	US 11,888,461 B2
	Acoustic wave device, acoustic wave filter, and composite filter device
Ryo Nakagawa, Nagaokakyo (JP); and Hideki Iwamoto, Nagaokakyo (JP)
Assigned to MURATA MANUFACTURING CO., LTD., Kyoto (JP)
Filed by Murata Manufacturing Co., Ltd., Nagaokakyo (JP)
Filed on Feb. 24, 2021, as Appl. No. 17/183,431.
Application 17/183,431 is a continuation of application No. PCT/JP2019/035185, filed on Sep. 6, 2019.
Claims priority of application No. 2018-168265 (JP), filed on Sep. 7, 2018.
Prior Publication US 2021/0194455 A1, Jun. 24, 2021
Int. Cl. H03H 9/02 (2006.01); H03H 9/25 (2006.01)

CPC H03H 9/02559 (2013.01) [H03H 9/02574 (2013.01); H03H 9/02724 (2013.01); H03H 9/25 (2013.01)]

20 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; and

a protection film covering at least a portion of the IDT electrode; wherein

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 T_LT, θ of an Euler angle of the lithium tantalate film is denoted by θ_LT, a wavelength normalized film thickness of the silicon oxide film is denoted by T_S, 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 T_E, 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 T_P, a propagation direction in the silicon support substrate is denoted by ψ_Si, and a wavelength normalized film thickness which is a thickness of the silicon support substrate normalized by the wavelength λ is denoted by T_Si, T_LT, θ_LT, T_S, T_E, T_P, and ψ_Siare set such that a value represented by Formula (1) below is larger than about −2.4:

where, 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 a crystal orientation of the silicon support substrate and a range of T_S, T_LT, and ψ_Si:

	TABLE 1

		Si(100)
		0 < T_LT< 0.2
		0 ≤ T_S< 0.2

		0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

a_TLT⁽²⁾	0	0
a_TLT⁽¹⁾	0	0
b_TLT⁽²⁾	0	0
c_TLT	0	0
a_TS⁽²⁾	0	0
a_TS⁽¹⁾	−5.857231176	−5.857231176
b_TS⁽²⁾	0	0
c_TS	0.148	0.148
a_TE⁽⁴⁾	0	0
a_TE⁽³⁾	0	0
a_TE⁽²⁾	−19.75255913	−19.75255913
a_TE⁽¹⁾	−2.877583447	−2.877583447
b_TE⁽⁴⁾	0	0
b_TE⁽³⁾	0	0
b_TE⁽²⁾	0.022736	0.022736
c_TE	0.242	0.242
a_ψSi⁽⁶⁾	0	0
a_ψSi⁽⁵⁾	0	0
a_ψSi⁽⁴⁾	0	0
a_ψSi⁽³⁾	0	0
a_ψSi⁽²⁾	0.004788767	0.004788767
a_ψSi⁽¹⁾	0.024306207	0.024306207
b_ψSi⁽⁶⁾	0	0
b_ψSi⁽⁵⁾	0	0
b_ψSi⁽⁴⁾	0	0
b_ψSi⁽³⁾	0	0
b_ψSi⁽²⁾	81.81	81.81
c_ψSi	8.7	8.7
a_θLT⁽²⁾	−0.008235936	−0.008235936
a_θLT⁽¹⁾	−0.021048278	−0.021048278
b_θLT⁽²⁾	65.16	65.16
c_θLT	−52.2	−52.2
d_TLTTS	0	0
d_TLTTE	0	0
d_TLTψSi	0	0
T_TLTθLT	0	0
d_TSTE	0	0
d_TSψSi	0	0
d_TSθLT	−0.786852571	−0.786852571
d_TEψSi	0	0
d_TEθLT	−0.237034335	−0.237034335
d_ψSiθLT	0	0
e	−1.499248378	−1.499248378
a_TP	−111692	−111692
b_TP	19239	19239
c_TP	−952.97	−952.97
d_TP	8.8027	8.8027
f_TP	1.0495	1.0495;

	TABLE 2

		Si(100)
		0.2 ≤ T_LT≤ 3.5
		0 ≤ T_S< 0.2

		0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

a_TLT⁽²⁾	0	125.5342427
a_TLT⁽¹⁾	−13.43961051	−7.643409732
b_TLT⁽²⁾	0	0.006076558
c_TLT	0.329807692	0.321186441
a_TS⁽²⁾	0	0
a_TS⁽¹⁾	−11.80744788	−10.05306878
b_TS⁽²⁾	0	0
c_TS	0.158653846	0.153389831
a_TE⁽⁴⁾	0	0
a_TE⁽³⁾	0	0
a_TE⁽²⁾	0	0
a_TE⁽¹⁾	0	−7.595099843
b_TE⁽⁴⁾	0	0
b_TE⁽³⁾	0	0
b_TE⁽²⁾	0	0
c_TE	0	0.366101695
a_ψSi⁽⁶⁾	0	0
a_ψSi⁽⁵⁾	0	0
a_ψSi⁽⁴⁾	0	0
a_ψSi⁽³⁾	0	0
a_ψSi⁽²⁾	0.003335792	0
a_ψSi⁽¹⁾	0.039268266	−0.013700762
b_ψSi⁽⁶⁾	0	0
b_ψSi⁽⁵⁾	0	0
b_ψSi⁽⁴⁾	0	0
b_ψSi⁽³⁾	0	0
b_ψSi⁽²⁾	191.7159763	0
c_ψSi	13.26923077	16.01694915
a_θLT⁽²⁾	−0.007476194	0
a_θLT⁽¹⁾	−0.010867175	−0.053997369
b_θLT⁽²⁾	69.19378698	0
c_θLT	−50.19230769	−50.59322034
d_TLTTS	0	0
d_TLTTE	0	0
d_TLTψSi	−0.629167148	−0.724576033
T_TLTθLT	0	0
d_TSTE	0	0
d_TSψSi	0	0.521919406
d_TSθLT	0	0
d_TEψSi	0	−0.523966449
d_TEθLT	0	0
d_ψSiθLT	0	0
e	−2.071831837	−3.228508418
a_TP	−111692	−111692
b_TP	19239	19239
c_TP	−952.97	−952.97
d_TP	8.8027	8.8027
f_TP	1.0495	1.0495;

	TABLE 3

		Si(100)
		0 < T_LT< 0.2
		0.2 ≤ T_S≤ 2.0

		0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

a_TLT⁽²⁾	0	0
a_TLT⁽¹⁾	−15.6141248	−15.6141248
b_TLT⁽²⁾	0	0
c_TLT	0.163309353	0.163309353
a_TS⁽²⁾	0	0
a_TS⁽¹⁾	−22.02440893	−22.02440893
b_TS⁽²⁾	0	0
c_TS	0.325179856	0.325179856
a_TE⁽⁴⁾	0	0
a_TE⁽³⁾	−248.4374004	−248.4374004
a_TE⁽²⁾	−36.57127964	−36.57127964
a_TE⁽¹⁾	13.88180854	13.88180854
b_TE⁽⁴⁾	0	0
b_TE⁽³⁾	0.000480119	0.000480119
b_TE⁽²⁾	0.020416128	0.020416128
c_TE	0.240647482	0.240647482
a_ψSi⁽⁶⁾	0	0
a_ψSi⁽⁵⁾	0	0
a_ψSi⁽⁴⁾	0	0
a_ψSi⁽³⁾	0	0
a_ψSi⁽²⁾	0.002456326	0.002456326
a_ψSi⁽¹⁾	0.048553126	0.048553126
b_ψSi⁽⁶⁾	0	0
b_ψSi⁽⁵⁾	0	0
b_ψSi⁽⁴⁾	0	0
b_ψSi⁽³⁾	0	0
b_ψSi⁽²⁾	279.6050929	279.6050929
c_ψSi	22.3381295	22.3381295
a_θLT⁽²⁾	0	0
a_θLT⁽¹⁾	0.005427275	0.005427275
b_θLT⁽²⁾	0	0
c_θLT	−50.35971223	−50.35971223
d_TLTTS	0	0
d_TLTTE	0	0
d_TLTψSi	0	0
T_TLTθLT	0	0
d_TSTE	41.63149071	41.63149071
d_TSψSi	−0.577179204	−0.577179204
d_TSθLT	0.603866778	0.603866778
d_TEψSi	0.134944598	0.134944598
d_TEθLT	0	0
d_ψSiθLT	0	0
e	−2.703317679	−2.703317679
a_TP	−111692	−111692
b_TP	19239	19239
c_TP	−952.97	−952.97
d_TP	8.8027	8.8027
f_TP	1.0495	1.0495;

	TABLE 4

			Si(100)
			0.2 ≤ T_LT≤ 3.5
			0.2 ≤ T_S≤2.0

			0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

a_TLT⁽²⁾	0	133.7896555
a_TLT⁽¹⁾	−7.761727985	−9.701155851
b_TLT⁽²⁾	0	0.006281971
c_TLT	0.315508021	0.306914894
a_TS⁽²⁾	0	0
a_TS⁽¹⁾	−20.35135077	−6.186650236
b_TS⁽²⁾	0	0
c_TS	0.297860963	0.298404255
a_TE⁽⁴⁾	0	0
a_TE⁽³⁾	0	0
a_TE⁽²⁾	110.8304316	0
a_TE⁽¹⁾	4.036561723	−8.229960495
b_TE⁽⁴⁾	0	0
b_TE⁽³⁾	0	0
b_TE⁽²⁾	0.006431411	0
c_TE	0.140374332	0.363297872
a_ψSi⁽⁶⁾	0	0
a_ψSi⁽⁵⁾	0	0
a_ψSi⁽⁴⁾	0	0
a_ψSi⁽³⁾	0	0
a_ψSi⁽²⁾	0.002534654	0.001652947
a_ψSi⁽¹⁾	0.024168138	−0.003241344
b_ψSi⁽⁶⁾	0	0
b_ψSi⁽⁵⁾	0	0
b_ψSi⁽⁴⁾	0	0
b_ψSi⁽³⁾	0	0
b_ψSi⁽²⁾	269.2484772	266.6845858
c_ψSi	21.4171123	20.26595745
a_θLT⁽²⁾	0	0
a_θLT⁽¹⁾	0	−0.066116428
b_θLT⁽²⁾	0	0
c_θLT	−90	−50.4787234
d_TLTTS	96.23533718	0
d_TLTTE	−66.46866878	0
d_TLTψSi	−0.404808481	−0.688053172
d_TLTθLT	0	0
d_TSTE	0	0
d_TSψSi	−0.733337318	0
d_TSθLT	0	0
d_TEψSi	0.584322518	−0.372994212
d_TEθLT	0	0
d_ψSiθLT	0	0
e	−3.679364607	−4.30794513
a_TP	−111692	−111692
b_TP	19239	19239
c_TP	−952.97	−952.97
d_TP	8.8027	8.8027
f_TP	1.0495	1.0495;

TABLE 5

	Si(110)
	0 < T_LT< 0.2
	0 ≤ T_S< 0.2

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90

a_TLT⁽²⁾	0	0	0	0
a_TLT⁽¹⁾	−16.69742899	−16.69742899	−33.56520202	0
b_TLT⁽²⁾	0	0	0	0
c_TLT	0.1675	0.1675	0.192857143	0
a_TS⁽²⁾	0	0	0	0
a_TS⁽¹⁾	15.90196012	15.90196012	0	0
b_TS⁽²⁾	0	0	0	0
c_TS	0.1525	0.1525	0	0
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	0	26.3030303	0
a_TE⁽¹⁾	0	0	−6.181053391	0
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0	0.006326531	0
c_TE	0	0	0.378571429	0
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	−0.000183963	−0.000183963	0	−0.000177142
a_ψSi⁽²⁾	−0.003236307	−0.003236307	0	0.002186084
a_ψSi⁽¹⁾	0.071460688	0.071460688	0.085067773	0.13561432
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	−5768.71875	−5768.71875	0	2642.857143
b_ψSi⁽²⁾	399.9375	399.9375	0	500
c_ψSi	65.25	65.25	34.28571429	55
a_θLT⁽²⁾	0	0	0	−0.00533662
a_θLT⁽¹⁾	0	0	0.070255628	0.032718563
b_θLT⁽²⁾	0	0	0	65.75963719
c_θLT	−90	−90	−51.42857143	−50.95238095
d_TLTTS	0	0	0	0
d_TLTTE	0	0	0	0
d_TLTψSi	1.873870705	1.873870705	0	0
d_TLTθLT	0	0	0	0
d_TSTE	0	0	0	0
d_TSψSi	0	0	0	0
d_TSθLT	0	0	0	0
d_TEψSi	0	0	0	0
d_TEθLT	0	0	0.716151515	0
d_ψSiθLT	0	0	−0.00729303	0.002110378
e	−0.957101918	−0.957101918	−1.63492254	−1.290881853
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 6

	Si(110)
	0.2 ≤ T_LT≤ 3.5
	0 ≤ T_S< 0.2

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90

a_TLT⁽²⁾	0	0	0	0
a_TLT⁽¹⁾	−23.96596978	−4.695531045	−7.344438725	−5.603099398
b_TLT⁽²⁾	0	0	0	0
c_TLT	0.34	0.3296875	0.338983051	0.306666667
a_TS⁽²⁾	0	0	0	0
a_TS⁽¹⁾	−23.18485905	0	0	0
b_TS⁽²⁾	0	0	0	0
c_TS	0.175555556	0	0	0
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	−43.48595551	−70.50554427	−41.95412638
a_TE⁽¹⁾	0	−2.467954545	−5.460437635	−2.19025056
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0.006875	0.006716461	0.006819556
c_TE	0	0.15	0.365254237	0.360666667
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	0	0	0.000119479	−0.000172812
a_ψSi⁽²⁾	0.018474062	0	0.003987724	0.002213009
a_ψSi⁽¹⁾	0.059131688	0	−0.047908658	0.073831446
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	0	0	−2384.203107	1647.952
b_ψSi⁽²⁾	81.55555556	0	216.791152	242.24
c_ψSi	35.33333333	0	30.76271186	62.6
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	0.009475371	0	0.026725166	0
b_θLT⁽²⁾	0	0	0	0
c_θLT	−49.3333333	−90	−49.83050847	−90
d_TLTTS	0	0	0	0
d_TLTTE	0	0	0	42.3018696
d_TLTψSi	0	0	0	0
d_TLTθLT	0.617240199	0	0	0
d_TSTE	0	0	0	0
d_TSψSi	2.612107038	0	0	0
d_TSθLT	2.129359248	0	0	0
d_TEψSi	0	0	0	0
d_TEθLT	0	0	0	0
d_ψSiθLT	0.871101002	0	0	0
e	−2.851861362	−2.210765625	−2.573237283	−2.440604203
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 7

	Si(110)
	0 < T_LT< 0.2
	0.2 ≤ T_S≤ 2.0

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90

a_TLT⁽²⁾	0	0	0	0
a_TLT⁽¹⁾	−10.87353735	−17.74612134	−16.74814911	−16.74814911
b_TLT⁽²⁾	0	0	0	0
c_TLT	0.167045455	0.158227848	0.168032787	0.168032787
a_TS⁽²⁾	92.14417413	275.6432031	0	0
a_TS⁽¹⁾	−6.141913324	−0.713377524	−9.071522271	−9.071522271
b_TS⁽²⁾	0.004213585	0.004749239	0	0
c_TS	0.339772727	0.317721519	0.314754098	0.314754098
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	−37.82699975	0	0	0
a_TE⁽¹⁾	4.315324766	3.259148162	−5.270739047	−5.270739047
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0.007147469	0	0	0
c_TE	0.153409091	0.138607595	0.356557377	0.356557377
a_ψSi⁽⁶⁾	0	0	−3.73552E−09	−3.73552E−09
a_ψSi⁽⁵⁾	0	0	−4.69013E−08	−4.69013E−08
a_ψSi⁽⁴⁾	0	0	1.07773E−05	1.07773E−05
a_ψSi⁽³⁾	0.000254041	−0.00026684	5.64997E−05	5.64997E−05
a_ψSi⁽²⁾	0.00704637	0.003350583	−0.007526984	−0.007526984
a_ψSi⁽¹⁾	−0.123432463	0.05687546	−0.035719404	−0.035719404
b_ψSi⁽⁶⁾	0	0	1801696668	1801696668
b_ψSi⁽⁵⁾	0	0	6726299.443	6726299.443
b_ψSi⁽⁴⁾	0	0	1035415.498	1035415.498
b_ψSi⁽³⁾	−1197.310014	2539.305207	3573.665857	3573.665857
b_ψSi⁽²⁾	188.2457386	286.0358917	720.1088417	720.1088417
c_ψSi	28.125	63.60759494	48.19672131	48.19672131
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	0.046748629	0.00460971	0	0
b_θLT⁽²⁾	0	0	0	0
c_θLT	−51.59090909	−50.75949367	−90	−90
d_TLTTS	0	0	0	0
d_TLTTE	0	105.3055279	0	0
d_TLTψSi	0	0	0	0
d_TLTθLT	0	0	0	0
d_TSTE	58.63016883	0	0	0
d_TSψSi	0.443510572	0.274149566	0	0
d_TSθLT	0	0	0	0
d_TEψSi	0.293912516	−0.280924747	0	0
d_TEθLT	0	0.457718571	0	0
d_ψSiθLT	0	−0.005165328	0	0
e	−1.722804167	−2.484892701	−2.976959016	−2.976959016
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 8

	Si(110)
	0.2 < T_LT≤ 3.5
	0.2 ≤ T_S≤ 2.0

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90	0 ≤ _ψSi< 45	45 ≤ _ψSi≤ 90

a_TLT⁽²⁾	0	0	0	39.48011293
a_TLT⁽¹⁾	−5.239160454	−5.820942031	−4.867344296	−2.496300587
b_TLT⁽²⁾	0	0	0	0.00654321
c_TLT	0.309375	0.302702703	0.286363636	0.288888889
a_TS⁽²⁾	24.40391167	40.38499201	20	40.45660337
a_TS⁽¹⁾	−2.128595361	−6.73354721	−3.626479228	−6.290401812
b_TS⁽²⁾	0.006013184	0.005624543	0	0.005617284
c_TS	0.3265625	0.275675676	0.31	0.272222222
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	−51.46488975	0	0
a_TE⁽¹⁾	−1.921891837	−0.509929613	−1.508039016	−0.870147512
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0.006479182	0	0
c_TE	0.153125	0.147297297	0.341818182	0.351388889
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	0	−0.000165117	0	−9.55404E−05
a_ψSi⁽²⁾	0.000936051	0.00475603	0	0.002198207
a_ψSi⁽¹⁾	−0.02141106	0.040196571	−0.017752634	0.036260775
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	0	2115.829763	0	1531.394676
b_ψSi⁽²⁾	246.9177246	196.5668371	0	199.8263889
c_ψSi	24.140625	57.97297297	21.13636364	60.41666667
a_θLT⁽²⁾	0	0	0	−0.003220943
a_θLT⁽¹⁾	0.023743346	0.023741003	0.038368027	0.005042496
b_θLT⁽²⁾	0	0	0	72.22222222
c_θLT	−50.078125	−48.51351351	−50.81818182	−50
d_TLTTS	0	0	0	−43.45862557
d_TLTTE	−35.16960363	−48.00382984	23.6423037	52.46703277
d_TLTψSi	0	0	0	0
d_TLTθLT	0	0	0	0
d_TSTE	0	0	0	0
d_TSψSi	0	0	0	0
d_TSθLT	0	0	0	0
d_TEψSi	0	0	0	0
d_TEθLT	0.234382842	0	0	−0.273892853
d_ψSiθLT	0	−0.00130658	−0.001221935	0
e	−2.175330984	−2.239116787	−2.271294054	−2.496300587
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 9

	Si(111)
	0 < T_LT< 0.2
	0 ≤ T_S< 0.2

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60

a_TLT⁽²⁾	0	0	0	0
a_TLT⁽¹⁾	16.07631847	20.22733656	30.72650306	27.83979251
b_TLT⁽²⁾	0	0	0	0
c_TLT	0.145833333	0.1625	0.159574468	0.158695652
a_TS⁽²⁾	0	0	0	0
a_TS⁽¹⁾	17.08812597	27.84866827	31.28009383	12.67453621
b_TS⁽²⁾	0	0	0	0
c_TS	0.154166667	0.172916667	0.161702128	0.163043478
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	−96.15629371	0	138.3065683	0
a_TE⁽¹⁾	−1.263589744	2.883915191	−9.345807167	−7.807789594
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0.006649306	0	0.006229063	0
c_TE	0.170833333	0.14375	0.369148936	0.345652174
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	0	0	0	0
a_ψSi⁽²⁾	0	0	0	−0.006862727
a_ψSi⁽¹⁾	−0.101535567	−0.012511908	−0.101466433	0.176438509
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	0	0	0	0
b_ψSi⁽²⁾	0	0	0	114.9456522
c_ψSi	24.375	44.375	22.0212766	37.5
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	0	0	0	0
b_θLT⁽²⁾	0	0	0	0
c_θLT	−90	−90	−90	−90
d_TLTTS	−477.9162005	−760.9473336	−1054.386561	−1044.340968
d_TLTTE	0	0	0	0
d_TLTψSi	0	1.332405924	0	0
d_TLTθLT	0	0	0	0
d_TSTE	0	−250.1524613	102.33575	105.8611165
d_TSψSi	0	0	0	−2.093429604
d_TSθLT	0	0	0	0
d_TEψSi	−0.613440559		1.201832187	−0.525734733
d_TEθLT	0	0	0	0
d_ψSiθLT	0	0	0	0
e	−0.553295028	−1.074792989	−1.290770348	−1.165057152
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 10

	Si(111)
	0.2 ≤ T_LT≤ 3.5
	0 ≤ T_S< 0.2

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60

a_TLT⁽²⁾	−262.3995984	−262.3995984	0	0
a_TLT⁽¹⁾	−59.70400634	−59.70400634	−18.45032018	−20.44479246
b_TLT⁽²⁾	0.004691358	0.004691358	0	0
c_TLT	0.355555556	0.355555556	0.332352941	0.331914894
a_TS⁽²⁾	0	0	0	0
a_TS⁽¹⁾	−73.33869606	−73.33869606	−9.963926388	−24.5747574
b_TS⁽²⁾	0	0	0	0
c_TS	0.185185185	0.185185185	0.166176471	0.165957447
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	0	0	0
a_TE⁽¹⁾	−19.84024877	−19.84024877	−8.905455835	−17.17093947
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0	0	0
c_TE	0.157407407	0.157407407	0.369117647	0.373404255
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	−4.69771E−05	−4.69771E−05	0	0
a_ψSi⁽³⁾	−0.000362538	−0.000362538	0	0
a_ψSi⁽²⁾	0.055133453	0.055133453	−0.004320224	0.021125116
a_ψSi⁽¹⁾	0.020862911	0.020862911	−0.110606012	−0.064218508
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	138552.1512	138552.1512	0	0
b_ψSi⁽³⁾	−78.36076818	−78.36076818	0	0
b_ψSi⁽²⁾	203.1635802	203.1635802	145.9775087	66.20642825
c_ψSi	33.05555556	33.05555556	19.41176471	34.46808511
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	−0.079155699	−0.079155699	000	0.057672719
b_θLT⁽²⁾	0	0	0	0
c_θLT	−49.81481481	−49.81481481	−90	−49.14893617
d_TLTTS	0	0	0	0
d_TLTTE	−254.5809235	−254.5809235	80.69948416	99.56817027
d_TLTψSi	2.260189055	2.260189055	0	0
d_TLTθLT	−0.785540829	−0.785540829	000	0
d_TSTE	−292.5762951	−292.5762951	0	0
d_TSψSi	−5.914103654	−5.914103654	−1.139436429	0
d_TSθLT	0	0	0	0
d_TEψSi	1.75463008	1.75463008	0.660099875	−3.844659844
d_TEθLT	0	0	0	0
d_ψSiθLT	0	0	0	0.006965097
e	−1.304804416	−1.304804416	−2.734683251	−3.115044468
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

TABLE 11

	Si(111)
	0 < T_LT< 0.2
	0.2 ≤ T_S≤ 2.0

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60

a_TLT⁽²⁾	0.003649147	0	0	0
a_TLT⁽¹⁾	−17.27824731	−24.3903101	−38.65647339	−21.91795924
b_TLT⁽²⁾	67.18624026	0	0	0
c_TLT	0.154098361	0.15631068	0.17	0.1575
a_TS⁽²⁾	84.63185118	0	148.7691928	140.0125491
a_TS⁽¹⁾	−6.307527081	−32.68184816	−15.38083251	−11.91949736
b_TS⁽²⁾	0.004461166	0	0.005012245	0.004623438
c_TS	0.352459016	0.345631068	0.331428571	0.33875
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	0	0	0
a_TE⁽¹⁾	2.909874306	8.840975559	−16.54803788	−0.024546617
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0	0	0
c_TE	0.135245902	0.148058252	0.372857143	0.33125
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	0	0	0	0
a_ψSi⁽²⁾	0	0.006216698	0	0
a_ψSi⁽¹⁾	−0.068574135	−0.018885558	−0.187578295	0.122573316
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	0	0	0	0
b_ψSi⁽²⁾	0	147.1439344	0	0
c_ψSi	22.62295082	43.10679612	22.71428571	39.1875
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	0.023219728	0.047846607	0.097088558	0.096327065
b_θLT⁽²⁾	0	0	0	0
c_θLT	−50.16393443	−50.38834951	−50.42857143	−51.25
d_TLTTS	0	−144.763071	0	0
d_TLTTE	0	0	−161.23455326	0
d_TLTψSi	−0.827435588	0	0	1.107475984
d_TLTθLT	0	0	0	0
d_TSTE	0	103.0553675	−65.68497311	0
d_TSψSi	0	−1.329400713	0.82928215	−0.646921162
d_TSθLT	0	0	0	0
d_TEψSi	−0.681669875	0.653050787	0.676734069	0.936807034
d_TEθLT	0	0	0.481989709	0.52746173
d_ψSiθLT	0	0	0	0
e	−1.560056382	−2.656750279	−2.259351603	−1.805786084
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;

and

TABLE 12

	Si(111)
	0.2 ≤ T_LT≤ 3.5
	0.2 ≤ T_S≤ 2.0

	0.05 ≤ T_E< 0.25	0.25 ≤ T_E≤ 0.45

	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60	0 ≤ _ψSi< 30	30 ≤ _ψSi≤ 60

a_TLT⁽²⁾	0	77.3065693	243.6937004	0
a_TLT⁽¹⁾	−13.49335267	−9.878165228	−6.309863061	−12.90130633
b_TLT⁽²⁾	0	0.00674795	0.006522811	0
c_TLT	0.300961538	0.297350993	0.29858156	0.306818182
a_TS⁽²⁾	133.2691939	160.4037443	82.71737336	100.5491122
a_TS⁽¹⁾	−9.215218873	−21.20902158	−9.283157312	−7.984268054
b_TS⁽²⁾	0.006618898	0.005353274	0.006382979	0.005704201
c_TS	0.314423077	0.303311258	0.3	0.311363636
a_TE⁽⁴⁾	0	0	0	0
a_TE⁽³⁾	0	0	0	0
a_TE⁽²⁾	0	90.39669198	0	0
a_TE⁽¹⁾	0.170720276	3.925569914	−15.08313602	−9.451928755
b_TE⁽⁴⁾	0	0	0	0
b_TE⁽³⁾	0	0	0	0
b_TE⁽²⁾	0	0.006615499	0	0
c_TE	0.15	0.147350993	0.363475177	0.346212121
a_ψSi⁽⁶⁾	0	0	0	0
a_ψSi⁽⁵⁾	0	0	0	0
a_ψSi⁽⁴⁾	0	0	0	0
a_ψSi⁽³⁾	0	0	0	0
a_ψSi⁽²⁾	−0.00740803	0	0	0
a_ψSi⁽¹⁾	−0.220502432	0.083594751	−0.104344279	0.088096624
b_ψSi⁽⁶⁾	0	0	0	0
b_ψSi⁽⁵⁾	0	0	0	0
b_ψSi⁽⁴⁾	0	0	0	0
b_ψSi⁽³⁾	0	0	0	0
b_ψSi⁽²⁾	135.4659763	0	0	0
c_ψSi	20.76923077	43.70860927	17.87234043	41.47727273
a_θLT⁽²⁾	0	0	0	0
a_θLT⁽¹⁾	−0.017420386	−0.012240534	0	0
b_θLT⁽²⁾	0	0	0	0
c_θLT	−50.28846154	−50.26490066	−90	−90
d_TLTTS	149.298265	220.9283416	135.5319056	135.1493422
d_TLTTE	0	0	0	−65.38520659
d_TLTψSi	0	0	0	−0.663828772
d_TLTθLT	−0.703824061	−0.739197646	0	0
d_TSTE	122.4270642	0	−94.62792088	0
d_TSψSi	0.714493384	−1.189155195	0	−1.017237669
d_TSθLT	0	0	0	0
d_TEψSi	0	0.558597609	0	0
d_TEθLT	0.734424122	0.628956462	0	0
d_ψSiθLT	−0.003900657	0.003268439	0	0
e	−2.246432623	−2.691572945	−3.425676672	−3.236112132
a_TP	−111692	−111692	−111692	−111692
b_TP	19239	19239	19239	19239
c_TP	−952.97	−952.97	−952.97	−952.97
d_TP	8.8027	8.8027	8.8027	8.8027
f_TP	1.0495	1.0495	1.0495	1.0495;