ACOUSTIC WAVE DEVICE, ACOUSTIC WAVE FILTER, AND COMPOSITE FILTER DEVICE

Abstract
An acoustic wave device includes a silicon oxide film, a lithium tantalate film, an IDT electrode, and a protection film that are laminated on a support substrate made of silicon. A wavelength normalized film thickness of a lithium tantalate film is denoted by TLT, an Euler angle is θLT, a wavelength normalized film thickness of the silicon oxide film is TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness is TE, a wavelength normalized film thickness of a protection film is TP, a propagation direction in the support substrate is ψSi, and a wavelength normalized film thickness of the support substrate is TSi. Values of TLT, θLT, TS, TE, TP, and ψSi are set such that Ih corresponding to an intensity of a response of a spurious response represented by Formula (1) is greater than about −2.4 in a spurious response.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention

The present invention relates to an acoustic wave device, an acoustic wave filter, and a composite filter device including a lithium tantalate film that is laminated on a support substrate made of silicon.


2. Description of the Related Art

A plurality of acoustic wave filters has been widely used in high frequency front end circuits of mobile phones and smartphones. For example, in a demultiplexer described in Japanese Unexamined Patent Application Publication No. 2014-68123, terminals of two or more band pass filters having different frequencies are connected in common. Each of the band pass filters is defined by a surface acoustic wave filter chip. Each surface acoustic wave filter chip includes a plurality of surface acoustic wave resonators.


An acoustic wave resonator described in Japanese Unexamined Patent Application Publication No. 2010-187373 discloses an acoustic wave device formed by laminating an insulation film made of silicon dioxide and a piezoelectric substrate made of lithium tantalate on a silicon support substrate. Bonding in the (111) plane of silicon enhances the heat resistance.


In an acoustic wave device described in Japanese Unexamined Patent Application Publication No. 2014-68123, a plurality of acoustic wave filters having different frequencies are connected in common on antenna terminal side.


The inventors of preferred embodiments of the present application have discovered that a plurality of spurious responses appear on a higher frequency side relative to the main mode used in an acoustic wave resonator in which a lithium tantalate film is laminated directly on or indirectly above a silicon support substrate. When such an acoustic wave resonator is used for an acoustic wave filter having a lower pass band in an acoustic wave device, a spurious response appearing in the acoustic wave filter may appear in a pass band of another acoustic wave filter having a higher pass band in the acoustic wave device. Thus, the filter characteristic of another acoustic wave filter may deteriorate.


SUMMARY OF THE INVENTION

Preferred embodiments of the present invention provide acoustic wave devices, acoustic wave filters, and composite filter devices that are each less likely to generate a ripple in another acoustic wave filter.


An acoustic wave device according to a preferred embodiment of the present invention includes a silicon support substrate, a silicon oxide film laminated above the silicon support substrate, a lithium tantalate film laminated above the silicon oxide film, an IDT electrode including an electrode finger and being provided above the lithium tantalate film, and a protection film covering at least a portion of the IDT electrode. When a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4:











?

.





?




indicates text missing or illegible when filed





Formula






(
1
)








Coefficients a, b, c, d, e, and f in Formula (1) are values described in Table 1 to Table 12 below that are determined in accordance with the crystal orientation of the silicon support substrate and the range of TS, TLT, and ψSi:










TABLE 1








Si(100)



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
−1.499243378
−1.499248378


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 2








Si(100)



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
0.329307692
0.321186441


aTS(2)
0
0


aTS(1)
−11.80744783
−10.05303878


bTS(2)
0
0


cTS
0.158653346
0.153389531


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
−0.623966449


dTEθLT
0
0


dψSiθLT
0
0


e
−2.071831837
−3.228508418


aTP
−11592
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 3








Si(100)



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


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495
















TABLE 4







Si(100)


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


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495
















TABLE 5







Si(110)


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 6







Si(110)


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
0.026725168
0


bθLT(2)
0
0
0
0


cθLT
−49.23333333
−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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 7







Si(110)


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 8







Si(110)


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
9
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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 9







Si(111)


0 < TLT < 0.2


0 ≤ 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)
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
0.369148938
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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 10







Si(111)


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
88027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 11







Si(111)


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495
















TABLE 12







Si(111)


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495









An acoustic wave device according to another preferred embodiment of the present invention includes a silicon support substrate, a silicon oxide film laminated above the silicon support substrate, a lithium tantalate film laminated above the silicon oxide film, an IDT electrode including an electrode finger and being provided above the lithium tantalate film, and a protection film covering at least a portion of the IDT electrode. When a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4:











?

.





?




indicates text missing or illegible when filed





Formula






(
1
)








Coefficients a, b, c, d, e, and f in Formula (1) are values described in Table 13 to Table 24 below that are determined in accordance with the crystal orientation of the silicon support substrate and the range of TS, TLT, and ψSi:









TABLE 13







Si(100)


0 < TLT < 0.2


0 ≤ TS < 2.0










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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599
















TABLE 14







Si(100)


0.2 ≤ TLT ≤ 3.5


0 ≤ TS < 2.0










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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599
















TABLE 15







Si(100)


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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599
















TABLE 16







Si(100)


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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599
















TABLE 17







Si(110)


0 < TLT < 0.2


0 ≤ 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)
−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
−1.789519626
−1.789519626
−1.789519626
−1.789519626


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599
















TABLE 18







Si(110)


0.2 ≤ TLT ≤ 3.5


0 ≤ 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
39.68139896
39.68139896


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)
0.00501471
0.00501471
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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 19








Si(110)



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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 20








Si(110)



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
0
0


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 21








Si(111)



0 < TLT < 0.2



0 ≤ 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)
−26.67263869
−6.49243933
−20.6157421
−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
11.58227648
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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 22








Si(111)



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
−3.454588617
−9.832405019
−3.13.2556866


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
−0.024352541
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
−49.73023077
−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

0.20688896
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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9288
−2.9183


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 23








Si(111)



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
0.039388924
−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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 24








Si(111)



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
−13.78321865
−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
−3.433873203
−1.746861763
3.363230821


bTS(2)
0
0
0
0


cTS
0
0.283443709
0.237804878
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
−50.59602549
−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
−0.608943368


dTSTE
0
113.1914288
−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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599.









An acoustic wave device according to another preferred embodiment of the present invention includes a silicon support substrate, a silicon oxide film laminated above the silicon support substrate, a lithium tantalate film laminated above the silicon oxide film, an IDT electrode including an electrode finger and being provided above the lithium tantalate film, and a protection film covering at least a portion of the IDT electrode. When a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4:











?

.





?




indicates text missing or illegible when filed





Formula






(
1
)








Coefficients a, b, c, d, e, and f in Formula (1) are values described in Table 25 to Table 36 below that are determined in accordance with the crystal orientation of the silicon support substrate and the range of TS, TLT, and ψSi:










TABLE 25








Si(100)



0 < TLT < 0.2



0 ≤ TS < 0.2










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












aTLT(2)
0
0


aTLT(1)
−16.39135305
−16.39135305


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)
0.018256046
0.018256046


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)
−0.00384323
−0.00384323


aψSi(1)
−0.009826773
−0.009826773


bψSi(6)
0
0


bψSi(5)
0
0


bψSi(4)
0
0


bψSi(3)
143.0843203
143.0843203


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


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 26








Si(100)



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)
239.0395546
239.0395546


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
−3.952626593
−3.952626593


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 27








Si(100)



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)
−10.09328536
−10.09328536


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)
−2.383237449
−2.383237449


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
−48.97435397
−48.97435397


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


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 28








Si(100)



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


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 29








Si(110)



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
0.164705382
0.164705382
0.164705382
0.164705382


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
52.58823525
52.58823525
52.58823525
52.58823525


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 30








Si(110)



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
0.160752638
0.160752638


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)
1435156.296
1435156.296
1705613.393
1705613.393


bψSi(3)
1798.436569
1798.436569
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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.353
−11.353


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 31








Si(110)



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)
−13.1565645
−13.1565645
−13.1565645
−13.1565645


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
0.232768362
0.232768362
0.232768362
0.232768362


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
0.034071552
0.034071552
0.034071552
0.034071552


dTEθLT
0
0
0
0


dψSiθLT
0
0
0
0


e
−1.687640015
−1.687640015
−1.687640015
−1.687640015


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1970
1.1970
1.1970
1.1970

















TABLE 32








Si(110)



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
2083705.643
0
0


bψSi(4)
1386257.115
1386257.115
0
0


bψSi(3)
−1267.413434
−1267.413434
1811.750092
0


bψSi(2)
895.5856198
895.5656198
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
−50.96335542


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 33








Si(111)



0 < TLT < 0.2



0.2 ≤ TS < 2.0










0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45












0 ≤ ψSi < 30
60 ≤ 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
0.160863565
0.160863565
0.160863565
0.160863565


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)
0.012599792
0.012599792
0.012599792
0.012599792


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
198.11
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 34








Si(111)



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
0.383333333


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
0.942906209
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
0.011255432
0.011265432


cTE
0.211111111
0.211111111
0.211111111
0.211311111


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)
−0.004525908
−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
−0.00045365


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 35








Si(111)



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
−0.488747027


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
30.54216857
30.54216867
30.54216857


aθLT(2)
0
0
0
0


aθLT(1)
0
0
0
0


bθLT(2)
0
0
0
0


cθLT
−90
−90
−90
−90


dTLTTS
4.821777356
4.821777856
4.821777856
4.821777856


dTLTTE
−4.14067246
−4.14067246
−4.14067246
−4.14057246


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
−0.240178015
−0.240178915


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.853
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 36








Si(111)



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
0.220585235
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
−0.3405495
−0.3405485
−0.3405485
−0.3405485


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978









An acoustic wave filter according to a preferred embodiment of the present invention includes a plurality of resonators, and at least one of the plurality of resonators is defined by an acoustic wave device according to a preferred embodiment of the present invention.


A composite filter device according to a preferred embodiment of the present invention includes N band pass filters having different pass bands where N is two or more, and one terminal of each of the N band pass filters is connected in common on an antenna terminal side. At least one of the N band pass filters excluding a band pass filter having a highest pass band includes one or more acoustic wave resonators. At least one of the one or more acoustic wave resonators is defined by an acoustic wave device according to a preferred embodiment of the present invention.


According to preferred embodiments of the present invention, it is possible to provide acoustic wave devices that are each less likely to generate a ripple in another acoustic wave filter that is connected in common, and to provide acoustic wave filters and composite filter devices that each include an acoustic wave device according to a preferred embodiment of the present invention.


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


FIGS. 1A and 1B are a schematic front sectional view of an acoustic wave device according to a first preferred embodiment of the present invention, and a schematic plan view of the acoustic wave device according to the first preferred embodiment of the present invention illustrating an electrode structure thereof.



FIG. 2 is a graph showing the admittance characteristic of an acoustic wave resonator.



FIG. 3 is a graph showing the relationship between a propagation direction ψSi in a single crystal Si layer and an intensity S11 of a response of a spurious response A.



FIG. 4 is a graph showing the relationship between a wavelength normalized film thickness TLT of a lithium tantalate film and the intensity S11 of a response of the spurious response A.



FIG. 5 is a graph showing the relationship between a cut angle (90°−θLT) of the lithium tantalate film and the intensity S11 of a response of the spurious response A.



FIG. 6 is a graph showing the relationship between a wavelength normalized film thickness TS of a SiO2 film and the intensity S11 of a response of the spurious response A.



FIG. 7 is a graph showing the relationship between a wavelength normalized film thickness TE of an IDT electrode and the intensity S11 of a response of the spurious response A.



FIG. 8 is a graph showing the relationship between a wavelength normalized film thickness TP of a protection film being a silicon oxide film and the intensity S11 of a response of the spurious response A.



FIG. 9 is a circuit diagram of a composite filter device including the acoustic wave device of the first preferred embodiment of the present invention.



FIG. 10 is a circuit diagram illustrating an acoustic wave filter including the acoustic wave device of the first preferred embodiment of the present invention and being used in the composite filter device.



FIG. 11A is a graph showing the filter characteristic of a composite filter device including an acoustic wave device of a comparative example, and FIG. 11B is a graph showing the filter characteristic of the composite filter device as the preferred embodiment of the present invention.



FIG. 12 is a graph showing the relationship between a wavelength normalized film thickness of the single crystal Si layer and responses of the spurious responses A, B, and C.



FIG. 13 is a graph showing the relationship between the propagation direction ψSi in the single crystal Si layer and the intensity S11 of a response of the spurious response B.



FIG. 14 is a graph showing the relationship between the wavelength normalized film thickness TLT of the lithium tantalate film and the intensity S11 of a response of the spurious response B.



FIG. 15 is a graph showing the relationship between the cut angle (90°−θLT) of the lithium tantalate film and the intensity S11 of a response of the spurious response B.



FIG. 16 is a graph showing the relationship between the wavelength normalized film thickness TS of the SiO2 film and the intensity S11 of a response of the spurious response B.



FIG. 17 is a graph showing the relationship between the wavelength normalized film thickness TE of the IDT electrode and the intensity S11 of a response of the spurious response B.



FIG. 18 is a graph showing the relationship between the wavelength normalized film thickness TP of the protection film being the silicon oxide film and the intensity S11 of a response of the spurious response B.



FIG. 19 is a graph showing the relationship between the propagation direction ψSi in the single crystal Si layer and the intensity S11 of a response of the spurious response C.



FIG. 20 is a graph showing the relationship between the wavelength normalized film thickness TLT of the lithium tantalate film and the intensity S11 of a response of the spurious response C.



FIG. 21 is a graph showing the relationship between the cut angle (90°−θLT) of the lithium tantalate film and the intensity S11 of a response of the spurious response C.



FIG. 22 is a graph showing the relationship between the wavelength normalized film thickness TS of the SiO2 film and the intensity S11 of a response of the spurious response C.



FIG. 23 is a graph showing the relationship between the wavelength normalized film thickness TE of the IDT electrode and the intensity S11 of a response of the spurious response C.



FIG. 24 is a graph showing the relationship between the wavelength normalized film thickness TP of the protection film being the silicon oxide film and the intensity S11 of a response of the spurious response C.



FIG. 25 is a graph showing the relationship between a film thickness of a LiTaO3 film and a Q characteristic in the acoustic wave device.



FIG. 26 is a graph showing the relationship between the film thickness of the LiTaO3 film and a temperature coefficient of frequency TCF in the acoustic wave device.



FIG. 27 is a graph showing the relationship between the film thickness of the LiTaO3 film and an acoustic velocity in the acoustic wave device.



FIG. 28 is a graph showing the relationship between the LiTaO3 film thickness and a fractional bandwidth.



FIG. 29 is a graph showing the relationship among the film thickness of the SiO2 film, material of a high acoustic velocity film, and the acoustic velocity.



FIG. 30 is a graph showing the relationship among the film thickness of the SiO2 film, an electromechanical coupling coefficient, and material of the high acoustic velocity film.



FIG. 31 is a partially enlarged front sectional view for describing a modification of an acoustic wave device according to a preferred embodiment of the present invention which thickness of the protection film is partially different.



FIG. 32 is a partially enlarged front sectional view for describing another modification of an acoustic wave device according to a preferred embodiment of the present invention in which thickness of the protection film is partially different.



FIG. 33 is a partially enlarged front sectional view for describing another modification of an acoustic wave device according to a preferred embodiment of the present invention in which thickness of the protection film is partially different.



FIG. 34 is a front sectional view illustrating a modification of the acoustic wave resonator used in an acoustic wave device according to a preferred embodiment of the present invention.



FIG. 35 is a front sectional view illustrating another modification of the acoustic wave resonator used in an acoustic wave device according to a preferred embodiment of the present invention.



FIG. 36 is a partially enlarged front sectional view for describing a modification of an acoustic wave device according to a preferred embodiment of the present invention in which the protection film is a laminated film.



FIG. 37 is a schematic diagram for describing crystal orientation Si (100).



FIG. 38 is a schematic diagram for describing crystal orientation Si (110).



FIG. 39 is a schematic diagram for describing crystal orientation Si (111).



FIG. 40 is a schematic configuration 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

Hereinafter, the present invention will be clarified by the description of preferred embodiments of the present invention with reference to drawings.


It should be noted that the preferred embodiments described in this description are merely exemplary, and that a partial replacement or a combination of configurations is possible between the different preferred embodiments.



FIG. 1A is a schematic front 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 of an electrode structure thereof.


An acoustic wave device 1 is a one-port acoustic wave resonator. The acoustic wave device 1 includes a single crystal Si layer 2 defining and functioning as a support substrate. A SiO2 film 3 as a silicon oxide film and a lithium tantalate film (LiTaO3 film) 4 are laminated above the single crystal Si layer 2. The lithium tantalate film 4 includes a first main surface 4a and a second main surface 4b opposite to each other. An IDT electrode 5 is provided above the first main surface 4a. Reflectors 6 and 7 are provided on both sides of the IDT electrode 5 in an acoustic wave propagation direction. The SiO2 film 3 as the silicon oxide film may include not only SiO2, but also silicon oxide, for example, in which SiO2 is doped with fluorine or the like. The silicon oxide film may be, for example, a multilayer structure including a plurality of layers made of silicon oxide. An intermediate layer made of, for example, titanium, nickel, or the like may be included between the plurality of layers. The thickness of the silicon oxide film in this case means the thickness of the entire multilayer structure.


A protection film 8 covers the IDT electrode 5 and the reflectors 6 and 7. The protection film 8 is preferably, for example, a silicon oxide film in the present preferred embodiment. However, the protection film 8 may be a film made of various dielectrics such as, for example, silicon oxynitride, silicon nitride, or the like. In addition, in the present preferred embodiment, the protection film 8 covers not only the upper side of an electrode finger of the IDT electrode 5, but also the upper surface of the lithium tantalate film 4 and the side surfaces of the electrode finger. However, the configuration of the protection film 8 is not limited thereto.


The inventors of preferred embodiments of the present application have discovered that responses are generated by spurious responses A, B, and C described below in the acoustic wave resonator in which a lithium tantalate film is laminated directly on or indirectly above the single crystal Si layer 2.



FIG. 2 is a graph showing the admittance characteristic of the acoustic wave resonator for describing the spurious responses A, B, and C. The admittance characteristic described in FIG. 2 is the admittance characteristic of the acoustic wave resonator with the following design parameters, and not of a preferred embodiment of the present invention.


Euler angles (TSi, θSi, ψSi) of the single crystal Si layer are (0°, 0°, 45°). The film thickness of the SiO2 film is about 0.30λ, the film thickness of the lithium tantalate film is about 0.30λ, and the Euler angles (TLT, θLT, ψLT) of the lithium tantalate film are (0°, −40°, 0°). The wavelength λ determined by the electrode finger pitch of the IDT electrode is about 1 μm. The IDT electrode includes laminated metal films in which an Al film and a Ti film are laminated, and has a thickness of about 0.05λ in terms of aluminum.


As shown in FIG. 2, the spurious responses A, B, and C appear on a higher frequency side relative to a main mode response in the acoustic wave resonator described above. The high and low order of frequencies of the spurious responses A, B, and C satisfies the relationship, spurious response A<spurious response B<spurious response C. The spurious response A is closest to the main mode.


In the acoustic wave device 1 of the present preferred embodiment, at least one of the responses of the spurious response A, the response of the spurious response B, and the response of the spurious response C is reduced or prevented.


The wavelength determined by the electrode finger pitch of the IDT electrode 5 is denoted by λ. The wavelength normalized film thickness of the lithium tantalate film 4 is denoted by TLT, the Euler angle θ of the lithium tantalate film is denoted by θLT, the wavelength normalized film thickness of the SiO2 film 3 is denoted by TS, the wavelength normalized film thickness of the IDT electrode 5 in terms of aluminum thickness is denoted by TE. The wavelength normalized film thickness of the protection film 8 is denoted by TP, where TP is the product of a value obtained when density of the protection film 8 is divided by density of silicon oxide and the wavelength normalized film thickness of the protection film 8 normalized by the wavelength λ. The propagation direction in the single crystal Si layer 2 is denoted by ψSi, and the wavelength normalized film thickness of the single crystal Si layer 2 is denoted by TSi. TLT, θLT, TS, TE, TP, and ψSi are set such that the value Ih represented by Formula (1) below for at least one of the spurious responses A, B, and C is greater than about −2.4 and the inequality TSi>about 20 is satisfied at the same time. Thus, at least one of the responses of the spurious responses A, B and C is effectively reduced or prevented. This will be described in detail below.


Note that, in the present description, the wavelength normalized film thickness is the value obtained when a film thickness is normalized by the wavelength λ determined by the electrode finger pitch of the IDT electrode. That is, the wavelength normalized film thickness is the value obtained when an actual thickness is divided by λ. The wavelength λ determined by the electrode finger pitch of the IDT electrode may be determined by an average value of the electrode finger pitches.


The density of the IDT electrode 5 is the value obtained from the density of the metal material constituting the IDT electrode 5, rather than a measured value. The density of aluminum is about 2698.9 kg/m3. This value is described in page 26 of “Handbook of Chemistry: Pure Chemistry II, 4th edition, The Chemical Society of Japan, published by Maruzen Publishing Co., Ltd. (1993)”.


Here, the density of the protection film 8 is the value obtained based on the density of the material of the protection film 8, rather than a measured value. The density of silicon oxide is about 2200 kg/m3. This value is described in page 922 of “Handbook of Chemistry: Applied Chemistry II, Materials, 4th edition, The Chemical Society of Japan, published by Maruzen Publishing Co., Ltd. (1993)”.


Note that, in the present description, the thickness of the protection film 8 refers to a thickness of the protection film in a portion positioned on the upper side of the electrode finger of the IDT electrode.










?








?



indicates text missing or illegible when filed






Formula






(
1
)








The coefficients a, b, c, d, e, and f in Formula (1) are values in Table 37 to Table 72 below. The values are specified in accordance with the type of spurious responses, the orientation (100), (110), or (111) of the single crystal Si layer 2, and the range of the wavelength normalized film thicknesses of the SiO2 film 3 and the lithium tantalate film 4, and the like.










TABLE 37








Si(100)



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


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 38








Si(100)



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
0.006076568


cTLT
0.329807692
0.321186441


aTS(2)
0
0


aTS(1)
−11.80744788
−10.05306878


bTS(2)
0
0


cTS
0.158653846
0.163389831


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)
191.71597630
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


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 39








Si(100)



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
0.002456328


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


aTP
−111692
−111692


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 40








Si(100)



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
−6.1866502361


bTS(2)
0
0


cTS
0.297860963
0.298404255


aTE(4)
0
0


aTE(3)
0
0


aTE(2)
110.8304316
0


aTE(1)
4.038561723
−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)
0.024768138
−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
−4.20794513


aTP
−111692
−1116921


bTP
19239
19239


cTP
−952.97
−952.97


dTP
8.8027
8.8027


fTP
1.0495
1.0495

















TABLE 41








Si(110)



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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 42








Si(111)



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
−5.603099395


bTLT(2)
0
0
0
0


cTLT
0.34
0.3296875
0.338983051
0.306666667


aTS(2)
0
0
0
0


aTS(1)
0
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
−41.95412633


aTE(1)
0
−2.467054545
−5.460437635
−2.19025056


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0.006875
0.006716461
0.006819565


cTE
0
0.15
0.36524237
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
−40.33333333
−90
−49.83050847
−90


dTLTTS
0
0
0
0


dTLTTE
0
0
0
42.3018696


dTLTψSi
0
0
0
0


dTLTθLT
0.817240199
0
0
0


dTSTE
0
0
0
0


dTSψSi
2.812107038
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
−2.861861362
−2.210765625
−2.573237288
−2.440604203


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 43








Si(110)



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
0.379772727
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)
0.007147489
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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 44








Si(110)



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
0.238838889


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)
−0.000165117
0
0
−9.554045−05


aψSi(2)
0.000936051
0.00475603
0
0.002198207


aψSi(1)
−0.02141106
0.040196571
−0.017152634
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
199.8263869


cψSi
24.140625
57.97297297
21.13636364
60.41666667


aθLT(2)
0
0
0
−0.003220943


aθLT(1)
0.023743348
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
0.24382842
0
0
−0.273892853


dψSiθLT
0
−0.00130658
−0.001221935
0


e
−2.175330984
−2.239116787
−2.271294054
−2.496300587


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.3027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 45








Si(111)



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
0.163043476


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
−96.15629371
0
138.3065683
0


aTE(1)
−1.283589744
2.88391591
−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
0.345852174


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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 46








Si(111)



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)
0.05513453
0.055133453
−0.004320224
0.021125116


aψSi(1)
0.020862911
0.020862911
−0.310605012
−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)
203.1635302
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
−292.5762961
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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 47








Si(111)



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
8.8475559
−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


aTP
−111692
−111692
−111692
−111692


bTP
19239
19239
19239
19239


cTP
−952.97
−962.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 48








Si(111)



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)
0.006382979
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
−54.62192085
0


dTSψSi
0.714493384
−1.189155195
0
−1.017237869


dTSθLT
0
0
0
0


dTEψSi
0
0.556597609
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


aTP
−111692
−111692
−111692
−111592


bTP
19239
19239
19239
19239


cTP
−952.97
−952.97
−952.97
−952.97


dTP
8.8027
8.8027
8.8027
8.8027


fTP
1.0495
1.0495
1.0495
1.0495

















TABLE 49








Si(100)



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
−0.003276583


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
72.43218274
72.43278214


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
0.0030951322
0.003095822


e
−5.638096455
−5.638096455


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599

















TABLE 50








Si(100)



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
0.14851519
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)
0.095785615
0.003836714


bψSi(6)
0
0


bψSi(5)
0
0


bψSi(4)
0
0


bψSi(3)
384.7407407
0


bψSi(2)
278.2222222
285.09566331


cψSi
21.33383333
20.892857141


aθLT(2)
0
0


aθLT(1)
0.043185248
0.033521037


bθLT(2)
0
0


cθLT
−50
−50.928571431


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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599

















TABLE 51








Si(100)



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
0.130323125


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)
4.84120465
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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599

















TABLE 52








Si(100)



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)
2.10793686
−0.578851453


bTE(4)
0
0


bTE(3)
0
0


bTE(2)
0.906775956
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)
0.05677734
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
−48.36085574
−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


aTP
0
0


bTP
0
0


cTP
−15.448
−15.448


dTP
−2.9188
−2.9188


fTP
1.0599
1.0599

















TABLE 53








Si(100)



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
0174380185
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
0.15043223
0150413223
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)
1129157.497
1129197.497
1129197.497
1129197.497


bψSi(3)
−1524.372995
−1524.372996
−1524.372996
−1524.372996


bψSi(2)
776.3813947
776.3813947
776.3813947
776.3813947


cψSi
41.52892562
41.52892562
41.522562
41.52692562


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
−1.7395E9626
−1.789519626
−1.789519626
−1.789519626


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.449


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 54








Si(100)



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
−3.8019359113
−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
35.12258065
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
−51.28571428


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 55








Si(100)



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
0.30563158
0.305263158
0.327872956
0.327672956


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
−130.6388144
−130.63881444


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
−0.000138558
−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)
0.015804665
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
−150.2428293


dTLTψSi
0
0
0.225309644
0.225100644


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.443


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 56








Si(100)



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
−73.23839451


aTE(1)
8.962154821
8.962154821
−5.710295136
−5.710295136


bTE(4)
0
0
0
0


bTE(3)
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
−0.093212695
−0.098212695
0
0


dTEθLT
0.32576925
0.32576925
0
0


dψSiθLT
0
0
0
0


e
−2.431352404
−2.431352404
−2.39032093
−2.39002093


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9183


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 57








Si(111)



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
−20.61574254
−27.06290014


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
0.14556262
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
0.35862089


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
−1.097992722
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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 58








Si(111)



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
−3.454983617
−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)
−6.97795964
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
−10.72534998


bTE(4)
0
0
0
0


bTE(3)
0
0
0
0


bTE(2)
0
0
0
0


cTE
0.15776699
0.124603375
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
49.9047619
14.19230769
43.04347826


aθLT(2)
0
0
0
0


aθLT(1)
0.06700163
0.042141715
0.055240362
0.061747928


bθLT(2)
0
0
0
0


cθLT
−48.33786409
−50.15873016
−49.76923077
−49.45852174


dTLTTS
116.7290786
−78.78450728
0
0


dTLTTE
0
85.46351408
−49.85282875
0


dTLTψSi
−0.70199108
0.445481139
0
0.604657146


dTLTθLT
−0.726496836
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
0.439380407
−0.6608739
−1.068569294


dψSiθLT
−0.005400134
0.002667922
−0.004937546
0.006290209


e
−4.209434885
−1.791079273
−3.48174155
−3.934527632


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 59








Si(111)



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)
−4.67350215
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
0.523030757


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
−79.384134758
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)
0.030122468
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
91.49418307
251.5375225


dTLTTE
0
0
−156.3654518
0


dTLTψSi
0.322255595
0
0
−0.289820964


dTLTθLT
−0.768436344
0
−0.735137765
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
−2.6286918.85
−1.980941925
−2.412296494


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9188
−2.9188
−2.9188
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 60








Si(111)



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
0.237804873
0.293037975


aTE(4)
0
0
0
0


aTE(3)
0
0
0
0


aTE(2)
0
0
86.38383552
0


aTE(1)
3.853394073
8.758511808
−1.867550529
−15.58616064


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
15.09146343
45


aθLT(2)
0
0
0
0


aθLT(1)
0
0.061867934
0.051566965
0.028929641


bθLT(2)
0
0
0
0


cθLT
−90
−50.59502649
−50.30487005
−50.55982025


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


aTP
0
0
0
0


bTP
0
0
0
0


cTP
−15.448
−15.448
−15.448
−15.448


dTP
−2.9186
−2.9188
−2.9186
−2.9188


fTP
1.0599
1.0599
1.0599
1.0599

















TABLE 61








Si(100)



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
−1639135605


bTLT(2)
0
0


cTLT
0.196774194
0.1967741941


aTS(2)
0
0


aTS(1)
−4.824831305
−4.824831305


bTS(2)
0
0


cTS
0.170967742
0.170967142


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
−1.7507631961


dTSθLT
0
0


dTEψSi
0
0


dTEθLT
0.466692151
0.466692151


dψSiθLT
0
0


e
−2.904746788
−2.904746788


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 62








Si(100)



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)
−20.38200262
−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)
−0.003758233
−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


aTP
0
0


bTP
0
0


cTP
19.811
19.311


dTP
−11.953
−11.953


fTP
3.1978
1.1978

















TABLE 63








Si(100)



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


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 64








Si(100)



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)
−0.00404832
−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


θ
−4.940340284
−4.940340284


aTP
0
0


bTP
0
0


cTP
19.811
19.811


dTP
−11.953
−11.953


fTP
1.1978
1.1978

















TABLE 65








Si(110)



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


θ
−1.678155024
−1.678155024
−1.678155024
−1.678155024


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 66








Si(110)



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)
   1.426E−06
   1.426E−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)
−0.92266284
−0.92266284
−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
40.2364649
40.2364649
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


θ
−2.543790382
−2.543790382
−2.964933907
−2.964933907


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 67








Si(110)



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


θ
−1.687640015
−1.687640015
−1.687640015
−1.687640015


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 68








Si(110)



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
0.376881254


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


θ
−2.390757235
−2.390757235
−2.548464154
−2.523994879


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 69








Si(111)



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


θ
−0.277577227
−0.277577227
−0.277577227
−0.277577227


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 70








Si(111)



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
−0.000426881
−0.000426881
−0.000426881
−0.000426881


θ
−0.446604617
−0.446604617
−0.446604617
−0.446604617


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 71








Si(111)



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


θ
−0.240178915
−0.240178915
−0.240178915
−0.240178915


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978

















TABLE 72








Si(111)



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


θ
−0.3405485
−0.3405485
−0.3405485
−0.3405485


aTP
0
0
0
0


bTP
0
0
0
0


cTP
19.811
19.811
19.811
19.811


dTP
−11.953
−11.953
−11.953
−11.953


fTP
1.1978
1.1978
1.1978
1.1978









The inventors of preferred embodiments of the present application variously changed the design parameters TLT, θLT, TS, TE, TP, ψSi and TSi, and determined how the intensity of the response becoming the spurious response A, B, or C changed.


Note that the absolute value of S11 was calculated as the intensity of the response of the spurious response when the above parameters were changed. The smaller the value of the absolute value of S11 in decibel is, the greater the intensity of the response of the spurious response is. When calculating S11, the overlap width of the electrode fingers was 20λ and the number of pairs of the electrode fingers was 94 pairs, and S11 was obtained with the one pair electrode finger model of the two-dimensional finite element method.


Note that the IDT electrode has a structure in which the metal films were laminated in the order of Ti/Pt/Ti/Al from the lithium tantalate film side. The thickness of the IDT electrode was changed by varying the thickness of the Pt film. Further, the wavelength normalized film thickness TE of the IDT electrode was calculated as the wavelength normalized film thickness in terms of aluminum thickness, using the mass of the entire IDT electrode estimated from the density of each metal film.


Spurious Response A

The acoustic wave resonator having the admittance characteristic shown in FIG. 2 is used as the reference structure. FIG. 3 to FIG. 8 are diagrams describing changes in the intensity S11 of the response of the spurious response A when the respective parameters are changed with respect to the reference structure. As described in FIG. 3, the intensity S11 of the response of the spurious response A changes when the propagation direction in the single crystal Si layer ψSi is changed within the range from about 0° to about 45° with respect to the reference structure.


Similarly, as described in FIG. 4, the intensity S11 of the response of the spurious response A also changes when the wavelength normalized film thickness TLT of the lithium tantalate film is changed.


Further, as described in FIG. 5, the intensity S11 of the response of the spurious response A also changes when the cut angle (90°−θLT) of the lithium tantalate film is changed.


As described in FIG. 6, the intensity S11 of the response of the spurious response A also changes when the wavelength normalized film thickness TS of the SiO2 film is changed.


As described in FIG. 7, the intensity S11 of the response of the spurious response A also changes when the wavelength normalized film thickness TE, which is the thickness of the IDT electrode in terms of aluminum, is changed.


As described in FIG. 8, the intensity S11 of the response of the spurious response A changes when the wavelength normalized film thickness TP of the protection film defined by a silicon oxide film is changed.


From FIG. 3 to FIG. 8, it is understood that the intensity of the response of the spurious response A may be adjusted by changing the parameters above. That is, by selecting the values of the parameters described above, the intensity of the response of the spurious response A may be reduced while maintaining the response of the main mode.


The inventors of preferred embodiments of the present application have discovered that Ih corresponding to the intensity of the response of the spurious response may be obtained by Formula (1) and the coefficients a, b, c, d, e, and f in Table 37 to Table 48, from the calculation results in FIG. 3 to FIG. 8 and the like.


The coefficients in Formula (1) have been discovered to be values described in Table 37 to Table 48 in accordance with the crystal orientation of the single crystal Si layer, the respective ranges of the wavelength normalized film thickness TLT of the lithium tantalate film, the Euler angle θLT of the lithium tantalate film, the wavelength normalized film thickness TS of the SiO2 film, the wavelength normalized film thickness TE of the IDT electrode, and the wavelength normalized film thickness TP of the protection film, and the propagation direction ψSi in the single crystal Si layer. Thus, the conditions of TIT, θLT, TS, TE, TP, and ψSi, where Ih1 corresponding to the intensity of the response of the spurious response A is greater than about −2.4 are determined.


In the composite filter device in which the plurality of acoustic wave filters are connected at one end, the intensity of the response of the spurious response is required to be greater than about −2.4 dB in S11. This is to make the influence negligible on the bandpass characteristic of another acoustic wave filter other than one acoustic wave filter. Typically, the ripple appearing in the pass band is required to be equal to or greater than about −0.8 dB from the viewpoint of ensuring the reception sensitivity in a mobile phone or the like. Meanwhile, it has been known that when the spurious response is present in the pass band of another acoustic wave filter, a ripple of approximately ⅓ of the intensity of the response of the spurious response is generated in the pass band of another filter. Accordingly, in order to make the ripple in the pass band equal to or greater than about −0.8 dB, the intensity S11 of the response of the spurious response may be set to be greater than about −2.4 dB.


With Ih for the spurious response A, the inequality Ih>about −2.4 is satisfied, and thus it is possible to effectively reduce or prevent the influence by the response of the spurious response A on the pass band of another acoustic wave filter. This will be described with reference to FIG. 9 to FIG. 12.



FIG. 9 is a circuit diagram of a composite filter device according to a preferred embodiment of the present invention. In a composite filter device 10, a first acoustic wave filter 11 to a fourth acoustic wave filter 14 are connected in common on an antenna terminal 15 side. FIG. 10 is a circuit diagram of the first acoustic wave filter 11. The first acoustic wave filter 11 includes a plurality of series arm resonators S1 to S3 and a plurality of parallel arm resonators P1 and P2. That is, the first acoustic wave filter 11 is a ladder filter, for example. The series arm resonators S1 to S3 and the parallel arm resonators P1 and P2 are defined by the acoustic wave device 1 according to the preferred embodiment described above.


Note that, in the present invention, the circuit configuration of the acoustic wave filter including the acoustic wave device according to a preferred embodiment of the present invention is not limited thereto. For example, an acoustic wave filter including a longitudinally coupled resonator acoustic wave filter may be employed. In this case, the longitudinally coupled resonator acoustic wave filter may be an acoustic wave device according to a preferred embodiment of the present invention. Alternatively, the acoustic wave resonator connected to the longitudinally coupled resonator acoustic wave filter may be defined by an acoustic wave device according to a preferred embodiment of the present invention.


Note that the pass bands of the first acoustic wave filter 11 to the fourth acoustic wave filter 14 are referred to as a first pass band to a fourth pass band.


The first pass band is on the lowest frequency side, and the pass band is higher in the order of the second pass band, the third pass band, and the fourth pass band. That is, the pass bands satisfy the relation, first pass band<second pass band<third pass band<fourth pass band.


For a comparison, a composite filter device of a comparative example was prepared in which the first acoustic wave filter was configured in the same manner as in the preferred embodiment of the preferred embodiment described above, except that the acoustic wave resonator of the reference structure was used. FIG. 11A describes a filter characteristic of a first acoustic wave filter and a second acoustic wave filter in the composite filter device of the comparative example. The solid line indicates a filter characteristic of the first acoustic wave filter, and the dashed line indicates a filter characteristic of the second acoustic wave filter. A large ripple appears in the second pass band. This is because a large response appears due to the spurious response A of the acoustic wave resonator used in the first acoustic wave filter.



FIG. 11B is a graph showing the filter characteristic of the composite filter device according to a preferred embodiment of the present invention. The solid line indicates a filter characteristic of the first acoustic wave filter, and the dashed line indicates a filter characteristic of the second acoustic wave filter. Here, the first acoustic wave filter is defined by the acoustic wave device of the preferred embodiment described above. Accordingly, no large ripple appears in the second pass band. That is, no large ripple appears in the pass band of the second acoustic wave filter being another filter. Thus, the deterioration of the filter characteristic in the second acoustic wave filter is less likely to occur.


As described above, in the composite filter device according to the present preferred embodiment, the response of the spurious response A is reduced or prevented in the acoustic wave filter defined by the acoustic wave device according to the preferred embodiment of the present invention described above. Thus, it is possible to effectively reduce or prevent the deterioration of the filter characteristic of another acoustic wave filter having a higher pass band relative to the pass band of the one acoustic wave filter.



FIG. 12 is a graph showing the relationship between the wavelength normalized film thickness of the single crystal Si layer 2 and the intensity S11 of the response of spurious responses A, B, and C. As is apparent from FIG. 12, the intensity of the response of each of spurious responses A, B, and C may be more effectively reduced or prevented when the inequality TSi>about 20 is satisfied.


Spurious Response B


FIG. 13 is a graph showing the relationship between the propagation direction ψSi in the single crystal Si layer and the intensity S11 of the response of the spurious response B. As is apparent from FIG. 13, the intensity S11 of the response of the spurious response B changes when ψSi is changed. Similarly, as described in FIG. 14, the intensity S11 of the response of the spurious response B also changes when the wavelength normalized film thickness TLT of the lithium tantalate film is changed. As described in FIG. 15, the intensity S11 of the response of the spurious response B also changes when the cut angle (90°−θLT) of the lithium tantalate film is changed. As described in FIG. 16, the intensity S11 of the response of the spurious response B also changes when the wavelength normalized film thickness TS of the SiO2 film is changed. Further, as described in FIG. 17, the intensity S11 of the response of the spurious response B also changes when the wavelength normalized film thickness TE of the IDT electrode in terms of aluminum is changed.


Still further, as described in FIG. 18, the intensity S11 of the response of the spurious response B also changes when the wavelength normalized film thickness TP of the protection film being a silicon oxide film is changed.


The coefficient values in Formula (1) for expressing Ih2 corresponding to the intensity of the response of the spurious response B were obtained from the calculation results in FIG. 13 to FIG. 18 and the like as in the case of the spurious response A. Ih2 corresponding to the intensity of the response of the spurious response B may be expressed when the coefficients in Formula (1) are determined as in Table 49 to Table 60 described above in accordance with the orientation (100), (110), or (111) of the single crystal Si layer, the respective ranges of the wavelength normalized film thickness TLT of the lithium tantalate film, the Euler angle θLT of the lithium tantalate film, the wavelength normalized film thickness TS of the SiO2 film, the wavelength normalized film thickness TE of the IDT electrode, the wavelength normalized film thickness TP of the protection film, and the propagation direction ψSi. The response of the spurious response B may be made sufficiently small by determining the conditions of TLT, θLT TS, TE, TP, and ψSi that make Ih2 greater than about −2.4, and by making the inequality TSi>about 20 be satisfied.


Spurious Response C


FIG. 19 is a graph showing the relationship between the propagation direction ψSi in the single crystal Si layer and the intensity S11 of the response of the spurious response C. As is apparent from FIG. 19, the intensity S11 of the response of the spurious response C changes when ψSi is changed. Similarly, as described in FIG. 20, the intensity S11 of the response of the spurious response C also changes when the wavelength normalized film thickness TLT of the lithium tantalate film is changed. As described in FIG. 21, the intensity S11 of the response of the spurious response C changes when the cut angle (90°−θLT) of the lithium tantalate film is changed. As described in FIG. 22, the intensity S11 of the response of the spurious response C also changes when the wavelength normalized film thickness TS of the SiO2 film is changed. Further, as described in FIG. 23, the intensity S11 of the response of the spurious response C also changes when the wavelength normalized film thickness TE of the IDT electrode in terms of aluminum is changed.


Still further, as described in FIG. 24, the intensity S11 of the response of the spurious response C also changes when the wavelength normalized film thickness TP of the protection film being a silicon oxide film is changed.


The coefficient values in Formula (1) for expressing Ih3 corresponding to the intensity of the response of the spurious response C were obtained from FIG. 19 to FIG. 24 and the like. That is, Ih3 corresponding to the intensity of the response of the spurious response C may be expressed when the coefficients in Formula (1) are determined as in Table 61 to Table 72 described above in accordance with Si (100), (110), or (111), further, the respective ranges of the wavelength normalized film thickness TLT of the lithium tantalate film, the Euler angle θLT of the lithium tantalate film, the wavelength normalized film thickness TS of the SiO2 film, the wavelength normalized film thickness TE of the IDT electrode, the wavelength normalized film thickness TP of the protection film, and the propagation direction ψSi. The response of the spurious response C may be made sufficiently small by determining the conditions of TLT, θLT, TS, TE, TP, and ψSi that make Ih3 greater than about −2.4, and by making the inequality TSi>about 20 be satisfied.


Preferably, the inequality Ih>about −2.4 is satisfied for all of the spurious responses A, B, and C. In this case, it is possible to effectively reduce or prevent the influence of the spurious responses A, B, and C on another acoustic wave filter. Alternatively, Ih for the spurious response A and the spurious response B, Ih for the spurious response A and the spurious response C, or Ih for the spurious response B and the spurious response C may satisfy the inequality Ih>about −2.4. In this case, it is possible to reduce or prevent the influence of two of the spurious responses A, B, and C.


Thickness of Lithium Tantalate Film

With the structures of preferred embodiments of the present invention, as described above, the spurious response tends to be confined in a portion where the SiO2 film 3 and the lithium tantalate film 4 are laminated. However, the spurious response is less likely to be confined by making the thickness of the lithium tantalate film 4 equal to or less than about 3.5λ, for example, since the laminated portion of the SiO2 film 3 and the lithium tantalate film 4 becomes thin.


More preferably, the film thickness of the lithium tantalate film 4 is equal to or less than about 2.5λ, for example, and in this case, the absolute value of the frequency temperature coefficient TCF may be made small. Further, preferably, the film thickness of the lithium tantalate film 4 is equal to or less than about 1.5λ, for example. In this case, the electromechanical coupling coefficient may easily be adjusted. Further, more preferably, the film thickness of the lithium tantalate film 4 is equal to or less than about 0.5λ, for example. In this case, the electromechanical coupling coefficient may be easily adjusted in a wide range.


Note that in Formula (1) described above:


a) The range of ψSi is 0°≤ψSi≤45° when Si (100) having the Euler angles (φSi=0°±5°, θSi=0°±5°, ψSi) is preferably used. Meanwhile, due to the symmetricity of the crystal structure of Si (100), ψSi and ψSi±(n×90°) are synonymous with each other (note that n=1, 2, 3 . . . ). Similarly, ψSi and −ψSi are synonymous with each other;


b) The range of ψSi is 0°≤ψSi≤90° when Si (110) having the Euler angles (φSi=−45°±5°, θSi=−90°±5°, ψSi) is used. Meanwhile, due to the symmetricity of the crystal structure of Si (110), ψSi and ψSi±(n×180°) are synonymous with each other (note that n=1, 2, 3 . . . ). Similarly, ψSi and ψSi are synonymous with each other; and


C) The range of ψSi is 0° about 60° when Si (111) having the Euler angles (φSi=−45°±5°, θSi=−54.73561°±5°, ψSi) is used. Meanwhile, due to the symmetricity of the crystal structure of Si (111), ψSi and ψSi±(n×120°) are synonymous with each other (note that n=1, 2, 3 . . . ).


Further, although the range of θLT is set to −180°<θLT about 0°, θLT and θLT+180° may be treated as synonymous with each other.


In the present description, for example, when the Euler angles (within the range of 0°±5°, θ, within the range of 0°±15°) is cited, “within the range of 0°±5°” means “within the range of equal to or greater than −5° and equal to or less than +5°”, and “within the range of 0°±15°” means “within the range of equal to or greater than −15° and equal to or less than +15°”. In the present description, for example, “within the range of 0°±5°” may simply be denoted by “0°+5°”.



FIG. 25 is a graph showing the relationship between the film thickness of the LiTaO3 film and the Q characteristic of an acoustic wave device in which a low acoustic velocity film made of SiO2 film of thickness of about 0.35λ and a piezoelectric film made of lithium tantalate having the Euler angles (0°, 140.0°, 0°) are laminated above a high acoustic velocity support substrate made of silicon. The vertical axis in FIG. 25 is a product of the Q factor and the fractional bandwidth (Of) of the resonator. FIG. 26 is a graph showing the relationship between the film thickness of the LiTaO3 film and the temperature coefficient of frequency TCF. FIG. 27 is a graph showing the relationship between the film thickness of the LiTaO3 film and the acoustic velocity. From FIG. 25, it is preferable that the film thickness of the LiTaO3 film be equal to or less than about 3.5λ, for example. In this case, the Q factor becomes higher relative to the case where the film thickness of the LiTaO3 film exceeds about 3.5λ. More preferably, the film thickness of the LiTaO3 film is equal to or less than about 2.5λ, for example, in order to further increase the Q factor.


From FIG. 26, when the film thickness of the LiTaO3 film is equal to or less than about 2.5λ, the absolute value of the frequency temperature coefficient TCF may be made smaller than in the case where the film thickness of the LiTaO3 film exceeds about 2.5λ. More preferably, the film thickness of the LiTaO3 film is equal to or less than about 2λ, for example, and in that case, the absolute value of the frequency temperature coefficient TCF may be made equal to or less than about 10 ppm/° C. In order to reduce the absolute value of the frequency temperature coefficient TCF, it is further preferable that the film thickness of the LiTaO3 film is reduced to equal to or less than about 1.5λ, for example.


From FIG. 27, when the film thickness of the LiTaO3 film exceeds about 1.5λ, the change in the acoustic velocity is extremely small.


Meanwhile, as described in FIG. 28, the fractional bandwidth changes significantly when the film thickness of the LiTaO3 film is in the range of equal to or greater than about 0.05λ and equal to or less than about 0.5λ. Accordingly, the electromechanical coupling coefficient may be adjusted in a wider range. In order to widen the adjustment range of the electromechanical coupling coefficient and the fractional bandwidth, therefore, it is preferable that the film thickness of the LiTaO3 film is in a range of equal to or greater than about 0.05λ and equal to or less than about 0.5λ, for example.



FIG. 29 is a graph showing the relationship between the film thickness (λ) of the SiO2 film and the acoustic velocity, and FIG. 30 is a graph showing the relationship between the film thickness (λ) of the SiO2 film and the electromechanical coupling coefficient. Here, each of a silicon nitride film, an aluminum oxide film, and a diamond film was used as the high acoustic velocity film under the low acoustic velocity film made of SiO2. The film thickness of the high acoustic velocity film was about 1.5λ. The acoustic velocity of the bulk wave in silicon nitride is about 6000 m/s, the acoustic velocity of the bulk wave in aluminum oxide is about 6000 m/s, and the acoustic velocity of the bulk wave in diamond is about 12800 m/s. As described in FIG. 29 and FIG. 30, the electromechanical coupling coefficient and the acoustic velocity hardly change even when the material of the high acoustic velocity film and the film thickness of the SiO2 film are changed. In particular, the electromechanical coupling coefficient hardly changes when the film thickness of the SiO2 film is equal to or greater than about 0.1λ and equal to or less than about 0.5λ regardless of the material of the high acoustic velocity film. Further, from FIG. 29, it is discovered that the acoustic velocity does not change when the film thickness of the SiO2 film is equal to or greater than about 0.3λ and equal to or less than about 2λ, regardless of the material of the high acoustic velocity film. Accordingly, preferably, the film thickness of the low acoustic velocity film made of silicon oxide is equal to or less than about 2λ, and more preferably equal to or less than about 0.5λ, for example.



FIG. 31 to FIG. 33 are partially enlarged front sectional views for describing each of modifications of a preferred embodiment of the present invention in which the thickness of the protection film is partially different in the acoustic wave resonator. In each modification illustrated in FIG. 31 to FIG. 33, the protection film 8 covers the lithium tantalate film 4, and the upper surface and the side surfaces of an electrode finger 5a of the IDT electrode 5. In the modification illustrated in FIG. 31, the thickness of the protection film 8 covering the side surfaces of the electrode finger 5a is smaller than the thickness of the protection film 8 covering the upper surface of the electrode finger 5a. In this case, the Q factor may be increased, and the electromechanical coupling coefficient may be increased. In more detail, since Qm of the protection film 8 is small, the Q of the acoustic wave resonator may be increased when the protection film 8 on the side surfaces of the electrode finger 5a is thin. Accordingly, the loss of the acoustic wave filter may be reduced. Further, the difference in acoustic impedance between the portion where the electrode finger 5a is provided and the gap between the electrode fingers 5a becomes small when the protection film 8 is provided on the lithium tantalate film 4. With this, the electromechanical coupling coefficient is reduced. However, the electromechanical coupling coefficient may be increased when the thickness of the protection film 8 on the side surfaces of the electrode finger 5a is small.


In the modification illustrated in FIG. 32, on the other hand, the thickness of the protection film 8 on the lithium tantalate film 4 is smaller than the thickness of the protection film 8 covering the upper surface of the electrode finger 5a. In this case as well, the electromechanical coupling coefficient may be increased. That is, the electromechanical coupling coefficient may be increased by reducing the thickness of the protection film 8 in the portion covering the lithium tantalate film 4.


In the modification illustrated in FIG. 33, the thickness of the protection film 8 on the lithium tantalate film 4 is larger than the thickness of the protection film 8 covering the upper surface of the electrode finger 5a. In this case, the electromechanical coupling coefficient may be reduced and a narrower band may be achieved.



FIG. 34 is a front sectional view for describing a modification of the acoustic wave resonator used in preferred embodiments of the present invention. The acoustic wave resonator of the present modification has the same or substantially the same configuration as that of the acoustic wave device 1 illustrated in FIG. 1A, except that the SiO2 film 3 is not provided. As described above, the acoustic wave resonator used in preferred embodiments of the present invention may have a structure in which the lithium tantalate film 4 is directly laminated on the single crystal Si layer 2. In that case, the thickness of the SiO2 film 3 is zero.



FIG. 35 is a front sectional view illustrating another modification of the acoustic wave resonator used in preferred embodiments of the present invention. In an acoustic wave device 1A, the protection film 8 is laminated on the upper surface of the electrode finger of the IDT electrode 5. The protection film 8 does not extend to the side surfaces of the electrode finger of the IDT electrode 5. As described above, the protection film 8 may be laminated on only the upper surface of the electrode finger.



FIG. 36 is a partially enlarged front sectional view for describing the structure in the case where the protection film 8 is a laminated film. The protection film 8 has a structure in which a first protection film layer 8a, a second protection film layer 8b, and a third protection film layer 8c are laminated. As described above, the protection film 8 may be a laminated film including the plurality of protection film layers. In this case, the wavelength normalized film thickness TP of the protection film 8 is obtained by the total sum of values, where each value is a product of a value obtained when the density of a protection film layer is divided by the density of silicon oxide and the wavelength normalized film thickness of the protection film layer. For example, when the first protection film layer 8a has the density of d1 and the wavelength normalized film thickness of t1, the second protection film layer 8b has the density of d2 and the wavelength normalized film thickness of t2, the third protection film layer 8c has the density of d3 and the wavelength normalized film thickness of t3, and silicon oxide has the density of d0, the wavelength normalized film thickness TP of the protection film 8 is expressed as TP=(d1/d0)t1+(d2/d0)t2+(d3/d0)t3.


As illustrated in FIG. 37, Si (100) means a substrate that is cut in a (100) plane orthogonal or substantially orthogonal to a crystal axis represented by the Miller index [100] in the crystal structure of silicon having a diamond structure. Note that a crystallographically equivalent plane, such as Si (010), for example, is also included.


As illustrated in FIG. 38, Si (110) means a substrate that is cut in a (110) plane orthogonal or substantially orthogonal to a crystal axis represented by the Miller index [110] in the crystal structure of silicon having a diamond structure. Note that other crystallographically equivalent planes are also included.


As illustrated in FIG. 39, Si (111) means a substrate that is cut in a (111) plane orthogonal or substantially orthogonal to a crystal axis represented by the Miller index [111] in the crystal structure of silicon having a diamond structure. Note that other crystallographically equivalent planes are also included.


The acoustic wave device of each of the above-described preferred embodiments may be used as a component for such as the composite filter device in a high frequency front end circuit. An example of such high frequency front end circuit according to a preferred embodiment of the present invention will be described below.



FIG. 40 is a schematic configuration diagram of a communication apparatus including a high frequency front end circuit. 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 connected to the antenna 202. The high frequency front end circuit 230 includes a composite filter device 210 and amplifiers 221 to 224. The composite filter device 210 includes a first filter 211 to a fourth filter 214. As the composite filter device 210, the above-described composite filter device according to the present preferred embodiment may be used. The composite filter device 210 includes an antenna common terminal 225 connected to the antenna 202. One terminal of each of the first filter 211 to the third filter 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 antenna common terminal 225. The output terminals of the first filter 211 to the third filter 213 are connected to the amplifiers 221 to 223, respectively. Further, the amplifier 224 is connected to an input terminal of the fourth filter 214.


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


The composite filter device according to the present preferred embodiment may be suitably used as the composite filter device 210 in the communication apparatus 240 described above.


The acoustic wave device according to a preferred embodiment of the present invention is preferably the above-described acoustic wave resonator. The acoustic wave filter according to a preferred embodiment of the present invention includes a plurality of resonators and at least one of the plurality of resonators may be defined by an acoustic wave device according to a preferred embodiment of the present invention.


The composite filter device according to the present preferred embodiment includes N band pass filters (N is two or more) having different pass bands as in the composite filter device 210 described above, and one terminal of each of the N band pass filters is connected in common on the antenna terminal side. In this case, at least one of the N band pass filters excluding the band pass filter having the highest pass band includes one or more acoustic wave resonators, and at least one of the one or more acoustic wave resonators may be an acoustic wave device according to a preferred embodiment of the present invention. In addition, in the N band pass filters, at least one of the band pass filters other than the acoustic wave filters including the acoustic wave device according to a preferred embodiment of the present invention may not be an acoustic wave filter. That is, the band pass filters connected in common may include a band pass filter other than an acoustic wave filter, such as an LC filter, for example. Preferably, N is three or more, for example, and the three or more band pass filters define the composite filter device for simultaneously transmitting and receiving signals of a plurality of communication bands. Further, the acoustic wave filter may be a ladder filter, for example.


The acoustic wave devices according to preferred embodiments of the present invention may each be used in various communication bands, and preferably, the pass band in the acoustic wave filter is a pass band of a communication band defined by the 3GPP standard.


The composite filter devices according to preferred embodiments of the present invention may include only a plurality of transmission filters, or may include a plurality of reception filters.


Preferred embodiments of the present invention may widely be used in a communication device, such as a mobile phone, for example, as a filter or a composite filter device, a front end circuit, and a communication apparatus applicable to a multi-band system.


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 silicon support substrate;a silicon oxide film laminated above the silicon support substrate;a lithium tantalate film laminated above the silicon oxide film;an IDT electrode including an electrode finger and being provided above the lithium tantalate film; anda protection film covering at least a portion of the IDT electrode; whereinwhen a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4:
  • 2. An acoustic wave device comprising: a silicon support substrate;a silicon oxide film laminated above the silicon support substrate;a lithium tantalate film laminated above the silicon oxide film;an IDT electrode including an electrode finger and being provided above the lithium tantalate film; anda protection film covering at least a portion of the IDT electrode; whereinwhen a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4;
  • 3. An acoustic wave device comprising: a silicon support substrate;a silicon oxide film laminated above the silicon support substrate;a lithium tantalate film laminated above the silicon oxide film;an IDT electrode having an electrode finger and being provided above the lithium tantalate film; anda protection film covering at least a portion of the IDT electrode; whereinwhen a wavelength determined by an electrode finger pitch of the IDT electrode is denoted by λ, a wavelength normalized film thickness of the lithium tantalate film is denoted by TLT, θ of an Euler angle of the lithium tantalate film is denoted by θLT, a wavelength normalized film thickness of the silicon oxide film is denoted by TS, a wavelength normalized film thickness of the IDT electrode in terms of aluminum thickness being a product of a wavelength normalized film thickness of the IDT electrode and a value obtained when density of the IDT electrode is divided by density of aluminum is denoted by TE, a wavelength normalized film thickness of the protection film being a product of a value obtained when density of the protection film is divided by density of silicon oxide and a wavelength normalized film thickness which is a thickness of the protection film normalized by the wavelength λ is denoted by TP, a propagation direction in the silicon support substrate is denoted by ψSi, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by TSi, TLT, θLT, TS, TE, TP, and ψSi are set such that a value represented by Formula (1) below is larger than about −2.4;
  • 4. The acoustic wave device according to claim 1, wherein the wavelength normalized film thickness TSi of the silicon support substrate is greater than about 20.
  • 5. The acoustic wave device according to claim 1, wherein a thickness of the lithium tantalate film is equal to or less than about 3.5λ.
  • 6. The acoustic wave device according to claim 1, wherein the protection film covers the lithium tantalate film and a side surface and an upper surface of the electrode finger of the IDT electrode, and a thickness of the protection film on the side surface of the electrode finger is smaller than a thickness of the protection film covering the upper surface of the electrode finger.
  • 7. The acoustic wave device according to claim 1, wherein the protection film covers the lithium tantalate film and a side surface and an upper surface of the electrode finger of the IDT electrode, and a thickness of the protection film on the lithium tantalate film is smaller than a thickness of the protection film covering the upper surface of the electrode finger.
  • 8. The acoustic wave device according to claim 1, wherein the protection film covers the lithium tantalate film and an upper surface and a side surface of the IDT electrode, and a thickness of the protection film on the lithium tantalate film is larger than a thickness of the protection film covering the upper surface of the electrode finger.
  • 9. The acoustic wave device according to claim 1, wherein the acoustic wave device is an acoustic wave resonator.
  • 10. 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.
  • 11. A composite filter device comprising: N band pass filters having different pass bands where N is two or more; whereinone terminal of each of the N band pass filters is connected in common on an antenna terminal side;at least one of the N band pass filters excluding a band pass filter having a highest pass band includes one or more acoustic wave resonators; andat least one of the one or more acoustic wave resonators is the acoustic wave device according to claim 1.
  • 12. The composite filter device according to claim 11, wherein N is three or more, and the three or more band pass filters simultaneously transmit and receive signals of a plurality of communication bands.
  • 13. The composite filter device according to claim 11, wherein N is three or more, and at least one of the three or more band pass filters is a ladder filter.
  • 14. 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 2.
  • 15. A composite filter device comprising: N band pass filters having different pass bands where N is two or more; whereinone terminal of each of the N band pass filters is connected in common on an antenna terminal side;at least one of the N band pass filters excluding a band pass filter having a highest pass band includes one or more acoustic wave resonators; andat least one of the one or more acoustic wave resonators is the acoustic wave device according to claim 2.
  • 16. 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 3.
  • 17. A composite filter device comprising: N band pass filters having different pass bands where N is two or more; whereinone terminal of each of the N band pass filters is connected in common on an antenna terminal side;at least one of the N band pass filters excluding a band pass filter having a highest pass band includes one or more acoustic wave resonators; andat least one of the one or more acoustic wave resonators is the acoustic wave device according to claim 3.
  • 18. The acoustic wave device according to claim 2, wherein a thickness of the lithium tantalate film is equal to or less than about 3.5λ.
  • 19. The acoustic wave device according to claim 3, wherein a thickness of the lithium tantalate film is equal to or less than about 3.5λ.
  • 20. The acoustic wave device according to claim 4, wherein a thickness of the lithium tantalate film is equal to or less than about 3.5λ.
Priority Claims (1)
Number Date Country Kind
2018-168265 Sep 2018 JP national
CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to Japanese Patent Application No. 2018-168265 filed on Sep. 7, 2018 and is a Continuation Application of PCT Application No. PCT/JP2019/035185 filed on Sep. 6, 2019. The entire contents of each application are hereby incorporated herein by reference.

Continuations (1)
Number Date Country
Parent PCT/JP2019/035185 Sep 2019 US
Child 17183431 US