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

Claim 0:
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 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 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 TS, TLT, and ψSi:, TABLE 1

Si(100)

0 < TLT < 0.2

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

aTLT(2)
0
0

aTLT(1)
0
0

bTLT(2)
0
0

cTLT
0
0

aTS(2)
0
0

aTS(1)
−5.857231176
−5.857231176

bTS(2)
0
0

cTS
0.148
0.148

aTE(4)
0
0

aTE(3)
0
0

aTE(2)
−19.75255913
−19.75255913

aTE(1)
−2.877583447
−2.877583447

bTE(4)
0
0

bTE(3)
0
0

bTE(2)
0.022736
0.022736

cTE
0.242
0.242

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
0
0

aψSi(2)
0.004788767
0.004788767

aψSi(1)
0.024306207
0.024306207

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
0
0

bψSi(2)
81.81
81.81

cψSi
8.7
8.7

aθLT(2)
−0.008235936
−0.008235936

aθLT(1)
−0.021048278
−0.021048278

bθLT(2)
65.16
65.16

cθLT
−52.2
−52.2

dTLTTS
0
0

dTLTTE
0
0

dTLTψSi
0
0

TTLTθLT
0
0

dTSTE
0
0

dTSψSi
0
0

dTSθLT
−0.786852571
−0.786852571

dTEψSi
0
0

dTEθLT
−0.237034335
−0.237034335

dψSiθLT
0
0

e
−1.499248378
−1.499248378

aTP
−111692
−111692

bTP
19239
19239

cTP
−952.97
−952.97

dTP
8.8027
8.8027

fTP
1.0495
1.0495;, TABLE 2

Si(100)

0.2 ≤ TLT ≤ 3.5

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

aTLT(2)
0
125.5342427

aTLT(1)
−13.43961051
−7.643409732

bTLT(2)
0
0.006076558

cTLT
0.329807692
0.321186441

aTS(2)
0
0

aTS(1)
−11.80744788
−10.05306878

bTS(2)
0
0

cTS
0.158653846
0.153389831

aTE(4)
0
0

aTE(3)
0
0

aTE(2)
0
0

aTE(1)
0
−7.595099843

bTE(4)
0
0

bTE(3)
0
0

bTE(2)
0
0

cTE
0
0.366101695

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
0
0

aψSi(2)
0.003335792
0

aψSi(1)
0.039268266
−0.013700762

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
0
0

bψSi(2)
191.7159763
0

cψSi
13.26923077
16.01694915

aθLT(2)
−0.007476194
0

aθLT(1)
−0.010867175
−0.053997369

bθLT(2)
69.19378698
0

cθLT
−50.19230769
−50.59322034

dTLTTS
0
0

dTLTTE
0
0

dTLTψSi
−0.629167148
−0.724576033

TTLTθLT
0
0

dTSTE
0
0

dTSψSi
0
0.521919406

dTSθLT
0
0

dTEψSi
0
−0.523966449

dTEθLT
0
0

dψSiθLT
0
0

e
−2.071831837
−3.228508418

aTP
−111692
−111692

bTP
19239
19239

cTP
−952.97
−952.97

dTP
8.8027
8.8027

fTP
1.0495
1.0495;, TABLE 3

Si(100)

0 < TLT < 0.2

0.2 ≤ TS ≤ 2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

aTLT(2)
0
0

aTLT(1)
−15.6141248
−15.6141248

bTLT(2)
0
0

cTLT
0.163309353
0.163309353

aTS(2)
0
0

aTS(1)
−22.02440893
−22.02440893

bTS(2)
0
0

cTS
0.325179856
0.325179856

aTE(4)
0
0

aTE(3)
−248.4374004
−248.4374004

aTE(2)
−36.57127964
−36.57127964

aTE(1)
13.88180854
13.88180854

bTE(4)
0
0

bTE(3)
0.000480119
0.000480119

bTE(2)
0.020416128
0.020416128

cTE
0.240647482
0.240647482

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
0
0

aψSi(2)
0.002456326
0.002456326

aψSi(1)
0.048553126
0.048553126

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
0
0

bψSi(2)
279.6050929
279.6050929

cψSi
22.3381295
22.3381295

aθLT(2)
0
0

aθLT(1)
0.005427275
0.005427275

bθLT(2)
0
0

cθLT
−50.35971223
−50.35971223

dTLTTS
0
0

dTLTTE
0
0

dTLTψSi
0
0

TTLTθLT
0
0

dTSTE
41.63149071
41.63149071

dTSψSi
−0.577179204
−0.577179204

dTSθLT
0.603866778
0.603866778

dTEψSi
0.134944598
0.134944598

dTEθLT
0
0

dψSiθLT
0
0

e
−2.703317679
−2.703317679

aTP
−111692
−111692

bTP
19239
19239

cTP
−952.97
−952.97

dTP
8.8027
8.8027

fTP
1.0495
1.0495;, TABLE 4

Si(100)

0.2 ≤ TLT ≤ 3.5

0.2 ≤ TS ≤2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

aTLT(2)
0
133.7896555

aTLT(1)
−7.761727985
−9.701155851

bTLT(2)
0
0.006281971

cTLT
0.315508021
0.306914894

aTS(2)
0
0

aTS(1)
−20.35135077
−6.186650236

bTS(2)
0
0

cTS
0.297860963
0.298404255

aTE(4)
0
0

aTE(3)
0
0

aTE(2)
110.8304316
0

aTE(1)
4.036561723
−8.229960495

bTE(4)
0
0

bTE(3)
0
0

bTE(2)
0.006431411
0

cTE
0.140374332
0.363297872

aψSi(6)
0
0

aψSi(5)
0
0

aψSi(4)
0
0

aψSi(3)
0
0

aψSi(2)
0.002534654
0.001652947

aψSi(1)
0.024168138
−0.003241344

bψSi(6)
0
0

bψSi(5)
0
0

bψSi(4)
0
0

bψSi(3)
0
0

bψSi(2)
269.2484772
266.6845858

cψSi
21.4171123
20.26595745

aθLT(2)
0
0

aθLT(1)
0
−0.066116428

bθLT(2)
0
0

cθLT
−90
−50.4787234

dTLTTS
96.23533718
0

dTLTTE
−66.46866878
0

dTLTψSi
−0.404808481
−0.688053172

dTLTθLT
0
0

dTSTE
0
0

dTSψSi
−0.733337318
0

dTSθLT
0
0

dTEψSi
0.584322518
−0.372994212

dTEθLT
0
0

dψSiθLT
0
0

e
−3.679364607
−4.30794513

aTP
−111692
−111692

bTP
19239
19239

cTP
−952.97
−952.97

dTP
8.8027
8.8027

fTP
1.0495
1.0495;, TABLE 5

Si(110)

0 < TLT < 0.2

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

aTLT(1)
−16.69742899
−16.69742899
−33.56520202
0

bTLT(2)
0
0
0
0

cTLT
0.1675
0.1675
0.192857143
0

aTS(2)
0
0
0
0

aTS(1)
15.90196012
15.90196012
0
0

bTS(2)
0
0
0
0

cTS
0.1525
0.1525
0
0

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
26.3030303
0

aTE(1)
0
0
−6.181053391
0

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0.006326531
0

cTE
0
0
0.378571429
0

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
−0.000183963
−0.000183963
0
−0.000177142

aψSi(2)
−0.003236307
−0.003236307
0
0.002186084

aψSi(1)
0.071460688
0.071460688
0.085067773
0.13561432

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
−5768.71875
−5768.71875
0
2642.857143

bψSi(2)
399.9375
399.9375
0
500

cψSi
65.25
65.25
34.28571429
55

aθLT(2)
0
0
0
−0.00533662

aθLT(1)
0
0
0.070255628
0.032718563

bθLT(2)
0
0
0
65.75963719

cθLT
−90
−90
−51.42857143
−50.95238095

dTLTTS
0
0
0
0

dTLTTE
0
0
0
0

dTLTψSi
1.873870705
1.873870705
0
0

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0.716151515
0

dψSiθLT
0
0
−0.00729303
0.002110378

e
−0.957101918
−0.957101918
−1.63492254
−1.290881853

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 6

Si(110)

0.2 ≤ TLT ≤ 3.5

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.34
0.3296875
0.338983051
0.306666667

aTS(2)
0
0
0
0

aTS(1)
−23.18485905
0
0
0

bTS(2)
0
0
0
0

cTS
0.175555556
0
0
0

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
−43.48595551
−70.50554427
−41.95412638

aTE(1)
0
−2.467954545
−5.460437635
−2.19025056

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0.006875
0.006716461
0.006819556

cTE
0
0.15
0.365254237
0.360666667

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0.000119479
−0.000172812

aψSi(2)
0.018474062
0
0.003987724
0.002213009

aψSi(1)
0.059131688
0
−0.047908658
0.073831446

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
−2384.203107
1647.952

bψSi(2)
81.55555556
0
216.791152
242.24

cψSi
35.33333333
0
30.76271186
62.6

aθLT(2)
0
0
0
0

aθLT(1)
0.009475371
0
0.026725166
0

bθLT(2)
0
0
0
0

cθLT
−49.3333333
−90
−49.83050847
−90

dTLTTS
0
0
0
0

dTLTTE
0
0
0
42.3018696

dTLTψSi
0
0
0
0

dTLTθLT
0.617240199
0
0
0

dTSTE
0
0
0
0

dTSψSi
2.612107038
0
0
0

dTSθLT
2.129359248
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0
0
0
0

dψSiθLT
0.871101002
0
0
0

e
−2.851861362
−2.210765625
−2.573237283
−2.440604203

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 7

Si(110)

0 < TLT < 0.2

0.2 ≤ TS ≤ 2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

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

bTLT(2)
0
0
0
0

cTLT
0.167045455
0.158227848
0.168032787
0.168032787

aTS(2)
92.14417413
275.6432031
0
0

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

bTS(2)
0.004213585
0.004749239
0
0

cTS
0.339772727
0.317721519
0.314754098
0.314754098

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
−37.82699975
0
0
0

aTE(1)
4.315324766
3.259148162
−5.270739047
−5.270739047

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0.007147469
0
0
0

cTE
0.153409091
0.138607595
0.356557377
0.356557377

aψSi(6)
0
0
−3.73552E−09
−3.73552E−09

aψSi(5)
0
0
−4.69013E−08
−4.69013E−08

aψSi(4)
0
0
1.07773E−05
1.07773E−05

aψSi(3)
0.000254041
−0.00026684
5.64997E−05
5.64997E−05

aψSi(2)
0.00704637
0.003350583
−0.007526984
−0.007526984

aψSi(1)
−0.123432463
0.05687546
−0.035719404
−0.035719404

bψSi(6)
0
0
1801696668
1801696668

bψSi(5)
0
0
6726299.443
6726299.443

bψSi(4)
0
0
1035415.498
1035415.498

bψSi(3)
−1197.310014
2539.305207
3573.665857
3573.665857

bψSi(2)
188.2457386
286.0358917
720.1088417
720.1088417

cψSi
28.125
63.60759494
48.19672131
48.19672131

aθLT(2)
0
0
0
0

aθLT(1)
0.046748629
0.00460971
0
0

bθLT(2)
0
0
0
0

cθLT
−51.59090909
−50.75949367
−90
−90

dTLTTS
0
0
0
0

dTLTTE
0
105.3055279
0
0

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
58.63016883
0
0
0

dTSψSi
0.443510572
0.274149566
0
0

dTSθLT
0
0
0
0

dTEψSi
0.293912516
−0.280924747
0
0

dTEθLT
0
0.457718571
0
0

dψSiθLT
0
−0.005165328
0
0

e
−1.722804167
−2.484892701
−2.976959016
−2.976959016

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 8

Si(110)

0.2 < TLT ≤ 3.5

0.2 ≤ TS ≤ 2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
39.48011293

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

bTLT(2)
0
0
0
0.00654321

cTLT
0.309375
0.302702703
0.286363636
0.288888889

aTS(2)
24.40391167
40.38499201
20
40.45660337

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

bTS(2)
0.006013184
0.005624543
0
0.005617284

cTS
0.3265625
0.275675676
0.31
0.272222222

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
−51.46488975
0
0

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0.006479182
0
0

cTE
0.153125
0.147297297
0.341818182
0.351388889

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
−0.000165117
0
−9.55404E−05

aψSi(2)
0.000936051
0.00475603
0
0.002198207

aψSi(1)
−0.02141106
0.040196571
−0.017752634
0.036260775

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
2115.829763
0
1531.394676

bψSi(2)
246.9177246
196.5668371
0
199.8263889

cψSi
24.140625
57.97297297
21.13636364
60.41666667

aθLT(2)
0
0
0
−0.003220943

aθLT(1)
0.023743346
0.023741003
0.038368027
0.005042496

bθLT(2)
0
0
0
72.22222222

cθLT
−50.078125
−48.51351351
−50.81818182
−50

dTLTTS
0
0
0
−43.45862557

dTLTTE
−35.16960363
−48.00382984
23.6423037
52.46703277

dTLTψSi
0
0
0
0

dTLTθLT
0
0
0
0

dTSTE
0
0
0
0

dTSψSi
0
0
0
0

dTSθLT
0
0
0
0

dTEψSi
0
0
0
0

dTEθLT
0.234382842
0
0
−0.273892853

dψSiθLT
0
−0.00130658
−0.001221935
0

e
−2.175330984
−2.239116787
−2.271294054
−2.496300587

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 9

Si(111)

0 < TLT < 0.2

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
0
0
0

aTLT(1)
16.07631847
20.22733656
30.72650306
27.83979251

bTLT(2)
0
0
0
0

cTLT
0.145833333
0.1625
0.159574468
0.158695652

aTS(2)
0
0
0
0

aTS(1)
17.08812597
27.84866827
31.28009383
12.67453621

bTS(2)
0
0
0
0

cTS
0.154166667
0.172916667
0.161702128
0.163043478

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
−96.15629371
0
138.3065683
0

aTE(1)
−1.263589744
2.883915191
−9.345807167
−7.807789594

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0.006649306
0
0.006229063
0

cTE
0.170833333
0.14375
0.369148936
0.345652174

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0
0
−0.006862727

aψSi(1)
−0.101535567
−0.012511908
−0.101466433
0.176438509

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
0
0
114.9456522

cψSi
24.375
44.375
22.0212766
37.5

aθLT(2)
0
0
0
0

aθLT(1)
0
0
0
0

bθLT(2)
0
0
0
0

cθLT
−90
−90
−90
−90

dTLTTS
−477.9162005
−760.9473336
−1054.386561
−1044.340968

dTLTTE
0
0
0
0

dTLTψSi
0
1.332405924
0
0

dTLTθLT
0
0
0
0

dTSTE
0
−250.1524613
102.33575
105.8611165

dTSψSi
0
0
0
−2.093429604

dTSθLT
0
0
0
0

dTEψSi
−0.613440559

1.201832187
−0.525734733

dTEθLT
0
0
0
0

dψSiθLT
0
0
0
0

e
−0.553295028
−1.074792989
−1.290770348
−1.165057152

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 10

Si(111)

0.2 ≤ TLT ≤ 3.5

0 ≤ TS < 0.2

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
−262.3995984
−262.3995984
0
0

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

bTLT(2)
0.004691358
0.004691358
0
0

cTLT
0.355555556
0.355555556
0.332352941
0.331914894

aTS(2)
0
0
0
0

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

bTS(2)
0
0
0
0

cTS
0.185185185
0.185185185
0.166176471
0.165957447

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

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

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.157407407
0.157407407
0.369117647
0.373404255

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
−4.69771E−05
−4.69771E−05
0
0

aψSi(3)
−0.000362538
−0.000362538
0
0

aψSi(2)
0.055133453
0.055133453
−0.004320224
0.021125116

aψSi(1)
0.020862911
0.020862911
−0.110606012
−0.064218508

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
138552.1512
138552.1512
0
0

bψSi(3)
−78.36076818
−78.36076818
0
0

bψSi(2)
203.1635802
203.1635802
145.9775087
66.20642825

cψSi
33.05555556
33.05555556
19.41176471
34.46808511

aθLT(2)
0
0
0
0

aθLT(1)
−0.079155699
−0.079155699
000
0.057672719

bθLT(2)
0
0
0
0

cθLT
−49.81481481
−49.81481481
−90
−49.14893617

dTLTTS
0
0
0
0

dTLTTE
−254.5809235
−254.5809235
80.69948416
99.56817027

dTLTψSi
2.260189055
2.260189055
0
0

dTLTθLT
−0.785540829
−0.785540829
000
0

dTSTE
−292.5762951
−292.5762951
0
0

dTSψSi
−5.914103654
−5.914103654
−1.139436429
0

dTSθLT
0
0
0
0

dTEψSi
1.75463008
1.75463008
0.660099875
−3.844659844

dTEθLT
0
0
0
0

dψSiθLT
0
0
0
0.006965097

e
−1.304804416
−1.304804416
−2.734683251
−3.115044468

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;, TABLE 11

Si(111)

0 < TLT < 0.2

0.2 ≤ TS ≤ 2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0.003649147
0
0
0

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

bTLT(2)
67.18624026
0
0
0

cTLT
0.154098361
0.15631068
0.17
0.1575

aTS(2)
84.63185118
0
148.7691928
140.0125491

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

bTS(2)
0.004461166
0
0.005012245
0.004623438

cTS
0.352459016
0.345631068
0.331428571
0.33875

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
0
0
0

aTE(1)
2.909874306
8.840975559
−16.54803788
−0.024546617

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0
0
0

cTE
0.135245902
0.148058252
0.372857143
0.33125

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
0
0.006216698
0
0

aψSi(1)
−0.068574135
−0.018885558
−0.187578295
0.122573316

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
0
147.1439344
0
0

cψSi
22.62295082
43.10679612
22.71428571
39.1875

aθLT(2)
0
0
0
0

aθLT(1)
0.023219728
0.047846607
0.097088558
0.096327065

bθLT(2)
0
0
0
0

cθLT
−50.16393443
−50.38834951
−50.42857143
−51.25

dTLTTS
0
−144.763071
0
0

dTLTTE
0
0
−161.23455326
0

dTLTψSi
−0.827435588
0
0
1.107475984

dTLTθLT
0
0
0
0

dTSTE
0
103.0553675
−65.68497311
0

dTSψSi
0
−1.329400713
0.82928215
−0.646921162

dTSθLT
0
0
0
0

dTEψSi
−0.681669875
0.653050787
0.676734069
0.936807034

dTEθLT
0
0
0.481989709
0.52746173

dψSiθLT
0
0
0
0

e
−1.560056382
−2.656750279
−2.259351603
−1.805786084

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;

and, TABLE 12

Si(111)

0.2 ≤ TLT ≤ 3.5

0.2 ≤ TS ≤ 2.0

0.05 ≤ TE < 0.25
0.25 ≤ TE ≤ 0.45

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

aTLT(2)
0
77.3065693
243.6937004
0

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

bTLT(2)
0
0.00674795
0.006522811
0

cTLT
0.300961538
0.297350993
0.29858156
0.306818182

aTS(2)
133.2691939
160.4037443
82.71737336
100.5491122

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

bTS(2)
0.006618898
0.005353274
0.006382979
0.005704201

cTS
0.314423077
0.303311258
0.3
0.311363636

aTE(4)
0
0
0
0

aTE(3)
0
0
0
0

aTE(2)
0
90.39669198
0
0

aTE(1)
0.170720276
3.925569914
−15.08313602
−9.451928755

bTE(4)
0
0
0
0

bTE(3)
0
0
0
0

bTE(2)
0
0.006615499
0
0

cTE
0.15
0.147350993
0.363475177
0.346212121

aψSi(6)
0
0
0
0

aψSi(5)
0
0
0
0

aψSi(4)
0
0
0
0

aψSi(3)
0
0
0
0

aψSi(2)
−0.00740803
0
0
0

aψSi(1)
−0.220502432
0.083594751
−0.104344279
0.088096624

bψSi(6)
0
0
0
0

bψSi(5)
0
0
0
0

bψSi(4)
0
0
0
0

bψSi(3)
0
0
0
0

bψSi(2)
135.4659763
0
0
0

cψSi
20.76923077
43.70860927
17.87234043
41.47727273

aθLT(2)
0
0
0
0

aθLT(1)
−0.017420386
−0.012240534
0
0

bθLT(2)
0
0
0
0

cθLT
−50.28846154
−50.26490066
−90
−90

dTLTTS
149.298265
220.9283416
135.5319056
135.1493422

dTLTTE
0
0
0
−65.38520659

dTLTψSi
0
0
0
−0.663828772

dTLTθLT
−0.703824061
−0.739197646
0
0

dTSTE
122.4270642
0
−94.62792088
0

dTSψSi
0.714493384
−1.189155195
0
−1.017237669

dTSθLT
0
0
0
0

dTEψSi
0
0.558597609
0
0

dTEθLT
0.734424122
0.628956462
0
0

dψSiθLT
−0.003900657
0.003268439
0
0

e
−2.246432623
−2.691572945
−3.425676672
−3.236112132

aTP
−111692
−111692
−111692
−111692

bTP
19239
19239
19239
19239

cTP
−952.97
−952.97
−952.97
−952.97

dTP
8.8027
8.8027
8.8027
8.8027

fTP
1.0495
1.0495
1.0495
1.0495;