( VCM ) in Lead Zirconate Titanate ( PZT )

International Conference on MEMS and Nanotechnology, ICMN’06 14-15 March 2006, Kuala Lumpur, Malaysia

MDD2 CONCEPT AND DESIGN OF A MICROMACHINED MINIATURE VARIABLE CAPACITANCE MOTOR (VCM) IN LEAD ZIRCONATE TITANATE (PZT) SUBSTRATE N. S. Ashraf Department of Electrical and Electronic Engineering Islamic University of Technology (Organisation of the Islamic Conference), Board Bazar, Gazipur – 1704, Bangladesh [email protected]

ABSTRACT Miniaturization of refrigeration systems makes the integrated heat removal system for electronic and optoelectronic systems possible without the need of external cooling system. The author1 has previously demonstrated the design and fabrication of a mesoscopic variable capacitance electrostatic motor (VCM) in silicon as an element of compressor unit of miniature refrigeration system. In this paper, the author proposes another mesoscopic VCM in Lead Zirconate Titanate (PZT) substrate with coupled piezoelectric and electrostatic actuation. The PZT VCM is capable of imparting sizeable rotational torque while benefiting from reduced fabrication process sequences compared to electrostatic VCM in silicon that was earlier reported in literature.

1. INTRODUCTION The miniaturization of nearly all types of devices and systems offers arguably revolutionary opportunities for commercial profit and beneficial technological advances (e.g., micromechanical, microfluidic, microthermal, micromagnetic, microoptical and microchemical). Specifically MEMS technology has enabled many types of sensors, actuators and systems to be reduced in size by orders of magnitude while radically transforming performance and cost of these systems by employing batch fabrication techniques and the economies of scale successfully exploited by the IC industry [1]. Miniaturization of refrigeration systems makes the integrated heat removal system for electronic and optoelectronic systems possible without the need of external cooling system. An integrated refrigeration system allows maintaining those electronic systems at temperatures below the ambient temperature. Without such cooling, devices operating at high power and high temperatures would not function properly or would function inefficiently in harsh environments such as adjacent to the engine of a vehicle, in the cockpit of an airplane or in the desert. Miniaturization and use of microfabrication processes lead to a cooling system that can be integrated into substrates of electronic and photonic modules which are inexpensively mass reproducible. Refrigeration can be achieved by the principle of vapor compression cycle. A typical vapor compression system consists of four components, namely, (1) evaporator, (2) compressor, (3) condenser and (4) expansion valve. Compressor’s performance in attainment of moderately high coefficient of performance (C.O.P.) in maintaining the designed temperature difference between the ambient and the system is a key requirement. Comparison of different alternatives for compression and actuation suggests that electrostatic actuation integrated with centrifugal compression is a viable option [2]. Electrostatic actuation by variable capacitance motor (VCM) is a promising and compatible technology which has been adopted by numerous researchers in the past. VCM can be categorized into three groups, namely top-drive, side-drive and harmonic side-drive. The top-drive VCM can achieve higher output torque due to larger changes in the rotor-stator overlapping capacitance as compared to the other two design types. This high output torque can be utilized to MEMS Design and Development

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generate higher output power essentially suited for applications mentioned for this type of centrifugal compressor. The author1 has previously demonstrated the design and fabrication of a mesoscopic variable capacitance electrostatic motor (VCM) in silicon as an element of compressor unit of miniature refrigeration system [3,4]. In this paper, the author proposes another mesoscopic VCM in Lead Zirconate Titanate (PZT) substrate with coupled piezoelectric and electrostatic actuation. The PZT VCM is capable of imparting sizeable rotational torque while benefiting from reduced fabrication process sequences compared to electrostatic VCM in silicon that was earlier reported in literature. The reduction in fabrication process sequence results from the removal of masking layer implementing low frictional bearing structure being essential for operation of VCM in silicon. Section two of this paper summarizes the actuation process and design considerations of VCM in general. Section three underlines the key focus of this paper, i.e., design parameters and kinematical analysis of VCM using PZT as the substrate. In section four, a comparative analysis of VCM in silicon and PZT, respectively, is undertaken to reflect performance from design parameter’s perspective. Finally in the concluding section, future work such as defining the fabrication process sequence of this proposed VCM in PZT is referred with relevance to this work.

2. ACTUATION PROCESS AND DESIGN CONSIDERATIONS OF VCM A VCM is a synchronous motor. Discrete conducting metal pads are deposited on rotor and stator built in silicon wafers. In the case of electrostatic actuation, when the two conducting pads with a small separation between them are slightly displaced with respect to each other, the resultant electro-quasistatic force has a component parallel to the surface of the pads which subsequently tends to realign the pads. Once the rotor rotates and the rotor pads get aligned with the stator pads, the excitation to the stator pads is switched off so that the rotor continues to rotate under its own inertia as shown Fig. 1 and Fig. 2, respectively. In the process of rotation, when the next set of rotor pads approach the stator pads, the excitation to the stator pads is switched on again. Thus the rotor and stator excitation are synchronized in this type of actuation [5]. The dynamics of this rotor can be expressed in terms of the capacitance between a rotor pad and a stator pad with its being a linear function of the overlap area between those two pads [5]. Since the overlap varies with rotation, so does the stator-rotor capacitance. Typically the separation between two neighboring pads is same as the width of any rotor pad. The stator-rotor capacitance has a triangular waveform. From energy balance of this motor, total electrical power input must be equal to the sum of the mechanical power output and the rate of increase of potential energy stored in the stator-rotor capacitance. This energy balance provides

1 2

ωT = V 2

dC dt

(1)

where T is the torque generated and ω is the rotational speed (rad s-1). This in order to achieve positive torque, the applied excitation should be zero whenever there is mutual overlap. Hence rotorstator capacitance decreases with time. A simple way to implement this requirement is to have the excitation as shown in Fig. 3 [6]. Here excitation is kept constant at Vo when C is increasing and 0 when C is decreasing (Fig. 3 (a) and Fig. 3 (b) respectively). As rotational speed is constant under steady state operation, the temporal variation of torque T is as shown in Fig. 3 (c). An important drawback of the simple motor shown in figure is that the motor will not be able to start on its own if all the pads are perfectly aligned. Since it is important to have a self-starting actuation for the compressor, there should be different number of pads for stator and rotor, respectively, such that these pads are not perfectly aligned at any rotational position of the rotor. The average torque thus produced has been calculated [2] 2 2 M r 2 ⎛ Ro − R I ⎜ T = ε rε o Vo ⎜ 24 d ⎝

where εo = 8.854 × 10-14 F cm-1

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⎞ ⎟ ⎟ ⎠

(2)


εr = dielectric constant of the medium in the gap d = gap thickness Mr = number of rotor pads RI = inner radius of rotor or stator pads Ro = outer radius of the rotor or stator pads

Fig. 1: Pictorial view of overlap of stator and rotor.

Fig. 2: Cross sectional view of stator and rotor.

V

(a) t

C (b) t

T

(c) t

Fig. 3: Timing diagrams: (a) excitation voltage versus time; (b) capacitance versus time and (c) torque versus time

3. DESIGN PARAMETERS AND KINEMATICAL ANALYSIS OF VCM USING PZT AS SUBSTRATE Using the above electrostatic actuation principle and employing the piezoelectric actuation of Lead Zirconate Titanate (PZT) piezoelectric material, a PZT VCM can be configured where the top surface constitutes the rotary disk of selected stator pads and the bottom surface constitutes the rotary disk of selected rotor pads as shown in Fig. 4 and Fig. 5, respectively. The two stator and rotor rotary


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disks in PZT can be conjoined together to form thickness as separation between the pads shown in Fig. 6. The coupled electrostatic and piezoelectric actuation takes place in the following way. When the rotor and stator pads overlap, electrostatic force develops due to finite separation between the pads and the finite parallel plate capacitance effect. This force has a component in the horizontal direction which deforms the piezoelectric crystal and according to the following equation; an excitation voltage between corresponding stator and rotor pad is developed.

Vz =

Qz d zx Fx d zx Fx z = = C C ε o ε r Az

(3)

where Vz = voltage applied between the top and bottom overlapping pads (considered to be in z direction) Qz = Total charge developed between the pads referenced above (C) dzx = charge sensitivity coefficient of the piezoelectric material (pC / N) for deformation in z direction and applied force in x direction Fx = Force applied in x direction (N) z = Thickness of the piezoelectric material εr = Dielectric constant of the piezoelectric material AZ = Cross sectional area of the overlapping pads perpendicular to the z plane C = Capacitance in (F) between the overlapping pads

Fig. 4: The cross section of the stator with film pads connected in three phase (a-b-c).

Fig. 5: The cross section of the rotor with film pads connected in three phase (a-b-c).


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Fig. 6 : Structure of the proposed PZT VCM. This effect is actually reversible, i.e., applying voltage between the two conducting ends of the PZT crystal causes the crystal to deform and analogous actuation force can be extracted. Now selecting the inner radius Ri of 2 mm and outer radius Ro of 12 mm for stator and rotor rotary disks respectively and choosing the thickness of the conjoined PZT material as z of 1mm, we can use the equation to find the value of Fx for an excitation voltage of 250 V where known values of dzx = 110 pC N-1 and εr = 1200 for PZT material are substituted. 110 × 10 −12 × Fx × 10 −3

(

8.854 × 10 −12 × 1200 × π × Ro − Ri 2

2

) = 250

⇒ Fx = 10615.14 N Due to the strain caused by this force on the PZT crystal, supposing the shape along the vertical axis z is changed by ∆lz, the following equation can be used to compute ∆lz.

σ=

∆l F = Eε = E z A z

∆l z = ⇒ ∆l z =

(4)

Fx z EAz

(5)

10615.14 × 10 −3

(

8.3 × 1010 × π × Ro − Ri 2

2

)

-7

= 2.91× 10 m. Then the torque created for rotation of rotor pads due to piezoelectric actuation, T = Fx ∆l z

(6)

⇒T = 3.09×10 N-m -3

As the piezoelectric actuation generates the torque so that rotor pads tend to realign with the stator pads after rotation, electrostatic actuation can be utilized to calculate the number of rotor pads which is a fabrication parameter for the mask used to deposit the metal films. Now using the equation of torque generated by electrostatic actuation, 2 2 R − Ri M 2 (7) T= Vo ε o ε r o 4 6z where M = Number of rotor pads. 3.09 × 10−3 × 4 × 6 × 10−3 ⇒M = 2 (250) × 1200 × 8.854 × 10−12 × 1.4 × 10− 4 = 798

(


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)


This value of rotor pad number can be configured easily within the minimum feature length which is more than few tens of micron length for a rotary disk perimeter of π×2Ro. The use of VCM in PZT substrate eliminates the need of fabrication of bearing structure and other complex circuitry used for levitation in the case of electrostatic VCM in silicon where the stator disk has to be held on top of the rotor disk to prevent accidental sticking and frictional effects. It can be derived from above equation that for electrostatic VCM motor, to obtain the same torque with the same number of rotor pads, the separation gap needs to be of the order of 10-7 m, causing a serious impediment to stable operation and also causing dielectric breakdown (R134a).

4. COMPARATIVE ANALYSIS OF PERFORMANCE PARAMETERS BETWEEN VCM IN SILICON AND VCM IN PZT A comparative analysis is presented here in terms of values obtained for rotational torque and power output between VCM in silicon and VCM in PZT, while the other design parameters are unchanged simultaneously for both of them. Using the value of the number of rotor pads, drive voltage and rotor inner and output radius as used or extracted in the preceding section, the electrostatic VCM in silicon requires a minimum value of separation gap of 3 µm for reliable operation of R-134a without breakdown. The value of relative dielectric constant of R-134a at room temperature and ambient pressure is 1.024. Substituting these values in equation (7), the maximum torque that can be obtained under the given parametric conditions is T = 8.79 × 10-4 N-m compared to the torque of 3.09 × 10-3 N-m obtained for VCM in PZT under the same parametric conditions. Thus for a uniform RPM of 266000 as reported in [4], power output Pout = T ω, where ω is angular speed in rad s-1. Power output for VCM in silicon is simply calculated as 24 watt and that of VCM in PZT is 86 watt, almost a four times more extractable power from the compressor made out of PZT VCM.

5. CONCLUSION In this paper the concept of a mesoscale variable capacitance motor in Lead Zirconate Titanate substrate is presented and kinematical analysis is performed. Comparison is made with previously reported VCM in silicon in terms of nearly four fold enhancement of driving torque and power output realizable from such motors in PZT substrates to be embedded in the compressor module. In future, the fabrication process sequence that practically conforms to the microfabrication processes on PZT materials will be pursued by the author.

REFERENCES [1] J. W. Judy, “Microelectromechanical systems (MEMS) : fabrication, design and applications”, Smart materials and structure (Institute of physics publishing), Vol. 10, 2001, pp 1115-1134 . [2] N. S. Ashraf, “Design Considerations and Thermodynamic Feasibility Study of a Mesoscale Refrigerator”, M.S. Thesis, Department of Electrical and Computer Engineering, University of Central Florida, Orlando, 1999. [3] N. S. Ashraf, H. C. Carter, K. Casey, L. C. Chow, S. Corban, M. K. Drost, A .J. Gumm, Z. Hao, A. Q. Hasan, J. S. Kapat, L. Kramer, M. Newton, K. B. Sundaram, J. Vaidya, C. C. Wong, K. Yerkes, “Design and analysis of a mesoscale refrigerator”, 1999 International Mechanical Engineering Congress and Exposition, Nashville, pp. 14-19. [4] R. Agarwal, Q. Hasan, N. Ashraf, K. B. Sundaram, L. C. Chow, J. S. Kapat, J. Vaidya, “Design and fabrication of a meso-scale variable capacitance motor for miniature heat pumps”, Journal of Micromechanics and Microengineering 13, 2003, pp. 1-7. [5] W. S. N. Trimmer and K. J. Gabriel, “Design Consideration for a Practical Electrostatic Micromotor, Sensors and Actuators, 11, 1987, pp. 189-206. [6] B. Bollee, “Electrostatic Motor”, Philips Tech. Rev., 30, 1969, pp 178-194.


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