Si SiO 2. Si 1 VASP Si 1,, Si-Si 0.28Å Si Si-Si 0.19Å Si 166 Si Å Si
|
|
|
- あやか おおばま
- 9 years ago
- Views:
Transcription
1
2 Si SiO 2. Si 1 VASP Si 1,, Si-Si 0.28Å Si Si-Si 0.19Å Si 166 Si Å Si
3 SiO Si Cz SiO VASP(Vienna Ab-initio Simulation Package) PAW(Projector Augmented Wave) MedeA Maple Pauling File SiO Si Si Si
4
5 1 1.1 SiO 2 Si Cz 1500 Si SiO 2 (O) Si SiO 2 SiO Si O 2 SiO 2 Si [1, 4] Si ( ) 1.2 Si Si 1/4 1.1 Si Si 1.1: Si 3
6 1.3 Cz Cz Si (feed) Si (seed) Si (SiO 2 ) 1500 ( 1.2(a)) Si Si Si ( 1.2(b)) Si [1, 3, 4] 1.2: Si [1] (a) (b) 1.4 SiO 2 SiO SiO 2, 4
7 Stishovite SiO SiO 2 [1] Cristobalite Tridymite 2, [8] 1.3: SiO SiO 2 Cz SiO 2 Si 1 Si 5
8 2 Schrödinger (First principles calculatons) VASP maple MedeA 2.1, ( adiabatic approximation) Schrödinger Hψ = ɛψ (2.1) ( d2 + V )ψ = ɛψ (2.2) dx2 [6] (Hamiltonian:H) (wave function:φ) (energy Eigen value:ɛ) (Kinetic Energy) (d 2 ψ/d 2 x) (Vψ) (potential:v) (nuclear potential) ( exchange-correlation interaction) 2.2 self consistent loop 6
9 [6] 2.2 VASP(Vienna Ab-initio Simulation Package) VASP ( PAW ) VASP [7] 2.3 PAW(Projector Augmented Wave) VASP PAW ( ) PAW ( ) PAW Blochl [11] GGA(Generalized Gradient Approximation) PAW(Projector Augmented Wave) : [4] PAW ( ) 2.4 MedeA MedeA 7
10 Windows VASP [6] VASP MedeA 2.5 Maple Maple 1980 [4] Maple 2.6 Pauling File Pauling File ,000 X 4 4 [10] 2.2 Pauling File SiO 2 SiO 2 O-Si-O Pauling File 2.2: [11] Si-O [Å] Si-O-Si [deg] stishovite coesite ,180 low-quartz low-cristobalite high-quartz 1.56, low-tridymite ,150,180 high-tridymite 1.54, ,170,180 8
11 3 Cz Si SiO 2 SiO 2 Si SiO 2 Si 1 SiO Si-O Si-O-Si SiO SiO SiO 2 8 E-V [ev/sio 2 ] [Å 3 /SiO 2 ] (Stishovite) (Stishovite) (Coesite) (Low Quartz) E-V VASP de δq δw de = δq δw (3.1) δq =0 δw rev = P dv de = P dv (3.2) P P = de dv 9 (3.3)
12 3.1: SiO 2 E-V (a) 8 E-V (b)stishovite coesite,coesite low quartz. (3.3) E-V 2 E-V [6] 3.1(b) VASP stishovite coesite low quartz E-V stishovite coesite coesite low quartz E-V ev/å 3 GPa 1[GPa] = [eV/Å 3 ] (3.4) (3.4) stishovite coesite coesite low quartz E-V : 2 [9] [GPa] [GPa] stishovite coesite coesite low-quartz
13 3.2 Si 1 Si 1 Si 3.2(a) Si (b) Si64 3.2: Si (a)si8 (b)si64 Si 3.3(a) 3.3(b) 3.3(c) Si 3.3(d) Si-Si Si Si Si cut-off 600eV k 0.3/Å,. 11
14 3.3: (a)si (b)puresi (c) (d) 12
15 3.4: Si 3.2 Si 2 Si-Si Si-O Si 3.2: Si 63+O1 [deg] [Å] [Å] [Å 3 ] [ev] Si-O-Si Si-O Si-Si SiO 2 Si-Si Si Si-Si 13
16 3.5 Si-Si 9 1 Si cut-off 600eV k 0.3/Å, Si 3.5: (a)si (b)si 3.6 site site (b) (c) site1 site2 site4 site2 site (c) site1 site2 site4 14
17 3.6: 9,(a) (b)(a) 3.7: (a) (b)site (c) b 3 [5] 15
18 site5 3.8(b) site1 site2 site4 site5 Si cutoff 520eV k 0.3/Å Si 3.8: Si 64 a b a c Si [eV] 3.7(b) site Si Si Si 6 Si-Si Si-Si 3.11 Si-Si 16
19 3.9: Si 1 (a) (b)(a) ,cutoff 600eV,k 0.3/Å Si eV Si Si 1 Si Si eV 2.4eV SiO 2 Si-O-Si 10 17
20 3.10: 3.9(a)
21 3.11: (a)[101] (b)[111] (c)(b) 19
22 3.3: 1 [Å] [deg] [ev] Si-O Si-Si Si-O-Si Si 63 O 1 (+Si 1 ) Si 64 O Si 64 O [3] Si-Si 2 Si 20
23 3.3 Si 2 SiO Si (c) ( 3.12(d)) ( 3.12(e)) : 2. a si.(b)si.(c).(d).(e). 21
24 3.4: 2 Si62+O2 energy Si-O-Si [Å] [ev] [Å] [deg] Si-O Si-Si Si-O 0.2Å Si-O-Si Si-Si Si Si 2 Si64 2 cutoff 520eV k 0.3/Å (a) (b) (c) [110],[001] Si Si Si Si Si 22
25 3.13: 2 Si-Si 3.14 a b, 3.6 Si 2 Si : 2,(a),(b)[110],(c)[001]. 23
26 3.15: Si. 3.5: Si 64 O 2 [Å] [deg] Si1-O1 Si3-O1 Si1-Si3 Si1-O1-Si eV Si 1 Si-Si 3.4 Si 4 3.2, eV, 2 3.0eV 4 24
27 3.6: Si 64 O 2 [Å] enegry a b c [Å 3 ] [ev] Si 4 5 Si 4 Si 64 4 cutoff 520eV k 0.3/Å 3.16: 25
28 a b [110] [001] c : Si 64 O 4 [Å] [deg] [Å] [Å 3 ] [ev] Si-O Si-Si Si-O-Si Si Si Si Si-Si Si Si Si Si cutoff 520eV k 0.3/Å 26
29 3.17: a [110] b [001] c 3.18: 1 (a) 4.(b)[110].(c)[110]. 27
30 a b c [001] [110] Si eV 3.19: 1 (a) 4.(b)[001].(c)[110] Si cutoff 520eV k 0.3/Å a b c [001] [110] Si 2 Si-Si Si-Si 28
31 3.20: 2 (a) 4.(b)[011].(c)[110] eV : 2 (a) 4 (b)[001].(c)[110]
32 3.22: 3.8: 4 Si 64 O 4 [Å] enegry a b c [Å 3 ] [ev] : 4 Si Si 64 O 4 [Å] Si1-O1 Si2-O2 Si3-O3 Si4-O : 4 Si Si 64 O 4 [deg] Si1-O1-Si5 Si2-O2-Si5 Si3-O3-Si5 Si4-O4-Si
33 3.5 SiO SiO 2 4 Si-O-Si 2 Si-O-Si 1 Si-O-Si 4 Si-O : BC-O Si-O Si-Si Si-O-Si [Å] [Å] [Å] [deg] Si 64 O , Si 64 O , , Si 64 O (a) 3.23(b)
34 3.23: (a) b 32
35 4 Si (O) Si-O Si-Si 2 Si Si Si diamond Si-O Si-Si Si Si-O 1 2 Si-Si 1 Si-Si 0.27Å 2 Si-Si 0.19Å 4 Si-Si 0.85Å SiO 2 33
36 34
37 [1] 2006 pp17-pp25 [2] ( 2002 [3] 1995 [4] Si SiO [5] Cz SiO Si SiGe 2008 [6] 2006 [7] VASP [8] 2003 pp187 [9] 1968 pp90 [10] P.Villars Pauling File User Manual (CRYSTAL IMPACT 2002) [11] VASP pp
SiC SiC QMAS(Quantum MAterials Simulator) VASP(Vienna Ab-initio Simulation Package) SiC 3C, 4H, 6H-SiC EV VASP VASP 3C, 4H, 6H-SiC (0001) (11 20) (1 1
QMAS SiC 7661 24 2 28 SiC SiC QMAS(Quantum MAterials Simulator) VASP(Vienna Ab-initio Simulation Package) SiC 3C, 4H, 6H-SiC EV VASP VASP 3C, 4H, 6H-SiC (0001) (11 20) (1 100) MedeA SiC QMAS - C Si (0001)
SiC Si Si Si 3 SiC Si SiC Metastable Solvent Epitaxy MSE MSE SiC MSE SiC SiC 3C,4H,6H-SiC 4H-SiC(11-20) 4H-SiC (0001) Si Si C 3 C 1
SiC 4718 20 2 21 SiC Si Si Si 3 SiC Si SiC Metastable Solvent Epitaxy MSE MSE SiC MSE SiC SiC 3C,4H,6H-SiC 4H-SiC(11-20) 4H-SiC (0001) Si Si C 3 C 1 1 4 1.1.................... 4 1.2 SiC........................
行列代数2010A
a ij i j 1) i +j i, j) ij ij 1 j a i1 a ij a i a 1 a j a ij 1) i +j 1,j 1,j +1 a i1,1 a i1,j 1 a i1,j +1 a i1, a i +1,1 a i +1.j 1 a i +1,j +1 a i +1, a 1 a,j 1 a,j +1 a, ij i j 1,j 1,j +1 ij 1) i +j a
( ) ( 40 )+( 60 ) Schrödinger 3. (a) (b) (c) yoshioka/education-09.html pdf 1
2009 1 ( ) ( 40 )+( 60 ) 1 1. 2. Schrödinger 3. (a) (b) (c) http://goofy.phys.nara-wu.ac.jp/ yoshioka/education-09.html pdf 1 1. ( photon) ν λ = c ν (c = 3.0 108 /m : ) ɛ = hν (1) p = hν/c = h/λ (2) h
4/15 No.
4/15 No. 1 4/15 No. 4/15 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = m ψ(r,t)+v(r)ψ(r,t) ψ(r,t) = ϕ(r)e iωt ψ(r,t) Wave function steady state m ϕ(r)+v(r)ϕ(r) = εϕ(r) Eigenvalue problem
V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H
199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n
003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........
* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *
* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *1 2004 1 1 ( ) ( ) 1.1 140 MeV 1.2 ( ) ( ) 1.3 2.6 10 8 s 7.6 10 17 s? Λ 2.5 10 10 s 6 10 24 s 1.4 ( m
2002.N.x.h.L.......g9/20
1 2 3 4 5 6 1 2 3 4 5 8 9 1 11 11 12 13 k 14 l 16 m 17 n 18 o 19 k 2 l 2 m 21 n 21 o 22 p 23 q 23 r 24 24 25 26 27 28 k 28 l 29 m 29 3 31 34 42 44 1, 8, 6, 4, 2, 1,2 1, 8 6 4 2 1, 8, 6, 4, 2, 1,2 1, 8
p = mv p x > h/4π λ = h p m v Ψ 2 Ψ
II p = mv p x > h/4π λ = h p m v Ψ 2 Ψ Ψ Ψ 2 0 x P'(x) m d 2 x = mω 2 x = kx = F(x) dt 2 x = cos(ωt + φ) mω 2 = k ω = m k v = dx = -ωsin(ωt + φ) dt = d 2 x dt 2 0 y v θ P(x,y) θ = ωt + φ ν = ω [Hz] 2π
PowerPoint プレゼンテーション
実空間差分法に基づく 第一原理電子構造 量子輸送特性計算 09/05/15 大阪大学大学院工学研究科小野倫也 Real-space first-principles calculation code The grand-state electronic structure is obtained by solving the Schrödinger (Kohn-Sham) equation 1 2
I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
No. 1261 2003. 4. 9 14 14 14 14 15 30 21 19 150 35 464 37 38 40 20 970 90 80 90 181130 a 151731 48 11 151731 42 44 47 63 12 a 151731 47 10 11 16 2001 11000 11 2002 10 151731 46 5810 2795195261998 151731
215 11 13 1 2 1.1....................... 2 1.2.................... 2 1.3..................... 2 1.4...................... 3 1.5............... 3 1.6........................... 4 1.7.................. 4
25 7 18 1 1 1.1 v.s............................. 1 1.1.1.................................. 1 1.1.2................................. 1 1.1.3.................................. 3 1.2................... 3
2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n
. X {x, x 2, x 3,... x n } X X {, 2, 3, 4, 5, 6} X x i P i. 0 P i 2. n P i = 3. P (i ω) = i ω P i P 3 {x, x 2, x 3,... x n } ω P i = 6 X f(x) f(x) X n n f(x i )P i n x n i P i X n 2 G(k) e ikx = (ik) n
1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r
![1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r](/thumbs/91/104998910.jpg "1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r")
11 March 2005 1 [ { } ] 3 1/3 2 + V ion (r) + V H (r) 3α 4π ρ σ(r) ϕ iσ (r) = ε iσ ϕ iσ (r) (1) KS Kohn-Sham [ 2 + V ion (r) + V H (r) + V σ xc(r) ] ϕ iσ (r) = ε iσ ϕ iσ (r) (2) 1 2 1 2 2 1 1 2 LDA Local
4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
RX501NC_LTE Mobile Router取説.indb
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 19 20 21 22 1 1 23 1 24 25 1 1 26 A 1 B C 27 D 1 E F 28 1 29 1 A A 30 31 2 A B C D E F 32 G 2 H A B C D 33 E 2 F 34 A B C D 2 E 35 2 A B C D 36
講 座 熱電研究のための第一原理計算入門 第1回 密度汎関数法による第一原理バンド計算 桂 1 はじめに ゆかり 東京大学 2 密度汎関数理論 第一原理 first-principles バンド計算とは 結晶構造 Schrödinger 方程式は 量子力学を司る基本方程式で 以外の経験的パラメータや
講 座 熱電研究のための第一原理計算入門 第1回 密度汎関数法による第一原理バンド計算 桂 1 はじめに ゆかり 東京大学 2 密度汎関数理論 第一原理 first-principles バンド計算とは 結晶構造 Schrödinger 方程式は 量子力学を司る基本方程式で 以外の経験的パラメータや任意パラメータを使わず 基 ある 定常状態において電子 i の状態を定義する波動 本的な物理方程式のみを用いて行う電子状態計算であ
Aharonov-Bohm(AB) S 0 1/ 2 1/ 2 S t = 1/ 2 1/2 1/2 1/, (12.1) 2 1/2 1/2 *1 AB ( ) 0 e iθ AB S AB = e iθ, AB 0 θ 2π ϕ = e ϕ (ϕ ) ϕ
1 13 6 8 3.6.3 - Aharonov-BohmAB) S 1/ 1/ S t = 1/ 1/ 1/ 1/, 1.1) 1/ 1/ *1 AB ) e iθ AB S AB = e iθ, AB θ π ϕ = e ϕ ϕ ) ϕ 1.) S S ) e iθ S w = e iθ 1.3) θ θ AB??) S t = 4 sin θ 1 + e iθ AB e iθ AB + e
[ ] Table
![[ ] Table](/thumbs/96/130290982.jpg "[ ] Table")
[] Te P AP OP [] OP c r de,,,, ' ' ' ' de,, c,, c, c ',, c mc ' ' m' c ' m m' OP OP p p p ( t p t p m ( m c e cd d e e c OP s( OP t( P s s t (, e e s t s 5 OP 5 5 s t t 5 OP ( 5 5 5 OAP ABP OBP ,, OP t(
26 2 3 4 5 8 9 6 7 2 3 4 5 2 6 7 3 8 9 3 0 4 2 4 3 4 4 5 6 5 7 6 2 2 A B C ABC 8 9 6 3 3 4 4 20 2 6 2 2 3 3 4 4 5 5 22 6 6 7 7 23 6 2 2 3 3 4 4 24 2 2 3 3 4 4 25 6 2 2 3 3 4 4 26 2 2 3 3 27 6 4 4 5 5
O157 6/23 7/4 6 25 1000 117,050 6 14:00~15:30 1 2 22 22 14:30~15:30 8 12 1 5 20 6 20 10 11 30 9 10 6 1 30 6 6 0 30 6 19 0 3 27 6 20 0 50 1 2 6 4 61 1 6 5 1 2 1 2 6 19 6 4 15 6 1 6 30 6 24 30 59
Gmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
日経テレコン料金表（2016年4月）
1 2 3 4 8,000 15,000 22,000 29,000 5 6 7 8 36,000 42,000 48,000 54,000 9 10 20 30 60,000 66,000 126,000 166,000 50 100 246,000 396,000 1 25 8,000 7,000 620 2150 6,000 4,000 51100 101200 3,000 1,000 201
73 p.1 22 16 2004p.152
1987 p.80 72 73 p.1 22 16 2004p.152 281895 1930 1931 12 28 1930 10 27 12 134 74 75 10 27 47.6 1910 1925 10 10 76 10 11 12 139 p.287 p.10 11 pp.3-4 1917 p.284 77 78 10 13 10 p.6 1936 79 15 15 30 80 pp.499-501
122011pp.139174 18501933
122011pp.139174 18501933 122011 1850 3 187912 3 1850 8 1933 84 4 1871 12 1879 5 2 1 9 15 1 1 5 3 3 3 6 19 9 9 6 28 7 7 4 1140 9 4 3 5750 58 4 3 1 57 2 122011 3 4 134,500,000 4,020,000 11,600,000 5 2 678.00m
29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23
29 2011 3 pp.55 86 19 1886 2 13 1 1 21 1888 1 13 2 3,500 3 5 5 50 4 1959 6 p.241 21 1 13 2 p.14 1988 p.2 21 1 15 29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 1
Microsoft Word - 映画『東京裁判』を観て.doc
1 2 3 4 5 6 7 1 2008. 2 2010, 3 2010. p.1 4 2008 p.202 5 2008. p.228 6 2011. 7 / 2008. pp.3-4 1 8 1 9 10 11 8 2008, p.7 9 2011. p.41 10.51 11 2009. p. 2 12 13 14 12 2008. p.4 13 2008, p.7-8 14 2008. p.126
() L () 20 1
() 25 1 10 1 0 0 0 1 2 3 4 5 6 2 3 4 9308510 4432193 L () 20 1 PP 200,000 P13P14 3 0123456 12345 1234561 2 4 5 6 25 1 10 7 1 8 10 / L 10 9 10 11 () ( ) TEL 23 12 7 38 13 14 15 16 17 18 L 19 20 1000123456
308 ( ) p.121
307 1944 1 1920 1995 2 3 4 5 308 ( ) p.121 309 10 12 310 6 7 ( ) ( ) ( ) 50 311 p.120 p.142 ( ) ( ) p.117 p.124 p.118 312 8 p.125 313 p.121 p.122 p.126 p.128 p.156 p.119 p.122 314 p.153 9 315 p.142 p.153
戦後の補欠選挙
1 2 11 3 4, 1968, p.429., pp.140-141. 76 2005.12 20 14 5 2110 25 6 22 7 25 8 4919 9 22 10 11 12 13 58154 14 15 1447 79 2042 21 79 2243 25100 113 2211 71 113 113 29 p.85 2005.12 77 16 29 12 10 10 17 18
2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3.
1 73 72 1 1844 11 9 1844 12 18 5 1916 1 11 72 1 73 2 1862 3 1870 2 1862 6 1873 1 3 4 3 4 7 2 3 4 5 3 5 4 2007 p. 117. 2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226.
1. 1.1....................... 1.2............................ 1.3.................... 1.4.................. 2. 2.1.................... 2.2..................... 2.3.................... 3. 3.1.....................