Proceedings of IMECE 8 8 ASME International Mechanical Engineering Congress and Exposition October 3-Noveber 6, 8, Boston, Massachusetts, SA ASME8-6786 CHAACTEIZATION AND MODELING OF CAPACITIVE MICOMACHINED LTASONIC TANSDCES FO DIAGNOSTIC LTASOND Christopher B. Doody and obert D. White* Mechanical Engineering Departent, Tufts niversity Medford, MA 55, SA r.white@tufts.edu Jaspreet S. Wadhwa and David F. Leerhirt Sonetics ltrasound, Inc. Ann Arbor, MI 489, SA ABSTACT This paper describes the characterization and odeling of capacitive icroachined ultrasonic transducers (cmts). Coputational odels of the transducers were produced through the cobined use of finite eleent analysis (FEA) and luped eleent odeling. Frequency response plots were generated for both transducers in air and water environents. Through the use of laser Doppler velocietry, transient step response and frequency sweep tests were perfored on single array eleents. These easureents are copared to the predicted results represented in the odels. The coputational results for both coupled and uncoupled arrays are copared, and show a significant increase in the array bandwidth due to coupling. Frequency sweep tests were also perfored on colun array eleents, and results were copared between driven and adjacent, non-driven coluns. INTODCTION Diagnostic edical ultrasound requires arrays of ultrasound transducers for both transit and receive operations. Piezoelectric crystals or piezocoposites have been utilized for ost existing coercial technology. ecently, capacitive icroachined ultrasound transducers (cmts) have becoe a copeting MEMS technology with soe attractive features; particularly the possibility of integrating signal processing, signal routing, and power *Address all correspondence to this author. electronics on chip with the transducers, and also the possibility of increased bandwidth. The design of cmts has been studied since the early 99 s []. esearchers have described a variety of cmt designs and odels [-]. Both luped eleent odeling and finite eleent analysis (FEA) have been eployed [3-4]. Measureents of device response often include transit and receive frequency response easureents in a water tank, and also device input electrical ipedance [-]. Laser interferoetry has also been used in at least one case to characterize cmt dynaics [5]. This paper presents a hybrid finite eleent/luped eleent odeling schee for cmt arrays, and copares the predictions to laser Doppler velocietry easureents. The cmts being tested were fabricated using layers coon to standard coercial CMOS processes. For this project, two designs of icroachined ultrasonic array eleents were considered. MODELING Luped Eleent Modeling Luped eleent acoustic odels were used in order to create a coputational odel of the transducers. Two coupled electrical-echanical acoustic odels of a single cmt eleent can be seen in Figure. The top odel represents the eleent in transit ode. In transit ode, the driving F voltage, V ac, is applied to the
FIGE : MECHANICAL-ELECTICAL LMPED ELEMENT MODEL OF THE TANSDCE IN TANSMIT MODE (TOP) AND ECEIVE MODE (BOTTOM). eleent s phrag. In transit ode, the output of the odel is the phrag s volue velocity,, which can be used to copute the farfield transitted pressure, as discussed later in the paper. The botto odel represents the eleent while in receive ode. In receive ode, an external acoustic pressure, P in, is applied to the phrag face. The result is a volue velocity which is converted to a current by the ideal transforer, feeding fro there into the receive electronics. The luped eleent acoustic odel incorporates environental loading, phrag ass, phrag acoustic copliance, the negative electrostatic spring, and backing cavity copliance. Many of these eleents were calculated analytically using known acoustic paraeters [6-7]. The environental ipedance, Z env, was coputed using the four coponents for a rigid baffled piston rating into an infinite half space for, valid for (ωa/c) < [7], Z env [ C [ M M s( + ( M + A + C + C A.44 ρ / A s)] ) + + ] A () c a () A ρ / ( π ) c a (3) M A a 8ρ /(3π ) (4) 3 ( ) ( ρ ) C 5.94 a / c (5)
where ρ and c represent the speed of sound and density for the environent, and s represents the Laplace transforation variable. The phrag oves in a bending shape as opposed to a perfect rigid piston. Therefore, a, representing the effective phrag radius, is equal to 8% of the physical radius for a bending circular plate, as deterined using finite eleent analysis. The electrostatic spring, C elect, is the only nonlinear eleent in the odel, but it can be treated as a short circuit as long as the bias voltage on the transducer is not approaching the pull-in voltage. If it cannot be treated as a short circuit, then the negative acoustic copliance associated with the electrostatic spring can be deterined, C elect A / K (6) where A represents the surface area of the phrag, and K represents the electrostatic spring (force/distance) of the transducer. In order to calculate K, linearized about a noinal deflection, d no, the following equation is used, d K ( ε no d + ε d 3 + ) ε 3 3 ( ) ( V ε bias ) (7) ρ P cav cav ρ (9) P where the density in the cavity is the density of air at atospheric pressure, ρ, ultiplied by the ratio of the cavity pressure to atospheric pressure. Finite Eleent Analysis Due to the coplex cross-sectional geoetry of the transducer designs, finite eleent analysis was used to deterine the phrag stiffness, effective phrag ass, and the electrostatic coupling for the transducer. COMSOL Multiphysics was used to ap the coplex geoetry of each transducer as an axisyetric cross-section. A basic layout of the transducer s cross section can be seen in Figure. In each case, the transducer is structured as an axisyetric cross-section, coprised of a bulk silicon base, several thin fil dielectric layers, and a passivation layer. Within the phrag region rests a top and botto conductor, as well as a vacuu-filled cavity resting in between the two. The two conductive layers for the variable parallel plate capacitor for electricalechanical coupling. The air gap acts as a sall echanical spring, entioned in the above section. In calculating the electrostatic spring equation, d no is the noinal height of the vacuu gap, ε is the perittivity of free space, d n and ε n are the height and perittivity of the other intervening dielectric layers, and V bias is the applied DC bias. It is iportant to note that K should have a negative value. For cmts with a low vacuu backing cavity, the copliance of the backing cavity ay not contribute uch stiffness, but ay be easily included. Within the transducer odel, there is a sall vacuu filled cavity located within the transducer, filled with a sall aount of residual air. This acts as a sall echanical spring as it is copressed by the otion of the phrag. The cavity copliance can be calculated by ( ρ ) C V / c (8) cav cav cav where V cav is the volue of the cavity, c is the speed of sound (not strongly affected by pressure), and ρ cav is the density of the rarefied air in the cavity, which ay be approxiated by FIGE : AXISYMMETIC COSS-SECTION OF THE TANSDCE. C, representing the in vacuo phrag acoustic copliance, was calculated using a linear elastic axisyetric static analysis. The acoustic copliance is the surface integral of air displaced by the phrag at DC in response to a unit applied pressure on the face of the transducer. A lower copliance indicates a stiffer phrag. An eigenfrequency analysis was then perfored on the sae odel in order to deterine the phrag effective ass, M according to M C f π () 3
where f is the first eigenfrequency in cycles per second. The FEA coputation was originally conducted for a transducer with a passivation layer coprised of PECVD nitride. However, a nuber of scenarios utilizing different passivation layer aterials, including Oxynitride and Parylene-C, as well as no passivation layer at all, were coputed as well. Coupling can be coputed by considering the parallel plate capacitor fored between the aluinu and the doped polysilicon with the two intervening dielectrics and the vacuu gap, ρ f P( r, t) e r ( t r ) jω c (4) where e is the density of the environent, f is the frequency of the drive, and c is the sound speed in the environent. Based on the above equations, and the acoustic odels displayed in Figure, the transit dynaics can be represented by the following transfer function, dno d d 3 N α + + V ε ε ε 3 ε bias () Note that N has units of Pa/V, or, equivalently, Ap/(/s) (in SI units). It is a bidirectional coupling constant for the ideal transforer. Alpha, α, is a nondiensional paraeter to account for incoplete electrode coverage, where < α<. When a transducer is in receive ode, it is driven by a unifor pressure applied to the top of it s phrag, in which a volue displaceent is deterined for the entire phrag,. However, when in transit ode, the unifor pressure is applied only to the electrodes, and a different volue displaceent,, is obtained. α is coputed by using FEA to run the two static siulations, and then applying the results to the following equation, α / () where different values for α will be obtained based on the geoetry and aterial properties of the transducer. With these paraeters in hand, the volue velocity in response to a given DC bias plus F drive voltage can be coputed. This volue velocity can be translated into a ebrane centerpoint displaceent by u u jω ctr (3) where u ctr is the ratio of the centerpoint displaceent to the volue displaceent taken fro the static finite eleent coputation. The pressure at a distance r fro the eleent can also be estiated by treating the eleent as a baffled siple source, assuing we are in the farfield and there are no reflections, H( s) V M s + Z env N s s + ( / C + / C + / C ) cav elect (5) Note that this is the volue velocity of the ebrane,, in response to the square of the applied voltage. Thus, if we are interested in the response at ω when driving with a DC bias, V dc, plus an AC pure tone at ω, with aplitude V ac, the volue velocity agnitude will be H (jω) ultiplied by V dc V ac. The receive dynaics can be represented by a second transfer function, ( s) H ( s) P( s) M s + Z env s + s ( / C + / C + / C ) cav elect (6) where P is an external driving pressure. It is iportant to note that P here does not include the pressure generated by the eleent in question, that loading is accounted for the in the environental ipedance, Z env. However, the external pressure could coe fro pressures generated by other cmts in the array, as will be discussed in a later section of this paper. The use of these transfer functions results in the creation of the frequency response plots displayed in the next section. 4
SINGLE ELEMENT ESLTS A frequency sweep test was also perfored on a single eleent transducer, in air, with a +9 V DC bias and a V PP F input. Laser Doppler velocietry (LDV) was used to easure the ebrane centerpoint response. Test results show a peak frequency of about 5 MHz, with an approxiate. n/v low-frequency gain. Centerpoint displaceent calculated fro the coputational odel was copared to the frequency sweep data obtained fro the single cmt eleent transducer. The coputational odel predicted a peak frequency of approxiately 6 MHz, siilar to the 5 MHz obtained fro the transducer chip. The experiental results show considerably larger displaceents at low frequencies than the odel predicts. A frequency plot coparison can be seen in Figure 5. The agnitude is the aplitude of the centerpoint displaceent noralized to the product of the applied DC bias and the aplitude of the F drive voltage. FIGE 3: MICOSCOPE PHOTOGAPH OF A SINGLE CMT ELEMENT. sing the coputational odel, frequency response plots were generated for a single eleent of the array in both air and water environents. The odels were also tested with different passivation layer aterials and thicknesses. A saple frequency response plot can be seen in Figure 4. In air, the priary resonance for this device is predicted to be 6. MHz, with a very narrow fractional bandwidth of.%. In the underwater environent, the odel predicts a 3.4 MHz center frequency, with a fractional bandwidth of 7% for the sae device. As a coparison, experiental results for transit operation in a water tank indicate an approxiate center frequency for this device of 3.3 MHz with 5% fractional bandwidth. Mag (n/v ) Phase (deg) - -4 5 5 Frequency esponse, Centerpoint Displaceent -5 Frequency (Hz) Air Water FIGE 4: MODELED TANSMIT FEQENCY ESPONSE FO A SINGLE ELEMENT IN AI AND WATE ENVIONMENTS. Mag (n/v ) Mag (n/v ) Phase (deg) - -4 4 - Frequency esponse, Centerpoint Displaceent - Measured -4 - -4 5 5 Frequency esponse, Centerpoint Displaceent - Modeled -5 Frequency (Hz) FIGE 5: FEQENCY ESPONSE COMPAISON BETWEEN COMPTATIONAL AND EXPEIMENTAL DATA. sing LDV, a transient step response was easured for a single eleent in air, for a to V step. The result is 5
shown in Figure 6. The step response shows the very high Q of the syste when operating in air, and a resonant frequency of 5 MHz, siilar to the high-q 6 MHz resonance predicted by the odel. The Q of the syste decreases draatically when suberged, both in coputation and in water tank experients. Model results illustrating this appear in Figure 4. Centerpoint esponse to a V Step In the coupled coputation, each eleent is forced not only by the electrostatic force but also by the pressures generated by the otion of all other eleents in the array. This leads to a atrix coputation, with a fully populated transfer function atrix including the phase lag and geoetric spreading of the baffled onopole pressure field for each individual eleent. The unknowns in the equation are the volue velocities of the eleents in the array, which can be calculate using the following equation, Displaceent (n) - - -3-4 - 3 4 5 Tie (µs) FIGE 6: A V TANSIENT STEP ESPONSE OF A SINGLE TANSDCE ELEMENT (LDV MEASEMENT). AAY COMPTATIONS AND ESLTS Array coputations have been carried out for a 55 eleent colunar array, an exaple of which can be seen in Figure 7. eleents H V + [ H P ( δ )] (7) n where δ n is the Kronecker delta function, and P n is the pressure field produced by the n th eleent at the th eleent s centerpoint. This pressure is a direct function of the volue velocity of the n th eleent, P n ρ π n se n c n s n n (8) where n is the distance between the th and n th eleents, s is the derivative operator, and e -Ts is the delay operator. For steady state, haronic drive coputations, s ay be replaced with jω, resulting in an algebraic atrix inversion to find the coplex volue velocities. The transfer functions H (s) and H (s) were given in equations (5) and (6). Once the volue velocities for all eleents are deterined fro the coupled coputation, the farfield pressure can be coputed by suing the onopole fields fro each eleent, ρ P( x, y, z, t) s ( t / c) π (9) where the ral distance,, fro the th eleent to the field point is ( x x) + ( y y) + ( z z) () FIGE 7: MICOSCOPE PHOTOGAPH OF A 55 ELEMENT COLMNA AAY. The array coputation shows a considerable increase in bandwidth for the array over the bandwidth of an individual eleent. Figure 8 copares the predicted pressure for the 55 eleent colunar array transitting into water at a 6
distance 7.5 fro the center of the array for a 4 V p pure AC drive. The two curves in the plot represent the result when each eleent in the array transits in isolation (labeled uncoupled ), and when the fully coupled solution is coputed. Mag (n/v ) - Frequency Sweep of Active Colun Array Eleent driven colun adjacent colun -4 Phase (deg) - - Frequency (Hz) Frequency Sweep of Dead Colun Array Eleent FIGE 8: COMPAISON BETWEEN COPLED AND NCOPLED COMPTATIONS. Frequency sweep tests were perfored on several colun array eleents grouped together on a single transducer. Soe of the eleent arrays tested had been shorted out during wirebonding, but were easured for coparison purposes. Siilar to the frequency sweep for the single eleent transducer, the tests were perfored in air, with a +9 V DC bias and a V PP F input. The obtained results can be seen in Figure 9. Tests results show a peak frequency of about. MHz, with an approxiate. n/v low-frequency gain for the active driven coluns. While the shorted colun arrays showed a siilar. n/v low-frequency gain, the results showed that peak frequency occurred uch lower, at about.3mhz. Coluns adjacent to the ones being driven were also tested. The arrays adjacent to the shorted out coluns showed siilar results. The arrays adjacent to the active coluns did not respond at the peak frequency CONCLSIONS A ethod of cobining FEA and luped eleent odeling for cmt eleents has been described. The odeling ethod is coputationally efficient, and leads to good predictions of the resonant frequency and bandwidth of individual eleents in both air and water environents. The low frequency agnitude of the coputation does not yet agree well with easureents; additional investigations are underway to deterine if this is a odeling or easureent artifact. Array coputations have been briefly described. The bandwidth predicted by a fully coupled coputation is uch wider than the uncoupled result Phase (deg) Mag (n/v ) - -4 - driven colun adjacent colun - Frequency (Hz) FIGE 9: FEQENCY ESPONSE COMPAISON BETWEEN ACTIVE AND DEAD COLMN AAY ELEMENTS. EFEENCES. Ladabau, I., Jin, X., Soh, H., Atalar, A., and Khuri- Yakub, B. Surface Microachined Capacitive ltrasonic Transducers. IEEE Transactions on ltrasonics, Ferroelectrics, and Frequency Control, 998, 45(3): p. 678-69.. Jin, X., Ladabau, I., Degertekin, F., Cales, S., and Khuri-Yakub, B. Fabrication and Characterization of Surface Microachined Capacitive ltrasonic Iersion Transducers. IEEE Journal of Microelectroechanical Systes, 999, 8(): p. - 4. 3. Lohfink, A., Eccardt, P.-C., Benecke, W., and Meixner, H. Derivation of a D CMT Model fro FEM esults for Linear and Nonlinear Equivalent Circuit Siulation. IEEE ltrasonics Syposiu, 3: p. 465-468. 4. Yaralioglu, G., Badi, M., Ergun, A., and Khuri-Yakub, B. Iproved Equivalent Circuit and Finite Eleent Method Modeling of Capacitive Microachined 7
ltrasonic Transducers. IEEE ltrasonics Syposiu, 3: p. 469-47. 5. Hansen, S., Turo, A., Degertekin, F., and Khuri-Yakub, B. Characterization of Capacitive Microachined ltrasonic Transducers in Air sing Optical Measureents. IEEE ltrasonics Syposiu, : p. 947-95. 6. Kinsler, L., Frey, A., Coppens, A., and Sanders, J. Fundaentals of Acoustics: Fourth Edition. John Wiley & Sons, Inc.. 7. Beranek, Leo. Acoustics. Aerican Institute of Physics. 986. 8