Reducing Inter-Element Acoustic Crosstalk

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 54, no. 6, june 2007

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Reducing Inter-Element Acoustic Crosstalk in Capacitive Micromachined Ultrasound Transducers Shiwei Zhou and John A. Hossack, Senior Member, IEEE

Abstract—The inter-element acoustic crosstalk problem in capacitive micromachined ultrasound transducer (CMUT) arrays is discussed in this paper. A transfer function matrix approach was used to derive modified transmit waveforms on adjacent elements to reduce the apparent acoustic crosstalk. The significance of this is that this technique relies on programmable waveforms, so that it yields a reduced crosstalk effect with no additional fabrication complexity if the requisite programmable waveform transmit circuits are available. The crosstalk reduction achieved by this method also was examined in combination with conventional (physical separation-based) crosstalk reduction approaches.

A CMUT transducer array structure was simulated in a two-dimensional (2-D) model using finite element analysis (FEA), and the crosstalk reduction method was tested for both small and large alternating current (AC) (ultrasonic) excitation conditions. A 25 dB crosstalk reduction was achieved for small AC excitation conditions in which approximately linear operation is encountered. When the AC excitation amplitude was large compared to the direct current (DC) bias, an “iterative harmonic cancellation” approach (also based on programmable waveform techniques) could be applied in combination with the crosstalk reduction method to minimize the inherently transmitted harmonics, and a similar crosstalk reduction effect of 25.5 dB was achieved. This method also can be combined with other structure-modification based crosstalk reduction approaches.

I. Introduction apacitive micromachined ultrasound transducers (CMUT) have attracted considerable attention recently and have been proposed and tested for medical diagnostic applications because they offer several technical and potential cost advantages with respect to conventional piezoelectric transducers [1], [2]. Research results have shown that CMUTs can achieve very broad frequency bandwidth [3], [4], resulting in improved image spatial resolution. Some CMUT fabrication processes are compatible with complementary metal oxide semiconductor (CMOS) process, and thus it is possible to tightly integrate electronics and the CMUT over a common silicon substrate [5], [6].

C

Manuscript received December 15, 2005; accepted January 8, 2007. This work was also supported in part by NIH NIBIB grants EB001826, EB002349 and DoD CDMRP W81XWH-04-1-0240.

The authors are with the Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22901 (e-mail: jh7fj@virginia.edu).

Digital Object Identifier 10.1109/TUFFC.2007.375

Since CMUT transducers are manufactured using semiconductor microlithography processes, the per-part cost is low when large volumes are fabricated. Moreover, the effective acoustic impedance of the CMUT membrane is well matched to the impedance of water or tissue. These advantages provide CMUT technology the potential to replace conventional PZT transducers, primarily in compact, high element count one-dimensional (1-D) or 2-D arrays [2], [7], ultrasound transducers for intravascular ultrasound imaging [8].

However, CMUTs have some problems that may limit their use in practical applications. One problem is that the overall device electromechanical conversion coupling is lower than a PZT transducer, unless the physical design is highly optimized and the device is biased with a direct current (DC) voltage that brings the membrane close to the collapse threshold [9], [10] (which increases the risk of membrane collapse). Also, a CMUT transducer operates nonlinearly because the output electrostatic force is approximately proportional to the square of the input electrical voltage, resulting in harmonic components in its transmitted signals. This problem makes CMUTs unsuitable for tissue harmonic imaging as it is impossible to distinguish harmonic signal generated by the human tissue from transmitted harmonic components. Several approaches have been proposed to solve the harmonic generation problem [11–13]. In our earlier work [11], we simulated and experimentally verified that 18.6 dB reduction in second harmonic generation was easily attainable.

The problem discussed in this paper is that, when built into an array transducer, the silicon-based CMUT devices potentially have significant acoustic crosstalk between array elements because the crosstalk may be coupled easily through the transducer-medium interface as well as via the silicon substrate [14], [15]. The silicon substrate is frequently single crystal and glass-like (i.e., very low acoustic loss). In this paper, we apply a transfer function matrix method based on programmable waveform technique to reduce the inter-element acoustic crosstalk [16].

Finite element analysis (FEA) simulation results were obtained for both small and large AC excitation conditions.

Other known crosstalk reduction methods are discussed as well for comparison purposes. These existing crosstalk reduction methods can be used in combination with the crosstalk cancellation approach to yield further reductions in net acoustic crosstalk.

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II. Background Inter-element crosstalk is a major concern for any array transducer that has continuous acoustic pathways among elements. Crosstalk can be broken into acoustic and electrical cross coupling components. Electrical crosstalk propagates at approximately the speed of light and is practically instantaneous for the dimensions found in the applications under consideration. Thus, electrical crosstalk typically manifests itself as enhanced brightness along the central image line rather than off-angle image artifact features resulting from spurious array-element sidelobes. Electrical crosstalk is controlled by carefully shielding individual electrical channels from the system, through the cable (if one exists), and the transducer electrical interconnection structure all the way to the active transducer element. Electrical crosstalk usually can be limited to approximately −35 dB in a well designed array [17]. Acoustic crosstalk is associated with relatively slow acoustic waves propagating between adjacent array elements. Interelement acoustic crosstalk has been investigated by many researchers for conventional PZT-based transducers, PZTepoxy 1:3 composite transducer arrays, and CMUTs [18].

CMUT transducers generally have high intrinsic acoustic crosstalk due to the Stoneley wave at the membrane-water interface and the lack of isolation cuts between elements, which results in continuous, low-loss, acoustic path between elements [14], [19]–[21].

The impact of crosstalk on the angular response of array elements also has been widely investigated [22]–[24].

It causes degradation of single-element, angular response as the main lobe of the angular response becomes narrower, and peaks (sidelobes) and nulls result in the singleelement, angular response. These sidelobes correspond to the constructive, or destructive, interference of delayed crosstalk associated waves as they propagate outward into the load media from various locations across the transducer array surface.

CMUT transducers have relatively high crosstalk because the membrane vibration may propagate acoustically to neighboring elements through the membrane-fluid interface, and through the low acoustic loss silicon substrate. In [14], different sources of acoustic crosstalk were identified.

One major source is the Stoneley wave propagating along the interface with the load media. Another factor is that the Lamb wave energy propagates in the thin silicon substrate and is mode-converted at the load interface resulting in perturbed, single-element, angular response. Both of these two types of waves easily can propagate to neighboring CMUT cells and contribute to the acoustic crosstalk between adjacent CMUT elements as well. (In this paper, a CMUT cell is defined as the smallest indivisible working unit in a CMUT device. Generally, a CMUT transducer element consists of many cells connected in parallel.)

There are multiple approaches attempting to reduce the acoustic crosstalk level in CMUTs. Mo et al. [25] investigated the crosstalk in micromachined diaphragm structures for ultrasound transducer arrays. They com-

pared the crosstalk performance among three different substrate geometries and observed that separated diaphragm element with no substrate underneath each element diaphragm (the substrate only provided support between neighboring elements) provided the least crosstalk. Roh and Khuri-Yakub [20] also have investigated the impact of the substrate thickness on the crosstalk. They attempted to use isolation trenches or extra separation walls between CMUT elements to reduce the acoustic crosstalk. Unfortunately, the results demonstrated that the impact of these methods on crosstalk were modest. The crosstalk level varied by less than 1 dB with different separation wall heights and trench depths; and reducing the substrate thickness from 1 mm to 50 µm reduced crosstalk by approximately 2 dB. Caronti et al. [15] also demonstrated similar results in FEA simulations, finding that an extra trench did not reduce crosstalk, and that the separation width between cells had almost no impact on crosstalk reduction.

In one of our previous works [16], we presented a transfer function matrix method based on programmable waveform technique to reduce the inter-element acoustic crosstalk. In this method, the transducer crosstalk performance in transmitting mode was described by a transfer function matrix. A group of required excitation and cancellation waveforms was calculated using the matrix to achieve preselected output (i.e., finite output from selected element and close to zero output from neighbors).

The method was tested successfully on PZT-array transducers using both FEA and experiments. In this paper, we further develop this method for application in CMUT transducers.

III. Methods In phased-array transducers, the total acoustic output in the field is a linear summation of ultrasound radiation from all the elements, when the nonlinear acoustic propagation effects can be neglected. Consequently, if crosstalk cancellation signals can be derived for adjacent elements with respect to a single driven element, the required excitation and crosstalk cancellation signals for all array channels can be derived by superimposing driven beamformed excitation functions with crosstalk cancellation signals. Some current “premium” diagnostic ultrasound scanner systems include programmable waveform transmitter circuits [26]. This makes it possible, at least in principle and after any requisite scanner engineering development, to use our approach for crosstalk reduction with no additional manufacturing cost.

In our method, a transducer transfer function matrix is created to describe the element performance and crosstalk behavior [16], and to relate inputs and outputs on all elements together. Using this matrix and a set of predefined, ideal outputs, required excitation and cancellation waveforms were calculated to cancel the inter-element acoustic crosstalk. The matrix solution is performed in the frequency domain, and it is assumed that the transducer be-

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zhou and hossack: reducing inter-element crosstalk in capacitive ultrasound transducers

Fig. 1. Crosstalk in a 3-element CMUT device example.

haves as a linear system. However, a CMUT transducer operates nonlinearly as the output electrostatic force in CMUT is approximately proportional to the square of the applied voltage. The relative contribution of harmonic frequency components in transmitted signals is dependent on the ratio of the AC excitation voltage to the DC bias voltage. Thus, in order to apply this method to CMUT array transducers effectively, the AC excitation signals should be much smaller than the DC bias voltage so as to permit the assumption of approximately linear operation to be valid. Using this assumption, the transfer function matrix method was applied for CMUT transducers in a similar manner as for PZT transducers. Although the intended element involves a large transmit voltage and a relatively large output signal, the crosstalk signals are sufficiently small to be more amenable to the small signal/linear operation approximation.

It should be observed that we are referring here to crosstalk reduction in the transmit mode of operation.

The transmit crosstalk cancellation problem is far more tractable than the receive crosstalk problem. Correction on receive is not amenable to the same type of analysis and requires a degree of signal subtraction that has the effect of enhancing effective noise. Additionally, it should be noted that the net two-way, single-element, angular response is described by the product of the transmit and receive angular responses. If a sidelobe is eliminated entirely in one direction, the net two-way response is still considerably improved. In the ideal situation, a sidelobe is reduced to approximately zero response, and thus the two-way product in the vicinity of the potential sidelobe is approximately zero.

Fig. 1 illustrates the inter-element acoustic crosstalk in a basic CMUT device, in which there are three elements, and the center element is the only element driven by the AC excitation. The undesired crosstalk signal is generated on the two adjacent elements, and it can be reduced by using the transfer function matrix method in several steps as explained below: Step 1: The function of the array transducer during the transmitting operation is described by a transfer function matrix (1). Because of the symmetry in the device, it can be assumed that the crosstalk from adjacent elements on both sides is the same. Therefore, there are effectively only two signal channels (driven and adjacent elements) involved, and the transfer function matrix has

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dimensions 2 × 2. The matrix components on the main diagonal, H11 and H22 , are the transmit frequency responses of the center and the adjacent element. It also can be assumed that all the elements have the same performance so that H11 = H22 . Other matrix components (H12 and H21 , and H12 = H21 ) represented crosstalk transfer function in frequency domain:

H11 H12 VDriven PDriven = .

(1) PAdjacent H21 H22 VAdjacent Step 2: Although all elements are connected to DC bias, a known AC excitation signal is applied only to the center element (“driven element”). The corresponding pressure outputs, PDriven , PAdjacent , are measured immediately above the membrane of the CMUT elements, so that the crosstalk output can be distinguished easily from diffracted components from driven elements. Thus, the matrix components are determined by dividing the output spectra by the input signal spectra in frequency domain and using the two assumptions in Step 1.

Step 3: Once the transfer function matrix is fully defined, the matrix is solved to find the required excitation signal on the driven element and the cancellation signal on the adjacent element, so that the desired output can be achieved, i.e., PDriven = ideal frequency response of the driven element and PAdjacent = 0.

There are a few variations of this matrix method [16].

As the number of elements in the array increases, the size of the matrix increases accordingly. If the crosstalk can be assumed to be significant on only a few neighboring elements, instead of the entire array, the standard square matrix will become a banded square matrix. For practical applications, the crosstalk cancellation signals may be programmed for fewer channels (less than the number of element in the array). In such cases, there are more measured outputs than the programmed inputs, meaning that the matrix has more rows than columns and requires a pseudoinverse solution. The procedure reduces the acoustic crosstalk from one element (the driven element). The same procedure can be extended to other elements in the array. The group of calculated required driving and cancellation waveforms can be directly applied to most elements in the array because of the symmetry condition and their identical crosstalk performance. Thereafter, the new modified excitation waveform and the necessary cancellation waveforms on the same element will be summed up for the transmit beamforming. All calculations performed in the frequency domain, and the final time domain excitation and cancellation waveforms obtained by taking inverse Fourier transforms.

IV. FEA Results It is established that, provided accurate material property characterization and device geometry are used, FEA is a reliable method for predicting acoustic device performance [27]–[29]. In particular, PZFlex (Weidlinger As-

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 54, no. 6, june 2007 TABLE I Principal Dimensions and Material Properties.

Material Silicon Silicon nitride Polyurethane

Density (kg/m3 )

Young’s modulus (×109 Pa)

Poisson’s ratio

Relative permittivity

2340 3270 1122

165 323 0.97

0.22 0.26 0.43

11.5 7.5 4.0

Fig. 2. The 2-D symmetric CMUT model in PZFlex (half).

sociates Inc., Los Altos, CA) has been validated against numerous experimental results, and it has been used for piezoelectric, electrostatic, and thermoelastic ultrasound transducer devices [11], [19], [30], [31]. In this paper, PZFlex was used for the FEA simulation. PZFlex is a commercially available software package with a nonlinear electrostatic solver that can be used for the simulation of CMUT transducers. It uses a time-domain solver that is efficient for large deformation transient problems (i.e., deformation comparable to the device dimensions), thus it is capable of calculating the entire frequency response within a single simulation operation. Principal material parameters are described in Table I1 .

Ideally, because of the complex geometry of CMUT transducers (multiple cells in one CMUT element), the inter-element crosstalk should be simulated using a 3-D model. However, in order to reduce the complexity and the intensive computation required by the 3-D modeling, a 2-D model with rectangular shape CMUT cells was created in PZFlex for the work in this paper. It was assumed that the length of each CMUT cell in elevation dimension was much larger than the width of the cell in azimuth dimension (infinite length in elevation), so that a 2-D model was valid. The FEA simulation started from a basic model in which there were three CMUT elements arranged side by side. In the simulations presented here, each transducer element consisted of three rectangular cells. A model with X-Y 2-D plane symmetry was used in this simulation so that only half of the device was actually simulated. The crosstalk was assumed to be significant only to the first adjacent neighbor element (improved, more extensive simulations will become practical as the computer processing power and memory cost/performance evolve). Fig. 2 1 Onda Corporation, “Tables of acoustic properties of materials,” http://www.ondacorp.com/tecref acoustictable.html, 2005.

Fig. 3. Small AC excitation signal: 10 MHz 6 V (peak), 35% fractional bandwidth.

illustrates half of the model—because a symmetry condition was applied along the center of the model. The element pitch was 158 µm, and each cell within one element had a 40-µm wide membrane. The silicon nitride membrane was 2-µm thick. The vacuum gap was 0.25-µm thick and was enclosed by the surrounding silicon nitride support walls. The substrate was 800-µm thick silicon wafer.

These dimensional values were selected to be comparable with those values in a typical CMUT device used by other research groups [5]. The DC bias voltage was 60 V (the collapse threshold on this structure was about 120 V), and a 10 MHz, 35% fractional bandwidth AC excitation pulse as shown in Fig. 3 was applied to the center (driven) element.

The amplitude of the AC driving signal was 6 V (10% of the DC bias), so that the AC excitation was much smaller than the DC bias; therefore, the operation was approximately linear.

In this PZFlex model, all three elements were subject to the DC bias voltage, but only the center element was driven by an AC excitation signal. The pressure output

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Fig. 4. Pressure outputs on the driven and its adjacent element before the crosstalk cancellation (small AC excitation).

was calculated immediately above the membrane, and it was averaged over the membrane width to approximate the integrated output of the entire element. Fig. 4 illustrates the pressure output measurement on both driven element and its adjacent element before any crosstalk cancellation.

The crosstalk on the adjacent element was measured at −31.5 dB compared to the output from the driven element.

Although the AC signal was much smaller than the DC bias, the nonlinear second harmonic was still identifiable in this simulation result. However, it was −40 dB below the fundamental frequency component on both driven and adjacent elements; therefore, it had minimal impact on crosstalk reduction.

A. Crosstalk Cancellation by the Transfer Function Matrix The transfer function matrix method was applied using the small AC excitation condition. Using the procedure presented in Section III and the simulation results in Fig. 4, the matrix was determined by dividing the output spectra by the input signal spectra in frequency domain (H11 = H22 , H12 = H21 ). An ideal pressure output was defined for the driven element, which had a similar frequency spectrum as the input signal, but with a slightly narrower bandwidth. The ideal output for the adjacent element was imposed to be zero. Thereafter, the matrix was solved and the required excitation signal on the driven element and the cancellation signal on the adjacent element were calculated (Fig. 5). Because this FEA model involved only two channels, a 2 × 2 matrix similar to that shown in (1) was used and directly solved. Fig. 6 illustrates the pressure output results on both driven and adjacent elements after the new required excitation and cancellation signals applied. The undesired crosstalk on the adjacent element was measured at −56.8 dB compared to the pressure output from the driven element. Hence, the crosstalk was reduced by 25.3 dB. B. Crosstalk Cancellation with Harmonic Reduction Although the matrix cancellation method was successful at small AC excitation conditions (e.g., <=10% DC

Fig. 5. The required excitation signal on the driven element and the crosstalk cancellation signal on the adjacent elements in the small AC excitation condition.

bias), for most practical medical ultrasound imaging applications, it is necessary that the CMUT device should be operated more aggressively with a higher AC excitation amplitude to achieve a useful output pressure level, and to obtain satisfactory signal-to-noise ratio (SNR). Therefore, it is critical to examine the performance of this crosstalk cancellation method using a high AC signal level, i.e., one in which the approximate linearity is not valid.

In the simulation below, the DC bias remained 60 V, but the AC excitation amplitude was increased from 6 V (10% of DC) to 30 V (50% of DC). The corresponding pressure outputs on the driven and adjacent elements without crosstalk cancellation are shown in Fig. 7. First, the inter-element crosstalk was −31.4 dB for the fundamental frequency component—almost the same as in the small AC excitation case, which implies that, regardless of the AC input amplitude, the inter-element acoustic crosstalk level was similar. The second finding was that the second harmonic frequency component was approximately −26 dB below the fundamental frequency component on both driven and adjacent elements, which was significantly higher than that in the small AC excitation case (−40 dB).

This was anticipated because CMUT transducers inherently produce harmonics as discussed above, and the relative strength of the harmonic component was related to

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Fig. 6. Pressure output on the driven and adjacent element after crosstalk cancellation (small AC excitation).

Fig. 7. Pressure outputs on the driven and its adjacent element before crosstalk cancellation at large AC excitation level.

TABLE II Crosstalk Comparison in Small and Large AC Excitation Cases (Both Before Crosstalk Cancellation).

Element Driven element output Adjacent element crosstalk

Small AC excitation case (Fig. 4) Fundamental 2nd harmonic component component 0 dB −31.5 dB

the amplitude ratio of the AC excitation and DC the bias.

The results from Figs. 4 and 7 are compared in Table II. It was observed that, although the CMUT transducer generated nonlinear acoustic output, the crosstalk propagation from the driven element to its adjacent element was approximately linear. In both small AC (Fig. 4) and large AC (Fig. 7) excitation cases, the undesired crosstalk output was always approximately −31.5 dB below the output from the driven element.

Fig. 8 illustrates the crosstalk reduction result obtained by using the same matrix cancellation approach in this high AC excitation voltage condition. The crosstalk on the adjacent element was successfully reduced from −31.4 dB to −56.9 dB for the fundamental frequency component

−41.5 dB −62 dB

Large AC excitation case (Fig. 7) Fundamental 2nd harmonic component component 0 dB −31.4 dB

−26.1 dB −47.9 dB

(25.5 dB reduction), which was similar to the result obtained in the small AC excitation condition. The inherently generated second harmonic frequency component was measured at −26.8 dB. These results indicate that, because the transfer function matrix method for crosstalk cancellation is based on linear systems analysis, it worked fine for the fundamental frequency component in which the CMUT is operating in an approximately linear manner. Due to the inherent nonlinearity of a CMUT, the matrix method was not able to cancel the crosstalk in the harmonic frequency band. However, the second harmonic frequency band was not intended to be used in the transmitting mode anyway, and there were several ways to suppress the second harmonic component in the signals [11].

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Fig. 8. Pressure outputs on the driven and its adjacent element after crosstalk cancellation at large AC excitation level.

Fig. 9. Pressure outputs on the driven and its adjacent element after crosstalk cancellation and harmonic suppression at large AC excitation level.

At this stage, an “iterative harmonic cancellation” technique [11] was included in our crosstalk reduction approach to minimize the inherently produced harmonic. This “iterative cancellation” method also is based on a waveform precompensation technique and has a similar virtue to the crosstalk cancellation method, in that it also requires no extra hardware processing or physical structure changes (assuming that the requisite programmable transmitters are available). The procedure that was used is described below.

Step 1: The harmonic components to be suppressed on both driven and adjacent elements were extracted (in the frequency domain) from the simulation results shown in Fig. 8.

Step 2: In a separate simulation, a small amplitude AC excitation with wide bandwidth (3 V peak amplitude, 20 MHz center frequency, 100% −6 dB fractional bandwidth) was used to determine the approximate transfer function of the device. Because the peak amplitude was only 5% of DC bias, an approximate linear operation can be assumed.

Step 3: The extracted harmonic frequency components were divided by this approximate transfer function in the

frequency domain. The division results were converted into time domain via inverse Fourier transform and were polarity-inverted to obtain the harmonic cancellation signals on both the driven and adjacent elements.

Step 4: The harmonic compensation signals were superimposed on the original excitation and cancellation inputs.

In this way, the required excitation and cancellation signals used for crosstalk reduction (in Fig. 8) were precompensated to minimize the inherent second harmonic frequency component.

Fig. 9 illustrates the simulation results after both the crosstalk reduction and harmonic suppression for high AC excitation level. The inter-element crosstalk was successfully reduced from −31.4 dB to −50 dB for the fundamental frequency component. The second harmonic was significantly reduced from −26 dB to approximately −50 dB. The “iterative harmonic cancellation” procedure was executed only once; hence, some higher harmonic frequency components were induced. However, this higher harmonic component was beyond the interested frequency range and was relatively weak (−35 dB or lower). Therefore, this harmonic component is amenable to standard filtering processes. Thus, the combined application of the transfer func-

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Fig. 10. One frame in the displacement “movie” showing the traveling wave on the membrane-water interface.

Fig. 11. Pressure outputs on the driven and its adjacent element with lossy separation wall (small AC excitation).

tion matrix method and the “iterative harmonic cancellation” approach successfully reduced both the undesired crosstalk and the transmitted second harmonic in the large AC excitation condition. The significance is that both approaches use digitized programmable waveforms, and they solve two major problems for CMUT array transducers without adding hardware cost or fabrication complexity.

Additionally, it was noticed that there was a mode located at approximately 2 MHz, appearing in both small and large AC excitation conditions. In the PZFlex FEA simulation, a displacement “movie” indicated that it was one type of Stoneley wave traveling laterally on the membrane-water interface. (Fig. 10 shows one membrane from the center element, one membrane from the adjacent element, and the water region in between.) The relative strength of this mode compared to the fundamental frequency component increased as the AC excitation amplitude increased. It was below −30 dB in the small AC excitation condition, and it was approximately −16 dB in the large AC excitation condition. The frequency of this mode remained almost unchanged when subject to different input signal frequencies. Furthermore, it was not affected by the crosstalk cancellation method. The crosstalk within the 2 MHz vicinity on the adjacent element was −5 dB below the 2 MHz frequency component on the driven element before and after crosstalk cancellation. Because the 2-D, FEA model with rectangular CMUT elements is not an exact representation of the actual CMUT device, a 3-D model with larger geometry dimensions and more CMUT elements is necessary to better understand and character-

ize this traveling, interface wave. In the context of this paper, the associated signal can be filtered out because it was well outside the frequency range of primary interest (8–12 MHz).

C. Other Measures to Reduce the Crosstalk Other crosstalk reduction approaches based on structure modification also were examined for comparison purposes. Because a large proportion of crosstalk energy propagates laterally at the membrane-fluid interface, a separation wall was simulated midway between the driven element and its adjacent neighbor. The polyurethane wall was 16-µm tall, 8-µm wide, and assumed to possess a high acoustic loss to maximally attenuate the crosstalk propagating along on the interface (Table I1 , [20]). The pressure output waveforms are displayed in Fig. 11. A comparison between Fig. 4 and Fig. 11 indicates that this lossy separation wall did resolve some of the crosstalk problem.

Crosstalk was reduced from −31.5 dB to −37.0 dB. A taller separation wall may provide better crosstalk reduction effect, but it may block the emitted ultrasound waves propagating at wide angles during B-mode imaging. Therefore, the height of the wall must be optimized to achieve an optimal balance.

Subsequently, an 8-µm wide, 400-µm deep trench (halfway into the substrate) was created right in the middle between the driven element and the adjacent element in the simulation; and a lossy polyurethane wall was extended into the trench (as a further modified approach

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Fig. 12. Pressure outputs on the driven and its adjacent element with lossy wall extended in the trench (small AC excitation).

Fig. 13. Pressure outputs on the driven and its adjacent element in FEA using thinner substrate and backing layer (small AC excitation).

derived from earlier research [14], [20]). Thus, the lossy polyurethane material assisted in blocking the crosstalk due to both Stoneley waves on the interface and Lamb waves inside the substrate. The pressure output results are illustrated in Fig. 12, and the undesired crosstalk on the adjacent element was reduced from −31.5 dB to −38.5 dB. Therefore, both the lossy separation wall and trench provided effective approaches for reducing the inter-element crosstalk.

In another attempt to reduce the crosstalk propagating through in the silicon substrate, the thickness of the silicon substrate was reduced from an original 800 µm to 200 µm, and a 1-mm tungsten-epoxy backing layer with 18 MRayls acoustic impedance (matched with the impedance of silicon substrate) was added beneath the silicon substrate.

The high acoustic attenuation and the matched impedance of the backing material is intended to dampen the crosstalk energy propagating in the substrate. However, the simulation result in Fig. 13 indicated that this method did not have significant impact on the crosstalk performance as the undesired crosstalk on the adjacent element was still measured at −32 dB. This result indicated that the major crosstalk pathway was the water-membrane interface, and the crosstalk propagated through the backing substrate was much less.

Based on the simulation results above, it was evident that some solutions based on CMUT structure modifications, such as isolation walls and trenches, offered effective reductions in the undesired crosstalk. However, the transfer function matrix method can provide a more impressive crosstalk minimization, and this transfer function matrix method can be combined with and applied to augment those physical, isolation-based methods. For large AC excitation conditions, the “iterative harmonic cancellation” approach [11] can be used in addition to each of those crosstalk reduction methods.

Fig. 14 demonstrates the crosstalk reduction result obtained using both the transfer function matrix method and an extra separation wall extended into a trench in the silicon substrate. The mechanical properties, physical locations, and dimensions of the separation wall and trench were the same as used for the result in Fig. 12. The transfer function matrix method was applied on this modified structure in both small and large AC excitation conditions. These results are summarized and compared with previous crosstalk reduction results in Table III. The combination of the two methods achieved better crosstalk reduction results (26.5 dB in small AC excitation conditions and 29.6 dB in large AC excitation conditions) than using either one method alone.

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Fig. 14. Pressure outputs on the driven and its adjacent element in FEA with lossy wall extended in the trench after crosstalk cancellation (small AC excitation).

TABLE III Combined Crosstalk Reduction Result of Both the Matrix Method and Physical Modifications.

Crosstalk level on the adjacent element Crosstalk reduction with respect to the original case 1 In large AC excitation conditions Crosstalk level on the adjacent element

1 Original method

2 Transfer function matrix method only

3 Separation wall and trench only

4 Methods 2 and 3 combined

−31.5 dB

−56.8 dB

−38.6 dB

−58 dB

—

−25.3 dB

−7.1 dB

−26.5 dB

1 Original method

2 Transfer function matrix method only

3 Separation wall and trench only

4 Methods 2 and 3 combined

−31.4 dB

−56.9 dB

−39.2 dB

−61 dB

−25.5 dB

−7.8 dB

−29.6 dB

Crosstalk reduction with respect to the original case 1

V. Conclusions In this paper, inter-element acoustic crosstalk in CMUT transducer arrays was analyzed and minimized by using a transfer function matrix approach to derive crosstalk cancellation signals.

Some current “premium” ultrasound scanners have the capability to program arbitrary-shaped transmitter voltage waveforms (e.g., Sequoia, Siemens Medical Solutions, Malvern, PA). In principle, the programmable waveform generators in those ultrasound systems enable the implementation of this technique at zero additional manufacturing cost. Therefore, this transfer function matrix approach can yield an extra improvement in addition to all regular crosstalk reduction efforts without added cost.

The transfer-function, matrix method was tested in two conditions: small AC excitation with approximate linearity assumption, and large AC excitation condition in which there was no linearity assumption. A basic CMUT transducer structure was simulated in a 2-D model using PZFlex, and crosstalk generated from the adjacent element was measured and analyzed. The transfer-function, matrix method demonstrated excellent crosstalk reduction results. Under small AC signal conditions, a 25 dB reduction was obtained. A 25.5 dB reduction was obtained under large AC signal conditions. When the AC excitation amplitude is large compared to the DC bias, the “iterative harmonic cancellation” approach was applied together with the crosstalk reduction method to suppress the inherently generated harmonics. Both techniques rely

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zhou and hossack: reducing inter-element crosstalk in capacitive ultrasound transducers

on programmable waveforms, and applying both of them together reduces the undesired, inter-element crosstalk and the transmitted harmonics without adding hardware cost or CMUT fabrication complexity. Several other crosstalk reduction approaches also were demonstrated to be effective ways to reduce the inter-element crosstalk, such as lossy separation walls and trenches. Moreover, the transfer-function, matrix method was applied on a physically modified CMUT structure (with an extra separation wall extended in a trench). The combined result produced a 26.5 dB crosstalk reduction in small AC excitation conditions and 29.6 dB in large AC excitation conditions.

This matrix approach may be applied for array transducers in a relatively straightforward manner in the transmit mode. One limitation of this method is that, for high amplitude, wide-band input signal, the inherent nonlinearity cannot be ignored, and the second harmonics of some low-frequency components still are located in the fundamental frequency band of the entire signal. This will somewhat affect the effectiveness of this linear crosstalk reduction method. In the receive mode, it is more problematic to attempt to remove the effects of crosstalk due to the compounded nature of the received data resulting from the desired element response and the crosstalk component added from adjacent elements. A signal subtraction approach could be used, but this inevitably would reduce SNR. The crosstalk investigation in this paper was focused on crosstalk in 1-D CMUT arrays using two dimensional FEA modeling. Further study and 3-D simulation of CMUT transducers (including multiple cell examples) will improve the understanding of the crosstalk in CMUTs and assist in making further contributions in crosstalk reduction.

Acknowledgment Paul Reynolds, Ph.D. (Weidlinger Associates Inc., Los Altos, CA) provided guidance on PZFlex finite element modeling.

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Shiwei Zhou was born in Beijing, China in 1974. He received the B.S. and M.S. degrees in optical-electrical engineering from the Beijing Institute of Technology, Beijing, China, in 1996 and 1999, respectively. He is currently working towards the Ph.D. degree in medical ultrasound imaging at the Department of Biomedical Engineering of the University of Virginia, Charlottesville, VA. His research interests are finite element analysis (FEA) modeling for various ultrasound transducers in-

cluding CMUTs, multi-layer transducers, and 2-D array transducers; applications of digital signal processing techniques in ultrasound; new transducer techniques and optimization.

John A. Hossack (S’90–M’92–SM’02) was born in Glasgow, Scotland, in 1964. He earned his B.Eng. Hons(I) degree in electrical electronic engineering from Strathclyde University, Glasgow, in 1986 and his Ph.D. degree in the same department in 1990. From 1990 to 1992, Dr. Hossack was a post doctoral researcher in the E. L. Ginzton Laboratory of Stanford University working under B. A. Auld’s guidance. His research was on modeling of 0:3 and 1:3 piezoelectric composite transducers. In 1992, he joined Acuson, Mountain View, CA, initially working on transducer design. During his time at Acuson his interests diversified into beamforming and 3-D imaging. Dr. Hossack was made a Fellow of Acuson for ‘excellence in technical contribution’ in 1999. In 2000 he joined the Biomedical Engineering Department at the University of Virginia, Charlottesville, VA. His current interests are in improved 3-D ultrasound imaging and high bandwidth transducers/signal processing. Dr. Hossack is a member of the IEEE and serves on both the Administrative Committee and the Technical Program Committee of the Ultrasonics Section. He also is an Associate Editor of the IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

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