Non-Reflective Electrode Cell for SAW with Quarter ... - IEEE Xplore

10.1109/ULTSYM.2012.0448

Non-Reflective Electrode Cell for SAW with Quarter-Wavelength Electrodes Sergey V. Biryukov, Günter Martin, Hagen Schmidt, and Manfred Weihnacht IFW Dresden, D-01069 Dresden, Germany

Abstract— Non-reflective interdigital transducers (IDTs) for surface acoustic waves (SAWs) are important elements for development of SAW devices with precise frequency responses. Until now a common way to have a non-reflective periodic cell of IDT at the resonance frequency is to use split electrodes with periodicity P/4 and finger width P/8, where P is the IDT period equal to the SAW wavelength. But for 2.45 GHz (ISM frequency band), standard lithography allows electrode (and gap) widths only to be about quarter-wavelength. Thus, a new structure solution for non-reflective IDT is required for high frequencies. A novel solution for non-reflective cell with two quarter-wavelength electrodes per one-wavelength period is based on 2D-periodic structure consisting of alternating active IDT tracks and passive reflector tracks. If tracks have equal apertures and if electrodes in adjacent tracks are shifted to each other by P/4, SAWs reflected from electrodes in adjacent tracks have equal amplitudes but with phases shifted by a half wavelength. So the reflected waves cancel each other and the total reflection from the structure should be equal to zero.

I.

phase shift between effective reflection and transduction centers can be created to achieve unidirectivity.

INTRODUCTION

Modern SAW devices for mobile communication systems and SAW applications like wireless sensors and radio frequency identification (ID) tags use frequencies jumped recently to the GHz range. But in this range the photolithographic limitations for electrode widths and gaps restrict production of low loss SAW structures because of their complex multi-electrode periodic cells. Thus the well-known standard non-reflective IDT with a periodic cell of width P equal to SAW wavelength λ contains four electrodes of λ 8 width per cell. In the case of the popular 1280YX LiNbO3 for frequencies in the vicinity of 2.45 GHz (ISM frequency band) the width of λ 8 means 0.2 μm. But current lithography process is limited to 0.3-0.4 μm resolution. So the electrode (and gap) width are restricted to about λ 5 ÷ λ 4 . A novel solution for non-reflective cell with two quarterwavelength electrodes per one-wavelength period is based on 2D-periodic structure [1], [2] proposed recently for singlephase unidirectional transducers (SPUDT). Such a structure is a multi-track solution consisting of alternating active IDT tracks and passive reflector tracks (Fig. 1). The structure is called active-passive-track unidirectional transducer or APTUDT. By shifting adjacent tracks relative to each other a

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Figure 1. Test structure including a real APTUDT. The arrow shows the forward direction of the test APTUDT.

The new operation principle for proposed 2D-periodic electrode structures is based on strong diffraction effects in contrast to conventional 1D-periodic structures, where these effects cause only a perturbation. A strong diffraction is provided by small track apertures (i.e. electrode lengths), comparable to the SAW wavelength. Then the active grating as a whole may contain, in general, both active and passive tracks. For efficiency, a lot of tracks are needed, which form 2D-periodic structures by a natural way. For the first time the unidirectional behavior of an APTUDT has been proven experimentally at low frequencies in vicinity of 430 MHz by means of an Al test structure on 1280YX LiNbO3 [1], [2]. The test setup comprises the

2012 IEEE International Ultrasonics Symposium Proceedings

APTUDT structure consisting of 12 parallel tracks, each with 60 periodic cells, and split-electrode IDTs on each side with apertures equal to total APTUDT aperture used as receiving IDTs (Fig 1). For the aperture of active IDT tracks At = P , the aperture of passive reflector tracks Ar = 1.5P , and electrode thickness ratio h P = 0.06 the resultant transmission behavior |S21| is depicted in Fig. 2, where the unidirectional effect is clearly visible. The effect is controlled by aperture ratio of active and passive tracks as well as by their mutual shift in propagation direction. S21

&M log MAG

10 dB per division

REF 0 dB

a partial case of a more general structure depicted in Fig. 3b. If active and passive tracks are shifted to each other by some value S from symmetric position depicted in Fig. 3a, then the system symmetry will be lost and SPUDT effect has to exist. In Fig. 3b such a shift of S 2 of active tracks to the left and of passive tracks to the right with respect to cell axis is shown. As known, any SPUDT periodic cell demonstrates two resonance peaks of its electrical admittance for each mode [3], [4]. The frequencies of such peaks are known as fundamental frequencies or stop band frequencies. The frequency difference between peak frequencies defines a value of a cell reflection coefficient, which can be investigated by this way in the required case of S → 0 . Certainly, for S > 0 , the SPUDT effect quantitatively depends also on transversal geometrical dimensions as At , Ar , busbar width b , gap width g , and the thickness h of electrode material, which are responsible for diffraction effects and field structure.

y

y S/2

START 400.000 000 MHz

STOP 460.000 000 MHz

Figure 2. Experimental verification of the APTUDT unidirectionality. Frequency dependence of |S21| for forward (red) and for backward (blue) directions (curve with higher and lower level in passband, respectively).

However, if electrodes in tracks have equal apertures and if electrodes in adjacent tracks are shifted to each other exactly by P/4, SAWs reflected from electrodes in adjacent tracks have equal amplitudes but with phases shifted by a half wavelength. So the reflected waves cancel each other and the total reflection from the structure should be equal to zero. Such simple reasoning has been checked by a correct 3D calculation of the periodic cell. II.

Ar

NON-REFLECTIVE ELECTRODE CELL

A periodic cell of APTUDT is shown in Fig. 3. It contains active interdigital transducer (IDT) tracks with IDT aperture At and passive reflector tracks with reflector aperture Ar . Width of busbars and width of electrode-busbar gaps are b and g , respectively. The electrode cell in Fig. 3 should be continued periodically in x direction of SAW propagation with period P and in transversal y direction with period Pt = 2( At + Ar ) + 4(b + g ) as shown in Fig. 1. In Fig. 3a the positions of electrodes and gaps are symmetric with respect to cell central axis (y-axis) and SPUDT effect is absent due to equivalence of both directions of propagation along x . This is the case of a possible nonreflective structure if apertures At and Ar of adjacent tracks are equal to each other. It is convenient to consider this case as

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S/2

b

At g

(a)

(b) x P

x

Figure 3. Periodic cell of an APTUDT in plane: symmetric case without SPUDT effect (a) and asymmetric case with SPUDT effect (b).


III.

NUMERICAL EXPERIMENTS Electrical admittance Y of Al electrode periodic cells (Fig.3) placed on a piezoelectric substrate as 1280YX LiNbO3 has been simulated by the 3D finite element method (FEM) using the computer program COMSOL Multiphysics. In x and y directions periodic boundary conditions are imposed. In the depth of substrate a damping medium is used in order to restrict the mesh region and to prevent reflections from the bottom. The result for symmetric case in Fig. 3a with geometrical parameters P = 1.6 μm, At = Ar = P , b = g = P 4 , S / P = 0 , and h P = 0.06 is depicted in Fig. 4. As mentioned above, because of equality of apertures of both tracks it is supposed to be the case of non-reflective structure. This statement will be checked latter. 1.5

Figure 5. 3D periodic cell and the normal displacement component distribution at the first resonance frequency: P = 1.6 μm, At = Ar= P, b = g= P/4, S/P = 0, h/P = 0.06, applied voltage is equal to 1V.

1.0 0.5 0.0 -0.5

mode 1

Im(Y), mS

-1.0 -1.5 -2.0 -2.5 -3.0 -3.5

mode 2

-4.5 2.34

2.36

2.38

2.40

2.42

2.44

2.46

2.48

2.50

2.52

Frequency, GHz Figure 4. Imaginary part of the periodic cell electrical admittance for symmetric case (SPUDT effect is absent) and non-reflective structure: P = 1.6 μm, At = Ar= P, b = g= P/4, S/P = 0, h/P = 0.06.

The first and the second frequency resonance peaks there correspond to the SAW modes like Rayleigh mode with dominating particle displacement fields normal to substrate surface (z-component). The field of the first mode (Fig. 5) has a quasi-flat amplitude distribution in transversal direction (along y-axis). The field of the second mode (Fig. 6) oscillates along this direction and it has larger field amplitude. It can be explained that the electrode structure with shifted electrodes in adjacent tracks is fitted better to the field of the second mode than to the field of the first mode. The cell reflection coefficient for shorted electrode grating, Rs , is defined by two resonance frequencies f s1 and f s 2 (fundamental frequencies) for each mode [5]: Rs = 2π

f s 2 − f s1 . f s 2 + f s1

(1)

Figure 6. 3D periodic cell and the normal displacement component distribution at the second resonance frequency: P = 1.6 μm, At = Ar= P, b = g= P/4, S/P = 0, h/P = 0.06, applied voltage is equal to 1V. 2.0

1.5

1.0

Im(Y), mS

-4.0

mode 2

0.5

mode 1

fs1

fs1

0.0

fs2

fs2

-0.5 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54

A slight shift S = 0.05P of tracks relatively each other (Fig.3b) results in a weak SPUDT effect and appearance of both frequencies f s1 and f s 2 for each mode (Fig. 7).

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Frequency, GHz Figure 7. Imaginary part of the periodic cell electrical admittance with a SPUDT effect: P = 1.6 μm, At = Ar= P, b = g= P/4, S=0.05P, h/P = 0.06.


Reflection coefficient (1) in the case of the second SAW mode for thickness ratios h P = 0.06 and h P = 0.001 is shown in Fig. 8 as a function of track shift S / P . Due to numerical problems for a small shift it is impossible to resolve resonance frequencies. Nevertheless, calculations show that the reflection coefficient tends to zero with S / P . In this limit case the frequency behavior of the 2D-periodic structure for h P = 0.06 is depicted in Fig. 4. Such behavior for electrode widths P 4 is similar to that of the well-known non-reflective 1D-periodic split-electrode structure (see the yellow structures in Fig. 1) but for electrode widths P 8 .

2.5

mode 2 2.0

Im(Y), mS

1.5

1.0

mode 1

0.5

0.06

fs1

fs1

0.0

fs2

fs2

-0.5

-1.0 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54

0.04

Frequency, GHz h/P = 0.06

Figure 9. Imaginary part of the periodic cell electrical admittance with SPUDT effect: P = 1.6 μm, At = Ar= P, b = g= P/4, S = P/8, h/P = 0.02.

0.03

0.06 mode 2

0.02 h/P = 0.001

0.05

0.01

0.00 0.000

0.025

0.050

0.075

0.100

0.125

0.150

S/P Figure 8. SAW reflection coefficient from a periodic cell for the second mode as a function of track shift S/P: P = 1.6 μm, At = Ar= P, b = g= P/4. Reflection coefficient tends to zero with S/P.

Note here, that in the case of piezoelectric substrate 1280YX LiNbO3 there is the additional possibility to build 2Dperiodic non-reflective structure for arbitrary track shift shown in Fig. 3b. The electrical admittance of such structure for S = P / 8 and h / P = 0.02 is depicted in Fig. 9. Reflection coefficient curve (1) for both modes as a function of electrode thickness ratio (Fig. 10) goes through zero between 0.02 and 0.03 thickness ratio. But this effect is caused by going through zero of a single Al electrode strip reflectivity. It is due to a mutual compensation of mechanical and electrical contributions to the reflectivity because of having different signs. IV. CONCLUSION A novel 2D-periodic structure with non-reflective periodic cell containing two quarter-wavelength electrodes per onewavelength period is proposed. Such a structure is a multi-track solution consisting of alternating active IDT tracks and passive reflector tracks with equal apertures. By shifting adjacent tracks relative to each other a phase shift between reflections in adjacent tracks can be made equal to half a wavelength. So the total reflection from the structure reduces to zero. By using this structure SAW devices for the GHz range can be implemented in spite of the current technological limitations.

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Reflection coefficient, |Rs|

Reflection coefficient, |Rs|

0.05

0.04

0.03

0.02

0.01

mode 1

0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

h/P Figure 10. SAW reflection coefficient from a periodic cell for the first and for the second SAW modes with track shift S = P/8 as a function of thickness ratio for Ar = At = P.

REFERENCES [1]

[2]

[3] [4]

[5]

S. V. Biryukov, G. Martin, H. Schmidt, and B. Wall, “Low-loss unidirectional transducer for high frequency surface acoustic wave devices,” J. Appl. Phys., vol. 110, no. 7, 076103/3 , 1 October 2011. S. V. Biryukov, G. Martin, H. Schmidt, and B. Wall, “SPUDT cell with one-wavelength period and quarter-wavelength electrodes,” in Proc. 2011 IEEE International Ultrasonics Symposium, pp. 1337-1340. K.Hashimoto, “Surface acoustic wave devices in telecommunications,” Berlin: Springer, 2000. S. V. Biryukov and M. Weihnacht, “The impedance method in the theory of surface acoustic waves in periodic structures,” J. Appl. Phys., vol. 96, no. 6, 15 September 2004, pp. 3117-3126. S. V. Biryukov and M. Weihnacht, “FEUDT periodic cell with different width electrodes”, in Proc. 2004 IEEE International Ultrasonics Symposium, pp. 2004-2007.
