Acoustic wave device, multiplexer, high-frequency front-end circuit, and communication apparatus

Information

  • Patent Grant
  • 10680577
  • Patent Number
    10,680,577
  • Date Filed
    Thursday, September 5, 2019
    5 years ago
  • Date Issued
    Tuesday, June 9, 2020
    4 years ago
Abstract
An acoustic wave device includes a silicon oxide film, a piezoelectric body made of lithium tantalate, and interdigital transducer electrodes stacked on a supporting substrate made of silicon, in which the values of the wave length-normalized film thickness and the Euler angle of the piezoelectric body made of lithium tantalate, the wave length-normalized film thickness of the silicon oxide film, the wave length-normalized film thickness of the interdigital transducer electrodes in terms of aluminum thickness, the propagation direction of the supporting substrate, and the wave length-normalized film thickness of the supporting substrate are set such that represented by Formula (1) for at least one of responses of first, second, and third higher-order modes is more than about −2.4, and TSi>20.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention

The present invention relates to an acoustic wave device, a multiplexer, a high-frequency front-end circuit, and a communication apparatus including a piezoelectric body made of lithium tantalate that is stacked on or above a supporting substrate made of silicon.


2. Description of the Related Art

Multiplexers have been widely used in high-frequency front-end circuits of cellular phones and smartphones. For example, a multiplexer defining and functioning as a splitter described in Japanese Unexamined Patent Application Publication No. 2014-68123 includes two or more band pass filters for different frequencies. Each of the band pass filters is formed of a surface acoustic wave filter chip. The surface acoustic wave filter chip includes multiple surface acoustic wave resonators.


Japanese Unexamined Patent Application Publication No. 2010-187373 discloses an acoustic wave device in which an insulating film made of silicon dioxide and a piezoelectric substrate made of lithium tantalate are stacked on a supporting substrate made of silicon. The heat resistance is increased by bonding the support substrate and the insulating film on a silicon (111) surface.


In the multiplexer as described in Japanese Unexamined Patent Application Publication No. 2014-68123, multiple acoustic wave filters for different frequencies are commonly connected on an antenna terminal side.


The inventors of preferred embodiments of the present invention have discovered that in the case where a structure in which a piezoelectric body made of lithium tantalate is stacked directly or indirectly on a supporting substrate made of silicon is included, multiple higher-order modes appear at higher frequencies than a main mode used. In the case where such an acoustic wave resonator is used for an acoustic wave filter associated with a lower frequency in a multiplexer, ripples due to the higher-order modes of the acoustic wave filter may appear in the pass band of another acoustic wave filter associated with a higher frequency in the multiplexer. That is, when a higher-order mode of the acoustic wave filter associated with a lower frequency in the multiplexer is located in the pass band of another acoustic wave filter associated with a higher frequency in the multiplexer, ripples occur in the pass band. This deteriorates the filter characteristics of another acoustic wave filter.


SUMMARY OF THE INVENTION

Preferred embodiments of the present invention provide acoustic wave devices, multiplexers, high-frequency front-end circuits including multiplexers, and communication apparatus in which ripples due to a higher-order mode are less likely to occur in another acoustic wave filter.


The inventors of preferred embodiments of the present invention have discovered that, as described below, in an acoustic wave device including a piezoelectric body made of lithium tantalate stacked directly or indirectly on a supporting substrate made of silicon, first to third higher-order modes described below appear at higher frequencies than the main mode.


The acoustic wave devices according to preferred embodiments of the present invention reduce or prevent at least one higher-order mode among the first, second, and third higher-order modes.


An acoustic wave device according to a preferred embodiment of the present invention includes a supporting substrate made of silicon, a silicon oxide film stacked on the supporting substrate, a piezoelectric body stacked on the silicon oxide film, the piezoelectric body being made of lithium tantalate, and interdigital transducer electrodes disposed on a main surface of the piezoelectric body, in which a wave length determined by the pitch of electrode fingers of the interdigital transducer electrodes is denoted by λ, the wave length-normalized film thickness of the piezoelectric body is denoted by TLT, the Euler angle θ of the piezoelectric body is denoted by θLT, the wave length-normalized film thickness of the silicon oxide film is denoted by TS, the wave length-normalized film thickness of the interdigital transducer electrodes of the interdigital transducer electrodes in terms of aluminum thickness is denoted by TE, a propagation direction in the supporting substrate is denoted by ψSi, and the wave length-normalized film thickness of the supporting substrate is denoted by TSi, TLT, θLT, TS, TE, and ψSi are set such that Ih represented by Formula (1) for at least one of responses of a first higher-order mode, a second higher-order mode, and a third higher-order mode is more than about −2.4, and TSi>about 20.










I
h

=



a

T
LT


(
2
)




(



(


T
LT

-

c

T
LT



)

2

-

b

T
LT


(
2
)



)


+


a

T
LT


(
1
)




(


T
LT

-

c

T
LT



)


+


a

T
S


(
2
)




(



(


T
S

-

c

T
S



)

2

-

b

T
S


(
2
)



)


+


a

T
S


(
1
)




(


T
S

-

c

T
S



)


+


a

T
E


(
4
)




(



(


T
E

-

c

T
E



)

4

-

b

T
E


(
4
)



)


+


a

T
E


(
3
)




(



(


T
E

-

c

T
E



)

3

-

b

T
E


(
3
)



)


+


a

T
E


(
2
)




(



(


T
E

-

c

T
E



)

2

-

b

T
E


(
2
)



)


+


a

T
E


(
1
)




(


T
E

-

c

T
E



)


+


a

ψ
Si


(
6
)




(



(


ψ
Si

-

c

ψ
Si



)

6

-

b

ψ
Si


(
6
)



)


+


a

ψ
Si


(
5
)




(



(


ψ
Si

-

c

ψ
Si



)

2

-

b

ψ
Si


(
5
)



)


+


a

ψ
Si


(
4
)




(



(


ψ
Si

-

c

ψ
Si



)

2

-

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
Si



)

2

-

b

ψ
Si


(
2
)



)


+


a

ψ
Si


(
1
)




(


ψ
Si

-

c

ψ
Si



)


+


a

θ
LT


(
2
)




(



(


θ
LT

-

c

θ
LT



)

2

-

b

θ
LT


(
2
)



)


+


a

θ
LT


(
1
)




(


θ
LT

-

c

θ
LT



)


+



d


T
LT



T
S





(


T
LT

-

c

T
LT



)




(


T
S

-

c

T
S



)


+



d


T
LT



T
E





(


T
LT

-

c

T
LT



)




(


T
E

-

c

T
E



)


+



d


T
LT



ψ
Si





(


T
LT

-

c

T
LT



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
LT



θ
LT





(


T
LT

-

c

T
LT



)




(


θ
LT

-

c

θ
LT



)


+



d


T
S



T
E





(


T
S

-

c

T
S



)




(


T
E

-

c

T
E



)


+



d


T
S



ψ
Si





(


T
S

-

c

T
S



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
S



θ
LT





(


T
S

-

c

T
S



)




(


θ
LT

-

c

θ
LT



)


+



d


T
E



ψ
Si





(


T
E

-

c

T
E



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
E



θ
LT





(


T
E

-

c

T
E



)




(


θ
LT

-

c

θ
LT



)


+



d


ψ
Si



θ
LT





(


ψ
Si

-

c

ψ
Si



)




(


θ
LT

-

c

θ
LT



)


+
e





Formula






(
1
)








Coefficients a, b, c, d, and e in Formula (1) are values presented in Tables 1 to 36 below in accordance with ranges of orientation of the supporting substrate either of (100), (110), or (111), the type of higher-order mode, the wave length-normalized film thickness of the silicon oxide film, the wave length-normalized film thickness of the piezoelectric body, and the propagation direction in the supporting substrate. In the case where the orientation of the supporting substrate is (100), ψSi is the angle between the propagation direction of an acoustic wave when viewed from the main surface side of the piezoelectric body on which the interdigital transducer electrodes are disposed and the Miller indices of silicon represented by a crystal direction of [100] when viewed from the above-written main surface side. In the case where the orientation of the supporting substrate is (110), ψSi is the angle between the propagation direction of an acoustic wave when viewed from the main surface side of the piezoelectric body on which the interdigital transducer electrodes are disposed and Miller indices of the silicon represented by crystal direction of [1-10] when viewed from the above-written main surface side. In the case where the orientation of the supporting substrate is (111), ψSi is the angle between the propagation direction of an acoustic wave when viewed from the main surface side of the piezoelectric body on which the interdigital transducer electrodes are disposed and Miller indices of the silicon represented by crystal direction of [1-10] when viewed from the above-written main surface side.












TABLE 1









Si(100)




First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
0
0



bTLT(2)
0
0



cTLT
0
0



aTS(2)
0
0



aTS(1)
−5.857231176
−5.857231176



bTS(2)
0
0



cTS
0.148
0.148



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−19.75255913
−19.75255913



aTE(1)
−2.877583447
−2.877583447



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.022736
0.022736



cTE
0.242
0.242



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.004788767
0.004788767



aψSi(1)
0.024306207
0.024306207



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
81.81
81.81



cψSi
8.7
8.7



aθLT(2)
−0.008235936
−0.008235936



aθLT(1)
−0.021048278
−0.021048278



bθLT(2)
65.16
65.16



cθLT
−52.2
−52.2



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
−0.786852571
−0.786852571



dTEψSi
0
0



dTEθLT
−0.237034335
−0.237034335



dψSiθLT
0
0



e
−1.499248378
−1.499248378




















TABLE 2









Si(100)




First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
125.5342427



aTLT(1)
−13.43961051
−7.643409732



bTLT(2)
0
0.006076558



cTLT
0.329807692
0.321186441



aTS(2)
0
0



aTS(1)
−11.80744788
−10.05306878



bTS(2)
0
0



cTS
0.158653846
0.153389831



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
0
−7.595099843



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0
0.366101695



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.003335792
0



aψSi(1)
0.039268266
−0.013700762



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
191.7159763
0



cψSi
13.26923077
16.01694915



aθLT(2)
−0.007476194
0



aθLT(1)
−0.010867175
−0.053997369



bθLT(2)
69.19378698
0



cθLT
−50.19230769
−50.59322034



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.629167148
−0.724576033



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0.521919406



dTSθLT
0
0



dTEψSi
0
−0.523966449



dTEθLT
0
0



dψSiθLT
0
0



e
−2.071831837
−3.228508418




















TABLE 3









Si(100)




First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−15.6141248
−15.6141248



bTLT(2)
0
0



cTLT
0.163309353
0.163309353



aTS(2)
0
0



aTS(1)
−22.02440893
−22.02440893



bTS(2)
0
0



cTS
0.325179856
0.325179856



aTE(4)
0
0



aTE(3)
−248.4374004
−248.4374004



aTE(2)
−36.57127964
−36.57127964



aTE(1)
13.88180854
13.88180854



bTE(4)
0
0



bTE(3)
0.000480119
0.000480119



bTE(2)
0.020416128
0.020416128



cTE
0.240647482
0.240647482



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.002456326
0.002456326



aψSi(1)
0.043553126
0.048553126



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
279.6050929
279.6050929



cψSi
22.3381295
22.3381295



aθLT(2)
0
0



aθLT(1)
0.005427275
0.005427275



bθLT(2)
0
0



cθLT
−50.35971223
−50.35971223



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
41.63149071
41.63149071



dTSψSi
−0.577179204
−0.577179204



dTSθLT
0.603866778
0.603866778



dTEψSi
0.134944598
0.134944598



dTEθLT
0
0



dψSiθLT
0
0



e
−2.703317679
−2.703317679




















TABLE 4









Si(100)




First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
133.7896555



aTLT(1)
−7.761727985
−9.701155851



bTLT(2)
0
0.006281971



cTLT
0.315508021
0.306914894



aTS(2)
0
0



aTS(1)
−20.35135077
−6.186650236



bTS(2)
0
0



cTS
0.297860963
0.298404255



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
110.8304316
0



aTE(1)
4.036561723
−8.229960495



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.006431411
0



cTE
0.140374332
0.363297872



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.002534654
0.001652947



aψSi(1)
0.024168138
−0.003241344



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
269.2484772
266.6845858



cψSi
21.4171123
20.26595745



aθLT(2)
0
0



aθLT(1)
0
−0.066116428



bθLT(2)
0
0



cθLT
−90
−50.4787234



dTLTTS
96.23533718
0



dTLTTE
−66.46866878
0



dTLTψSi
−0.404808481
−0.688053172



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
−0.733337318
0



dTSθLT
0
0



dTEψSi
0.584322518
−0.372994212



dTEθLT
0
0



dψSiθLT
0
0



e
−3.679364607
−4.30794513




















TABLE 5









Si(100)




Second higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−5.687707928
−5.687707928



bTLT(2)
0
0



cTLT
0.139506173
0.139506173



aTS(2)
0
0



aTS(1)
5.653643283
5.653643283



bTS(2)
0
0



cTS
0.148148148
0.148148148



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−1.004369706
−1.004369706



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.255555556
0.255555556



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
−0.000197083
−0.000197083



aψSi(2)
−0.003376583
−0.003376583



aψSi(1)
0.118081927
0.118081927



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
−379.4708632
−379.4708632



bψSi(2)
278.0521262
278.0521262



cψSi
23.14814815
23.14814815



aθLT(2)
0
0



aθLT(1)
0.128631041
0.128631041



bθLT(2)
0
0



cθLT
−49.32098765
−49.32098765



dTLTTS
0
0



dTLTTE
72.43278274
72.43278274



dTLTψSi
0.604747502
0.604747502



dTLTθLT
−1.743618251
−1.743618251



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0.994157261
0.994157261



dTEψSi
0
0



dTEθLT
0.280889881
0.280889881



dψSiθLT
0.003095822
0.003095822



e
−5.638096455
−5.638096455




















TABLE 6









Si(100)




Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
7.809960834
4.249755245



bTLT(2)
0
0



cTLT
0.30962963
0.302857143



aTS(2)
0
0



aTS(1)
0
−0.800874586



bTS(2)
0
0



cTS
0
0.150714286



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−3.563479635
9.07053135



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.148518519
0.353571429



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
−0.000160979
0



aψSi(2)
−0.000757552
0.001332545



aψSi(1)
0.095765615
0.003836714



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
384.7407407
0



bψSi(2)
278.2222222
285.0956633



cψSi
21.33333333
20.89285714



aθLT(2)
0
0



aθLT(1)
0.043185248
0.033521037



bθLT(2)
0
0



cθLT
−50
−50.92857143



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.383208698
−0.220029295



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0
0.974673109



dTEψSi
0
0



dTEθLT
1.01389349
−1.078939399



dψSiθLT
0
0.002899732



e
−5.569590226
−5.29442278




















TABLE 7









Si(100)




Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−11.51287
−11.51287



bTLT(2)
0
0



cTLT
0.136328125
0.136328125



aTS(2)
0
0



aTS(1)
6.022608826
6.022608826



bTS(2)
0
0



cTS
0.305859375
0.305859375



aTE(4)
0
0



aTE(3)
−180.607873
−180.607873



aTE(2)
−1.347493816
−1.347493816



aTE(1)
4.841204365
4.841204365



bTE(4)
0
0



bTE(3)
−0.000227051
−0.000227051



bTE(2)
0.019179688
0.019179688



cTE
0.25625
0.25625



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.001342794
−0.001342794



aψSi(1)
0.25625
0.25625



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
275.7568359
275.7568359



cψSi
0.25625
0.25625



aθLT(2)
0
0



aθLT(1)
0.153688205
0.153688205



bθLT(2)
0
0



cθLT
−49.140625
−49.140625



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
−1.180623763
−1.180623763



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0.41394071
0.41394071



dψSiθLT
0.003203013
0.003203013



e
−4.433641408
−4.433641408




















TABLE 8









Si(100)




Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
119.666412
118.2359738



aTLT(1)
4.447768142
2.271979446



bTLT(2)
0.006371047
0.00699901



cTLT
0.31147541
0.30631068



aTS(2)
0
0



aTS(1)
0
−3.805216895



bTS(2)
0
0



cTS
0
0.298543689



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
117.8354557
121.7109482



aTE(1)
2.107193686
−0.578851453



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.006775956
0.006610661



cTE
0.15
035631068



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.001658706
0



aψSi(1)
0.005677734
0.003834195



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
272.5477022
0



cψSi
20.90163934
20.02427184



aθLT(2)
0
0



aθLT(1)
0.051921544
0.050011808



bθLT(2)
0
0



cθLT
−48.36065574
−48.93203883



dTLTTS
0
0



dTLTTE
61.26575286
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
−82.22932804



dTSψSi
0
0



dTSθLT
0
−0.470524678



dTEψSi
0
0



dTEθLT
0.904198722
−0.776132158



dψSiθLT
0.003410501
0.003906326



e
−5.339814906
−5.463687811




















TABLE 9









Si(100)




Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−16.39135605
−16.39135605



bTLT(2)
0
0



cTLT
0.196774194
0.196774194



aTS(2)
0
0



aTS(1)
−4.824831305
−4.824831305



bTS(2)
0
0



cTS
0.170967742
0.170967742



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−45.57608817
−45.57608817



aTE(1)
−10.80005563
−10.80005563



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.018296046
0.018296046



cTE
0.303225806
0.303225806



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000172048
0.000172048



aψSi(2)
−0.00384923
−0.00384923



aψSi(1)
−0.009826773
−0.009826773



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
143.0843208
143.0843208



bψSi(2)
215.8688866
215.8688866



cψSi
22.25806452
22.25806452



aθLT(2)
0
0



aθLT(1)
0.066799879
0.066799879



bθLT(2)
0
0



cθLT
−50.16129032
−50.16129032



dTLTTS
0
0



dTLTTE
−112.847682
−112.847682



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
−1.750763196
−1.750763196



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0.466692151
0.466692151



dψSiθLT
0
0



e
−2.904746788
−2.904746788




















TABLE 10









Si(100)




Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−8.135537689
−8.135537689



bTLT(2)
0
0



cTLT
0.311659193
0.311659193



aTS(2)
0
0



aTS(1)
−20.38200282
−20.38200282



bTS(2)
0
0



cTS
0.149327354
0.149327354



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−3.460675692
−3.460675692



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.267488789
0.267488789



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.003759233
−0.003759233



aψSi(1)
0.015931998
0.015931998



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
239.0395946
239.0395946



cψSi
18.90134529
18.90134529



aθLT(2)
0
0



aθLT(1)
0.017576249
0.017576249



bθLT(2)
0
0



cθLT
−49.9103139
−49.9103139



dTLTTS
−152.1817236
−152.1817236



dTLTTE
0
0



dTLTψSi
−0.359387178
−0.359387178



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0.911415415
0.911415415



dTEψSi
0
0



dTEθLT
0.275815872
0.275815872



dψSiθLT
0
0



e
−3.952626598
−3.952626598




















TABLE 11









Si(100)




Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−26.36951471
−26.36951471



bTLT(2)
0
0



cTLT
0.161538462
0.161538462



aTS(2)
0
0



aTS(1)
−10.09828536
−10.09828536



bTS(2)
0
0



cTS
0.321025641
0.321025641



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−21.38297597
−21.38297597



aTE(1)
−2.383287449
−2.383287449



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.01947666
0.01947666



cTE
0.270512821
0.270512821



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000176024
0.000176024



aψSi(2)
−0.001397911
−0.001397911



aψSi(1)
−0.107515297
−0.107515297



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
−282.3623122
−282.3623122



bψSi(2)
255.2071006
255.2071006



cψSi
23.84615385
23.84615385



aθLT(2)
0
0



aθLT(1)
0.085112984
0.085112984



bθLT(2)
0
0



cθLT
−48.97435897
−48.97435897



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.816828716
−0.816828716



dTLTθLT
0.865519967
0.865519967



dTSTE
0
0



dTSψSi
−0.538336559
−0.538336559



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0
0



dψSiθLT
0.002971652
0.002971652



e
−3.504362202
−3.504362202




















TABLE 12









Si(100)




Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−6.371850196
−6.371850196



bTLT(2)
0
0



cTLT
0.292192192
0.292192192



aTS(2)
0
0



aTS(1)
−0.609606885
−0.609606885



bTS(2)
0
0



cTS
0.2996997
0.2996997



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
0
0



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0
0



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000224133
0.000224133



aψSi(2)
−0.004048532
−0.004048532



aψSi(1)
−0.126847922
−0.126847922



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
1375.85979
1375.85979



bψSi(2)
281.2555799
281.2555799



cψSi
19.77477477
19.77477477



aθLT(2)
0
0



aθLT(1)
0.056146223
0.056146223



bθLT(2)
0
0



cθLT
−49.48948949
−49.48948949



dTLTTS
94.47145497
94.47145497



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
−0.568942451
−0.568942451



dTEψSi
0
0



dTEθLT
0
0



dψSiθLT
0.005654813
0.005654813



e
−4.940340284
−4.940340284



















TABLE 13









Si(110)



First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−16.69742899
−16.69742899
−33.56520202
0


bTLT(2)
0
0
0
0


cTLT
0.1675
0.1675
0.192857143
0


aTS(2)
0
0
0
0


aTS(1)
15.90196012
15.90196012
0
0


bTS(2)
0
0
0
0


cTS
0.1525
0.1525
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
26.3030303
0


aTE(1)
0
0
−6.181053391
0


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.006326531
0


cTE
0
0
0.378571429
0


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
−0.000183963
−0.000183963
0
−0.000177142


aψSi(2)
−0.003236307
−0.003236307
0
0.002186084


aψSi(1)
0.071460688
0.071460688
0.085067773
0.13561432


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
−5768.71875
−5768.71875
0
2642.857143


bψSi(2)
399.9375
399.9375
0
500


cψSi
65.25
65.25
34.28571429
55


aθLT(2)
0
0
0
−0.005336622


aθLT(1)
0
0
0.070255628
0.032718563


bθLT(2)
0
0
0
65.75963719


cθLT
−90
−90
−51.42857143
−50.95238095


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
1.873870705
1.873870705
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0.716151515
0


dψSiθLT
0
0
−0.00729303
0.002110378


e
−0.957101918
−0.957101918
−1.634922542
−1.290881853


















TABLE 14









Si(110)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−23.96596978
−4.695531045
−7.344438725
−5.603099398


bTLT(2)
0
0
0
0


cTLT
0.34
0.3296875
0.338983051
0.306666667


aTS(2)
0
0
0
0


aTS(1)
−23.18485905
0
0
0


bTS(2)
0
0
0
0


cTS
0.175555556
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−43.48595551
−70.50554427
−41.95412638


aTE(1)
0
−2.467954545
−5.460437635
−2.19025056


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006875
0.006716461
0.006819556


cTE
0
0.15
0.365254237
0.360666667


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0.000119479
−0.000172812


aψSi(2)
0.018474062
0
0.003987724
0.002213009


aψSi(1)
0.059131688
0
−0.047908658
0.073831446


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
−2384.203107
1647.952


bψSi(2)
81.55555556
0
216.791152
242.24


cψSi
35.33333333
0
30.76271186
62.6


aθLT(2)
0
0
0
0


aθLT(1)
0.009475371
0
0.026725166
0


bθLT(2)
0
0
0
0


cθLT
−49.33333333
−90
−49.83050847
−90


dTLTTS
0
0
0
0


dTLTTE
0
0
0
42.3018696


dTLTψSi
0
0
0
0


dTLTθLT
0.617240199
0
0
0


dTSTE
0
0
0
0


dTSψSi
2.612107038
0
0
0


dTSθLT
2.129359248
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0.871101002
0
0
0


e
−2.851861362
−2.210765625
−2.573237288
−2.440604203


















TABLE 15









Si(110)



First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−10.87353735
−17.74612134
−16.74814911
−16.74814911


bTLT(2)
0
0
0
0


cTLT
0.167045455
0.158227848
0.168032787
0.168032787


aTS(2)
92.14417413
275.6432031
0
0


aTS(1)
−6.141913324
−0.713377524
−9.071522271
−9.071522271


bTS(2)
0.004213585
0.004749239
0
0


cTS
0.339772727
0.317721519
0.314754098
0.314754098


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−37.82699975
0
0
0


aTE(1)
4.315324766
3.259148162
−5.270739047
−5.270739047


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.007147469
0
0
0


cTE
0.153409091
0.138607595
0.356557377
0.356557377


aψSi(6)
0
0
−3.73552E−09
−3.73552E−09


aψSi(5)
0
0
−4.69013E−08
−4.69013E−08


aψSi(4)
0
0
1.07773E−05
1.07773E−05


aψSi(3)
0.000254041
−0.000266841
5.64997E−05
5.64997E−05


aψSi(2)
0.00704637
0.003350583
−0.007526984
−0.007526984


aψSi(1)
−0.123432463
0.05687546
−0.035719404
−0.035719404


bψSi(6)
0
0
1801696668
1801696668


bψSi(5)
0
0
6726299.443
6726299.443


bψSi(4)
0
0
1035415.498
1035415.498


bψSi(3)
−1197.310014
2539.305207
3573.665857
3573.665857


bψSi(2)
188.2457386
286.0358917
720.1088417
720.1088417


cψSi
28.125
63.60759494
48.19672131
48.19672131


aθLT(2)
0
0
0
0


aθLT(1)
0.046748629
0.00460971
0
0


bθLT(2)
0
0
0
0


cθLT
−51.59090909
−50.75949367
−90
−90


dTLTTS
0
0
0
0


dTLTTE
0
105.3055279
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
58.63016883
0
0
0


dTSψSi
0.443510572
0.274149566
0
0


dTSθLT
0
0
0
0


dTEψSi
0.293912516
−0.280924747
0
0


dTEθLT
0
0.457718571
0
0


dψSiθLT
0
−0.005165328
0
0


e
−1.722804167
−2.484892701
−2.976959016
−2.976959016


















TABLE 16









Si(110)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
39.48011293


aTLT(1)
−5.239160454
−5.820942031
−4.867344296
−2.496300587


bTLT(2)
0
0
0
0.00654321


cTLT
0.309375
0.302702703
0.286363636
0.288888889


aTS(2)
24.40391167
40.38499201
0
40.45660337


aTS(1)
−2.128595361
−6.73354721
−3.626479228
−6.290401812


bTS(2)
0.006013184
0.005624543
0
0.005617284


cTS
0.3265625
0.275675676
0.31
0.272222222


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−51.46488975
0
0


aTE(1)
−1.921891837
−0.509929613
−1.508039016
−0.870147512


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006479182
0
0


cTE
0.153125
0.147297297
0.341818182
0.351388889


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
−0.000165117
0
−9.55404E−05


aψSi(2)
0.000936051
0.00475603
0
0.002198207


aψSi(1)
−0.02141106
0.040196571
−0.017752634
0.036260775


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
2115.829763
0
1531.394676


bψSi(2)
246.9177246
196.5668371
0
199.8263889


cψSi
24.140625
57.97297297
21.13636364
60.41666667


aθLT(2)
0
0
0
−0.003220943


aθLT(1)
0.023743346
0.023741003
0.038368027
0.005042496


bθLT(2)
0
0
0
72.22222222


cθLT
−50.078125
−48.51351351
−50.81818182
−50


dTLTTS
0
0
0
−43.45862557


dTLTTE
−35.16960363
−48.00382984
23.6423037
52.46703277


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0.234382842
0
0
−0.273892853


dψSiθLT
0
−0.00130658
−0.001221935
0


e
−2.175330984
−2.239116787
−2.271294054
−2.496300587


















TABLE 17









Si(110)



Second higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−7.587457615
−7.587457615
−7.587457615
−7.587457615


bTLT(2)
0
0
0
0


cTLT
0.174380165
0.174380165
0.174380165
0.174380165


aTS(2)
0
0
0
0


aTS(1)
−3.979714537
−3.979714537
−3.979714537
−3.979714537


bTS(2)
0
0
0
0


cTS
0.150413223
0.150413223
0.150413223
0.150413223


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−0.865040993
−0.865040993
−0.865040993
−0.865040993


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.245867769
0.245867769
0.245867769
0.245867769


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
5.87537E−07
5.87537E−07
5.87537E−07
5.87537E−07


aψSi(3)
−8.59015E−07
−8.59015E−07
−8.59015E−07
−8.59015E−07


aψSi(2)
−0.001948222
−0.001948222
−0.001948222
−0.001948222


aψSi(1)
−0.027558032
−0.027558032
−0.027558032
−0.027558032


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
1129197.497
1129197.497
1129197.497
1129197.497


bψSi(3)
−1524.372996
−1524.372996
−1524.372996
−1524.372996


bψSi(2)
776.3813947
776.3843947
776.3813947
776.3813947


cψSi
41.52892562
41.52892562
41.52892562
41.52892562


aθLT(2)
0
0
0
0


aθLT(1)
0.018744549
0.018744549
0.018744549
0.018744549


bθLT(2)
0
0
0
0


cθLT
−49.25619835
−49.25619835
−49.25619835
−49.25619835


dTLTTS
140.6234074
140.6234074
140.6234074
140.6234074


dTLTTE
−25.20654793
−25.20654793
−25.20654793
−25.20654793


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−1.789519626
−1.789519626
−1.789519626
−1.789519626


















TABLE 18









Si(110)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
39.68139696
39.68139696


aTLT(1)
−3.912934705
−3.912934705
−3.801935963
−3.801935963


bTLT(2)
0
0
0.00692398
0.00692398


cTLT
0.306451613
0.306451613
0.297857143
0.297857143


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
1.912614784
1.912614784
−6.089810932
−6.089810932


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.148924731
0.148924731
0.347857143
0.347857143


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
8.78847E−06
8.78847E−06


aψSi(2)
−0.0004718
−0.0004718
−0.000160567
−0.000160567


aψSi(1)
0.003265633
0.003265633
−0.023574651
−0.023574651


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
2351.597668
2351.597668


bψSi(2)
847.4765869
847.4765869
880.2091837
880.2091837


cψSi
35.32258065
35.32258065
43.07142857
43.07142857


aθLT(2)
0.005014741
0.005014741
0
0


aθLT(1)
0.023115164
0.023115164
0.030121011
0.030121011


bθLT(2)
67.0626662
67.0626662
0
0


cθLT
−49.62365591
−49.62365591
−51.28571429
−51.28571429


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0.125572529
0.125572529


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0.563162206
0.563162206
−0.417002414
−0.417002414


dψSiθLT
0
0
0
0


e
−2.002512986
−2.002512986
−2.550158637
−2.550158637


















TABLE 19









Si(110)



Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
2.992014692
2.992014692
−1.461725087
−1.461725087


bTLT(2)
0
0
0
0


cTLT
0.156390977
0.156390977
0.155345912
0.155345912


aTS(2)
0
0
0
0


aTS(1)
−9.089925228
−9.089925228
−1.247751383
−1.247751383


bTS(2)
0
0
0
0


cTS
0.305263158
0.305263158
0.327672956
0.327672956


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
−130.6388144
−130.6388144


aTE(1)
5.773590917
5.773590917
−0.010504162
−0.010504162


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.006662711
0.006662711


cTE
0.166541353
0.166541353
0.341823899
0.341823899


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
1.03604E−05
1.03604E−05


aψSi(2)
−0.000377109
−0.000377109
−0.000138558
−0.000138558


aψSi(1)
−0.013702515
−0.013702515
−0.028102653
−0.028102653


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
3096.349671
3096.349671


bψSi(2)
792.2381141
792.2381141
957.6361695
957.6361695


cψSi
41.39097744
41.39097744
43.20754717
43.20754717


aθLT(2)
0
0
0
0


aθLT(1)
0.015804666
0.015804666
0.028892246
0.028892246


bθLT(2)
0
0
0
0


cθLT
−49.32330827
−49.32330827
−49.62264151
−49.62264151


dTLTTS
0
0
−44.5976835
−44.5976835


dTLTTE
80.90186655
80.90186655
−150.2428298
−150.2428298


dTLTψSi
0
0
0.225109644
0.225109644


dTLTθLT
0
0
0
0


dTSTE
29.68261053
29.68261053
47.35851038
47.35851038


dTSψSi
0.136750854
0.136750854
0
0


dTSθLT
0
0
0
0


dTEψSi
−0.146211814
−0.146211814
0
0


dTEθLT
0.41229257
0.41229257
0
0


dψSiθLT
0
0
0
0


e
−2.596813807
−2.596813807
−2.049341112
−2.049341112


















TABLE 20









Si(110)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−2.80791074
−2.80791074
0
0


bTLT(2)
0
0
0
0


cTLT
0.3069869
0.3069869
0
0


aTS(2)
0
0
0
0


aTS(1)
−5.618098986
−5.618098986
0
0


bTS(2)
0
0
0
0


cTS
0.286462882
0.286462882
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
−73.23839461
−73.23839461


aTE(1)
8.962154821
8.962154821
−5.710295136
−5.710295136


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.007310763
0.007310763


cTE
0.167467249
0.167467249
0.330930233
0.330930233


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
0.003677309
0.003677309
0
0


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
40.93886463
40.93886463
0
0


aθLT(2)
0.00527863
0.00527863
0
0


aθLT(1)
0.008431458
0.008431458
0
0


bθLT(2)
66.00179249
66.00179249
0
0


cθLT
−50.61135371
−50.61135371
−90
−90


dTLTTS
63.6265441
63.6265441
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
57.20229582
57.20229582
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
−0.098212695
−0.098212695
0
0


dTEθLT
0.32576925
0.32576925
0
0


dψSiθLT
0
0
0
0


e
−2.431352404
−2.431352404
−2.39032093
−2.39032093


















TABLE 21









Si(110)



Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−11.04825287
−11.04825287
−11.04825287
−11.04825287


bTLT(2)
0
0
0
0


cTLT
0.164705882
0.164705882
0.164705882
0.164705882


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−12.86806521
−12.86806521
−12.86806521
−12.86806521


aTE(1)
39.88235294
39.88235294
39.88235294
39.88235294


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.019258131
0.019258131
0.019258131
0.019258131


cTE
0.286470588
0.286470588
0.286470588
0.286470588


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.000762445
−0.000762445
−0.000762445
−0.000762445


aψSi(1)
−0.031584918
−0.031584918
−0.031584918
−0.031584918


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
749.7716263
749.7716263
749.7716263
749.7716263


cψSi
52.58823529
52.58823529
52.58823529
52.58823529


aθLT(2)
−0.004115091
−0.004115091
−0.004115091
−0.004115091


aθLT(1)
0.023260981
0.023260981
0.023260981
0.023260981


bθLT(2)
81.16252976
81.16262976
81.16262976
81.16262976


cθLT
−50.11764706
−50.11764706
−50.11764706
−50.11764706


dTLTTS
0
0
0
0


dTLTTE
−32.35244505
−32.35244505
−32.35244505
−32.35244505


dTLTψSi
0.348515389
0.348515389
0.348515389
0.348515389


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0.000823202
0.000823202
0.000823202
0.000823202


e
−1.678155024
−1.678155024
−1.678155024
−1.678155024


















TABLE 22









Si(110)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
34.01092867
34.01092867


aTLT(1)
−3.294448859
−3.294448859
−2.996122319
−2.996122319


bTLT(2)
0
0
0.005572031
0.005572031


cTLT
0.328378378
0.328378378
0.31344086
0.31344086


aTS(2)
0
0
0
0


aTS(1)
2.752851676
2.752851676
−1.564359965
−1.564359965


bTS(2)
0
0
0
0


cTS
0.162837838
0.162837838
0.160752688
0.160752688


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−4.548790211
−4.548790211
−1.370514553
−1.370514553


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.165540541
0.165540541
0.355913978
0.355913978


aψSi(6)
0
0
0
0


aψSi(5)
−7.03888E−08
−7.03888E−08
−3.78178E−08
−3.78178E−08


aψSi(4)
  1.4265E−06
  1.4265E−06
9.79065E−07
9.79065E−07


aψSi(3)
0.000180358
0.000180358
9.73597E−05
9.73597E−05


aψSi(2)
−0.002681874
−0.002681874
−0.00192926
−0.00192926


aψSi(1)
−0.092266284
−0.092266284
−0.04329175
−0.04329175


bψSi(6)
0
0
0
0


bψSi(5)
11701030.08
11701030.08
24265475.25
24265475.25


bψSi(4)
1439156.296
1439156.296
1705613.393
1705613.393


bψSi(3)
1798.436559
1798.436559
6938.899332
6938.899332


bψSi(2)
930.5183985
930.5183985
1060.880593
1060.880593


cψSi
40.23648649
40.23648649
40.08064516
40.08064516


aθLT(2)
0
0
0
0


aθLT(1)
0.046000242
0.046000242
0.001380272
0.001380272


bθLT(2)
0
0
0
0


cθLT
−49.52702703
−49.52702703
−50.05376344
−50.05376344


dTLTTS
−136.9978702
−136.9978702
−73.06084164
−73.06084164


dTLTTE
0
0
0
0


dTLTψSi
0
0
0.096651605
0.096651605


dTLTθLT
0
0
0
0


dTSTE
0
0
−56.78924979
−56.78924979


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.081014811
0.081014811
0
0


dTEθLT
0
0
−0.194432704
−0.194432704


dψSiθLT
0
0
0.000875955
0.000875955


e
−2.543790382
−2.543790382
−2.964933907
−2.964933907


















TABLE 23









Si(110)



Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−13.1565646
−13.1565646
−13.1565646
−13.1565646


bTLT(2)
0
0
0
0


cTLT
0.179661017
0.179661017
0.179661017
0.179661017


aTS(2)
−54.97015257
−54.97015257
−54.97015257
−54.97015257


aTS(1)
1.195559996
1.195559996
1.195559996
1.195559996


bTS(2)
0.006496856
0.006496856
0.006496856
0.006496856


cTS
0.299435028
0.299435028
0.299435028
0.299435028


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−12.83875925
−12.83875925
−12.83875925
−12.83875925


aTE(1)
−2.591177902
−2.591177902
−2.591177902
−2.591177902


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.02062115
0.02062115
0.02062115
0.02062115


cTE
0.282768362
0.282768362
0.282768362
0.282768362


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.00094978
−0.00094978
−0.00094978
−0.00094978


aψSi(1)
−0.016861509
−0.016861509
−0.016861509
−0.016861509


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
−0.00094978
−0.00094978
−0.00094978
−0.00094978


cψSi
44.83050847
44.83050847
44.83050847
44.83050847


aθLT(2)
0
0
0
0


aθLT(1)
0.020120147
0.020120147
0.020120147
0.020120147


bθLT(2)
0
0
0
0


cθLT
−50.50847458
−50.50847458
−50.50847458
−50.50847458


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0.250474306
0.250474306
0.250474306
0.250474306


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.031071552
0.031071552
0.031071552
0.031071552


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−1.687640015
−1.687640015
−1.687640015
−1.687640015


















TABLE 24









Si(110)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−8.387315737
−8.387315737
−11.34973266
−6.017883428


bTLT(2)
0
0
0
0


cTLT
0.313377926
0.313377926
0.291082803
0.294578313


aTS(2)
0
0
0
0


aTS(1)
0.140898252
0.140898252
3.107378473
2.287606243


bTS(2)
0
0
0
0


cTS
0.299331104
0.299331104
0.277707006
0.296385542


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−1.209727849
−1.209727849
−4.259242642
−1.280235687


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.152006689
0.152006689
0.343630573
0.351204819


aψSi(6)
0
0
0
0


aψSi(5)
−2.33027E−08
−2.33027E−08
0
0


aψSi(4)
7.78115E−07
7.78115E−07
0
0


aψSi(3)
5.59108E−05
5.59108E−05
−0.000194818
0


aψSi(2)
−0.002410767
−0.002410767
0.000247924
0


aψSi(1)
−0.027662563
−0.027662563
0.12904143
−0.026766472


bψSi(6)
0
0
0
0


bψSi(5)
2083705.649
2083705.649
0
0


bψSi(4)
1386257.115
1386257.115
0
0


bψSi(3)
−1267.413434
−1267.413434
1811.750092
0


bψSi(2)
895.5856198
895.5856198
293.105197
0


cψSi
42.14046823
42.14046823
19.39490446
67.95180723


aθLT(2)
0
0
0
0


aθLT(1)
0.020067585
0.020067585
−0.011988832
0.032566601


bθLT(2)
0
0
0
0


cθLT
−49.73244147
−49.73244147
−49.61783439
−50.96385542


dTLTTS
0
0
0
0


dTLTTE
0
0
0
41.29194486


dTLTψSi
0
0
−0.203585177
0.376861254


dTLTθLT
0
0
−0.273779971
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
−0.20937463


dTSθLT
−0.349110894
−0.349110894
0
0


dTEψSi
0
0
0
0


dTEθLT
−0.216865482
−0.216865482
0
0


dψSiθLT
0
0
0.00120304
0


e
−2.390757235
−2.390757235
−2.548464154
−2.523994879


















TABLE 25









Si(111)



First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
16.07631847
20.22733656
30.72650306
27.83979251


bTLT(2)
0
0
0
0


cTLT
0.145833333
0.1625
0.159574468
0.158695652


aTS(2)
0
0
0
0


aTS(1)
17.08812597
27.84866827
31.28009383
12.67453621


bTS(2)
0
0
0
0


cTS
0.154166667
0.172916667
0.161702128
0.163043478


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−96.15629371
0
138.3065683
0


aTE(1)
−1.263589744
2.883915191
−9.345807167
−7.807789594


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.006649306
0
0.006229063
0


cTE
0.170833333
0.14375
0.369148936
0.345652174


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
−0.006862727


aψSi(1)
−0.101535567
−0.012511908
−0.101466433
0.176438509


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
114.9456522


cψSi
24.375
44.375
22.0212766
37.5


aθLT(2)
0
0
0
0


aθLT(1)
0
0
0
0


bθLT(2)
0
0
0
0


cθLT
−90
−90
−90
−90


dTLTTS
−477.9162005
−760.9473336
−1054.386561
−1044.340968


dTLTTE
0
0
0
0


dTLTψSi
0
1.332405924
0
0


dTLTθLT
0
0
0
0


dTSTE
0
−250.1524613
102.33575
105.8611165


dTSψSi
0
0
0
−2.093429604


dTSθLT
0
0
0
0


dTEψSi
−0.613440559
0
1.201832187
−0.525734733


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−0.55329028
−1.074792989
−1.290770348
−1.165057152


















TABLE 26









Si(111)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
−262.3995984
−262.3995984
0
0


aTLT(1)
−59.70400634
−59.70400634
−18.45032018
−20.44479246


bTLT(2)
0.004691358
0.004691358
0
0


cTLT
0.355555556
0.355555556
0.332352941
0.331914894


aTS(2)
0
0
0
0


aTS(1)
−73.33869606
−73.33869606
−9.963926388
−24.5747574


bTS(2)
0
0
0
0


cTS
0.185185185
0.185185185
0.166176471
0.165957447


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−19.84024877
−19.84024877
−8.905455835
−17.17093947


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.157407407
0.157407407
0.369117647
0.373404255


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
−4.69771E−05
−4.69771E−05
0
0


aψSi(3)
−0.000362538
−0.000362538
0
0


aψSi(2)
0.055133453
0.055133453
−0.004320224
0.021125116


aψSi(1)
0.020862911
0.020862911
−0.110606012
−0.064218508


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
138552.1512
138552.1512
0
0


bψSi(3)
−78.36076818
−78.36076818
0
0


bψSi(2)
203.1635802
203.1635802
145.9775087
66.20642825


cψSi
33.05555556
33.05555556
19.41176471
34.46808511


aθLT(2)
0
0
0
0


aθLT(1)
−0.079155699
−0.079155699
0
0.057672719


bθLT(2)
0
0
0
0


cθLT
−49.81481481
−49.81481481
−90
−49.14893617


dTLTTS
0
0
0
0


dTLTTE
−254.5809235
−254.5809235
80.69948416
99.56817027


dTLTψSi
2.260189055
2.260189055
0
0


dTLTθLT
−0.785540829
−0.785540829
0
0


dTSTE
−292.5762951
−292.5762951
0
0


dTSψSi
−5.914103654
−5.914103654
−1.139436429
0


dTSθLT
0
0
0
0


dTEψSi
1.75463008
1.75463008
0.660099875
−3.844659844


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0.006965097


e
−1.304804416
−1.304804416
−2.734683251
−3.115044468


















TABLE 27









Si(111)



First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0.003649147
0
0
0


aTLT(1)
−17.27824731
−24.3903101
−38.65647339
−21.91795924


bTLT(2)
67.18624026
0
0
0


cTLT
0.154098361
0.15631068
0.17
0.1575


aTS(2)
84.63185118
0
148.7691928
140.0125491


aTS(1)
−6.307527081
−32.68184816
−15.38083251
−11.91949736


bTS(2)
0.004461166
0
0.005012245
0.004623438


cTS
0.352459016
0.345631068
0.331428571
0.33875


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
2.909874306
8.840975559
−16.54803788
−0.024546617


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.135245902
0.148058252
0.372857143
0.33125


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0.006216698
0
0


aψSi(1)
−0.068574135
−0.018885558
−0.187578295
0.122573316


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
147.1439344
0
0


cψSi
22.62295082
43.10679612
22.71428571
39.1875


aθLT(2)
0
0
0
0


aθLT(1)
0.023219728
0.047846607
0.097088558
0.096327065


bθLT(2)
0
0
0
0


cθLT
−50.16393443
−50.38834951
−50.42857143
−51.25


dTLTTS
0
−144.763071
0
0


dTLTTE
0
0
−161.2345526
0


dTLTψSi
−0.827435588
0
0
1.107475984


dTLTθLT
0
0
0
0


dTSTE
0
103.0553675
−65.68497311
0


dTSψSi
0
−1.329400713
0.82928215
−0.646921162


dTSθLT
0
0
0
0


dTEψSi
−0.681669875
0.653050787
0.676734069
0.936807034


dTEθLT
0
0
0.481989709
0.52746173


dψSiθLT
0
0
0
0


e
−1.560056382
−2.656750279
−2.259351603
−1.805786084


















TABLE 28









Si(111)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
77.3065693
243.6937004
0


aTLT(1)
−13.49335267
−9.878165228
−6.309863061
−12.90130633


bTLT(2)
0
0.00674795
0.006522811
0


cTLT
0.300961538
0.297350993
0.29858156
0.306818182


aTS(2)
133.2691939
160.4037443
82.71737336
100.5491122


aTS(1)
−9.215218873
−21.20902158
−9.283157312
−7.984268054


bTS(2)
0.006618898
0.005353274
0.006382979
0.005704201


cTS
0.314423077
0.303311258
0.3
0.311363636


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
90.39669198
0
0


aTE(1)
0.170720276
3.925569914
−15.08313602
−9.451928755


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006615499
0
0


cTE
0.15
0.147350993
0.363475177
0.346212121


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.00740803
0
0
0


aψSi(1)
−0.220502432
0.083594751
−0.104344279
0.088096624


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
135.4659763
0
0
0


cψSi
20.76923077
43.70860927
17.87234043
41.47727273


aθLT(2)
0
0
0
0


aθLT(1)
−0.017420386
−0.012240534
0
0


bθLT(2)
0
0
0
0


cθLT
−50.28846154
−50.26490066
−90
−90


dTLTTS
149.298265
220.9283416
135.5319056
135.1493422


dTLTTE
0
0
0
−65.38520659


dTLTψSi
0
0
0
−0.663828772


dTLTθLT
−0.703824061
−0.739197646
0
0


dTSTE
122.4270642
0
−94.62792088
0


dTSψSi
0.714493384
−1.189155195
0
−1.017237669


dTSθLT
0
0
0
0


dTEψSi
0
0.558597609
0
0


dTEθLT
0.734424122
0.628956462
0
0


dψSiθLT
−0.003900657
0.003268439
0
0


e
−2.246432623
−2.691572945
−3.425676672
−3.236112132


















TABLE 29









Si(111)



Second higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−26.67263869
−6.49243933
−20.61574251
−21.06290014


bTLT(2)
0
0
0
0


cTLT
0.15443038
0.175438596
0.160759494
0.156896552


aTS(2)
0
0
0
0


aTS(1)
−7.971316395
7.232224634
−16.40433051
−3.920556446


bTS(2)
0
0
0
0


cTS
0.14556962
0.133333333
0.144303797
0.144827586


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−110.7824708
−133.1826499
0


aTE(1)
12.77975858
−10.04988717
5.027045348
−5.686378626


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006463527
0.006582278
0


cTE
0.151265823
0.144736842
0.35
0.35862069


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
−0.007219474
0


aψSi(1)
0.028716852
0.04192074
−0.016815807
0.008780601


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
125.0280404
0


cψSi
9.683544304
50
11.58227848
48.10344828


aθLT(2)
0.01035547
0
0
0.014789077


aθLT(1)
0.162093889
0.106646805
0.164306798
0.04587348


bθLT(2)
61.8811088
0
0
55.43995244


cθLT
−49.62025316
−50.35087719
−51.01265823
−51.20689655


dTLTTS
−609.1883956
−724.6623011
−297.9828576
−203.214973


dTLTTE
−215.420422
0
159.6303697
0


dTLTψSi
0
−3.771938969
2.003207828
−2.014745526


dTLTθLT
1.80686724
0
2.218853872
0


dTSTE
0
−307.4269587
0
0


dTSψSi
0
0
−1.097992723
0


dTSθLT
1.985202008
0
2.104127874
0


dTEψSi
0
0
−1.451355926
0


dTEθLT
−203.386471
1.145649707
0
0


dψSiθLT
2.42647485
0.004357557
0
0


e
−5.019952207
−2.13826109
−3.235663805
−3.326865691


















TABLE 30









Si(111)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
45.51074293
−94.44342524
0


aTLT(1)
0.788515154
−3.454988617
−9.832405019
−3.192556866


bTLT(2)
0
0.006485261
0.006459172
0


cTLT
0.298058252
0.295238095
0.298461538
0.298913043


aTS(2)
0
0
0
0


aTS(1)
−8.97795964
1.31344944
0
0


bTS(2)
0
0
0
0


cTS
0.142718447
0.147619048
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
9.791468713
0.170587985
−0.71523762
−10.72534988


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.15776699
0.124603175
0.356153846
0.347826087


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0.003924448
0.001661439
0
0.00657999


aψSi(1)
0.15776699
−0.024952541
0.02404454
−0.067389114


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
148.4588557
132.0861678
0
152.6937618


cψSi
15.29126214
46.9047619
14.19230769
43.04347826


aθLT(2)
0
0
0
0


aθLT(1)
0.06700163
0.042141715
0.055240362
0.061747926


bθLT(2)
0
0
0
0


cθLT
−48.73786408
−50.15873016
−49.76923077
−49.45652174


dTLTTS
116.7290786
−78.78450728
0
0


dTLTTE
0
85.46351406
−49.85282875
0


dTLTψSi
−0.70199108
0.445481139
0
0.604657146


dTLTθLT
−0.726496636
0
0
0


dTSTE
0
−116.360096
0
0


dTSψSi
0
−0.622709588
0
0


dTSθLT
2.041329502
−0.339115637
0
0


dTEψSi
0
0.20688896
0
0


dTEθLT
0.774150432
0.489880407
−0.6608739
−1.068569294


dψSiθLT
−0.005400114
0.002667922
−0.004937546
0.006290209


e
−4.209434885
−1.791078273
−3.48174155
−3.934527612


















TABLE 31









Si(111)



Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−4.673850215
0
−8.8586067
−1.957300157


bTLT(2)
0
0
0
0


cTLT
0.141509434
0
0.153125
0.16


aTS(2)
82.42811022
0
87.42203531
0


aTS(1)
−7.905282467
−4.948155925
−0.569845134
0.521030757


bTS(2)
0.006949092
0
0.006037326
0


cTS
0.294339623
0.314583333
0.297916667
0.285


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
53.51232744
−79.38404758
0
0


aTE(1)
10.58973083
10.26534018
8.135327356
−7.251553825


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.006016376
0.005677083
0
0


cTE
0.183962264
0.1375
0.336458333
0.37


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0.001429494


aψSi(1)
0.010122468
0.039888924
−0.016592245
−0.004853684


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
145.6875


cψSi
11.88679245
48.4375
14.0625
45.75


aθLT(2)
0
0
0
0


aθLT(1)
−0.005093912
0.011098836
0.047530531
0.04750516


bθLT(2)
0
0
0
0


cθLT
−50
−50.41666667
−50.72916667
−49.75


dTLTTS
0
0
91.19418307
251.5375225


dTLTTE
0
0
−156.3654518
0


dTLTψSi
0.322255595
0
0
−0.289820964


dTLTθLT
−0.768436344
0
−0.735737765
0


dTSTE
0
75.51836907
0
0


dTSψSi
−0.512402643
0.300543357
−0.724013025
0.245746891


dTSθLT
0
0
0
0


dTEψSi
0
0
−0.50556971
0


dTEθLT
0
0
0
0


dψSiθLT
0
0.002842264
0
0


e
−2.770026639
−2.638591885
−1.980941925
−2.412296494


















TABLE 32









Si(111)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
4.449764983
0
−13.78321665
−10.59163435


bTLT(2)
0
0
0
0


cTLT
0.321052632
0
0.309146341
0.303164557


aTS(2)
0
0
0
0


aTS(1)
0
−3.433673203
−1.746861763
3.363230821


bTS(2)
0
0
0
0


cTS
0
0.283443709
0.287804878
0.293037975


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
86.18383552
0


aTE(1)
3.853394073
8.768511808
−1.867550529
−15.68616064


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.007157942
0


cTE
0.181578947
0.135430464
0.356097561
0.363291139


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
0.014178515
0.049910217
−0.008697771
0.012742666


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
12.63157895
45.99337748
15.09146341
45


aθLT(2)
0
0
0
0


aθLT(1)
0
0.061867934
0.051566965
0.028929641


bθLT(2)
0
0
0
0


cθLT
−90
−50.59602649
−50.30487805
−50.56962025


dTLTTS
0
0
0
−103.0440888


dTLTTE
0
0
0
0


dTLTψSi
−0.181721459
0
0
0


dTLTθLT
0
0
0
−0.608943868


dTSTE
0
113.1914268
−75.04640382
−82.04954672


dTSψSi
0
0
−0.554356722
0.673316097


dTSθLT
0
0
0
0


dTEψSi
0
0
−0.512800103
0


dTEθLT
0
0
−0.656702553


dψSiθLT
0
0
0
0


e
−2.401219798
−3.18651044
−3.93030224
−4.143483981


















TABLE 33









Si(111)



Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60














aTLT(2)
0
0
0
0


aTLT(1)
−3.047618237
−3.047618237
−3.047618237
−3.047618237


bTLT(2)
0
0
0
0


cTLT
0.160869565
0.160869565
0.160869565
0.160869565


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
11.21750437
11.21750437
11.21750437
11.21750437


aTE(2)
−3.666215654
−3.666215654
−3.666215654
−3.666215654


aTE(1)
−0.035248162
−0.035248162
−0.035248162
−0.035248162


bTE(4)
0
0
0
0


bTE(3)
0.000381688
0.000381688
0.000381688
0.000381688


bTE(2)
0.012589792
0.012589792
0.012589792
0.012589792


cTE
0.245652174
0.245652174
0.245652174
0.245652174


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.003582211
−0.003582211
−0.003582211
−0.003582211


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
35.86956522
35.86956522
35.86956522
35.86956522


aθLT(2)
−0.000596775
−0.000596775
−0.000596775
−0.000596775


aθLT(1)
0.003385783
0.003385783
0.003385783
0.003385783


bθLT(2)
77.88279773
77.88279773
77.88279773
77.88279773


cθLT
−47.82608696
−47.82608696
−47.82608696
−47.82608696


dTLTTS
0
0
0
0


dTLTTE
−2.939323227
−2.939323227
−2.939323227
−2.939323227


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
−0.000442922
−0.000442922
−0.000442922
−0.000442922


e
−0.277577227
−0.277577227
−0.277577227
−0.277577227


















TABLE 34









Si(111)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
0
0
0
0


bTLT(2)
0
0
0
0


cTLT
0
0
0
0


aTS(2)
0
0
0
0


aTS(1)
6.03484153
6.03484153
6.03484153
6.03484153


bTS(2)
0
0
0
0


cTS
0.183333333
0.183333333
0.183333333
0.183333333


aTE(4)
−215.3850281
−215.3850281
−215.3850281
−215.3850281


aTE(3)
54.12265846
54.12265846
54.12265846
54.12265846


aTE(2)
0.942905209
0.942905209
0.942905209
0.942905209


aTE(1)
−1.08045121
−1.08045121
−1.08045121
−1.08045121


bTE(4)
0.000339332
0.000339332
0.000339332
0.000339332


bTE(3)
0.000317558
0.000317558
0.000317558
0.000317558


bTE(2)
0.011265432
0.011265432
0.011265432
0.011265432


cTE
0.211111111
0.211111111
0.211111111
0.211111111


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.004526908
−0.004526908
−0.004526908
−0.004526908


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
27.5
27.5
27.5
27.5


aθLT(2)
−0.00046365
−0.00046365
−0.00046365
−0.00046365


aθLT(1)
0.005349146
0.005349146
0.005349146
0.005349146


bθLT(2)
57.09876543
57.09876543
57.09876543
57.09876543


cθLT
−46.11111111
−46.11111111
−46.11111111
−46.11111111


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
45.80413521
45.80413521
45.80413521
45.80413521


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
−0.071786246
−0.071786246
−0.071786246
−0.071786246


dψSiθLT
−0.000425881
−0.000425881
−0.000425881
−0.000425881


e
−0.446604617
−0.446604617
−0.446604617
−0.446604617


















TABLE 35









Si(111)



Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−2.477108842
−2.477108842
−2.477108842
−2.477108842


bTLT(2)
0
0
0
0


cTLT
0.137349398
0.137349398
0.137349398
0.137349398


aTS(2)
0
0
0
0


aTS(1)
−0.488747927
−0.488747927
−0.488747927
−0.488747927


bTS(2)
0
0
0
0


cTS
0.336144578
0.336144578
0.336144578
0.336144578


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−1.973253274
−1.973253274
−1.973253274
−1.973253274


aTE(1)
−0.124870592
−0.124870592
−0.124870592
−0.124870592


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.017915517
0.017915517
0.017915517
0.017915517


cTE
0.256024096
0.256024096
0.256024096
0.256024096


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
 7.6083E−07
 7.6083E−07
 7.6083E−07
 7.6083E−07


aψSi(3)
7.21121E−06
7.21121E−06
7.21121E−06
7.21121E−06


aψSi(2)
−0.000857107
−0.000857107
−0.000857107
−0.000857107


aψSi(1)
−0.00490823
−0.00490823
−0.00490823
−0.00490823


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
105622.9088
105622.9088
105622.9088
105622.9088


bψSi(3)
−217.2019476
−217.2019476
−217.2019476
−217.2019476


bψSi(2)
208.4409929
208.4409929
208.4409929
208.4409929


cψSi
30.54216867
30.54216867
30.54216867
30.54216867


aθLT(2)
0
0
0
0


aθLT(1)
0
0
0
0


bθLT(2)
0
0
0
0


cθLT
−90
−90
−90
−90


dTLTTS
4.821777856
4.821777856
4.821777856
4.821777856


dTLTTE
−4.14067246
−4.14067246
−4.14067246
−4.14067246


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.024454063
0.024454063
0.024454063
0.024454063


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−0.240178915
−0.240178915
−0.240178915
−0.240178915


















TABLE 36









Si(111)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
0
0
0
0


bTLT(2)
0
0
0
0


cTLT
0
0
0
0


aTS(2)
0
0
0
0


aTS(1)
0.380779889
0.380779889
0.380779889
0.380779889


bTS(2)
0
0
0
0


cTS
0.285294118
0.285294118
0.285294118
0.285294118


aTE(4)
−165.3225345
−165.3225345
−165.3225345
−165.3225345


aTE(3)
23.65923214
23.65923214
23.65923214
23.65923214


aTE(2)
2.256295059
2.256295059
2.256295059
2.256295059


aTE(1)
−0.292409126
−0.292409126
−0.292409126
−0.292409126


bTE(4)
0.00051583
0.00051583
0.00051583
0.00051583


bTE(3)
0.00070344
0.00070344
0.00070344
0.00070344


bTE(2)
0.015017301
0.015017301
0.015017301
0.015017301


cTE
0.220588235
0.220588235
0.220588235
0.220588235


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.004846255
−0.004846255
−0.004846255
−0.004846255


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
29.55882353
29.55882353
29.55882353
29.55882353


aθLT(2)
0
0
0
0


aθLT(1)
0.00165846
0.00165846
0.00165846
0.00165846


bθLT(2)
0
0
0
0


cθLT
−48.52941176
−48.52941176
−48.52941176
−48.52941116


dTLTTS
−0.04933649
−0.04933649
−0.04933649
−0.04933649


dTLTTE
−0.021023839
−0.021023839
−0.021023839
−0.021023839


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
−7.074776252
−7.074776252
−7.074776252
−7.074776252


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
−0.00049898
−0.00049898
−0.00049898
−0.00049898


e
−0.3405485
−0.3405485
−0.3405485
−0.3405485









In an acoustic wave device according to a preferred embodiment of the present invention, Ih for each of the first and second higher-order modes is more than about −2.4.


In an acoustic wave device according to a preferred embodiment of the present invention, Ih for each of the first and third higher-order modes is more than about −2.4.


In an acoustic wave device according to a preferred embodiment of the present invention, Ih for each of the second and third higher-order modes is more than about −2.4.


In an acoustic wave device according to a preferred embodiment of the present invention, preferably, Ih for each of the first, second, and third higher-order modes is more than about −2.4. In this case, all of the responses of the first higher-order mode, the second higher-order mode, and the third higher-order mode are able to be effectively reduced or prevented.


In an acoustic wave device according to a preferred embodiment of the present invention, the piezoelectric body has a thickness of about 3.5λ or less.


In an acoustic wave device according to a preferred embodiment of the present invention, the piezoelectric body has a thickness of about 2.5λ or less.


In an acoustic wave device according to a preferred embodiment of the present invention, the piezoelectric body has a thickness of about 1.5λ or less.


In an acoustic wave device according to a preferred embodiment of the present invention, the piezoelectric body has a thickness of about 0.5λ or less.


In an acoustic wave device according to a preferred embodiment of the present invention, an acoustic wave resonator is provided as the acoustic wave device.


An acoustic wave filter according to a preferred embodiment of the present invention includes multiple resonators, in which at least one of the multiple resonators is defined by an acoustic wave device according to a preferred embodiment of the present invention. Thus, the acoustic wave filter in which at least one of the responses of the first, second, and third higher-order modes is reduced or prevented is provided.


A multiplexer according to a preferred embodiment of the present invention includes N acoustic wave filters (where N is 2 or more) having different pass bands, one terminal of each of the N acoustic wave filters being commonly connected on an antenna terminal side, in which at least one acoustic wave filter among the N acoustic wave filters excluding an acoustic wave filter having a highest-frequency pass band includes multiple acoustic wave resonators, and at least one acoustic wave resonator among the multiple acoustic wave resonators is defined by an acoustic wave device according to a preferred embodiment of the present invention.


Preferably, the multiplexers according to preferred embodiments of the present invention are each used as a composite filter device for carrier aggregation.


A high-frequency front-end circuit according to a preferred embodiment of the present invention includes an acoustic wave filter including an acoustic wave device according to a preferred embodiment of the present invention and a power amplifier connected to the acoustic wave filter.


A communication apparatus according to a preferred embodiment of the present invention includes a high-frequency front-end circuit including an acoustic wave filter that includes an acoustic wave device according to a preferred embodiment of the present invention and a power amplifier connected to the acoustic wave filter, and an RF signal processing circuit.


In the acoustic wave devices, the multiplexers, the high-frequency front-end circuits, and the communication apparatuses according to preferred embodiments of the present invention, at least one of the response of the first higher-order mode, the response of the second higher-order mode, and the response of the third higher-order mode located at higher frequencies than the main mode is able to be effectively reduced or prevented. Thus, in the multiplexers, the high-frequency front-end circuits, and the communication apparatuses including the acoustic wave devices according to preferred embodiments of the present invention, ripples due to the higher-order mode are less likely to occur in another band pass filter having a pass band with a higher frequency than the acoustic wave device.


The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings.





BRIEF DESCRIPTION OF THE DRAWINGS


FIG. 1A is a schematic elevational cross-sectional view of an acoustic wave device according to a first preferred embodiment of the present invention, and FIG. 1B is a schematic plan view illustrating the electrode structure of the acoustic wave device according to the first preferred embodiment of the present invention.



FIG. 2 illustrates admittance characteristics of an acoustic wave resonator.



FIG. 3 illustrates the relationship between the propagation direction ψSi in a single-crystal Si layer and the strength S11 of the response of a first higher-order mode.



FIG. 4 illustrates the relationship between the wave length-normalized film thickness TLT of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the first higher-order mode.



FIG. 5 illustrates the relationship between the cut angle (90°+θLT) of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the first higher-order mode.



FIG. 6 illustrates the relationship between the wave length-normalized film thickness TS of a SiO2 film and the strength S11 of the response of the first higher-order mode.



FIG. 7 illustrates the relationship between the wave length-normalized film thickness TE of interdigital transducer electrodes and the strength S11 of the response of the first higher-order mode.



FIG. 8 is a circuit diagram of a multiplexer including an acoustic wave device according to the first preferred embodiment of the present invention.



FIG. 9 is a circuit diagram of an acoustic wave filter that includes the acoustic wave device according to the first preferred embodiment of the present invention and is used in a multiplexer.



FIG. 10A illustrates the filter characteristics of a multiplexer including an acoustic wave device of a comparative example, and FIG. 10B illustrates the filter characteristics of a multiplexer according to the first preferred embodiment of the present invention.



FIG. 11 illustrates the relationship between the wave length-normalized film thickness of a single-crystal Si layer and the maximum phases of responses of the first, second, and third higher-order modes.



FIG. 12 illustrates the relationship between the propagation direction ψSi in a single-crystal Si layer and the strength S11 of the response of the second higher-order mode.



FIG. 13 illustrates the relationship between the wave length-normalized film thickness TLT of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the second higher-order mode.



FIG. 14 illustrates the relationship between the cut angle (90°+θLT) of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the second higher-order mode.



FIG. 15 illustrates the relationship between the wave length-normalized film thickness TS of a SiO2 film and the strength S11 of the response of the second higher-order mode.



FIG. 16 illustrates the relationship between the wave length-normalized film thickness TE of interdigital transducer electrodes and the strength S11 of the response of the second higher-order mode.



FIG. 17 illustrates the relationship between the propagation direction ψSi in a single-crystal Si layer and the strength S11 of the response of the third higher-order mode.



FIG. 18 illustrates the relationship between the wave length-normalized film thickness TLT of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the third higher-order mode.



FIG. 19 illustrates the relationship between the cut angle (90°+θLT) of a piezoelectric body made of lithium tantalate and the strength S11 of the response of the third higher-order mode.



FIG. 20 illustrates the relationship between the wave length-normalized film thickness TS of a SiO2 film and the strength S11 of the response of the third higher-order mode.



FIG. 21 illustrates the relationship between the wave length-normalized film thickness TE of interdigital transducer electrodes and the strength S11 of the response of the third higher-order mode.



FIG. 22 illustrates the relationship between the film thickness of a LiTaO3 film in an acoustic wave device and the quality factor.



FIG. 23 illustrates the relationship between the film thickness of a LiTaO3 film in an acoustic wave device and the temperature coefficient of frequency TCF.



FIG. 24 illustrates the relationship between the film thickness of a LiTaO3 film in an acoustic wave device and the acoustic velocity.



FIG. 25 illustrates the relationship between the film thickness of a LiTaO3 film and the band width ratio.



FIG. 26 illustrates the relationships among the film thickness of a SiO2 film, materials of high-acoustic-velocity films, and the acoustic velocity.



FIG. 27 illustrates the relationships among the film thickness of a SiO2 film, the electromechanical coupling coefficient, and materials of high-acoustic-velocity films.



FIG. 28 is a block diagram of a communication apparatus including a high-frequency front-end circuit according to a preferred embodiment of the present invention.





DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments according to the present invention will be described in detail below with reference to the attached drawings so as to clarify the present invention.


Preferred embodiments described in this specification are illustrative. It should be noted that partial replacement and combination of configurations in different preferred embodiments may be made.



FIG. 1A is a schematic elevational cross-sectional view of an acoustic wave device according to a first preferred embodiment of the present invention, and FIG. 1B is a schematic plan view illustrating the electrode structure thereof.


An acoustic wave device 1 is preferably a one-port acoustic wave resonator, for example. The acoustic wave device 1 includes a single-crystal Si layer 2 defining and functioning as a supporting substrate made of silicon. The term “supporting substrate made of silicon” includes a supporting substrate including only of silicon; and a supporting substrate made of a material including silicon as a main component and impurities. A SiO2 film 3 defining and functioning as a silicon oxide film and a piezoelectric body 4 made of lithium tantalate (LiTaO3) are stacked on the single-crystal Si layer 2. The piezoelectric body 4 includes first and second main surfaces 4a and 4b opposed to each other. Interdigital transducer electrodes 5 are disposed on the first main surface 4a. Reflectors 6 and 7 are disposed on both sides of the interdigital transducer electrodes 5 in the propagation direction of an acoustic wave. The SiO2 film 3 defining and functioning as a silicon oxide film may include not only SiO2 but also, for example, silicon oxide in which SiO2 is doped with fluorine or the like. In FIG. 1A, the SiO2 film 3 is directly on the single-crystal Si layer 2, the piezoelectric body 4 is directly on the SiO2 film 3, and the Interdigital transducer electrodes 5 are disposed directly on the piezoelectric body 4. However, the SiO2 film 3 may be indirectly on (or above) the single-crystal Si layer 2, the piezoelectric body 4 may be indirectly on (or above) the SiO2 film 3, and the Interdigital transducer electrodes 5 may be disposed indirectly on (or above) the piezoelectric body 4.


The inventors of preferred embodiments of the present invention have discovered that in an acoustic wave resonator having such a structure in which a piezoelectric body made of lithium tantalate is stacked directly or indirectly on the single-crystal Si layer 2, responses due to first, second, and third higher-order modes are generated.



FIG. 2 illustrates admittance characteristics of an acoustic wave resonator in order to explain first to third higher-order modes. The admittance characteristics illustrated in FIG. 2 are admittance characteristics of an acoustic wave resonator that has design parameters described below and that is not a preferred embodiment of the present invention.


The single-crystal Si layer has Euler angles ( Si, θSi, ψSi)=(0°, 0°, 45°). The SiO2 film has a film thickness of about 0.30λ. The piezoelectric body made of lithium tantalate has a film thickness of about 0.30λ. The piezoelectric body made of lithium tantalate has Euler angles (φLT, θLT, ψLT)=(0°, −40°, 0°) The wave length λ determined by the pitch of electrode fingers of the interdigital transducer electrodes is about 1 μm. Each of the interdigital transducer electrodes is defined by a stacked metal film in which an Al film and a Ti film are stacked, and each interdigital transducer electrode has a thickness of about 0.05λ in terms of aluminum.


As is apparent from FIG. 2, in the acoustic wave resonator described above, each of the responses of the first higher-order mode, the second higher-order mode, and the third higher-order mode appears at higher frequencies than the response of the main mode. Regarding the frequency positions, a position of response of first higher-order mode is lower than a position of response of second higher-order mode and a position of response of third higher-order mode, and the position of response of the second higher-order mode is lower than the position of response of the third higher-order mode. The response of the first higher-order mode is closest to the response of the main mode. However, FIG. 2 is an example, and the positional relationship of the frequencies of the modes may be switched, depending on conditions, such as the electrode thickness.


A feature of the acoustic wave device 1 according to the present preferred embodiment is the fact that at least one of the response of the first higher-order mode, the response of the second higher-order mode, and the response of the third higher-order mode is reduced or prevented.


The wave length determined by the pitch of the electrode fingers of the interdigital transducer electrodes 5 is denoted by λ. The wave length-normalized film thickness of the piezoelectric body 4 made of lithium tantalate is denoted by TLT. The Euler angle θ of the piezoelectric body made of lithium tantalate is denoted by θLT. The wave length-normalized film thickness of the SiO2 film 3 is denoted by TS. The wave length-normalized film thickness of the interdigital transducer electrodes 5 in terms of aluminum thickness is denoted by TE. The propagation direction in the single-crystal Si layer 2 is denoted by ψSi. The wave length-normalized film thickness of the single-crystal Si layer 2 is denoted by TSi. TLT, θLT, TS, TE, and ψSi are set such that Ih represented by Formula (1) for at least one of the responses of the first higher-order mode, the second higher-order mode, and the third higher-order mode is preferably more than about −2.4, and TSi>about 20, for example. Thus, the at least one of the responses of the first, second, and third higher-order modes is effectively reduced or prevented. This will be described in detail below.


In this specification, the wave length-normalized film thickness is a value obtained by normalizing the thickness of the film to the wave length λ determined by the pitch of the electrode fingers of the interdigital transducer electrodes. Thus, a value obtained by dividing actual thickness of the film by λ is the wave length-normalized film thickness. The wave length λ determined by the pitch of the electrode fingers of the interdigital transducer electrodes may be determined by the average pitch of the electrode fingers.










I
h

=



a

T
LT


(
2
)




(



(


T
LT

-

c

T
LT



)

2

-

b

T
LT


(
2
)



)


+


a

T
LT


(
1
)




(


T
LT

-

c

T
LT



)


+


a

T
S


(
2
)




(



(


T
S

-

c

T
S



)

2

-

b

T
S


(
2
)



)


+


a

T
S


(
1
)




(


T
S

-

c

T
S



)


+


a

T
E


(
4
)




(



(


T
E

-

c

T
E



)

4

-

b

T
E


(
4
)



)


+


a

T
E


(
3
)




(



(


T
E

-

c

T
E



)

3

-

b

T
E


(
3
)



)


+


a

T
E


(
2
)




(



(


T
E

-

c

T
E



)

2

-

b

T
E


(
2
)



)


+


a

T
E


(
1
)




(


T
E

-

c

T
E



)


+


a

ψ
Si


(
6
)




(



(


ψ
Si

-

c

ψ
Si



)

6

-

b

ψ
Si


(
6
)



)


+


a

ψ
Si


(
5
)




(



(


ψ
Si

-

c

ψ
Si



)

2

-

b

ψ
Si


(
5
)



)


+


a

ψ
Si


(
4
)




(



(


ψ
Si

-

c

ψ
Si



)

2

-

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
Si



)

2

-

b

ψ
Si


(
2
)



)


+


a

ψ
Si


(
1
)




(


ψ
Si

-

c

ψ
Si



)


+


a

θ
LT


(
2
)




(



(


θ
LT

-

c

θ
LT



)

2

-

b

θ
LT


(
2
)



)


+


a

θ
LT


(
1
)




(


θ
LT

-

c

θ
LT



)


+



d


T
LT



T
S





(


T
LT

-

c

T
LT



)




(


T
S

-

c

T
S



)


+



d


T
LT



T
E





(


T
LT

-

c

T
LT



)




(


T
E

-

c

T
E



)


+



d


T
LT



ψ
Si





(


T
LT

-

c

T
LT



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
LT



θ
LT





(


T
LT

-

c

T
LT



)




(


θ
LT

-

c

θ
LT



)


+



d


T
S



T
E





(


T
S

-

c

T
S



)




(


T
E

-

c

T
E



)


+



d


T
S



ψ
Si





(


T
S

-

c

T
S



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
S



θ
LT





(


T
S

-

c

T
S



)




(


θ
LT

-

c

θ
LT



)


+



d


T
E



ψ
Si





(


T
E

-

c

T
E



)




(


ψ
Si

-

c

ψ
Si



)


+



d


T
E



θ
LT





(


T
E

-

c

T
E



)




(


θ
LT

-

c

θ
LT



)


+



d


ψ
Si



θ
LT





(


ψ
Si

-

c

ψ
Si



)




(


θ
LT

-

c

θ
LT



)


+
e





Formula






(
1
)








In Formula (1), coefficients a, b, c, d, and e are values presented in Tables 37 to 72 below in accordance with ranges of, for example, the type of higher-order mode, the orientation of the single-crystal Si layer 2 either of (100), (110), or (111), the wave length-normalized film thickness of the SiO2 film 3, the wave length-normalized film thickness of the piezoelectric body made of lithium tantalate, and the propagation direction in the single-crystal Si layer 2.












TABLE 37









Si(100)




First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
0
0



bTLT(2)
0
0



cTLT
0
0



aTS(2)
0
0



aTS(1)
−5.857231176
−5.857231176



bTS(2)
0
0



cTS
0.148
0.148



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−19.75255913
−19.75255913



aTE(1)
−2.877583447
−2.877583447



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.022736
0.022736



cTE
0.242
0.242



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.004788767
0.004788767



aψSi(1)
0.024306207
0.024306207



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
81.81
81.81



cψSi
8.7
8.7



aθLT(2)
−0.008235936
−0.008235936



aθLT(1)
−0.021048278
−0.021048278



bθLT(2)
65.16
65.16



cθLT
−52.2
−52.2



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
−0.786852571
−0.786852571



dTEψSi
0
0



dTEθLT
−0.237034335
−0.237034335



dψSiθLT
0
0



e
−1.499248378
−1.499248378




















TABLE 38









Si(100)




First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
125.5342427



aTLT(1)
−13.43961051
−7.643409732



bTLT(2)
0
0.006076558



cTLT
0.329807692
0.321186441



aTS(2)
0
0



aTS(1)
−11.80744788
−10.05306878



bTS(2)
0
0



cTS
0.158653846
0.153389831



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
0
−7.595099843



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0
0.366101695



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.003335792
0



aψSi(1)
0.039268266
−0.013700762



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
191.7159763
0



cψSi
13.26923077
16.01694915



aθLT(2)
−0.007476194
0



aθLT(1)
−0.010867175
−0.053997369



bθLT(2)
69.19378698
0



cθLT
−50.19230769
−50.59322034



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.629167148
−0.724576033



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0.521919406



dTSθLT
0
0



dTEψSi
0
−0.523966449



dTEθLT
0
0



dψSiθLT
0
0



e
−2.071831837
−3.228508418




















TABLE 39









Si(100)




First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−15.6141248
−15.6141248



bTLT(2)
0
0



cTLT
0.163309353
0.163309353



aTS(2)
0
0



aTS(1)
−22.02440893
−22.02440893



bTS(2)
0
0



cTS
0.325179856
0.325179856



aTE(4)
0
0



aTE(3)
−248.4374004
−248.4374004



aTE(2)
−36.57127964
−36.57127964



aTE(1)
13.88180854
13.88180854



bTE(4)
0
0



bTE(3)
0.000480119
0.000480119



bTE(2)
0.020416128
0.020416128



cTE
0.240647482
0.240647482



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.002456326
0.002456326



aψSi(1)
0.048553126
0.048553126



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
279.6050929
279.6050929



cψSi
22.3381295
22.3381295



aθLT(2)
0
0



aθLT(1)
0.005427275
0.005427275



bθLT(2)
0
0



cθLT
−50.35971223
−50.35971223



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
41.63149071
41.63149071



dTSψSi
−0.577179204
−0.577179204



dTSθLT
0.603866778
0.603866778



dTEψSi
0.134944598
0.134944598



dTEθLT
0
0



dψSiθLT
0
0



e
−2.703317679
−2.703317679




















TABLE 40









Si(100)




First higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
133.7896555



aTLT(1)
−7.761727985
−9.701155851



bTLT(2)
0
0.006281971



cTLT
0.315508021
0.306914894



aTS(2)
0
0



aTS(1)
−20.35135077
−6.186650236



bTS(2)
0
0



cTS
0.297860963
0.298404255



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
110.8304316
0



aTE(1)
4.036561723
−8.229960495



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.006431411
0



cTE
0.140374332
0.363297872



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
0.002534654
0.001652947



aψSi(1)
0.024168138
−0.003241344



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
269.2484772
266.6845858



cψSi
21.4171123
20.26595745



aθLT(2)
0
0



aθLT(1)
0
−0.066116428



bθLT(2)
0
0



cθLT
−90
−50.4787234



dTLTTS
96.23533718
0



dTLTTE
−66.46866878
0



dTLTψSi
−0.404808481
−0.688053172



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
−0.733337318
0



dTSθLT
0
0



dTEψSi
0.584322518
−0.372994212



dTEθLT
0
0



dψSiθLT
0
0



e
−3.679364607
−4.30794513




















TABLE 41









Si(100)




Second higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−5.687707928
−5.687707928



bTLT(2)
0
0



cTLT
0.139506173
0.139506173



aTS(2)
0
0



aTS(1)
5.653643283
5.653643283



bTS(2)
0
0



cTS
0.148148148
0.148148148



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−1.004369706
−1.004369706



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.255555556
0.255555556



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
−0.000197083
−0.000197083



aψSi(2)
−0.003376583
−0.003376583



aψSi(1)
0.118081927
0.118081927



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
−379.4708632
−379.4708632



bψSi(2)
278.0521262
278.0521262



cψSi
23.14814815
23.14814815



aθLT(2)
0
0



aθLT(1)
0.128631041
0.128631041



bθLT(2)
0
0



cθLT
−49.32098765
−49.32098765



dTLTTS
0
0



dTLTTE
72.43278274
72.43278274



dTLTψSi
0.604747502
0.604747502



dTLTθLT
−1.743618251
−1.743618251



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0.994157261
0.994157261



dTEψSi
0
0



dTEθLT
0.280889881
0.280889881



dψSiθLT
0.003095822
0.003095822



e
−5.638096455
−5.638096455




















TABLE 42









Si(100)




Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
7.809960834
4.249755245



bTLT(2)
0
0



cTLT
0.30962963
0.302857143



aTS(2)
0
0



aTS(1)
0
−0.800874586



bTS(2)
0
0



cTS
0
0.150714286



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−3.563479635
9.07053135



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.148518519
0.353571429



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
−0.000160979
0



aψSi(2)
−0.000757552
0.001332545



aψSi(1)
0.095765615
0.003836714



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
384.7407407
0



bψSi(2)
278.2222222
285.0956633



cψSi
21.33333333
20.89285714



aθLT(2)
0
0



aθLT(1)
0.043185248
0.033521037



bθLT(2)
0
0



cθLT
−50
−50.92857143



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.383208698
−0.220029295



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0
0.974573109



dTEψSi
0
0



dTEθLT
1.01389349
−1.078939399



dψSiθLT
0
0.002899732



e
−5.569590226
−5.29442278




















TABLE 43









Si(100)




Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−11.51287
−11.51287



bTLT(2)
0
0



cTLT
0.136328125
0.136328125



aTS(2)
0
0



aTS(1)
6.022608826
6.022608826



bTS(2)
0
0



cTS
0.305859375
0.305859375



aTE(4)
0
0



aTE(3)
−180.607873
−180.607873



aTE(2)
−1.347493816
−1.347493816



aTE(1)
4.841204365
4.841204365



bTE(4)
0
0



bTE(3)
−0.000227051
−0.000227051



bTE(2)
0.019179688
0.019179688



cTE
0.25625
0.25625



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.001342794
−0.001342794



aψSi(1)
0.25625
0.25625



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
275.7568359
275.7568359



cψSi
0.25625
0.25625



aθLT(2)
0
0



aθLT(1)
0.153688205
0.153688205



bθLT(2)
0
0



cθLT
−49.140625
−49.140625



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
−1.180623763
−1.180623763



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0.41394071
0.41394071



dψSiθLT
0.003203013
0.003203013



e
−4.433641408
−4.433641408




















TABLE 44









Si(100)




Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
119.666412
118.2359738



aTLT(1)
4.447768142
2.271979446



bTLT(2)
0.006371047
0.00699901



cTLT
0.31147541
0.30631068



aTS(2)
0
0



aTS(1)
0
−3.805216895



bTS(2)
0
0



cTS
0
0.298543689



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
117.8354557
121.7109482



aTE(1)
2.107193686
−0.578851453



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.006775956
0.006610661



cTE
0.15
0.35631068



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.001658706
0



aψSi(1)
0.005677734
0.003834195



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
272.5477022
0



cψSi
20.90163934
20.02427184



aθLT(2)
0
0



aθLT(1)
0.051921544
0.050011808



bθLT(2)
0
0



cθLT
−48.36065574
−48.93203883



dTLTTS
0
0



dTLTTE
61.26575286
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
−82.22932804



dTSψSi
0
0



dTSθLT
0
−0.470524678



dTEψSi
0
0



dTEθLT
0.904198722
−0.776132158



dψSiθLT
0.003410501
0.003906326



e
−5.339814906
−5.463687811




















TABLE 45









Si(100)




Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−16.39135605
−16.39135605



bTLT(2)
0
0



cTLT
0.196774194
0.196774194



aTS(2)
0
0



aTS(1)
−4.824831305
−4.824831305



bTS(2)
0
0



cTS
0.170967742
0.170967742



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−45.57608817
−45.57608817



aTE(1)
−10.80005563
−10.80005563



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.018296046
0.018296046



cTE
0.303225806
0.303225806



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000172048
0.000172048



aψSi(2)
−0.00384923
−0.00384923



aψSi(1)
−0.009826773
−0.009826773



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
143.0843208
143.0843208



bψSi(2)
215.8688866
215.8688866



cψSi
22.25806452
22.25806452



aθLT(2)
0
0



aθLT(1)
0.066799879
0.066799879



bθLT(2)
0
0



cθLT
−50.16129032
−50.16129032



dTLTTS
0
0



dTLTTE
−112.847682
−112.847682



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
−1.750763196
−1.750763196



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0.466692151
0.466692151



dψSiθLT
0
0



e
−2.904746788
−2.904746788




















TABLE 46









Si(100)




Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−8.135537689
−8.135537689



bTLT(2)
0
0



cTLT
0.311659193
0.311659193



aTS(2)
0
0



aTS(1)
−20.38200282
−20.38200282



bTS(2)
0
0



cTS
0.149327354
0.149327354



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
−3.460675692
−3.460675692



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0.267488789
0.267488789



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0
0



aψSi(2)
−0.003759233
−0.003759233



aψSi(1)
0.015931998
0.015931998



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
0
0



bψSi(2)
239.0395946
239.0395946



cψSi
18.90134529
18.90134529



aθLT(2)
0
0



aθLT(1)
0.017576249
0.017576249



bθLT(2)
0



cθLT
−49.9103139
−49.9103139



dTLTTS
−152.1817236
−152.1817236



dTLTTE
0
0



dTLTψSi
−0.359387178
−0.359387178



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
0.911415415
0.911415415



dTEψSi
0
0



dTEθLT
0.275815872
0.275815872



dψSiθLT
0
0



e
−3.952626598
−3.952626598




















TABLE 47









Si(100)




Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−26.36951471
−26.36951471



bTLT(2)
0
0



cTLT
0.161538462
0.161538462



aTS(2)
0
0



aTS(1)
−10.09828536
−10.09828536



bTS(2)
0
0



cTS
0.321025641
0.321025641



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
−21.38297597
−21.38297597



aTE(1)
−2.383287449
−2.383287449



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0.01947666
0.01947666



cTE
0.270512821
0.270512821



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000176024
0.000176024



aψSi(2)
−0.001397911
−0.001397911



aψSi(1)
−0.107515297
−0.107515297



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
−282.3623122
−282.3623122



bψSi(2)
255.2071006
255.2071006



cψSi
23.84615385
23.84615385



aθLT(2)
0
0



aθLT(1)
0.085112984
0.085112984



bθLT(2)
0
0



cθLT
−48.97435897
−48.97435897



dTLTTS
0
0



dTLTTE
0
0



dTLTψSi
−0.816828716
−0.816828716



dTLTθLT
0.865519967
0.865519967



dTSTE
0
0



dTSψSi
−0.538336559
−0.538336559



dTSθLT
0
0



dTEψSi
0
0



dTEθLT
0
0



dψSiθLT
0.002971652
0.002971652



e
−3.504362202
−3.504362202




















TABLE 48









Si(100)




Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45















aTLT(2)
0
0



aTLT(1)
−6.371850196
−6.371850196



bTLT(2)
0
0



cTLT
0.292192192
0.292192192



aTS(2)
0
0



aTS(1)
−0.609606885
−0.609606885



bTS(2)
0
0



cTS
0.2996997
0.2996997



aTE(4)
0
0



aTE(3)
0
0



aTE(2)
0
0



aTE(1)
0
0



bTE(4)
0
0



bTE(3)
0
0



bTE(2)
0
0



cTE
0
0



aψSi(6)
0
0



aψSi(5)
0
0



aψSi(4)
0
0



aψSi(3)
0.000224133
0.000224133



aψSi(2)
−0.004048532
−0.004048532



aψSi(1)
−0.126847922
−0.126847922



bψSi(6)
0
0



bψSi(5)
0
0



bψSi(4)
0
0



bψSi(3)
1375.85979
1375.85979



bψSi(2)
281.2555799
281.2555799



cψSi
19.77477477
19.77477477



aθLT(2)
0
0



aθLT(1)
0.056146223
0.056146223



bθLT(2)
0
0



cθLT
−49.48948949
−49.48948949



dTLTTS
94.47145497
94.47145497



dTLTTE
0
0



dTLTψSi
0
0



dTLTθLT
0
0



dTSTE
0
0



dTSψSi
0
0



dTSθLT
−0.568942451
−0.568942451



dTEψSi
0
0



dTEθLT
0
0



dψSiθLT
0.005654813
0.005654813



e
−4.940340284
−4.940340284



















TABLE 49









Si(110)



First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−16.69742899
−16.69742899
−33.56520202
0


bTLT(2)
0
0
0
0


cTLT
0.1675
0.1675
0.192857143
0


aTS(2)
0
0
0
0


aTS(1)
15.90196012
15.90196012
0
0


bTS(2)
0
0
0
0


cTS
0.1525
0.1525
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
26.3030303
0


aTE(1)
0
0
−6.481053391
0


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.006326531
0


cTE
0
0
0.378571429
0


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
−0.000183963
−0.000183963
0
−0.000177142


aψSi(2)
−0.003236307
−0.003236307
0
0.002186084


aψSi(1)
0.071460688
0.071460688
0.085067773
0.13561432


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
−5768.71875
−5768.71875
0
2642.857143


bψSi(2)
399.9375
399.9375
0
500


cψSi
65.25
65.25
34.28571429
55


aθLT(2)
0
0
0
−0.005336622


aθLT(1)
0
0
0.070255628
0.032718563


bθLT(2)
0
0
0
65.75963719


cθLT
−90
−90
−51.42857143
−50.95238095


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
1.873870705
1.878870705
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0.716151515
0


dψSiθLT
0
0
−0.00729303
0.002110378


e
−0.957101918
−0.957101918
−1.634922542
−1.290881853


















TABLE 50









Si(110)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−23.96596978
−4.695531045
−7.344438725
−5.603099398


bTLT(2)
0
0
0
0


cTLT
0.34
0.3296875
0.338983051
0.306666667


aTS(2)
0
0
0
0


aTS(1)
−23.18485905
0
0
0


bTS(2)
0
0
0
0


cTS
0.175555556
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−43.48595551
−70.50554427
−41.95412638


aTE(1)
0
−2.467954545
−5.460437635
−2.19025056


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006875
0.006716461
0.006819556


cTE
0
0.15
0.365254237
0.360666667


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0.000119479
−0.000172812


aψSi(2)
0.018474062
0
0.003987724
0.002213009


aψSi(1)
0.059131688
0
−0.047908658
0.073831446


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
−2384.203107
1647.952


bψSi(2)
81.55555556
0
216.791152
242.24


cψSi
35.33333333
0
30.76271186
62.6


aθLT(2)
0
0
0
0


aθLT(1)
0.009475371
0
0.026725166
0


bθLT(2)
0
0
0
0


cθLT
−49.33333333
−90
−49.83050847
−90


dTLTTS
0
0
0
0


dTLTTE
0
0
0
42.3018696


dTLTψSi
0
0
0
0


dTLTθLT
0.617240199
0
0
0


dTSTE
0
0
0
0


dTSψSi
2.612107038
0
0
0


dTSθLT
2.129359248
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0.871101002
0
0
0


e
−2.851861362
−2.210765625
−2.573237288
−2.440604203


















TABLE 51









Si(110)



First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−10.87353735
−17.74612134
−16.74814911
−16.74814911


bTLT(2)
0
0
0
0


cTLT
0.167045455
0.158227848
0.168032787
0.168032787


aTS(2)
92.14417413
275.6432031
0
0


aTS(1)
−6.141913324
−0.713377524
−9.071522271
−9.071522271


bTS(2)
0.004213585
0.004749239
0
0


cTS
0.339772727
0.317721519
0.314754098
0.314754098


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−37.82699975
0
0
0


aTE(1)
4.315324766
3.259148162
−5.270739047
−5.270739047


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.007147469
0
0
0


cTE
0.153409091
0.138607595
0.356557377
0.356557377


aψSi(6)
0
0
−3.73552E−09
−3.73552E−09


aψSi(5)
0
0
−4.69013E−08
−4.69013E−08


aψSi(4)
0
0
1.07773E−05
1.07773E−05


aψSi(3)
0.000254041
−0.000266841
5.64997E−05
5.64997E−05


aψSi(2)
0.00704637
0.003350583
−0.007526984
−0.007526984


aψSi(1)
−0.123432463
0.05687546
−0.035719404
−0.035719404


bψSi(6)
0
0
1801696668
1801696668


bψSi(5)
0
0
6726299.443
6726299.443


bψSi(4)
0
0
1035415.498
1035415.498


bψSi(3)
−1197.310014
2539.305207
3573.665857
3573.665857


bψSi(2)
188.2457386
286.0358917
720.1088417
720.1088417


cψSi
28.125
63.60759494
48.19672131
48.19672131


aθLT(2)
0
0
0
0


aθLT(1)
0.046748629
0.00460971
0
0


bθLT(2)
0
0
0
0


cθLT
−51.59090909
−50.75949367
−90
−90


dTLTTS
0
0
0
0


dTLTTE
0
105.3055279
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
58.63016883
0
0
0


dTSψSi
0.443510572
0.274149566
0
0


dTSθLT
0
0
0
0


dTEψSi
0.293912516
−0.280924747
0
0


dTEθLT
0
0.457718571
0
0


dψSiθLT
0
−0.005165328
0
0


e
−1.722804167
−2.484892701
−2.976959016
−2.976959016


















TABLE 52









Si(110)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
39.48011293


aTLT(1)
−5.239160454
−5.820942031
−4.867344296
−2.496300587


bTLT(2)
0
0
0
0.00654321


cTLT
0.309375
0.302702703
0.286363636
0.288888889


aTS(2)
24.40391167
40.38499201
0
40.45660337


aTS(1)
−2.128595361
−6.73354721
−3.626479228
−6.290401812


bTS(2)
0.006013184
0.005624543
0
0.005617284


cTS
0.3265625
0.275675676
0.31
0.272222222


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−51.46488975
0
0


aTE(1)
−1.921891837
−0.509929613
−1.508039016
−0.870147512


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006479182
0
0


cTE
0.153125
0.147297297
0.341818182
0.351388889


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
−0.000165117
0
−9.55404E−05


aψSi(2)
0.000936051
0.00475603
0
0.002198207


aψSi(1)
−0.02141106
0.040196571
−0.017752634
0.036260775


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
2115.829763
0
1531.394676


bψSi(2)
246.9177246
196.5668371
0
199.8263889


cψSi
24.140625
57.97297297
21.13636364
60.41666667


aθLT(2)
0
0
0
−0.003220943


aθLT(1)
0.023743346
0.023741003
0.038368027
0.005042496


bθLT(2)
0
0
0
72.22222222


cθLT
−50.078125
−48.51351351
−50.81818182
−50


dTLTTS
0
0
0
−43.45862557


dTLTTE
−35.16960363
−48.00382984
23.6423037
52.46703277


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0.234382842
0
0
−0.273892853


dψSiθLT
0
−0.00130658
−0.001221935
0


e
−2.175330984
−2.239116787
−2.271294054
−2.496300587


















TABLE 53









Si(110)



First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−7.587457615
−7.587457615
−7.587457615
−7.587457615


bTLT(2)
0
0
0
0


cTLT
0.174380165
0.174380165
0.174380165
0.174380165


aTS(2)
0
0
0
0


aTS(1)
−3.979714537
−3.979714537
−3.979714537
−3.979714537


bTS(2)
0
0
0
0


cTS
0.150413223
0.150413223
0.150413223
0.150413223


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−0.865040993
−0.865040993
−0.865040993
−0.865040993


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.245867769
0.245867769
0.245867769
0.245867769


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
5.87537E−07
5.87537E−07
5.87537E−07
5.87537E−07


aψSi(3)
−8.59015E−07
−8.59015E−07
−8.59015E−07
−8.59015E−07


aψSi(2)
−0.001948222
−0.001948222
−0.001948222
−0.001948222


aψSi(1)
−0.027558032
−0.027558032
−0.027558032
−0.027558032


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
1129197.497
1129197.497
1129197.497
1129197.497


bψSi(3)
−1524.372996
−1524.372996
−1524.372996
−1524.372996


bψSi(2)
776.3813947
776.3813947
776.3813947
776.3813947


cψSi
41.52892562
41.52892562
41.52892562
41.52892562


aθLT(2)
0
0
0
0


aθLT(1)
0.018744549
0.018744549
0.018744549
0.018744549


bθLT(2)
0
0
0
0


cθLT
−49.25619835
−49.25619835
−49.25619835
−49.25619835


dTLTTS
140.6234074
140.6234074
140.6234074
140.6234074


dTLTTE
−25.20654793
−25.20654793
−25.20654793
−25.20654793


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−1.78.9519626
−1.789519626
−1.789519626
−1.789519626


















TABLE 54









Si(110)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
39.68139696
39.68139696


aTLT(1)
−3.912934705
−3.912934705
−3.801935963
−3.801935963


bTLT(2)
0
0
0.00692398
0.00692398


cTLT
0.306451613
0.306451613
0.297857143
0.297857143


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
1.912614784
1.912614784
−6.089810932
−6.089810932


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.148924731
0.148924731
0.347857143
0.347857143


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
8.78847E−06
8.78847E−06


aψSi(2)
−0.0004718
−0.0004718
−0.000160567
−0.000160567


aψSi(1)
0.003265633
0.003265633
−0.023574651
−0.023574651


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
2351.597668
2351.597668


bψSi(2)
847.4765869
847.4765869
880.2091837
880.2091837


cψSi
35.32258065
35.32258065
43.07142857
43.07142857


aθLT(2)
0.005014741
0.005014741
0
0


aθLT(1)
0.023115164
0.023115164
0.030121011
0.03012011


bθLT(2)
67.0626662
67.0626662
0
0


cθLT
−49.62365591
−49.62365591
−51.28571429
−51.28571429


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0.125572529
0.125572529


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0.563162206
0.563162206
−0.417002414
−0.417002414


dψSiθLT
0
0
0
0


e
−2.002512986
−2.002512986
−2.550158637
−2.550158637


















TABLE 55









Si(110)



Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
2.992014692
2.992014692
−1.461725087
−1.461725087


bTLT(2)
0
0
0
0


cTLT
0.156390977
0.156390977
0.155345912
0.155345912


aTS(2)
0
0
0
0


aTS(1)
−9.089925228
−9.089925228
−1.247751383
−1.247751383


bTS(2)
0
0
0
0


cTS
0.305263158
0.305263158
0.327672956
0.327672956


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
−130.6388144
−130.6388144


aTE(1)
5.773590917
5.773590917
−0.010504162
−0.010504162


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.006662711
0.006662711


cTE
0.166541353
0.166541353
0.341823899
0.341823899


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
1.03604E−05
1.03604E−05


aψSi(2)
−0.000377109
−0.000377109
−0.000138558
−0.000138558


aψSi(1)
−0.013702515
−0.013702515
−0.028102653
−0.028102653


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
3096.349671
3096.349671


bψSi(2)
792.2381141
792.2381141
957.6361695
957.6361695


cψSi
41.39097744
41.39097744
43.20754717
43.20754717


aθLT(2)
0
0
0
0


aθLT(1)
0.015804666
0.015804666
0.028892246
0.028892246


bθLT(2)
0
0
0
0


cθLT
−49.32330827
−49.32330827
−49.62264151
−49.62264151


dTLTTS
0
0
−44.5976835
−44.5976835


dTLTTE
80.90186655
80.90186655
−150.2428298
−150.2428298


dTLTψSi
0
0
0.225109644
0.225109644


dTLTθLT
0
0
0
0


dTSTE
29.68261053
29.68261053
47.35851038
47.35851038


dTSψSi
0.136750854
0.136750854
0
0


dTSθLT
0
0
0
0


dTEψSi
−0.146211814
−0.146211814
0
0


dTEθLT
0.41229257
0.41229257
0
0


dψSiθLT
0
0
0
0


e
−2.596813807
−2.596813807
−2.049341112
−2.049341112


















TABLE 56









Si(110)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−2.80791074
−2.80791074
0
0


bTLT(2)
0
0
0
0


cTLT
0.3069869
0.3069869
0
0


aTS(2)
0
0
0
0


aTS(1)
−5.618098986
−5.618098986
0
0


bTS(2)
0
0
0
0


cTS
0.286462882
0.286462882
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
−73.23839461
−73.23839461


aTE(1)
8.962154821
8.962154821
−5.710295136
−5.710295136


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.007310763
0.007310763


cTE
0.167467249
0.167467249
0.330930233
0.330930233


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
0.003677309
0.003677309
0
0


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
40.93886463
40.93886463
0
0


aθLT(2)
0.00527863
0.00527863
0
0


aθLT(1)
0.008431458
0.008431458
0
0


bθLT(2)
66.00179249
66.00179249
0
0


cθLT
−50.61135371
−50.61135371
−90
−90


dTLTTS
63.6265441
63.6265441
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
57.20229582
57.20229582
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
−0.098212695
−0.098212695
0
0


dTEθLT
0.32576925
0.32576925
0
0


dψSiθLT
0
0
0
0


e
−2.431352404
−2.431352404
−2.39032093
−2.39032093


















TABLE 57









Si(110)



Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−11.04825287
−11.04825287
−11.04825287
−11.04825287


bTLT(2)
0
0
0
0


cTLT
0.164705882
0.164705882
0.164705882
0.164705882


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−12.86806521
−12.86806521
−12.86806521
−12.86806521


aTE(1)
39.88235294
39.88235294
39.88235294
39.88235294


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.019258131
0.019258131
0.019258131
0.019258131


cTE
0.286470588
0.286470588
0.286470588
0.286470588


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.000762445
−0.000762445
−0.000762445
−.0.000762445


aψSi(1)
−0.031584918
−0.031584918
−0.031584918
−0.031584918


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
749.7716263
749.7716263
749.7716263
749.7716263


cψSi
52.58823529
52.58823529
52.58823529
52.58823529


aθLT(2)
−0.004115091
−0.004115091
−0.004115091
−0.004115091


aθLT(1)
0.023260981
0.023260981
0.023260981
0.023260981


bθLT(2)
81.16262976
81.16262976
81.16262976
81.16262976


cθLT
−50.11764706
−50.11764706
−50.11764706
−50.11764706


dTLTTS
0
0
0
0


dTLTTE
−32.35244505
−32.35244505
−32.35244505
−32.35244505


dTLTψSi
0.348515389
0.348515389
0.348515389
0.348515389


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
0.000823202
0.000823202
0.000823202
0.000823202


e
−1.678155024
−1.678155024
−1.678155024
−1.678155024


















TABLE 58









Si(110)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
34.01092867
34.01092867


aTLT(1)
−3.294448859
−3.294448859
−2.996122319
−2.996122319


bTLT(2)
0
0
0.005572031
0.005572031


cTLT
0.328378378
0.328378378
0.31344086
0.31344086


aTS(2)
0
0
0
0


aTS(1)
2.752851676
2.752851676
−1.564359965
−1.564359965


bTS(2)
0
0
0
0


cTS
0.162837838
0.162837838
0.160752688
0.160752688


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−4.548790211
−4.548790211
−1.370514553
−1.370514553


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.165540541
0.165540541
0.355913978
0.355913978


aψSi(6)
0
0
0
0


aψSi(5)
−7.03888E−08
−7.03888E−08
−3.78178E−08
−3.78178E−08


aψSi(4)
 1.4265E−06
 1.4265E−06
9.79065E−07
9.79065E−07


aψSi(3)
0.000180358
0.000180358
9.73597E−05
9.73597E−05


aψSi(2)
−0.002681874
−0.002681874
−0.00192926
−0.00192926


aψSi(1)
−0.092266284
−0.092266284
−0.04329175
−0.04329175


bψSi(6)
0
0
0
0


bψSi(5)
11701030.08
11701030.08
24265475.25
24265475.25


bψSi(4)
1439156.296
1439156.296
1705613.393
1705613.393


bψSi(3)
1798.436559
1798.436559
6938.899332
6938.899332


bψSi(2)
930.5183985
930.5183985
1060.880593
1060.880593


cψSi
40.23648649
40.23648649
40.08064516
40.08064516


aθLT(2)
0
0
0
0


aθLT(1)
0.046000242
0.046000242
0.001380272
0.001380272


bθLT(2)
0
0
0
0


cθLT
−49.52702703
−49.52702703
−50.05376344
−50.05376344


dTLTTS
−136.9978702
−136.9978702
−73.06084164
−73.06084164


dTLTTE
0
0
0
0


dTLTψSi
0
0
0.096651605
0.096651605


dTLTθLT
0
0
0
0


dTSTE
0
0
−56.78924979
−56.78924979


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.081014811
0.081014811
0
0


dTEθLT
0
0
−0.194432704
−0.194432704


dψSiθLT
0
0
0.000875955
0000875955


e
−2.543790382
−2.543790382
−2.964933907
−2.964933907


















TABLE 59









Si(110)



Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 60
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−13.1565646
−13.1565646
−13.1565646
−13.1565646


bTLT(2)
0
0
0
0


cTLT
0.179661017
0.179661017
0.179661017
0.179661017


aTS(2)
−54.97015257
−54.97015257
−54.97015257
−54.97015257


aTS(1)
1.195559996
1.195559996
1.195559996
1.195559996


bTS(2)
0.006496856
0.006496856
0.006496856
0.006496856


cTS
0.299435028
0.299435028
0.299435028
0.299435028


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−12.83875925
−12.83875925
−12.83875925
−12.83875925


aTE(1)
−2.591177902
−2.591177902
−2.591177902
−2.591177902


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.02062115
0.02062115
0.02062115
0.02062115


cTE
0.282768362
0.282768362
0.282768362
0.282768362


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.00094978
−0.00094978
−0.00094978
−0.00094978


aψSi(1)
−0.016861509
−0.016861509
−0.016861509
−0.016861509


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
−0.00094978
−0.00094978
−0.00094978
−0.00094978


cψSi
44.83050847
44.83050847
44.83050847
44.83050847


aθLT(2)
0
0
0
0


aθLT(1)
0.020120147
0.020120147
0.020120147
0.020120147


bθLT(2)
0
0
0
0


cθLT
−50.50847458
−50.50847458
−50.50847458
−50.50847458


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0.250474306
0.250474306
0.250474306
0.250474306


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.031071552
0.031071552
0.031071552
0.031071552


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−1.687640015
−1.687640015
−1.687640015
−1.687640015


















TABLE 60









Si(110)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90















aTLT(2)
0
0
0
0


aTLT(1)
−8.387315737
−8.387315737
−11.34973266
−6.017883428


bTLT(2)
0
0
0
0


cTLT
0.313377926
0.313377926
0.291082803
0.294578313


aTS(2)
0
0
0
0


aTS(1)
0.14098252
0.140898252
3.107378473
2.287606243


bTS(2)
0
0
0
0


cTS
0.299331104
0.299331104
0.277707006
0.296385542


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−1.209727849
−1.209727849
−4.259242642
−1.280235687


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.152006689
0.152006689
0.343630573
0.351204819


aψSi(6)
0
0
0
0


aψSi(5)
−2.33027E−08
−2.33027E−08
0
0


aψSi(4)
7.78115E−07
7.78115E−07
0
0


aψSi(3)
5.59108E−05
5.59108E−05
−0.000194818
0


aψSi(2)
−0.002410767
−0.002410767
0.000247924
0


aψSi(1)
−0.027662563
−0.027662563
0.12904143
−0.026766472


bψSi(6)
0
0
0
0


bψSi(5)
2083705.649
2083705.649
0
0


bψSi(4)
1386257.115
1386257.115
0
0


bψSi(3)
−1267.413434
−1267.413434
1811.750092
0


bψSi(2)
895.5856198
895.5856198
293.105197
0


cψSi
42.14046823
42.14046823
19.39490446
67.95180723


aθLT(2)
0
0
0
0


aθLT(1)
0.020067585
0.020067585
−0.011988832
0.032566601


bθLT(2)
0
0
0
0


cθLT
−49.73244147
−49.73244147
−49.61783439
−50.96385542


dTLTTS
0
0
0
0


dTLTTE
0
0
0
41.29194486


dTLTψSi
0
0
−0.203585177
0.376861254


dTLTθLT
0
0
−0.273779971
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
−0.20937463


dTSθLT
−0.349110894
−0.349110894
0
0


dTEψSi
0
0
0
0


dTEθLT
−0.216865482
−0.216865482
0
0


dψSiθLT
0
0
0.00120304
0


e
−2.390757235
−2.390757235
−2.548464154
−2.523994879


















TABLE 61









Si(111)



First higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
16.07631847
20.22733656
30.72650306
27.83979251


bTLT(2)
0
0
0
0


cTLT
0.145833333
0.1625
0.159574468
0.158695652


aTS(2)
0
0
0
0


aTS(1)
17.08812597
27.84866827
31.28009383
12.67453621


bTS(2)
0
0
0
0


cTS
0.154166667
0.172916667
0.161702128
0.163043478


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−96.15629371
0
138.3065683
0


aTE(1)
−1.263589744
2.883915191
−9.345807167
−7.807789594


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.006649306
0
0.006229063
0


cTE
0.170833333
0.14375
0.369148936
0.345652174


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
−0.006862727


aψSi(1)
−0.101535567
−0.012511908
−0.101466433
0.176438509


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
114.9456522


cψSi
24.375
44.375
22.0212766
37.5


aθLT(2)
0
0
0
0


aθLT(1)
0
0
0
0


bθLT(2)
0
0
0
0


cθLT
−90
−90
−90
−90


dTLTTS
−477.9162005
−760.9473336
−1054.386561
−1044.340968


dTLTTE
0
0
0
0


dTLTψSi
0
1.332405924
0
0


dTLTθLT
0
0
0
0


dTSTE
0
−250.1524613
102.33575
105.8611165


dTSψSi
0
0
0
−2.093429604


dTSθLT
0
0
0
0


dTEψSi
−0.613440559
0
1.201832187
−0.525734733


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−0.553295028
−1.074792989
−1.290770348
−1.165057152


















TABLE 62









Si(111)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
−262.3995984
−262.3995984
0
0


aTLT(1)
−59.70400634
−59.70400634
−18.45032018
−20.44479246


bTLT(2)
0.004691358
0.004691358
0
0


cTLT
0.355555556
0.355555556
0.332352941
0.331914894


aTS(2)
0
0
0
0


aTS(1)
−73.33869606
−73.33869606
−9.963926388
−24.5747574


bTS(2)
0
0
0
0


cTS
0.185185185
0.185185185
0.166176471
0.165957447


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
−19.84024877
−19.84024877
−8.905455835
−17.17093947


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.157407407
0.157407407
0.369117647
0.373404255


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
−4.69771E−05
−4.69771E−05
0
0


aψSi(3)
−0.000362538
−0.000362538
0
0


aψSi(2)
0.055133453
0.055133453
−0.004320224
0.02112516


aψSi(1)
0.020862911
0.020862911
−0.110606012
−0.064218508


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
138552.1512
138552.1512
0
0


bψSi(3)
−78.36076818
−78.36076818
0
0


bψSi(2)
203.1635802
203.1635802
145.9775087
66.20642825


cψSi
33.05555556
33.05555556
19.41176471
34.46808511


aθLT(2)
0
0
0
0


aθLT(1)
−0.079155699
−0.079155699
0
0.057672719


bθLT(2)
0
0
0
0


cθLT
−49.81481481
−49.81481481
−90
−49.14893617


dTLTTS
0
0
0
0


dTLTTE
−254.5809235
−254.5809235
80.69948416
99.56817027


dTLTψSi
2.260189055
2.260189055
0
0


dTLTθLT
−0.785540829
−0.785540829
0
0


dTSTE
−292.5762951
−292.5762951
0
0


dTSψSi
−5.914103654
−5.914103654
−1.139436429
0


dTSθLT
0
0
0
0


dTEψSi
1.75463008
1.75463008
0.660099875
−3.844659844


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0.006965097


e
−1.304804416
−1.304804416
−2.734683251
−3.115044468


















TABLE 63









Si(111)



First higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0.003649147
0
0
0


aTLT(1)
−17.27824731
−24.3903101
−38.65647339
−21.91795924


bTLT(2)
67.18624026
0
0
0


cTLT
0.154098361
0.15631068
0.17
0.1575


aTS(2)
84.63185118
0
148.7691928
140.0125491


aTS(1)
−6.307527081
−32.68184816
−15.38083251
−11.91949736


bTS(2)
0.004461166
0
0.005012245
0.004623438


cTS
0.352459016
0.345631068
0.331428571
0.33875


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
2.909874306
8.840975559
−16.54803788
−0.024546617


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.135245902
0.148058252
0.372857143
0.33195


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0.006216698
0
0


aψSi(1)
−0.068574135
−0.018885558
−0.187578295
0.122573316


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
147.1439344
0
0


cψSi
22.62295082
43.10679612
22.71428571
39.1875


aθLT(2)
0
0
0
0


aθLT(1)
0.023219728
0.047846607
0.097088558
0.096327065


bθLT(2)
0
0
0
0


cθLT
−50.16393443
−50.38834951
−50.42857143
−51.25


dTLTTS
0
−144.763071
0
0


dTLTTE
0
0
−161.2345526
0


dTLTψSi
−0.827435588
0
0
1.107475984


dTLTθLT
0
0
0
0


dTSTE
0
103.0553675
−65.68497311
0


dTSψSi
0
−1.329400713
0.82928215
−0.646921162


dTSθLT
0
0
0
0


dTEψSi
−0.681669875
0.653050787
0.676734069
0.936807034


dTEθLT
0
0
0.481989709
0.52746173


dψSiθLT
0
0
0
0


e
−1.560056382
−2.656750279
−2.259351603
−1.805786084


















TABLE 64









Si(111)



First higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
77.3065693
243.6937004
0


aTLT(1)
−13.49335267
−9.878165228
−6.309863061
−12.90130633


bTLT(2)
0
0.00674795
0.006522811
0


cTLT
0.300961538
0.297350993
0.29858156
0.306818182


aTS(2)
133.2691939
160.4037443
82.71737336
100.5491122


aTS(1)
−9.215218873
−21.20902158
−9.283157312
−7.984268054


bTS(2)
0.006618898
0.005353274
0.006382979
0.005704201


cTS
0.314423077
0.303311258
0.3
0.311363636


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
90.39669198
0
0


aTE(1)
0.170720276
3.925569914
−15.08313602
−9.451928755


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006615499
0
0


cTE
0.15
0.147350993
0.363475177
0.346212121


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
−0.00740803
0
0
0


aψSi(1)
−0.220502432
0.083594751
−0.104344279
0.088096624


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
135.4659763
0
0
0


cψSi
20.76923077
43.70860927
17.87234043
41.47727273


aθLT(2)
0
0
0
0


aθLT(1)
−0.017420386
−0.012240534
0
0


bθLT(2)
0
0
0
0


cθLT
−50.28846154
−50.26490066
−90
−90


dTLTTS
149.298265
220.9283416
135.5319056
135.1493422


dTLTTE
0
0
0
−65.38520659


dTLTψSi
0
0
0
−0.663828772


dTLTθLT
−0.703824061
−0.739197646
0
0


dTSTE
122.4270642
0
−94.62792088
0


dTSψSi
0.714493384
−1.189155195
0
−1.017237669


dTSθLT
0
0
0
0


dTEψSi
0
0.558597609
0
0


dTEθLT
0.734424122
0.628956462
0
0


dψSiθLT
−0.003900657
0.003268439
0
0


e
−2.246432623
−2.691572945
−3.425676672
−3.236112132


















TABLE 65









Si(111)



Second higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−26.67263869
−6.49243933
−20.61574251
−21.06290014


bTLT(2)
0
0
0
0


cTLT
0.15443038
0.175438596
0.160759494
0.156896552


aTS(2)
0
0
0
0


aTS(1)
−7.971316395
7.232224634
−16.40433051
−3.920556446


bTS(2)
0
0
0
0


cTS
0.14556962
0.133333333
0.144303797
0.144827586


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
−110.7824708
−133.1826499
0


aTE(1)
12.77975858
−10.04988717
5.027045348
−5.686378626


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006463527
0.006582278
0


cTE
0.151265823
0.144736842
0.35
0.35862069


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
−0.007219474
0


aψSi(1)
0.028716852
0.04192074
−0.016815807
0.008780601


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
125.0280404
0


cψSi
9.683544304
50
11.58227848
48.10344828


aθLT(2)
0.01035547
0
0
0.014789077


aθLT(1)
0.162093889
0.106646805
0.164306798
0.04587348


bθLT(2)
61.8811088
0
0
55.43995244


cθLT
−49.62025316
−50.35087719
−51.01265823
−51.20689655


dTLTTS
−609.1883956
−724.6623011
−297.9828576
−203.214973


dTLTTE
−215.420422
0
159.6303697
0


dTLTψSi
0
−3.771938969
2.003207828
−2.014745526


dTLTθLT
1.80686724
0
2.218853872
0


dTSTE
0
−307.4269587
0
0


dTSψSi
0
0
−1.097992723
0


dTSθLT
1.985202008
0
2.104127874
0


dTEψSi
0
0
−1.451355926
0


dTEθLT
−203.386471
1.145649707
0
0


dψSiθLT
2.42647485
0.004357557
0
0


e
−5.019952207
−2.13826109
−3.235663805
−3.326865691


















TABLE 66









Si(111)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
45.51074293
−94.44342524
0


aTLT(1)
0.788515154
−3.454988617
−9.832405019
−3.192556866


bTLT(2)
0
0.006485261
0.006459172
0


cTLT
0.298058252
0.295238095
0.298461538
0.298913043


aTS(2)
0
0
0
0


aTS(1)
−8.97795964
1.31344944
0
0


bTS(2)
0
0
0
0


cTS
0.142718447
0.147619048
0
0


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
0
0


aTE(1)
9.791468713
0.170587985
−0.71523762
−10.72534988


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.15776699
0.124603175
0.356153846
0.347826087


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0.003924448
0.001661439
0
0.00657999


aψSi(1)
0.15776699
−0.024952541
0.02404454
−0.067389114


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
148.4588557
132.0861678
0
152.6937618


cψSi
15.29126214
46.9047619
14.19230769
43.04347826


aθLT(2)
0
0
0
0


aθLT(1)
0.06700163
0.042141715
0.055240362
0.061747926


bθLT(2)
0
0
0
0


cθLT
−48.73786408
−50.15873016
−49.76923077
−49.45652174


dTLTTS
116.7290786
−78.78450728
0
0


dTLTTE
0
85.46351406
−49.85282875
0


dTLTψSi
−0.70199108
0.445481139
0
0.604657146


dTLTθLT
−0.726496636
0
0
0


dTSTE
0
−116.360096
0
0


dTSψSi
0
−0.622709588
0
0


dTSθLT
2.041329502
−0.339115637
0
0


dTEψSi
0
0.20688896
0
0


dTEθLT
0.774150432
0.439880407
−0.6608739
−1.068569294


dψSiθLT
−0.005400114
0.002667922
−0.004937546
0.006290209


e
−4.209434885
−1.791078273
−3.48174155
−3.934527612


















TABLE 67









Si(111)



Second higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−4.673850215
0
−8.8586067
−1.957300157


bTLT(2)
0
0
0
0


cTLT
0.141509434
0
0.153125
0.16


aTS(2)
82.42811022
0
87.42203531
0


aTS(1)
−7.905282467
−4.948155925
−0.569845134
0.521030757


bTS(2)
0.006949092
0
0.006037326
0


cTS
0.294339623
0.314583333
0.297916667
0.285


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
53.51232744
−79.38404758
0
0


aTE(1)
10.58973083
10.26534018
8.135327356
−7.251553825


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.006016376
0.005677083
0
0


cTE
0.183962264
0.1375
0.336458333
0.37


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0.001429494


aψSi(1)
0.010122468
0.039888924
−0.016592245
−0.004853684


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
145.6875


cψSi
11.88679245
48.4375
14.0625
45.75


aθLT(2)
0
0
0
0


aθLT(1)
−0.005093912
0.011098836
0.047530531
0.04750516


bθLT(2)
0
0
0
0


cθLT
−50
−50.41666667
−50.72916667
−49.75


dTLTTS
0
0
91.19418307
251.5375225


dTLTTE
0
0
−156.3654518
0


dTLTψSi
0.322255595
0
0
−0.289820964


dTLTθLT
−0.768436344
0
−0.735737765
0


dTSTE
0
75.51836907
0
0


dTSψSi
−0.512402643
0.300543357
−0.724013025
0.245746891


dTSθLT
0
0
0
0


dTEψSi
0
0
−0.50556971
0


dTEθLT
0
0
0
0


dψSiθLT
0
0.002842264
0
0


e
−2.770026639
−2.638591885
−1.980941925
−2.412296494


















TABLE 68









Si(111)



Second higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
4.449764983
0
−13.78321665
−10.59163435


bTLT(2)
0
0
0
0


cTLT
0.321052632
0
0.309146341
0.303164557


aTS(2)
0
0
0
0


aTS(1)
0
−3.433673203
−1.746861763
3.363230821


bTS(2)
0
0
0
0


cTS
0
0.283443709
0.287804878
0.293037975


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
86.18383552
0


aTE(1)
3.853394073
8.768511808
−1.867550529
−15.68616064


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0.007157942
0


cTE
0.181578947
0.135430464
0.356097561
0.363291139


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
0.014178515
0.049910217
−0.008697771
0.012742666


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
12.63157895
45.99337748
15.09146341
45


aθLT(2)
0
0
0
0


aθLT(1)
0
0.061867934
0.051566965
0.028929641


bθLT(2)
0
0
0
0


cθLT
−90
−50.59602649
−50.30487805
−50.56962025


dTLTTS
0
0
0
−103.0440888


dTLTTE
0
0
0
0


dTLTψSi
−0.181721459
0
0
0


dTLTθLT
0
0
0
−0.608943868


dTSTE
0
113.1914268
−75.04640382
−82.04954672


dTSψSi
0
0
−0.554356722
0.673316097


dTSθLT
0
0
0
0


dTEψSi
0
0
−0.512800103
0


dTEθLT
0
0
−0.656702553
0


dψSiθLT
0
0
0
0


e
−2.401219798
−3.18651044
−3.93030224
−4.143483981


















TABLE 69









Si(111)



Third higher-order mode



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−3.047618237
−3.047618237
−3.047618237
−3.047618237


bTLT(2)
0
0
0
0


cTLT
0.160869565
0.160869565
0.160869565
0.160869565


aTS(2)
0
0
0
0


aTS(1)
0
0
0
0


bTS(2)
0
0
0
0


cTS
0
0
0
0


aTE(4)
0
0
0
0


aTE(3)
11.21750437
11.21750437
11.21750437
11.21750437


aTE(2)
−3.666215654
−3.666215654
−3.666215654
−3.666215654


aTE(1)
−0.035248162
−0.035248162
−0.035248162
−0.035248162


bTE(4)
0
0
0
0


bTE(3)
0.000381688
0.000381688
0.000381688
0.000381688


bTE(2)
0.012589792
0.012589792
0.012589792
0.012589792


cTE
0.245652174
0.245652174
0.245652174
0.245652174


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.003582211
−0.003582211
−0.003582211
−0.003582211


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
35.86956522
35.86956522
35.86956522
35.86956522


aθLT(2)
−0.000596775
−0.000596775
−0.000596775
−0.000596775


aθLT(1)
0.003385783
0.003385783
0.003385783
0.003385783


bθLT(2)
77.88279773
77.88279773
77.88279773
77.88279773


cθLT
−47.82608696
−47.82608696
−47.82608696
−47.82608696


dTLTTS
0
0
0
0


dTLTTE
−2.939323227
−2.939323227
−2.939323227
−2.939323227


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
−0.000442922
−0.000442922
−0.000442922
−0.000442922


e
−0.277577227
−0.277577227
−0.277577227
−0.277577227


















TABLE 70









Si(111)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
0
0
0
0


bTLT(2)
0
0
0
0


cTLT
0
0
0
0


aTS(2)
0
0
0
0


aTS(1)
6.03484153
6.03484153
6.03484153
6.03484153


bTS(2)
0
0
0
0


cTS
0.183333333
0.183333333
0.183333333
0.183333333


aTE(4)
−215.3850281
−215.3850281
−215.3850281
−215.3850281


aTE(3)
54.12265846
54.12265846
54.12265846
54.12265846


aTE(2)
0.942905209
0.942905209
0.942905209
0.942905209


aTE(1)
−1.08045121
−1.08045121
−1.08045121
−1.08045121


bTE(4)
0.000339332
0.000339332
0.000339332
0.000339332


bTE(3)
0.000317558
0.000317558
0.000317558
0.000317558


bTE(2)
0.011265432
0.011265432
0.011265432
0.011265432


cTE
0.211111111
0.211111111
0.211111111
0.211111111


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.004526908
−0.004526908
−0.004526908
−0.004526908


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
27.5
27.5
27.5
27.5


aθLT(2)
−0.00046365
−0.00046365
−0.00046365
−0.00046365


aθLT(1)
0.005349146
0.005349146
0.005349146
0.005349146


bθLT(2)
57.09876543
57.09876543
57.09876543
57.09876543


cθLT
−46.11111111
−46.11111111
−46.11111111
−46.11111111


dTLTTS
0
0
0
0


dTLTTE
0
0
0
0


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
45.80413521
45.80413521
45.80413521
45.80413524


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
−0.071786246
−0.071786246
−0.071786246
−0.071786246


dψSiθLT
−0.000425881
−0.000425881
−0.000425881
−0.000425881


e
−0.446604617
−0.446604617
−0.446604617
−0.446604617


















TABLE 71









Si(111)



Third higher-order mode



0 < TLT < 0.2



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
−2.477108842
−2.477108842
−2.477108842
−2.477108842


bTLT(2)
0
0
0
0


cTLT
0.137349398
0.137349398
0.137349398
0.137349398


aTS(2)
0
0
0
0


aTS(1)
−0.488747927
−0.488747927
−0.488747927
−0.488747927


bTS(2)
0
0
0
0


cTS
0.336144578
0.336144578
0.336144578
0.336144578


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−1.973253274
−1.973253274
−1.973253274
−1.973253274


aTE(1)
−0.124870592
−0.124870592
−0.124870592
−0.124870592


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0.017915517
0.017915517
0.017915517
0.017915517


cTE
0.256024096
0.256024096
0.256024096
0.256024096


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
 7.6083E−07
 7.6083E−07
 7.6083E−07
 7.6083E−07


aψSi(3)
7.21121E−06
7.21121E−06
7.21121E−06
7.21121E−06


aψSi(2)
−0.000857107
−0.000857107
−0.000857107
−0.000857107


aψSi(1)
−0.00490823
−0.00490823
−0.00490823
−0.00490823


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
105622.9088
105622.9088
105622.9088
105622.9088


bψSi(3)
−217.2019476
−217.2019476
−217.2019476
−217.2019476


bψSi(2)
208.4409929
208.4409929
208.4409929
208.4409929


cψSi
30.54216867
30.54216867
30.54216867
30.54216867


aθLT(2)
0
0
0
0


aθLT(1)
0
0
0
0


bθLT(2)
0
0
0
0


cθLT
−90
−90
−90
−90


dTLTTS
4.821777856
4.821777856
4.821777856
4.821777856


dTLTTE
−4.14067246
−4.14067246
−4.14067246
−4.14067246


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
0
0
0
0


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0.024454063
0.024454063
0.024454063
0.024454063


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−0.240178915
−0.240178915
−0.240178915
−0.240178915


















TABLE 72









Si(111)



Third higher-order mode



0.2 ≤ TLT ≤ 3.5



0.2 ≤ TS ≤ 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60
0 ≤ ψSi < 30
30 ≤ ψSi ≤ 60















aTLT(2)
0
0
0
0


aTLT(1)
0
0
0
0


bTLT(2)
0
0
0
0


cTLT
0
0
0
0


aTS(2)
0
0
0
0


aTS(1)
0.380779889
0.380779889
0.380779889
0.380779889


bTS(2)
0
0
0
0


cTS
0.285294118
0.285294118
0.285294118
0.285294118


aTE(4)
−165.3225345
−165.3225345
−165.3225345
−165.3225345


aTE(3)
23.65923214
23.65923214
23.65923214
23.65923214


aTE(2)
2.256295059
2.256295059
2.256295059
2.256295059


aTE(1)
−0.292409126
−0.292409126
−0.292409126
−0.292409126


bTE(4)
0.00051583
0.00051583
0.00051583
0.00051583


bTE(3)
0.00070344
0.00070344
0.00070344
0.00070344


bTE(2)
0.015017301
0.015017301
0.015017301
0.015017301


cTE
0.220588235
0.220588235
0.220588235
0.220588235


aψSi(6)
0
0
0
0


aψSi(5)
0
0
0
0


aψSi(4)
0
0
0
0


aψSi(3)
0
0
0
0


aψSi(2)
0
0
0
0


aψSi(1)
−0.004846255
−0.004846255
−0.004846255
−0.004846255


bψSi(6)
0
0
0
0


bψSi(5)
0
0
0
0


bψSi(4)
0
0
0
0


bψSi(3)
0
0
0
0


bψSi(2)
0
0
0
0


cψSi
29.55882353
29.55882353
29.55882353
29.55882353


aθLT(2)
0
0
0
0


aθLT(1)
0.00165846
0.00165846
0.00165846
0.00165846


bθLT(2)
0
0
0
0


cθLT
−48.52941176
−48.52941176
−48.52941176
−48.52941176


dTLTTS
−0.04933649
−0.04933649
−0.04933649
−0.04933649


dTLTTE
−0.021023839
−0.021023839
−0.021023839
−0.021023839


dTLTψSi
0
0
0
0


dTLTθLT
0
0
0
0


dTSTE
−7.074776252
−7.074776252
−7.074776252
−7.074776252


dTSψSi
0
0
0
0


dTSθLT
0
0
0
0


dTEψSi
0
0
0
0


dTEθLT
0
0
0
0


dψSiθLT
−0.00049898
−0.00049898
−0.00049898
−0.00049898


e
−0.3405485
−0.3405485
−0.3405485
−0.3405485









The inventors of preferred embodiments of the present invention have examined how the strength of the responses of the first higher-order mode, the second higher-order mode, and the third higher-order mode change by variously changing the design parameters of TLT, θLT, TS, TE, ψSi, and TSi.


As the strength of response of the higher-order mode when the parameters are changed, the absolute value of S11 was determined. A smaller decibel value of the absolute value of S11 indicates a higher strength of the response of the higher-order mode. In the case of calculating S11, the intersecting width of the electrode fingers was 20λ, the number of pairs of the electrode fingers was 94, and S11 was determined by a two-dimensional finite element method using an electrode single-pair model.


The interdigital transducer electrodes had a structure in which metal films were stacked in order of Ti/Pt/Ti/Al from the piezoelectric body side. The thickness of the interdigital transducer electrodes was changed by changing the thickness of the Pt film. As the wave length-normalized film thickness TE of the interdigital transducer electrodes, a wave length-normalized film thickness in terms of aluminum thickness was determined using the total mass of the interdigital transducer electrodes estimated from the density of each of the metal films.


First Higher-Order Mode


An acoustic wave resonator having the admittance characteristics illustrated in FIG. 2 is used as a reference structure. FIGS. 3 to 7 each illustrate a change in the strength S11 of the response of the first higher-order mode when the parameters are changed with respect to the reference structure. FIG. 3 indicates that the strength S11 of the response of the first higher-order mode changes when the propagation direction ψSi in the single-crystal Si layer changes from about 0° to about 45° with respect to the reference structure.


Similarly, FIG. 4 indicates that the strength S11 of the response of the first higher-order mode changes also when the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate changes.


As illustrated in FIG. 5, the strength S11 of the response of the first higher-order mode changes also when the cut angle (90°+θLT) of the piezoelectric body made of lithium tantalate changes.


As illustrated in FIG. 6, the strength S11 of the response of the first higher-order mode changes also when the wave length-normalized film thickness TS of the SiO2 film changes.


As illustrated in FIG. 7, the strength S11 of the response of the first higher-order mode changes also when the wave length-normalized film thickness TE of the interdigital transducer electrodes in terms of Al thickness changes.



FIGS. 3 to 7 indicate that the strength of the response of the first higher-order mode is able to be adjusted by changing these parameters. That is, the strength of the response of the first higher-order mode is able to be reduced by selecting the values of the parameters while the response of the main mode is maintained.


From the calculation results of FIGS. 3 to 7 and the like, the inventors of preferred embodiments of the present invention have derived the fact that Ih corresponding to the strength of the response of the higher-order mode is determined from the Formula (1) described above and the coefficients a, b, c, d, and e in Tables 37 to 72.


The inventors of preferred embodiments of the present invention have discovered that the coefficients in Formula (1) are values presented in Table 37 to 40, Tables 49 to 52, or Tables 61 to 64 in accordance with the ranges of the crystal orientation of the single-crystal Si layer, the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate, the wave length-normalized film thickness TS of the SiO2 film, the wave length-normalized film thickness TE of the interdigital transducer electrodes, and the propagation direction ψSi in the single-crystal Si layer. Thus, the conditions of TLT, θLT, TS, TE, and ψSi when Ih1 corresponding to the strength of the response of the first higher-order mode is more than about −2.4 are determined.


In a multiplexer in which multiple acoustic wave filters are connected at one terminal of each filter, the response of a higher-order mode in any one of the multiple acoustic wave filters is required to have a strength S11 of more than about −2.4 dB. This is because the influence on transmission characteristics of acoustic wave filters other than the one of the multiple acoustic wave filters is negligible. In cellular phones and the like, for example, usually, ripples appearing in a pass band of a filter are required to be about −0.8 dB or more from the viewpoint of ensuring the receiver sensitivity. It has been discovered that in the case where a higher-order mode of one acoustic wave filter is in the pass band of another acoustic wave filter, ripples having a strength of about ⅓ of the strength of the response of the higher-order mode occur in the pass band of another filter. Thus, in order to achieve ripples having a magnitude of about −0.8 dB or more in the pass band of another filter, the strength S11 of the response of the higher-order mode of one filter may be more than about −2.4 dB.


Additionally, in the acoustic wave device 1 according to the first preferred embodiment, TSi>20.


Regarding the first higher-order mode, Ih is larger than about −2.4 (Ih>−2.4), and TSi is larger than about 20 (TSi>20). It is thus possible to effectively reduce or prevent the influence of the response of the first higher-order mode on the pass band of another acoustic wave filter. This will be described with reference to FIGS. 8 to 11.



FIG. 8 is a circuit diagram of a multiplexer. In a multiplexer 10, first to fourth acoustic wave filters 11 to 14 are commonly connected on the antenna terminal 15 side. FIG. 9 is a circuit diagram of a first acoustic wave filter 11. The first acoustic wave filter 11 includes multiple series-arm resonators S1 to S3 and multiple parallel-arm resonators P1 and P2. That is, the first acoustic wave filter 11 is a ladder filter. The series-arm resonators S1 to S3 and the parallel-arm resonators P1 and P2 are defined by the acoustic wave devices 1.


In preferred embodiments of the present invention, the circuit configuration of the acoustic wave filter including the acoustic wave device is not limited thereto. For example, an acoustic wave filter including a longitudinally coupled resonator acoustic wave filter may be used. In this case, the longitudinally coupled resonator acoustic wave filter may be the acoustic wave device. An acoustic wave resonator coupled to the longitudinally coupled resonator acoustic wave filter may be defined by the acoustic wave device according to preferred embodiments of the present invention.


Pass bands of the first to fourth acoustic wave filters 11 to 14 are referred to as a first pass band to a fourth pass band. Regarding the frequency positions, preferably, first pass band<second pass band<third pass band<fourth pass band.


For comparison, a multiplexer including a first acoustic wave filter according to a comparative example was provided as in the foregoing preferred embodiment, except that the acoustic wave resonator having the reference structure described above was used. That is, in the multiplexer of the comparative example, the acoustic wave resonator having the reference structure and having the admittance characteristics illustrated in FIG. 2 was used in place of the acoustic wave device 1 of the present preferred embodiment described above. FIG. 10A illustrates filter characteristics of the first acoustic wave filter and a second acoustic wave filter in the multiplexer of the comparative example. A solid line indicates the filter characteristics of the first acoustic wave filter. A broken line indicates the filter characteristics of the second acoustic wave filter. Band A indicates the pass band of the first acoustic wave filter. Band B indicates the pass band of the second acoustic wave filter. A large ripple appears in the second pass band. This is because the response of the first higher-order mode of the acoustic wave resonator used in the first acoustic wave filter largely appears.



FIG. 10B illustrates filter characteristics of a multiplexer according to a preferred embodiment of the present invention. A solid line indicates the filter characteristics of the first acoustic wave filter. A broken line indicates the filter characteristics of the second acoustic wave filter. Here, the first acoustic wave filter is defined by the acoustic wave device according to the foregoing preferred embodiment. Thus, a large ripple does not appear in the second pass band. That is, in the pass band of the second acoustic wave filter, which is another filter, a large ripple does not appear. Thus, the filter characteristics of the second acoustic wave filter are not easily degraded.


As described above, in the multiplexer according to a preferred embodiment of the present invention, the response of the first higher-order mode is reduced or prevented in the acoustic wave filter including the acoustic wave device according to a preferred embodiment of the present invention. It is thus possible to effectively reduce or prevent the deterioration of the filter characteristics of another acoustic wave filter having a higher-frequency pass band than the acoustic wave filter.



FIG. 11 illustrates the relationship between the wave length-normalized film thickness of the single-crystal Si layer 2 and the maximum phases of responses of the first, second, and third higher-order modes. FIG. 11 indicates that when TSi>20, it is possible to effectively reduce or prevent the strength of the response of each of the first higher-order mode, the second higher-order mode, and the third higher-order mode.


Second Higher-Order Mode



FIG. 12 illustrates the relationship between the propagation direction ψSi in the single-crystal Si layer and the strength S11 of the response of the second higher-order mode. As is apparent from FIG. 12, the strength S11 of the response of the second higher-order mode changes when ψSi changes. Similarly, as illustrated in FIG. 13, the strength S11 of the response of the second higher-order mode changes when the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate changes. As illustrated in FIG. 14, the strength S11 of the response of the second higher-order mode changes also when the cut angle (90°+θLT) of the piezoelectric body made of lithium tantalate changes. As illustrated in FIG. 15, the strength S11 of the response of the second higher-order mode changes also when the wave length-normalized film thickness TS of the SiO2 film changes. As illustrated in FIG. 16, the strength S11 of the response of the second higher-order mode changes also when the wave length-normalized film thickness TE of the interdigital transducer electrodes in terms of Al changes.


From the calculation results of FIGS. 12 to 16 and the like, similarly to the case of the first higher-order mode, the coefficients in Formula (1) for expressing Ih2 corresponding to the strength of the response of the second higher-order mode were determined. When the coefficients of Formula (1) are set as described in Tables 41 to 44, Tables 53 to 56, or Tables 65 to 68 in accordance with ranges of the orientation of the single-crystal Si layer of (100), (110), or (111), the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate, the wave length-normalized film thickness TS of the SiO2 film, the wave length-normalized film thickness TE of the interdigital transducer electrodes, and the propagation direction ψSi, Ih2 corresponding to the strength of the response of the second higher-order mode are able to be expressed. In particular, in the case where the conditions of TLT, θLT, TS, TE, and ψSi when Ih2 is about −2.4 or more are determined and where TSi is larger than about 20 (TSi>20), the response of the second higher-order mode is also able to be sufficiently reduced.


Third Higher-Order Mode



FIG. 17 illustrates the relationship between the propagation direction ψSi in the single-crystal Si layer and the strength S11 of the response of the third higher-order mode. As is apparent from FIG. 17, the strength S11 of the response of the third higher-order mode changes when ψSi changes. Similarly, as illustrated in FIG. 18, the strength S11 of the response of the third higher-order mode changes also when the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate changes. As illustrated in FIG. 19, the strength S11 of the response of the third higher-order mode changes also when the cut angle (90°+θLT) of the piezoelectric body made of lithium tantalate changes. As illustrated in FIG. 20, the strength S11 of the response of the third higher-order mode changes also when the wave length-normalized film thickness TS of the SiO2 film changes. As illustrated in FIG. 21, the strength S11 of the response of the third higher-order mode changes also when the wave length-normalized film thickness TE of the interdigital transducer electrodes in terms of Al changes.


From FIGS. 17 to 21 and the like, the coefficients in Formula (1) for expressing Ih3 corresponding to the strength of the response of the third higher-order mode were determined. When the coefficients of Formula (1) are set as described in Tables 45 to 48, Tables 57 to 60, or Tables 69 to 72 in accordance with ranges of the orientation of the single-crystal Si layer of (100), (110), or (111), the wave length-normalized film thickness TLT of the piezoelectric body made of lithium tantalate, the wave length-normalized film thickness TS of the SiO2 film, the wave length-normalized film thickness TE of the interdigital transducer electrodes, and the propagation direction ψSi, Ih3 corresponding to the strength of the response of the third higher-order mode are able to be expressed. In particular, in the case where the conditions of TLT, θLT, TS, TE, and ψSi when Ih3 is about −2.4 or more are determined and where TSi is larger than about 20 (TSi>20), the response of the third higher-order mode is able to also be sufficiently reduced.


Regarding Ih for all of the first higher-order mode, the second higher-order mode, and the third higher-order mode, Ih>−about 2.4 is preferable. In this case, it is possible to effectively reduce or prevent the influence of the first to third higher-order modes on another acoustic wave filter. Regarding Ih for the first higher-order mode and the second higher-order mode, Ih for the first higher-order mode and the third higher-order mode, or Ih for the second higher-order mode and the third higher-order mode, Ih>about −2.4 may preferably be used. In this case, it is possible to reduce or prevent the influence of two higher-order modes selected from the first to third higher-order modes.


In the case of using the structure of preferred embodiments of the present invention, as described above, a higher-order mode tends to be confined in a portion where the SiO2 film 3 and the piezoelectric body 4 are stacked. However, in the case where the piezoelectric body 4 has a thickness of about 3.5λ or less, the stacked portion of the SiO2 film 3 and the piezoelectric body 4 has a small thickness. Thus, the higher-order mode is not easily confined therein.


More preferably, the piezoelectric body 4 made of lithium tantalate has a thickness of about 2.5λ or less, for example. In this case, the absolute value of the temperature coefficient of frequency TCF is able to be reduced. Even more preferably, the piezoelectric body 4 made of lithium tantalate has a thickness of about 1.5λ or less, for example. In this case, the electromechanical coupling coefficient is able to be easily adjusted. Still even more preferably, the piezoelectric body 4 made of lithium tantalate has a thickness of about 0.5λ or less, for example. In this case, the electromechanical coupling coefficient is able to be easily adjusted in a wide range.


In Formula (1),


a) In the case of using Si(100) (Euler angles (φSi=0±5°, θSi=0±5°, ψSi)), the range of ψSi is preferably 0°≤ψSi≤45°, for example. However, from the symmetry of the crystal structure of Si(100), ψSi and ψSi±(n×90°) have the same meaning (where n=1, 2, 3 . . . ). Similarly, ψSi and −ψSi have the same meaning.


b) In the case of using Si(110) (Euler angles (φSi=−45±5°, θSi=−90±5°, ψSi)), the range of ψSi is preferably 0°≤ψSi≤90°, for example. However, from the symmetry of the crystal structure of Si(110), ψSi and ψSi±(n×180°) have the same meaning (where n=1, 2, 3 . . . ). Similarly, ψSi and −ψSi have the same meaning.


c) In the case of using Si(111) (Euler angles (φSi=−45±5°, θSi=−54.73561±5°, ψSi)), the range of ψSi is preferably 0°≤ψSi≤60° for example. However, from the symmetry of the crystal structure of Si(111), ψSi and ψSi±(n×120°) have the same meaning (where n=1, 2, 3 . . . ). Similarly, ψSi and −ψSi have the same meaning.


The range of θLT is −180°<θLT≤0°. θLT and θLT+180° may be treated as having the same meaning.


In this specification, for example, the range of “0°±5°” in the Euler angles (0°±5°, θ, 0°±15°) means within the range about −5° or more and about +5° or less. The range of 0°±15° means within the range of about −15° or more and about +15° or less.



FIG. 22 illustrates, in an acoustic wave device in which a low-acoustic-velocity film made of a SiO2 film having a thickness of about 0.35λ and a piezoelectric film made of lithium tantalate with Euler angles of (0°, 140.0°, 0°) are stacked on a high-acoustic-velocity supporting substrate made of silicon, the relationship between the film thickness of the LiTaO3 film and the quality factor. The vertical axis of FIG. 22 is the product of the quality characteristics and the band width ratio (Δf) of the resonator. FIG. 23 illustrates the relationship between the film thickness of the LiTaO3 film and the temperature coefficient of frequency TCF. FIG. 24 illustrates the film thickness of the LiTaO3 film and the acoustic velocity. From FIG. 22, the film thickness of the LiTaO3 film is preferably about 3.5λ or less, for example. In this case, the quality factor is high, compared with the case of a film thickness of more than about 3.5λ. More preferably, the film thickness of the LiTaO3 film is about 2.5λ or less, for example, in order to further increase the quality factor.


From FIG. 23, in the case where the LiTaO3 film has a thickness of about 2.5λ or less, the absolute value of the temperature coefficient of frequency TCF is able to be reduced, compared with the case of a film thickness of more than about 2.5λ. More preferably, the film thickness of the LiTaO3 film is about 2λ or less, for example. In this case, the absolute value of the temperature coefficient of frequency TCF is able to be about 10 ppm/° C. or less. To reduce the absolute value of the temperature coefficient of frequency TCF, the film thickness of the LiTaO3 film is more preferably about 1.5λ or less, for example.


From FIG. 24, when the film thickness of the LiTaO3 film is more than 1.5λ, a change in acoustic velocity is markedly small.


As illustrated in FIG. 25, however, when the film thickness of the LiTaO3 film is in the range of about 0.05λ or more and about 0.5λ or less, the band width ratio changes greatly. Thus, the electromechanical coupling coefficient is able to be adjusted in a wider range. To extend the adjustment ranges of the electromechanical coupling coefficient and the band width ratio, the film thickness of the LiTaO3 film is preferably in the range of about 0.05λ or more and about 0.5λ or less, for example.



FIG. 26 illustrates the relationship between the film thickness of SiO2 (λ) and the acoustic velocity, and FIG. 27 illustrates the relationship between the film thickness of SiO2 (λ) and the electromechanical coupling coefficient. The acoustic wave device according to preferred embodiments of the present invention may include a low-acoustic-velocity film and a high-acoustic-velocity film disposed between the single-crystal Si layer and the piezoelectric body. Here, for example, a silicon nitride film, an aluminum oxide film, or a diamond film was preferably used as a high-acoustic-velocity film disposed below the low-acoustic-velocity film made of SiO2. The low-acoustic-velocity film refers to a film in which the acoustic velocity of a bulk wave that propagates through the low-acoustic-velocity film is lower than the acoustic velocity of an acoustic wave that propagates through the piezoelectric body. The high-acoustic-velocity film refers to a film in which the acoustic velocity of a bulk wave that propagates through the high-acoustic-velocity film is higher than the acoustic velocity of an acoustic wave that propagates through the piezoelectric body. The film thickness of the high-acoustic-velocity film was 1.5λ. The acoustic velocity of a bulk wave that propagates through silicon nitride is about 6,000 m/s. The acoustic velocity of a bulk wave that propagates through aluminum oxide is about 6,000 m/s. The acoustic velocity of a bulk wave that propagates through diamond is about 12,800 m/s. As illustrated in FIGS. 26 and 27, when the material of the high-acoustic-velocity film and the film thickness of the SiO2 film are changed, the electromechanical coupling coefficient and the acoustic velocity are little changed. In particular, as illustrated in FIG. 27, when the film thickness of the SiO2 film is about 0.1λ or more and about 0.5λ or less, the electromechanical coupling coefficient is little changed regardless of the material of the high-acoustic-velocity film. As illustrated in FIG. 26, when the film thickness of the SiO2 film is about 0.3λ or more and about 2λ or less, the acoustic velocity is unchanged regardless of the material of the high-acoustic-velocity film. Thus, the film thickness of the low-acoustic-velocity film made of silicon oxide is preferably about 2λ or less, and more preferably about 0.5λ or less, for example.


The acoustic wave device of each preferred embodiment may be used as a component, such as a multiplexer, used in a high-frequency front-end circuit. An example of such a high-frequency front-end circuit will be described below.



FIG. 28 is a schematic block diagram of a communication apparatus including a high-frequency front-end circuit according to a preferred embodiment of the present invention. A communication apparatus 240 includes an antenna 202, a high-frequency front-end circuit 230, and an RF signal processing circuit 203. The high-frequency front-end circuit 230 is a circuit section connected to the antenna 202. The high-frequency front-end circuit 230 includes a multiplexer 210 and amplifiers 221 to 224 to define and function as power amplifiers. The multiplexer 210 includes first to fourth filters 211 to 214. As the multiplexer 210, a multiplexer according to a preferred embodiment of the present invention may preferably be used. The multiplexer 210 includes a common antenna terminal 225 connected to the antenna 202. One terminal of each of the first to third filters 211 to 213 defining and functioning as reception filters and one terminal of the fourth filter 214 defining and functioning as a transmission filter are connected in common to the common antenna terminal 225. Output terminals of the first to third filters 211 to 213 are connected to the amplifiers 221 to 223, respectively. The input terminal of the fourth filter 214 is connected to the amplifier 224.


The output terminals of the amplifiers 221 to 223 are connected to the RF signal processing circuit 203. The input terminal of the amplifier 224 is connected to the RF signal processing circuit 203.


The multiplexer according to the present preferred embodiment may be appropriately used as the multiplexer 210 in the communication apparatus 240.


Multiplexer according to preferred embodiments of the present invention may include multiple transmission filters and multiple reception filters. The multiplexer includes n band-pass filters where n is 2 or more. Thus, a duplexer is also included in a multiplexer in the present invention.


Filters, multiplexers that can be used for a multiband system, front-end circuits, and communication apparatuses according to preferred embodiments of the present invention can be widely used for communication equipment such as mobile phones, for example.


While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.

Claims
  • 1. An acoustic wave device, comprising: a supporting substrate made of silicon;a silicon oxide film stacked on or above the supporting substrate;a piezoelectric body stacked on or above the silicon oxide film, the piezoelectric body being made of lithium tantalate; andinterdigital transducer electrodes disposed on or above a main surface of the piezoelectric body; whereinwhere a wave length determined by a pitch of electrode fingers of the interdigital transducer electrodes is denoted by λ, a wave length-normalized film thickness of the piezoelectric body is denoted by TLT, an Euler angle θ of the piezoelectric body is denoted by θLT, a wave length-normalized film thickness of the silicon oxide film is denoted by TS, a wave length-normalized film thickness of the interdigital transducer electrodes in terms of aluminum thickness is denoted by TE, a propagation direction in the supporting substrate is denoted by ψSi, and a wave length-normalized film thickness of the supporting substrate is denoted by TSi, TLT, θLT, TS, TE, and ψSi are set such that Ih represented by Formula (1) below for at least one of responses of a first higher-order mode, a second higher-order mode, and a third higher-order mode is more than about −2.4, and TSi>20;
  • 2. The acoustic wave device according to claim 1, wherein Ih for each of the first and second higher-order modes is more than about −2.4.
  • 3. The acoustic wave device according to claim 1, wherein Ih for each of the first and third higher-order modes is more than about −2.4.
  • 4. The acoustic wave device according to claim 1, wherein Ih for each of the second and third higher-order modes is more than about −2.4.
  • 5. The acoustic wave device according to claim 1, wherein Ih for each of the first, second, and third higher-order modes is more than about −2.4.
  • 6. The acoustic wave device according to claim 1, wherein the piezoelectric body has a thickness of about 3.5λ or less.
  • 7. The acoustic wave device according to claim 6, wherein the piezoelectric body has a thickness of about 2.5λ or less.
  • 8. The acoustic wave device according to claim 6, wherein the piezoelectric body has a thickness of about 1.5λ or less.
  • 9. The acoustic wave device according to claim 6, wherein the piezoelectric body has a thickness of about 0.5λ or less.
  • 10. The acoustic wave device according to claim 1, wherein the acoustic wave device is an acoustic wave resonator.
  • 11. An acoustic wave filter, comprising: a plurality of resonators; whereinat least one of the plurality of resonators is defined by the acoustic wave device according to claim 1.
  • 12. The acoustic wave filter according to claim 11, wherein Ih for each of the first and second higher-order modes is more than about −2.4.
  • 13. The acoustic wave filter according to claim 11, wherein Ih for each of the first and third higher-order modes is more than about −2.4.
  • 14. The acoustic wave filter according to claim 11, wherein Ih for each of the second and third higher-order modes is more than about −2.4.
  • 15. The acoustic wave filter according to claim 11, wherein Ih for each of the first, second, and third higher-order modes is more than about −2.4.
  • 16. The acoustic wave filter according to claim 11, wherein the piezoelectric body has a thickness of about 3.5λ or less.
  • 17. A multiplexer, comprising: N acoustic wave filters, where N is 2 or more, having different pass bands; whereinone terminal of each of the N acoustic wave filters is commonly connected on an antenna terminal side;at least one acoustic wave filter among the N acoustic wave filters excluding an acoustic wave filter having a highest-frequency pass band includes a plurality of acoustic wave resonators; andat least one acoustic wave resonator among the plurality of acoustic wave resonators is defined by the acoustic wave device according to claim 1.
  • 18. The multiplexer according to claim 17, wherein the multiplexer is a composite filter device for carrier aggregation.
  • 19. A high-frequency front-end circuit, comprising: an acoustic wave filter including the acoustic wave device according to claim 1; anda power amplifier connected to the acoustic wave filter.
  • 20. A communication apparatus, comprising: a high-frequency front-end circuit including an acoustic wave filter that includes the acoustic wave device according to claim 1, and a power amplifier connected to the acoustic wave filter; andan RF signal processing circuit.
Priority Claims (1)
Number Date Country Kind
2017-044689 Mar 2017 JP national
CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to Japanese Patent Application No. 2017-044689 filed on Mar. 9, 2017 and is a Continuation Application of PCT Application No. PCT/JP2018/008913 filed on Mar. 8, 2018. The entire contents of each application are hereby incorporated herein by reference.

US Referenced Citations (10)
Number Name Date Kind
4449107 Asai et al. May 1984 A
7213314 Abbott May 2007 B2
7589452 Hauser Sep 2009 B2
8436510 Yamane May 2013 B2
20040226162 Miura et al. Nov 2004 A1
20100182101 Suzuki Jul 2010 A1
20130285768 Watanabe et al. Oct 2013 A1
20130300519 Tamasaki et al. Nov 2013 A1
20150280689 Nakamura et al. Oct 2015 A1
20180102755 Takamine Apr 2018 A1
Foreign Referenced Citations (8)
Number Date Country
58-56513 Apr 1983 JP
2004-343359 Dec 2004 JP
2010-187373 Aug 2010 JP
2014-068123 Apr 2014 JP
2015-073331 Apr 2015 JP
2015-111845 Jun 2015 JP
2015-188123 Oct 2015 JP
2016208236 Dec 2016 WO
Non-Patent Literature Citations (1)
Entry
Official Communication issued in International Patent Application No. PCT/JP2018/008913 dated Apr. 10, 2018.
Related Publications (1)
Number Date Country
20200007109 A1 Jan 2020 US
Continuations (1)
Number Date Country
Parent PCT/JP2018/008913 Mar 2018 US
Child 16561244 US