Si SiO 2. Si 1 VASP Si 1,, Si-Si 0.28Å Si Si-Si 0.19Å Si 166 Si Å Si
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- あやか おおばま
- 7 years ago
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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........................
QMI_10.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 σ τ x u u x t ux, t) u 3.1 t x P ux, t) Q θ P Q Δx x + Δx Q P ux + Δx, t) Q θ P u+δu x u x σ τ P x) Q x+δx) P Q x 3.1: θ P θ Q P Q equation of motion P τ Q τ σδx
QMI_09.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 3.1.2 σ τ 2 2 ux, t) = ux, t) 3.1) 2 x2 ux, t) σ τ 2 u/ 2 m p E E = p2 3.2) E ν ω E = hν = hω. 3.3) k p k = p h. 3.4) 26 3 hω = E = p2 = h2 k 2 ψkx ωt) ψ 3.5) h
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9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint (
9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)
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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
QMI13a.dvi
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18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
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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
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第8章 位相最適化問題
8 February 25, 2009 1 (topology optimizaiton problem) ( ) H 1 2 2.1 ( ) V S χ S : V {0, 1} S (characteristic function) (indicator function) 1 (x S ) χ S (x) = 0 (x S ) 2.1 ( ) Lipschitz D R d χ Ω (Ω D)
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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
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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
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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
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