Microsoft Word - SPM_guidebook_v014_azuma.docx SPMAFMKPFMDFTB(,Density Functional Based Tight Binding Method) SPM 11.1 DFTB
11.1.a
3N ),,,( 21 rrrrrrrrrrrr N Lψ 3 ( )ρ r E[ρ]3N
ρ(r) ),,,( 21 rrrrrrrrrrrr N Lψ ρ(r) Hohenberg-Kohn[1]
E[ρ]E[ρ] ρ [1] E[ρ]E[ρ][2][3] ρ(r)N{ ( )}
j ψ rrrr Kohn-Sham[4]
( ) ( ) ( ) eff ext
′−∫ ρ(r )(r )(r )(r )
r r r rr r r rr r r rr r r r r rr rr rr r
…(1)
127
ψ rrrr(3) ρ(r)E )(rrrrextV Coulomb xcE 1(LDA) )(rrrrxcv xcE (LDA)[5] LDA 11.1.b
s pd SPM { }( )iP rrrr Bloch[6]
128
∑ +−= • N
ai
i
11.1.c DFTB
[ ] ∑∑ ∫ ≠ −
++ ′−
′ ′++
−=
2 ρψ
ρ ψ …(6) [7] nψ Kohn-Sham nf nψ extV Coulombρ xcE aZ a nf ρ
)()()( 0 rrrrrrrrrrrr δρρρ += (6)
129
[ ]
repE 0H repE δρ 2E Bloch
∑= i
( )∑ ∑∑ ∈
aq 0
∑ ∈
∫= )(rrrrrrrrρdN
aq atomfreeneutral
0 (9) )(rrrrnψ nε nε nf FE )(rrrrnψ nf (8)(9)(7)(7) repE [7] 11.2 STM
80STM 100STM
131
() LEED()STM Si(111)-7x7[11]( 140)Au(100)-26x5[12]( 141)
()kkkkkkkk )(kkkkE () 1B
142 [15][15][15][15]
143 [16][16][16][16]
11.2.b
Bardeen [17] TS VVTH ++= T SV TV S T
S
SSS
S
T
TTT
T
inEVTH
inEVTH
=+≈
=+≈
νννν
ψψψ
ψψψ …(10) T 0≈SV S ST += (10) FE
133
rrrrrrrr eVEE TT −= νν
S
π −−== →
SSTST
144
[18,19](11)δΓ=1.0 eV [19]
( ) ( ) ( )}∫
∑ ∫
S E
( ) ( ) 22
B
( )
( ) ( ) ),()()(
),()( ~
)()(
*
*
2
2
22
2
( ) ( ) ( )[
( ) ( ) ( )
( ) ( ) ( )
⋅+⋅−+
⋅+⋅−+
−⋅−≈
∫
∫
−=
−=
( )
( ) ( )( )+−+

−×
−=
∈
∈
∫
∑ ∫
2
ε+
Si(001)Si(001)Si(001)Si(001)----3x1:H3x1:H3x1:H3x1:H
GUIGUIGUIGUI
150 ((dI/dV)/(I/V)) 149 150 151 151 dI/dV[18]
140
( )
∑∑
∑ ∑
≠∂
∂ −
∂
∂ −




∂
∂ +





∂
∂ −
∂
∂ −=
∂
∂ −=
141

( ) ( ) ( )tklzFhuzk dt
dz zzm
2
a 11.4.d
142
143
BΦ A B
e V AB Φ−Φ
= ΔV e
DFTB DFTB -V q q q q DFTB q q
A B
Φ A
Φ B
156 Si(001) 157 Si(001) 4 (LCPD) LCPD
146
11.6.a
Project Editor"Setup""Component"[Add Tip] - [Database]"tip_si4"
"Component"[Add Sample] - [Database] "hsi001-dfh"
147

"Component" - "Tip" - "ScanArea""w", "d", "h""15", "15", "0" (Main View"show scan area")
GUI"DFTB" "Calculation"
Project Editor"DFTB"
11.6.b STSSi(001)-3x1:H 17 Si(001)-3x1:H
Project Editor"DFTB" "mode""DFTB_STS" "two_body_parameter_folder""h-c-si" "tip_bias_voltage""minimum" "maximum""Ndiv""-4.0""+4.0" "100"
Project Editor"DFTB" "mode""DFTB_AFM " "two_body_parameter_folder""h-c-si" “tip” ” amplitude”, "k_cantilever", "resonant_freq""160", "41", "172" "tip"-"Ndiv""X","Y""20""Z"
11.6.d
SPMGUI [New]-[File] "OK" Project Editor"Setup" "Component"[Add Tip] - [Database]"tip_hsi4" "Component"[Add Sample] - [Database] "surf_si001n" 1."Component" - "Tip" - "Position" "x", "y""-7", "-6" 2."Component" - "Tip" - "DistanceFromSamples""4" "Component" - "Tip" - "ScanArea" "w", "d", "h""15.350140", "15.350140", "0" GUI"DFTB" "Calculation"
151