Acoustic wave device
An acoustic wave device includes a silicon substrate, a first high-acoustic-velocity film on the silicon substrate, a first low-acoustic-velocity film on the first high-acoustic-velocity film, a second low-acoustic-velocity film on the first low-acoustic-velocity film, a second high-acoustic-velocity film on the second low-acoustic-velocity film, a piezoelectric film on the second high-acoustic-velocity film, and an IDT electrode on the piezoelectric film. Acoustic velocities of bulk waves propagating through the first and second high-acoustic-velocity films are higher than an acoustic velocity of an acoustic wave propagating through the piezoelectric film. Acoustic velocities of bulk waves propagating through the first and second low-acoustic-velocity films are lower than an acoustic velocity of a bulk wave propagating through the piezoelectric film. Materials of the first and second low-acoustic-velocity films are different from each other.
1 . An acoustic wave device comprising:
a silicon substrate;
a first high-acoustic-velocity film on the silicon substrate;
a first low-acoustic-velocity film on the first high-acoustic-velocity film;
a second low-acoustic-velocity film on the first low-acoustic-velocity film;
a second high-acoustic-velocity film on the second low-acoustic-velocity film;
a piezoelectric film on the second high-acoustic-velocity film; and
an IDT electrode on the piezoelectric filmi wherein
an acoustic velocity of a bulk wave propagating through the first high-acoustic-velocity film and an acoustic velocity of a bulk wave propagating through the second high-acoustic-velocity film are higher than an acoustic velocity of an acoustic wave propagating through the piezoelectric film;
an acoustic velocity of a bulk wave propagating through the first low-acoustic-velocity film and an acoustic velocity of a bulk wave propagating through the second low-acoustic-velocity film are lower than an acoustic velocity of a bulk wave propagating through the piezoelectric film; and
a material of the first low-acoustic-velocity film and a material of the second low-acoustic-velocity film are different from each other.
2 . The acoustic wave device according to claim 1 , wherein a thickness of the first high-acoustic-velocity film is equal to or larger than a thickness of the second high-acoustic-velocity film.
3 . The acoustic wave device according to claim 2 , wherein a thickness of the first low-acoustic-velocity film is equal to or larger than a thickness of the second low-acoustic-velocity film.
4 . The acoustic wave device according to claim 2 , wherein a thickness of the first high-acoustic-velocity film is equal to or larger than a thickness of the first low-acoustic-velocity film.
5 . The acoustic wave device according to claim 2 , wherein the first low-acoustic-velocity film or the second low-acoustic-velocity film is a SiO 2 film.
6 . The acoustic wave device according to claim 2 , wherein the piezoelectric film is a LiTaO 3 film or a LiNbO 3 film.
7 . The acoustic wave device according to claim 2 , wherein the piezoelectric film is a LiTaO 3 film or a LiNbO 3 film.
8 . The acoustic wave device according to claim 1 , wherein a thickness of the first low-acoustic-velocity film is equal to or larger than a thickness of the second low-acoustic-velocity film.
9 . The acoustic wave device according to claim 8 , wherein a thickness of the first high-acoustic-velocity film is equal to or larger than a thickness of the first low-acoustic-velocity film.
10 . The acoustic wave device according to claim 8 , wherein the first low-acoustic-velocity film or the second low-acoustic-velocity film is a SiO 2 film.
11 . The acoustic wave device according to claim 1 , wherein a thickness of the first high-acoustic-velocity film is equal to or larger than a thickness of the first low-acoustic-velocity film.
12 . The acoustic wave device according to claim 1 , wherein the first low-acoustic-velocity film or the second low-acoustic-velocity film is a SiO 2 film.
13 . The acoustic wave device according to claim 1 , wherein the piezoelectric film is a LiTaO 3 film or a LiNbO 3 film.
14 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (111);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], Euler angles of the piezoelectric film are defined as (LTφ, LTθ, LTψ), and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], the t_LT[λ], the LTθ, and the Siψ are thicknesses and angles within a range in which a phase derived from Equation 1 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
=(−64.7738492449743)+0.799535874292877
*(Siψ−23.2121158601201)+−0.00639116627879308
*( LT θ−131.246414694454)+228.498817195313
*(( t _ LT [λ])−0.180166902154725)+−551.916118464126
*(( t _SiN−2[λ])−0.0291537442599814)+1142.73591823813
*(( t _Ta2O5[λ])−0.0421024373013005)+155.359547985879
*(( t _SiO2[λ])−0.121307841752057)+−29.8438742957074
*(( t _SiN−1[λ])−0.263987107029325)+−0.0245466642133507*((Siψ−23.2121158601201)
*(Siψ−23.2121158601201)−540.379061966296)+−0.00862413439802871
*((Siψ−23.2121158601201)*( LT θ−131.246414694454))+0.249067774425361
*(( LT θ−131.246414694454)*( LT θ−131.246414694454)−5.81473016925011)+
6.93659125135011
*((Siψ−23.2121158601201)*(( t _ LT [λ])−0.180166902154725))+10.0784200297745
*(( LT θ−131.246414694454)*(( t _ LT [λ])−0.180166902154725))+116.492602498829
*((( t _ LT [λ])−0.180166902154725)
*(( t _ LT [λ])−0.180166902154725)−0.000346559038760835)+6.96592368109737
*((Siψ−23.2121158601201)*(( t _SiN−2[λ])−0.0291537442599814))+−15.0647392900912*
(( LT θ−131.246414694454)*(( t _SiN−2[λ])−0.0291537442599814))+3185.48452246456
*((( t _ LT [λ])−0.180166902154725)*(( t _SiN−2[λ])−0.0291537442599814))+
6533.48929488482
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−2[λ])−0.0291537442599814)−0.000458154170897422)+7.78801893149455
*((Siψ−23.2121158601201)*(( t _Ta2O5[λ])−0.0421024373013005))+53.7418010590521
(( LT θ−131.246414694454)*(( t _Ta2O5[λ])−0.0421024373013005))+6146.78344504674
*((( t _ LT [λ])−0.180166902154725)*(( t _Ta2O5[λ])−0.0421024373013005))+−
14578.5920718871
*((( t _SiN−2[λ])−0.0291537442599814)*(( t _Ta2O5[λ])−0.0421024373013005))
+28614.912170246
*((( t _Ta2O5[λ])−0.0421024373013005)*(( t _Ta2O5[λ])−0.0421024373013005)−
0.000324766882084902)+4.59563385312738
*((Siψ−23.2121158601201)*(( t _SiO2[λ])−0.121307841752057))+1.7616110343796
*(( LT θ−131.246414694454)*(( t _SiO2[λ])−0.121307841752057))+1984.12416812403
*((( t _ LT [λ])−0.180166902154725)*(( t _SiO2[λ])−0.121307841752057))+−202.795292688935
*((( t _SiN−2[λ])−0.0291537442599814)*(( t _SiO2[λ])−0.121307841752057))+
5166.03124069752
*((( t _Ta2O5[λ])−0.0421024373013005)
*(( t _SiO2[λ])−0.121307841752057))+−346.648683117878*(( t _SiO2[λ])−0.121307841752057)
*(( t _SiO2[λ])−0.121307841752057)−0.0017442053041025)+1.13949852542765
*((Siψ−23.2121158601201)*(( t _SiN−1[λ])−0.263987107029325))+−2.10309868792554
*(( LT θ−131.246414694454)*(( t _SiN−1[λ])−0.263987107029325))+342.49568371403*
(( t _ LT [λ])−0.180166902154725)*(( t _SiN−1[λ])−0.263987107029325))+735.741591105701
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−1[λ])−0.263987107029325))+−2014.8497951455
*((( t _Ta2O5[λ])−0.0421024373013005)*(( t _SiN−1[λ])−0.263987107029325))+
131.054784086532
*((( t _SiO2[λ])−0.121307841752057)*(( t _SiN−1[λ]A)−0.263987107029325))+
145.441965448516
*((( t _SiN−1[λ])−0.263987107029325)*(( t _SiN−1[λ])−0.263987107029325)−
0.0132035793109828). Equation 1
15 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (111);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], Euler angles of the piezoelectric film are defined as (LTφ, LTθ, LTψ), and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], the t_LT[λ], the LTθ, and the Siψ are thicknesses and angles within a range in which a phase derived from Equation 2 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
=(−49.4236088933048)+0.927126211958592
*(Siψ−23.2121158601201)+0.680023816107774*( LT θ−131.246414694454)+
213.742276430449
*(( t _ LT [λ])−0.180166902154725)+−606.139116757393
*(( t _SiN−2[λ])−0.0291537442599814)+692.814216558718
*(( t _Ta2O5[λ])−0.0421024373013005)+195.183979143557
*(( t _SiO2[λ])−0.121307841752057)+−83.0452792358909
*(( t _SiN−1[λ])−0.263987107029325)+−0.0279599052855905*((Siψ−23.2121158601201)
*(Siψ−23.2121158601201)−540.379061966296)+−0.0139285317562481
*((Siψ−23.2121158601201)*( LT θ−131.246414694454))+0.293983576167198
*(( LT θ−131.246414694454)*( LT θ−131.246414694454)−5.81473016925011)+
9.82906312217327
*((Siψ−23.2121158601201)*( t _ LT [λ])−0.180166902154725))+20.4897039882144
*(( LT θ−131.246414694454)*(( t _ LT [λ])−0.180166902154725))+−1822.1825017687
*((( t _ LT [λ])−0.180166902154725)
*(( t _ LT [λ])−0.180166902154725)−0.000346559038760835)+6.57985243569614
*((Siψ−23.2121158601201)*(( t _SiN−2[λ])−0.0291537442599814))+−16.3487857288392
*(( LT θ−131.246414694454)*(( t _SiN−2[λ])−0.0291537442599814))+3022.4142953683
*((( t _ LT [λ])−0.180166902154725)*(( t _SiN−2[λ])−0.0291537442599814))+
6106.28960321182
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−2[λ])−0.0291537442599814)−0.000458154170897422)+7.61287198883346
*((Siψ−23.2121158601201)*(( t _Ta2O5[λ])−0.0421024373013005))+32.0420324509525
*(( LT θ−131.246414694454)*(( t _Ta2O5[λ])−0.0421024373013005))+−5600.23059801591
*((( t _ LT [λ])−0.180166902154725)*(( t _Ta2O5[λ])−0.0421024373013005))+−
12480.4143612638
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _Ta2O5[λ])−0.0421024373013005))+9462.56388912554
*((( t _Ta2O5[λ])−0.0421024373013005)
*(( t _Ta2O5[λ])−0.0421024373013005)−0.000324766882084902)+4.75660770269025
*((Siψ−23.2121158601201)*(( t _SiO2[λ])−0.121307841752057))+3.138310645423
*(( LT θ−131.246414694454)*(( t _SiO2[λ])−0.121307841752057))+782.245112149574
*((( t _ LT [λ])−0.180166902154725)*(( t _SiO2[λ])−0.121307841752057))+−1849.48045553917
*((( t _SiN−2[λ])−0.0291537442599814)*(( t _SiO2[λ])−0.121307841752057))+−
657.25929805289
*((( t _Ta2O5[λ])−0.0421024373013005)
*(( t _SiO2[λ])−0.121307841752057))+−111.444658339511*((( t _SiO2[λ])−
0.121307841752057)
*(( t _SiO2[λ])−0.121307841752057)−0.0017442053041025)+1.37817174855647
*((Siψ−23.2121158601201)*(( t _SiN−1[λ])−0.263987107029325))+−1.7087256650039
*(( LT θ−131.246414694454)*(( t _SiN−1[λ])−0.263987107029325))+−396.636995545448
*((( t _ LT [λ])−0.180166902154725)*(( t _SiN−1[λ])−0.263987107029325))+434.882453748749
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−1[λ])−0.263987107029325))+−1660.0685005439
*((( t _Ta2O5[λ])−0.0421024373013005)*(( t _SiN−1[λ])−0.263987107029325))+
106.322544176659
*((( t _SiO2[λ])−0.121307841752057)*(( t _SiN−1[λ]A)−0.263987107029325))+
172.372246831877
*((( t _SiN−1[λ])−0.263987107029325)
*(( t _SiN−1[λ])−0.263987107029325)−0.0132035793109828). Equation 2
16 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (111);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], Euler angles of the piezoelectric film are defined as (LTφ, LTθ, LTψ), and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], the t_LT[λ], the LTθ, and the Siψ are thicknesses and angles within a range in which a phase derived from Equation 3 below is equal to or larger than about −70 deg:
Phase of spurious wave [deg]
=(−49.446344512493)+0.926632614160644
*(Siψ−23.2121158601201)+0.689805009201412*( LT θ−131.246414694454)+
213.186056884304
*(( t _ LT [λ])−0.180166902154725)+−605.162234862408
*(( t _SiN−2[λ])−0.0291537442599814)+693.090367188157
*(( t _Ta2O5[λ])−0.0421024373013005)+194.973246854906
*(( t _SiO2[λ])−0.121307841752057)+−82.9891258698242
*(( t _SiN−1[λ])−0.263987107029325)+−0.0279312228697236*((Siψ−23.2121158601201)
*(Siψ−23.2121158601201)−540.379061966296)+−0.0129242968044351
*((Siψ−23.2121158601201)*( LT θ−131.246414694454))+0.285438486600616
*(( LT θ−131.246414694454)*( LT θ−131.246414694454)−5.81473016925011)+
9.7873873803375
*((Siψ−23.2121158601201)*(( t _ LT [λ])−0.180166902154725))+20.1009127346539
*(( LT θ−131.246414694454)*(( t _ LT [λ])−0.180166902154725))+−1845.21253448418
*((( t _ LT [λ])−0.180166902154725)
*(( t _ LT [λ])−0.180166902154725)−0.000346559038760835)+6.50543677488646
*((Siψ−23.2121158601201)*(( t _SiN−2[λ]−0.0291537442599814))+−17.1312681888354
*(( LT θ−131.246414694454)*(( t _SiN−2[λ])−0.0291537442599814))+3096.79723705848
*((( t _ LT [λ])−0.180166902154725)*(( t _SiN−2[λ])−0.0291537442599814))+
6184.77577365764
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−2[λ])−0.0291537442599814)−0.000458154170897422)+7.56134934721394
*((Siψ−23.2121158601201)*(( t _Ta2O5[λ])−0.0421024373013005))+31.4231915519825
*(( LT θ−131.246414694454)*(( t _Ta2O5[λ])−0.0421024373013005))+−5550.14180216517
*((( t _ LT [λ])−0.180166902154725)*(( t _Ta2O5[λ])−0.0421024373013005))+−
12378.8114606327
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _Ta2O5[λ])−0.0421024373013005))+9488.76758932007
*((( t _Ta2O5[λ])−0.0421024373013005)
*(( t _Ta2O5[λ])−0.0421024373013005)−0.000324766882084902)+4.72906984538813
*((Siψ−23.2121158601201)*(( t _SiO2[λ])−0.121307841752057))+2.92834698440594
*(( LT θ−131.246414694454)*(( t _SiO2[λ])−0.121307841752057))+795.397518262681
*((( t _ LT [λ])−0.180166902154725)*(( t _SiO2[λ])−0.121307841752057))+−1810.07736779714
*((( t _SiN−2[λ])−0.0291537442599814)*(( t _SiO2[λ])−0.121307841752057))+−
633.635642829976
*((( t _Ta2O5[λ])−0.0421024373013005)
*(( t _SiO2[λ])−0.121307841752057))+−115.182409805846*((( t _SiO2[λ])−
0.121307841752057)
*(( t _SiO2[λ])−0.121307841752057)−0.0017442053041025)+1.36398286740725
*((Siψ−23.2121158601201)*(( t _SiN−1[λ])−0.263987107029325))+−1.83297695480188
*(( LT θ−131.246414694454)*(( t _SiN−1[λ])−0.263987107029325))+−387.007695236215
*((( t _ LT [λ])−0.180166902154725)*(( t _SiN−1[λ])−0.263987107029325))+456.19886315614
*((( t _SiN−2[λ])−0.0291537442599814)
*(( t _SiN−1[λ])−0.263987107029325))+−1644.59679209231
*((( t _Ta2O5[λ])−0.0421024373013005)*(( t _SiN−1[λ])−0.263987107029325))+
113.144234117703
*((( t _SiO2[λ])−0.121307841752057)*(( t _SiN−1[λ])−0.263987107029325))+
173.438761951382
*((( t _SiN−1[λ])−0.263987107029325)*(( t _SiN[λ])−0.263987107029325)−
0.0132035793109828). Equation 3
17 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (110),
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], and the Siψ are thicknesses and an angle within a range in which a phase derived from Equation 4 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
=(−35.4828976785632)+−565.645491469017
*(( t _SiN−2[λ])−0.0350204955532028)+1015.0372961359
*(( t _Ta2O5[λ])−0.0349996340079728)+144.752343074804
*(( t _SiO2[λ])−0.125000914980053)+−46.0415586945303
*(( t _SiN−1[λ])−0.224927716575792)+1.04686816500004
*((Siψ[deg])−45.0067708523954)+10682.9573639156*((( t _SiN−2[λ])
−0.0350204955532028)
*(( t _SiN−2[λ])−0.0350204955532028)−0.000399831223602513)+−13343.4260197881
*((( t _SiN−2[λ])−0.0350204955532028)
*(( t _Ta2O5[λ])−0.0349996340079728))+14953.0137418577
*((( t _Ta2O5[λ])−0.0349996340079728)
*(( t _Ta2O5[λ])−0.0349996340079728)−0.000400054898669248)+739.132582722994
*((( t _SiN−2[λ])−0.0350204955532028)*(( t _SiO2[λ])−0.125000914980053))+
4235.91445978005
*((( t _Ta2O5[λ])−0.0349996340079728)*(( t _SiO2[λ])−0.125000914980053))+
209.756610061409
*((( t _SiO2[λ])−0.125000914980053)
*(( t _SiO2[λ])−0.125000914980053)−0.00250052611269396)+575.276037855751
*((( t _SiN−2[λ])−0.0350204955532028)
*(( t _SiN−1[λ])−0.224927716575792))+−1900.54066286617
*((( t _Ta2O5[λ])−0.0349996340079728)
*(( t _SiN−1[λ])−0.224927716575792))+−361.044865348212*((( t _SiO2[λ])−
0.125000914980053)
*(( t _SiN−1[λ])−0.224927716575792))+−12.6866065936889*((( t _SiN−1[λ])−
0.224927716575792)
*(( t _SiN−1[λ])−0.224927716575792)−0.0131316741294957)+−15.0286853820076
*((( t _SiN−2[λ])−0.0350204955532028)*((Siψ)−45.0067708523954))+2.30649064625795
*((( t _Ta2O5[λ])−0.0349996340079728)*((Siψ)−45.0067708523954))+−2.93242042531494
*((( t _SiO2[λ])−0.125000914980053)*((Siψ)−45.0067708523954))+0.490207176672433
*((( t _SiN−1[λ])−0.224927716575792)*((Siψ)−45.0067708523954))+0.0236394426428729
*(((Siψ)−45.0067708523954)*((Siψ[deg])−45.0067708523954)−825.841735805153). Equation 4
18 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (110);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], and the Siψ are thicknesses and an angle within a range in which a phase derived from Equation 5 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
=(−21.043074633666)+−607.846047314191
*(( t _SiN−2[λ])−0.0350204955532028)+835.570016969633
*(( t _Ta2O5[λ])−0.0349996340079728)+218.780632745606
*(( t _SiO2[λ])−0.125000914980053)+−72.9770468417362
*(( t _SiN−1[λ])−0.224927716575792)+0.771180072449541
*((Siψ)−45.0067708523954)+9068.29091824635*((( t _SiN−2[λ])−0.0350204955532028)
*(( t _SiN−2[λ])−0.0350204955532028)−0.000399831223602513)+−13159.8293417283
*((( t _SiN−2[λ])−0.0350204955532028)
*(( t _Ta2O5[λ])−0.0349996340079728))+−12965.3688204255
*((( t _Ta2O5[λ])−0.0349996340079728)
*(( t _Ta2O5[λ])−0.0349996340079728)−0.000400054898669248)+−902.346601423572
*((( t _SiN−2[λ])−0.0350204955532028)*(( t _SiO2[λ])−0.125000914980053))+−
104.997375301657
*((( t _Ta2O5[λ])−0.0349996340079728)*(( t _SiO2[λ])−0.125000914980053))+
372.567242377661
*((( t _SiO2[λ])−0.125000914980053)
*(( t _SiO2[λ])−0.125000914980053)−0.00250052611269396)+278.515543336254
*((( t _SiN−2[λ])−0.0350204955532028)
*(( t _SiN−1[λ])−0.224927716575792))+−2340.42700220237
*((( t _Ta2O5[λ])−0.0349996340079728)*(( t _SiN−1[λ])−0.224927716575792))+
58.3334367716085
*((( t _SiO2[λ])−0.125000914980053)*(( t _SiN−1[λ])−0.224927716575792))+
21.2408634563023
*((( t _SiN−1[λ])−0.224927716575792)
*(( t _SiN−1[λ])−0.224927716575792)−0.0131316741294957)+−12.3569961396514
*((( t _SiN−2[λ])−0.0350204955532028)*((Siψ)−45.0067708523954))+6.43899440226174*
((( t _Ta2O5[λ])−0.0349996340079728)*((Siψ)−45.0067708523954))+−4.05208515458274
*((( t _SiO2[λ])−0.125000914980053)*((Siψ)−45.0067708523954))+0.851602997008135
*((( t _SiN−1[λ])−0.224927716575792)*((Siψ)−45.0067708523954))+0.0186630077404119
*(((Siψ)−45.0067708523954)*((Siψ)−45.0067708523954)−825.841735805153). Equation 5
19 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (100);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], and the Siψ are thicknesses and an angle within a range in which a phase derived from Equation 6 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
4.23722010895326+−957.681500681962
*(( t _SiN−2[λ])−0.032371987951807)+585.864572529366
*(( t _Ta2O5[λ])−0.0343161281489591)+−70.8133543143104
*(( t _SiO2[λ])−0.124755271084337)+−16.2945641374395
*(( t _SiN−1[λ])−0.224798055859809)+−0.502977915315552
*(Siψ−25.0116374589266)+8018.80873572765*((( t _SiN−2[λ])−0.032371987951807)
*(( t _SiN−2[λ])−0.032371987951807)−0.000382941581152127)+−9183.68752253472
*((( t _SiN−2[λ])−0.032371987951807)
*(( t _Ta2O5[λ])−0.0343161281489591))+−3967.44233744993
*((( t _Ta2O5[λ])−0.0343161281489591)
*(( t _Ta2O5[λ])−0.0343161281489591)−0.000397417039992328)+−219.740749864906
*((( t _SiN−2[λ])−0.032371987951807)*(( t _SiO2[λ])−0.124755271084337))+
2921.19191101444
*((( t _Ta2O5[λ])−0.0343161281489591)*(( t _SiO2[λ])−0.124755271084337))+
71.8751971324423
*((( t _SiO2[λ])−0.124755271084337)
*(( t _SiO2[λ])−0.124755271084337)−0.00251119250370505)+−277.396742510064
*((( t _SiN−2[λ])−0.032371987951807)*(( t _SiN−1[λ])−0.224798055859809))+−
345.970595680112
*((( t _Ta2O5[λ])−0.0343161281489591)
*(( t _SiN−1[λ])−0.224798055859809))+−178.32292070599*((( t _SiO2[λ])−0.124755271084337)
*(( t _SiN−1[λ])−0.224798055859809))+76.2377854978502*((( t _SiN−1[λ])−
0.224798055859809)
*(( t _SiN−1[λ])−0.224798055859809)−0.0131300933916187)+8.30689126408323
*((( t _SiN−2[λ])−0.032371987951807)*(Siψ−25.0116374589266))+−37.8147686019012
*((( t _Ta2O5[λ])−0.0343161281489591)*(Siψ−25.0116374589266))+−9.06470966220628
*((( t _SiO2[λ])−0.124755271084337)*(Siψ−25.0116374589266))+0.152787017528357
*((( t _SiN−1[λ])−0.224798055859809)*(Siψ−25.0116374589266))+0.0532078049680315
*((Siψ−25.0116374589266)*(Siψ−25.0116374589266)−291.798878808268). Equation 6
20 . The acoustic wave device according to claim 1 , wherein
a plane orientation of the silicon substrate is (100);
both of the first high-acoustic-velocity film and the second high-acoustic-velocity film are SiN films, the first low-acoustic-velocity film is a SiO 2 film, the second low-acoustic-velocity film is a Ta 2 O 5 film, and the piezoelectric film is a LiTaO 3 film; and
a wavelength defined by an electrode finger pitch of the IDT electrode is represented as λ, a thickness of the first high-acoustic-velocity film is defined as t_SiN−1[λ], a thickness of the second high-acoustic-velocity film is defined as t_SiN−2[λ], a thickness of the first low-acoustic-velocity film is defined as t_SiO2[λ], a thickness of the second low-acoustic-velocity film is defined as t_Ta2O5[λ], a thickness of the piezoelectric film is defined as t_LT[λ], and Euler angles of the silicon substrate are defined as (Siφ, Siθ, Siψ), the t_SiN−1[λ], the t_SiN−2[λ], the t_SiO2[λ], the t_Ta2O5[λ], and the Siψ are thicknesses and an angle within a range in which a phase derived from Equation 7 below is equal to or less than about −70 deg:
Phase of spurious wave [deg]
=7.99511640601924+−921.506922121376
*(( t _SiN−2[λ])−0.032371987951807)+586.197692765577
*(( t _Ta2O5[λ])−0.0343161281489591)+−19.6299727359544
*(( t _SiO2[λ])−0.124755271084337)+−38.2671139134079
*(( t _SiN−1[λ])−0.224798055859809)+−0.384667404398566
*(Siψ−25.0116374589266)+7292.21326291196*((( t _SiN−2[λ])−0.032371987951807)
*(( t _SiN−2[λ])−0.032371987951807)−0.000382941581152127)+−8838.66675333011
*((( t _SiN−2[λ])−0.032371987951807)
*(( t _Ta2O5[λ])−0.0343161281489591))+−11789.7264976743
*((( t _Ta2O5[λ])−0.0343161281489591)
*(( t _Ta2O5[λ])−0.0343161281489591)−0.000397417039992328)+−28.4853757228835
*((( t _SiN−2[λ])−0.032371987951807)*(( t _SiO2[λ])−0.124755271084337))+
1749.37647871597
*((( t _Ta2O5[λ])−0.0343161281489591)*(( t _SiO2[λ])−0.124755271084337))+
594.755965541834
*((( t _SiO2[λ])−0.124755271084337)
*(( t _SiO2[λ])−0.124755271084337)−0.00251119250370505)+−486.955268584051
*((( t _SiN−2[λ])−0.032371987951807)*(( t _SiN−1[λ])−0.224798055859809))+−
829.859217960196
*((( t _Ta2O5[λ])−0.0343161281489591)
*(( t _SiN−1[λ]A)−0.224798055859809))+−285.613819272102*((( t _SiO2[λ])−
0.124755271084337)
*(( t _SiN−1[λ])−0.224798055859809))+118.153648828838*((( t _SiN−1[λ])−
0.224798055859809)
*(( t _SiN−1[λ])−0.224798055859809)−0.0131300933916187)+9.20315325922817
*((( t _SiN−2[λ])−0.032371987951807)*(Siψ−25.0116374589266))+−39.0707606971878
*((( t _Ta2O5[λ])−0.0343161281489591)*(Siψ−25.0116374589266))+−6.93828445692585
*((( t _SiO2[λ])−0.124755271084337)*(Siψ−25.0116374589266))+−0.327228438235882
*((( t _SiN−1[λ])−0.224798055859809)*(Siψ−25.0116374589266))+0.0471426960942093
*((Siψ−25.0116374589266)*(Siψ−25.0116374589266)−291.798878808268). Equation 7