On the Generation of High-Frequency Acoustic Energy with Polyvinylidene Fluoride

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On the Generation of High-Frequency Acoustic Energy with Polyvinylidene Fluoride
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  IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-27, NO. 6, NOVEMBER 1980 295 On the Generation of High-Frequency Acoustic Energy with Polyvinylidene Fluoride ROBERT G. SWARTZ,MEMBER, EEE, AND JAMES D. PLUMMER, MEMBER, IEEE Absrracr-The piezoelectric polymer polyvinylidene fluoride PVF2) has recently shown great promise in medical imaging applications when combined with integrated circuit technology o form a broadband acoustic detector. The application of polyvinylidene fluoride as a gen- erator of acoustic energy in the 1-10 MHz frequency range is con- sidered. The acoustic response of rigidly backed PVFz to voltage and current-source electrical drive s analyzed, and the broadband nature of the response to current-source drive s demonstrated. Measured values of the dielectric parameters of VFz re presented and used to calculate the effects rising from the frequency-dependent ielec- tric constant and associated dielectric loss. The multiple-layer stack, a mechanical transformer, is proposed as a method for ncreasing the available output power from a transducer. Experimental n- vestigation of this theoretical modeling s described. T I INTRODUCTION HE piezoelectric polymer polyvinylidene fluoride (PVFz has previously demonstrated suitability as an ultrasonic detector in medical imaging applications because of the close acoustic impedance match between it and body tissues. In particular recent work has demonstrated the viability of mono. lithic silicon/PVFz acoustic sensors [ 1 , 2] . An example of this type of transducer structure s shown in Fig. 1.  A sheet of PVFz is glued to the surface of a silicon wafer. Electrical contact to the PVFz is accomplished by means of electrodes evaporated on the PVFz and on n SiOz layer adjacent to the silicon surface. Diffused within the silicon are the source and drain regions of a metal-oxide semiconductor MOS) transis- tor, with the lower electrode of the PVFz constituting the ex- tended gate of the MOS field-effect transistor (MOSFET). When an incident longitudinal acoustic wave modulates the thickness of the PVFz layer, an electrical signal resulting from piezoelectric action in the transducer appears directly on he gate of the MOS transistor. The MOSFET may then be em- ployed either to amplify this signal or, as a multiplexer, to select for further processing one signal from an array of trans- ducer elements. Simple theory predicts that this piezoelectric/oxide/semi- conductor field-effect transistor (POSFET) will display the broadband frequency characteristic plotted in Fig. 2 [l]. This response has been experimentally verified sing a large array composed of 34 elements [2]. Manuscript received August 13, 1979; revised August 25, 1980. This work was supported partially under National Institutes of Health Grant No. 2 P50 GM-l7940 and partially under Office of Naval Research Contract No. N00014-78-C-0614. ford University, Stanford, CA 94305. He is now with Bell Labora- tories, Holmdel, NJ 07733. ford University, McCullough Bldg., Rm. 14, Stanford, CA 94305. R. G. Swartz was with the Stanford Electronics Laboratories, tan- J D. Plurnmer is with the Stanford Electronics Laboratories, tan- EPOXY = 5 LOWER ELECTRODE Si02nISp P-,(lOO), SILICON Fig. 1. PVFz-MOSFET transducer [l] 2] 0.40 N a 0.20 z O U E -36 FREQUENCY -72 -108 - -144 -180- - PvF2 X/4 - b) TRANSDUCER Fig. 2. Output-voltage/input-stress ransfer relationship for the AI4 resonant PVFz transducer. l = 30 p. (a) Magnitude of V,ut/Tin. b) PhW of V,,t/Tin. The POSFET receiving transducer technology indicates the promise of PVF2. The most functionally flexible transducer, however, is one that can both transmit and receive. This paper focuses, therefore, on nswers to the following questions. Can PVFz be used to generate high-frequency acoustic What are the advantages and the best approach o trans- energy? mitting with PVF2 ? 0018-9537/80/1100-0295 00.75 0 1980 IEEE  296 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-27, NO. 6 NOVEMBER 1980 Generation of acoustic energy with WF2 at frequencies above 1 MHz (the range required for medical imaging) has been reported [3] -[5]. The results obtained from those n- vestigations were generally exploratory in nature, demonstrat- ing the existence and form of an coustical output. This paper proceeds further, valuating the potential and means of ppli- cation of PVFz, articularly in comparison to the commonly used ceramic piezoelectric materials. The inherent acoustic properties of PVF2 are its broadband response resulting from its acoustic near match to water (the major constituent of body issues), it’s mechanical flexibility, and it’s wide acceptance angle. The following problems, how- ever, are associated with using PVF2 as a transmitter. Low Dielectric Constant: PVF2 has a very low dielectric constant in comparison to such materials as lead-zirconate- titanate (PZT). At 2 MHz, for example, the dielectric con- stant of PVFz is approximately 11.5 eo versus 830 eo for PZT-SA. This implies that the input electrical impedance of PVFz is very high in comparison to that of a PZT composite. To generate equal amounts of output acoustic power, there- fore, a much higher PVF2 drive voltage is required. plex dielectric constant of PVFz s large at frequencies 2 500 kHz. Because this loss is responsible for the dissipation of most of the input lectric power, only a relatively small frac- tion appears at the acoustic port. This inherent loss cannot be removed by inductive tuning. Low kF. The greatest electromechanical coupling coeffi- cient kT reported for PVFz is 0.205 [6] while for PZT-5A, it is 0.49 [7]. The square of this number s a measure of the ratio of the transferred lectromechanical energy to the total input energy. With equal amounts of vailable input electrical power, therefore, the PZT ransducer will generate greater acoustic output. These last two problems cannot be resolved with currently available materials although superior polymers, in time, may be developed. The disadvantage of the low dielectric constant can be minimized by the use of multiple ayers discussed in Section IV. In addition the broadband PVF2 frequency re- sponse may make all of the above characteristics acceptable depending on particular system applications. The transducer configuration discussed here is an ideal in- finitely high impedance-backed PVF2 layer. There is little ad- vantage seen in a matched impedance backing, except to raise the resonant frequency, because such a backing would result in excessive power exiting through the ear acoustic port. High Dielectric Loss: The imaginary component of the com- 11. TRANSMITTING FREQUENCY ESPONSE OF THE PVF2 TRANSDUCER NEGLECTING DIELECTRIC oss In a piezoelectric transducer external tuning of the lectrical port is critical for maximizing sensitivity. A series inductor is commonly used to tune out the input apacitance of the trans- ducer at the operating frequency, and the eal part of the elec- trical source impedance s chosen to match the eal transducer impedance [g]. In a material with low mechanical loss, how- ever, a small k, implies a relatively high electrical Q. Induc- tive tuning of PVFz can thus esult in a severely reduced band- width. This is especially undesirable inasmuch as broadband Fig. 3. Mason-model equivalent circuit for rigidly backed WF2 trans- ducer operated in thickness extensional mode with voltage source drive. 6or FREQUENCY MHz) Fig. 4. Calculated output power versus frequency for rigidly backed PVF2 transducer with voltage source electrical drive. Dielectric losses and frequency dependence of dielectric constant are neglected. operation is the principal advantage gained by the use of PVF2. Initially, therefore, the esponse of PVFz when driven by an untuned ideal voltage source is analyzed. For simplicity the dielectric loss is initially neglected although its effect will be considered in the next section. If the transducer s modeled by means of the Mason model [9] as shown in Fig. 3, the transfer function may be derived as and the output power (plotted versus frequency in Fig. 4) is Pout = Fout l 2ZwA where Fout s the output force and ,A is the acoustic im- pedance of the water load. The esponse peaks near the fre- quency where the thickness of the transducer s one-fourth wavelength. Because this characteristic has low Q, smooth bandshape, a clean short-duration impulse response is ex- pected [8]. tion loss” which is here defined to be - 10 log Pout/Pin) where Pout/Pin s the ratio of transducer coustic output power to available electrical input power with specified elec- trical tuning parameters. The lowest insertion loss is normally obtained when the transducer at its resonance is conjugately matched to the source although this arely provides the maxi- mum bandwidth. Insertion loss arises as a result of electrical impedance mismatch, dissipative mechanisms within the trans- ducer, and output coupling to the rear acoustic port and ex- One measure of the efficiency of a transducer is the “inser-  SWARTZ AND PLUMMER: HIGH-FREQUENCY ACOUSTIC ENERGY 291 0 17 34 51 6.3 FREOUENCY MHz) a) W , 1 1 0 17 34 51 8 FREOUENCY MHz1 b) Fig. 5. Insertion loss versus frequency for rigidly backed 30 p PVF2. Area = 1 cm2, electrical source impedance = 1.1 a an 6~ = 0, fixed dielectric constant, no dielectric loss. a) Untuned PVF2 transducer. b) nductively tuned transducer, series inductance = 0.375 pH. traneous modes. Only impedance mismatch and dielectric loss are thought to e of consequence for the arge area rigidly backed PVF2 transducer. The output power with 1 V drive for a 1 cm2, 100 pm PVF2 transducer in which dielectric loss is neglected, peaks at about 50 pW. An inductively tuned, commercial broadband ceramic transducer of similar dimensions, with no front-matching layers will deliver 60 pW (as calculated for a Panametrics VIP- 5-1/2 I transducer with the same drive, based on measured im- pedance and insertion-loss data) [lo]. The output power of a tuned ceramic transducer with proper front-matching and backing layers, however, can be 100 times greater. Fig. 5 plots the calculated insertion loss of rigidly backed 30 pm PVF2 as a function of frequency. The result of Fig. 5(a) is calculated with the source esistance equal to the real impedance of the transducer at resonance, but with no external tuning inductor. Fig. 5(b) illustrates the effect of series inductive tuning. The insertion loss in Fig. 5(a) is primarily a result of reactive im- pedance mismatch at the electrical port since dielectric losses have been neglected in these calculations. As can be seen tun- ing reduces insertion loss but also severely reduces bandwidth. The insertion oss of the untuned PVF2 transducer s about 25 dB at the X/4 resonance. In an optimized ceramic trans- ducer, however, 5 dB or less can be expected with little reduc- tion in bandwidth. The spectral characteristic of an untuned PVF2 transducer driven by a voltage source (Fig. 4) is smooth and broad, but t lacks the low-frequency esponse of the PVF2 POSFET re- ceiver (Fig. 2) that extends ideally to dc. The condition re- quired for this characteristic s that the transducer's electrical port be capacitively loaded only, a constraint satisfied by the MOSFET gate in Fig. 1. The equivalent mode of operation for 0 5 10 15 20 FREOUENCY MHz) Fig. 6. Output power versus frequency for rigidly-backed, current- source-driven PVF2. Area= 1 cm2, tan 6~ = 0 = 30 p, 1 A elec- trical drive, fvted dielectric constant, dielectric losses neglected. Fig. 7. Equivalent circuit for rigidly backed PVF2 far below resonance. a transmitting PVF2 structure is obtained when the transducer is driven by a current source. When a current source is sub- stituted for the oltage source in the Mason model of Fig. 3, the transfer relationship can be derived as Fout - h 1 Ii, jw 1 (jZo/Z,) ot PZ 3) which leads to a transmission spectrum of the form of Fig. 2. Consequently the calculated acoustic output power (plotted in Fig. 6 for 30 pm PVF2), displays the same broad frequency response. Calculation of the input impedance of the igidly backed PVF2 transducer far below resonance (using the Mason model of Fig. 3) yields the equivalent circuit of Fig. 7. In the deriva- tion the low-frequency assumptions re made that To cot i?l+ zo/pl >> 2 . The principal components of the low-frequency model are the clamped capacitance CO he dielectric loss re- sistance R , and the radiation esistance R representing ac- tual acoustic output power. The broadband nature of the response under current drive can be understood by ecogniz- ing that the radiation esistance R of PVF2 operated in the quarter-wave resonance mode is virtually frequency indepen- dent below resonance. Because of the rigid acoustic backing any electric-field-induced strain must appear as displacement of the front urface of the transducer. The current-source-driven mode f operation of PVF2 has the following advantages. 0 The overall impulse response is better than for other lec- trical drive methods because the frequency response ex- tends over a broader range. 0 The phase of the transfer characteristic will vary linearly  298 IEEE TRANSACTIONS ON SONICS ND ULTRASONICS, VOL. SU-27, NO. 6, NOVEMBER 1980 below the resonant frequency, necessary requirement for distortion-free transmission [ 1 ]. 0 Extension of the response to frequencies far below reso- nance indicates that a single PVFz transducer could be used over a wide range of operating frequencies. Although an ideal current source cannot be obtained at all frequencies, the requirement for broadband operation of this type is simply that the current-source output mpedance must be much higher than the electrical input impedance of the transducer. This method is impractical at low frequencies be- cause there the voltage developed across the essentially capaci- tive transducer impedance becomes very large. 111. EFFECT OF DIELECTRIC OSS Dielectric loss has been neglected in the above calculations which is a reasonable procedure for typical ceramic trans- ducers. The high k, of these piezoelectric materials makes acoustic loading rather than dielectric loss a dominant factor in the electrical Q. As a consequence most electrical power is coupled to the acoustic ports and elatively little is lost in the ceramic dielectric. Other researchers [12], however, have reported the high dielectric loss in PVFz . Fig. 8 shows measurements obtained in the present study of the ielectric constant and loss tangent of a 30 prn sample of uniaxially stretched and poled Kureha PVFz film. These curves were obtained by measuring the elec- trical input impedance of an coustically unloaded film suffi- ciently far enough below the half-wave resonance frequency so that Yi, = wC 1 + C J 5) which for PVF2 (where e:,/&~, , << l), becomes A Yi, jwc =io er - je ) = wAd l where E and E are the real and imaginary parts of the com- plex dielectric constant and e''/~' & tan a~ he dielectric loss tangent [ 131 . Earlier calculations of the lectromechanical transfer rela- tionships and frequency response have assumed a uniform di- electric constant. It is not difficult to include the variation of E with frequency within the standard Mason model; however, the dependence of the lastic and piezoelectric factors on fre- quency should be determined as well. Such parameters have been measured as a function of temperature for PVF2 [6], but there is an absence of knowledge of their variation with frequency. Although frequency-independent elastic and piezo- electric constants are assumed in the calculations to follow, the variation of the dielectric constant is included. A property of a PVFz transducer operating in the /4 mode is that, in the absence of dielectric or mechanical loss, con- servation of energy requires that the real electric input power must equal the output acoustic ower inasmuch as very little energy is coupled into the back acoustic port. In the resence of dielectric loss, however, this is no longer true. When tan 6 is nonzero the power lssipated in the loss resistance R6 (1 - j tan aE (6) 0; 1 1 lb Ih :4 l do FREQUENCY MHz) Fig. 8. Dielectric parameters of PVF2 versus frequency. a) Dielectric constant for PVFz. b) Dielectric loss tangent tan 6~) or PVFz. ENLARGED OUTPUT FREQUENCY MHz) Pig. 9. Electrical input and acoustic output power in the presence of dielectric loss. Area = 1 cm2, I = 30 p 1 A current source drive. (see Fig. 7) can greatly exceed that acoustically radiated. Fig. 9 is a plot of the alculated acoustic output and lectrical input power as a function of frequency for 30 pm PVF2 transducer under current-source rive; the measured variations of the dielectric constant and dielectric loss have been in- cluded. The curves were obtained from the Mason model in Fig. 3. It can be seen that the spectral characteristic of the acoustic output esponse is relatively unaffected by dielectric loss; however, the discrepancy between the real input and out- put power indicates that most lectrical power is dissipated within the body of the transducer. his has the following im- portant implications. 0 The transducer will be internally heated by this ielectric dissipation. Internal heating may eventually raise the tem- perature to the point where the PVF2 material s depoled. The maximum duty ycle for transducer operation WLU de- pend, therefore, on the peak ower used for transmitting  SWART2 AND PLUMMER: HIGH-FREQUENCY ACOUSTIC ENERGY 299 100 ’t ITPUT 75r and on the thermal conductivity of the arious compo- nents of the transducer structure. The dielectric-loss component cannot be tuned inductively. The theoretical insertion oss plotted in Fig. 5(b) where S has been neglected appears low at the tuned frequency. Actually, however, even with tuning, most of the lectrical input power is dissipated. This constitutes an inherent minimum insertion oss regardless of the electrical-drive method employed. As can be seen in Fig. 9 the acoustic output power/electrical input power ratio is minimum at the quarter-wave resonance frequency where (for 30 PVF2) it is approximately 8.5 dB. Fig. 10 plots the calculated input electrical and output acoustic power versus frequency for current-source-driven PVFz which has been inductively parallel-tuned. In Fig. lO(a) the transducer has been tuned elow its resonance frequency. Its “inherent” untunable insertion loss is approximately 15 dB which compares poorly to well-designed modern ceramic trans- ducers, and its frequency esponse has deteriorated substan- tially. Fig. 1O(b) is the predicted response of a PVFz transducer inductively tuned very near the resonance frequency. The minimum insertion oss remains approximately 9.5 dB, but the bandshape is more uniform hich implies a cleaner impulse re- sponse. A transmitting transducer tuned at esonance may be an acceptable alternative to a ceramic transducer in applica- tions where other features of PVFz prove advantageous. the predicted results in this section, we turn to an alternative technique for improving the overall transmit efficiency of the simple PVFz structure. Before proceeding with experimental verification of some of Fig. 11. Multiple-layer transmitter. 6000r 0 Fig. 12. Acoustic output power versus frequency for rigidly backed PVFz stack. Area = 1 cm’, stack thickness = 100 p, number of layers = 1, 2,4,6, 8, 10; V electrical drive. N MULTIPLE AYERS As discussed in Section I the low dielectric constant of PVF2 relative to that of ceramic piezoelectric materials can present a problem in transmitting applications. For example, using a 100 V signal generator, it is possible to generate an acoustic output intensity of 20 W/cm’ at 5 MHz in an elec- trically tuned efficient ceramic transducer. It can be shown from the data in igs. 8 and 9 that because of its lower di- electric constant, the generation f a comparable acoustic output intensity would require an 800 V signal in a PVF2 transducer h/4 resonant at 5 MHz [9]. output from a voltage source-driven PVFz transducer, how- ever, by use of the multiple-layer stack (Fig. l l), a technique commonly used in receiving transducer applications [ 1 S] . The transducer is backed by a high acoustic impedance, and the materials of the alternating ayers have reversed polarity. The following features of this scheme can be understood by ecog- nizing that the layers are electrically in parallel and acousti- cally in series. Linvill [ 141 has proposed a method for increasing the power 0 The transducer is resonant at a frequency where the total stack thickness is one-quarter wavelength. 0 For a constant total stack thickness and voltage-source in- put, the acoustic output ower increases as the square of the number N of layers within the stack; that is, For a transducer thickness of 100 pm, the calculated output power versus frequency is plotted in Fig. 12 for various num- bers of layers (dielectric loss has again been neglected). The
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