Multiplexer, high-frequency front end circuit, and communication device
A multiplexer includes N acoustic wave filters each including one end connected in common and having a different pass band, in which when the N acoustic wave filters are in order from a side of a lower frequency of the pass band, at least one n-th acoustic wave filter among the N acoustic wave filters excluding an acoustic wave filter having the highest frequency of the pass band includes one or more acoustic wave resonators including a support substrate, a silicon nitride film laminated on the support substrate, a silicon oxide film laminated on the silicon nitride film, a piezoelectric body laminated on the silicon oxide film, and an IDT electrode provided on the piezoelectric body. All acoustic wave filters having a pass band in a higher frequency than a frequency of a pass band of the n-th acoustic wave filter satisfy f h1_t (n) >f u (m) or f h1_t (n) <f l (m) .
1. A multiplexer comprising:
N acoustic wave filters each including one end connected in common and having different pass bands, where, N is an integer equal to or greater than 2; wherein
when the N acoustic wave filters include a first acoustic wave filter, a second acoustic wave filter, . . . , and an N-th acoustic wave filter in order from a side of a lower frequency of the pass band, at least one acoustic wave filter n, where 1≤n<N, among the N acoustic wave filters excluding an acoustic wave filter having the highest frequency of the pass band includes one or more acoustic wave resonators;
a t-th acoustic wave resonator among the one or more acoustic wave resonators includes:
a support substrate having Euler angles (φ Si , θ Si , ψ Si ) and made of silicon;
a silicon nitride film on the support substrate;
a silicon oxide film on the silicon nitride film;
a piezoelectric body on the silicon oxide film, having Euler angles (φ LT in a range of about 0° 5 , θ LT , yLT in a range of about 0° 15 ), and made of lithium tantalate; and
an interdigital transducer (IDT) electrode on the piezoelectric body;
when a wavelength determined by an electrode finger pitch of the IDT electrode is denoted as Δ in the t-th acoustic wave resonator, a thickness normalized by the wavelength λ is denoted as a wavelength normalized thickness, when setting values of T LT as a wavelength normalized thickness of the piezoelectric body, θ LT as an Euler angle of the piezoelectric body, T S as a wavelength normalized thickness of the silicon oxide film, T N as a wavelength normalized thickness of the silicon nitride film, T E as a wavelength normalized thickness of the IDT electrode converted to a thickness of aluminum, obtained by a product of a value obtained by dividing a density of the IDT electrode by a density of aluminum and a wavelength normalized thickness of the IDT electrode, ψ Si , as a propagation orientation in the support substrate, and T Si as a wavelength normalized thickness of the support substrate, at least one of frequencies f hs_t (n) of first, second, and third higher-order modes, where, s is 1, 2, or 3, and a case in which s is 1 indicates a frequency of the first higher-order mode, a case in which s is 2 indicates a frequency of the second higher-order mode, and a case in which s is 3 indicates a frequency of the third higher-order mode, determined by an expression (1) and an expression (2) below determined by the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , and all m-th acoustic wave filters, wherein n<m≤N, each having a pass band of a higher frequency than a frequency of a pass band of the n-th acoustic wave filter satisfy an expression (3) or an expression (4) below:
V
=
a
T
(
3
)
(
(
T
+
c
)
3
+
b
(
3
)
)
+
a
T
(
2
)
(
(
T
+
c
)
2
+
b
(
2
)
)
+
a
(
1
)
(
T
+
c
)
+
a
(
2
)
(
(
T
S
+
c
)
2
+
b
(
2
)
)
+
a
T
S
(
1
)
(
T
S
+
c
T
)
+
a
(
2
)
(
(
T
N
+
c
)
2
+
b
(
2
)
)
+
a
T
(
1
)
(
T
N
+
c
T
)
+
a
T
E
(
1
)
(
T
E
+
c
T
E
)
+
a
ψ
(
5
)
(
(
ψ
Si
+
c
ψ
)
5
+
b
(
5
)
)
+
a
ψ
(
4
)
(
(
ψ
Si
+
c
ψ
Si
)
4
+
b
ψ
(
4
)
)
+
a
ψ
Si
(
3
)
(
(
ψ
Si
+
c
ψ
Si
)
3
+
b
ψ
Si
(
3
)
)
+
a
ψ
Si
(
2
)
(
(
ψ
Si
+
c
ψ
)
2
+
b
ψ
Si
(
2
)
)
+
a
ψ
Si
(
1
)
(
ψ
Si
+
c
ψ
Si
)
+
e
;
Expression
(
1
)
f
h
s
_
t
(
n
)
=
V
h
s
_
t
λ
t
(
n
)
,
(
s
=
1
,
2
,
3
)
;
Expression
(
2
)
f
hs
_
t
(
n
)
>
f
u
(
m
)
;
Expression
(
3
)
f
hs
_
t
(
n
)
<
f
l
(
m
)
;
Expression
(
4
)
the f hs_t (n) represents a frequency of a higher-order mode corresponding to the s in the t-th acoustic wave resonator included in n-th the acoustic wave filter;
the λ t (n) is a wavelength determined by the electrode finger pitch of the IDT electrode in the t-th acoustic wave resonator included in the n-th acoustic wave filter;
the f u (m) is a frequency of a high band side end portion of the pass band in each of the m-th acoustic wave filters;
the f l (m) is a frequency of a low band side end portion of the pass band in each of the m-th acoustic wave filters; and
each coefficient in the expression (1) is each value shown in Table 1, Table 2, or Table 3 indicated below for each value of the s and each crystal orientation of the support substrate:
TABLE 1
s = 1,
First
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (3)
0
0
0
a TLT (2)
0
0
0
a TLT (1)
−128.109974
−84.392576
−78.4352
b TLT (3)
0
0
0
b TLT (2)
0
0
0
c TLT
−0.2492038
−0.247604
−0.24838
a TS (2)
0
0
0
a TS (1)
−109.6889
−182.2936559
−485.867
b TS (2)
0
0
0
c TS
−0.249363
−0.2498958
−0.24942
a TN (2)
−337.59528
−198.4171235
−264.804
a TN (1)
−109.08389
38.137636
−20.3216
b TN (2)
−0.0262274
−0.04671597
−0.04389
c TN
−0.29617834
0.369166
−0.34988
a TE (1)
175.4682
13.0363945
0
c TE
−0.14826
−0.14979166
0
a ψSi (5)
0
0
0
a ψSi (4)
0
0.000489723
0.000503
a ψSi (3)
0.0236358
−5.09E−05
0.006871
a ψSi (2)
−0.0357088
−1.01733189
−0.80395
a ψSi (1)
−34.8157175
0
−5.57553
b ψSi (5)
0
0
0
b ψSi (4)
0
−2150682.513
−352545
b ψSi (3)
0
−21460.18941
2095.94
b ψSi (2)
−288.415605
−36.8125
−33.3025
c ψSi
−22.5
−36.8125
−33.3025
e
5251.687898
5092.365583
4851.236
TABLE 2
s = 2,
Second
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (3)
0
0
0
a TLT (2)
2285.602094
3496.38329
−2357.61
a TLT (1)
−538.88053
−1081.86178
−1308.55
b TLT (3)
0
0
0
b TLT (2)
−0.0016565
−0.001741462
−0.00166
c TLT
−0.251442
−0.2501547
−0.2497
a TS (2)
−3421.09725
−4927.3017
−3633.11
a TS (1)
−1054.253
−992.33158
−1006.69
b TS (2)
−0.0016565
−0.2551083
−0.00166
c TS
−0.2514423
0.2551
−0.25019
a TN (2)
1042.56084
−423.87007
−135.325
a TN (1)
159.11219
80.7948
−106.73
b TN (2)
−0.02613905
−0.05219411
−0.0486
c TN
−0.2961538
−0.36996
−0.39884
a TE (1)
−171.153846
−637.391944
−585.696
c TE
0.15
−0.151238
−0.14932
a ψSi (5)
0
0
0
a ψSi (4)
0
−0.00098215
−0.00016
a ψSi (3)
−0.0038938
−0.002109232
−0.00037
a ψSi (2)
−0.00306409
2.25463
0.224668
a ψSi (1)
2.8538478
23.6872514
1.243381
b ψSi (5)
0
0
0
b ψSi (4)
0
−2959279.229
−399785
b ψSi (3)
234.60436
−21928.45828
5.712562
b ψSi (2)
−289.82063
−1407.041187
−535.077
c ψSi
22.78846
−39.1640886
−29.9806
e
5282.98076
5338.606811
5411.395
TABLE 3
s = 3,
Third
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (3)
0
0
0
a TLT (2)
0
0
3595.754
a TLT (1)
−782.3425
−1001.237815
−592.246
b TLT (3)
0
0
0
b TLT (2)
0
0
−0.00164
c TLT
−0.254819
−0.2578947
−0.25367
a TS (2)
−14897.59116
0
0
a TS (1)
−599.8312
−686.9212563
−438.155
b TS (2)
−0.00162005
0
0
c TS
−0.25682
−0.25546558
−0.25562
a TN (2)
0
0
0
a TN (1)
0
125.557557
15.72663
b TN (2)
0
0
0
c TN
0
−0.349392713
−0.40872
a TE (1)
−154.8823
−764.8758717
−290.54
c TE
−0.14819277
−0.15303646
−0.15149
a ψSi (5)
0
0
0
a ψSi (4)
0
0
−0.00073
a ψSi (3)
0.010467682
−0.000286554
−0.00318
a ψSi (2)
−0.196913569
0.67197739
0.969126
a ψSi (1)
−0.3019959
0.197549
0.359421
b ψSi (5)
0
0
0
b ψSi (4)
0
−0.000204665
0
b ψSi (3)
0
−14837.92017
670.2052
b ψSi (2)
−240.3687037
−1590.306348
−525.572
c ψSi
24.4578313
−41.9028
−31.1239
e
5730.906036
5574.008097
5675.837.
2. The multiplexer according to claim 1 , wherein the wavelength normalized thickness T Si of the support substrate satisfies T Si >about 4.
3. The multiplexer according to claim 2 , wherein T Si >about 10 is satisfied.
4. The multiplexer according to claim 3 , wherein T Si >about 20 is satisfied.
5. The multiplexer according to claim 1 , wherein the wavelength normalized thickness of the piezoelectric body is equal to or less than about 3.5λ.
6. The multiplexer according to claim 5 , wherein the wavelength normalized thickness of the piezoelectric body is equal to or less than about 2.5λ.
7. The multiplexer according to claim 5 , wherein the wavelength normalized thickness of the piezoelectric body is equal to or less than about 1.5λ.
8. The multiplexer according to claim 5 , wherein the wavelength normalized thickness of the piezoelectric body is equal to or less than about 0.5λ.
9. The multiplexer according to claim 1 , further comprising:
an antenna terminal to which one ends of the plurality of acoustic wave filters are connected in common; wherein
the multiplexer is a composite filter in which three or more acoustic wave filters are connected in common on a side of the antenna terminal.
10. The multiplexer according to claim 9 , wherein the multiplexer is a composite filter device for carrier aggregation.
11. The multiplexer according to claim 1 , wherein the values of the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , are selected such that the frequencies f hs_t (n) of the first and second higher-order modes satisfy the expression (3) or the expression (4).
12. The multiplexer according to claim 1 , wherein the values of the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , are selected such that the frequencies f hs_t (n) of the first and third higher-order modes satisfy the expression (3) or the expression (4).
13. The multiplexer according to claim 1 , wherein the values of the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , are selected such that the frequencies f hs_t (n) of the second and third higher-order modes satisfy the expression (3) or the expression (4).
14. The multiplexer according to claim 1 , wherein the values of the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , are selected such that all the frequencies f hs_t (n) of the first, second, and third higher-order modes satisfy the expression (3) or the expression (4).
15. The multiplexer according to claim 1 , the multiplexer further comprising:
an antenna terminal to which one ends of the plurality of acoustic wave filters are connected in common; wherein
the acoustic wave resonator satisfying the expression (3) or the expression (4) is an acoustic wave resonator of the one or more acoustic wave resonators which is closest to the antenna terminal.
16. The multiplexer according to claim 1 , wherein all of the one or more acoustic wave resonators are each the acoustic wave resonator satisfying the expression (3) or the expression (4).
17. The multiplexer according to claim 1 , wherein the multiplexer is a duplexer.
18. The multiplexer according to claim 1 , wherein the acoustic wave filter including the one or more acoustic wave resonators is a ladder filter including a plurality of serial arm resonators and a plurality of parallel arm resonators.
19. A multiplexer comprising:
N acoustic wave filters each including one end connected in common and having different pass bands, where, N is an integer equal to or greater than 2; wherein
when the N acoustic wave filters include a first acoustic wave filter, a second acoustic wave filter, and . . . , an N-th acoustic wave filter in order from a side of a lower frequency of the pass band, at least one n-th acoustic wave filter, wherein 1≤n<N, among the N acoustic wave filters excluding an acoustic wave filter having the highest frequency of the pass band includes one or more acoustic wave resonators;
a t-th acoustic wave resonator among the one or more acoustic wave resonators includes:
a support substrate having Euler angles (φ Si , θ Si , ψ Si ) and made of silicon;
a silicon nitride film on the support substrate;
a silicon oxide film on the silicon nitride film;
a piezoelectric body on the silicon oxide film, having Euler angles (φ LT in a range of about 0°±5°, θ LT , ψ LT in a range of about 0°±15°), and made of lithium tantalate; and
an interdigital transducer (IDT) electrode on the piezoelectric body;
when a wavelength determined by an electrode finger pitch of the IDT electrode is denoted as λ in the t-th acoustic wave resonator, a thickness normalized by the wavelength λ is denoted as a wavelength normalized thickness, when setting values of T LT as a wavelength normalized thickness of the piezoelectric body, θ LT as an Euler angle of the piezoelectric body, T S as a wavelength normalized thickness of the silicon oxide film, T N as a wavelength normalized thickness of the silicon nitride film, T E as a wavelength normalized thickness of the IDT electrode converted to a thickness of aluminum, obtained by a product of a value obtained by dividing a density of the IDT electrode by a density of aluminum and a wavelength normalized thickness of the IDT electrode, ψ Si as a propagation orientation in the support substrate, and T Si as a wavelength normalized thickness of the support substrate, at least one of frequencies f hs_t (n) of first, second, and third higher-order modes, where s is 1, 2, or 3, and a case in which s is 1 indicates a frequency of the first higher-order mode, a case in which s is 2 indicates a frequency of the second higher-order mode, and a case in which s is 3 indicates a frequency of the third higher-order mode, determined by an expression (5) and an expression (2) below determined by the T LT , the θ LT , the T S , the T N , the T E , the ψ Si , and the T Si , and all m-th acoustic wave filters (n<m≤N) each having a pass band of a higher frequency than a frequency of a pass band of the n-th acoustic wave filter satisfy an expression (3) or an expression (4)
V
h
=
a
T
LT
(
2
)
(
(
T
LT
-
c
T
)
2
-
b
T
(
2
)
)
+
a
(
1
)
(
T
LT
-
c
T
)
+
a
(
2
)
(
(
T
S
-
c
T
S
)
2
-
b
T
(
2
)
)
+
a
T
S
(
1
)
(
T
S
-
c
T
)
+
a
T
N
(
3
)
(
(
T
N
-
c
T
N
)
3
-
b
T
N
(
3
)
)
+
a
T
N
(
2
)
(
(
T
N
-
c
T
N
)
2
-
b
T
N
(
2
)
)
+
a
T
N
(
1
)
(
T
N
-
c
T
N
)
+
a
T
E
(
1
)
(
T
E
-
c
T
E
)
+
a
ψ
Si
(
4
)
(
(
ψ
Si
-
c
ψ
Si
)
4
-
b
ψ
Si
(
4
)
)
+
a
ψ
Si
(
3
)
(
(
ψ
Si
-
c
ψ
Si
)
3
-
b
ψ
Si
(
3
)
)
+
a
ψ
Si
(
2
)
(
(
ψ
Si
-
c
ψ
)
2
-
b
ψ
(
2
)
)
+
a
ψ
(
1
)
(
ψ
Si
-
c
ψ
Si
)
+
a
θ
LT
(
1
)
(
θ
LT
-
c
θ
LT
)
+
d
T
LT
T
S
(
T
LT
-
c
T
LT
)
(
T
S
-
c
T
)
+
d
(
T
LT
-
c
LT
)
(
T
N
-
c
T
N
)
+
d
(
T
LT
-
c
T
LT
)
(
ψ
Si
-
c
ψ
Si
)
+
d
T
S
T
N
(
T
S
-
c
T
S
)
(
T
N
-
c
T
N
)
+
d
T
N
ψ
Si
(
T
N
-
c
T
N
)
(
ψ
Si
-
c
ψ
Si
)
+
d
T
θ
LT
(
T
N
-
c
T
N
)
(
θ
LT
-
c
θ
LT
)
+
d
T
ψ
Si
(
T
E
-
c
T
E
)
(
ψ
Si
-
c
ψ
Si
)
+
d
(
ψ
Si
-
c
ψ
Si
)
(
θ
LT
-
c
θ
LT
)
+
e
;
Expression
(
5
)
f
h
s
_
t
(
n
)
=
V
h
s
_
t
λ
t
(
n
)
,
(
s
=
1
,
2
,
3
)
;
Expression
(
2
)
f
hs
_
t
(
n
)
>
f
u
(
m
)
;
Expression
(
3
)
f
hs
_
t
(
n
)
<
f
l
(
m
)
;
Expression
(
3
)
the f hs_t (n) represents a frequency of a higher-order mode corresponding to the s in the t-th acoustic wave resonator included in the n-th acoustic wave filter;
the λ t (n) is a wavelength determined by the electrode finger pitch of the IDT electrode in the t-th acoustic wave resonator included in the n-th acoustic wave filter;
the f u (m) is a frequency of a high band side end portion of the pass band in each of the m-th acoustic wave filters;
the f l (m) is a frequency of a low band side end portion of the pass band in each of the m-th acoustic wave filters; and
each coefficient in the expression (5) is each value shown in Table 4, Table 5, or Table 6 below for each value of the s and each crystal orientation of the support substrate:
TABLE 4
s = 1,
First
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (2)
0
0
0
a TLT (1)
0
0
0
b TLT (2)
0
0
0
c TLT
0
0
0
a TS (2)
0
0
0
a TS (1)
0
0
534.5188318
b TS (2)
0
0
0
c TS
0
0
0.249010293
a TN (3)
0
0
0
a TN (2)
0
0
0
a TN (1)
0
0
−36.51741324
b TN (3)
0
0
0
b TN (2)
0
0
0
c TN
0
0
0.35114806
a TE (1)
0
0
0
c TE
0
0
0
a ψSi (4)
0
0
0.000484609
a ψSi (3)
0.022075968
0
0.005818261
a ψSi (2)
−0.18782287
0.081701713
−0.805302371
a ψSi (1)
−33.85785847
10.57201342
−4.785681077
b ψSi (4)
0
0
351437.8188
b ψSi (3)
806.2400011
0
−1862.605341
b ψSi (2)
270.2635345
986.4812738
471.945355
c ψSi
20.26171875
37.73795535
32.87410926
a θLT (1)
0
0
0
c θLT
0
0
0
d TLTTS
0
0
0
d TLTTN
0
0
0
d TLTψSi
0
0
0
d TSTN
0
0
1862.994192
d TNψSi
0
0
0
d TNθLT
0
0
0
d TEψSi
0
0
0
d ψSiθLT
0
0
0
e
5317.859375
5103.813161
4853.204861
TABLE 5
s = 2,
Second
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (2)
0
0
0
a TLT (1)
−608.2898721
−1003.471473
−1270.018362
b TLT (2)
0
0
0
c TLT
0.25
0.253954306
0.249121666
a TS (2)
0
0
0
a TS (1)
−1140.654415
−1030.75867
−1039.830158
b TS (2)
0
0
0
c TS
0.249966079
0.255272408
0.250032531
a TN (3)
−3219.596725
0
2822.963403
a TN (2)
555.8662451
0
−264.9680504
a TN (1)
465.8636149
53.04201209
−288.9461645
b TN (3)
0.001081155
0
0.000392787
b TN (2)
0.04654949
0
0.48934743
c TN
0.378426052
0.376449912
0.392908263
a TE (1)
0
−622.7635558
−614.5885324
c TE
0
0.151274165
0.156815224
a ψSi (4)
0
−0.00096736
−0.000227305
a ψSi (3)
0
−0.006772454
−0.00220017
a ψSi (2)
0
2.203099663
0.31727324
a ψSi (1)
0.833288758
28.15768206
0.648998523
b ψSi (4)
0
2959964.533
396965.3474
b ψSi (3)
0
19143.61126
87.44425969
b ψSi (2)
0
1447.367657
532.0008856
c ψSi
22.51017639
40.50966608
29.90240729
a θLT (1)
−1.501270796
−2.076046604
−2.376979261
c θLT
−52.08683853
−50.82249561
−49.04879636
d TLTTS
0
0
0
d TLTTN
0
0
0
d TLTψSi
0
16.61849238
0
d TSTN
0
1820.795615
1482.11565
d TNψSi
0
3.625908485
−3.131543418
d TNθLT
0
0
1607.412093
d TEψSi
0
0
0
d ψSiθLT
0
0
0.089566113
e
5326.187246
5356.110093
5418.323508
TABLE 6
s = 3,
Third
Higher-
Order
Mode
Si(100)
Si(110)
Si(111)
a TLT (2)
−14710.45271
0
0
a TLT (1)
−764.4056124
−942.2882121
−582.1313356
b TLT (2)
0.001558682
0
0
c TLT
0.257243963
0.255679719
0.251712062
a TS (2)
−21048.18754
0
0
a TS (1)
−508.6730943
−705.5211128
−400.0368899
b TS (2)
0.001583662
0
0
c TS
0.257243963
0.254751848
0.254357977
a TN (3)
0
0
0
a TN (2)
0
0
0
a TN (1)
0
97.59462013
24.94240828
b TN (3)
0
0
0
b TN (2)
0
0
0
c TN
0
0.367793031
0.404280156
a TE (1)
−276.7311066
−747.0884117
0
c TE
0.1494796
0.152164731
0
a ψSi (4)
0
0
−0.00075146
a ψSi (3)
0.011363183
0.003532214
−0.002666357
a ψSi (2)
−0.23320473
0.218669312
1.006728665
a ψSi (1)
0.214067146
−11.24365221
0.523191515
b ψSi (4)
0
0
381500.5075
b ψSi (3)
180.0564368
20914.04622
−493.6094588
b ψSi (2)
257.0498426
1548.182277
530.6814032
c ψSi
22.31890092
39.72544879
30.82490272
a θLT (1)
0
0
−1.551626054
c θLT
0
0
−49.16731518
d TLTTS
−13796.64706
0
1575.283126
d TLTTN
0
0
0
d TLTψSi
30.35701585
0
0
d TSTN
0
0
0
d TNψSi
0
0
0
d TNθLT
0
0
0
d TEψSi
28.27908094
0
0
d ψSiθLT
0
0
−0.086544362
e
5700.075407
5563.854277
5688.418884.