JP3302462B2 - Surface acoustic wave device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a surface acoustic wave device using lithium tetraborate single crystal (Li ₂ B ₄ O ₇ ).

[0002]

2. Description of the Related Art A surface acoustic wave device is a circuit element that performs signal processing by converting an electric signal into a surface wave, and is used for a filter, a resonator, a delay line, and the like. Usually, a metal electrode called an interdigital transducer (IDT, comb-shaped electrode, IDT) is provided on an elastic substrate (piezoelectric substrate) having piezoelectricity to perform conversion and reverse conversion from an electric signal to a surface wave. I have. The characteristics of the surface acoustic wave device depend on the propagation characteristics of the surface acoustic wave propagating through the piezoelectric substrate. In particular, a piezoelectric substrate having a high propagation speed of a surface acoustic wave is required to cope with an increase in the frequency of a surface acoustic wave device.

As a substrate material used for a surface acoustic wave device,
Crystal, lithium tantalate (LiTaO_Three), D
Lithium Obate (LiNbO)_Three), Lithium tetraborate
(Li _TwoB_FourO₇) Etc. are known. Also, elastic surface
Rayleigh waves are used as surface acoustic waves used in wave devices.
(Rayleigh Wave) and leaky waves (Le
aky wave, pseudo surface acoustic wave, leaky surface acoustic wave)
Is mainly known.

A Rayleigh wave is a surface wave that propagates on the surface of an elastic body and propagates without dissipating its energy into the piezoelectric substrate, ie, theoretically without propagation loss. As a substrate material used for a surface acoustic wave device using a Rayleigh wave, an ST-cut quartz crystal with a propagation speed of 3100 m / sec, X-112−Y LiTaO with a propagation speed of 3300 m / sec
₃ , 4000 m / sec 128 ゜ YX LiNbO
₃ , 45 ° X-Z Li ₂ B ₄ O at 3400 m / sec
There are _seven . Quartz has excellent temperature stability but poor piezoelectricity. Conversely, lithium tantalate (LiTaO ₃ ) is excellent in piezoelectricity but inferior in temperature stability. In recent years, lithium tetraborate single crystal (Li ₂ B ₄ O ₇ ) has been attracting attention as a material satisfying both the temperature stability characteristic and the piezoelectric characteristic (for example, Japanese Patent Publication No. 2-44169, Japanese Patent Publication No. Sho 63).
No. -40044).

On the other hand, use of a surface acoustic wave (leakage surface acoustic wave), which is called a leaky wave and propagates while dissipating energy in the depth direction of an elastic body, has been studied. In general, a leaky wave has a large propagation loss due to radiation and cannot be used for a surface acoustic wave device, but can be used because the propagation loss is relatively small at a special cutting angle and propagation direction. For example, if the propagation speed is 3900 m / se
LST cut crystal of c, 36 ゜ Y of 4200m / sec
-X LiTaO _3, 41 of 4500m / sec ° Y-
X LiNbO ₃ , 4500 m / sec, 64 ° YX
LiNbO _{3 and the} like are known.

As described above, the conventionally known piezoelectric material has a propagation speed of only about 4500 m / sec at most, and thus cannot cope with further higher frequencies. From this point of view, the present inventors have further developed the leaky wave theory, and have set the cutout angle and propagation direction of lithium tetraborate in Euler angles (0 ° to 45 °, 45 ° to 50 °, 80 °).゜ ~ 90 ゜)
It has been clarified that a surface acoustic wave with a very high propagation velocity and a low propagation loss, which has not been known so far, exists within a range equivalent thereto (Japanese Patent Application No. 05-042642).

[0007]

In order to be used as a surface acoustic wave device, at least one IDT is required. When an electrode is formed on a piezoelectric substrate, it is expected that the propagation characteristics of the surface acoustic wave will change due to the effect of mass loading of the electrode and the like. Therefore, there should be a structure such as an optimum electrode finger thickness and electrode finger width of the IDT that gives good surface acoustic wave propagation characteristics.

However, in the Euler angle display (0 °-
Regarding lithium tetraborate (45 °, 45 ° to 50 °, 80 ° to 90 °), the structure of the IDT that provides good surface acoustic wave propagation characteristics, such as the optimal electrode finger thickness and electrode finger width, is not limited. No knowledge was obtained. On the other hand, one of the causes of deteriorating the characteristics of the surface acoustic wave filter is multiple reflection by an electrode, and a double-electrode IDT is widely used to suppress this (TWBristol et al: “A
pplication of double electorodes in aoustic surfac
edevice design ", proc.IEEE Ultrasonics Symp., p.343
(1972), AJDe Vries etal: "Reflection of surface w
ave from three types of IDtransducers ", ibid., p.
353 (1972)). The double electrode IDT has an electrode finger polarity of 2
The electrode fingers are arranged at equal intervals, and the electrode fingers are arranged at the same period.

For such a double electrode IDT,
In Euler angle display (0 ° -45 °, 45 ° -50 °, 8
With respect to lithium tetraborate (0 ° to 90 °), no knowledge has been obtained on an optimum structure such as an electrode finger film thickness and an electrode finger width that provides good surface acoustic wave propagation characteristics. A first object of the present invention is to provide a method in which a cutout angle and a propagation direction of lithium tetraborate are represented by Euler angles (0 ° to 45 °,
45 ° to 50 °, 80 ° to 90 °) and an IDT within the range equivalent thereto, and a surface acoustic wave which is faster than a fast transverse wave of a bulk wave propagating in the same direction and does not exceed a longitudinal wave. An object of the present invention is to provide an optimal electrode structure of an IDT that exhibits good propagation characteristics for a surface acoustic wave device used.

A second object of the present invention is that the cut-out angle and the propagation direction of lithium tetraborate are expressed in Euler angles (from 0 ° to 0 °).
45 °, 45 ° to 50 °, 80 ° to 90 °) and a double electrode IDT in the range equivalent thereto, and the propagation speed is faster than the fast transverse wave of the bulk wave propagating in the same direction and exceeds the longitudinal wave. It is an object of the present invention to provide an optimal electrode structure of a double electrode IDT that exhibits good propagation characteristics for a surface acoustic wave device using no surface acoustic wave.

[0011]

According to a first aspect of the present invention, there is provided a surface acoustic wave device comprising: a piezoelectric substrate made of a single crystal of lithium tetraborate; and a surface acoustic wave which is formed, excited, received, and reflected on the surface of the piezoelectric substrate. In the surface acoustic wave device having an electrode for propagation, the electrode is formed of a metal containing aluminum as a main component, and the electrodes are arranged such that one electrode finger is interposed between the electrodes. It has a pair of comb-shaped electrodes, and the cut-out angle of the surface of the piezoelectric substrate and the propagation direction of the surface acoustic wave are represented by Eulerian angles (0 ° to 45 °, 45 °).
° to 50 °, 80 ° to 90 °) and the equivalent range. The period of the electrode finger is P, the width of the electrode finger is M, and the thickness h of the electrode is the elasticity. Normalized film thickness h / λ of the electrode normalized by the wavelength λ of the surface wave
Is given by the following formula: 0.0165−0.0565 × (M / P) +0.05
0 × (M / P) ² ≦ (h / λ) ≦ 0.0320−0.0
737 × (M / P) + 0.0667 × (M / P) ² , and the velocity of the surface acoustic wave is equal to or higher than the velocity of the fast transverse wave of the bulk wave propagating in the same direction, and the velocity of the longitudinal wave. Is not exceeded.

A surface acoustic wave device according to a second aspect of the present invention comprises: a piezoelectric substrate made of a single crystal of lithium tetraborate; and a piezoelectric substrate formed on the surface of the piezoelectric substrate, which excites and receives surface acoustic waves.
In a surface acoustic wave device having an electrode for reflection and propagation, the electrode is formed of a metal containing aluminum as a main component, and the electrodes are arranged such that two electrode fingers are interposed between each other. A pair of comb-shaped electrodes, and the cutout angle of the surface of the piezoelectric substrate and the propagation direction of the surface acoustic wave are represented by Eulerian angles (0 ° to 45 °, 45 ° to 50 °).
°, 80 ° to 90 °) and a range equivalent thereto, wherein the period of the electrode finger is P, the width of the electrode finger is M, and the film thickness h of the electrode is the thickness of the surface acoustic wave. The normalized thickness h / λ of the electrode normalized by the wavelength λ is 0.0335−0.0791 × (M / P) +0.058.
4 × (M / P) ² ≦ (h / λ) ≦ 0.0835-0.1
65 × (M / P) + 0.143 × (M / P) ² , and the velocity of the surface acoustic wave is equal to or higher than the velocity of the fast transverse wave of the bulk wave propagating in the same direction, and the velocity of the longitudinal wave. Is not exceeded.

[0013] In the above invention, the substrate cut surface, which is the surface of the piezoelectric substrate, may be (011), (345),
It is desirable to use (255), (231), (356) and the like. In particular, within the range where the (011) plane can be used as the substrate cutout surface, that is, within the range equivalent to (0 ° to 2 °, 45 ° to 50 °, 88 ° to 90 °) in Euler angle display. It is desirable that the electrodes are formed so that the propagation direction of the surface acoustic wave is in the same direction.

[0014]

First, the characteristic theory of the Rayleigh wave and the leaky wave will be described. The characteristics of Rayleigh waves and leaky waves can be calculated from the relational equations described below (JJ Campbell, WR Jones, "A Method for Estimatin
g OptimalCrystal Cuts and Propagation Directions f
or Excitation of PiezoelectricSurface Waves ", IEEE
transaction on Sonics and Ultrasonics, vol.SU-15,
No. 4, pp. 209-217, (1968); TCLim, GWFarnell, "
Character of Pseudo Surface Waves on Anisotropic C
rystals ", The Journal of Acoustical Society of Amer
ica, vol. 45, no. 4, pp. 845-851, (1968)).

In general, the propagation characteristics of a surface acoustic wave propagating on the surface of a piezoelectric substrate can be obtained by solving a charge equation obtained by quasi-electrostatic approximation of the equation of motion and Maxwell's equation under certain boundary conditions. The equation of motion and the equation of charge are shown below.

[0016]

(Equation 1)

[0017]

(Equation 2) Here, c _ijkl (i, j, k, l = 1, 2, 3) is an elastic constant tensor, e _kij (i, j, k = 1, 2, 3) is a piezoelectric constant tensor, and ε _ik (i , K = 1, 2, 3) is the tensor of the dielectric constant, and ρ is the density. U _i represents each direction in the coordinate system shown in FIG. 1 (X ₁ is the propagation direction of the surface acoustic wave,
X ₂ is the propagation direction X of the surface acoustic wave contained in the piezoelectric substrate surface
Direction perpendicular to the _1, shows a displacement of the X ₃ and perpendicular to the X ₁ and X _2), [Phi represents the electrostatic potential, respectively represented by the following formula.

[0018]

(Equation 3)

[0019]

(Equation 4) However, alpha is x ₃ horizontal damping constant, beta _i is amplitude constant, kappa
Is the wave number, t is time, and v is the phase velocity. First, the procedure for calculating the Rayleigh wave will be described. Assuming a real phase velocity v, the equation (3) indicating the displacement U _i and the equation (4) indicating the electrostatic potential Φ are substituted into the equation of motion (1) and the equation (2) of the electric flux density continuity. Then, by rearranging the amplitude constant β _i , an eighth-order equation of the attenuation constant α having a real number as a coefficient is obtained. By solving this eighth-order equation, a solution of a conjugate complex number for the attenuation constant α can be obtained.

In order to be a surface wave, the amplitude of the wave
Since it must be reduced in the depth direction, the attenuation
The number α is a solution whose imaginary part is negative [Im (α (n)) <0, n
= 1, 2, 3, 4]. chosen
Four amplitude constants β corresponding to the respective damping constants α₁~
β_FourIs calculated. Referring to the corresponding amplitude constant βi
Thus, the four damping constants α are x₁Mainly displacement in direction
The longitudinal wave component to be min, x _TwoDirection or x_ThreeMainly displacement in direction
Two types of transverse wave components and electrostatic potential as main components
It can be seen that they correspond to the respective electromagnetic wave components. This
Since these four surface acoustic wave components can propagate,
Displacement U of each direction of transportable surface acoustic wave_iAnd electrostatic potential
Φ is a linear combination of the four modes as
Can be represented.

[0021]

(Equation 5)

[0022]

(Equation 6) Here, A ⁽ⁿ⁾ indicates the amplitude ratio of each mode. Next, the propagation characteristics of the surface acoustic wave are solved by giving boundary conditions to the above equations (5) and (6). The boundary conditions, the mechanical boundary conditions indicating that the stress of the elastic body surface is zero [in _{x 3 = 0, T 13 =} T 23 = T 33 = 0]
When the piezoelectric substrate surface is open, i.e., [in _{x 3 = 0, D 3 =} 0] electrical boundary requirements that x ₃ direction component of electric flux density at the surface is zero and, in the case of surface shorting The boundary condition that the potential on the surface is zero [Φ = 0 at x ₃ = 0] is satisfied. By determining the phase velocity v that satisfies these boundary conditions, the propagation characteristics of a surface acoustic wave called a Rayleigh wave can be solved.

Next, the calculation procedure of the leaky wave will be described.
In the above calculation of the Rayleigh wave, the above equation (3),
When the damping constant α is obtained by substituting (4) into the equations (1) and (2), the damping constant α
May be real instead of conjugate complex. For example, assuming a phase velocity v faster than the Rayleigh wave, one of the transverse wave components (hereinafter referred to as “first transverse wave component”)
The imaginary part of the damping constant α corresponding to is zero (that is, the real root)
And there is a component that does not attenuate in the depth direction of the piezoelectric substrate. Therefore, the energy of the surface acoustic wave is not completely concentrated on the substrate surface, but is dissipated in the depth direction of the piezoelectric substrate, so that a propagation loss occurs.

In this case, when the phase velocity v is calculated as a complex number as a numerical expression of the propagation loss, the coefficient of the eighth-order equation for obtaining the attenuation constant α is also a complex number. From the eight solutions of the attenuation constant α, three solutions are selected which correspond to three components other than the first transverse wave component and whose amplitude decreases in the depth direction of the substrate. Further, as another solution, a solution corresponding to the first transverse wave component and having an amplitude increasing in the depth direction of the substrate is selected, and the above-described boundary conditions are given to the above equations (5) and (6). Thus, the propagation characteristic of the surface acoustic wave is solved. The surface acoustic wave solved in this way is generally called a leaky wave (leakage surface acoustic wave).

Next, when the cutout angle of the substrate and the propagation direction of the surface acoustic wave are set to specific ranges, the inventors of the present invention have two types of transverse wave components in the piezoelectric substrate with the longitudinal wave component as the main component. The existence of a surface acoustic wave (this SAW) that propagates on the surface of the piezoelectric substrate while radiating as a wave was predicted and confirmed by simulation. This SAW is a further development of the leaky wave theory. Assuming a real phase velocity v faster than the leaky wave, the imaginary parts of the damping constants corresponding to the two types of transverse wave components are both zero (that is, There are two types of components that do not attenuate in the depth direction of the piezoelectric substrate.

In the simulation of the present SAW, when the above equations (3) and (4) are substituted into the equations (1) and (2) to obtain the attenuation constant α from the phase velocity v expanded to a complex number, 2 A solution whose amplitude increases in the depth direction of the substrate is selected for each of the three types of shear wave components (the first shear wave component and the second shear wave component), and the longitudinal wave component is set as the other two attenuation constants α. And a solution whose amplitude decreases in the depth direction of the substrate corresponding to the electromagnetic wave component. That is, this SAW
Is a surface acoustic wave that propagates on the surface while radiating energy into the substrate using two types of transverse wave components as bulk waves.

From the phase velocity v thus obtained, x
The phase velocity v _{p in one} direction, the electromechanical coupling coefficient k ² , the propagation loss L, and the frequency temperature coefficient TCF were determined. The following equation shows the phase velocity v _p , the electromechanical coupling coefficient k ² , the propagation loss L, and the frequency temperature coefficient TCF.

[0028]

(Equation 7)

[0029]

(Equation 8)

[0030]

(Equation 9)

[0031]

(Equation 10) Here, v _po, v _ps is the surface electrical open respectively, x ₁ direction of the phase velocity of the electrical short, alpha is the thermal expansion coefficient of the x ₁ direction. The simulation was performed for the purpose of calculating the surface acoustic wave characteristics when the cutout angle and the propagation direction of the lithium tetraborate single crystal substrate were changed.
The propagation characteristics in an arbitrary cutout angle and propagation direction can be obtained by calculating the elastic constant, piezoelectric constant, and dielectric constant converted by the Euler angles (φ, θ, ψ). In addition, bulk waves (longitudinal waves, fast transverse waves,
The phase velocity of the slow transverse wave was calculated.

Next, FIG.
This will be described with reference to FIGS. FIGS. 2 to 4 show a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate, and the propagation direction of the surface acoustic wave is represented by an Eulerian angle (0 °, θ, 90 °). °) and the phase velocity v of the surface acoustic wave when the angle θ is changed
_p, electromechanical coupling coefficient k ^2, the simulation results of the propagation loss L per SAW wave.

As shown in FIG. 2, the phase velocity of the present SAW is always 5,000 to 7,500 m / s even when the angle θ changes.
ec, which is very fast, faster than the fast transverse wave of the bulk wave, and does not exceed the phase velocity of the longitudinal wave. Further, as shown in FIG. 3, the present SAW is generated in a wide range of angles θ of 25 ° to 90 °, and is 0.6% or more when the angle θ is 38 ° to 70 °, in particular, the angle θ is 40 °. 1% at ~ 60 °
The above electromechanical coupling coefficient is obtained. Further, as shown in FIG. 4, when the angle θ is about 55 ° or less, the propagation loss is small.

Therefore, this SAW has an angle θ of 38 °.
Within the range of up to 55 °, the electromechanical coupling coefficient is large and the propagation loss is small. In particular, when the angle θ is in the range of 45 ° to 50 °, the propagation loss becomes smaller. In these ranges, the Rayleigh wave is 3000, which is about half that of the SAW.
Since the speed is 4000 m / sec, there is no leaky wave.

5 to 7 show the phase velocity v _p and the electromechanical coupling coefficient k when the propagation direction of the surface acoustic wave is represented by an Eulerian angle (15 °, θ, 90 °) and the angle θ is changed. ^2. Simulation results of propagation loss L. FIGS. 8 to 10 show the phase velocity v _p and the electromechanical coupling coefficient k ² when the propagation direction of the surface acoustic wave is represented by an Eulerian angle (30 °, θ, 90 °) and the angle θ is changed. And simulation results of the propagation loss L.

FIGS. 11 to 13 show the phase velocity v _p when the propagation direction of the surface acoustic wave is represented by Eulerian angles (45 °, θ, 90 °) and the angle θ is changed, and the electromechanical coupling. It is a simulation result of the coefficient k ² and the propagation loss L. As is apparent from FIGS. 2 to 13, considering the symmetry of lithium tetraborate, the Euler angles (φ,
angle θ is 30 ° to 90 ° regardless of the angle φ of θ, ψ)
The present SAW having a high phase velocity exists within the range of, and when the angle θ is within the range of 38 ° to 55 °, the present SAW is
It can be seen that the phase velocity is high, the electromechanical coupling coefficient is large, and the propagation loss is small. In particular, when the angle θ is 45 ° to 50 °
In this range, the propagation loss of the present SAW is even smaller. Further, the phase velocity of the present SAW is faster than the fast transverse wave of the bulk wave, and does not exceed the phase velocity of the longitudinal wave.

Next, the propagation characteristics of the surface acoustic wave on the (011) cut surface of the piezoelectric substrate ((0 °, 47.3 °, で in Eulerian angle)) were calculated by simulation. FIG.
16 to 16 show Euler angles (0 °, 47.3 °,
ψ) and simulation results of the phase velocity v _p , the electromechanical coupling coefficient k ² , and the propagation loss L when the angle ψ is changed.

As shown in FIG. 14, the phase velocity of this SAW is always 7000 to 7500 m / s even when the angle θ changes.
ec and very fast. Also, as shown in FIG.
In the present SAW, the angle ψ exists in the range of 40 ° to 90 °, and a high electromechanical coupling coefficient is obtained in the range of the angle ψ of 80 ° to 90 °. Further, as shown in FIG. 16, the propagation loss of the present SAW becomes very low when the angle ψ is 88 ° to 90 °. Therefore, in the present SAW, when the angle ψ is 90 °, the electromechanical coupling coefficient becomes maximum and the propagation loss becomes minimum.

Next, the propagation characteristics of the surface acoustic wave when the propagation direction of the surface acoustic wave was (0 °, 47.3 °, 90 °) in the Eulerian angle representation were calculated by simulation. 17 to 20 show phase velocities v when the electrode material is a metal material containing aluminum as a main component and the film thickness of the electrode is changed.
_It shows calculation results of _p , electromechanical coupling coefficient k ² , propagation loss L, and frequency temperature coefficient TCF. In this simulation calculation, the electrical open, that the electric flux density at the interface with x ₃ direction between the metal film and the substrate is zero [in _{x 3 = 0, D 3 =} 0] means, electrical shorts Is calculated as meaning that the potential of the metal film is zero [Φ = 0 when x ₃ = 0].

When the normalized film thickness h / λ obtained by normalizing the electrode film thickness h with the wavelength λ of the surface acoustic wave is changed from 0.0% to 6.0%, as shown in FIG. Gradually decreases, and as shown in FIG. 18, the electromechanical coupling coefficient is 1.2%.
To 3.1%. In addition, when the normalized film thickness h / λ is in the range of 0.0% to 6.0%, as shown in FIG. 19, it can be seen that the propagation loss is as low as 0.01 dB / λ or less. Further, as shown in FIG. 20, excellent temperature characteristics of about 20 ppm / ° C. or less are obtained as the frequency temperature coefficient when the normalized film thickness h / λ is in the range of 0.0% to 5.0%.

Next, in order to confirm the properties of this SAW,
The displacement and the potential distribution in the depth direction of the substrate were calculated.
FIGS. 21 and 22 show simulation results when the normalized thickness of the electrode (aluminum) is 3% when the propagation direction of the surface acoustic wave is represented by Eulerian angles (0 °, 47.3 °, 90 °). It is. FIG. 21 shows a calculation result in the case of electrical opening, and FIG. 22 shows a calculation result in the case of electrical short.
21 and 22, the horizontal axis represents the displacement U ₁ (x ₁ direction displacement), the displacement U ₃ (x ₃ direction of displacement), a relative amplitude value of the electrostatic potential [Phi, the vertical axis normalized by the wavelength This is the normalized depth from the substrate surface.

As apparent from FIGS. 21 and 22, the displacement and electrostatic potential of the surface acoustic wave are concentrated near the substrate surface, and the longitudinal wave component is dominant. As described above, the cut-out angle and the propagation direction of the surface acoustic wave of the lithium tetraborate single crystal substrate are represented by Eulerian angles (0 ° to 45 °, 45 ° to 50 °,
80 ° to 90 °) and an equivalent range, a surface acoustic wave utilizing a surface acoustic wave having a sufficiently low propagation loss, a higher propagation velocity than Rayleigh waves and leaky waves, and a sufficiently large electromechanical coupling coefficient. A wave device can be realized.

The lithium tetraborate single crystal has a point group of 4 m.
m, and the characteristics of the surface acoustic wave also have a predetermined symmetry. Therefore, the direction indicated by the Eulerian angle is (0 ° to 36 °).
0 °, 45 ° to 50 °, and 80 ° to 100 °). Next, the inventor of the present application uses a surface acoustic wave in which the speed of the surface acoustic wave is equal to or higher than the speed of the fast transverse wave of the bulk wave propagating in the same direction and does not exceed the speed of the longitudinal wave. The cutout angle of the surface and the propagation direction of the surface acoustic wave are represented by Euler angles (0 ° to
45 °, 45 ° to 50 °, 80 ° to 90 °) and the optimum electrode finger width and electrode finger thickness of the IDT made of aluminum formed on the substrate so as to fall within the range equivalent thereto. Was.

A simulation was performed using the model shown in FIG. Electrode fingers are formed at a pitch P on the piezoelectric substrate. The width of the electrode finger is M, and the film thickness is h. Electrode fingers having different polarities are alternately arranged one by one. The propagation characteristics of the surface acoustic wave of the IDT of the model shown in FIG.
1 due to periodic perturbation effect by electrode finger (strip)
The next black reflection occurs, and frequency dispersion occurs in the propagation constant κ (wave number). First, the frequency dispersion of the propagation constant κ is simulated. The displacement U _i and the electrostatic displacement φ of the surface acoustic wave are expressed by the sum of the following spatial harmonics using Floquet's theorem.

[0045]

[Equation 11]

[0046]

(Equation 12)Where the damping constant α^{(m, n)}And the amplitude constant β_i ^{(m, n)}Is the expression
(3) can be obtained in the same manner as in equation (4).
Harmonic amplitude constant A^{(m, n)}Are given by Equations (11) and (12)
Is given by giving the following boundary conditions. Elastic boundary
As a field condition, the displacement U under the strip₁, U_Two, U_Three
And x_ThreeStress T in the direction_3jIs continuous and between strips
Is x_ThreeStress T in the direction_3jIs zero and the electrical boundary condition
The static potential φ is constant under the strip,
X_ThreeDensity D in the direction _ThreeApply continuation.
In the model shown in FIG. 23, when the electric terminals are opened.
(Open strip) has zero charge on the strip, short circuit
In the case of (short-circuit strip), the electrostatic potential φ on the strip
Gives zero. From the above simulation, we can see that
The propagation constant κ for the wave number ω can be obtained. What
The next absorption m of the space harmonic is a sufficiently large finite number.
Is simulating.

Generally, the condition of black reflection where the propagation constant κ is the first order (Re (κ) = π / P, P is the strip period length)
A stop band, which is a frequency band that satisfies
The frequencies at both ends of the stop band with respect to the open strip are f _1o and f _2o, and the frequencies at both ends of the stop band with respect to the short-circuit strip row are f _1s and f _2s. things the f _2o, and f _2s. Then, the resonance frequency coincides with the end f _1s of the stop band of the short strip, and the anti-resonance frequency coincides with the end f _1o of the stop band of the open strip. This f
Than _1s and ^{_{f 1o k 2 = (f 1o}} -f 1s) / f can be determined electromechanical coupling coefficient k ² from the relationship of _1o. The attenuation component (Im (κ) = 0) of the propagation constant κ is zero at both ends of the stop band in the case of a Rayleigh wave, but is not zero in the case of a leaky wave and the present SAW.

Therefore, the attenuation component of the propagation constant κ near the resonance frequency f _1s and the anti-resonance frequency f _1o , which are important in the actual device as the propagation characteristics in the IDT and the reflection strip, is obtained from the propagation constant κ obtained by the above simulation. alpha _1s, alpha _1o, and the resonance frequency f _1s, was evaluated for propagation characteristics by the electromechanical coupling coefficient k ² obtained from the anti-resonance frequency f _1o.

In the simulation, the cut-out angle and the propagation direction of the lithium tetraborate single crystal substrate are represented by Euler angles (0 ° to 45 °, 45 ° to 50 °, 80 ° to 90 °).
ＩＤ) and an IDT made of aluminum is formed on the substrate so as to fall within the range equivalent thereto, and the speed of the surface acoustic wave is equal to or higher than the speed of the fast transverse wave of the bulk wave propagating in the same direction. In a surface acoustic wave device using a surface acoustic wave that does not exceed, the propagation characteristics of the surface acoustic wave when the electrode finger width and the electrode finger thickness of the IDT are changed (stop band edge frequency, propagation loss, electromechanical coupling coefficient) Was calculated.

The simulation results will be described in detail with reference to the drawings. FIGS. 24 to 28 show that the cutout angle and the propagation direction of the surface acoustic wave of the lithium tetraborate single crystal substrate are represented by Euler angles (0 °, 47.3 °, 90 °), that is, the X-axis of the (011) plane. The calculation result of the propagation characteristics of the present surface acoustic wave (the present SAW) in the surface acoustic wave device in which the IDT containing aluminum as a main component is formed so that the propagation direction is perpendicular to the direction is shown. Here, the frequency is P = 50
cm (λ = 2P = 1 m).

FIG. 24 shows the stop band edge frequency (f _1s ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.3 and the electrode finger film thickness h / λ is changed. ,
f _2s , f _1o , f _2o ), the frequency of the free part (f _free ), and the frequency of the metal part (f _metal ) (FIG. 24)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 24)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 24)
(C)).

The electrode finger thickness h is set to a value twice as long as the electrode cycle (λ =
2P), the normalized film thickness h / λ is from 0.0 to 3.
When it is changed to 0%, as shown in FIG.
And the stop bandwidth (f_2o−f_1o),
(F_2s−f_1s) Becomes wider, as shown in FIG.
The electromechanical coupling coefficient k^TwoIncreased from 1.0 to 3.5%
In particular, when the normalized film thickness h / λ is about 0.4% or more,
Mechanical coupling coefficient k^TwoIs 1.5% or more. FIG. 24 (b)
As shown in the figure, the normalized loss h / λ is about 2%.
The value increases sharply as described above, but when the normalized film thickness h / λ is small.
Is relatively small. α _1sIs less than about 1.6%, α_1oIs about
At 1.9% or less, the propagation loss becomes 0.05 dB / λ or less.
In particular, α_1sIs minimum around 1.1%.

Therefore, when the electrode finger width M / P is 0.3, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 0.4% to 1.6%. , The propagation loss is reduced. FIG. 25 shows the stop band edge frequencies (f _1s , f) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.4 and the electrode finger thickness h / λ is changed.
_2s , f _1o , f _2o ), the calculation results of the free portion frequency (f _free ) and the metal portion frequency (f _metal ) (FIG. 25)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 25)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 25)
(C)).

The electrode finger thickness h is set to a value twice as long as the electrode period (λ =
2P), the normalized film thickness h / λ is from 0.0 to 3.
When it is changed to 0%, as shown in FIG.
And the stop bandwidth (f_2o−f_1o),
(F_2s−f_1s) Becomes wider, as shown in FIG.
The electromechanical coupling coefficient k^TwoIncreased from 1.2 to 3.9%
In particular, when the normalized film thickness h / λ is about 0.2% or more,
Mechanical coupling coefficient k^TwoIs 1.5% or more. FIG. 25 (b)
As shown in the figure, the normalized loss h / λ is about 2%.
The value increases sharply as described above, but when the normalized film thickness h / λ is small.
Is relatively small. α _1sIs less than about 1.3%, α_1oIs about
At 1.6% or less, the propagation loss becomes 0.05 dB / λ or less.
In particular, α_1sIs minimum around 0.9%.

Therefore, when the electrode finger width M / P is 0.4, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 0.2% to 1.3%. , The propagation loss is reduced. FIG. 26 shows the stop band edge frequencies (f _1s , f ₁ ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.5 and the electrode finger thickness h / λ is changed.
_2s , f _1o , f _2o ), the calculation results of the free portion frequency (f _free ) and the metal portion frequency (f _metal ) (FIG. 26)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 26)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 26)
(C)).

The electrode finger thickness h is set to a value twice as long as the electrode period (λ =
2P), the normalized film thickness h / λ is from 0.0 to 3.
When it is changed to 0%, as shown in FIG. 26A, the stop band width (f _2o −f _1o ) for open and short circuit,
(F _2s −f _1s ) increases, and as shown in FIG. _26C , the electromechanical coupling coefficient k ² increases from 1.4 to 4.1%, and in particular, the normalized film thickness h / λ increases. electromechanical coupling coefficient k ² is about 0.07% or more is 1.5% or more. FIG.
As shown in (b), the propagation loss sharply increases when the normalized film thickness h / λ is about 2% or more, but is relatively small when the normalized film thickness h / λ is small. α _1s is about 1.2% or less, α _1o
Is about 1.4% or less, the propagation loss is 0.05 dB / λ or less, and α _1s becomes minimum especially near 0.8%.

Therefore, when the electrode finger width M / P is 0.5, the normalized thickness h / λ of the electrode finger is 0.07% to 1.2%.
In the range, the electromechanical coupling coefficient k ² is large, the propagation loss is reduced. FIG. 27 shows the stop band edge frequencies (f _1s , f _1s ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.6 and the electrode finger thickness h / λ is changed.
f _2s , f _1o , f _2o ), the frequency of the free part (f _free ) and the frequency of the metal part (f _metal ) (FIG. 27)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 27)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 27)
(C)).

The electrode finger thickness h is set to a value twice as long as the electrode period (λ =
2P), the normalized film thickness h / λ is from 0.0 to 3.
When it is changed to 0%, as shown in FIG. 27A, the stop band width (f _2o −f _1o ) for open and short circuit,
(F _2s −f _1s ) increases, and as shown in FIG. 27C, the electromechanical coupling coefficient k ² increases from 1.4 to 4.0%, and in particular, the normalized film thickness h / λ increases. electromechanical coupling coefficient k ² is about 0.05% or more is 1.5% or more. FIG.
As shown in (b), the propagation loss sharply increases when the normalized film thickness h / λ is about 2% or more, but is relatively small when the normalized film thickness h / λ is small. α _1s is about 1.2% or less, α _1o
Is about 1.4% or less, the propagation loss is 0.05 dB / λ or less, and α _1s becomes minimum especially near 0.8%.

Therefore, when the electrode finger width M / P is 0.6, the normalized thickness h / λ of the electrode finger is 0.05% to 1.2%.
In the range, the electromechanical coupling coefficient k ² is large, the propagation loss is reduced. FIG. 28 shows the stop band end frequencies (f _1s , f _1s , f 2) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.7 and the electrode finger thickness h / λ is changed.
f _2s , f _1o , f _2o ), the frequency of the free part (f _free ) and the frequency of the metal part (f _metal ) (FIG. 28)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 28)
(B)), Calculation result of electromechanical coupling coefficient k ² (FIG. 28)
(C)).

The electrode finger thickness h is set to a value twice as long as the electrode period (λ =
2P), the normalized film thickness h / λ is from 0.0 to 3.
When it is changed to 0%, as shown in FIG. _{28A, the} stop band width (f _2o −f _1o ) for open and short circuit,
(F _2s −f _1s ) increases, and as shown in FIG. _28C , the electromechanical coupling coefficient k ² increases from 1.4 to 3.8%, and in particular, the normalized film thickness h / λ increases. electromechanical coupling coefficient k ² is about 0.15% or more is 1.5% or more. FIG.
As shown in (b), the propagation loss sharply increases when the normalized film thickness h / λ is about 2% or more, but is relatively small when the normalized film thickness h / λ is small. α _1s is less than about 1.3%, α _1o
Is about 1.5% or less, the propagation loss becomes 0.05 dB / λ or less, and α _1s becomes minimum especially around 0.9%.

Therefore, when the electrode finger width M / P is 0.7, the normalized thickness h / λ of the electrode finger is 0.15% to 1.3%.
In the range, the electromechanical coupling coefficient k ² is large, the propagation loss is reduced. FIG. 29 shows the optimum region of the electrode finger width M / P and the normalized film thickness h / λ where the electromechanical coupling coefficient k ² is large and the propagation loss is small, as apparent from the above description.
Are shown as hatched areas.

When this optimum area is expressed by a mathematical formula, 0.0165−0.0565 × (M / P) +0.050
0 × (M / P) ² ≦ (h / λ) ≦ 0.0320−0.0
737 × (M / P) + 0.0667 × (M / P) ²

When the normalized film thickness h / λ of the electrode finger at which α _1s is minimized is expressed by a mathematical formula, h / λ = 0.0210−0.0462 × (M / P) +
0.0417 × (M / P) ² .

In the above simulation, the cutout angle of the lithium tetraborate single crystal substrate and the propagation direction of the surface acoustic wave are represented by Euler angles (0 °, 47.3 °, 90 °).
゜), but in Euler angle display (0 ° to 45 °, 4
The same result can be obtained by extending the range to 5 ° to 50 °, 80 ° to 90 °). Next, the inventor of the present application uses a surface acoustic wave in which the speed of the surface acoustic wave is equal to or higher than the speed of the fast transverse wave of the bulk wave propagating in the same direction and does not exceed the speed of the longitudinal wave. The cutout angle of the surface and the propagation direction of the surface acoustic wave are represented by Euler angles (0 ° to 4 °).
5 °, 45 ° to 50 °, 80 ° to 90 °) and the optimum electrode finger width and electrode finger thickness of the double electrode IDT made of aluminum formed on the substrate so as to fall within the range equivalent thereto. Determined by

A simulation was performed using the model shown in FIG. Electrode fingers are formed at a pitch P on the piezoelectric substrate. The width of the electrode finger is M, and the film thickness is h. Two electrode fingers having different polarities are alternately arranged. The propagation characteristics of the surface acoustic wave of the double electrode IDT of the model shown in FIG. 30 were evaluated by the same simulation method as that of the model shown in FIG.

In the simulation, the cut-out angle and the propagation direction of the lithium tetraborate single crystal substrate are represented by Euler angles (0 ° to 45 °, 45 ° to 50 °, 80 ° to 90 °).
Ii) and a double electrode IDT made of aluminum is formed on the substrate so as to fall within the range equivalent thereto, and the velocity of the surface acoustic wave is equal to or higher than the velocity of the fast transverse wave of the bulk wave propagating in the same direction. In a surface acoustic wave device using a surface acoustic wave that does not exceed the velocity, the propagation characteristics of the surface acoustic wave when the electrode finger width and electrode finger thickness of the double electrode IDT are changed (stop band edge frequency, propagation loss, electric (Mechanical coupling coefficient).

The simulation result will be described in detail with reference to the drawings. In FIG. 31 to FIG. 36, the cutout angle and the propagation direction of the surface acoustic wave of the lithium tetraborate single crystal substrate are represented by Euler angles (0 °, 47.3 °, 90 °), that is, the X-axis of the (011) plane. Double electrode IDT mainly composed of aluminum so that the propagation direction is perpendicular to the
4 shows calculation results of propagation characteristics of the present surface acoustic wave (the present SAW) in the surface acoustic wave device in which is formed. Here, the frequency was standardized as P = 25 cm (λ = 4P = 1 m).

FIG. 31 shows the stop band edge frequency (f _1s ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.3 and the electrode finger film thickness h / λ is changed. ,
f _2s , f _1o , f _2o ), the frequency of the free part (f _free ) and the frequency of the metal part (f _metal ) (FIG. 31)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 31)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 31)
(C)).

The electrode finger thickness h is set to a value four times the electrode period (λ =
4P), the normalized film thickness h / λ standardized from 0.0 to 5.
When it is changed to 0%, as shown in FIG. _31A , the stop band edge frequencies (f _1s , f _2s , f _1o , f _2o ) gradually decrease, and as shown in FIG. increases from the electromechanical coupling coefficient k ² is 1.0 to 3.2%, in particular, is 1.5% or more electromechanical coupling coefficient k ² is a normalized film thickness h / lambda of about 1.5% or more . As shown in FIG. 31 (b), α _1s
Is about 4.7% or less, α _1o is about 3.8% or less, and the propagation loss is 0.05 dB / λ or less. In particular, α _1s is 2.8%
It becomes minimum near.

Therefore, when the electrode finger width M / P is 0.3, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 1.5% to 4.7%. , The propagation loss is reduced. FIG. 32 shows the stop band edge frequencies (f _1s , f ₁ ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.4 and the electrode finger film thickness h / λ is changed.
_2s , f _1o , f _2o ), the calculation result of the free portion frequency (f _free ), and the metal portion frequency (f _metal ) (FIG. 32)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 32)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 32)
(C)).

The electrode finger thickness h is set to a value four times the electrode period (λ =
4P), the normalized film thickness h / λ standardized from 0.0 to 5.
When it is changed to 0%, as shown in FIG. 32A, the stop band end frequencies (f _1s , f _2s , f _1o , f _2o ) gradually decrease, and as shown in FIG. increases from the electromechanical coupling coefficient k ² is 1.0 to 3.2%, in particular, is 1.5% or more electromechanical coupling coefficient k ² is a normalized film thickness h / lambda of about 1.2% or more . As shown in FIG. 32 (b), α _1s
Is about 4.0% or less, α _1o is about 3.4% or less, and the propagation loss is 0.05 dB / λ or less. In particular, α _1s is 2.3%
It becomes minimum near.

Therefore, when the electrode finger width M / P is 0.4, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 1.2% to 4.0%. , The propagation loss is reduced. FIG. 33 shows the stop band edge frequencies (f _1s , f ₁ ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.5 and the electrode finger thickness h / λ is changed.
_2s , f _1o , f _2o ), the frequency of the free part (f _free ) and the frequency of the metal part (f _metal ) (FIG. 33)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 33)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 33)
(C)).

The electrode finger thickness h is set to a value four times the electrode period (λ =
4P), the normalized film thickness h / λ standardized from 0.0 to 5.
When it is changed to 0%, as shown in FIG. 33 (a), the stop band edge frequencies (f _1s , f _2s , f _1o , f _2o ) gradually decrease, and as shown in FIG. increases from the electromechanical coupling coefficient k ² is 1.0 to 3.5%, in particular, is 1.5% or more electromechanical coupling coefficient k ² is a normalized film thickness h / lambda of about 0.8% or more . As shown in FIG. 33 (b), α _1s
Is about 3.8% or less, α _1o is about 3.1% or less, and the propagation loss is 0.05 dB / λ or less. In particular, α _1s is 2.1%
It becomes minimum near.

Therefore, when the electrode finger width M / P is 0.5, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 0.8% to 3.8%. , The propagation loss is reduced. FIG. 34 shows the stop band edge frequencies (f _1s , f ₁ ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.6 and the electrode finger thickness h / λ is changed.
_2s , f _1o , f _2o ), the calculation result of the frequency of the free part (f _free ) and the frequency of the metal part (f _metal ) (FIG. 34)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 34)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 34)
(C)).

The electrode finger thickness h is set to a value four times the electrode period (λ =
4P), the normalized film thickness h / λ standardized from 0.0 to 5.
When it is changed to 0%, the stop band end frequencies (f _1s , f _2s , f _1o , f _2o ) gradually decrease as shown in FIG. 34 (a), and as shown in FIG. 34 (c), increases from the electromechanical coupling coefficient k ² is 1.2 to 3.3%, in particular, is 1.5% or more electromechanical coupling coefficient k ² is a normalized film thickness h / lambda of about 0.7% or more . As shown in FIG. 34 (b), α _1s
Is about 3.5% or less, α _1o is about 2.8% or less, and the propagation loss is 0.05 dB / λ or less. In particular, α _1s is 2.0%
It becomes minimum near.

Therefore, when the electrode finger width M / P is 0.6, the electromechanical coupling coefficient k ² is large when the normalized thickness h / λ of the electrode finger is in the range of 0.7% to 3.5%. , The propagation loss is reduced. FIG. 35 shows stop band edge frequencies (f _1s , f ₁ ) when the electrode finger width (M / P) normalized by the electrode finger pitch P is 0.7 and the electrode finger film thickness h / λ is changed.
_2s , f _1o , f _2o ), the calculation results of the free portion frequency (f _free ) and the metal portion frequency (f _metal ) (FIG. 35)
(A)), calculation results of propagation loss (α _1s , α _1o ) (FIG. 35)
(B)), calculation results of the electromechanical coupling coefficient k ² (FIG. 35)
(C)).

The electrode finger thickness h is set to a value four times the electrode period (λ =
4P), the normalized film thickness h / λ standardized from 0.0 to 5.
When it is changed to 0%, the stop band edge frequencies (f _1s , f _2s , f _1o , f _2o ) gradually decrease as shown in FIG. 35 (a), and as shown in FIG. 35 (c), increases from the electromechanical coupling coefficient k ² is 1.2 to 3.0%, in particular, is 1.5% or more electromechanical coupling coefficient k ² is a normalized film thickness h / lambda of about 0.7% or more . As shown in FIG. 35 (b), α _1s
Is about 3.8% or less, α _1o is about 2.8% or less, and the propagation loss is 0.05 dB / λ or less. In particular, α _1s is 1.8%
It becomes minimum near.

Therefore, the electrode finger width M / P is 0.7
When the normalized thickness h / λ of the electrode finger is 0.7% to 3.8%,
Range, the electromechanical coupling coefficient k^TwoLarge and low propagation loss
It will be cheap. From the above explanation, the electromechanical connection
Coefficient k^TwoIs large and the propagation loss α _1sThe electrode becomes smaller
FIG. 3 shows the optimum areas of the finger width M / P and the normalized film thickness h / λ.
6 is shown as a hatched area.

When this optimum area is expressed by a mathematical formula, 0.0335−0.0791 × (M / P) +0.058
4 × (M / P) ² ≦ (h / λ) ≦ 0.0835-0.1
653 × (M / P) + 0.1429 × (M / P) ²

The optimum area of the electrode finger width M / P and the normalized film thickness h / λ where the electromechanical coupling coefficient k ² is large and the propagation loss α _1o is small can be expressed by the following equation: −0.0791 × (M / P) +0.058
4 × (M / P) ² ≦ (h / λ) ≦ 0.0599−0.0
932 × (M / P) + 0.0686 × (M / P) ²

When the normalized thickness h / λ of the electrode finger at which α _1s is minimized is expressed by a mathematical formula, h / λ = 0.0870−0.3601 × (M / P) +
0.6643 × (M / P) ² −0.4167 × (M / P
P) It becomes ³ .

In the above simulation, the cutout angle of the lithium tetraborate single crystal substrate and the propagation direction of the surface acoustic wave are represented by Euler angles (0 °, 47.3 °, 90 °).
゜), but in Euler angle display (0 ° to 45 °, 4
The same result can be obtained by extending the range to 5 ° to 50 °, 80 ° to 90 °).

[0083]

EXAMPLE A surface acoustic wave device according to a first example of the present invention will be described with reference to FIGS. FIG. 37 shows a surface acoustic wave device according to this embodiment. The surface acoustic wave device according to the present embodiment is a transversal filter having a main surface of (01
1) An input IDT 22 and an output IDT 22 having the same structure are provided on the surface of a piezoelectric substrate 21 made of lithium tetraborate single crystal, which is a plane.
23, the input IDT22 and the output IDT2.
3, the input IDT 22 and the output IDT 23
Short-circuit strips 24 having the same period and the same opening length are formed.

The input IDT 22 and the output IDT 23 each have 20 pairs, an electrode finger pitch of 4 μm, and an aperture length of 400 μm.
And the propagation direction of the surface acoustic wave is represented by an Eulerian angle (0
°, 47.3 °, 90 °). The input IDT 22, the output IDT 23, and the shorting strip 24 are formed of an aluminum film having the same thickness, and are formed so that the propagation direction of the surface acoustic wave is perpendicular to the X-axis direction.

The frequencies at both ends of the stop band are measured from the frequencies at both ends of a large attenuation region based on the reflection of the stop band generated in the main lobe of the pass frequency characteristic. The propagation loss is determined by setting the propagation path length to 400 μm, 800 μm, 1200 μm.
The electromechanical coupling coefficient k ² was measured from the change in the insertion loss at the stop band edge frequency when it was changed to μm.
It was measured from 2,23 input admittances.

FIG. 38 shows the frequency at both ends of the stop band (FIG. 38A) and the propagation loss ( FIG.
8 (b)) and the measurement results (●, Δ) of the electromechanical coupling coefficient k ² (FIG. 38 (c)) are shown together with the calculation results (solid line). As is clear from FIG. 38, the experimental results and the calculation results show a relatively good agreement, and the propagation loss is very small when the electrode finger thickness is around 1%, and the electromechanical coupling coefficient k ² is about 2. It turned out to be 1%.

A surface acoustic wave device according to a second embodiment of the present invention will be described with reference to FIGS. FIG. 39 shows a surface acoustic wave device according to this embodiment. The surface acoustic wave device according to the present embodiment is a transversal filter, and has a main surface of (0
11) An input IDT2 of a double electrode having the same structure is provided on the surface of the piezoelectric substrate 21 made of lithium tetraborate single crystal, which is a plane.
2 and an output IDT 23 are formed.
In the propagation area between the output IDT 23 and the
A shorting strip 24 having the same period and the same opening length as the DT 22 and the output IDT 23 is formed.

The input IDT 22 and the output IDT 23 each have 20 pairs, an electrode finger pitch of 4 μm, and an aperture length of 400 μm.
And the propagation direction of the surface acoustic wave is represented by an Eulerian angle (0
°, 47.3 °, 90 °). The input IDT 22, the output IDT 23, and the shorting strip 24 are formed of an aluminum film having the same thickness, and are formed so that the propagation direction of the surface acoustic wave is perpendicular to the X-axis direction.

The frequency at both ends of the stop band is
In the case of a trip, since the reflection amount is almost 0, it is obtained
Can not do. Therefore, the frequency at both ends of the stop band
Number f _1s, F_1oThe center frequency of the
Evaluation was made at the center frequency of the inlobe. The propagation loss is
The path length was changed to 400 μm, 800 μm, 1200 μm
Measurement from the change in insertion loss at the center frequency when
Mechanical coupling coefficient k^TwoAre the input electrodes of the double electrode IDTs 22 and 23.
It was measured by domitance.

FIG. 40 shows the center frequency of the stop band (FIG. 38A) and the propagation loss (FIG. 38A) when the electrode finger line width is 0.5 with respect to the electrode finger cycle and the electrode finger film thickness is changed. 38
(B)) The measurement results (○) of the electromechanical coupling coefficient k ² (FIG. 38 (c)) are shown together with the calculation results (solid line, broken line). As is clear from FIG. 40, the experimental results and the calculated results show a relatively good agreement, the propagation loss is small when the electrode finger thickness is around 2%, and the electromechanical coupling coefficient k ² is about 2.
It turned out that it was 4%.

The present invention is not limited to the above embodiment, but can be variously modified. For example, the surface acoustic wave device of the present invention may have a different structure from the surface acoustic wave device of the above embodiment.
For example, the present invention can be applied to a resonator type filter in which an IDT is provided between a pair of grating reflectors and a resonator. Also, a structure in which many IDTs are connected in parallel (IID
The present invention can also be applied to a surface acoustic wave device having a (T structure).

[0092]

As described above, according to the first aspect, the piezoelectric substrate made of lithium tetraborate single crystal and the piezoelectric substrate formed on the surface of the piezoelectric substrate for exciting, receiving, reflecting, and propagating surface acoustic waves are provided. In a surface acoustic wave device having an electrode, the electrode is formed of a metal containing aluminum as a main component,
The electrode has a pair of comb-shaped electrodes arranged such that one electrode finger is interposed between the electrodes, and the cutout angle of the surface of the piezoelectric substrate and the propagation direction of the surface acoustic wave are represented by Eulerian angles (0
° to 45 °, 45 ° to 50 °, 80 ° to 90 °) and the equivalent range. The period of the electrode finger is P, the width of the electrode finger is M, and the film thickness h of the electrode. Is normalized by the wavelength λ of the surface acoustic wave.
The following formula: 0.0165-0.0565 x (M / P) + 0.050
0 × (M / P) ² ≦ (h / λ) ≦ 0.0320−0.0
737 × (M / P) + 0.0667 × (M / P) ² , the electromechanical imaging coefficient k ² is large,
A surface acoustic wave device that has a small propagation loss and uses a high-speed surface acoustic wave that is faster than the speed of a fast transverse wave of a bulk wave can be realized.

According to the second aspect of the present invention, there is provided a piezoelectric substrate made of lithium tetraborate single crystal, and electrodes formed on the surface of the piezoelectric substrate for exciting, receiving, reflecting, and propagating surface acoustic waves. In the surface acoustic wave device, the electrode is formed of a metal containing aluminum as a main component, and the electrode is
It has a pair of comb-shaped electrodes arranged such that two electrode fingers are interposed between each other, and the cut-out angle of the surface of the piezoelectric substrate and the propagation direction of the surface acoustic wave are represented by Eulerian angles (0 ° to 45 °).
°, 45 ° to 50 °, 80 ° to 90 °) and the equivalent range, and the period of the electrode finger is P,
Assuming that the width of the electrode finger is M and the electrode thickness h is normalized by the wavelength λ of the surface acoustic wave, the normalized film thickness h / λ of the electrode is 0.0335−0.0791 × (M / P). +0.058
4 × (M / P) ² ≦ (h / λ) ≦ 0.0835-0.1
65 × (M / P) + 0.143 × (M / P) ² , the electromechanical imaging coefficient k ² is large,
A surface acoustic wave device that has a small propagation loss and uses a high-speed surface acoustic wave that is faster than the speed of a fast transverse wave of a bulk wave can be realized.

Further, this range is defined as (0 ° -2 °, 45 °
５０50 °, 88 ° -90 °) and equivalent ranges, the propagation loss is sufficiently low, the propagation speed is high, and
A surface acoustic wave device using a surface acoustic wave having a sufficient electromechanical coupling coefficient can be realized.

[Brief description of the drawings]

FIG. 1 is a diagram showing a coordinate system and boundary conditions used for simulation of a surface acoustic wave.

FIG. 2 shows a cutout angle and a propagation direction (0 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. it is a graph showing a simulation result of the phase velocity v _p in the case of changing the angle theta.

[FIG. 3] Aluminum aluminum on the surface of a lithium tetraborate single crystal substrate
Surface acoustic wave device with electrodes composed mainly of
The cutting angle of the lithium tetraborate single crystal substrate and
When the angle θ of the propagation direction (0 °, θ, 90 °) is changed
Electromechanical coupling coefficient k ^TwoShow simulation results
This is a graph.

FIG. 4 shows a cutout angle and a propagation direction (0 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. 6 is a graph showing simulation results of the propagation loss L when the angle θ is changed.

FIG. 5 shows a cutout angle and a propagation direction (15 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. it is a graph showing a simulation result of the phase velocity v _p in the case of changing the angle theta.

FIG. 6 shows a cutout angle and a propagation direction (15 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. is a graph showing the simulation results of the electromechanical coefficient k ² in the case of changing the angle theta.

FIG. 7 shows a cutout angle and a propagation direction (15 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. 6 is a graph showing simulation results of the propagation loss L when the angle θ is changed.

FIG. 8 shows a cutout angle and a propagation direction (30 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. it is a graph showing a simulation result of the phase velocity v _p in the case of changing the angle theta.

FIG. 9 shows a cutout angle and a propagation direction (30 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. is a graph showing the simulation results of the electromechanical coefficient k ² in the case of changing the angle theta.

FIG. 10 shows a cutout angle and a propagation direction (30 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. 6 is a graph showing simulation results of the propagation loss L when the angle θ is changed.

FIG. 11 shows a cutout angle and a propagation direction (45 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. it is a graph showing a simulation result of the phase velocity v _p in the case of changing the angle theta.

FIG. 12 shows a cutout angle and a propagation direction (45 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. is a graph showing the simulation results of the electromechanical coefficient k ² in the case of changing the angle theta.

FIG. 13 shows a cutout angle and a propagation direction (45 °, θ, 90 °) of a lithium tetraborate single crystal substrate in a surface acoustic wave device in which an electrode mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. 6 is a graph showing simulation results of the propagation loss L when the angle θ is changed.

FIG. 14 shows a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate, and the propagation direction 変 化 is changed on the (011) cut surface of the lithium tetraborate single crystal substrate. Phase velocity v _p
6 is a graph showing a simulation result of FIG.

FIG. 15 shows a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate, by changing the propagation direction 変 化 on the (011) cut surface of the lithium tetraborate single crystal substrate. is a graph showing the simulation results of the electromechanical coefficient k ² of if.

FIG. 16 shows that in a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate, the propagation direction 変 化 is changed on the (011) cut surface of the lithium tetraborate single crystal substrate. 9 is a graph showing a simulation result of a propagation loss L in a case where the transmission loss L has occurred.

FIG. 17 shows a cut-off angle and a propagation direction of the lithium tetraborate single crystal substrate in the surface acoustic wave device in which an electrode containing aluminum as a main component is formed on the surface of the lithium tetraborate single crystal substrate. 3 °, 90 °), and is a graph showing simulation results of the phase velocity v _p when the normalized film thickness h / λ of the electrode is changed.

FIG. 18 is a diagram illustrating a surface acoustic wave device in which an electrode containing aluminum as a main component is formed on the surface of a lithium tetraborate single crystal substrate. 3 °, 90 °) and a graph showing a simulation result of the electromechanical coupling coefficient k ² when the normalized film thickness h / λ of the electrode is changed.

FIG. 19 is a diagram illustrating a surface acoustic wave device in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate. 3 is a graph showing simulation results of the propagation loss L when the normalized thickness h / λ of the electrode is changed.

FIG. 20 is a diagram illustrating a surface acoustic wave device in which an electrode containing aluminum as a main component is formed on the surface of a lithium tetraborate single crystal substrate. 3 °, 90 °), and is a graph showing simulation results of the frequency temperature coefficient TCF when the normalized film thickness h / λ of the electrode is changed.

FIG. 21 shows a surface acoustic wave in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate so that the propagation direction of the surface acoustic wave is (0 °, 47.3 °, 90 °). 6 is a graph showing a simulation result of displacement distributions U ₁ and U ₃ and a potential distribution Φ in the depth direction of the substrate when the substrate surface is electrically open in the apparatus.

FIG. 22 shows a surface acoustic wave in which an electrode mainly composed of aluminum is formed on the surface of a lithium tetraborate single crystal substrate so that the propagation direction of the surface acoustic wave is (0 °, 47.3 °, 90 °). 6 is a graph showing simulation results of displacement distributions U ₁ and U ₃ and a potential distribution Φ in the depth direction of the substrate when the substrate surface is electrically short-circuited in the apparatus.

FIG. 23 is a diagram showing a model used for simulation of the surface acoustic wave device according to the first invention.

FIG. 24 is a diagram illustrating a cut-out angle and a propagation direction of a lithium tetraborate single crystal substrate in an Eulerian angle display (0 °, 47.3 °, 9
0 °), the electrode finger width M / P is 0.3, and the electrode finger thickness h
10 is a graph showing simulation results of stop band edge frequency (FIG. 10A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when / λ is changed.

FIG. 25 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in an Eulerian angle display (0 °, 47.3 °, 9
0 °), the electrode finger width M / P is 0.4, and the electrode finger thickness h
10 is a graph showing simulation results of stop band edge frequency (FIG. 10A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when / λ is changed.

FIG. 26 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in an Eulerian angle display (0 °, 47.3 °, 9
0 °), the electrode finger width M / P is 0.5, and the electrode finger thickness h
10 is a graph showing simulation results of stop band edge frequency (FIG. 10A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when / λ is changed.

FIG. 27 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in an Eulerian angle display (0 °, 47.3 °, 9
0 °), the electrode finger width M / P is 0.6, and the electrode finger thickness h
10 is a graph showing simulation results of stop band edge frequency (FIG. 10A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when / λ is changed.

FIG. 28 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in Euler angles (0 °, 47.3 °, 9
0 °), the electrode finger width M / P is 0.7, and the electrode finger thickness h
10 is a graph showing simulation results of stop band edge frequency (FIG. 10A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when / λ is changed.

FIG. 29 is a diagram illustrating a surface acoustic wave device in which an IDT containing aluminum as a main component is formed on the surface of a lithium tetraborate single crystal substrate, in which the electromechanical coupling coefficient is large and the propagation loss is small; It is a graph which shows the optimal area of normalized film thickness h / λ.

FIG. 30 is a diagram showing a model used for simulation of the surface acoustic wave device according to the second invention.

FIG. 31 shows a cutout angle and a propagation direction of a lithium tetraborate single crystal substrate in Euler angle display in a surface acoustic wave device in which a double electrode IDT mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. °, 4
7.3 °, 90 °), the electrode finger width M / P is 0.3,
Simulation results of the stop band edge frequency (FIG. 9A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when the electrode finger thickness h / λ is changed are shown. It is a graph shown.

FIG. 32 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate expressed in Euler angles (0) °, 4
7.3 °, 90 °), the electrode finger width M / P is 0.4,
Simulation results of the stop band edge frequency (FIG. 9A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when the electrode finger thickness h / λ is changed are shown. It is a graph shown.

FIG. 33 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in Euler angle display in a surface acoustic wave device in which a double electrode IDT mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. °, 4
7.3 °, 90 °), the electrode finger width M / P is 0.5,
Simulation results of the stop band edge frequency (FIG. 9A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when the electrode finger thickness h / λ is changed are shown. It is a graph shown.

FIG. 34 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate expressed by an Eulerian angle in a surface acoustic wave device in which a double electrode IDT mainly containing aluminum is formed on the surface of a lithium tetraborate single crystal substrate. °, 4
7.3 °, 90 °), the electrode finger width M / P is 0.6,
Simulation results of the stop band edge frequency (FIG. 9A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when the electrode finger thickness h / λ is changed are shown. It is a graph shown.

FIG. 35 shows a cut-off angle and a propagation direction of a lithium tetraborate single crystal substrate in Euler angle display in a surface acoustic wave device in which a double electrode IDT containing aluminum as a main component is formed on the surface of a lithium tetraborate single crystal substrate. °, 4
7.3 °, 90 °), the electrode finger width M / P is 0.7,
Simulation results of the stop band edge frequency (FIG. 9A), propagation loss (FIG. 10B), and electromechanical coupling coefficient (FIG. 10C) when the electrode finger thickness h / λ is changed are shown. It is a graph shown.

FIG. 36 is a diagram illustrating a surface acoustic wave device in which a double electrode IDT containing aluminum as a main component is formed on the surface of a lithium tetraborate single crystal substrate, the electromechanical coupling coefficient is large, the propagation loss is small, and the electrode finger width M / P and normalized film thickness h
6 is a graph showing an optimum region of / λ.

FIG. 37 is a diagram showing a surface acoustic wave device according to a first embodiment of the present invention.

38A and 38B show the frequency at both ends of the stop band and the propagation loss when the electrode finger thickness is changed in the surface acoustic wave device according to the first embodiment of the present invention. 3) is a graph showing the measurement results and simulation results of the electromechanical coupling coefficient (FIG. 3C).

FIG. 39 is a diagram showing a surface acoustic wave device according to a first embodiment of the present invention.

40A and 40B show the frequency at both ends of the stop band and the propagation loss when the electrode finger thickness is changed in the surface acoustic wave device according to the first embodiment of the present invention. 3) is a graph showing the measurement results and simulation results of the electromechanical coupling coefficient (FIG. 3C).

[Explanation of symbols]

 Reference Signs List 21 piezoelectric substrate 22 input IDT 23 output IDT 24 short-circuit strip 25 electrode finger 26 insulating layer 27 insulating layer

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) H03H 9/25 H03H 9/145

Claims (3)

(57) [Claims] 1. A surface acoustic wave device comprising: a piezoelectric substrate made of a lithium tetraborate single crystal; and an electrode formed on a surface of the piezoelectric substrate, for exciting, receiving, reflecting, and propagating a surface acoustic wave. The electrode is formed of a metal containing aluminum as a main component, and the electrode has a pair of comb-shaped electrodes arranged such that one electrode finger is inserted between each other, and a cutout angle of a surface of the piezoelectric substrate. And the propagation direction of the surface acoustic wave is represented by Eulerian angles (0 ° to 45 °, 45 ° to 50 °, 80 ° to 90 °).
°) and the equivalent range thereof, wherein the period of the electrode finger is P, the width of the electrode finger is M, and the film thickness h of the electrode is normalized by the wavelength λ of the surface acoustic wave. The normalized film thickness h / λ of the electrode is expressed by the following formula: 0.0165−0.0565 × (M / P) +0.050
0 × (M / P) ² ≦ (h / λ) ≦ 0.0320−0.0
737 × (M / P) + 0.0667 × (M / P) ² , and the velocity of the surface acoustic wave is equal to or higher than the velocity of the fast transverse wave of the bulk wave propagating in the same direction, and the velocity of the longitudinal wave. Surface acoustic wave device characterized by not exceeding. 2. A surface acoustic wave device comprising: a piezoelectric substrate made of a lithium tetraborate single crystal; and electrodes formed on a surface of the piezoelectric substrate, for exciting, receiving, reflecting, and propagating surface acoustic waves. The electrode is formed of a metal containing aluminum as a main component, and the electrode has a pair of comb-shaped electrodes arranged such that two electrode fingers are interposed between each other, and a cutout angle of a surface of the piezoelectric substrate. And the propagation direction of the surface acoustic wave is represented by Eulerian angles (0 ° to 45 °, 45 ° to 50 °, 80 ° to 90 °).
°) and the equivalent range thereof, wherein the period of the electrode finger is P, the width of the electrode finger is M, and the film thickness h of the electrode is normalized by the wavelength λ of the surface acoustic wave. The normalized film thickness h / λ of the electrode is expressed by the following equation: 0.0335−0.0791 × (M / P) +0.058
4 × (M / P) ² ≦ (h / λ) ≦ 0.0835-0.1
653 × (M / P) + 0.1429 × (M / P) ² , wherein the velocity of the surface acoustic wave is equal to or greater than the velocity of the fast transverse wave of the bulk wave propagating in the same direction, and the velocity of the longitudinal wave Surface acoustic wave device characterized by not exceeding. 3. The surface acoustic wave device according to claim 1, wherein the cutout angle of the surface of the piezoelectric substrate and the propagation direction of the surface acoustic wave are represented by Eulerian angles (0 ° to 2 °, 45 ° to 50 °).
°, 88 ° to 90 °) and the equivalent range.