Acoustic wave device

1. An acoustic wave device comprising:

a support substrate made of silicon;

a piezoelectric layer directly or indirectly on the support substrate; and

an interdigital transducer (IDT) electrode on the piezoelectric layer; wherein

when a wavelength defined by an electrode finger pitch of the IDT electrode is λ, a thickness of the piezoelectric layer is about 1λ or less; and

V L , which is an acoustic velocity of a longitudinal wave component of a bulk wave propagating through the piezoelectric layer, satisfies Unequal Equation (2) below in relation to an acoustic velocity V Si-1 determined by Equation (1) below:

V Si-1 =( V 2 ) 1/2 (m/sec)  Equation (1);

V Si-1 ≤V L   Unequal Equation (2);

V 2 in Equation (1) is a solution of Equation (3);

Ax 3 +Bx 2 +Cx+D= 0  Equation (3);

V 1 , V 2 , and V 3 , which are three solutions of Equation (3), have a relationship of V 1 ≤V 2 ≤V 3 ;

in Equation (3), A, B, C, and D are values determined by following Equations (3A), (3B), (3C), and (3D) below, respectively:

A=−ρ 3   Equation (3A);

B=ρ 2 ( L 11 +L 22 +L 33 )  Equation (3B);

C =ρ( L 21 2 +L 23 2 +L 31 2 −L 11 ·L 33 −L 22 ·L 33 −L 11 ·L 22 )  Equation (3C); and

D= 2· L 21 ·L 23 ·L 31 +L 11 ·L 22 ·L 33 −L 31 2 ·L 22 −L 11 ·L 23 2 −L 21 2 ·L 33    Equation (3D);

in Equations (3A), (3B), (3C), or (3D), ρ represents a density (g/cm 3 ) of silicon, and L 11 , L 22 , L 33 , L 21 , L 31 , and L 23 are values determined by Equations (4A), (4B), (4C), (4D), (4E), and (4F) below, respectively:

L 11 =c 11 ·a 1 2 +c 44 ·a 2 2 +c 44 ·a 3 2   Equation (4A);

L 22 =c 44 ·a 1 2 +c 11 ·a 2 2 +c 44 ·a 3 2   Equation (4B);

L 33 =c 44 ·a 1 2 +c 44 ·a 2 2 +c 11 ·a 3 2   Equation (4C);

L 21 =( c 12 +c 44 )· a 2 ·a 1   Equation (4D);

L 31 =( c 12 +c 44 )· a 1 ·a 3   Equation (4E); and

L 23 =( c 44 +c 12 )· a 3 ·a 2   Equation (4F);

in Equations (4A), (4B), (4C), (4D), (4E), and (4F), c 11 , c 12 , and c 44 are elastic constants (N/m 2 ) of silicon, respectively, and a 1 , a 2 , and a 3 are values determined by Equations (5A), (5B), and (5C) below, respectively:

a 1 =cos(φ)·cos(ψ)−sin(φ)·cos(θ)·sin(ψ)  Equation (5A);

a 2 =sin(φ)·cos(ψ)+cos(φ)·cos(θ)·sin(ψ)  Equation (5B); and

a 3 =sin(θ)·sin(ψ)  Equation (5C);

where φ, θ, and ψ in Equations (5A), (5B), and (5C) are φ, θ, and ψ in a silicon crystal orientation (φ, θ, ψ).

2. The acoustic wave device according to claim 1 , wherein V L , which is the acoustic velocity of the longitudinal wave component of the bulk wave propagating through the piezoelectric layer, satisfies Unequal Equation (7) below in relation to an acoustic velocity V Si-2 determined by Equation (6) below:

V Si-2 =( V 3 ) 1/2 (m/sec)  Equation (6)

V Si-2 ≤V L   Unequal Equation (7).

3. The acoustic wave device according to claim 1 , wherein an acoustic velocity V SH0 of an SH 0 mode propagating through the piezoelectric layer and V L , which is the acoustic velocity of the longitudinal wave component of the bulk wave propagating through the piezoelectric layer, satisfy following Unequal equation (8) below in relation to the acoustic velocity V Si-1 determined by the Unequal Equation (2):

V SH0 ≤V Si-1 ≤V L   Unequal Equation (8).

4. The acoustic wave device according to claim 1 , wherein

a low-acoustic-velocity film is provided between the support substrate and the piezoelectric layer; and

an acoustic velocity of a bulk wave propagating through the low-acoustic-velocity film is lower than an acoustic velocity of the bulk wave propagated through the piezoelectric layer.

5. The acoustic wave device according to claim 4 , wherein

a high-acoustic-velocity film is provided between the support substrate and the low-acoustic-velocity film; and

an acoustic velocity of a bulk wave propagating through the high-acoustic-velocity film is higher than the acoustic velocity of the acoustic wave propagating through the piezoelectric layer.

6. The acoustic wave device according to claim 5 , wherein a thickness of the high-acoustic-velocity film is about 0.6λ or less.

7. The acoustic wave device according to claim 4 , wherein a thickness of the low-acoustic-velocity film is about 2λ or less.

8. The acoustic wave device according to claim 4 , wherein a thickness of the low-acoustic-velocity film is substantially equal to or less than the thickness of the piezoelectric layer.

9. The acoustic wave device according to claim 1 , wherein a cavity is provided between the support substrate and the piezoelectric layer.

10. The acoustic wave device according to claim 1 , wherein the piezoelectric layer includes lithium tantalate.

11. The acoustic wave device according to claim 1 , wherein the piezoelectric layer is made of lithium niobate.

12. The acoustic wave device according to claim 1 , wherein the thickness of the piezoelectric layer is about 0.15λ or less.

13. The acoustic wave device according to claim 1 , wherein a first reflector and a second reflector are provided on opposing sides of the IDT electrode in an acoustic wave propagation direction.

14. The acoustic wave device according to claim 1 , wherein the IDT electrode includes aluminum.

15. The acoustic wave device according to claim 1 , wherein a dielectric film is provided on the IDT electrode.

16. The acoustic wave device according to claim 1 , a thickness of the IDT electrode 6 is between about 0.025λ and about 0.08λ.

17. The acoustic wave device according to claim 4 , wherein a thickness of the low-acoustic-velocity film is between about 0.15λ and about 0.3λ.