer. 5. Result and discussion 5.1. The effect of resonant frequency of structure Eq. (20) indicates the relationship between the strain caused from input voltage and the output voltage. On basis of the equation, the response of micro touch sensor to electric input has been discussed. The physical parameters of the structure used in calculation are listed in Table 1. We excited the system in term of different excited frequency when actuated voltage was unchanged. Fig. 7 shows

5 L. Du et al. / Sensors and Actuators A 107 (2003) Table 1 Physical parameters of sensor unit Ti substrate PZT actuator PZT sensor Length (mm) Width (mm) Thickness ( m) Density (kg/m 3 ) Young s modulus (N/m 2 ) d 31 (mv) C p (F) Input voltage (V) 10 Fig. 7. The relationship between frequency and output voltage. the relationship between excited frequency and output voltage of micro touch sensor unit. Fig. 8 shows the relationship between excited frequency and amplitude of vibration of micro touch sensor unit. In the figures, the solid circle lines are experiment curves of output voltage, and the square lines are calculation curves of output voltage. It is interesting to note that mode 3 has the highest output voltage, which means the micro touch sensor unit has the high sensitivity at this resonant frequency. Decrease of experimental resonance frequency at mode 3 is regarded as caused due to Young s modulus and damping effect of PZT layer. In this case, we could not measure the Young modulus of PZT layer made from hydrothermal method. Therefore, in the analysis, the Young s modulus is regarded as N/m 2, this is bulk-type PZT material data. It indicated that choosing a suitable excited frequency is one method of improving the sensitivity of micro touch sensor Optimal configuration The major interest here is directed to obtain the best geometrical conditions that allow good employment of the PZT thin-film as actuator as well as sensor. In contrast, the position and the dimensions of the PZT actuators can produce very significant changes in the dynamic response of the system [4]. For this reason, the optimal design variables such as the length and the location of the PZT thin-film sense and actuation layers are examined in the following section. The use of Eq. (20) will greatly simplify the search of the optimal length and location of the PZT sense layer. The optimization problem can be concluded as: to find the length and location of PZT sense layer to make the output voltage V o to be maximal. It is easy to recognize that the effects of the length and location of the sense layer only take place in the term ( max Φ i x x s2 x s1 ) = max [ Φi x (x s2) i x (x s1) ] (21) If the parameter P represents the location and L p represents the length of sense layer respectively, where P is the coordinate of central point of sense layer, and they are shown in Fig. 9, then x 1 = P 2 1 (L p), x 2 = P (L p) (22) We now assume that the length L p of the sense layer is fixed and look for an optimal value of P, which is to maximize the value of the output voltage. In order to do so, it is necessary to impose that P ( Φ i x x 2 x 1 ) = 0 (23) This leads to the condition 2 Φ i x 2 = 2 Φ x1 x 2 (24) x2 Fig. 8. The relationship between frequency and amplitude. Fig. 9. Optimal shape of micro touch sensor unit.

6 12 L. Du et al. / Sensors and Actuators A 107 (2003) 7 13 Table 2 Optimal length of actuation and sense layers Excited mode Ratio of length a/l Output voltage (mv) First Second Third Fourth On the other hand, when the position P of the sense layer is fixed, its length L p will be found by imposing ( ) Φ i x 2 L p x = 0 (25) x 1 This leads to the condition 2 Φ i x 2 = 2 Φ i x1 x 2 (26) x2 To obtain the optimal values of the position P and the length L p, both Eqs. (24) and (26) must be satisfied. Because the second derivative of mode function is proportional to curvature, the solution of the problem is found whenever a sense layer is placed on the beam so that the strain in x 1 and x 2 is zero. In the case of optimizing length and location of PZT thin-film actuation layer, the optimal object function is deflection w(x, t)of cantilever beam. Based on the similar pro- Fig. 10. Equipment of verification experiment. cedure mentioned above, the conclusions similar to Eqs. (24) and (26) can be obtained. As mentioned above, in order to obtain the maximum output voltage V o of micro touch sensor so as to improve its sensitivity, two edges of sense and actuation layers must be placed between two consecutive points at which the strain becomes zero. Their center points lay near a location where the highest strain takes place [2]. Based on the analysis, the optimal configuration of a touch sensor unit is obtained and is shown in Fig. 9. In Fig. 9, a represents the distance from fixed end to left edges of sense and actuation layers. L represents the length of cantilever beam. The optimization results of designing actuation and sense layers are listed in Table 2. Fig. 11. The relationship between location of sense, actuation layers and output voltage. (a) Optimal PZT thin-film actuation and sense layer to excite mode 1. (b) Optimal PZT thin-film actuation and sense layer to excite mode 2. (c) Optimal PZT thin-film actuation and sense layer to excite mode 3. (d) Optimal PZT thin-film actuation and sense layer to excite mode 4.

7 L. Du et al. / Sensors and Actuators A 107 (2003) The physical parameters of the structure used in the simulation are listed in Table Verification experiment The equipment for verification experiment is shown in Fig. 10. In this experiment, aluminum thin-film is first vaporized on the surface of PZT film as electrodes in order to fabricate actuation and sense layers. The lengths of actuation and sense layers are 2, 2.5, 3, 4 and 5 mm, respectively. The lengths of cantilevers are all 5 mm. We excited the system in term of the first fourth resonant frequency when driving voltage is unchanged. The driving voltage of the actuation layer is 10 V p p. Contact material was finger. The contact direction is shown in Fig. 10. Fig. 11 shows the relationship between location of actuation, sense layer and output voltage of micro touch sensor unit. In the figures, the closed circles are the measured values of output voltage and the solid circles lines are theoretical simulation curves. The solid square lines are strain distribution curves. Fig. 11 indicates that the location and length of actuation and sense layers affect the output voltage of touch sensor directly. The results of calculation simulation and experiment show that two edges of sense and actuation layers should lie between two consecutive points at which the strain becomes zero; and the center points of them should lay near a location where the highest strain takes place. In the case when the first fourth resonant frequencies are excited, the optimal configuration of PZT touch sensor unit is the case when a/l is set about 0.5 for exciting the third mode. 6. Conclusions A mathematical model was derived in order to improve the sensitivity of micro touch sensor. Based on the model, the effect of frequency response on electric output of micro touch sensor unit was discussed, and optimized configuration of micro touch sensor unit was obtained from both sides of theory and experiment. By choosing the optimal configuration of micro touch sensor unit and excited frequency of structure the sensitivity of micro touch sensor array can be improved. References [1] K.-H. Ip, P.-C. Tse, Optimal configuration of a piezoelectric patch for vibration control of isotropic rectangular plates, Smart Mater. Struct. 10 (2001) [2] E.F. Crawley, J. de Luis, Use of piezoelectric actuators as elements of intelligent structures, AIAA J. 25 (1987) [3] E.K. Dimitriadis, C.R. Fuller, C.A. Rogers, Piezoelectric actuators for distributed vibration excitation of thin plates, J. Vibrat. Acoustics 113 (1989) [4] R. Barboni, A. Mannini, E. Fantini, P. Gaudenzi, Optimal placement of PZT actuators for the control of beam dynamics, Smart Mater. Struct. 9 (2000) [5] G. Kwon, F. Arai, T. Fukuda, K. Itoigawa, Y. Thukahara, Micro touch sensor array made by hydrothermal method, in: Proceeding of the 2001 International Symposium on MHS, 2001, pp [6] L. Du, F. Arai, G. Kwon, T. Fukuda, K. Itoigawa, Y. Tukahara, Dynamic analysis of micro touch sensor array synthesized by hydrothermal method, in: Proceeding of the IEEE ICRA, 2002, pp [7] T. Abe, M.L. Reed, RF-magnetron sputtering of piezoelectric lead zirconate actuator films using composite target, Proc. IEEE MEMS 94 (1994) [8] P. Muralt, PZT thin-films for microsensors and actuators: where do we stand? IEEE Trans. Ultrasonics, Ferroelec. Frequency Control 47 (4) (2000) [9] G. Yi, Z. Wu, M. Sayer, Preparation of (PbZr, Ti)O 3 thin-film by sol gel processing: electrical, optical and electro-optic properties, Jpn. J. Appl. Phys. 64 (1988) [10] H. Funakubo, K. Imashita, N. Kieda, N. Mizutani, Formulation of epitaxial Pb(Zr, Ti)O 3 film by CVD, Nippon Seramikkushu Kyoukai Gakujyutsu Ronbunshi 99 (1991) [11] K. Shimomura, T. Tsurumi, Y. Ohba, M. Daimon, Preparation of lead zirconate titanate thin-film by hydrothermal method, Jpn. J. Appl. Phys. 30 (1991) [12] Y. Ohba, M. Miyauchi, T. Tsurumi, M. Daimon, Analysis of bending displacement of lead zirconate titanate thin-film synthesized by hydrothermal method, Jpn. J. J. Appl. Phys. 32 (1993) [13] Y. Ohba, K. Arita, T. Tsurumi, M. Daimon, Analysis of interfacial phase between substrates and lead zirconate titanium thin-film synthesized by hydrothermal method, Jpn. J. Appl. Phys. 33 (1994) [14] T. Morita, M. Kuribayashi, T. Higuchi, A cylindrical micro ultrasonic motor using PZT thin-film deposited by single hydrothermal method, IEEE Trans. Ultrasonics, Ferroelec. Frequency Control 45 (5) (1998) [15] A.A. Shabana, Theory of vibration, in: Discrete and Continuous System, vol. 2, Springer-Verlag, Berlin, 1991, pp [16] Z. Wu, X. Bao, V.K. Vandan, V. Vvaradan, R. Barboni, Light-weight robot using piezoelectric motor, sensor and actuator, Smart Mater. Struct. 1 (1992)