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Acoustic lens for capacitive micromachined ultrasonic transducers

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2014 J. Micromech. Microeng. 24 085007

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1. Introduction

Minimally invasive tumor coagulation using focused ultra-sound devices holds great promise in treating patients without the need for traditional surgical procedures. Especially, high intensity focused ultrasound (HIFU) has become an emerging modern therapy in which ultrasound energy is locally absorbed in a millimeter-sized focal region to induce tissue necrosis without damaging intervening tissues [1, 2]. In the past two decades, piezoelectric transducers have been dominantly used for HIFU treatments in the liver, kidney and prostate [3]. However, due to high self-heating and low thermal con-ductivity of piezoelectric materials, water cooling circulation is needed for degassing around the piezoelectric transducer

during the high-power therapeutic operation and thus makes the piezoelectric ultrasound transducer bulky and difficult to miniaturize [4, 5].

Compared to piezoelectric transducers, capacitive micromachined ultrasonic transducers (CMUTs) have become highly competitive with regard to fabrication and performance [6]. Because CMUTs are fabricated on silicon substrates using either surface micromachining or fusion-bonding processes, they can be easily fabricated for a wide range of frequencies and sizes with submicron accuracy [7]. In terms of perfor-mance, CMUTs have wide bandwidth in immersion and high efficiency [8]. Additionally, thanks to the high thermal conductivity of the silicon substrate, CMUTs have been dem-onstrated to be less self-heating than piezoelectric transducers

Journal of Micromechanics and Microengineering

Acoustic lens for capacitive micromachined ultrasonic transducers

Chienliu Chang1, Kamyar Firouzi1, Kwan Kyu Park2, Ali Fatih Sarioglu1, Amin Nikoozadeh1, Hyo-Seon Yoon1, Srikant Vaithilingam1, Thomas Carver1 and Butrus T Khuri-Yakub1

1 Edward L Ginzton Laboratory, Center for Nanoscale Science and Engineering, Stanford University, Stanford, CA 94305, USA2 Department of Mechanical Engineering, Hanyang University, Seoul, Republic of Korea

E-mail: clchang6@ntu.edu.tw

Received 5 January 2014, revised 21 May 2014Accepted for publication 6 June 2014Published 15 July 2014

AbstractCapacitive micromachined ultrasonic transducers (CMUTs) have great potential to compete with traditional piezoelectric transducers in therapeutic ultrasound applications. In this paper we have designed, fabricated and developed an acoustic lens formed on the CMUT to mechanically focus ultrasound. The acoustic lens was designed based on the paraxial theory and made of silicone rubber for acoustic impedance matching and encapsulation. The CMUT was fabricated based on the local oxidation of silicon (LOCOS) and fusion-bonding. The fabricated CMUT was verified to behave like an electromechanical resonator in air and exhibited wideband response with a center frequency of 2.2 MHz in immersion. The fabrication for the acoustic lens contained two consecutive mold castings and directly formed on the surface of the CMUT. Applied with ac burst input voltages at the center frequency, the CMUT with the acoustic lens generated an output pressure of 1.89 MPa (peak-to-peak) at the focal point with an effective focal gain of 3.43 in immersion. Compared to the same CMUT without a lens, the CMUT with the acoustic lens demonstrated the ability to successfully focus ultrasound and provided a viable solution to the miniaturization of the multi-modality forward-looking endoscopes without electrical focusing.

Keywords: capacitive micromachined ultrasonic transducer (CMUT), acoustic lens, high intensity focused ultrasound (HIFU), poly-dimethylsiloxane (PDMS), focus, mold, bonding

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without the need of artificially forced cooling in high power applications [9, 10]. Eliminating the requirement for bulky cooling systems, CMUTs are advantageous over conventional piezoelectric transducers in HIFU applications, especially for the miniaturization of HIFU systems [10–13].

To ease a patient’s suffering during the long surgery time, it is desirable to produce the tissue necrosis as rapidly as pos-sible. Therefore, converging the ultrasound emitted from the transducer to deliver with high power density is a perpetual goal for HIFU. Generally, concentrating ultrasound energy can be accomplished by focusing electrically or mechanically [2, 14, 15]. In our laboratory a concentric ring array of CMUTs had been demonstrated for the ultrasound focusing intended for HIFU applications [10]. For this electrical focusing opera-tion the concentric ring array needs the electronics to shift the phase of the pressure wave from each element to produce constructive interference of the wave fronts at the focal point. Compared to electrical focusing, mechanical focusing, such as by using an acoustic lens or a concave focusing radiator, can greatly alleviate the integration complexity, the space requirement of interconnects and the power consumption of driving electronics, and particularly benefits the development of the therapeutic HIFU endoscopes for minimal invasive sur-gery [2, 11, 14, 15].

To focus ultrasound mechanically, a spherically shaped array is often employed in piezoelectric transducers with the size up to several inches. Furthermore, due to the non-planar structure of the spherically shaped array, it is very laborious to individually assemble its elements accompanied with inter-connects onto a spherical concave, and is thus not compatible with the traditional planar batch processes commonly used in semiconductor and micromachining industries. In our labora-tory, a flexible CMUT array with polymer refilled between elements as linkage has been demonstrated [16]. Based on this method it seemed possible to fabricate a spherically- shaped CMUT array that can form a concave transducer to focus ultrasound mechanically. However, adapting this flex-ible CMUT process to form a spherically shaped array turned out to be challenging, because the silicon membrane and the silicon ribbon springs used as interconnects between neigh-boring elements may easily break under large deformation when shaping a spherical focused array [16]. In other words, forming a spherically shaped array using the flexible CMUT process notably increases the complexity in fabrication and assembly and hardly achieves acceptable yield of the devices. To circumvent these technical issues, directly forming an acoustic lens onto a CMUT seemed to be a better choice than forming a spherically shaped array to produce a focused ultra-sound field.

Among the polymers often used for acoustic lenses, poly-dimethylsiloxane (PDMS) has been widely used as an acoustic lens material for piezoelectric ultrasound transducers [17, 18]. It is a biocompatible substance providing the matching of acoustic impedance needed for efficient acoustic transmission and the ideal viscoelastic behavior changing from rubbery at low frequency to glassy at high frequency [19, 20]. Recently, PDMS was used to electrically insulate or encapsulate CMUTs in immersion to create flexible arrays and to suppress acoustic

crosstalk [16, 19–21]. In addition, PDMS has been proven to preserve the pull-in voltage of the CMUT thanks to its low static Young’s modulus [20]. These advantageous attributes of PDMS in ultrasound including high dielectric breakdown and thermal stability present great potential to be utilized in HIFU applications with CMUTs.

Because of those technical considerations and the motiva-tion above, we designed and developed an acoustic PDMS lens on the CMUT intended for HIFU applications. Our ulti-mate goal is to develop a multi-modality forward-looking endoscope for both imaging and therapeutic applications at the same time [11]. In the following sections we first describe the design for the acoustic lens on the CMUT. Based on the lens design, we demonstrated the fabrication of the CMUT and the acoustic PDMS lens. Next, the CMUT without the lens was measured to verify for functionality and device char-acteristics. Finally, compared to the CMUT without the lens, the CMUT with the acoustic PDMS lens was then character-ized and simulated to verify the focused ultrasound.

2. Design of acoustic lens

The acoustic lens was initially designed based on the par-axial theory or Fresnel approximation in geometrical optics, assuming a plane wave front emitted in a direction normal to the transducer surface [13, 18, 22, 23]. Figure 1 illustrates the schematic for the acoustic lens focusing on the axial plane. By applying Snell’s law in the paraxial approximation, the radius of curvature (ROC) for a convex spherical acoustic lens can be derived as follows:

⎛⎝⎜

⎞⎠⎟= ⋅ −ROC F

C

C1geo

medium

lens (1)

where Fgeo is the geometric focal length, Cmedium is the speed of sound of the medium and Clens is the speed of sound of the lens material. First, PDMS (Sylgard 160 silicon elastomer, Dow Corning, Midland, MI) and water were selected to be the lens material and the medium in this paper, because they acoustically match each other near the acoustic impedance of human tissue [20]. The convex lens was thus determined to focus ultrasound due to Clens< Cmedium in this case. Table 1 lists

Figure 1. Schematic of acoustic lens focusing for a CMUT.

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the material properties for this convex lens design, where the homogenized liver is also presented as a reference to human tissue [10, 14, 18, 20, 23– 24]. Soybean oil was also temporarily used as the medium for the CMUT without insulating encap-sulation in the later experiments. Given a center frequency (f = Cmedium/ λ) and an aperture size (D, the diameter of the transducer), we can start to calculate the parameters including the thickness of the lens (TL), depth of view (DOV) or depth of field, and focal gain as follows [15, 18]:

= − −⎜ ⎟⎛⎝

⎞⎠TL ROC ROC

D

22

2 (2)

⎛⎝⎜

⎞⎠⎟

F

DDOV 7.1

geo2

λ= ⋅ ⋅ (3)

πλ

πλ

≡ = ⋅⋅

= ⋅⋅

=P

P

D

F

a

F

Z

FFocal gain

4F

o

R2

geo

2

geo geo (4)

where λ is the wavelength of the acoustic wave propagating in the medium, a ( = D/ 2) is the radius of the transducer, PF is the pressure amplitude at the focus, Po is the pressure amplitude on the face of the transducer aperture and ZR is the Rayleigh distance (ZR= πa2/ λ). The focal gain defined as the ratio of the pressure amplitude at the focal length to the pressure ampli-tude on the transducer surface is often used as a measure of the strength of focusing (referring to equation (3.46) of [14] or equation (6.33a) of [34]). The attenuation loss in the lens (PDMS) can be then expressed as follows:

α= + ⋅ ⋅ βTC TL fLoss (in dB) ( ) (5)

where TC is the thickness of the collar which acts as an addi-tional thickness of the lens along the propagating path, α is the material attenuation of the lens and β = 1.4 for PDMS [20]. As seen in table 1, the attenuation loss in the media including water and soybean oil is comparably much smaller than in the PDMS (the lens material), so it can be neglected in short ranges. Taking the attenuation in the lens into account, the effective focal gain for the lens can be calculated as follows:

Effective focal gain Focal gain·10Loss20= − (6)

The center frequency was first chosen as 2.2 MHz in immersion, since 2.2 MHz is within the typical frequency range targeted for HIFU applications between 1 MHz and 10 MHz [1, 2, 5]. As described in the following section, a CMUT with the same center frequency in immersion was then designed and fabricated with a diameter of 4.8 mm, which was intended to be accommodated into the lumen of the imaging ring array for a multi-modality forward-looking endoscope developed in our laboratory [11].

After surveying appropriate off- the- shelf available stain-less steel balls served as a lens mold described later, ROC, namely the radius of the steel ball, was chosen as 2.78 mm (7/ 64 inch). Pursuant to those aforementioned assumptions, derived equations and physical geometries, the designed parameters for the acoustic PDMS lens on the CMUT were calculated as listed in table 2. It was noted that the lens diam-eter D’ of 4.85 mm was determined to be slightly greater than the CMUT diameter D of 4.8 mm to provide a maximum toler-ance of around 25 μm for the alignment between the lens and the CMUT.

3. CMUT design and fabrication

We first designed the key physical parameters of a CMUT, such as the membrane thickness and the gap height in the cavity, based on the theoretical electromechanical models and the equivalent circuits for CMUTs developed in our labo-ratory [25–28]. For CMUT fabrication the wafer-bonding process and the sacrificial release process have been devel-oped [7]. For a given center frequency and a total transducer area, an optimized high power CMUT requires a relatively thick vibrating membrane (or plate) and a larger gap height compared to a conventional imaging CMUT [20]. Therefore, the wafer-bonding process was chosen to fabricate the CMUT since the membrane thickness was designed to be 6 μm for the center frequency of 2.2 MHz in immersion. Similar to [29], the CMUT was fabricated by utilizing the local oxidation of silicon (LOCOS) to benefit from the excellent gap height con-trol and the uniformity across the wafer.

A highly conductive (0.01–0.02 Ohm-cm) single crystal sil-icon (SCS) wafer was first prepared as a substrate wafer. Thin stoichiometric silicon nitride Si3N4 with thickness of 168 nm on the top of a thin thermally grown silicon oxide SiO2 with

Table 1. Material properties for acoustic lens design, where f is the frequency in MHz.

Material PDMS (Sylgard® 160) Water (at 20 °C) Soybean oil Homogenized liver

Longitudinal wave velocity (m/ s) 950 1483 1430 1550Density (kg/ m3) 1580 998 930 1060Acoustic impedance (MRayls) 1.5 1.48 1.33 1.643Attenuation (dB/ mm) 0.4 f1.4 2.2 × 10 − 4 f2 4.7 × 10 − 2 f1.12 8 × 10 − 3 f1.85

Reference [18, 20, 23] [14, 24] [10] [10]

Table 2. Designed parameters of the acoustic lens.

Design parameter Value Unit

Frequency, f 2.2 MHzSpeed of sound in water, Cmedium 1483 m/ secWavelength, λ 674 μmDiameter of the CMUT, D 4.8 mmDiameter of the lens, D’ 4.85 mmRadius of curvature, ROC 2.78 mmDiameter of the molding ball 7/32 inchGeometric focal length, Fgeo 4.96 mmThickness of lens, TL 1.42 mmThickness of collar, TC 0.7 mmDepth of view, DOV 5 mmFocal gain 5.53 (none)Loss (in dB) 2.43 (none)Effective focal gain 4.18 (none)

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thickness of 58 nm was deposited by using low pressure chem-ical vapor deposition (LPCVD) on the wafer. This insulating oxide–nitride bilayer served as an oxygen-blocking layer and was then patterned and etched to expose the silicon substrate for the subsequent LOCOS step. A thermally grown oxide was then formed on the area of the exposed silicon with LOCOS to achieve the target step height of 470 nm. Compared to the fabrication of the wafer-bonded CMUTs utilizing LOCOS in [29], here we skipped the formation of the protruding silicon bumps at the beginning without compromise of device perfor-mance and design specifications.

Next, a silicon-on-insulator (SOI) wafer with a 6 μm thick active layer of Si <1 0 0 > was prepared and bonded on the top of the previous LOCOS wafer using fusion bonding. The LOCOS oxide layer served later as the post of the CMUT had a very low surface roughness of less than 0.5 nm RMS to promise the success of the fusion bonding. The handling layer of the SOI wafer was then wet etched in hot tetramethylammonium

hydroxide (TMAH) solution. The buried oxide layer served as an etch stop layer for the TMAH etching was then removed by buffered oxide etch (BOE), leaving the 6 μm thick active layer of membrane (or plate) covering the cavities. The CMUT ele-ments were defined by separating the 6 μm thick membrane with a dry etching step. To form the bottom (ground) elec-trode, a portion of the LOCOS oxide layer was etched to expose the silicon substrate. A 200 nm thick aluminum (Al) layer was deposited for providing better conductance, and the top (signal or hot) and bottom (ground) electrodes were then defined on the membrane (or plate) and the silicon substrate, respectively. The CMUT wafer was finally diced with the pro-tection of a coated photoresist layer. Figure  2(a) illustrates the schematic for the cross section of the fabricated CMUT, where only three cells are illustrated for schematic purposes. Each chip has several elements, which has different numbers of CMUT cells ranging from 1 to 745. In this paper, we used a 745-cell element with the fill factor of 70.8 %, which is the

Figure 2. CMUT device: (a) schematic for the cross section of the CMUT and (b) the optical micrograph of the fabricated CMUT attached on the PCB. Note that only three cells are illustrated in (a) for schematic purposes. In fact, the tested CMUT in this paper has a total of 745 cells, which is the biggest circular CMUT element with diameter D of 4.8 mm as shown in the left of (b).

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biggest circular single-element CMUT with diameter D of 4.8 mm as shown in the left of figure 2(b), for modeling and experiments.

After dicing and cleaning, a CMUT chip was attached to a customized printed circuit board (PCB) with epoxy and then electrically connected with gold wires bonded between the CMUT pads and the PCB as shown in figure 2(b). It was noted that several gold wires were bonded between the signal elec-trode and the PCB to endure possible large current when driving the CMUT. Finally, all the conductive portions including the pads and the gold wires were covered with ultraviolet-curable epoxy to avoid any possible electrical shorting during opera-tion. Table 3 lists the parameters for the CMUT mainly obtained from the measurements during fabrication.

4. Fabrication of acoustic lens

Figure 3 illustrates the fabrication process of the PDMS lens on the CMUT. The lens fabrication utilized the technique of typical mold castings, since PDMS is not photo patternable and plasma-etchable. Two molds were consecutively made in our process: One was a metal convex mold which was formed as the same shape as the final PDMS lens (figure 3(a)), and the other one was a polyurethane concave mold transferred from the previous metal convex mold (figure 3(c)).

First, to imitate the shape of the acoustic lens based on our design, the ball made of stainless steel (super-corrosion-resistant SS ball, Type 316, diameter 7/ 32’’, McMaster-Carr, Elmhurst, IL) was chosen for making the convex mold, as shown in figure  3(a). According to equa-tion (2), the radius of the ball (ROC) was chosen to be greater than the radius of the CMUT (D/ 2). Figure 4(a) illustrates the design sketch of the convex mold, which involves an alu-minum cylinder and a steel ball placed at the center of the cylinder. The dimensions on the sketch are in mm. The cyl-inder had a drilled through- hole with screw threads inside as shown in figure 4(b). Since the height of the ball determines the lens thickness directly, so we used the screw to adjust the height of the ball accurately before gluing it to the cyl-inder. Here the height of the metal ball was measured using

a micrometer with an accuracy of 25 μm. Next, we glued the ball into the drilled hole and filled in the ditch around the ball with epoxy. After shaving the epoxy in the ditch around the ball with a razor blade, it was leveled to the top sur-face of the cylinder. After curing the epoxy and polishing the metal mold, as shown in figure 4 (c), a little epoxy blob (Elmer’s glue, Columbus, OH) was placed on the edge of the top surface of the cylinder to form a dowel, which was later removed from the mold to make a hole into which the PDMS could be injected to form the PDMS lens. As also shown in figure  3(b) and figure  4(c), a thin polypropylene sleeve was cut for making the sidewall of the mold to confine the

Table 3. Physical parameters of the CMUT.

Device parameter Value Unit

Center frequency, f 2.2 MHzThickness of silicon substrate wafer 400 μmDiameter of the CMUT, D 4.8 mmNumber of circular cells in the CMUT 745 (none)Diameter of the cell membrane, d 148 μmThickness of membrane, t 6 μmDensity of membrane 2329 kg/ m3

Young’s modulus of membrane 148 GPaPoisson’s ratio of membrane 0.177 (none)Initial gap height in the cavity, g 0.474 μmMinimum bonded width, bmin 5 μmThickness of insulating SiO2 layer 58 nmRelative permittivity of insulating SiO2 layer 3.78 (none)Thickness of insulation Si3N4 layer 168 nmRelative permittivity of insulating Si3N4 layer 5.7 (none)Thickness of top Al electrode 200 nmFill factor 70.8% (none)

Figure 3. Fabrication process of the acoustic lens on a CMUT: (a) making a convex mold; (b) pouring polyurethane in the convex mold; (c) polyurethane concave mold released from the convex mold; (d) placing the polyurethane mold onto the CMUT; (e) casting PDMS into the cavity; and (f) removing the polyurethane mold and finishing the PDMS lens. (TL: thickness of the lens, TC: thickness of the collar, and D’: diameter of the lens)

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liquid polyurethane later. The metal mold and the inside of the plastic sleeve were then sprayed with a thin wax film to prevent the polyurethane from sticking to them. After wrap-ping the sleeve around the cylinder and clamping with hose clamps, the gap was sealed where it meets the aluminum cyl-inder with hot melt glue to keep it watertight. Additionally, we assembled a wax-sprayed plastic slab on the top of the sleeve and made a small funnel out of a chopped pipette on the sidewall of the sleeve with hot melt glue as well.

The two-parts polyurethane (polyurethane poly 75–80 and 75 series RTV liquid mold rubbers, Polytek Development Corp, Easton, PA) was mixed up with the ratio of 2 A: 1B by weight and then poured into the funnel as shown in figure 3(b). The level of the polyurethane was high enough for forming a flat surface on the side of the plastic slab, as

shown in figure 4(d), so that the polyurethane mold could be clearly seen through during the later alignment. We put it in the vacuum oven at 65 °C to speed up the curing and removed the bubbles under vacuum, and then released the concave polyurethane mold from the convex mold, as illustrated in figure 3(c). Figure 4(e) shows the cured polyurethane mold after peeling it off from the metal convex mold and all the plastic mold forms.

Next, the polyurethane mold was placed on the top of the CMUT for casting the PDMS lens, as illustrated in figure 3(d). On this stage a transparent polycarbonate fixture was prepared and assembled for clamping the polyurethane mold onto the PCB, as shown in figure 4(f). It was noted that the CMUT chip had been attached with epoxy and wire-bonded on the PCB beforehand, as explained and shown in figure 2(b). Because the

Figure 4. Fabrication process of the acoustic lens on a CMUT: (a) design drawings with unit in mm; (b) machined components for the convex mold; (c) assembly of the convex mold; (d) casting polyurethane; (e) polyurethane concave mold; (f) aligning the polyurethane mold with the CMUT; (g) magnification of the aligned mold and the CMUT; (h) casting PDMS; (i) PDMS lens formed on the CMUT. (D’= 4.85 mm)

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adhesion between PDMS and the PCB was weak, the surface of the PCB around the CMUT chip was coated with adhe-sion promoter (SS4004P, Momentive Performance Materials Inc. Waterford, NY) to increase interfacial adhesion. Similar with making the previous convex mold, a chopped pipette was also glued into the sprue of the polyurethane mold to make a funnel for the subsequent PDMS injection. The inside of the polyurethane mold was coated with wax for ease of sub-sequent releasing and then placed on the PCB aligned with the CMUT manually. Figure 4(g) shows that the polyurethane mold was well aligned over the CMUT by seeing through the transparent polycarbonate fixture and the yellowish trans-lucent polyurethane mold. Once the alignment was finished, they were clamped in place by tightening the screw bolts. As aforementioned, the acoustic lens was designed to be bigger than the CMUT by 50 μm in diameter, the alignment with a tolerance less than 25 μm was achieved manually under optical microscope.

After the alignment and tightening the fixture, the next step was to cast PDMS on the CMUT chip, as illustrated in figure 3(e). The gray two parts PDMS liquid was fully mixed with the ratio of 1:1 by weight and injected into the cavity between the polyurethane mold and the PCB, as shown in figure  4(h), followed by a vacuum chamber degassing step and a curing cycle at 50 °C for 12 h. After the PDMS was fully cured, the polyurethane mold was released off to get the final PDMS lens covering the CMUT, as illustrated in figure 3(f). Due to this molding casting for the lens fabrication, the collar portion was formed between the acoustic lens and the CMUT to obtain higher adhesion and full encapsulation to the whole CMUT chip and the PCB, as also illustrated in figure  3(f) [18]. Therefore, the thickness of the collar introduced addi-tional attenuation loss along the propagating path in the lens material, as expressed in equation (6) above. Even though the

adhesion promoter (SS4004P) had been applied, the adhe-sion between the PDMS and the PCB was found to be still weak. To prevent the PDMS peeling off, we applied silicone (Translucent RTV 108, Momentive Performance Materials Inc. Waterford, NY) around the interface between the PDMS and the PCB to enhance adhesion. Finally, the PDMS lens was successfully formed on the top of the CMUT, as shown in figure 4 (i).

PDMS can be considered as a type of silicone rubber or silicone elastomer. Silicone rubber has relatively low acoustic impedance close to 1.0 MRayl and low Young’s modulus, so it could be a good candidate for the lens constituting material. One needs the lens to have an impedance that matches that of water, but a velocity that is lower than water in order to focus. We use this type of PDMS (Sylgard 160) for this particular property. The only downside to this PDMS is the attenuation, which is relatively high. Other large families of materials that might be considered for use in an acoustic lens is urethanes or polyurethanes. As with silicone rubber, polyurethanes are available in a wide range of hardnesses and can be filled to increase their density and acoustic properties. In addition, polyurethanes are usually firmer, more abrasion resistant, and more adhesive to the substrate than silicone rubbers. With polyurethanes, you also have the option of curing some of them by UV rather than heat and time, which might make them more suitable for mass production. However, they have toxic isocyanates in their curing agents and relatively shorter shelf lives. Compared to polyurethanes, PDMS is chemically inert and non-toxic when cured, which was also a reason why we chose PDMS as the lens material for the CMUT. In brief, to choose a proper material for acoustic lens, the transducer, the medium and the properties of the lens including acoustic impedance, acoustic speed, Young’s modulus, adhesion and manufacturability should be considered.

Figure 5. Input electrical admittance of the CMUT: (a) amplitude and (b) phase.

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5. Characterization of CMUT without lens

Prior to casting the PDMS lens, the CMUT without a lens was first verified for functionality and device characteristics by measuring the electrical input impedance in air (Model 4294 A, Agilent Technologies Inc., Santa Clara, CA), as shown in figure 5. Since the CMUT had been already attached on the PCB and could be applied voltages through the connec-tors (sub miniature type A, SMA) on the PCB, the reference plane of the RF calibration was directly done up to the SMA connectors. It meant that wiring effects, such as additional parasitic capacitance and serial resistance, were involved in the following measurement results. The electrical input impedance was measured by sweeping the frequency of a small ac excitation (50 mV) superimposed on the top of a dc bias voltage. At the same time as the impedance measurement, different dc bias voltages (Stanford Research Instruments PS 310, Stanford Research Systems Inc., Sunnyvale, CA) were in turn applied close to the pull-in voltage, which was found to be around 173 V. It exhibited that the resonant frequency decreased due to the spring softening effect as the applied dc voltage was increased, while the peak magnitude of the admit-tance (the inverse of impedance) increased proportionally to the maximum velocity (or displacement) of the membrane. According to the amplitudes and the phases of the measured input admittance shown in figure 5, the CMUT was found to behave like an electromechanical resonator in air.

The frequency response of the CMUT without a lens was then investigated in immersion to verify our design specifi-cations. Because at this moment the CMUT without PDMS lens had no insulating encapsulation or coating on the top, for this measurement the CMUT was immersed in soybean oil (table 1) to prevent unwanted electrical shorting. The operating conditions for this bandwidth measurement for the CMUT without a lens in immersion are listed in table 4. As shown in figure 6(a), the CMUT was applied with a 60 V unipolar square pulse with a pulse width of 50 ns, which was equivalent to a bandwidth of 40 MHz fully covering the char-acteristic bandwidth of the CMUT operated in immersion. This 60 Vac voltage, approximating an impulse, was superim-posed on a 100 V dc bias voltage, so that the instantaneous maximum input voltage was up to 93 % of the pull-in voltage while keeping the CMUT uncollapsed. No leak current was observed after applying the voltages.

The ultrasound pressure wave generated by the CMUT propagated through soybean oil and was then measured by using a hydrophone (Model HNP-0400, ONDA Corp.,

Sunnyvale, CA). The signal measured by the hydrophone was amplified 20 dB with a standard preamplifier (AH-2010-25, ONDA Corp.) and fed into an oscilloscope via a non-switch-able DC block. The measured signal of acoustic pressure was then transformed into acoustic pressure, as shown in figure 6(b).

Comparing figure  6(a) and (b), the output peak-to-peak acoustic pressure with a delay of 7.1 μsec presented that the hydrophone was positioned at the distance of 10.6 mm from the surface of the CMUT to ensure measuring the output pressure in the far field. Here the far field was defined as the

Table 4. Operation parameters for the bandwidth measurement of the CMUT without a lens immersed in soybean oil.

Operation parameter Value and unit

Delay 7.1 μsDistance between the CMUT surface and the hydrophone 10.6 mmDC bias voltage, Vdc − 100 VAC excitation voltage, Vac (peak-to-peak) 80.8 VWaveform Pulse: 1 cycle, unipolar square wave 60 V

Pulse period: 50 nsBurst period: 10 ms

Acoustic pressure received by hydrophone (peak-to-peak) 0.255 MPa

Figure 6. Bandwidth measurement for the CMUT without a lens immersed in soybean oil: (a) the input pulse voltage Vac; (b) the output pressure measured using the hydrophone in the far field; and (c) the normalized frequency spectrum of the output pressure.

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region positioned at distances from the transducer surface greater than a2/ λ, which was around 8.55 mm in this study. After applying a fast Fourier transform to the measured pres-sure signal, the CMUT demonstrated a center frequency fo of 2.2 MHz and a 3 dB bandwidth (BW) of 1.61 MHz, equivalent to a 3 dB fractional bandwidth (FBW) of 73 %, as shown in figure 6(c). These results indicated that the CMUT without any coating was successfully fabricated and functioned well in the wide frequency range of interest. It was noted that the signal of the acoustic pressure here was raw and not compensated for the frequency response of the ONDA hydrophone, because we intended to directly compare the difference between the CMUTs with and without PDMS lenses under the same con-ditions later. If compensated with the frequency response of the hydrophone, this CMUT would inherently have an FBW slightly higher than 73 % above. This fusion-bonded CMUT has a smaller FBW of 73 % than surface-micromachined CMUTs. This smaller FBW is attributed to the thick mem-brane and the large cell size. Based on the aforementioned experiments performed in both air and oil, we definitely knew

that this ‘bare’ CMUT was an ‘alive and good’ device, and qualified to be integrated with an acoustic lens subsequently.

6. Characterization of the acoustic lens on the CMUT

The purpose of an acoustic lens on the CMUT is to concentrate ultrasound to increase the pressure at the focus for therapeutic applications like HIFU. Since therapeutic ultrasound is usu-ally excited at a single frequency like burst-waves, a wide bandwidth is no longer critical. In the following experiments the output pressure of the CMUT with lens was investigated.

The PDMS lens on the CMUT was characterized in immer-sion as shown in figure 7. Figure 7(a) illustrates a schematic of the experimental setup and figure  7(b) shows a close-up view of the acoustic PDMS lens during this experiment. The experimental setup here was the same with the previous measurement for the impulse response of the CMUT without a lens, except adding the PDMS lens and the medium changed

Figure 7. Experimental setup for characterizing the acoustic PDMS lens on the CMUT: (a) the schematic of the experimental setup and (b) a close view of the PDMS lens during the experiment. Note that only three cells are illustrated in figure 7(a). In fact, as explained in figure 2 previously, the tested CMUT has a total of 745 cells.

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from soybean oil to water. Note that in fact the tested CMUT has 745 cells as aforementioned, though only three cells in the CMUT are illustrated in figure  7(a) for schematic pur-poses. Since the CMUT was covered by PDMS lens and its peripheries on the PCB were insulating, the CMUT could be immersed in a reservoir of water without shorting the circuits. The PCB was fixed on a motorized and electronically con-trolled x- y translation stage. The CMUT was scanned in the far field by using the ONDA hydrophone on the plane parallel to the CMUT surface with 0.2 mm step size to locate on the axis of the acoustic beam as accurately as possible.

The ac signal generated by a function generator (Model 33250 A, Agilent Technology, Santa Clara, CA) was amplified by using a RF power amplifier (Model ENI 320 L, Electronics & Innovation, Ltd. Rochester, NY) with a fixed nominal gain of 50 dB. The dc bias voltage supplied by using a high voltage power supply (PS310, Stanford Research Systems Inc. Sunnyvale, CA) was applied on the CMUT through a homemade bias- tee composed of a dc- blocking capacitor of 0.56 μF and a resistor of 1 MOhm. The pressure signal

measured by the hydrophone was synchronized with the input ac voltage applied on the CMUT and fed into an oscilloscope (Infinium 54825 A, Agilent Technology, Santa Clara, CA). All the signals were collected via general purpose interface bus (GPIB) from the oscilloscope to a personal computer.

A ac voltage of 10 cycle 137 V peak-to-peak cosine burst generated at the fundamental frequency fo of 2.2 MHz, i.e. the center frequency of the CMUT, from the ac power supply was superimposed on the top of a − 100 V dc bias voltage via the bias-tee. The superimposed input voltage (Vac+ Vdc) applied to the CMUT was measured from the node between the CMUT and the bias-tee as shown in figure 8(a). The instan-taneous maximum input voltage reached about 97 % of the pull in voltage, so that the electromechanical coupling of the CMUT was nearly maximized while keeping it uncollapsed [28]. No leak current was observed after applying the voltages. The operating conditions for this pressure measurement of the CMUT with PDMS lens in immersion are listed in table 5.

The acoustic pressure generated from the CMUT surface propagated through the PDMS lens and water. The hydro-phone was positioned at the distance of around 4.3 mm from the surface of the CMUT to measure the acoustic pressure. Acoustic pressure measured by the hydrophone was scanned on the horizontal plane parallel to the CMUT surface in the far field to reach the location of the maximum acoustic pres-sure, namely the axial pressure of the CMUT. Figure  8(b) shows the axial pressure received by the hydrophone and the instantaneous maximum peak-to-peak pressure was found to be around 1.89 MPa, which was exactly the axial pressure (peak-to-peak) at the focal point as later shown in figure 9. As shown in figure  8(b), the first received burst was obviously the pressure wave propagated directly from the CMUT to the hydrophone. The following secondary burst was recognized as the wave which was first reflected from the water–air inter-face and then reflected from the PCB surface.

Figure 8(c) shows the normalized frequency spectrum of the received pressure by applying fast Fourier transform to the signal of the measured output pressure in figure 8(b). It was found that the second harmonic wave resonated at 2fo of 4.4 MHz was around − 18 dB with respect to the fundamental harmonic at fo of 2.2 MHz. Pursuant to the nonlinearity of the CMUT pressure resulting from the square dependence of electrostatic voltage, the pressure ratio of the second harmonic to the fundamental harmonic is theoretically pro-portional to the ratio of Vac/ (4 Vdc) and thus calculated to be around − 9 dB under the combination of the applied Vdc and Vac voltages in this case [30]. Additionally, taking into account the CMUT’s impulse response of around − 11 dB at 2fo of 4.4 MHz shown in figure 6(c), the total pressure ratio of the second harmonic to the fundamental harmonic was estimated to be around − 20 dB, which was very close to the measured pressure ratio of − 18 dB at 2fo of 4.4 MHz as shown in figure 8(c).

After reaching the axial location of the CMUT by scan-ning with the hydrophone, the profile of the axial pressure was then measured by positioning the hydrophone along the axis of the CMUT, as shown in figure 9. This profile of the axial pressure for the CMUT with a PDMS lens immersed in

Figure 8. Pressure measurement for the CMUT with PDMS lens immersed in water: (a) the superimposed input voltage (Vdc+ Vac); (b) the output pressure measured using the hydrophone near the focal point; and (c) the normalized frequency spectrum of the output pressure.

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water had been corrected with the speed of sound in PDMS to reveal the real distance from the CMUT surface. For com-parison the profile of the axial pressure for the same CMUT without lens immersed in soybean oil under the same opera-tion conditions was measured and is shown in figure 9. For the CMUT without a lens the maximum axial pressure of 1.1 MPa took place at a distance of around 8.9 mm from the CMUT surface. On the other hand, compared to the designed geometric focal length of 4.96 mm from the CMUT surface listed in table 2, for the CMUT with a PDMS lens the max-imum axial pressure of 1.89 MPa drifted toward the CMUT surface at 4.3 mm, as shown in figure  9. This drift of the focused ultrasound toward to the transducer surface was due to the diffraction of the acoustic waves as they propagated through an acoustic lens [14, 15].

Assuming the CMUT to be a piston transducer with the same size surrounded by the medium (water), i.e. a pressure release surface, the output pressure exerted from the CMUT surface can be simply estimated to be around 0.55 MPa, which is equal to a half magnitude of the maximum axial pressure for the CMUT without a lens [14, 15]. Based on this assumption of a piston-transducer surrounded by a pressure release sur-face, the effective focal gain was estimated to be around 3.43.

To have a better approximation based on the same assumption of the piston transducer, we calculated the acoustic field by using the finite element method (FEM) using Comsol simulation software (Comsol Multiphysics, Comsol, Inc. Burlington, MA). All the physical dimen-sions and material properties including the lens and medium (water) listed in table  1 and 2 were applied in the two dimensional (2D) axisymmetric FEM model. All the external boundaries of the computational domain were defined as an absorbing boundary condition, that is to say they were infinite without reflection. The piece of the left edge which lies inside the lens, i.e. the CMUT surface, had a pressure excitation. To ease the FEM simulation effort it was set to be operated in continuous wave (CW) mode. The output pressure with amplitude of 0.275 MPa, equiv-alent to the estimated output pressure (peak-to-peak) of 0.55 MPa emitted from the CMUT surface, was applied on the pressure boundary as the CW excitation. The simulated axial pressure profile and field are presented in figure 9 and figure 10. Table 6 lists the results of the design, the meas-urement and the FEM simulation for the acoustic PDMS lens on the CMUT. As shown in figure 9, the maxima of the experimental and simulated pressures took place at around the same position and these two pressure profiles behaved similarly. Additionally, as listed in table  6, the experimental focal length of the CMUT with a lens was measured to be 4.3 mm, which is very close to the simu-lated one of 4.22 mm. The DOV and for the experimental and simulated pressure profiles also matched each other closely with a deviation less than 0.5 mm, as shown in figure 9 and table 6. According to figure 9 and table 6, we

Table 5. Operation parameters for the pressure measurement of the CMUT with a PDMS lens immersed in water.

Operation parameter Value and unit

Delay 3.38 μsDistance between the CMUT surface and the hydrophone 4.3 mmDC bias voltage, Vdc − 100 VAC excitation voltage, Vac (peak-to-peak) 137 VWaveform Pulse: 10 cycles, cosine wave

Frequency: 2.2 MHzBurst period: 10 ms

Acoustic pressure received by hydrophone (peak-to-peak) 1.89 MPa

Figure 9. The measured axial pressures (peak-to-peak) of the CMUTs with and without the acoustic PDMS lenses, and the simulated axial pressure of the CMUT with a lens.

Figure 10. 2D view of the FEM simulation of the pressure field for the CMUT with a PDMS lens.

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could conclude that the two foci of the experimental and simulated pressure coincided at around the same position.

In the simulation the focal point is located 4.22 mm from the CMUT surface with the maximum axial pressure of 1.64 MPa, and the simulated focal gain was thus calculated to be 2.98. Compared to the measurement results, the deviation of the simulation could be ascribed to the overestimated loss in the lens and the assumption of a piston-transducer model instead of a CMUT element with 745 vibrating membranes of cells. Besides, for expediency we applied an absorbing boundary surrounding the CMUT in the FEM simulation and assumed a pressure release surface for calculating the effective focal gains, which were different from the real solid boundaries including the silicon substrate and the PCB plate upon which the CMUT was located.

Compared to the design based on the paraxial approxi-mation, the FEM simulation of the pressure field based on the assumption of a piston transducer still provided a better approximation to the measurement results, especially for the focal length and the DOV. As also shown in figure 9 and 10, the simulated pressure field inside the lens exhibited even higher than that at the focal point due to internal reflection. Compared to the designed focal gain, it indicated that the decline of the measured effective focal gain could be mainly attributed to the internal loss inside the lens.

The deviations between the designed, measured and sim-ulated results could come from dimensional errors of the machined mold, finite acoustic impedance mismatch between materials, misalignment between the lens mold and CMUT, internal reflection and absorption in the lens, diffraction loss, off-axis measurement of acoustic pressure, and the assump-tions of a piston transducer model employed in the calculation and the FEM simulation. Furthermore, the paraxial assump-tion employed in lens design was based on the ray tracing of a single frequency wave, which was substantially different from the wideband nature of the CMUT.

Possible ways to reduce these acoustic attenuations include employing a thinner lens with planar phase-shift patterns like a Fresnel lens [31], utilizing impedance- designable material [18], and optimizing the lens with highly accurate simulation and modeling before fabrica-tion [32]. Furthermore, to optimize the power efficiency for transmitting ultrasound with a CMUT, a matching network, such as an inductor, can be added between the bias-tee and the CMUT for better RF impedance matching at the center frequency in operation [33]. Testing of all aforementioned improvements is currently taking place to achieve efficiently focused ultrasound with CMUTs.

7. Conclusion

In summary, we have designed, fabricated and characterized an acoustic PDMS lens on a CMUT for ultrasound focusing. The acoustic lens was designed based on the paraxial theory in geometrical optics. The single-element CMUT with 4.8 mm diameter was design and fabricated using fusion-bonding and LOCOS processes and consisted of total 745 CMUT cells with 6 μm membrane thickness, 0.47 μm gap and 148 μm diameter for one cell. The fabricated CMUT was verified to behave like an electromechanical resonator in air and performed wideband response with a FBW of 73 % in immersion. The acoustic PDMS lens formed on the CMUT device involved two consecutive mold castings and align-ment. Under the burst operation applied with the maximum peak-to-peak input voltages up to 97 % of the pull-in voltage, the CMUT with the acoustic PDMS lens produced a focused axial acoustic pressure (peak-to-peak) of 1.89 MPa with a DOF of 4.1 mm and an effective focal gain of 3.43 at the center frequency of 2.2 MHz. Compared to the design based on the paraxial approximation, the FEM simulation of the pressure field employing the assumption of a piston trans-ducer provided a better approximation to the measurement results and indicated that the decline of the measured effec-tive focal gain could be attributed to the internal loss inside the lens. These results demonstrated that the CMUT with an acoustic PDMS lens could provide effective mechanical focusing and showed promising potential for therapeutic HIFU applications, especially for the miniaturization of multi modality forward-looking ultrasound endoscopes in the future.

Acknowledgment

The molds and lens were fabricated in the Stanford Nano Shared Facilities. The CMUTs were fabricated in the Stanford Nanofabrication Facility (SNF) at the Center for Integrated Systems (CIS) and the experiments were conducted in the Ginzton Laboratory at Stanford University. The authors would like to thank the researchers in the Professor Khuri-Yakub Laboratory and the staff at the Ginzton Laboratory of Stan-ford University. The authors also would like to thank Dr Omer Oralkan of North Carolina State University, Mr Douglas N Stephens of the University of California at Davis, and Dr Ben Chui of Ben Chui MEMS/ Nano Consulting for their help and valuable discussions.

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Table 6. Designed, measured, and simulated parameters for the acoustic PDMS lens on the CMUT.

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Measured value

Simulat-ed value Unit

Focal length 4.96 (= Fgeo) 4.3 4.22 mmDepth of view, DOV 5 4.1 4.17 mmEffective focal gain 4.18 3.43 2.98 (None)

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