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Air-coupled MUMPs capacitive micromachined ultrasonic transducers with resonant cavities
Ultrasonics 52 (2012) 482–489
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Air-coupled MUMPs capacitive micromachined ultrasonic transducers with resonant cavities Alberto Octavio Manzanares ⇑, Francisco Montero de Espinosa CAEND, UPM-CSIC, C/Serrano, 144, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 14 June 2011 Received in revised form 20 October 2011 Accepted 25 October 2011 Available online 4 November 2011 Keywords: Capacitive micromachined ultrasonic transducer MUMPs Helmholtz resonator Air-coupled ultrasonic transducers
a b s t r a c t This work reports performance improvements of air-coupled capacitive micromachined ultrasonic transducers (CMUTs) using resonant cavities. In order to perform this work, we have designed and manufactured a CMUT employing multi-user microelectromechanical systems (MEMS) processes (MUMPs). The transducer was designed using Helmholtz resonator principles. This was characterised by the dimensions of the cavity and several acoustic ports, which had the form of holes in the CMUT plate. The MUMPs process has the advantage of being low cost which allows the manufacture of economic prototypes. In this paper we show the effects of the resonant cavities and acoustic ports in CMUTs using laser Doppler vibrometry and acoustical measurements. We also use Finite Element (FE) simulations in order to support experimental measurements. The results show that it is possible to enhance the output pressure and bandwidth in air by tuning the resonance frequency of the plate (fp) with that of the Helmholtz resonator (fH). The experimental measurements show the plate resonance along with an additional resonance in the output pressure spectrum. This appears due to the effect of the new resonant cavities in the transducer. FE simulations show an increase of 11 dB in the output pressure with respect to that of a theoretical vacuum-sealed cavity MUMPs CMUT by properly tuning the transducer. The bandwidth has been also analyzed by calculating the mechanical Q factor of the tuned CMUT. This has been estimated as 4.5 compared with 7.75 for the vacuum-sealed cavity MUMPs CMUT. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Non-destructive ultrasonic inspection systems have been designed over the years to test materials and structures. The coupling media is a key parameter. Immersion transducers are the most common option since liquids are particularly suitable for ultrasonic propagation [1]. Nevertheless, some structures could be damaged by contact with liquids [2] or contact could be unsuitable. In recent years, air-coupled ultrasonic transducers have been developed in order to meet these needs [3–5]. Ultrasonic systems based on piezoelectric ceramics have been used successfully [6]. However, their use generally results in a lack of resolution when performing ultrasonic imaging due to their working frequency. This is being addressed by the development of high-frequency electrostatic transducers. Schindel et al. [7] developed an electrostatic transducer based on a micromachined backplate and a diaphragm made of a commercially available dielectric film, such as Kapton or Mylar. Several works have demonstrated the efficiency of these transducers [8]. Haller and Khuri-Yakub made the first ⇑ Corresponding author. Present address: INAMOL, Universidad de Castilla-La Mancha, Campus Tecnológico de la Antigua Fábrica de Armas, Avda. de Carlos III, s/ n, 45071 Toledo, Spain. Tel.: +34 925268800x5572; fax: +34 925268849. E-mail address: [email protected] (A. Octavio Manzanares). 0041-624X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2011.10.011
electrostatic transducers completely manufactured by means of micromachining techniques [9]. This was termed the capacitive micromachined ultrasonic transducer (CMUT). From that day on, lithography methods allowed to make any form of cell (the basic structure of a CMUT element), any shape of plate (as explained in [10], plate is the appropriate term for the moving part of a CMUT cell) and array element size. This was a crucial step towards the improvement of the resolution of ultrasonic imaging systems. Since CMUTs have demonstrated improved resolution, large bandwidth and high efficiency in liquid media, they have been mainly used in immersion applications such as medical imaging [11]. Moreover, air-coupled CMUTs have been also studied and applied [12]. Nevertheless, a complete air-coupled ultrasonic inspection system based on CMUTs has not yet been reported. An increment of the bandwidth of CMUTs is needed in order to improve their efficiency in air (particularly in air coupled non-destructive evaluation (NDE) applications where short ring down time should be used). In this paper we use the theory of acoustic resonators with the aim of improving the output pressure and bandwidth of air-coupled CMUTs. Previous work showed how a particular acoustic resonator could improve the behaviour of electrostatic transducers [13]. In this work, the use of a resonant conduit in the cavity of electrostatic transducers is proposed in order to obtain fluidic amplification. In the present work, we propose a different
A. Octavio Manzanares, F. Montero de Espinosa / Ultrasonics 52 (2012) 482–489
approach aimed at designing a CMUT based on the behaviour of a Helmholtz resonator [14]. A basic Helmholtz resonator consists of an enclosure with an open hole (denoted as an acoustic port). A resonant system is produced due to the compliance of the air in the enclosure coupled to the mass of air in the port and at the opening. Examples of acoustic systems based on Helmholtz resonators to reinforce certain harmonics are the bass-reflex speakers and musical instruments such as the African djembe. The major challenge of manufacturing such a micromachined transducer is the fabrication process. Since the cavity resonance frequency depends on the cavity volume, and the size and length of the acoustic ports, the fabrication process should be as reliable and repeatable as possible. The fabrication of the transducer presented here has been carried out using a standard process provided by MEMSCAP (MEMSCAP SA, Bernin, France) within their commercially available processes known as multi-user microelectromechanical systems (MEMS) processes (MUMPs). The main advantage of the chosen process (PolyMUMPs) is that it is more cost effective than a custom process, and has reasonable repeatability and reliability [15]. The only drawback is the limitation due to the standardization of the process parameters concerning structural materials and layer dimensions. Previous CMUT designs made using PolyMUMPs are presented in Refs. [16–18]. 2. MUMPs CMUT fabrication 2.1. Fabrication technology The PolyMUMPs process is basically characterised by the use of three heavily doped polysilicon layers and a gold layer (denoted Poly0, Poly1, Poly2 and Metal, respectively) as the structural materials for MEMS fabrication. Since it is a standard process, the foundry defines the thicknesses of each of these layers (0.5 lm, 2 lm, 1.75 lm and 0.5 lm respectively). The process always starts with the deposition of a 0.6 lm thick silicon nitride layer over an n-type silicon wafer heavily doped at its surface. This provides electrical isolation between the silicon substrate and the structural layers. The user can manufacture a specific device through the design of the masks POLY0, POLY1, POLY2, METAL and three more masks (ANCHOR1, ANCHOR2 and POLY1_POLY2_VIA) that provide anchorage and contact areas of the structural layers. In order to construct micro plates, three more masks are provided to create etch holes (HOLE1, HOLE2 and HOLEM). These are aimed at removing the sacrificial layers of the process (1st Oxide and 2nd Oxide). The disposition of the PolyMUMPs layers presented here has been used in previous work [16–18]. It employs a Poly0-Poly1configuration made up of Poly0 as the CMUT bottom electrode and Poly1 as the plate and top electrode (Fig. 1). As the polysilicon used is highly conductive, there is no need to perform plate metallization. The metal layer is used for electrical routing. A CMUT made using this configuration presents a voltage limitation because of the absence of isolation between electrodes. Electrical short may occur if the plate collapses onto the bottom electrode. The silicon substrate could be used as the bottom electrode by breaching the silicon nitride. This provides electrical
Fig. 1. A cross-section of a MUMPs CMUT cell using the Poly0–Poly1 configuration.
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contact with the silicon substrate at these breach areas and electrical isolation between electrodes. Several designs that use the silicon substrate as the bottom electrode have been presented [17]. Nevertheless, the Poly0–Poly1 configuration used in this paper has been more widely used and tested. 2.2. Helmholtz resonator MUMPs CMUT design The main aim of this work consists of using resonator theory to improve the efficiency of air-coupled CMUT transducers. Specifically, the CMUT transducer presented here was intended to work as a Helmholtz resonator. As previously mentioned, this kind of systems consists of an enclosed cavity with one or several acoustic ports. Then, when air is forced into the cavity through these ports, the cavity pressure is enhanced and the system tends to overcompensate the change in compression. This causes the air to oscillate outwards and inwards at a frequency known as Helmholtz frequency (fH). The value of this frequency depends on the geometry of the system and is given by the equation:
c fH ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A Vðl þ dÞ
ð1Þ
where c is the velocity of sound, A the surface of the acoustic ports, V the volume of the cavity and l the acoustic port length. d is an endcorrection factor whose value depends on the distribution and shape of the acoustic ports, and has been widely studied in the literature [14]. The behaviour of this kind of system can be compared with a mass-spring system where the volume of the air in the acoustic ports and at their openings could be represented as a mass moving due to the compliance of the air in the cavity. For systems where the acoustic driver is a membrane or a plate (such as a bass-reflex loudspeakers or the CMUT presented here), two resonators are coupled. The plate itself has its frequency response with a first resonance with central frequency at fp. It drives the Helmholtz resonator producing radiation at approximately fH. The theory of acoustic resonators [14,19] demonstrates that when the plate moves at a frequency near fH, the radiation from the plate and that from the acoustic ports are produced in phase causing a constructive interference. This has been experimentally observed in [20]. This operational mode will be denoted here as tuned CMUT operation. The behaviour of these electromechanical devices can be modelled and tested in function of frequency using electrical or mechanical parameters such as electrical impedance, plate displacement or output pressure. When tuned, these parameters show two peaks in their responses with similar amplitude near fp. By definition, the Helmholtz frequency fH is the frequency at the local minimum between these two resonances. Since fH depends on the transducer geometry, the limitations of the PolyMUMPs fabrication process are important in realising the tuned device. In fact, the plate surface is practically the only parameter that can be modified when designing a CMUT with the process described here. Because of this, the design methodology followed in this work consists of calculating the resonance frequency of a square plate and the Helmholtz frequency for a range of plate lengths. The correct plate length corresponds to that which matches fH and fp. In Fig. 2 values1 of fp as a function of the length of the plate for different boundary conditions are depicted (solid lines). The lower values (blue line) correspond to squared shaped plates with simply-supported boundary conditions (SS) and the higher values (red line) correspond to plates with clamped boundary conditions (C). These values were calculated using the following equations [21] 1 Please note that Fig. 2 will appear in B/W in print and colour in the web version. Based on this, please approve the footnote 1 which explains this.
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Fig. 2. The Helmholtz Resonator area for MUMPs CMUTs.
sffiffiffiffiffiffi D fp ðSSÞ ¼ 2 a qh
p
ð2Þ Fig. 4. A photograph of 4 CMUT cells in an element containing 2 29 cells.
42 sffiffiffiffiffiffi p D fp ðCÞ ¼ 3 2 a qh
ð3Þ
where a is the length of the plate, q is the polysilicon density, h is the plate thickness and D is the flexural rigidity defined by
near to the clamped condition has been implemented since fH and fp(C) are similar for this plate length. Five CMUT elements made up of 2 cells per element width and 29 cells per element length were fabricated. Fig. 4 shows a photograph of 4 cells in an element.
3
D¼
Eh 12ð1 t2 Þ
ð4Þ
E and t are the Young’s modulus and the Poisson’s ratio of the polysilicon respectively. Since plate boundary conditions are previously unknown, we have considered that fp is between the values fp(SS) and fp(C) for a specific plate length. fH has been calculated using Eq. (1) considering plate lengths up to 100 lm and four square shaped etch holes in the plate (this is the minimum number of holes for this plate size following the PolyMUMPs design rules). Then, plate lengths from 80 lm to 170 lm and 16 etch holes (which corresponds to the minimum number of holes for this plate size) were also considered. The length of the acoustic port (l) corresponds to the plate thickness (h), the size of the holes corresponds to the minimum applicable length (5 lm) and we have taken an end-correction factor value of
pffiffiffi d ¼ 0:96 A
ð5Þ
which corresponds to an arbitrary aperture [21]. Fig. 2 shows a shaded area, denoted as the Helmholtz resonator area, where fH is between fp(SS) and fp(C). This indicates all plate lengths within this range that are candidates for use in the design. Fig. 3 shows the chosen CMUT cell design. The transducer consists of CMUT cells with 150 lm-side square shaped plates with 16 holes. Each of these holes has a length of 5 lm. The graphed curves in Fig. 2 show that a plate that has boundary conditions that are
3. Methodology The methodology used in this work consisted of performing laser Doppler vibrometry (LDV) and acoustical measurements, and then using them to adjust and validate a FE model. The FE model was then used to perform a comparison between a properly tuned CMUT and a conventional vacuum-sealed cavity CMUT. 3.1. Experimental methods 3.1.1. Laser Doppler vibrometry measurements The LDV measurements were performed using a Polytec system MSV-400 (Polytec GmbH, Waldbronn, Germany) at University of Castilla-La Mancha (Ciudad Real, Spain). The system is capable of supplying different driving voltage signals in order to perform the desired measurement. The bias voltage was supplied by a Keithley 2400 General-Purpose SourceMeter (Keithley Intruments, Inc., Cleveland, OH, USA). 3.1.2. Acoustical measurements The acoustic performance of the transducer was analysed using measurement of its output pressure. This was achieved using a transmit-receive system using a piezoelectric transducer based on a PZ27 ceramic as a receiver [6] with its central frequency at 1.45 MHz. The CMUT transducer was biased using an Agilent N5751A DC System Power Supply (Agilent Technologies, Inc., CA, USA) and driven through an Agilent 33250A arbitrary function generator (Agilent Technologies, Inc., CA, USA). The received signal was acquired through an Agilent DSO6014A Oscilloscope (Agilent Technologies, Inc., CA, USA). 3.2. FE simulations
Fig. 3. A MUMPs CMUT single cell design.
FE simulations were carried out using the commercial package ANSYS (ANSYS Inc., Canonsburg, PA, USA). A MUMPs CMUT 3-D model was developed to support the experimental measurements. Since the CMUT cell design is symmetric with respect to two planes, the model could be reduced to one quarter of the whole cell design (Fig. 5). This model is based on the ANSYS TRANS126
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and the squeeze-film damping due to the flow of air in the acoustic ports. These are represented in the equivalent circuit [22] shown in Fig. 6. This equivalent circuit includes the CMUT fixed capacitance (C0), the impedance of the plate (ZP), the plate radiation impedance (ZR), the acoustic mass of the air in the cavity (MAB), the acoustic compliance due to the compression of the air in the cavity (CAB), the ports radiation impedance (ZRP), the acoustic mass of the air in the ports (MAP) and the mentioned losses RMD (material damping), RAB (absorption losses) and RAP (squeeze-film losses due to the viscosity of the fluid). These parameters have been widely studied in the literature [23]. The air compression in the holes has been considered negligible since the Reynolds number given by
Re ¼
Fig. 5. An ANSYS model of one quarter of a CMUT cell and the surrounding medium (air). (a) Model: cell and medium. (b) Detail of the CMUT cell.
elements behaviour. These are specifically assigned for coupled structural and electrostatic problems. ANSYS is capable of automatically creating a set of these elements by using the command macro EMTGEN. It uses the initial gap and relative permittivity as inputs. Once the macro is executed, it calculates the capacitance of the whole transducer by assigning a portion of the electrode area to each TRANS126 element upper node. The rest of the model consists of structural SOLID45 elements to construct the plate, FLUID30 to model the surrounding medium and FLUID130 to set infinite boundary conditions at the boundary of the model. This last was done in order to minimise the reflections back into the fluid. In order to calculate the acoustic pressure in the surrounding medium, FLUID30 air elements adjacent to SOLID45 elements require a different configuration. These have displacement and pressure degrees of freedom active in order to couple the structural field with the fluid elements. These also require the activation of the ANSYS fluid–structure interface (FSI) flag at the interface nodes. The material properties used are listed in Table 1. Once the model was validated through the experimental measurements, it was then modified in order to compare the MUMPs CMUT behaviour with that of a theoretical vacuum-sealed cavity MUMPs CMUT. This was done using ANSYS MESH200 elements to simulate vacuum conditions beneath the plate and holes. Changes in the geometry of the original model were also made in order to study resonant cavity effects in the transducer output pressure. 3.2.1. Helmholtz resonator and sources of loss in FE simulations The main sources of loss present in this kind of device are material damping, losses due to the acoustic absorption in the cavity Table 1 The material properties used in FE analysis. Polysilicon Young’s modulus (GPa) Poisson’s ratio Density (kg/m3) Relative permittivity Velocity of sound (m/s) a
Extracted from [15].
169a 0.22 2330
Air
1.21 1.0006 340
xd2 q0 g
ð6Þ
yields in a small number which indicates that a laminar flow is produced [24]. It uses x as the angular frequency, d as the height of the air gap, q0 as the density of the air and g as the dynamic coefficient of viscosity. Then, the compliance that models the squeeze stiffness has not been included. ANSYS supports modelling of squeeze-film damping (using FLUID136 and FLUID138 elements), material damping (through a constant material damping coefficient) and acoustic absorption (using the material property MU for FLUID30 elements in contact with the structure and activating the surface load label IMPD at the interface nodes between FLUID30 and SOLID45). Since RMD and RAP mainly produce a constant damping and the absorption losses have been considered small, the damping of the system has been modelled solely by the material damping in order to perform a more straightforward study. It is well known that the losses in the system affect the device performance. However, the mentioned sources of loss are not the causes of the cavity resonance. The two characteristic peaks in the frequency response of a tuned system with a Helmholtz resonator are produce due to the parallel resonant circuit made up of the compliance CAB and the inductance MAP (neglecting the acoustic port radiation). When the system is working at fH, the equivalent impedance of MAP and CAB is an open circuit so that the velocity of the plate (u1) tends to zero. This works as a notch filter which affects the plate resonance if fH is close to fp. At this situation the acoustic radiation of the system predominantly comes from the acoustic ports. Furthermore, this radiation from the acoustic ports is in phase with that from the plate. Since the acoustic mass of the air in the ports has been modelled by assigning the corresponding material properties to the FLUID30 elements in the holes and the compliance of the air in the cavity has been modelled by the FLUID30 elements that forms the cavity volume, the effects of the Helmholtz resonator can be studied using the present ANSYS model. 4. Results 4.1. Plate displacement The LDV system was used to obtain the plate displacement at the centre of a transducer plate as a function of frequency. This identified fp and the resonant cavity effects of the plate displacement. One 1-D array element made up of 2 cells per element width and 29 cells per element length was biased using 40 V and driven with a 3 V amplitude sinusoidal voltage with a frequency from 800 kHz to 2 MHz. Fig. 7 shows the result of this measurement (solid line) along with the result of the FE simulation (dashed line). Here, two resonances appear. The first one corresponds to fp, which
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Fig. 6. Equivalent circuit of a transmitting CMUT with Helmholtz resonator in air. Vs is the applied driving voltage at a bias point, / is the transformer ratio of the equivalent circuit, P the applied pressure, u1 the velocity of the plate, u2 the velocity of air particles in the cavity and u3 the velocity of air particles in the ports.
Fig. 7. The measured and simulated displacement of a MUMPs CMUT plate at its centre as a function of frequency in response to a 40 V bias and a 3 V amplitude driving voltage.
occurs at 1.2 MHz. The second resonance (fp2), which is at around 1.6 MHz, should correspond to the effect of the Helmholtz resonator and thus the frequency that corresponds to the inflexion point between these resonances is fH. The FE result agrees well with the experimental measurement except for the second resonance that appears at around 1.7 MHz, slightly higher than expected. The second resonance appears somewhat weaker in both cases. Since fH is sensitive to changes in geometry, the small difference between the experimental and simulated result are assumed to be due to differences between the model and the actual design and due to the possible effects of losses and squeeze stiffness that have not been taken into account and could shift the Helmholtz frequency. This result shows how the resonant cavity apparently causes the plate to vibrate at another frequency close to fp. The output pressure measurements in the next section show how both resonances affect to the CMUT behaviour. 4.2. Transducer output pressure 4.2.1. Experimental output pressure A piezoelectric air-coupled transducer was used as a receiver in order to perform acoustical measurements [6]. The experiment was done by positioning the transducer in front of an active CMUT element at a distance of 1 cm. The CMUT was biased using 40 V dc and driven with a 10-volt amplitude pulse. The signal acquired by the piezoelectric transducer is shown in Fig. 8. In order to obtain the CMUT output pressure as a function of frequency, several steps were followed. First, the FFT of the piezoelectric transducer pulseecho signal was calculated. This result is shown in Fig. 9. This result was divided by two so as to obtain the piezoelectric transducer frequency characteristic. Then, the deconvolution of the piezoelectric transducer impulse response from the received signal was computed. This was done in order to remove the influence of the receiver in the CMUT frequency response. The resulting output pressure
Fig. 8. The received signal for a transducer separation of 1 cm.
Fig. 9. The FFT of the piezoelectric transducer pulse-echo signal.
amplitude in dB relative to the maximum pressure emitted at a point at 1 cm from the transducer face is shown in Fig. 10 (solid line). As shown in Fig. 7, in Fig. 10 the first resonance at 1.2 MHz corresponds to fp, and the second at 1.63 MHz is that produced due to the resonator effect (fp2). The local minimum between these peaks occurs at 1.35 MHz and corresponds to fH. Unlike the plate displacement measurements, the effect of the second resonance is more apparent in the acoustical measurements. In fact, this resonance is higher than that for the plate radiation. Nevertheless, the separation between peaks and the weakness of the second resonance at fp2 in the curve shown in Fig. 7 indicate that the expected improvement was not achieved at all due to the evident inequality between fH and fp. Nevertheless, the second peak which appears at 1.63 MHz in the output pressure measurement presents a quality factor (Q) of 6.7 and has a considerable relative output level that demonstrates that an improvement could be achievable using a properly tuned device. The simulation result is also shown in Fig. 10 (dashed line). It confirms the deviation of the second resonance peak due to small
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control of the residual stresses within the plates upon manufacture in order to make a good prediction of fp and thus obtain a properly tuned device.
Fig. 10. The MUMPs CMUT element output pressure from measurement and simulation.
geometrical differences between the model and the actual transducer and the possible effect of the neglected squeeze stiffness in the Helmholtz frequency. The relative difference of amplitude between the peak at fp2 and fp in the simulated curve (which is different in the experimental measurement) could be due to the neglected effect of acoustic absorption in the cavity. Studying the equivalent circuit of Fig. 6 one can see that the influence of the second resonance decreases when acoustic absorption is taken into account. Even so, the model is sufficient for the reported work. In the following sections, two model modifications are presented. They were used to obtain a better insight into the effects of resonant cavities in CMUTs.
4.2.2. MUMPs CMUT versus vacuum-sealed cavity MUMPs CMUT Fig. 11 shows the comparison of the proposed MUMPs CMUT simulated output pressure with that of the same CMUT with a vacuum-sealed cavity. The most noticeable effect is the absence of the second resonance in the curve that corresponds to the vacuumsealed cavity MUMPs CMUT. This confirms that the second resonance appears due to the effect of the resonant cavity. It is seen that the MUMPs CMUT transducer has not improved since its output pressure at 1.2 MHz is 5 dB with respect to the vacuumsealed cavity MUMPs CMUT maximum output pressure and the bandwidth is almost the same at frequencies near fp. This result was obtained for the same plate displacement in each case. This is due to the resulting inequality between fH and fp (fH = 1.35 MHz and fp = 1.2 MHz). Since fH and fp are sensitive to changes in geometry, it is essential to have good control of the fabrication process. Moreover, is also desirable to have precise knowledge of the material properties and the design parameters as well as have a good
Fig. 11. The simulated MUMPs CMUT and vacuum-sealed cavity MUMPs CMUT output pressure in dB relative to the maximum output pressure of the vacuumsealed cavity MUMPs CMUT.
4.2.3. Tuned CMUT versus vacuum-sealed cavity MUMPs CMUT Comparing the previous results with the theoretical values of fH and fp, it can be said that fp is within the expected range but fH is slightly higher than that previously estimated. Thus, a modification of several design parameters would be needed, such us the hole size or the cell cavity volume in order to properly tune the transducer. Since the hole size cannot be changed due to the limitations of PolyMUMPs, the cavity volume is the only parameter that can be modified through changes in the plate size. This will also produce changes in fp since its value is inversely proportional to the square of the plate length. In particular, the transducer needs a smaller plate in order to tune fp–fH. Then, it would be possible to obtain a PolyMUMPs tuned CMUT by studying the convergence of fH and fp as the plate length is modified. Nevertheless, this would imply an increase in the working frequency, and this could be critical for air-coupled ultrasonic applications. In order to illustrate this, a further FE model was constructed in order to obtain an approximate idea of the benefits of using a CMUT that employs a Helmholtz resonator. Since a change in plate length would produce a deviation in fp, the new model (tuned CMUT) was built by modifying the gap between CMUT electrodes. This maintains the value of fp allowing a better comparison of this transducer with the vacuum-sealed cavity MUMPs CMUT. This change is not realisable with PolyMUMPs since this distance is standardised. Fig. 12 shows the displacement at the centre of the plates for each of the FE models. The tuned CMUT plate displacement simulation was obtained using a gap of 5 lm between electrodes. In order to compare the output pressure of these devices, they were excited using a driving voltage such that the plate displacement was of similar magnitude. The curves that correspond to the MUMPs CMUT model and that of the vacuum-sealed cavity MUMPs CMUT were obtained by driving each transducer model with a 3 V amplitude sinusoidal signal and a 40-volt bias. The plate displacement yields an output pressure as shown in Fig. 11. In the case of the tuned CMUT, the same bias voltage was used. However, a 30 V amplitude sinusoidal voltage was required to achieve the same displacement. This is because of the increase of the gap height. This reduces the CMUT sensitivity since the transformer ratio of the equivalent circuit model of electromechanical transducers is inversely proportional to the square of the gap height [25]. This means that the electrostatic force acting on the plate will be small compared to that of a small-gap CMUT. The result shows that the characteristic peaks in the response of the tuned CMUT device appear with nearly the same amplitude.
Fig. 12. The displacement of the plate centre of the MUMPs CMUT, vacuum-sealed cavity MUMPs CMUT and tuned CMUT.
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Fig. 13. The simulated tuned CMUT and vacuum-sealed cavity MUMPs CMUT output pressure in dB relative to the maximum output pressure of the tuned CMUT.
This is a conventional indicator which indicates when the system reaches the tuned condition. Furthermore, Fig. 12 also shows that fH is 1.2 MHz. Under this condition, the output pressure was calculated at a point 180 lm from the centre of the plate. This result is shown in Fig. 13. Here, a tuned CMUT output pressure that is 11 dB higher than that of the vacuum-sealed cavity MUMPs CMUT has been obtained. Moreover, the bandwidth has been increased due to the resonant cavity. The quality factor (Q) has been estimated as 4.5 compared with 7.75 for the vacuum-sealed cavity device.
5. Conclusions A new approach for air-coupled CMUT has been presented. Unlike other CMUT devices that use non-sealed cavities [9,13,26], this design uses a resonant cavity in order to enhance the output pressure and bandwidth. The resonant cavity is based on a Helmholtz resonator design. Acoustic radiation occurs from several acoustic ports (holes) and the plate. A CMUT working under this principle was constructed using the PolyMUMPs standard fabrication process. The behaviour of this type of system was observed through several experimental results. These show that an additional resonance appears in the transducer output pressure spectrum due to the effect of the resonant cavity. Furthermore, the separation between peaks and the weakness of the second resonance at fp2 in the displacement measurement indicate that the expected improvement has not been achieved due to the inequality between fH and fp. Nevertheless, the quality factor (Q) of 6.7 and the relative output level of the output pressure measurement at fp2 demonstrates that an improvement could be achievable using a properly tuned device. FE simulations of the CMUT output pressure show that the resonance which corresponds to fp (1.2 MHz) has been calculated at 5 dB with respect to that of a theoretical conventional system with a vacuum-sealed cavity. Moreover, the bandwidth of this resonance has been estimated to be nearly equal in each case. This also confirms that the tuned condition was not achieved with this design. Since the values of fH and fp are sensitive to the design parameters, small differences between the initial design theoretical parameters and the actual parameters were found to produce significant deviations of these frequency values. As an illustrative example, a FE model of a properly tuned CMUT (with a gap height of 5 lm) has been presented in order to show the benefits of this kind of transducer. The simulated results obtained have been compared with that of a simulated conventional CMUT, and show that the tuned system can achieve an output pressure that is 11 dB greater than that of the vacuum-sealed cavity device. Moreover, its bandwidth is seen increased (Q = 4.5). This comparison was
made by ensuring the same peak plate displacement for both CMUT devices, although in order to achieve this, the tuned CMUT required a driving voltage ten-times larger than the vacuum-sealed cavity MUMPs CMUT. This is due to the relatively large gap between electrodes in this particular tuned CMUT design. Thus, it seems possible to enhance the output pressure and bandwidth of air-coupled CMUT transducers by using the theory of Helmholtz resonators. However, a further experimental study of properly tuned devices is required in order to accurately quantify these improvements. Moreover, a study towards the improvement of the sensitivity is needed in order to reduce the driving voltage level needed for achieving high output pressure levels. This is currently addressed by constructing a specially designed structure in the cavity with the purpose of decreasing the gap between electrodes while maintaining the cavity volume (i.e., column-like structure). The fabrication of such a transducer would require a specialised production process. Acknowledgements The authors acknowledge the Department of Electrical, Electronic, Automatic and Communication Engineering in the University of Castilla-La Mancha (Ciudad Real, Spain) for their support. References [1] I. Krautkraemer, H. Krautkraemer, Ultrasonic Testing of Materials, fourth fully revised ed., Springer-Verlag, Berlin, 1989. [2] W.A. Grandia, C.M. Fortunko, NDE applications of air-coupled ultrasonic transducers, in: Proceedings of the IEEE Ultrasonics Symposium, 1995, pp. 697–709. [3] F. Massa, Ultrasonic transducers for use in air, in: Proceedings of the IEEE, 1965, pp. 1363–1371. [4] H. Loertscher, B. Grandia, J. Strycek, W.A. Grandia, Airscan transducers, technique and applications, in: NDT.net, 1996, pp. 1–4. [5] T.R. Gururaja, W.A. Schulze, L.E. Cross, R.E. Newham, B.A. Auld, Y.J. Wang, Piezoelectric composite materials for ultrasonic transducer applications. Part I: Resonant modes of vibration of PZT rod-polymer composites, IEEE Transactions on Sonics and Ultrasonics 32 (1985) 481–498. [6] F. Montero de Espinosa, T.E. Gomez, A. Albareda, R. Perez, J.A. Casals, High sensitive piezoelectric transducers for NDE air borne applications, in: Proceedings of the IEEE Ultrasonics Symposium, 2000, pp. 1073–1076. [7] D.W. Schindel, D.A. Hutchins, L. Zou, M. Sayer, The design and characterization of micromachined air-coupled capacitance transducers, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42 (1995) 42–50. [8] T.-H. Gan, D.A. Hutchins, D.R. Billson, D.W. Schindel, High-resolution, aircoupled ultrasonic imaging of thin materials, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 50 (2003) 1516–1524. [9] M.I. Haller, B.T. Khuri-Yakub, A surface micromachined electrostatic ultrasonic air transducer, in: Proceedings of the IEEE Ultrasonics Symposium, 1994, pp. 1241–1244. [10] M. Kupnik, I.O. Wygant, B.T. Khuri-Yakub, Finite element analysis of stress stiffening effects in CMUTS, in: Ultrasonics Symposium, 2008. IUS 2008. IEEE, 2008, pp. 487–490. [11] K.A. Wong, S. Panda, I. Ladabaum, Curved micromachined ultrasonic transducers, in: Proceedings of the IEEE Ultrasonics Symposium, 2003, pp. 572–576. [12] I.O. Wygant, M. Kupnik, J.C. Windsor, W.M. Wright, M.S. Wochner, G.G. Yaralioglu, M.F. Hamilton, B.T. Khuri-Yakub, 50 kHz Capacitive micromachined ultrasonic transducers for generation of highly directional sound with parametric arrays, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 56 (2009) 193–203. [13] E. Campbell, W. Galbraith, G. Hayward, A new electrostatic transducer incorporating fluidic amplification, in: Proceedings of the IEEE Ultrasonics Symposium, 2006, pp. 1445–1448. [14] U. Ingard, On the theory and design of acoustic resonator, The Journal of the Acoustical Society of America 25 (1953) 1037–1061. [15] W.N. Sharpe, B. Yuan, R. Vaidyanathan, R.L. Edwards, Measurements of Young’s modulus, Poisson’s ratio, and Tensile strength of polysilicon, in: Proceedings of the Tenth IEEE International Workshop on Microelectromechanical Systems, Nagoya, Japan, 1997, pp. 424–429. [16] I.J. Oppenheim, A. Jain, D.W. Greve, Electrical characterization of coupled and uncoupled MEMS ultrasonic transducers, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 50 (2003) 297–304. [17] A. Octavio, C.J. Martín, Y. Gómez-Ullate, O. Martínez, L. Gómez-Ullate, F. Montero de Espinosa, P. Gatta, M. Domínguez, Design and characterization of air coupled ultrasonic transducers based on MUMPs, in: Proceedings of the IEEE Ultrasonics Symposium, 2006.
A. Octavio Manzanares, F. Montero de Espinosa / Ultrasonics 52 (2012) 482–489 [18] J. Liu, C. Oakley, R. Shandas, Capacitive micromachined ultrasonic transducers using commercial multi-user MUMPs process: capability and limitations, Ultrasonics 49 (2009) 765–773. [19] W. Marshall Leach, Introduction to electroacoustics & audio amplifier design, third ed., Kendall/Hunt Publishing Company, 2003. [20] A. Octavio Manzanares, F. Montero de Espinosa Freijo, Ultrasonic transducers with resonant cavities as emitters for air-borne applications, Boletín de la Sociedad Española de Cerámica y Vidrio 48 (2009) 205–209. [21] A.W. Leissa, Vibration of plates, in: NASA SP, 160, 1969. [22] W.P. Mason, Electromechanical Transducers and Wave Filters, Van Nostrand, New York, NY, 1942.
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[23] L.L. Beranek, Acoustics, first ed., Acoust. Soc. of America, New York, 1954. [24] T. Veijola, Compact model for a MEM perforation cell with viscous, spring, and inertial forces, Microfluidics and Nanofluidics 6 (2009) 203–219. [25] A.S. Ergun, G.G. Yaralioglu, B.T. Khuri-Yakub, Capacitive micromachined ultrasonic transducers: theory and technology, Journal of Aerospace Engineering 16 (2003) 76–84. [26] S.T. Hansen, A. Turo, F.L. Degertekin, B.T. Khuri-Yakub, Characterization of capacitive micromachined ultrasonic transducers in air using optical measurements, in: Ultrasonics Symposium, 2000 IEEE, 2000, vol. 941, pp. 947–950.
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Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Air-coupled MUMPs capacitive micromachined ultrasonic transducers with resonant cavities Alberto Octavio Manzanares ⇑, Francisco Montero de Espinosa CAEND, UPM-CSIC, C/Serrano, 144, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 14 June 2011 Received in revised form 20 October 2011 Accepted 25 October 2011 Available online 4 November 2011 Keywords: Capacitive micromachined ultrasonic transducer MUMPs Helmholtz resonator Air-coupled ultrasonic transducers
a b s t r a c t This work reports performance improvements of air-coupled capacitive micromachined ultrasonic transducers (CMUTs) using resonant cavities. In order to perform this work, we have designed and manufactured a CMUT employing multi-user microelectromechanical systems (MEMS) processes (MUMPs). The transducer was designed using Helmholtz resonator principles. This was characterised by the dimensions of the cavity and several acoustic ports, which had the form of holes in the CMUT plate. The MUMPs process has the advantage of being low cost which allows the manufacture of economic prototypes. In this paper we show the effects of the resonant cavities and acoustic ports in CMUTs using laser Doppler vibrometry and acoustical measurements. We also use Finite Element (FE) simulations in order to support experimental measurements. The results show that it is possible to enhance the output pressure and bandwidth in air by tuning the resonance frequency of the plate (fp) with that of the Helmholtz resonator (fH). The experimental measurements show the plate resonance along with an additional resonance in the output pressure spectrum. This appears due to the effect of the new resonant cavities in the transducer. FE simulations show an increase of 11 dB in the output pressure with respect to that of a theoretical vacuum-sealed cavity MUMPs CMUT by properly tuning the transducer. The bandwidth has been also analyzed by calculating the mechanical Q factor of the tuned CMUT. This has been estimated as 4.5 compared with 7.75 for the vacuum-sealed cavity MUMPs CMUT. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Non-destructive ultrasonic inspection systems have been designed over the years to test materials and structures. The coupling media is a key parameter. Immersion transducers are the most common option since liquids are particularly suitable for ultrasonic propagation [1]. Nevertheless, some structures could be damaged by contact with liquids [2] or contact could be unsuitable. In recent years, air-coupled ultrasonic transducers have been developed in order to meet these needs [3–5]. Ultrasonic systems based on piezoelectric ceramics have been used successfully [6]. However, their use generally results in a lack of resolution when performing ultrasonic imaging due to their working frequency. This is being addressed by the development of high-frequency electrostatic transducers. Schindel et al. [7] developed an electrostatic transducer based on a micromachined backplate and a diaphragm made of a commercially available dielectric film, such as Kapton or Mylar. Several works have demonstrated the efficiency of these transducers [8]. Haller and Khuri-Yakub made the first ⇑ Corresponding author. Present address: INAMOL, Universidad de Castilla-La Mancha, Campus Tecnológico de la Antigua Fábrica de Armas, Avda. de Carlos III, s/ n, 45071 Toledo, Spain. Tel.: +34 925268800x5572; fax: +34 925268849. E-mail address: [email protected] (A. Octavio Manzanares). 0041-624X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2011.10.011
electrostatic transducers completely manufactured by means of micromachining techniques [9]. This was termed the capacitive micromachined ultrasonic transducer (CMUT). From that day on, lithography methods allowed to make any form of cell (the basic structure of a CMUT element), any shape of plate (as explained in [10], plate is the appropriate term for the moving part of a CMUT cell) and array element size. This was a crucial step towards the improvement of the resolution of ultrasonic imaging systems. Since CMUTs have demonstrated improved resolution, large bandwidth and high efficiency in liquid media, they have been mainly used in immersion applications such as medical imaging [11]. Moreover, air-coupled CMUTs have been also studied and applied [12]. Nevertheless, a complete air-coupled ultrasonic inspection system based on CMUTs has not yet been reported. An increment of the bandwidth of CMUTs is needed in order to improve their efficiency in air (particularly in air coupled non-destructive evaluation (NDE) applications where short ring down time should be used). In this paper we use the theory of acoustic resonators with the aim of improving the output pressure and bandwidth of air-coupled CMUTs. Previous work showed how a particular acoustic resonator could improve the behaviour of electrostatic transducers [13]. In this work, the use of a resonant conduit in the cavity of electrostatic transducers is proposed in order to obtain fluidic amplification. In the present work, we propose a different
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approach aimed at designing a CMUT based on the behaviour of a Helmholtz resonator [14]. A basic Helmholtz resonator consists of an enclosure with an open hole (denoted as an acoustic port). A resonant system is produced due to the compliance of the air in the enclosure coupled to the mass of air in the port and at the opening. Examples of acoustic systems based on Helmholtz resonators to reinforce certain harmonics are the bass-reflex speakers and musical instruments such as the African djembe. The major challenge of manufacturing such a micromachined transducer is the fabrication process. Since the cavity resonance frequency depends on the cavity volume, and the size and length of the acoustic ports, the fabrication process should be as reliable and repeatable as possible. The fabrication of the transducer presented here has been carried out using a standard process provided by MEMSCAP (MEMSCAP SA, Bernin, France) within their commercially available processes known as multi-user microelectromechanical systems (MEMS) processes (MUMPs). The main advantage of the chosen process (PolyMUMPs) is that it is more cost effective than a custom process, and has reasonable repeatability and reliability [15]. The only drawback is the limitation due to the standardization of the process parameters concerning structural materials and layer dimensions. Previous CMUT designs made using PolyMUMPs are presented in Refs. [16–18]. 2. MUMPs CMUT fabrication 2.1. Fabrication technology The PolyMUMPs process is basically characterised by the use of three heavily doped polysilicon layers and a gold layer (denoted Poly0, Poly1, Poly2 and Metal, respectively) as the structural materials for MEMS fabrication. Since it is a standard process, the foundry defines the thicknesses of each of these layers (0.5 lm, 2 lm, 1.75 lm and 0.5 lm respectively). The process always starts with the deposition of a 0.6 lm thick silicon nitride layer over an n-type silicon wafer heavily doped at its surface. This provides electrical isolation between the silicon substrate and the structural layers. The user can manufacture a specific device through the design of the masks POLY0, POLY1, POLY2, METAL and three more masks (ANCHOR1, ANCHOR2 and POLY1_POLY2_VIA) that provide anchorage and contact areas of the structural layers. In order to construct micro plates, three more masks are provided to create etch holes (HOLE1, HOLE2 and HOLEM). These are aimed at removing the sacrificial layers of the process (1st Oxide and 2nd Oxide). The disposition of the PolyMUMPs layers presented here has been used in previous work [16–18]. It employs a Poly0-Poly1configuration made up of Poly0 as the CMUT bottom electrode and Poly1 as the plate and top electrode (Fig. 1). As the polysilicon used is highly conductive, there is no need to perform plate metallization. The metal layer is used for electrical routing. A CMUT made using this configuration presents a voltage limitation because of the absence of isolation between electrodes. Electrical short may occur if the plate collapses onto the bottom electrode. The silicon substrate could be used as the bottom electrode by breaching the silicon nitride. This provides electrical
Fig. 1. A cross-section of a MUMPs CMUT cell using the Poly0–Poly1 configuration.
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contact with the silicon substrate at these breach areas and electrical isolation between electrodes. Several designs that use the silicon substrate as the bottom electrode have been presented [17]. Nevertheless, the Poly0–Poly1 configuration used in this paper has been more widely used and tested. 2.2. Helmholtz resonator MUMPs CMUT design The main aim of this work consists of using resonator theory to improve the efficiency of air-coupled CMUT transducers. Specifically, the CMUT transducer presented here was intended to work as a Helmholtz resonator. As previously mentioned, this kind of systems consists of an enclosed cavity with one or several acoustic ports. Then, when air is forced into the cavity through these ports, the cavity pressure is enhanced and the system tends to overcompensate the change in compression. This causes the air to oscillate outwards and inwards at a frequency known as Helmholtz frequency (fH). The value of this frequency depends on the geometry of the system and is given by the equation:
c fH ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A Vðl þ dÞ
ð1Þ
where c is the velocity of sound, A the surface of the acoustic ports, V the volume of the cavity and l the acoustic port length. d is an endcorrection factor whose value depends on the distribution and shape of the acoustic ports, and has been widely studied in the literature [14]. The behaviour of this kind of system can be compared with a mass-spring system where the volume of the air in the acoustic ports and at their openings could be represented as a mass moving due to the compliance of the air in the cavity. For systems where the acoustic driver is a membrane or a plate (such as a bass-reflex loudspeakers or the CMUT presented here), two resonators are coupled. The plate itself has its frequency response with a first resonance with central frequency at fp. It drives the Helmholtz resonator producing radiation at approximately fH. The theory of acoustic resonators [14,19] demonstrates that when the plate moves at a frequency near fH, the radiation from the plate and that from the acoustic ports are produced in phase causing a constructive interference. This has been experimentally observed in [20]. This operational mode will be denoted here as tuned CMUT operation. The behaviour of these electromechanical devices can be modelled and tested in function of frequency using electrical or mechanical parameters such as electrical impedance, plate displacement or output pressure. When tuned, these parameters show two peaks in their responses with similar amplitude near fp. By definition, the Helmholtz frequency fH is the frequency at the local minimum between these two resonances. Since fH depends on the transducer geometry, the limitations of the PolyMUMPs fabrication process are important in realising the tuned device. In fact, the plate surface is practically the only parameter that can be modified when designing a CMUT with the process described here. Because of this, the design methodology followed in this work consists of calculating the resonance frequency of a square plate and the Helmholtz frequency for a range of plate lengths. The correct plate length corresponds to that which matches fH and fp. In Fig. 2 values1 of fp as a function of the length of the plate for different boundary conditions are depicted (solid lines). The lower values (blue line) correspond to squared shaped plates with simply-supported boundary conditions (SS) and the higher values (red line) correspond to plates with clamped boundary conditions (C). These values were calculated using the following equations [21] 1 Please note that Fig. 2 will appear in B/W in print and colour in the web version. Based on this, please approve the footnote 1 which explains this.
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Fig. 2. The Helmholtz Resonator area for MUMPs CMUTs.
sffiffiffiffiffiffi D fp ðSSÞ ¼ 2 a qh
p
ð2Þ Fig. 4. A photograph of 4 CMUT cells in an element containing 2 29 cells.
42 sffiffiffiffiffiffi p D fp ðCÞ ¼ 3 2 a qh
ð3Þ
where a is the length of the plate, q is the polysilicon density, h is the plate thickness and D is the flexural rigidity defined by
near to the clamped condition has been implemented since fH and fp(C) are similar for this plate length. Five CMUT elements made up of 2 cells per element width and 29 cells per element length were fabricated. Fig. 4 shows a photograph of 4 cells in an element.
3
D¼
Eh 12ð1 t2 Þ
ð4Þ
E and t are the Young’s modulus and the Poisson’s ratio of the polysilicon respectively. Since plate boundary conditions are previously unknown, we have considered that fp is between the values fp(SS) and fp(C) for a specific plate length. fH has been calculated using Eq. (1) considering plate lengths up to 100 lm and four square shaped etch holes in the plate (this is the minimum number of holes for this plate size following the PolyMUMPs design rules). Then, plate lengths from 80 lm to 170 lm and 16 etch holes (which corresponds to the minimum number of holes for this plate size) were also considered. The length of the acoustic port (l) corresponds to the plate thickness (h), the size of the holes corresponds to the minimum applicable length (5 lm) and we have taken an end-correction factor value of
pffiffiffi d ¼ 0:96 A
ð5Þ
which corresponds to an arbitrary aperture [21]. Fig. 2 shows a shaded area, denoted as the Helmholtz resonator area, where fH is between fp(SS) and fp(C). This indicates all plate lengths within this range that are candidates for use in the design. Fig. 3 shows the chosen CMUT cell design. The transducer consists of CMUT cells with 150 lm-side square shaped plates with 16 holes. Each of these holes has a length of 5 lm. The graphed curves in Fig. 2 show that a plate that has boundary conditions that are
3. Methodology The methodology used in this work consisted of performing laser Doppler vibrometry (LDV) and acoustical measurements, and then using them to adjust and validate a FE model. The FE model was then used to perform a comparison between a properly tuned CMUT and a conventional vacuum-sealed cavity CMUT. 3.1. Experimental methods 3.1.1. Laser Doppler vibrometry measurements The LDV measurements were performed using a Polytec system MSV-400 (Polytec GmbH, Waldbronn, Germany) at University of Castilla-La Mancha (Ciudad Real, Spain). The system is capable of supplying different driving voltage signals in order to perform the desired measurement. The bias voltage was supplied by a Keithley 2400 General-Purpose SourceMeter (Keithley Intruments, Inc., Cleveland, OH, USA). 3.1.2. Acoustical measurements The acoustic performance of the transducer was analysed using measurement of its output pressure. This was achieved using a transmit-receive system using a piezoelectric transducer based on a PZ27 ceramic as a receiver [6] with its central frequency at 1.45 MHz. The CMUT transducer was biased using an Agilent N5751A DC System Power Supply (Agilent Technologies, Inc., CA, USA) and driven through an Agilent 33250A arbitrary function generator (Agilent Technologies, Inc., CA, USA). The received signal was acquired through an Agilent DSO6014A Oscilloscope (Agilent Technologies, Inc., CA, USA). 3.2. FE simulations
Fig. 3. A MUMPs CMUT single cell design.
FE simulations were carried out using the commercial package ANSYS (ANSYS Inc., Canonsburg, PA, USA). A MUMPs CMUT 3-D model was developed to support the experimental measurements. Since the CMUT cell design is symmetric with respect to two planes, the model could be reduced to one quarter of the whole cell design (Fig. 5). This model is based on the ANSYS TRANS126
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and the squeeze-film damping due to the flow of air in the acoustic ports. These are represented in the equivalent circuit [22] shown in Fig. 6. This equivalent circuit includes the CMUT fixed capacitance (C0), the impedance of the plate (ZP), the plate radiation impedance (ZR), the acoustic mass of the air in the cavity (MAB), the acoustic compliance due to the compression of the air in the cavity (CAB), the ports radiation impedance (ZRP), the acoustic mass of the air in the ports (MAP) and the mentioned losses RMD (material damping), RAB (absorption losses) and RAP (squeeze-film losses due to the viscosity of the fluid). These parameters have been widely studied in the literature [23]. The air compression in the holes has been considered negligible since the Reynolds number given by
Re ¼
Fig. 5. An ANSYS model of one quarter of a CMUT cell and the surrounding medium (air). (a) Model: cell and medium. (b) Detail of the CMUT cell.
elements behaviour. These are specifically assigned for coupled structural and electrostatic problems. ANSYS is capable of automatically creating a set of these elements by using the command macro EMTGEN. It uses the initial gap and relative permittivity as inputs. Once the macro is executed, it calculates the capacitance of the whole transducer by assigning a portion of the electrode area to each TRANS126 element upper node. The rest of the model consists of structural SOLID45 elements to construct the plate, FLUID30 to model the surrounding medium and FLUID130 to set infinite boundary conditions at the boundary of the model. This last was done in order to minimise the reflections back into the fluid. In order to calculate the acoustic pressure in the surrounding medium, FLUID30 air elements adjacent to SOLID45 elements require a different configuration. These have displacement and pressure degrees of freedom active in order to couple the structural field with the fluid elements. These also require the activation of the ANSYS fluid–structure interface (FSI) flag at the interface nodes. The material properties used are listed in Table 1. Once the model was validated through the experimental measurements, it was then modified in order to compare the MUMPs CMUT behaviour with that of a theoretical vacuum-sealed cavity MUMPs CMUT. This was done using ANSYS MESH200 elements to simulate vacuum conditions beneath the plate and holes. Changes in the geometry of the original model were also made in order to study resonant cavity effects in the transducer output pressure. 3.2.1. Helmholtz resonator and sources of loss in FE simulations The main sources of loss present in this kind of device are material damping, losses due to the acoustic absorption in the cavity Table 1 The material properties used in FE analysis. Polysilicon Young’s modulus (GPa) Poisson’s ratio Density (kg/m3) Relative permittivity Velocity of sound (m/s) a
Extracted from [15].
169a 0.22 2330
Air
1.21 1.0006 340
xd2 q0 g
ð6Þ
yields in a small number which indicates that a laminar flow is produced [24]. It uses x as the angular frequency, d as the height of the air gap, q0 as the density of the air and g as the dynamic coefficient of viscosity. Then, the compliance that models the squeeze stiffness has not been included. ANSYS supports modelling of squeeze-film damping (using FLUID136 and FLUID138 elements), material damping (through a constant material damping coefficient) and acoustic absorption (using the material property MU for FLUID30 elements in contact with the structure and activating the surface load label IMPD at the interface nodes between FLUID30 and SOLID45). Since RMD and RAP mainly produce a constant damping and the absorption losses have been considered small, the damping of the system has been modelled solely by the material damping in order to perform a more straightforward study. It is well known that the losses in the system affect the device performance. However, the mentioned sources of loss are not the causes of the cavity resonance. The two characteristic peaks in the frequency response of a tuned system with a Helmholtz resonator are produce due to the parallel resonant circuit made up of the compliance CAB and the inductance MAP (neglecting the acoustic port radiation). When the system is working at fH, the equivalent impedance of MAP and CAB is an open circuit so that the velocity of the plate (u1) tends to zero. This works as a notch filter which affects the plate resonance if fH is close to fp. At this situation the acoustic radiation of the system predominantly comes from the acoustic ports. Furthermore, this radiation from the acoustic ports is in phase with that from the plate. Since the acoustic mass of the air in the ports has been modelled by assigning the corresponding material properties to the FLUID30 elements in the holes and the compliance of the air in the cavity has been modelled by the FLUID30 elements that forms the cavity volume, the effects of the Helmholtz resonator can be studied using the present ANSYS model. 4. Results 4.1. Plate displacement The LDV system was used to obtain the plate displacement at the centre of a transducer plate as a function of frequency. This identified fp and the resonant cavity effects of the plate displacement. One 1-D array element made up of 2 cells per element width and 29 cells per element length was biased using 40 V and driven with a 3 V amplitude sinusoidal voltage with a frequency from 800 kHz to 2 MHz. Fig. 7 shows the result of this measurement (solid line) along with the result of the FE simulation (dashed line). Here, two resonances appear. The first one corresponds to fp, which
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Fig. 6. Equivalent circuit of a transmitting CMUT with Helmholtz resonator in air. Vs is the applied driving voltage at a bias point, / is the transformer ratio of the equivalent circuit, P the applied pressure, u1 the velocity of the plate, u2 the velocity of air particles in the cavity and u3 the velocity of air particles in the ports.
Fig. 7. The measured and simulated displacement of a MUMPs CMUT plate at its centre as a function of frequency in response to a 40 V bias and a 3 V amplitude driving voltage.
occurs at 1.2 MHz. The second resonance (fp2), which is at around 1.6 MHz, should correspond to the effect of the Helmholtz resonator and thus the frequency that corresponds to the inflexion point between these resonances is fH. The FE result agrees well with the experimental measurement except for the second resonance that appears at around 1.7 MHz, slightly higher than expected. The second resonance appears somewhat weaker in both cases. Since fH is sensitive to changes in geometry, the small difference between the experimental and simulated result are assumed to be due to differences between the model and the actual design and due to the possible effects of losses and squeeze stiffness that have not been taken into account and could shift the Helmholtz frequency. This result shows how the resonant cavity apparently causes the plate to vibrate at another frequency close to fp. The output pressure measurements in the next section show how both resonances affect to the CMUT behaviour. 4.2. Transducer output pressure 4.2.1. Experimental output pressure A piezoelectric air-coupled transducer was used as a receiver in order to perform acoustical measurements [6]. The experiment was done by positioning the transducer in front of an active CMUT element at a distance of 1 cm. The CMUT was biased using 40 V dc and driven with a 10-volt amplitude pulse. The signal acquired by the piezoelectric transducer is shown in Fig. 8. In order to obtain the CMUT output pressure as a function of frequency, several steps were followed. First, the FFT of the piezoelectric transducer pulseecho signal was calculated. This result is shown in Fig. 9. This result was divided by two so as to obtain the piezoelectric transducer frequency characteristic. Then, the deconvolution of the piezoelectric transducer impulse response from the received signal was computed. This was done in order to remove the influence of the receiver in the CMUT frequency response. The resulting output pressure
Fig. 8. The received signal for a transducer separation of 1 cm.
Fig. 9. The FFT of the piezoelectric transducer pulse-echo signal.
amplitude in dB relative to the maximum pressure emitted at a point at 1 cm from the transducer face is shown in Fig. 10 (solid line). As shown in Fig. 7, in Fig. 10 the first resonance at 1.2 MHz corresponds to fp, and the second at 1.63 MHz is that produced due to the resonator effect (fp2). The local minimum between these peaks occurs at 1.35 MHz and corresponds to fH. Unlike the plate displacement measurements, the effect of the second resonance is more apparent in the acoustical measurements. In fact, this resonance is higher than that for the plate radiation. Nevertheless, the separation between peaks and the weakness of the second resonance at fp2 in the curve shown in Fig. 7 indicate that the expected improvement was not achieved at all due to the evident inequality between fH and fp. Nevertheless, the second peak which appears at 1.63 MHz in the output pressure measurement presents a quality factor (Q) of 6.7 and has a considerable relative output level that demonstrates that an improvement could be achievable using a properly tuned device. The simulation result is also shown in Fig. 10 (dashed line). It confirms the deviation of the second resonance peak due to small
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control of the residual stresses within the plates upon manufacture in order to make a good prediction of fp and thus obtain a properly tuned device.
Fig. 10. The MUMPs CMUT element output pressure from measurement and simulation.
geometrical differences between the model and the actual transducer and the possible effect of the neglected squeeze stiffness in the Helmholtz frequency. The relative difference of amplitude between the peak at fp2 and fp in the simulated curve (which is different in the experimental measurement) could be due to the neglected effect of acoustic absorption in the cavity. Studying the equivalent circuit of Fig. 6 one can see that the influence of the second resonance decreases when acoustic absorption is taken into account. Even so, the model is sufficient for the reported work. In the following sections, two model modifications are presented. They were used to obtain a better insight into the effects of resonant cavities in CMUTs.
4.2.2. MUMPs CMUT versus vacuum-sealed cavity MUMPs CMUT Fig. 11 shows the comparison of the proposed MUMPs CMUT simulated output pressure with that of the same CMUT with a vacuum-sealed cavity. The most noticeable effect is the absence of the second resonance in the curve that corresponds to the vacuumsealed cavity MUMPs CMUT. This confirms that the second resonance appears due to the effect of the resonant cavity. It is seen that the MUMPs CMUT transducer has not improved since its output pressure at 1.2 MHz is 5 dB with respect to the vacuumsealed cavity MUMPs CMUT maximum output pressure and the bandwidth is almost the same at frequencies near fp. This result was obtained for the same plate displacement in each case. This is due to the resulting inequality between fH and fp (fH = 1.35 MHz and fp = 1.2 MHz). Since fH and fp are sensitive to changes in geometry, it is essential to have good control of the fabrication process. Moreover, is also desirable to have precise knowledge of the material properties and the design parameters as well as have a good
Fig. 11. The simulated MUMPs CMUT and vacuum-sealed cavity MUMPs CMUT output pressure in dB relative to the maximum output pressure of the vacuumsealed cavity MUMPs CMUT.
4.2.3. Tuned CMUT versus vacuum-sealed cavity MUMPs CMUT Comparing the previous results with the theoretical values of fH and fp, it can be said that fp is within the expected range but fH is slightly higher than that previously estimated. Thus, a modification of several design parameters would be needed, such us the hole size or the cell cavity volume in order to properly tune the transducer. Since the hole size cannot be changed due to the limitations of PolyMUMPs, the cavity volume is the only parameter that can be modified through changes in the plate size. This will also produce changes in fp since its value is inversely proportional to the square of the plate length. In particular, the transducer needs a smaller plate in order to tune fp–fH. Then, it would be possible to obtain a PolyMUMPs tuned CMUT by studying the convergence of fH and fp as the plate length is modified. Nevertheless, this would imply an increase in the working frequency, and this could be critical for air-coupled ultrasonic applications. In order to illustrate this, a further FE model was constructed in order to obtain an approximate idea of the benefits of using a CMUT that employs a Helmholtz resonator. Since a change in plate length would produce a deviation in fp, the new model (tuned CMUT) was built by modifying the gap between CMUT electrodes. This maintains the value of fp allowing a better comparison of this transducer with the vacuum-sealed cavity MUMPs CMUT. This change is not realisable with PolyMUMPs since this distance is standardised. Fig. 12 shows the displacement at the centre of the plates for each of the FE models. The tuned CMUT plate displacement simulation was obtained using a gap of 5 lm between electrodes. In order to compare the output pressure of these devices, they were excited using a driving voltage such that the plate displacement was of similar magnitude. The curves that correspond to the MUMPs CMUT model and that of the vacuum-sealed cavity MUMPs CMUT were obtained by driving each transducer model with a 3 V amplitude sinusoidal signal and a 40-volt bias. The plate displacement yields an output pressure as shown in Fig. 11. In the case of the tuned CMUT, the same bias voltage was used. However, a 30 V amplitude sinusoidal voltage was required to achieve the same displacement. This is because of the increase of the gap height. This reduces the CMUT sensitivity since the transformer ratio of the equivalent circuit model of electromechanical transducers is inversely proportional to the square of the gap height [25]. This means that the electrostatic force acting on the plate will be small compared to that of a small-gap CMUT. The result shows that the characteristic peaks in the response of the tuned CMUT device appear with nearly the same amplitude.
Fig. 12. The displacement of the plate centre of the MUMPs CMUT, vacuum-sealed cavity MUMPs CMUT and tuned CMUT.
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Fig. 13. The simulated tuned CMUT and vacuum-sealed cavity MUMPs CMUT output pressure in dB relative to the maximum output pressure of the tuned CMUT.
This is a conventional indicator which indicates when the system reaches the tuned condition. Furthermore, Fig. 12 also shows that fH is 1.2 MHz. Under this condition, the output pressure was calculated at a point 180 lm from the centre of the plate. This result is shown in Fig. 13. Here, a tuned CMUT output pressure that is 11 dB higher than that of the vacuum-sealed cavity MUMPs CMUT has been obtained. Moreover, the bandwidth has been increased due to the resonant cavity. The quality factor (Q) has been estimated as 4.5 compared with 7.75 for the vacuum-sealed cavity device.
5. Conclusions A new approach for air-coupled CMUT has been presented. Unlike other CMUT devices that use non-sealed cavities [9,13,26], this design uses a resonant cavity in order to enhance the output pressure and bandwidth. The resonant cavity is based on a Helmholtz resonator design. Acoustic radiation occurs from several acoustic ports (holes) and the plate. A CMUT working under this principle was constructed using the PolyMUMPs standard fabrication process. The behaviour of this type of system was observed through several experimental results. These show that an additional resonance appears in the transducer output pressure spectrum due to the effect of the resonant cavity. Furthermore, the separation between peaks and the weakness of the second resonance at fp2 in the displacement measurement indicate that the expected improvement has not been achieved due to the inequality between fH and fp. Nevertheless, the quality factor (Q) of 6.7 and the relative output level of the output pressure measurement at fp2 demonstrates that an improvement could be achievable using a properly tuned device. FE simulations of the CMUT output pressure show that the resonance which corresponds to fp (1.2 MHz) has been calculated at 5 dB with respect to that of a theoretical conventional system with a vacuum-sealed cavity. Moreover, the bandwidth of this resonance has been estimated to be nearly equal in each case. This also confirms that the tuned condition was not achieved with this design. Since the values of fH and fp are sensitive to the design parameters, small differences between the initial design theoretical parameters and the actual parameters were found to produce significant deviations of these frequency values. As an illustrative example, a FE model of a properly tuned CMUT (with a gap height of 5 lm) has been presented in order to show the benefits of this kind of transducer. The simulated results obtained have been compared with that of a simulated conventional CMUT, and show that the tuned system can achieve an output pressure that is 11 dB greater than that of the vacuum-sealed cavity device. Moreover, its bandwidth is seen increased (Q = 4.5). This comparison was
made by ensuring the same peak plate displacement for both CMUT devices, although in order to achieve this, the tuned CMUT required a driving voltage ten-times larger than the vacuum-sealed cavity MUMPs CMUT. This is due to the relatively large gap between electrodes in this particular tuned CMUT design. Thus, it seems possible to enhance the output pressure and bandwidth of air-coupled CMUT transducers by using the theory of Helmholtz resonators. However, a further experimental study of properly tuned devices is required in order to accurately quantify these improvements. Moreover, a study towards the improvement of the sensitivity is needed in order to reduce the driving voltage level needed for achieving high output pressure levels. This is currently addressed by constructing a specially designed structure in the cavity with the purpose of decreasing the gap between electrodes while maintaining the cavity volume (i.e., column-like structure). The fabrication of such a transducer would require a specialised production process. Acknowledgements The authors acknowledge the Department of Electrical, Electronic, Automatic and Communication Engineering in the University of Castilla-La Mancha (Ciudad Real, Spain) for their support. References [1] I. Krautkraemer, H. Krautkraemer, Ultrasonic Testing of Materials, fourth fully revised ed., Springer-Verlag, Berlin, 1989. [2] W.A. Grandia, C.M. Fortunko, NDE applications of air-coupled ultrasonic transducers, in: Proceedings of the IEEE Ultrasonics Symposium, 1995, pp. 697–709. [3] F. Massa, Ultrasonic transducers for use in air, in: Proceedings of the IEEE, 1965, pp. 1363–1371. [4] H. Loertscher, B. Grandia, J. Strycek, W.A. Grandia, Airscan transducers, technique and applications, in: NDT.net, 1996, pp. 1–4. [5] T.R. Gururaja, W.A. Schulze, L.E. Cross, R.E. Newham, B.A. Auld, Y.J. Wang, Piezoelectric composite materials for ultrasonic transducer applications. Part I: Resonant modes of vibration of PZT rod-polymer composites, IEEE Transactions on Sonics and Ultrasonics 32 (1985) 481–498. [6] F. Montero de Espinosa, T.E. Gomez, A. Albareda, R. Perez, J.A. Casals, High sensitive piezoelectric transducers for NDE air borne applications, in: Proceedings of the IEEE Ultrasonics Symposium, 2000, pp. 1073–1076. [7] D.W. Schindel, D.A. Hutchins, L. Zou, M. Sayer, The design and characterization of micromachined air-coupled capacitance transducers, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42 (1995) 42–50. [8] T.-H. Gan, D.A. Hutchins, D.R. Billson, D.W. Schindel, High-resolution, aircoupled ultrasonic imaging of thin materials, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 50 (2003) 1516–1524. [9] M.I. Haller, B.T. Khuri-Yakub, A surface micromachined electrostatic ultrasonic air transducer, in: Proceedings of the IEEE Ultrasonics Symposium, 1994, pp. 1241–1244. [10] M. Kupnik, I.O. Wygant, B.T. Khuri-Yakub, Finite element analysis of stress stiffening effects in CMUTS, in: Ultrasonics Symposium, 2008. IUS 2008. IEEE, 2008, pp. 487–490. [11] K.A. Wong, S. Panda, I. Ladabaum, Curved micromachined ultrasonic transducers, in: Proceedings of the IEEE Ultrasonics Symposium, 2003, pp. 572–576. [12] I.O. Wygant, M. Kupnik, J.C. Windsor, W.M. Wright, M.S. Wochner, G.G. Yaralioglu, M.F. Hamilton, B.T. Khuri-Yakub, 50 kHz Capacitive micromachined ultrasonic transducers for generation of highly directional sound with parametric arrays, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 56 (2009) 193–203. [13] E. Campbell, W. Galbraith, G. Hayward, A new electrostatic transducer incorporating fluidic amplification, in: Proceedings of the IEEE Ultrasonics Symposium, 2006, pp. 1445–1448. [14] U. Ingard, On the theory and design of acoustic resonator, The Journal of the Acoustical Society of America 25 (1953) 1037–1061. [15] W.N. Sharpe, B. Yuan, R. Vaidyanathan, R.L. Edwards, Measurements of Young’s modulus, Poisson’s ratio, and Tensile strength of polysilicon, in: Proceedings of the Tenth IEEE International Workshop on Microelectromechanical Systems, Nagoya, Japan, 1997, pp. 424–429. [16] I.J. Oppenheim, A. Jain, D.W. Greve, Electrical characterization of coupled and uncoupled MEMS ultrasonic transducers, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 50 (2003) 297–304. [17] A. Octavio, C.J. Martín, Y. Gómez-Ullate, O. Martínez, L. Gómez-Ullate, F. Montero de Espinosa, P. Gatta, M. Domínguez, Design and characterization of air coupled ultrasonic transducers based on MUMPs, in: Proceedings of the IEEE Ultrasonics Symposium, 2006.
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