Patent ID: 11888461
Assignee: MURATA MANUFACTURING CO., LTD.
Field: Basic communication processes (Electrical engineering)
Classification: CPC H | IPC H

Claim 12:
13. 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 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;, I
       h
      
      =
      
       
        (
        
         
          
           a
           
            T
            
             L
             ⁢
             T
            
           
           
            (
            2
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                T
                
                 L
                 ⁢
                 T
                
               
               -
               
                c
                
                 T
                 
                  L
                  ⁢
                  T
                 
                
               
              
              )
             
             2
            
            -
            
             b
             
              T
              LT
             
             
              (
              2
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            
             L
             ⁢
             T
            
           
           
            (
            1
            )
           
          
          ⁢
          
           (
           
            
             T
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              T
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            S
           
           
            (
            2
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                T
                S
               
               -
               
                c
                
                 T
                 S
                
               
              
              )
             
             2
            
            -
            
             b
             
              T
              S
             
             
              (
              2
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            S
           
           
            (
            1
            )
           
          
          ⁢
          
           (
           
            
             T
             S
            
            -
            
             c
             
              T
              S
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            B
           
           
            (
            4
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                T
                E
               
               -
               
                c
                
                 T
                 E
                
               
              
              )
             
             4
            
            -
            
             b
             
              T
              E
             
             
              (
              4
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            E
           
           
            (
            3
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                T
                E
               
               -
               
                c
                
                 T
                 E
                
               
              
              )
             
             3
            
            -
            
             b
             
              T
              E
             
             
              (
              3
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            E
           
           
            (
            2
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                T
                E
               
               -
               
                c
                
                 T
                 E
                
               
              
              )
             
             2
            
            -
            
             b
             
              T
              E
             
             
              (
              2
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            T
            E
           
           
            (
            1
            )
           
          
          ⁢
          
           (
           
            
             T
             E
            
            -
            
             c
             
              T
              E
             
            
           
           )
          
         
         +
         
          
           a
           
            Ψ
            Si
           
           
            (
            6
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                Ψ
                Si
               
               -
               
                c
                
                 Ψ
                 Si
                
               
              
              )
             
             6
            
            -
            
             b
             
              Ψ
              Si
             
             
              (
              6
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            Ψ
            
             S
             ⁢
             i
            
           
           
            (
            5
            )
           
          
          (
          
           
            
             (
             
              
               Ψ
               Si
              
              -
              
               c
               
                Ψ
                Si
               
              
             
             )
            
            5
           
           -
           
            b
            
             Ψ
             Si
            
            
             (
             5
             )
            
           
          
          )
         
         +
         
          
           a
           
            Ψ
            
             S
             ⁢
             i
            
           
           
            (
            4
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                Ψ
                Si
               
               -
               
                c
                
                 Ψ
                 
                  S
                  ⁢
                  i
                 
                
               
              
              )
             
             4
            
            -
            
             b
             
              Ψ
              
               S
               ⁢
               i
              
             
             
              (
              4
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            Ψ
            
             S
             ⁢
             i
            
           
           
            (
            3
            )
           
          
          (
          
           
            
             (
             
              
               Ψ
               
                S
                ⁢
                i
               
              
              -
              
               c
               
                Ψ
                Si
               
              
             
             )
            
            3
           
           -
           
            b
            
             Ψ
             Si
            
            
             (
             3
             )
            
           
          
          )
         
         +
         
          
           a
           
            Ψ
            Si
           
           
            (
            2
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                Ψ
                Si
               
               -
               
                c
                
                 Ψ
                 
                  S
                  ⁢
                  i
                 
                
               
              
              )
             
             2
            
            -
            
             b
             
              Ψ
              Si
             
             
              (
              2
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            Ψ
            Si
           
           
            (
            1
            )
           
          
          ⁢
          
           (
           
            
             Ψ
             
              S
              ⁢
              i
             
            
            -
            
             c
             
              Ψ
              
               S
               ⁢
               i
              
             
            
           
           )
          
         
         +
         
          
           a
           
            θ
            
             L
             ⁢
             T
            
           
           
            (
            2
            )
           
          
          ⁢
          
           (
           
            
             
              (
              
               
                θ
                
                 L
                 ⁢
                 T
                
               
               -
               
                c
                
                 θ
                 
                  L
                  ⁢
                  T
                 
                
               
              
              )
             
             2
            
            -
            
             b
             
              θ
              
               L
               ⁢
               T
              
             
             
              (
              2
              )
             
            
           
           )
          
         
         +
         
          
           a
           
            θ
            
             L
             ⁢
             T
            
           
           
            (
            1
            )
           
          
          ⁢
          
           (
           
            
             θ
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              θ
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             L
             ⁢
             
              T
              T
             
             ⁢
             S
            
           
          
          ⁢
          
           (
           
            
             T
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              T
              
               L
               ⁢
               T
              
             
            
           
           )
          
          ⁢
          
           (
           
            
             T
             S
            
            -
            
             c
             
              T
              S
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             L
             ⁢
             
              T
              T
             
             ⁢
             E
            
           
          
          ⁢
          
           (
           
            
             T
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              T
              
               L
               ⁢
               T
              
             
            
           
           )
          
          ⁢
          
           (
           
            
             T
             E
            
            -
            
             c
             
              T
              E
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             L
             ⁢
             
              T
              Ψ
             
             ⁢
             Si
            
           
          
          ⁢
          
           (
           
            
             T
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              T
              
               L
               ⁢
               T
              
             
            
           
           )
          
          ⁢
          
           (
           
            
             Ψ
             
              S
              ⁢
              i
             
            
            -
            
             c
             
              Ψ
              
               S
               ⁢
               i
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             L
             ⁢
             
              T
              θ
             
             ⁢
             L
             ⁢
             T
            
           
          
          ⁢
          
           (
           
            
             T
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              T
              
               L
               ⁢
               T
              
             
            
           
           )
          
          ⁢
          
           (
           
            
             θ
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              θ
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             S
             
              T
              E
             
            
           
          
          ⁢
          
           (
           
            
             T
             S
            
            -
            
             c
             
              T
              S
             
            
           
           )
          
          ⁢
          
           (
           
            
             T
             E
            
            -
            
             c
             
              T
              E
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             
              S
              Ψ
             
             ⁢
             S
             ⁢
             i
            
           
          
          ⁢
          
           (
           
            
             T
             S
            
            -
            
             c
             
              T
              S
             
            
           
           )
          
          ⁢
          
           (
           
            
             Ψ
             
              S
              ⁢
              i
             
            
            -
            
             c
             
              Ψ
              
               S
               ⁢
               i
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             
              S
              θ
             
             ⁢
             L
             ⁢
             T
            
           
          
          ⁢
          
           (
           
            
             T
             S
            
            -
            
             c
             
              T
              S
             
            
           
           )
          
          ⁢
          
           (
           
            
             θ
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              θ
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             
              E
              Ψ
             
             ⁢
             S
             ⁢
             i
            
           
          
          ⁢
          
           (
           
            
             T
             E
            
            -
            
             c
             
              T
              E
             
            
           
           )
          
          ⁢
          
           (
           
            
             Ψ
             
              S
              ⁢
              i
             
            
            -
            
             c
             
              Ψ
              
               S
               ⁢
               i
              
             
            
           
           )
          
         
         +
         
          
           d
           
            T
            
             
              E
              θ
             
             ⁢
             L
             ⁢
             T
            
           
          
          ⁢
          
           (
           
            
             T
             E
            
            -
            
             c
             
              T
              E
             
            
           
           )
          
          ⁢
          
           (
           
            
             θ
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              θ
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         
          
           d
           
            Ψ
            ⁢
            S
            ⁢
            
             i
             θ
            
            ⁢
            L
            ⁢
            T
           
          
          ⁢
          
           (
           
            
             Ψ
             
              S
              ⁢
              i
             
            
            -
            
             c
             
              Ψ
              Si
             
            
           
           )
          
          ⁢
          
           (
           
            
             θ
             
              L
              ⁢
              T
             
            
            -
            
             c
             
              θ
              
               L
               ⁢
               T
              
             
            
           
           )
          
         
         +
         e
        
        )
       
       ⁢
       
        (
        
         
          
           a
           
            T
            P
           
          
          ⁢
          
           T
           P
           4
          
         
         +
         
          
           b
           
            T
            P
           
          
          ⁢
          
           T
           P
           3
          
         
         +
         
          
           c
           
            T
            P
           
          
          ⁢
          
           T
           P
           2
          
         
         +
         
          
           d
           
            T
            P
           
          
          ⁢
          
           T
           p
          
         
         +
         
          f
          
           T
           P
          
         
        
        )
       
      
     
     ;
    
   
   
    
     Formula
     ⁢
        
     
      (
      1
      )
     
    
   
  
 

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

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
−0.003376583

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 < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE < 0.45

aTLT(2)
0
0

aTLT(1)
7.809960834
4.249755245

bTLT(2)
0
0

cTLT
0.30962963
0.302857143

aTS(2)
0
0

aTS(1)
0
−0.800874586

bTS(2)
0
0

cTS
0
0.150714286

aTE(4)
0
0

aTE(3)
0
0

aTE(2)
0
0

aTE(1)
−3.563479635
9.07053135

bTE(4)
0
0

bTE(3)
0
0

bTE(2)
0
0

cTE
0.148518519
0.353571429

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
−0.000160979
0

aψSi(2)
−0.000757552
0.001332545

aψSi(1)
0.095765615
0.003836714

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
384.7407407
0

bψSi(2)
278.2222222
285.0956633

cψSi
21.33333333
20.89285714

aθLT(2)
0
0

aθLT(1)
0.043185248
0.033521037

bθLT(2)
0
0

cθLT
−50
−50.92857143

dTLTTS
0
0

dTLTTE
0
0

dTLTψSi
−0.383208698
−0.220029295

dTLTθLT
0
0

dTSTE
0
0

dTSψSi
0
0

dTSθLT
0
0.974573109

dTEψSi
0
0

dTEθLT
1.01389349
−1.078939399

dψSiθLT
0
0.002899732

e
−5.569590226
−5.29442278

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)

−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 < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.174380165
0.174380165
0.174380165
0.174380165

aTS(2)
0
0
0
0

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

bTS(2)
0
0
0
0

cTS
0.150413223
0.150413223
0.150413223
0.150413223

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.245867769
0.245867769
0.245867769
0.245867769

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

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

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

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

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
1129197.497
1129197.497
1129197.497
1129197.497

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

bψSi(2)
776.3813947
776.3813947
776.3813947
776.3813947

cψSi
41.52892562
41.52892562
41.52892562
41.52892562

aθLT(2)
0
0
0
0

aθLT(1)
0.018744549
0.018744549
0.018744549
0.018744549

bθLT(2)
0
0
0
0

cθLT
−49.25619835
−49.25619835
−49.25619835
−49.25619835

dTLTTS
140.6234074
140.6234074
140.6234074
140.6234074

dTLTTE
−25.20654793
−25.20654793
−25.20654793
−25.20654793

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0
0

dψSiθLT
0
0
0
0

e
−1.789519626
−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 < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
39.68139696
39.68139696

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

bTLT(2)
0
0
0.00692398
0.00692398

cTLT
0.306451613
0.306451613
0.297857143
0.297857143

aTS(2)
0
0
0
0

aTS(1)
0
0
0
0

bTS(2)
0
0
0
0

cTS
0
0
0
0

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

aTE(1)
1.912614784
1.912614784
−6.089810932
−6.089810932

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.148924731
0.148924731
0.347857143
0.347857143

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
8.78847E−06
8.78847E−06

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

aψSi(1)
0.003265633
0.003265633
−0.023574651
−0.023574651

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
2351.597668
2351.597668

bψSi(2)
847.4765869
847.4765869
880.2091837
880.2091837

cψSi
35.32258065
35.32258065
43.07142857
43.07142857

aθLT(2)
0.005014741
0.005014741
0
0

aθLT(1)
0.023115164
0.023115164
0.030121011
0.030121011

bθLT(2)
67.0626662
67.0626662
0
0

cθLT
−49.62365591
−49.62365591
−51.28571429
−51.28571429

dTLTTS
0
0
0
0

dTLTTE
0
0
0
0

dTLTψSi
0
0
0.125572529
0.125572529

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0.563162206
0.563162206
−0.417002414
−0.417002414

dψSiθLT
0
0
0
0

e
−2.002512986
−2.002512986
−2.550158637
−2.550158637

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

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
−90
−90

dTLTTS
63.6265441
63.6265441
0
0

dTLTTE
0
0
0
0

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
57.20229582
57.20229582
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
−0.098212695
−0.098212695
0
0

dTEθLT
0.32576925
0.32576925
0
0

dψSiθLT
0
0
0
0

e
−2.431352404
−2.431352404
−2.39032093
−2.39032093

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 < 0.2

0.0 5 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.15443038
0.175438596
0.160759494
0.156896552

aTS(2)
0
0
0
0

aTS(1)
−7.971316395
7.232224634
−16.40433051
−3.920556446

bTS(2)
0
0
0
0

cTS
0.14556962
0.133333333
0.144303797
0.144827586

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
−110.7824708
−133.1826499
0

aTE(1)
12.77975858
−10.04988717
5.027045348
−5.686378626

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0.006463527
0.006582278
0

cTE
0.151265823
0.144736842
0.35
0.35862069

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
−0.007219474
0

aψSi(1)
0.028716852
0.04192074
−0.016815807
0.008780601

bψSi(6)
0
0
0
0

bψSi(5)
0
0

0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
125.0280404
0

cψSi
9.683544304
50
11.58227848
48.10344828

aθLT(2)
0.01035547
0
0
0.014789077

aθLT(1)
0.162093889
0.106646805
0.164306798
0.04587348

bθLT(2)
61.8811088
0
0
55.43995244

cθLT
−49.62025316
−50.35087719
−51.01265823
−51.20689655

dTLTTS
−609.1883956
−724.6623011
−297.9828576
−203.214973

dTLTTE
−215.420422
0
159.6303697
0

dTLTψSi
0
−3.771938969
2.003207828
−2.014745526

dTLTθLT
1.80686724
0
2.218853872
0

dTSTE
0
−307.4269587
0
0

dTSψSi
0
0
−1.097992723
0

dTSθLT
1.985202008
0
2.104127874
0

dTEψSi
0
0
−1.45135593
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
−3.454988617
−9.832405019
−3.192556866

bTLT(2)
0
0.006485261
0.006459172
0

cTLT
0.298058252
0.295238095
0.298461538
0.298913043

aTS(2)
0
0
0
0

aTS(1)
−8.97795964
1.31344944
0
0

bTS(2)
0
0
0
0

cTS
0.142718447
0.147619048
0
0

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

aTE(1)
9.791468713
0.170587985
−0.71523762
−10.72534988

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.15776699
0.124603175
0.356153846
0.347826087

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0.003924448
0.001661439
0
0.00657999

aψSi(1)
0.15776699
−0.024952541
0.02404454
−0.067389114

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
148.4588557
132.0861678
0
152.6937618

cψSi
15.29126214
46.9047619
14.19230769
43.04347826

aθLT(2)
0
0
0
0

aθLT(1)
0.06700163
0.042141715
0.055240362
0.061747926

bθLT(2)
0
0
0
0

cθLT
−48.73786408
−50.15873016
−49.76923077
−49.45652174

dTLTTS
116.7290786
−78.78450728
0
0

dTLTTE
0
85.46351406
−49.85282875
0

dTLTψSi
−0.70199108
0.445481139
0
0.604657146

dTLTθLT
−0.726496636
0
0
0

dTSTE
0
−116.360096
0
0

dTSψSi
0
−0.622709588
0
0

dTSθLT
2.041329502
−0.339115637
0
0

dTEψSi
0
0.20688896
0
0

dTEθLT
0.774150432
0.439880407
−0.6608739
−1.068569294

dψSiθLT
−0.005400114
0.002667922
−0.004937546
0.006290209

e
−4.209434885
−1.791078273
−3.48174155
−3.934527612

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 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
0.039888924
−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
20

aθLT(1)
−0.005093912
0.011098836
0.047530531
0.04750516

bθLT(2)
0
0
0
0

cθLT
−50
−50.4166667
−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;

and, 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
−13.78321665
−10.59163435

bTLT(2)
0
0
0
0

cTLT
0.321052632
0
0.309146341
0.303164557

aTS(2)
0
0
0
0

aTS(1)
0
−3.433673203
−1.746861763
3.363230821

bTS(2)
0
0
0
0

cTS
0
0.283443709
0.287804878
0.293037975

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
86.18383552
0

aTE(1)
3.853394073
8.768511808
−1.86755053
−15.6861606

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0.007157942
0

cTE
0.181578947
0.135430464
0.356097561
0.363291139

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
0
0

aψSi(1)
0.014178515
0.049910217
−0.008697771
0.012742666

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
0
0

cψSi
12.63157895
45.99337748
15.09146341
45

aθLT(2)
0
0
0
0

aθLT(1)
0
0.061867934
0.051566965
0.028929641

bθLT(2)
0
0
0
0

cθLT
−90
−50.59602649
−50.30487805
−50.56962025

dTLTTS
0
0
0
−103.0440888

dTLTTE
0
0
0
0

dTLTψSi
−0.181721459
0
0
0

dTLTθLT
0
0
0
−0.608943868

dTSTE
0
113.1914268
−75.04640382
−82.04954672

dTSψSi
0
0
−0.554356722
0.673316097

dTSθLT
0
0
0
0

dTEψSi
0
0
−0.512800103
0

dTEθLT
0
0
−0.656702553
0

dψSiθLT
0
0
0
0

e
−2.401219798
−3.18651044
−3.93030224
−4.143483981

aTP
0
0
00
0

bTP
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.