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Title:
ELECTROACOUSTIC TRANSDUCER WITH IMPROVED SUPPRESSION OF UNWANTED MODES
Document Type and Number:
WIPO Patent Application WO/2015/007319
Kind Code:
A1
Abstract:
An improved electroacoustic transducer with an improved mode profile (VP) is provided. The transducer comprises a velocity profile with a periodic structure (PS) and an edge structure (ES) flanking the periodic structure. The velocity profile also allows to suppress the SH wave mode.

Inventors:
YOON JIMAN (DE)
MAYER MARKUS (DE)
EBNER THOMAS (DE)
RÖSLER ULRIKE (DE)
RUILE WERNER (DE)
Application Number:
PCT/EP2013/065227
Publication Date:
January 22, 2015
Filing Date:
July 18, 2013
Export Citation:
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Assignee:
EPCOS AG (DE)
International Classes:
H03H9/02; H03H9/145
Domestic Patent References:
WO2012132238A12012-10-04
Foreign References:
JPS5883418A1983-05-19
US6791236B12004-09-14
US20130051588A12013-02-28
JP2001267880A2001-09-28
US20110068655A12011-03-24
EP1871006A12007-12-26
EP1962424A12008-08-27
US7576471B12009-08-18
US20130051588A12013-02-28
US7538637B22009-05-26
US7939987B12011-05-10
Other References:
JIMAN YOON ET AL.: "Two Dimensional Periodic Array of Reflection Centers on Electrodes in SAW Resonators", ULTRASONIC SYMPOSIUM, October 2012 (2012-10-01), pages 1798 - 1801
See also references of EP 3022841A1
Attorney, Agent or Firm:
EPPING HERMANN FISCHER PATENTANWALTSGESELLSCHAFT MBH (Munich, DE)
Download PDF:
Claims:
Claims :

1. An electroacoustic transducer (TD) , comprising

- a longitudinal direction (x) and a transversal direction (y) orthogonal to the longitudinal direction (x) ,

- a transversal velocity profile (VP) of acoustic waves propagating in the transducer (TD) ,

- an acoustically active region (AAR) ,

wherein

- the transversal velocity profile (VP) has a periodic structure (PS) in the active region (AAR) ,

- the periodic structure (PS) has a plurality of minimal values and a plurality of maximal values larger than the minimal values,

- the periodic structure (PS) is flanked on both sides by an edge structure (ES) of the transversal velocity profile

(VP) , the velocity (v) in the edge structure (ES) being lower than the maximal values of the periodic structure

(PS) ,

- the piezoelectric material is Li b03.

2. An electroacoustic transducer (TD) , comprising

- a longitudinal direction (x) and a transversal direction (y) orthogonal to the longitudinal direction (x) ,

- a transversal velocity profile (VP) of acoustic waves propagating in the transducer (TD) ,

- an acoustically active region (AAR) ,

wherein

- the transversal velocity profile (VP) has a periodic structure (PS) in the active region (AAR) ,

- the periodic structure (PS) has a plurality of minimal values and a plurality of maximal values larger than the minimal values, - the periodic structure (PS) is flanked on both sides by an edge structure (ES) of the transversal velocity profile (VP) , the velocity (v) in the edge structure (ES) being higher than the minimal values of the periodic structure (PS),

- the piezoelectric material is LiTa03.

3. The transducer (TD) of the previous claim comprising dummy fingers .

4. The transducer (TD) of one of the previous claims, where the edge structure (ES) comprises two stripes per unit cell, each of the two stripes being arranged directly next to a respective side of the periodic structure (PS) .

5. The transducer (TD) of claim 4, where the stripes of the edge structure (ES) have a length 1 being larger than 50 % of a periodic length of the periodic structure (PS) . 6. The transducer of claim 4, where the stripes of the edge structure have a length 1 being smaller than 50 % of a periodic length of the periodic structure (PS) .

7. The transducer (TD) of the one of the previous claims, comprising

- two stripes of a gap structure (GS)

where

- in the gap structure (GS) the velocity (v) is larger than the maximal value of the velocity (v) of the periodic structure (PS) ,

- the active region (AAR) is arranged between the two stripes of the gap structure (GS) .

8. The transducer (TD) of the previous claim, where the gap structure's (GS) stripes have a length from 0.5 λ to 10 λ or from 2 λ to 4 λ. 9. The transducer (TD) of one the two previous claims, where the gap structure (GS) has a metallization ratio n from 0.2 to 0.8.

10. The transducer (TD) of one of the previous claim,

comprising

- a piezoelectric substrate (SU) ,

- two busbars (BB) arranged on the substrate (SU) and aligned parallel to the longitudinal direction (x) ,

- interdigitated electrode fingers (EF) , each arranged on the substrate (SU) , connected to one of the busbars (BB) , and aligned parallel to the transversal direction (y) .

11. The transducer (TD) of one of the previous claims, where the transversal velocity profile (VP) is adjusted via one or more measures selected from:

- reduced velocity (v) by increased mass loading by increased finger (EF) width,

- reduced velocity (v) by increased mass loading by increased finger (EF) thickness,

- reduced velocity (v) by increased mass loading by

additional material deposited on the electrode fingers (EF) ,

- reduced velocity (v) in the gap structure (GS) by increased mass loading by dummy patches in a gap region corresponding to the gap structure (GS) ,

- reduced velocity (v) by increased mass loading by material deposited in stripes on the electrode fingers (EF) , - increased velocity (v) by reduced mass loading by reduced finger (EF) width,

- increased velocity (v) by reduced mass loading by reduced finger (EF) thickness,

- increased velocity (v) by reduced mass loading by material removed from the electrode fingers (EF) .

Description:
Description

Electroacoustic transducer with improved suppression of unwanted modes

The present invention refers to electroacoustic transducers with improved profiles of the acoustical wave mode.

Electroacoustic transducers may be used in RF filters working with acoustical waves. An according filter can comprise one or more electroacoustic resonators in one or more acoustic tracks. The resonators comprise transducers with interdigi- tating electrode fingers, each of which is connected to one of two busbars of the transducer. Utilizing the piezoelectric effect the transducer converts an electromagnetic RF signal into acoustic waves and vice versa.

Possible implementations of electroacoustic transducers are SAW transducers (SAW = Surface Acoustic Wave) or GBAW trans- ducers (GBAW = Guided Bulk Acoustic Wave) .

If unwanted wave modes are not suppressed in resonators the electrical properties of respective RF filters are deterio ¬ rated .

From EP 1 871 006 Al and from EP 1 962 424 Al SAW transducers are known. Aperture weighting is used to suppress unwanted transversal modes. From US 7,576,471 Bl, US 2013/051588 Al and from US 7,538,637 B2 transducers operating in a piston mode are known to sup ¬ press unwanted transversal modes. From US 7,939,987 Bl further means such as two dimensional reflectors are known to suppress transversal modes.

From the article "Two Dimensional Periodic Array of Reflec- tion Centers on Electrodes in SAW Resonators" (Jiman Yoon et al., Ultrasonic Symposium, 2012, IEEE, Oct 2012, p. 1798 - 1801) means for shaping the fundamental mode in a transducer are known. However, spurious modes such as SH modes (SH = Shear Horizontal) also lead to deterioration of the electrical properties of RF filters.

It is, thus, an object to provide an electroacoustic trans- ducer allows improved electrical properties of respective filters. In particular, it is an object to provide a trans ¬ ducer in which both, transversal modes and SH modes are suf ¬ ficiently suppressed. For this purpose, electroacoustic transducers according to the independent claims are provided. The dependent claims provide preferred embodiments of the invention.

Two transducers schemes are presented: One for transducers with Li b03 as the piezoelectric material and one for trans ¬ ducers with LiTa03 as the piezoelectric material.

An electroacoustic transducer with Li b03 as the piezoelec ¬ tric material comprises a longitudinal direction and a trans- versal direction orthogonal to the longitudinal direction. The longitudinal direction defines the main propagation di ¬ rection of the acoustic waves. The transversal direction mainly defines the orientation of electrode fingers of the transducer .

The transducer further comprises a transversal velocity pro- file of acoustic waves propagating in the transducer and an acoustically active region. The acoustically active region is mainly defined as the overlap region of electrode fingers of opposite polarity, i.e. as the area in which acoustic waves propagating in the longitudinal direction are excited when an RF signal is applied to the transducer.

The transversal velocity profile has a periodic structure in this active region. The periodic structure has a plurality of minimal values and a plurality of maximal values larger than the minimal values. Further, the periodic structure is flanked on both sides by an edge structure of the transversal velocity profile. The velocity in the edge structure is lower than the maximal values of the periodic structure. It is possible that the periodic structure has two outermost sections with a maximum velocity.

I.e. there are two stripes of a lower velocity per unit cell arranged next to the periodic structure within the active re- gion. Here, the unit cell denotes a segment of the acoustic track with a length in the longitudinal direction of the acoustic wavelength λ.

An electroacoustic transducer with LiTa03 as the piezoelec- trie material comprises a longitudinal direction and a trans ¬ versal direction orthogonal to the longitudinal direction. The longitudinal direction defines the main propagation di ¬ rection of the acoustic waves. The transversal direction mainly defines the orientation of electrode fingers of the transducer .

The transducer further comprises a transversal velocity pro- file of acoustic waves propagating in the transducer and an acoustically active region. The acoustically active region is mainly defined as the overlap region of electrode fingers of opposite polarity, i.e. as the area in which acoustic waves propagating in the longitudinal direction are excited when an RF signal is applied to the transducer.

The transversal velocity profile has a periodic structure in this active region. The periodic structure has a plurality of minimal values and a plurality of maximal values larger than the minimal values. Further, the periodic structure is flanked on both sides by an edge structure of the transversal velocity profile. The velocity in the edge structure is higher than the minimal values of the periodic structure. It is possible that the periodic structure has two outermost sections with a minimum velocity.

I.e. there are two stripes of a higher velocity in each unit cell arranged next to the periodic structure within the ac- tive region.

Especially in transducers with LiTa03 being the piezoelectric substrate the presence of dummy fingers may be preferred. The two stripes per unit cell can extend over the length of the transducer resulting in a total number of two stripes per transducer . The velocity profile can be a Δν/ν waveguide. I. e. the peri ¬ odic structure can be a part of Δν/ν waveguide.

The periodic structure and the edge structure establish a re- gion of stripes of chosen velocity values extending in the longitudinal direction.

The wording "periodic structure" denotes the shape of the ve ¬ locity profile in the transversal direction. In the periodic structure the velocity profile, thus, comprises identical sections of higher and lower velocity being arranged next to one another and extending in the transversal direction.

The periodic structure can consist of a sinusoidal structure, a saw tooth structure, a square-wave structure. However, the periodic structure can be built-up of a combination of these structures .

It is possible that the periodic structure has a periodicity in the periodic length but the amplitude of minimum and maximum velocity values follow a profile, e. g. a parabola, sine function or a cosine function.

It was found that the combination of the periodic structure and the edge structure define a velocity profile in the ac ¬ tive region of a transducer in which not only unwanted transversal modes but also SH modes are effectively suppressed or even eliminated. This is surprising as conventional means only can suppress one of two or more unwanted modes, i.e., only unwanted transversal modes, and reduce the efficiency of the transducer. In one embodiment the edge structure comprises two stripes per unit cell being arranged directly next to a respective side of the periodic structure. Thus, the edge structure di ¬ rectly flanks the periodic structure with no other section in between.

In principle, the length of the edge structure is not limited to the periodic length of the periodic structure. The length can be larger than the periodic length or smaller than the periodic length. However, in one embodiment, especially work ¬ ing with Li b03 as the piezoelectric material, the edge structure has a length 1 being larger than 50 % of a period, i.e. the periodic length, of the periodic structure. In one embodiment, especially working with LiTa03 as the pie ¬ zoelectric material, the edge structure has a length 1 being smaller than 50 % of a period, i.e. the periodic length, of the periodic structure. The phrase "length" when referred to the transducer itself means the extension in the longitudinal direction. The phrase "width" when referred to the transducer itself means the ex ¬ tension in the transversal direction. The phrase "length" when referred to an electrode finger or to the velocity profile means the extension in the transver ¬ sal direction. The phrase "width" when referred to an elec ¬ trode finger or to the velocity profile means the extension in the longitudinal direction.

In one embodiment the transducer further comprises one stripe of a gap structure per unit cell flanking the edge structure, the number of electrode fingers per unit cell In the acousti- cally active region is twice the number of the electrode fin ¬ gers in the gap region. Thus, only one stripe of the gap structure exists in each unit cell. In the gap structure the velocity is larger than the maximal value of the periodic structure. The active region is arranged between the longitu ¬ dinal sections of the gap structure, i.e. the gap structure is not a part of the active region.

It is possible that the gap structure corresponds to an area of piezoelectric material of the transducer where the ends of electrode fingers of one polarity oppose elements, e.g. the busbar itself or dummy fingers connected to the busbar, of the respective other electrode. In one embodiment the gap structure's stripes have a length from 0.5 λ to 10 λ or, especially, from 2 λ to 4 λ. Here, the phrase "length" denotes the extension along the transversal direction . Here, λ denotes the wavelength of the wanted acoustic waves propagating in the longitudinal direction. The wavelength λ is mainly defined by the periodic length of the finger struc ¬ ture, e.g. of the average periodic length, of the transducer. The gap structure can be flanked by structures of reduced ve ¬ locity. The reduction of the velocity may be caused by an in ¬ crease of the finger width or by the mass loading which may be achieved by an additional metal layer. In one embodiment the gap structure has a metallization ratio n between 0.2 and 0.8. The metallization ratio n is defined as

n = ( wi +W2+...+w n ) /λ where wi denotes the width of the i-th electrode finger of electrode fingers within a distance of length λ along the longitudinal direction. In a conventional transducer in the active region n equals 2. In a splitfinger transducer n may equal 4. In the region of the acoustic track corresponding to the gap structure only electrode fingers of one polarity may be present. Thus, n may equal 1. In one embodiment the transducer comprises a piezoelectric substrate, two busbars arranged on the substrate and aligned parallel to the longitudinal direction and interdigitated electrode fingers. The fingers are arranged on the substrate, connected to one of the busbars, and aligned parallel to the transversal direction.

The overlap of fingers of opposite polarity defines the ac ¬ tive region. The presence of the electrode fingers on the substrate estab ¬ lish a convenient way to shape the velocity profile: With the mass of the fingers, the fingers acoustic impedance and elec ¬ tric resistivity details of the wave propagation, especially the wave velocity, can be manipulated. Increasing the mass loading of the substrate at a place of the substrate - e.g. via material of the electrode structure of the busbars and electrode fingers - mainly leads to a decrease of the wave velocity. Increasing the stiffness parameters of the acoustic track - e.g. via a material with a high Young's Modulus - mainly leads to an increase of the velocity.

In one embodiment, accordingly, the transversal velocity pro ¬ file is adjusted via one or more measures selected from: - reduced velocity by increased mass loading by increased finger width,

- reduced velocity by increased mass loading by increased finger thickness,

- reduced velocity by increased mass loading by additional material deposited on the electrode fingers,

- reduced velocity in the gap region by increased mass load ¬ ing by dummy patches in the gap region,

- reduced velocity by increased mass loading by material de- posited in stripes on the electrode fingers,

- increased velocity by reduced mass loading by reduced fin ¬ ger width,

- increased velocity by reduced mass loading by reduced fin ¬ ger thickness,

- increased velocity by reduced mass loading by material re ¬ moved from the electrode fingers.

The metallization ratio n in regions of a lower velocity can be in the range from 0.3 to 0.8. Values between 0.4 and 0.75 may be preferred.

The metallization ratio n in regions of a higher velocity can be in the range from 0.15 to 0.75. Values between 0.2 and 0.6 may be preferred.

The periodic length in the periodic structure can be in the range from 0.2 to 3 λ, λ being the acoustic wavelength (in the longitudinal direction) . The ratio between the length of the higher velocity divided by the periodic length can be in the range from 0.2 to 0.8. A ratio between 0.4 and 0.6 may be preferred. For Li b03 substrates the following is true: The length of the sections of the edge structure may be in the range from 0.2 λ to 3 λ. Lengths between 0.3 λ and 2.5 λ may be pre ¬ ferred .

For Li a03 substrates the following is true: The length of the sections of the edge structure may be in the range from 0.1 λ to 1 λ. Lengths between 0.2 λ and 0.7 λ may be preferred .

It is possible that the transversal velocity profile com ¬ prises further periodic or aperiodic or symmetric or asymmet ¬ ric structure. However, it is also possible that the trans ¬ versal velocity profile in the acoustic track consists of the above mentioned structures.

With an transducer as described above the normalized overlap integral <Φ | Ψ η > for the fundamental mode n = 1 can be in the range of 0.95 or above. As the overlap integral describes the match between the (normalized) excitation function Φ and the (normalized) wave mode shape Ψ η and as the different modes Ψ η are orthogonal a value just below 1 prevents higher modes to be excited. Brief description of the figures

The transducer is explained in greater detail on the basis of exemplary and not limiting embodiments and associated figures below .

Fig. 1 shows the orientation of the longitudinal direction x with respect to the transversal direction y. Fig. 2 shows the transversal velocity profile v along the transversal direction y.

Fig. 3 shows the orientation of the transducer with re- spect to the longitudinal direction x and the transversal direction y.

Fig. 4 illustrates a possible causal connection between the velocity profile and a physical realization of the transducer's electrode structure. shows the conductance of the transducer as de ¬ scribed above compared to the conductance of con ¬ ventional transducers. shows the velocity profile and the profile of the fundamental mode of the improved transducer the conductance of which is shown in FIG. 5. shows the velocity profile of the second symmetric wave mode of an embodiment of the transducer to ¬ gether with the mode profile and the absolute value of the mode profile. shows the velocity profile and the respective mode profile and its absolute value of the third symmet ric wave mode.

FIG. 9 shows the velocity profile and the respective mode profile and its absolute value of the fourth sym ¬ metric wave mode. shows the velocity profile and the mode profile and its respective absolute value of the fifth symmet ¬ ric wave mode. shows the frequency-dependent conductance of a transducer with a 2D periodic array with patches compared to the conductance of a conventional transducer . shows the velocity profile and the wave mode and its respective absolute value of the transducer having the frequency characteristic shown in FIG 11. shows an embodiment of a transducer' s electrode structure . shows another embodiment of an electrode structure having an increased finger width in a region corre sponding to the gap structure. shows an embodiment of electrode structures having a reduced finger width in the region corresponding to the gap structure. shows an embodiment of electrode structures comprising dummy finger patches arranged within the region corresponding to the gap structure. FIG. 17 shows stripes comprising a dielectric material ar ¬ ranged in the region corresponding to the gap structure . FIG. 18 shows an embodiment of electrode structures

comprising metal bars arranged on a dielectric ma ¬ terial arranged on the electrode fingers and the bus bars .

FIG. 19 shows an embodiment of a transducer structure where material is removed in the active region to reduce the mass loading. FIG. 20 shows an embodiment of a transducer structure with individual additional masses arranged on each side of the electrode fingers to increase the mass load ¬ ing . FIG. 21 shows electrode structures the material of which is partially removed to obtain the respective velocity profile .

FIG. 22 shows an embodiment of electrode structures with additional material deposited on locally etched electrode structures.

FIG. 23 shows electrode fingers with recesses. FIG. 24 shows electrode structures with additional metal bars in the region correlated to the gap structure and with recesses in the electrode fingers estab ¬ lishing the periodic structure. Detailed description

FIG. 1 shows a substrate SU which may comprise piezoelectric material such as lithium niobate (LiNbOs) or lithium tanta- late (Li aOs) . x denotes the longitudinal direction, y de ¬ notes the transversal direction. Interdigital transducers are arranged in such a way that the main direction of propagation is parallel to the x-direction. Accordingly, a crystal cut of the substrate SU is chosen to obtain a high coupling coeffi ¬ cient .

FIG. 2 illustrates the velocity profile VP of acoustic waves propagating in the substrate SU shown in FIG. 1. The velocity profile has a periodic structure PS which is flanked by edge structures ES in such a way that the periodic structure PS is arranged between the edge structures ES in the transversal direction y. The periodic structure PS comprises areas with a relative high velocity v and areas with a relative low veloc- ity. The areas of high and low velocity alternate in such a way that a periodic velocity profile in the periodic struc ¬ ture is obtained. The velocity in the edge structure is lower than the maximum velocity in the periodic structure PS. The velocity in the edge structure may be equal to the lowest velocity in the periodic structure. However, the velocity in the edge structure ES may differ from the lowest velocity in the periodic structure. Also, the length of the edge struc ¬ ture is not limited. However, it may be preferred that the length of the respective stripe of the edge structure ES is larger than half of the periodic length of the periodic structure PS. Here the phrase "length" denotes the extension of the edge structure in the transversal direction. FIG. 3 shows the orientation of the transducer TD comprising bus bars BB and electrode fingers EF with respect to the lon ¬ gitudinal direction x and the transversal direction y. The area in which the electrode fingers of opposite electrodes overlap is called the acoustically active region AAR. The bus bars are oriented parallel to the longitudinal direction x. The electrode fingers EF are oriented parallel to the trans ¬ versal direction y.

When an RF signal is applied to the bus bars and the bus bars have opposite polarities, an acoustic wave is excited in the piezoelectric substrate SU. FIG. 4 shows the connection of the electrode structure and the velocity profile v. The velocity of acoustic waves at the surface or an interface of a piezoelectric material depends on the mass loading at the interface. A higher mass loading and/or a higher reflection decreases the velocity. However, higher elastic constants of a material deposited on the pie ¬ zoelectric material increases the velocity. Thus, the shape of the velocity profile v along the transversal direction y can directly depend on geometric structures of the material arranged on the piezoelectric substrate, e.g. the electrode structures comprising the bus bars BB and the electrode fin ¬ gers EF. To obtain the periodic structure of the velocity profile VP, the electrode fingers EF may have a shape with a corresponding periodic symmetry. To obtain minima in the velocity profile, the local finger width can be increased com- pared to sections where the velocity should be maximal and the according finger width is, thus, reduced. Further, in order to obtain the edge structure with a reduced velocity com ¬ pared to the maximal velocity within the periodic structure, the finger width can be larger in the area corresponding to the edge structure compared to the area corresponding to the highest velocities in the periodic structure. FIG. 5 shows the conductance curves of two transducers. The frequency-dependent conductance of a conventional transducer is denoted as "1" while the conductance of an improved trans ¬ ducer is denoted as "2". Especially at a frequency of ap- proximately 910 MHz, the conventional transducer offers a peak deriving from the SH mode. A resonance in the improved transducer is efficiently suppressed.

The transducer, of which the frequency-dependent conductance is shown in FIG. 5, has a velocity profile shown in FIG. 6. The velocity profile VP has a periodic structure between two structures deviating from the periodic structure, namely the edge structure ES. In the velocity profile VP shown in FIG. 6, the fundamental mode FM is formed. The combination of the periodic structure and the edge structure ES allows to effi ¬ ciently suppress the SH mode while also no or nearly no transversal modes are excited.

FIG. 7 shows a velocity profile and the corresponding symmet- ric wave mode profile together with its absolute value. As can be seen, the amplitude of the mode profile with a posi ¬ tive displacement is mainly equal to the amplitude of the mode profile with a negative displacement in the periodic structure. Thus, the areas of positive and negative displace- ments, i.e. the value of the integral of the mode profile mainly vanishes and the excitation strength of the second symmetric mode is minimized.

FIG. 8 shows, similar to the situation shown in FIG. 7, the mode profile and its absolute value of the velocity profile already shown in FIG. 7. Again, the amplitude of positive and negative displacements are mainly equal. Thus, the excitation strength of the third symmetric mode profile is minimized. FIG. 9 shows the mode profile of the fourth symmetric wave mode. Again, the amplitude of positive and negative displace ¬ ments are mainly equal. Thus, the excitation strength of the fourth symmetric wave mode is minimized.

FIG. 10 shows the mode profile and its absolute value of the fifth symmetric wave mode. Again, the excitation strength is minimized as the shape of the velocity structure with the edge structure flanking the periodic structure is an effi- cient means to suppress higher order modes.

FIG. 11 shows conductance curves of a conventional trans ¬ ducer, curve "1" and of a transducer where the velocity in the edge structure is equal to the highest velocity in the periodic structure, curve "2". Further, the velocity in the periodic structure or in the active region (the velocity pro ¬ file is shown in FIG. 12) is very slow so that the transversal mode, of which the wavelength is equal or similar to the transversal periodicity, is bounded. As a result, a plurality of resonances in the frequency-dependent conductance - as shown by curve 2 - are obtained.

FIG. 12 shows the velocity profile corresponding to conduc ¬ tance curve 2 of FIG. 11. Since the transversal mode is bounded, the shape of the mode profile becomes cosine-like. A comparison between the mode profile shown in FIG. 12 and the absolute value of the mode profile reveals that the negative displacement has a smaller amplitude than the positive dis ¬ placement. As a result, the signal is not cancelled out com- pletely and the plurality of resonances shown in FIG. 11 are obtained . Thus, the depth of the velocity profile should not exceed critical values. The waveguide parameters have to be chosen in such a way that the highest bounded mode has a lower num ¬ ber than the mode responsible for the second resonances as shown in curve 2 of FIG. 11.

The highest bounded mode - denoted as n max - that a wave guide can contain is a function of the aperture and the track and gap velocity: n max = 2 A fo sqrt [l/(v t rack) 2 - 1/

Here, A denotes the aperture, fo denotes the resonance fre ¬ quency, Vtrac k is the lowest velocity in the active region. V gap is the velocity in the gap structure.

FIG. 13 shows a basic embodiment where the periodic structure of the velocity profile is obtained by an according periodic finger width variation in the electrodes.

FIG. 14 is an embodiment of a transducer where a reduced ve ¬ locity in the gap structure is obtained by an increase of the finger width of the electrodes in the area corresponding to the gap structure.

FIG. 15 shows an embodiment of a transducer structure where the velocity in the gap structure is increased by a reduced finger width in the corresponding section of the electrodes. FIG. 16 shows an embodiment where mass loading is increased to reduce the velocity in the gap structure by additional dummy fingers arranged in such a way that the distance be- tween the bus bar and an electrode finger is reduced to a minimum.

FIG. 17 shows an embodiment of a transducer where a dielec- trie material, e.g. comprising a silicon dioxide, is arranged in two stripes in the gap structure corresponding region.

FIG. 18 shows an embodiment of a transducer where the elec ¬ trode fingers are covered with a dielectric material, e.g. silicon dioxide. The left part of FIG. 18 shows a top view onto the transducer where two stripes of metal increase the mass loading to reduce the velocity in the gap structure cor ¬ responding region. The right part of FIG. 18 shows a cross- section through the transducer showing that the dielectric material is arranged between the metal stripes and the elec ¬ trodes .

As a dielectric material DS is arranged between the electrode fingers EF and the stripes for increased mass loading MS, the stripes MS can comprise a metal. This is in contrast to FIG. 17 where the stripes are directly arranged on the electrode fingers. Thus, an insulating material is preferred in the em ¬ bodiment shown in FIG. 17. FIG. 19 shows on the left-hand side a top view onto a trans ¬ ducer structure and the thickness of the respective metalli ¬ zation of the electrode fingers along the transversal direc ¬ tion (right-hand side) . In the active region, the thickness of the metallization is reduced. In the region corresponding to the gap structure, the thickness is larger than in the ac ¬ tive region. Thus, a velocity profile in which the velocity in the gap structure is reduced compared to the periodic structure is obtained. FIG. 20 shows an embodiment of a transducer where the trans ¬ ducer structure is covered with a dielectric material DM. In order to increase the mass loading, individual segments of a material with a high density, e.g. a metal, are arranged on the respective electrode fingers of the edge structure. As the additional material is arranged directly on the electrode material and not isolated from the electrodes via the dielec ¬ tric material DM, the segments of the additional material should not be in direct contact with each other.

FIG. 21 shows an important aspect in forming the velocity profile shown in the upper right part of FIG. 21: The lower part of FIG. 21 shows that the height of the metallization establishing the electrode fingers can be varied along the transversal direction to adjust the velocity profile. A peri ¬ odic profile can be etched into the electrode finger to ob ¬ tain the periodic structure PS. The thicknesses in the re ¬ gions corresponding to the edge structures and the gap struc ¬ tures can be adjusted accordingly.

FIG. 22 shows a further embodiment of the transducer shown in FIG. 21 where further to the etching to obtain different thicknesses in the electrode structure, a dielectric, e.g. a silicon dioxide, is arranged on the electrode structures. Further, another material is deposited in stripes in the gap regions to adjust the velocity profile.

FIG. 23 shows an embodiment where recesses are structured into the electrode fingers to provide a physical basis for the periodic structure of the velocity profile.

FIG. 24 shows further to the recesses of FIG. 23 in the elec ¬ trode fingers material bars, e.g. metal bars, in the areas corresponding to the gap structure as a physical realization of the velocity setting.

List of reference symbols:

1, 2: frequency-dependent conductance of a transducer

AAR: acoustically active region

BB: bus bar

DM: dielectric material

DS : dielectric stripe

EF: electrode finger

ES : edge structure

FM: frequency modulation

GS : gap structure

MS : metallic stripe

PS : periodic structure

SU: substrate

TD: transducer

: velocity

VP: velocity profile

x : longitudinal direction

y: transversal direction