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

Claim 16:
17. 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; 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 ο, 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 25 to Table 36 below that are determined in accordance with a crystal orientation of the silicon support substrate and a 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)
−16.39135605
−16.39135605

bTLT(2)
0
0

cTLT
0.196774194
0.196774194

aTS(2)
0
0

aTS(1)
−4.824831305
−4.824831305

bTS(2)
0
0

cTS
0.170967742
0.170967742

aTE(4)
0
0

aTE(3)
0
0

aTE(2)
−45.57608817
−45.57608817

aTE(1)
−10.80005563
−10.80005563

bTE(4)
0
0

bTE(3)
0
0

bTE(2)
0.018296046
0.018296046

cTE
0.303225806
0.303225806

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
0.000172048
0.000172048

aψSi(2)
−0.00384923
−0.00384923

aψSi(1)
−0.009826773
−0.009826773

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
143.0843208
143.0843208

bψSi(2)
215.8688866
215.8688866

cψSi
22.25806452
22.25806452

aθLT(2)
0
0

aθLT(1)
0.066799879
0.066799879

bθLT(2)
0
0

cθLT
−50.16129032
−50.16129032

dTLTTS
0
0

dTLTTE
−112.847682
−112.847682

dTLTψSi
0
0

dTLTθLT
0
0

dTSTE
0
0

dTSψSi
−1.750763196
−1.750763196

dTSθLT
0
0

dTEψSi
0
0

dTEθLT
0.466692151
0.466692151

dψSiθLT
0
0

e
−2.904746788
−2.904746788

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)
239.0395946
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
19.811

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)
−10.09828536
−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 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 ψSi ≤ 90
0 ≤ ψSi < 45
45 ≤ ψSi ≤ 90

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.164705882
0.164705882
0.164705882
0.164705882

aTS(2)
0
0
0
0

aTS(1)
0
0
0
0

bTS(2)
0
0
0
0

cTS
0
0
0
0

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

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

aTE(1)
39.88235294
39.88235294
39.88235294
39.88235294

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0.019258131
0.019258131
0.019258131
0.019258131

cTE
0.286470588
0.286470588
0.286470588
0.286470588

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

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

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
749.7716263
749.7716263
749.7716263
749.7716263

cψSi
52.58823529
52.58823529
52.58823529
52.58823529

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

aθLT(1)
0.023260981
0.023260981
0.023260981
0.023260981

bθLT(2)
81.16262976
81.16262976
81.16262976
81.16262976

cθLT
−50.11764706
−50.11764706
−50.11764706
−50.11764706

dTLTTS
0
0
0
0

dTLTTE
−32.35244505
−32.35244505
−32.35244505
−32.35244505

dTLTψSi
0.348515389
0.348515389
0.348515389
0.348515389

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0
0

dψSiθLT
0.000823202
0.000823202
0.000823202
0.000823202

e
−1.678155024
−1.678155024
−1.678155024
−1.678155024

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
0.160752688
0.160752688

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.165540541
0.165540541
0.355913978
0.355913978

aψSi(6)
0
0
0
0

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

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

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

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

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

bψSi(6)
0
0
0
0

bψSi(5)
11701030.08
11701030.08
24265475.25
24265475.25

bψSi(4)
1439156.296
1439156.296
1705613.393
1705613.393

bψSi(3)
1798.436559
1798.436559
6938.899332
6938.899332

bψSi(2)
930.5183985
930.5183985
1060.880593
1060.880593

cψSi
40.23648649
40.23648649
40.08064516
40.08064516

aθLT(2)
0
0
0
0

aθLT(1)
0.046000242
0.046000242
0.001380272
0.001380272

bθLT(2)
0
0
0
0

cθLT
−49.52702703
−49.52702703
−50.05376344
−50.05376344

dTLTTS
−136.9978702
−136.9978702
−73.06084164
−73.06084164

dTLTTE
0
0
0
0

dTLTψSi
0
0
0.096651605
0.096651605

dTLTθLT
0
0
0
0

dTSTE
0
0
−56.78924979
−56.78924979

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0.081014811
0.081014811
0
0

dTEθLT
0
0
−0.194432704
−0.194432704

dψSiθLT
0
0
0.000875955
0.000875955

e
−2.543790382
−2.543790382
−2.964933907
−2.964933907

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 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)
−13.1565646
−13.1565646
−13.1565646
−13.1565646

bTLT(2)
0
0
0
0

cTLT
0.179661017
0.179661017
0.179661017
0.179661017

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

aTS(1)
1.195559996
1.195559996
1.195559996
1.195559996

bTS(2)
0.006496856
0.006496856
0.006496856
0.006496856

cTS
0.299435028
0.299435028
0.299435028
0.299435028

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

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

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0.02062115
0.02062115
0.02062115
0.02062115

cTE
0.282768362
0.282768362
0.282768362
0.282768362

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

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

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

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

cψSi
44.83050847
44.83050847
44.83050847
44.83050847

aθLT(2)
0
0
0
0

aθLT(1)
0.020120147
0.020120147
0.020120147
0.020120147

bθLT(2)
0
0
0
0

cθLT
−50.50847458
−50.50847458
−50.50847458
−50.50847458

dTLTTS
0
0
0
0

dTLTTE
0
0
0
0

dTLTψSi
0.250474306
0.250474306
0.250474306
0.250474306

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0.031071552
0.031071552
0.031071552
0.031071552

dTEθLT
0
0
0
0

dψSiθLT
0
0
0
0

e
−1.687640015
−1.687640015
−1.687640015
−1.687640015

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 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
2083705.649
0
0

bψSi(4)
1386257.115
1386257.115
0
0

bψSi(3)
−1267.41343
−1267.41343
1811.750092
0

bψSi(2)
895.5856198
895.5856198
293.105197
0

cψSi
42.14046823
42.14046823
19.39490446
67.95180723

aθLT(2)
0
0
0
0

aθLT(1)
0.020067585
0.020067585
−0.011988832
0.032566601

bθLT(2)
0
0
0
0

cθLT
−49.73244147
−49.73244147
−49.61783439
−50.96385542

dTLTTS
0
0
0
0

dTLTTE
0
0
0
41.29194486

dTLTψSi
0
0
−0.203585177
0.376861254

dTLTθLT
0
0
−0.273779971
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
−0.20937463

dTSθLT
−0.349110894
−0.349110894
0
0

dTEψSi
0
0
0
0

dTEθLT
−0.216865482
−0.216865482
0
0

dψSiθLT
0
0
0.00120304
0

e
−2.390757235
−2.390757235
−2.548464154
−2.523994879

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 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.160869565
0.160869565
0.160869565
0.160869565

aTS(2)
0
0
0
0

aTS(1)
0
0
0
0

bTS(2)
0
0
0
0

cTS
0
0
0
0

aTE(4)
0
0
0
0

aTE(3)
11.21750437
11.21750437
11.21750437
11.21750437

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

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

bTE(4)
0
0
0
0

bTE(3)
0.000381688
0.000381688
0.000381688
0.000381688

bTE(2)
0.012589792
0.012589792
0.012589792
0.012589792

cTE
0.245652174
0.245652174
0.245652174
0.245652174

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
0
0

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
0
0

cψSi
35.86956522
35.86956522
35.86956522
35.86956522

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

aθLT(1)
0.003385783
0.003385783
0.003385783
0.003385783

bθLT(2)
77.88279773
77.88279773
77.88279773
77.88279773

cθLT
−47.82608696
−47.82608696
−47.82608696
−47.82608696

dTLTTS
0
0
0
0

dTLTTE
−2.939323227
−2.939323227
−2.939323227
−2.939323227

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0
0

dψSiθLT
−0.000442922
−0.000442922
−0.000442922
−0.000442922

e
−0.277577227
−0.277577227
−0.277577227
−0.277577227

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 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
0.183333333

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

aTE(3)
54.12265846
54.12265846
54.12265846
54.12265846

aTE(2)
0.942905209
0.942905209
0.942905209
0.942905209

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

bTE(4)
0.000339332
0.000339332
0.000339332
0.000339332

bTE(3)
0.000317558
0.000317558
0.000317558
0.000317558

bTE(2)
0.011265432
0.011265432
0.011265432
0.011265432

cTE
0.211111111
0.211111111
0.211111111
0.211111111

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
0
0

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
0
0

cψSi
27.5
27.5
27.5
27.5

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

aθLT(1)
0.005349146
0.005349146
0.005349146
0.005349146

bθLT(2)
57.09876543
57.09876543
57.09876543
57.09876543

cθLT
−46.11111111
−46.11111111
−46.11111111
−46.11111111

dTLTTS
0
0
0
0

dTLTTE
0
0
0
0

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
45.80413521
45.80413521
45.80413521
45.80413521

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
−0.071786246
−0.071786246
−0.071786246
−0.071786246

dψSiθLT
−0.000425881
−0.000425881
−0.000425881
−0.000425881

e
−0.446604617
−0.446604617
−0.446604617
−0.446604617

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
−0.488747927

bTS(2)
0
0
0
0

cTS
0.336144578
0.336144578
0.336144578
0.336144578

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

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

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0.017915517
0.017915517
0.017915517
0.017915517

cTE
0.256024096
0.256024096
0.256024096
0.256024096

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

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

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

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

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
105622.9088
105622.9088
105622.9088
105622.9088

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

bψSi(2)
208.4409929
208.4409929
208.4409929
208.4409929

cψSi
30.54216867
30.54216867
30.54216867
30.54216867

aθLT(2)
0
0
0
0

aθLT(1)
0
0
0
0

bθLT(2)
0
0
0
0

cθLT
−90
−90
−90
−90

dTLTTS
4.821777856
4.821777856
4.821777856
4.821777856

dTLTTE
−4.14067246
−4.14067246
−4.14067246
−4.14067246

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0.024454063
0.024454063
0.024454063
0.024454063

dTEθLT
0
0
0
0

dψSiθLT
0
0
0
0

e
−0.240178915
−0.240178915
−0.240178915
−0.240178915

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;

and, 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
0.220588235
0.220588235
0.220588235

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
0
0

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

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
0
0

cψSi
29.55882353
29.55882353
29.55882353
29.55882353

aθLT(2)
0
0
0
0

aθLT(1)
0.00165846
0.00165846
0.00165846
0.00165846

bθLT(2)
0
0
0
0

cθLT
−48.52941176
−48.52941176
−48.52941176
−48.52941176

dTLTTS
−0.04933649
−0.04933649
−0.04933649
−0.04933649

dTLTTE
−0.021023839
−0.021023839
−0.021023839
−0.021023839

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
−7.074776252
−7.074776252
−7.074776252
−7.074776252

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0
0

dψSiθLT
−0.00049898
−0.00049898
−0.00049898
−0.00049898

e
−0.3405485
−0.3405485
−0.3405485
−0.3405485

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.