CN113714070A

CN113714070A - Design method of broadband capacitive micro-machined ultrasonic transducer with mixed diaphragm structure

Info

Publication number: CN113714070A
Application number: CN202110841066.3A
Authority: CN
Inventors: 王红亮; 黄霄; 蔚丽俊; 何常德; 张文栋; 丁琦
Original assignee: North University of China
Current assignee: North University of China
Priority date: 2021-07-26
Filing date: 2021-07-26
Publication date: 2021-11-30
Anticipated expiration: 2041-07-26
Also published as: CN113714070B

Abstract

The invention relates to an ultrasonic transducer in the fields of ultrasonic imaging, medical diagnosis, nondestructive testing, liquid flow measurement, fault location, biochemical gas detection and the like, in particular to a design method of a broadband capacitive micro-mechanical ultrasonic transducer with a mixed diaphragm structure. A method for designing broadband capacitive micro-mechanical ultrasonic transducer with mixed diaphragm structure includes integrating on a chip and arrangingN×NA plurality of CMUT cells of a rectangular array,Nis odd; each row of CMUT bins is provided withNThe CMUT micro-elements with different transmitting sound pressure frequencies are formed, and the CMUT micro-elements in different rows are all formed by the CMUT micro-elementsNArranging and composing micro elements; each row of CMUT elements are arranged in a mode that the frequency of the transmitting sound pressure is sequentially increased or decreased, and the increasing and decreasing arrangement sequence of two adjacent rows is opposite; in each row of CMUT micro-elements, the emission sound pressure frequencies of adjacent micro-elements are overlapped; the resonance frequency of the centrally located micro-element in each row of CMUT micro-elements is the same as the resonance frequency of the whole capacitive micromachined ultrasonic transducer.

Description

Design method of broadband capacitive micro-machined ultrasonic transducer with mixed diaphragm structure

Technical Field

The invention relates to an ultrasonic transducer in the fields of ultrasonic imaging, medical diagnosis, nondestructive testing, liquid flow measurement, fault location, biochemical gas detection and the like, in particular to a design method of a broadband capacitive micro-mechanical ultrasonic transducer with a mixed diaphragm structure.

Background

The ultrasonic wave has the characteristics of high frequency, concentrated energy, strong penetrating power, good directivity and the like, and is widely applied to the fields of ultrasonic imaging, medical diagnosis, nondestructive testing, liquid flow measurement, fault location, biochemical gas detection and the like. Among other things, in ultrasound imaging applications, the ultrasound transducer directly determines the imaging resolution and the probe depth of the imaging system. The higher the resonant frequency of the transducer, the higher the imaging resolution, the easier it is to obtain high quality images, however, as the resonant frequency increases, the detection depth will decrease, so that the imaging range of the imaging system is limited, and therefore, the imaging resolution and the detection depth are a pair of mutually restrictive factors. In order to balance the contradiction between the two as much as possible, the frequency range of the ultrasonic transducer should be widened, so that the imaging resolution and the detection depth show good performance in the frequency range, and the imaging quality of the ultrasonic imaging system is improved. The broadband ultrasonic transducer can be applied to the field of ultrasonic imaging to improve the imaging quality, and has unique advantages in many other application occasions. In flow measurement or ranging applications, the transmission time of an ultrasonic pulse needs to be measured, and the accuracy of transmission time measurement can be improved by using a broadband ultrasonic transducer. In ultrasonic identification applications, the wide bandwidth ultrasonic transducer can reduce the pulse width and improve the axial resolution. In conclusion, the research and design of the broadband ultrasonic transducer have important practical significance.

Micro-Electro-Mechanical systems (MEMS) technology has been rapidly developed since the 19 th century, and a new ultrasonic transducer, a Capacitive Micromachined Ultrasonic Transducer (CMUT), has been developed. The piezoelectric ultrasonic transducer is gradually replaced by the piezoelectric ultrasonic transducer by virtue of the advantages of easy processing, suitability for batch production and the like, and becomes a new generation of mainstream ultrasonic transducer.

Compared with the piezoelectric ultrasonic transducer, the CMUT has significant advantages in structural design, process manufacturing and integration with a front-end signal circuit. First the CMUT does not need to add an impedance matching layer, while it has a larger bandwidth and sensitivity. Secondly, CMUTs possess a large frequency range. In addition, the CMUT can be integrated with the signal conditioning circuit to form a chip, so that the influence of external interference signals introduced in the module connection process and parasitic capacitance among the signal conditioning circuits is reduced, the size of the transducer is reduced, and the miniaturization design of the ultrasonic imaging system is realized. In addition, the CMUT has the advantages of simple manufacturing process and low manufacturing cost. Based on the advantages, the CMUT gradually replaces the piezoelectric ultrasonic transducer to become a neutral flow column of the broadband ultrasonic imaging transducer. Meanwhile, the design and performance optimization of the broadband CMUT structure become a research hotspot of scholars at home and abroad.

Experts and scholars in various countries propose various methods to widen the frequency band of CMUT and manufacture broadband ultrasonic transducers with excellent performance. Hall na et al optimize the mass distribution of the film by loading a patterned film on a uniform rectangular film of silicon nitride, obtaining a broadband response. On the basis, the two-electrode structure is designed, electrodes are respectively deposited on the two sides and the center of the film, the harmonic signal receiving is enhanced, and the frequency band of a transmission signal is further widened. By adjusting the values of the film thickness, the film radius, the electrode radius and the cavity height, the Bayram Can et al optimize the CMUT micro-elements to obtain the maximum gain bandwidth product, and on the basis, two and three micro-elements with different sizes are respectively arranged to form array elements, thereby further improving the bandwidth of the CMUT. Olcum Selim et al studied methods to increase the bandwidth of single CMUT micro-elements and CMUT arrays in the air domain. Firstly, establishing a Meisen equivalent circuit model to perform equivalent circuit simulation on the CMUT micro element, and the result shows that when the characteristic frequency is fixed, the larger the radius-thickness ratio of the CMUT micro element vibrating membrane is, the wider the bandwidth is. In addition, in order to increase the bandwidth of the CMUT array, three CMUT microelements of different center frequencies are combined to form an interleaved CMUT array, and a relative bandwidth of 60% or more is obtained in the air domain. Manzanares a O et al propose a method of designing an air-coupled CMUT using the principle of helmholtz resonators, using a perforated resonant cavity instead of a conventional vacuum sealed cavity to increase the output pressure and bandwidth of the CMUT. Finite element simulation results indicate that the designed CMUT can improve output pressure and bandwidth in air. Apte Nikhil et al propose a CMUT structure with a cavity with vent holes. By reasonably selecting the size, the number and the position of the vent holes, the membrane squeezing effect can be controlled, so that the bandwidth of the CMUT is improved. They designed two CMUT devices with the vent area ratio of 0.05% and 1%, and performed finite element simulation and practical test, and the results showed that the relative bandwidths of the two CMUT devices in the air domain were 19% and 36%, respectively. Adelegan O J et al designed both ring and spiral air-coupled CMUTs. They first performed simulation analysis using ANSYS and then tested using a prototype with anodic bonding, which showed a-6 dB relative bandwidth of the designed air-coupled CMUT in the air domain of 12%. Zhang Hui et al designed and fabricated a 16-element air-coupled CMUT array based on SOI wafer bonding technology. The use of circular membranes of the same size for all the cells broadens the bandwidth of the CMUT array by reducing the membrane quality. Tests show that the designed air-coupled CMUT array resonant frequency is 215KHz, and the-3 dB relative bandwidth in the air domain reaches 15.7%.

Chee Ryan k.w. et al produced a multi-frequency ultrasonic transducer by staggering films with radii of 82 μm and 36 μm. Tests show that the working frequency of the ultrasonic transducer in water is 0.6 to 7.32MHz, and the relative bandwidth of-6 dB reaches 170%. Compared with an ultrasonic transducer consisting of a uniform film, the bandwidth is improved by 40%. Although the above scheme improves the bandwidth, the improvement range is limited, and the actual requirement cannot be met.

Disclosure of Invention

The invention provides a design method of a broadband capacitive micro-machined ultrasonic transducer with a mixed diaphragm structure, which aims to solve the technical problems of low transmitting sound pressure and receiving sensitivity, poor directivity, low bandwidth and the like of the conventional CMUT.

The invention is realized by adopting the following technical scheme: a method for designing broadband capacitive micro-mechanical ultrasonic transducer with mixed diaphragm structure includes integrating on a chip and arrangingN×NA plurality of CMUT cells of a rectangular array,Nis odd; each row of CMUT bins is provided withNThe CMUT micro-elements with different transmitting sound pressure frequencies are formed, and the CMUT micro-elements in different rows are all formed by the CMUT micro-elementsNArranging and composing micro elements; each row of CMUT elements are arranged in a mode that the frequency of the transmitting sound pressure is sequentially increased or decreased, and the increasing and decreasing arrangement sequence of two adjacent rows is opposite; in each row of CMUT micro-elements, the emission sound pressure frequencies of adjacent micro-elements are overlapped; the resonance frequency of the centrally located micro-element in each row of CMUT micro-elements is the same as the resonance frequency of the whole capacitive micromachined ultrasonic transducer.

In order to improve the transmission sound pressure, the reception sensitivity, the directivity, and the bandwidth characteristics of the CMUT, a plurality of CMUT micro-cells may be arranged in a specific rule to constitute the CMUT. The constituent CMUTs can be generally classified into two types, one is uniformly arranged by the same micro-cells, and the other is staggered by different micro-cells. When CMUT is startedNWhen the same elements are formed, the parameter values of the transmitting sound pressure, the receiving sensitivity and the like of the same elements are single elementsNAnd (4) doubling. When CMUT is startedNWhen composed of different micro-cells, each of which effectively transmits signals in a very small frequency range, the bandwidth of the overall CMUT will increase. The transmission sound pressure bandwidth situation of a CMUT theoretically composed of three different bins is shown in fig. 1. Wherein, the center frequencies of the three micro-elements are adjacent, and the frequency ranges are not overlapped; in the graph (b), the center frequencies of the three types of micro-elements are adjacent, and the frequency ranges are partially crossed and overlapped.

As can be seen from fig. 1, the superposition of the frequency ranges of the transmission sound pressures of the CMUT consisting of three different microelements can achieve the intended purpose of improving the bandwidth. However, in the graph (a), the difference between the resonant frequencies of the three types of micro-elements is large, so that the main peak of the CMUT cannot be smoothly transited, and the obtained frequency range is not flat enough, thereby affecting the quality of the output sound pressure. And the three selected infinitesimal resonance frequencies in the graph (b) are adjacent, the frequency ranges are partially crossed and overlapped, and the problem that the whole CMUT frequency range is not flat enough is improved.

Based on the principle, the invention designs the CMUT with the micro-element mixed structure, as shown in FIG. 2. The thicknesses of the micro-element vibration films forming the CMUT are the same, the micro-element vibration films sequentially decrease from left to right in the uppermost row, namely the frequency of the CMUT micro-element sequentially increases, and the micro-element vibration films sequentially increase from left to right in the next row, namely the frequency of the CMUT micro-element sequentially decreases; the frequency is increased while ensuring that the frequency ranges of the micro-elements are overlapped. Among the cells constituting the CMUT, a cell having the same resonance frequency as that of the CMUT is called a center cell, and this cell is a main design body of the CMUT, and the frequency range can be adjusted by increasing or decreasing the number of other frequency cells, thereby obtaining the CMUT with an appropriate bandwidth.

Under the same size, the micro element arrangement mode design (the frequency of the micro elements in the same row is increased or decreased, the arrangement sequence of adjacent rows is opposite) adopted by the invention can distribute more micro elements, thereby not only effectively utilizing the size of the wafer, but also improving the transmitting sound pressure intensity of the whole transducer;

at the same time, the design can reduce the fluctuation of the effective bandwidth amplitude.

Furthermore, the distance between every two adjacent CMUT micro-elements in each row of CMUT micro-elements is as small as possible; the pitch of adjacent CMUT cells in each column of CMUT cells is as small as possible.

When the filling factor of the micro-element array is increased (namely the distance between adjacent micro-elements of each row and each column is reduced), the bandwidth of the micro-element array is increased.

The invention also provides a method for judging how to determine the number of the infinitesimal elements on the basis of the array arrangement, which comprises the following steps: when the resonant frequency and-6 dB relative bandwidth of the whole capacitive micro-machined ultrasonic transducer are determined, the number of micro elements with different sizes is determined according to the following rule:

the ratio of the overlapping frequency of two adjacent infinitesimal elements to the absolute bandwidth of any one of the two adjacent infinitesimal elements is recorded as the frequency crossing range of the adjacent infinitesimal elementsw(ii) a Absolute bandwidth of-6 dB of infinitesimalnWith its resonant frequencyfRatio ofIs recorded as a relative bandwidth of-6 dBx(ii) a The-6 dB relative bandwidth of the entire capacitive micromachined ultrasonic transduceryCan be expressed as:

y=x+(N-1)(1-w)x (1)

obtained from (1)

（2）

WhereinxIt is known empirically that the-6 dB relative bandwidth of a CMUTyGiven as an index before design; for differentyAndwtaking values to obtain correspondingNA value;Nthe calculated value is rounded up, and when the calculated result is obtainedNWhen the number of the channels is odd, selectingNOne infinitesimal element is needed, and when the result is calculatedNEven number, should be selectedN+1 infinitesimal. The invention also discloses a method for determining the resonance frequency of each infinitesimal element on the basis of determining the number of the infinitesimal elements, which comprises the following steps: the sounding vibration frequency of each infinitesimal is determined according to the following rule: the central micro-element of each row of CMUTs is marked as the 0 th micro-element, the micro-element adjacent to the central micro-element is marked as the 1 st micro-element, the micro-element adjacent to the 1 st micro-element is marked as the 2 nd micro-element, and so on, the micro-element at the edge is marked as the second micro-elementKEach element; take the case of left-to-right frequency increment of the bins as an example, whereiniThe resonance frequency of an individual infinitesimal element is calculated by the following formula:

（3）

f ₀is the resonant frequency of the entire central infinitesimal,BW _iis as followsiAbsolute bandwidth of an individual infinitesimal; the symbol selects "+" when the bin is to the left of the center bin and "-" when the bin is to the right.

The first order resonance frequency of CMUT microelements is:

（4）

whereinaIn order to obtain a micro-element vibration film radius,hin order to make the thickness of the film be micro-element vibration,ρthe density of the film material is the micro-element vibration,Eis the Young modulus of the infinitesimal vibration film material,σthe Poisson ratio of the infinitesimal vibration film material;

when the resonance frequency and the bandwidth of the capacitive micro-machined ultrasonic transducer are given, the resonance frequency of the central micro-element is determined, and then the radius and the thickness of the vibration film of the central micro-element can be calculated according to a formula (4); selecting the radius of the infinitesimal vibration film to be as small as possible according to the process conditions; the thicknesses of the micro-element vibration films forming the CMUT are the same, and after the thickness of the vibration film of the central micro-element is determined, the thicknesses of other micro-element vibration films are determined; first, theiThe resonance frequency of each infinitesimal element is calculated according to the formula (3), and the obtained frequency and the thickness of the vibration film are substituted into the formula (4) to obtain the secondiThe individual infinitesimal vibrates the radius of the membrane.

The method of the invention provides a brand-new array arrangement mode which can effectively improve the bandwidth of the micro-element array, thereby improving the transmitting sound pressure, receiving sensitivity and directivity of the CMUT array; at the same time, the design can reduce the fluctuation of the effective bandwidth amplitude.

The invention also provides a method for determining the number of the microelements in the microelement array and the resonant frequency of each microelement, so that the method has more definite guidance in practical application.

Drawings

The sound pressure bandwidth of the CMUT in both arrangements of fig. 1.

Fig. 2 is a schematic diagram of a mixed micro-element CMUT model.

Fig. 3 is a schematic diagram of CMUT model composed of three types of microcell sizes.

Fig. 4 illustrates CMUT bandwidth composed of three types of microcell sizes.

Figure 5 CMUT bandwidth with a microcell pitch of 60 μm.

Figure 6 CMUT bandwidth with 120 μm microcell spacing.

Fig. 7 is a schematic diagram of a CMUT model composed of five types of microcell sizes.

Fig. 8 illustrates CMUT bandwidths composed of five types of microcell sizes.

Figure 9 CMUT frequency bandwidths (cross schematic) made up of different infinitesimal sizes.

FIG. 10 is a schematic diagram of CMUT structure (w=20%)。

CMUT bandwidth of fig. 11: (w=20%)。

FIG. 12 is a schematic diagram of CMUT structure (w=50%)。

Fig. 13 CMUT bandwidth (w=50%)。

Fig. 14 shows the CMUT structure (w=80%)。

Fig. 15 CMUT bandwidth (w=80%)。

Figure 16 schematic diagram of CMUT structure in water area.

CMUT bandwidth in water of fig. 17.

Detailed Description

Example 1 finite element simulation analysis of broadband CMUT

This example establishes a CMUT structure composed of three types of vibrating membrane elements having dimensions of 59 μm to 2.6 μm, 60 μm to 2.6 μm, and 61 μm to 2.6 μm, respectively, and the resonant frequencies of the three types of elements in air are 3.13MHz, 3.02MHz, and 2.93MHz, respectively, and the structural parameters are shown in table 1, the number of elements is 9, and the pitch is 5 μm, respectively. The bandwidth of the CMUT in the air domain was obtained by COMSOL finite element simulation analysis and MATLAB calculation. The specific analysis process is as follows:

a CMUT finite element simulation model as shown in fig. 3 is built in COMSOL, then materials are added, physical field conditions are configured, grid division is performed, corresponding research types and solvers are configured, post-processing is performed, and the overall setting method is the same as that of embodiment 2, where the dc bias voltage selects collapse voltage 44V corresponding to a micro-element with a vibrating membrane size of 60 μm-2.6 μm, and the frequency of the ac excitation voltage is set to 3 MHz. This is because the resonance frequency of the CMUT cell designed in this embodiment is 3MHz, and the resonance frequency corresponding to the CMUT cell having the vibrating membrane size of 60 μm to 2.6 μm is exactly 3MHz, and therefore this cell is the center cell. The resulting bandwidth profile of a CMUT consisting of three different sized microcell structures is shown in fig. 4.

As can be seen from fig. 4, the bandwidth of the CMUT composed of three different sizes of the microcell structures is increased, thus proving that the designed microcell hybrid structure can improve the bandwidth of the CMUT.

Example 2 bandwidth performance analysis of broadband CMUT

The embodiment respectively changes the micro element spacing and the number of micro elements with different sizes, analyzes the influence of the spacing and the number on the CMUT bandwidth, and further optimizes the bandwidth characteristics of the CMUT.

The effect of the infinitesimal spacing on the CMUT bandwidth characteristics is analyzed first. Selecting a CMUT model composed of three different sizes of microelements adopted in the previous embodiment, setting the spacing between the microelements to 60 μm and 120 μm, respectively, performing finite element modeling analysis and MATLAB calculation in COMSOL, and finally obtaining the bandwidth condition of the CMUT when adopting different infinitesimal spacings, the results of which are shown in fig. 5 and fig. 6, respectively.

Comparing fig. 4, fig. 5 and fig. 6, it is found that the variation of the micro element spacing may affect the bandwidth condition of the CMUT. When the distance between the CMUT micro-elements is 5 μm, the-6 dB absolute bandwidth of the CMUT is 0.4 MHz; when the pitch is 60 μm, the-6 dB absolute bandwidth of the CMUT is 0.3 MHz; the-6 dB absolute bandwidth of the CMUT is 0.2MHz when the pitch is 120 μm. It can be seen that the bandwidth of a CMUT decreases as its bin pitch increases. This is because the CMUT's fill factor gradually decreases with increasing cell pitch, and when the fill factor is lower, each cell membrane acts more like a separate element, pushing the medium both towards the normal direction and the side, and the dynamic mass of the medium increases, resulting in a decrease in CMUT bandwidth. Therefore, in the CMUT design process, the microcell spacing should be reduced as much as possible to increase the bandwidth of the CMUT.

Then, a CMUT finite element model composed of five different infinitesimal sizes was constructed, in which the radii of the infinitesimal vibrating membranes constituting the CMUT were 58 μm, 59 μm, 60 μm, 61 μm, and 62 μm, respectively, the thickness of the membrane was 2.6 μm, and the remaining structural parameters are as shown in table 2, and the corresponding resonance frequencies in air were 3.24MHz, 3.13MHz, 3.02MHz, 2.93MHz, and 2.83MHz, respectively. By comparing the bandwidth characteristics of the CMUT consisting of three different infinitesimal sizes and the CMUT consisting of five different infinitesimal sizes, the influence of the number of infinitesimal sizes on the bandwidth characteristics of the CMUT is finally analyzed. The specific analysis process of the CMUT bandwidth characteristics composed of five different size microelements is as follows:

a CMUT finite element simulation model composed of five vibrating membrane dimensions as shown in fig. 7 was built in COMSOL, the structure was composed of 25 microelements, the spacing between each infinitesimal was 5 μm, the dc bias voltage was set to 44V, the frequency of the ac excitation voltage was set to 3MHz, and then the material was added to configure the physical field. The physical field is selected from an electromechanical field, a pressure acoustic field and a transient field, wherein the action domain of the electromechanical field is a CMUT (micro-machined. Selecting the applicable boundaries of the multiple physical fields, the software will automatically couple the two physical fields. Adding two terminals in the electromechanical field, setting the type as electric potential, and setting one electric potential value as electric potentialV _dc+f(t)，V _dcAndf(t) are applied as a DC bias voltage and an AC excitation voltage between the upper and lower electrodes of the CMUT cell, respectively. WhereinV _dcAre set to the collapse voltages of the CMUT cells respectively,f(t) frequency was 3MHz, amplitude was 1V, for 5 cycles. The scope selection upper electrode. The other potential value is set to 0 and the substrate is domain selected. The purpose of applying a DC bias voltage and an AC excitation voltage between the upper and lower electrodes of the CMUT micro-element is realized by setting the two terminal conditions. Spherical wave radiation is added in pressure acoustics and transient fields and acts on an environment domainTo the outer boundary of (a). The spherical wave radiation can absorb the ultrasonic waves emitted by the CMUT, so that errors due to reflection of the ultrasonic waves at the boundary can be avoided. And then carrying out grid division and solver setting. The research type selects transient analysis, the solving range is 0-20 mu s, the step length is 0.1 mu s, and the solver selects a transient solver. And finally, solving, wherein a solving result obtained by finite element analysis can be seen in a result option, the obtained sound pressure data is derived, MATLAB is used for further analysis and processing, and finally the bandwidth condition of the CMUT formed by the five micro-element structures with different sizes as shown in FIG. 8 is obtained.

Comparing fig. 4 and fig. 8, it can be seen that the number of different sizes of micro-elements affects the bandwidth characteristics of the CMUT. When the CMUT is respectively composed of three micro-elements with different sizes, the-6 dB absolute bandwidth is 0.4 MHz; when composed of five different sizes of microelements, the-6 dB absolute bandwidth of the CMUT is 0.7 MHz. It can be seen that as the number of different sizes of micro-elements constituting the CMUT increases, the bandwidth thereof becomes wider. Therefore, in order to increase the bandwidth of the CMUT, the CMUT should be selected to be composed of a plurality of different sizes of micro-cells.

Embodiment 3 broadband CMUT design method

From the above analysis of the embodiments, it can be seen that the CMUT with the micro-element hybrid structure can achieve the purpose of improving the bandwidth. The number of different size elements and the individual element size are the main structural parameters of the CMUT and they directly affect the resonance frequency and bandwidth of the CMUT. Therefore, in the CMUT design process, an appropriate number of bins and bin size should be selected. Wherein the infinitesimal dimensions can be described in terms of the thickness and radius of the vibrating membrane. On one hand, the thickness and radius of the vibrating membrane determine the resonance frequency of the infinitesimal element; on the other hand, when the thickness and radius of the film are determined, the radius of the electrode, cavity, etc. is determined accordingly. This embodiment mainly describes the selection principles of the number of different size micro-elements and the thickness and radius of the vibrating membrane of each micro-element when the CMUT resonant frequency and the-6 dB relative bandwidth are determined.

It can be seen from the analysis that when there is cross-overlapping of frequency ranges of adjacent micro-cells, the CMUT has better bandwidth characteristics. As shown in FIG. 9, two adjacent bins are overlapped in frequencymAnd infinitesimal absolute bandwidthnThe ratio of (a) to (b) is recorded as the frequency crossing range of adjacent infinitesimal elements, and since the absolute frequencies of two adjacent infinitesimal elements are close, the absolute frequency of any one infinitesimal element can be selected here. Absolute bandwidth of-6 dB of infinitesimalnWith its resonant frequencyfThe ratio of (d) is reported as-6 dB relative bandwidth. Assuming a frequency crossing range ofwThe-6 dB relative bandwidth of each element isxThe number of different size infinitesimal elements isNThen-6 dB relative bandwidth of the constituent CMUTsyCan be expressed as:

y=x+(N-1)(1-w)x （1）

analysis of the above formula shows that when the frequency ranges of adjacent micro-elements constituting the CMUT are determined, only the-6 dB relative bandwidth of the micro-elements and the number of micro-elements with different sizes need to be known, so that the-6 dB relative bandwidth of the CMUT can be calculated. Conversely, when the CMUT micro-cell and the-6 dB relative bandwidth of the CMUT are known, the number of required micro-cells of different sizes can be calculatedNAs shown in the following formula:

（2）

typically, -6dB relative bandwidth of CMUT micro-cellsxIt can be learned from previous experience that the-6 dB relative bandwidth of CMUTyAs an index, is given before the design. In order to set the resonance frequency of the central micro-element as the resonance frequency of the CMUT, the number of micro-elements on the left and right sides of the central micro-element should be the same, so the number of micro-elements with different sizesNShould be odd. When the result of calculationNWhen the number of the channels is odd, selectingNOne infinitesimal element is needed, and when the result is calculatedNEven number, should be selectedN+1 infinitesimal.

The central micro element of the CMUT is marked as the 0 th micro element, the micro element adjacent to the central micro element is marked as the 1 st micro element, the micro element adjacent to the 1 st micro element is marked as the 2 nd micro element, and so on, the micro element at the edge is marked as the second micro elementKAnd (4) micro elements. Take the case of left-to-right frequency increment of the bins as an example, whereiniThe resonance frequency of an individual infinitesimal element is calculated by the following formula:

（3）

f ₀is the resonance frequency of the CMUT(s),BW _iis as followsiAbsolute bandwidth of a single infinitesimal. The symbol selects "+" when the bin is to the left of the center bin and "-" when the bin is to the right.

The primary consideration in CMUT design is the resonant frequency. When the frequency of the applied excitation signal is equal to the resonance frequency of the transducer, the vibration film resonates to obtain a larger displacement, and at this time, the CMUT obtains a larger transmission sound pressure and reception sensitivity, and the conversion efficiency is optimized.

The first order resonant frequency of a peripherally clamped circular vibrating membrane CMUT is:

（4）

whereinaIn order to obtain a micro-element vibration film radius,hin order to make the thickness of the film be micro-element vibration,ρthe density of the film material is the micro-element vibration,Eis a Young modulus of a infinitesimal vibration film material,σis the Poisson's ratio of the infinitesimal vibration film material.

Since the resonance frequency of the central micro-element is the same as the resonance frequency of the CMUT. Therefore, when the resonance frequency and bandwidth of the CMUT are given, the resonance frequency of the central micro-element is determined accordingly, and then the radius and thickness of the vibrating membrane of the central micro-element can be calculated according to the formula (4). In this process, the radius of the vibrating membrane should be selected to be smaller in combination with the process level of the laboratory, so as to increase the radius-thickness ratio of the CMUT vibrating membrane, and obtain a wide bandwidth CMUT micro-cell. Since the thicknesses of the vibrating membranes of the micro-elements constituting the CMUT are the same, when the thickness of the vibrating membrane of the center micro-element is determined, the thicknesses of the vibrating membranes of the other micro-elements are determined accordingly. Furthermore, aiThe resonance frequency of each infinitesimal element can be calculated according to the formula (3), and the obtained frequency and the thickness of the vibration film are substituted into the formula (4) to obtain the vibration filmCan solve toiThe individual infinitesimal vibrates the radius of the membrane. Up to this point, the number of different size micro-elements constituting the CMUT and the vibration membrane parameters of each micro-element can be obtained.

Example 4 air Domain broadband CMUT Structure design and finite element analysis

From previous studies, CMUT cells with-6 dB relative bandwidth of about 10% in the air domain can be designed. On the basis, the invention designs the CMUT with the resonant frequency of 3MHz and the relative bandwidth of-6 dB not less than 50% in the air, verifies the correctness of the formula and analyzes the frequency cross range of adjacent micro-elementswImpact on CMUT bandwidth characteristics. Here, the number of the first and second electrodes,w20%, 50%, 80% respectively. The number of different size bins it requires by calculation is shown in table 3.

When in usewAt 20%, the number of different sizes of micro-elements required is calculated by the formula (2)NAn even number of 6, at which point the number of bins should be selectedN+1, so at least 7 different sizes of infinitesimal elements are selected to be combined to meet the design requirements. The resonance frequency of each infinitesimal element can be calculated according to the formula (13), which is: 2.33MHz, 2.53MHz, 2.86MHz, 3MHz, 3.24MHz, 3.5MHz, 3.78 MHz.

The CMUT structure shown in fig. 10 is designed according to the above analysis, and then modeled and analyzed by COMSOL finite element simulation software, and finally the bandwidth condition of the CMUT is obtained as shown in fig. 11.

As can be seen from FIG. 11, whenwAt 20%, the designed CMUT has a resonant frequency of 3MHz in the air domain, an absolute bandwidth of-6 dB of 1.7MHz, and a relative bandwidth of 56.7%, which meets the design requirements. But in the-6 dB frequency range, the curve fluctuation is large, which is caused by the small frequency crossing range between the micro-elements.

When in usewAt 50%, it can be calculated according to the formulas (2) and (3), and at least 9 different frequencies of the infinitesimal are needed to be combined to meet the design requirement, wherein the resonance frequency of each infinitesimal is respectively：2.44MHz、2.57MHz、2.7MHz、2.85MHz、3MHz、3.15MHz、3.3MHz、3.47MHz、3.65MHz。

The CMUT structure model was then constructed in COMSOL as shown in fig. 12. Through finite element analysis, the bandwidth condition of the CMUT as shown in fig. 13 is finally obtained.

As can be seen from FIG. 13, whenwAt 50%, the designed CMUT has a resonant frequency in the air domain of 3MHz, an absolute bandwidth of-6 dB of 1.51MHz, and a relative bandwidth of 50.3%, and meets the design requirements. In addition, in the frequency range of-6 dB, the curve has two frequencies with larger fluctuation, more than 5dB and flatter rest places.

When in usewAt least 21 different frequency infinitesimal elements are required to be combined to meet the design requirement when the resonance frequency is 80 percent according to the calculation of a formula, wherein the resonance frequency of each infinitesimal element is respectively 2.45MHz, 2.5MHz, 2.55MHz, 2.6MHz, 2.66MHz, 2.71MHz, 2.77MHz, 2.82MHz, 2.88MHz, 2.94MHz, 3MHz, 3.06MHz, 3.12MHz, 3.18MHz, 3.24MHz, 3.31MHz, 3.38MHz, 3.44MHz, 3.51MHz, 3.58MHz and 3.66 MHz.

The CMUT structure shown in fig. 14 is designed according to the above analysis, and then modeled and analyzed by COMSOL finite element simulation software, and finally the bandwidth condition of the CMUT is obtained as shown in fig. 15.

As can be seen from FIG. 15, whenwAt 80%, the designed CMUT has a resonant frequency in the air domain of 3MHz, an absolute bandwidth of-6 dB of 1.49MHz, and a relative bandwidth of 49.7%, which approximately meets the design requirements. In addition, in a frequency range of-6 dB, curve fluctuation is small and does not exceed 5dB, and the whole is relatively flat.

From the above analysis, whenwThe CMUT designed according to the formulas (2) and (3) achieves the requirement of 3MHz in air and 50% in-6 dB relative bandwidth at 20%, 50%, and 80%, respectively. Therefore, the principle of selecting the main structural parameters of the broadband CMUT provided by the invention has feasibility, and can be used as a theoretical basis for designing the broadband CMUT structure. When in usew20%, the frequency curve of the CMUT is not flat in the range of-6 dB, and the fluctuation is large, which is not favorable for the normal operation of the broadband CMUT; when in usew50% of its frequency curveThe line is much flat, with fluctuations exceeding 6dB at only two frequencies; when in usewThe frequency curve of the CMUT is 80 percent, the CMUT frequency curve is the most flat, the fluctuation does not exceed 5dB, and the requirement of the broadband CMUT is well met. From this, it is understood that the larger the frequency crossing range between adjacent microelements, the flatter the frequency curve of the CMUT formed, and the better the bandwidth characteristics. Therefore, in the design process of the broadband CMUT, the frequency crossing range between adjacent cells should be as large as possible, usually greater than 50%, so as to obtain better bandwidth characteristics.

Example 5 Water area broadband CMUT Structure design and finite element analysis

From previous studies, CMUT cells with-6 dB relative bandwidth of about 20% in the water domain can be designed. On the basis, the invention designs the CMUT with the resonance frequency of 1.1MHz and the relative bandwidth of 6dB not less than 80% in a water area, and further verifies the correctness of the formula. From the foregoing analysis, it can be known that the larger the frequency crossing range between adjacent microelements is, the flatter the frequency curve of the CMUT is, and the better the bandwidth characteristic is, so herew80% is selected.

Calculating the number of required micro elements with different sizes by the formula (2)NIs even 16, the number of bins should be selectedN+1, so at least 17 different sizes of infinitesimal elements are selected to be combined to meet the design requirements. The resonance frequency of each infinitesimal can be calculated according to the formula (3) and is respectively 0.8MHz, 0.83MHz, 0.86MHz, 0.9MHz, 0.94MHz, 0.98MHz, 1.02MHz, 1.06MHz, 1.1MHz, 1.14MHz, 1.18MHz, 1.23MHz, 1.28MHz, 1.33MHz, 1.38MHz, 1.44MHz and 1.50 MHz.

The CMUT structure shown in fig. 16 is designed according to the above analysis, and then modeled and analyzed by COMSOL finite element simulation software, and finally the bandwidth condition of the CMUT is obtained, as shown in fig. 17.

As can be seen from fig. 17, the resonant frequency of the designed CMUT in the water area is 1.1MHz, the absolute bandwidth of-6 dB is 0.89MHz, and the relative bandwidth is 81%, which meets the design requirements, thereby proving that the method provided by the present invention can provide a reference for the structural design of the wideband CMUT in the water area. The manufacturing method of each infinitesimal element is wafer bonding or sacrificial layer sacrificial process, and the process is the prior art.

Claims

1. A design method for broadband capacitive micro-mechanical ultrasonic transducer with mixed diaphragm structure is characterized by comprising the steps of integrating on a chip and arrangingN×NA plurality of CMUT cells of a rectangular array,Nis odd; each row of CMUT bins is provided withNThe CMUT micro-elements with different transmitting sound pressure frequencies are formed, and the CMUT micro-elements in different rows are all formed by the CMUT micro-elementsNArranging and composing micro elements; each row of CMUT elements are arranged in a mode that the frequency of the transmitting sound pressure is sequentially increased or decreased, and the increasing and decreasing arrangement sequence of two adjacent rows is opposite; in each row of CMUT micro-elements, the emission sound pressure frequencies of adjacent micro-elements are overlapped; the resonance frequency of the centrally located micro-element in each row of CMUT micro-elements is the same as the resonance frequency of the whole capacitive micromachined ultrasonic transducer.

2. The method according to claim 1, wherein the pitch between adjacent CMUT cells in each row of CMUT cells is as small as possible; the pitch of adjacent CMUT cells in each column of CMUT cells is as small as possible.

3. The method for designing a hybrid diaphragm structure broadband capacitive micromachined ultrasonic transducer according to claim 1 or 2, wherein the frequency of the transmission sound pressure of the CMUT micro-elements is determined by the radius and thickness thereof, and after the thickness is determined, the smaller the radius, the larger the frequency of the transmission sound pressure.

4. The method for designing a hybrid diaphragm structure broadband capacitive micromachined ultrasonic transducer according to claim 1 or 2, wherein when the resonant frequency and-6 dB relative bandwidth of the entire capacitive micromachined ultrasonic transducer are determined, the number of different sized microelements is determined according to the following rules:

the ratio of the overlapping frequency of two adjacent infinitesimal elements to the absolute bandwidth of any one of the two adjacent infinitesimal elements is recorded as the frequency crossing range of the adjacent infinitesimal elementsw(ii) a Absolute bandwidth of-6 dB of infinitesimalnWith its resonant frequencyfThe ratio of (d) is recorded as-6 dB relative bandwidthx(ii) a The-6 dB relative bandwidth of the entire capacitive micromachined ultrasonic transduceryCan be expressed as:

y=x+(N-1)(1-w)x (1)

obtained from (1)

（2）

WhereinxIt is known empirically that the-6 dB relative bandwidth of a CMUTyGiven as an index before design; for differentyAndwtaking values to obtain correspondingNA value;Nthe calculated value is rounded up, and when the calculated result is obtainedNWhen the number of the channels is odd, selectingNOne infinitesimal element is needed, and when the result is calculatedNEven number, should be selectedN+1 infinitesimal.

5. The method for designing a broadband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure according to claim 4, wherein the sound-generating vibration frequency of each infinitesimal element is determined according to the following rule: the central micro-element of each row of CMUTs is marked as the 0 th micro-element, the micro-element adjacent to the central micro-element is marked as the 1 st micro-element, the micro-element adjacent to the 1 st micro-element is marked as the 2 nd micro-element, and so on, the micro-element at the edge is marked as the second micro-elementKEach element; take the case of left-to-right frequency increment of the bins as an example, whereiniThe resonance frequency of an individual infinitesimal element is calculated by the following formula:

（3）

6. The method for designing a broadband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure of claim 5, wherein the first-order resonance frequency of the CMUT elements is:

（4）

whereinaIn order to obtain a micro-element vibration film radius,hin order to obtain the thickness of the infinitesimal vibration film,ρis the density of the infinitesimal vibration film material,Eis the Young modulus of the infinitesimal vibration film material,σthe Poisson ratio of the infinitesimal vibration film material;

7. The method for designing a wideband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure as claimed in claim 6, wherein the resonant frequency in the air domain is 3MHz, and the-6 dB relative bandwidth is not less than 50%wIf =20%, it is calculated by the formula (2)NThe calculation result is 6, and the number of micro elements in each row is takenN+1= 7; the resonance frequencies of 7 infinitesimal elements calculated by the formula (3) are respectively: 2.33MHz, 2.53MHz, 2.86MHz, 3MHz, 3.24MHz, 3.5MHz, 3.78 MHz.

8. The method for designing a wideband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure as claimed in claim 6, wherein the resonant frequency in the air domain is 3MHz, and the-6 dB relative bandwidth is not less than 50%wWhen =50%, it is calculated by the formula (2)NThe calculation result is 9; the formula (3) calculates that the resonance frequencies of 9 infinitesimals are respectively: 2.44MHz, 2.57MHz, 2.7MHz, 2.85MHz, 3MHz, 3.15MHz, 3.3MHz, 3.47MHz, 3.65 MHz.

9. The method for designing a wideband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure as claimed in claim 6, wherein the resonant frequency in the air domain is 3MHz, and the-6 dB relative bandwidth is not less than 50%wIf =80%, it is calculated by the formula (2)NThe calculation result is 21; the formula (3) calculates that the resonance frequencies of 21 infinitesimals are respectively: 2.45MHz, 2.5MHz, 2.55MHz, 2.6MHz, 2.66MHz, 2.71MHz, 2.77MHz, 2.82MHz, 2.88MHz, 2.94MHz, 3MHz, 3.06MHz, 3.12MHz, 3.18MHz, 3.24MHz, 3.31MHz, 3.38MHz, 3.44MHz, 3.51MHz, 3.58MHz, 3.66 MHz.

10. The method for designing a wideband capacitive micromachined ultrasonic transducer with a hybrid diaphragm structure as claimed in claim 6, wherein the resonant frequency in a water area is 1.1MHz, and the-6 dB relative bandwidth is not less than 80%wIf =80%, it is calculated by the formula (2)NThe calculation result is 16, and the number of the infinitesimal is 17; the formula (3) calculates that the resonance frequencies of 17 infinitesimals are respectively: 0.8MHz, 0.83MHz, 0.86MHz, 0.9MHz, 0.94MHz, 0.98MHz, 1.02MHz, 1.06MHz, 1.1MHz, 1.14MHz, 1.18MHz, 1.23MHz, 1.28MHz, 1.33MHz, 1.38MHz, 1.44MHz, 1.50 MHz.