Design and Analysis of MEMS based Composite Piezoelectric Ultrasonic Transducer

With the rapid growth of technology, micro scale devices are p laying a dominant role in mechanical and optoelectronic devices. Characteristics like min iaturization, mult iplicity and microelectronics help these devices to sense, control and actuate on micro scale with effects on macro scale. Micro devices like composite transducers are widely used in medical, industrial and space applications because they are relatively simple and easy to interface with other devices and also provide better resolution and easy installation. The present work reports the design and simulat ion of composite piezoelectric ultrasonic transducer, where susceptance was computed by applying AC potential for various piezoceramic materials i.e., Nepec 6, Quartz, Pzt-8. In this, an eigen frequency analysis is fo llowed by a frequency response analysis to calculate the input admittance as a function of the excitation frequency. To make this design, COMSOL Mult iphysics software is used. The transducer designed with PZT-8 has exh ibited better sensitivity than others. These transducers are widely used in non-destructive testing (NDT), weld ing, machin ing, medical imaging etc.


Introduction
Control is mo re important than information processing; it imp lies that there is a d irect interaction with the physical world. Control systems include sensors and actuators, which help us to ensu re that auto mat ion systems can man age activities and environments in desired ways. In this context MEM S has been identified as one of the most pro mising technologies for the 21st Century and has the potential to revo lut ion ize both industrial and consu mer p roducts by c o mb in in g s ilico n -b as e d mic r o e le ct ro n ics w ith micro mach ining technology [1][2][3][4][5][6][7]. They usually consist of a central unit that processes data, the microprocessor and several co mponents that interact with the outside such as micro sensors [8][9]. Th is techniques use micro system-based devices that have the potential to dramatically effect of all of our lives and the way we live by p roviding the min iaturized devices. A micro-electro mechanical system (M EMS) is a process technology used to create tiny integrated devices or systems that combine mechanical and electrical co mponents. They are fab ricated us ing integ rated circu it (IC) batch processing techniques and can range in s ize fro m a few micro met res to millimetres. These devices (or systems) have the ability to sense, control and actuate on the micro scale, and generate effects on the macro scale. In this context, there has been increasing demand for ultrasonic transducers due to its potential applications, including non-destructive testing (NDT), welding machining, cleaning, underwater communicat ion, navigation, map building, ultrasonic surgery, etc. Among different types of transducers viz., sonic, ultrasonic and mega sonic, ultrasonic transducers usually work at a frequency range fro m 20 kHz to 200 kHz [10]. Features like high acoustic efficiency, mechanical flexibility, low mechanical Q, low cross talk and low acoustic impedance made these transducers to be used in wide range of applications. Generally this sensor works by emitting a short burst of 40 kHz u ltrasonic sound from a p iezoelectric transducer. Ultrasonic transducer playsan important ro le in both generating and receiving ultrasound in an ultrasonic measurement system. In general, they are co mplex electro mechanical devices that are difficu lt to characterize and design. The sensitivity and resolution of the device entirely depend upon the piezocomposite materials being used. There are h igh resolutions producing devices in the market wh ich are built by using lead metaniobate piezoceramic o r piezoelectric poly mers. But these are showing low sensitivity as most of the acoustic energy is absorbed in the backing and materials efficiency is lowered. As these transducers involve both the combination of electrical and mechanical co mponents, it is difficult to for us to analyse them. Whereas a Piezoelectric ceramic and a passive polymer are co mbined to get a piezo co mposite, which helps us to design the transducer that is producing better results than the conventional piezoelectric devices [11] Thus, the present study is mainly focused on design of composite piezoelectric u ltrasonic transducer with three different piezoelectric materials and computation of susceptance as a function of excitation frequency for the proposed structure.

Theoretical Background
To generate and measure the ultrasonic pulses, the composite transducer is working based on the phenomenon of piezoelectric effect. Piezoelectric ceramics and single crystal materials are the two main materials which are used for generation of piezoelectric effect in the transducers. Lead zirconate titanate, also called PZT is the most common piezoelectric ceramic which is used today along with other materials like sodium tungstates, lithiu m tantalite, lead titanate, zinc o xide, bariu m t itanate and bariu m strontium titanate. On the other hand single crystal materials like magnesiu m niobate-lead titanate are also used in manufacturing of these transducers along with galliu m phosphate, quartz and tourmaline. These crystals provide the flexib ility in designing, so that they can be made into various shapes to achieve different vibration modes, which help the transducer in operating fro m lo w kHz range up to the MHz range. The piezoelectric effects generated when mechanical stress is applied between surfaces of a solid dielectric. Conversely when a voltage is applied across certain surfaces of a solid then it undergoes a mechanical distortion and exhibits the piezoelectric effect. As piezoelectricity is the combined effect of the electrical behaviour of the material i.e., D = Є E (1) Where D is the electric charge density displacement (electric d isplacement), ε is permittiv ity and E is electric field strength. Linear elasticity equations are coupled with electrostatic charge equations by means of electric constants to obtain a reasonable model of this interaction. So the stress charge form of equations is as follo ws T = C E . S -e t . E (2) D = e . S + Є S . E (3) Where S is the stress, et is the permittivity at constant strain, T is the stress. When stress is applied these crystals bends in different ways at different frequencies, but they will be resonating within narrow frequency ranges. Some of the transducers which use the piezoelectric materials are phonograph cartridges, microphones, and strain gauges that produce an electrical output from a mechanical input. But a mechanical output from an electrical input can be observed in earphones and ultrasonic transmitters. Generally electrostatic transducers have very high initial cost and very low system resistance but whereas piezo transducers are less expensive thereby making its construction best suited for harsh environments.

Use of Comsol Multiphysics
The software package selected to model and simulate the MEMS co mposite ultrasonic transducer was COM SOL Multiphysics Version 4.2 a.It is a powerful interactive environment fo r modelling and Multiphysics were selected because there was previous experience and expertise regarding its use as well as confidence in its capabilities. This provides the flexib ility of selecting the required vertex for applying the inputs by rotating the geometry in the work plane. This consists of material library where we can find different material branches like M EMS, semiconductors(Ga As, Ge¸C[100] etc), insulators(Al2 O3,Si2 O3), poly mers and piezoelectric (Bariu m sodium niobate, Lithiu m niobate, Lead zirconate titanate etc) can be selected.

Design Process
The design of composite piezoelectric transducer starts fro m defin ing parameters for the required geometry, selection of necessary material and addition of physical interfaces. For modelling, certain instructions must be followed. First, selection of piezo electric devices (pzd) and then eigenfrequency analysis was chosen. For required shape, first circle with radius 27.5e-3m. Later, bezier polygon is chosen and its segments are located in the control point sub section by adding the value of x in row 2 for about 0.03 in the add linear button. Now this structure is rotated for about 10 degrees and converted to solid. To reduce memo ry requirements, we use the structural symmetry by cutting along its mid plane wh ich is perpendicular to central axis. After cutting the geometry, now by locating the points fro m the work p lane, the final 3-D model can be obtained as shown in Fig. 1. Variables must be defined for the susceptance so the compensating factors, symmetry and degree of wedge is taken into consideration, fro m which mesh can be generated as shown in Fig. 2.
The composite piezoelectric ultrasonic device has a cylindrical geometry. This model consists of a piezoceramic (NEPEC 6)and two Langevin type transducers in which a disk is sandwiched between a pair of alu min iu m d isks by means of adhesive (ARALDITE) i.e., the layers are organized as follows alu min iu m layer-adhesive layer-piezoceramic layer-adhesive layer-alu min iu m layer. During the modelling of the geometry, do mains must be selected so that the required material can be inserted in the proper area and they are as follows.    This type of construction is used for sonar transducers and is of practical importance because it provides design flexib ility by choosing material co mbinations and dimensions [12]. One of the p iezoceramic materials, lead zirconate titanate is most popular choice for medical ultrasonic transducer. This offer high electro mechanical coupling a wide selection of dielectric constants which made pzt-8 pro minent in selection during the construction of med ical transducers. The material constants used during the design of transducer are tabulated in Table 1.

Input Parameters
Calculating the susceptance for the geometry requires selection of the boundary conditions for the terminal, ground and symmetry position so that the input parameters can be applied. Here as we are modelling only for the upper part of the transducer, this condition lead to the application o f the potential fo r about half of the total peak value i.e., 0.5 volts.
Electrical terminal is selected in boundary 6 so that the voltage can be applied to it fo rm terminal type. Where the ground is selected to boundary 3 fro m electrical boundary conditions. The condition for satisfying the symmet ry is made by select ing the boundaries in the model fro m 1-5, 7, and 8.The expression for these conditions are given by equations, 1). Terminal ∫ ∂Ω ρ s d s =Q 0 .
3). Sy mmetry n.u = 0. Linear elastic material model is used here for which equation is given by C = C (E, V), in which E represents young' s modulus and V for Poisson' s ratio.

Simulation
Simu lation co mprises of two phases, where in first one lowest eigen modes are calculated by rep lacing the expression of displacement field and the other one involves the application of the frequency swept. Deformat ions are observed after the expression is replaced to susceptance. Since we applied AC potential between the electrical terminals on both sides of the electrode surface, the imaginary part of the admittance i.e., susceptance is calculated. This can be computed by knowing the ratio of total current applied and voltage supplied for the given structure. Where the maximu m allo wed potential is one volt peak for the first four lowest eigen frequency.

Results and Discussion
Using software, two kinds of studies has been explored i.e., study 1 for calculat ion of the lowest eigen modes, Whereas the study 2 corresponds to the frequency domain case in which frequency swept is noted down for the first four eigen frequencies. The range of the frequency is given form 20e 3 to106e 3 and for a step about 2e 3 deformation is observed by plotting on the material. No w the displacement field , Z component is selected form the solid mechan ics of piezoelectric devices by rep lacing the expression of surface 1. Eigen modes and slices of deformations are observed by plotting the surface 1 for three different materials, which are shown in Figu re 7 and 8. Total d isplacement can be observed for the model, after the app licat ion of the frequency swept. Later slices are formed for the model which helps in analysing the internal deformation. 1-Dimensional graph is obtained by replacing the expression to susceptance for the vertex one, which shows the relat ion between the susceptance and frequency. The first material we considered for analysis was Nepec 6 where the min imu m and maximu m deformat ions are -1.7719x10 -8 and 2.2744x10 -7 respectively for the eigenfrequency 43196.272163, wh ich is shown in Fig. 7a. But when Quart z was used the deformation values for minimu m and maximu m are 5.066x10 -10 and -52589x10 -8 respectively, which can be observed in Fig. 7b. When Pzt-8 is subjected to test for computation of eigen modes, the deformation can be noted from   The min imu m and maximu m total displacements values in meters for the model when Nepec 6 material is used are 4.4729x10 -8 and2.6688x10 -7 respectively. Whereas for the frequency swept of freq(44)=1.60e5, the displacement values are 5.8919x10 -12 and 9.0897x10 -10 , which are shown in the form of the slices and can be observed fro m Fig. 8a and 10 a respectively. When Quartz material is used, the range is fro m 9.3404x10 -9 to 5.6433x10 -8 and after frequency is applied the displacement values are 8.3578x10 -22 to 2.8866x10 -19 ,as shown in Fig. 8b and 10b respectively. On the other hand, from the Fig. 8c and 11c, Pzt-8 resulted in the displacement range from 4.8305x10 -8 to 2.7847x10-7, whereas after application of frequency, the minimu m to maximu m displacement range is from 2.3308x10 -10 to 2.3358x10 -8 respectively.
When input susceptance is calculated as an function o f excitat ion frequency, the maximu m susceptance value is 0.005 Siemens with min imu m value of -0.0035 Siemens for the Nepec 6 material, wh ich is shown in Fig. 11 a. Whereas Quartz material resulted for the ma ximu m and minimu m in the values in the range of 6x10 6 with the minimu m of 0.2x10 5 that are shown in Fig. 11 b. On the other hand the susceptance value is 0.015 Siemens for the Pzt-8 material, which is shown in Fig. 11 c. a) Results obtained when NEPEC 6 mate rial is used. b) Results obtaine d when Quartz mate rial is used. c) Results obtaine d when PZT -8 material is use d. Figure 11. Input susceptance as a function of excitation frequency

Conclusions
MEMS composite ultrasonic transducer was designed and simu lated using COMSOL Multiphysics version 4.2 a with three different piezoelectric materials. We have analysed the susceptance results as a function of excitation frequency for the four lowest eigenfrequencies of the structure. Fro m the analysis of these results, the proposed composite transducer used PZT-8 material was exh ibit ing better value of susceptance rather than other materials. Thus it allowed us to conclude that the PZT-8 u ltrasonic transducer exhibits better sensitivity which can find many non destructive testing applications.