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1 4 1.1 5 1.1.1 5 1.1. 5 1.1.3 5 1.1.4 CVD 7 1. 8 1..1 8 1.. SPE 10 1.3 11 1.1 13. 14..1 Tesoff 14.. Lennad-Jones 17.3 18.4 19.5 0.6 Langevn.7 3.7.1 SPE 3.7. 4.7.3 6 3 SPE 8 3.1 9 3. [111] SPE 9 3..1 000K 9 3.. 400K 33 3..3 600K 35 3..4 35 3.3 [001] SPE 39 3.3.1 000K 39
3 3.3. 41 3.3.3 43 3.4 46 4 47 4.1 48 4. 48 4.3 48 4.3.1 48 4.3. 51 4.4 54 4.5 55 5 56 5.1 57 5. 57 58 59 60 A Tesoff 61
1 4
5 1.1 1.1.1 1945 S 1.1. (1690K 1400 S 500 TFT Table 1-1 Slcon cystal and devces. CVD + CVD TFT (Slcon On Glass TFT 1.1.3 (a CZ (Fg. 1-1 300m
6 単結晶シリコン シードチャックシード結晶 シリコン融液 Fg. 1-1 Image of CZ Method. (b CVD (Chemcal Vapo Deposton SH 4 PVD (Physcal Vapo Deposton CVD CVD CVD TFT
7 成膜ガス ガスノズル 排気 ヒーター ウェーハ Fg. 1- Image of a CVD equpment. SH 4 SH + H SH SH SH S + H Fg. 1-3 Smplest example of eacton scheme of SH 4 CVD pocess. 1.1.4 CVD 0.1m (=100nm MOS 1 nm (=10 Å 3 4 CVD Cu CVD CVD CVD
8 1. 1..1 Stllnge-Webe Tesoff Tght-Bndng (a Stllnge-Webe Stllnge Webe [1] j> E = v (, j, k (1.1 (, j + v3 j> k > j v ( = ε f ( / σ v 3 (, j, k k = ε h, σ σ, θ k j jk + h, σ σ, θ jk k kj + h,, θ σ σ k (1.
9 p q 1 A( B + exp, ( < a f ( = a 0, ( a γ γ exp + g( θ, ( < a and (,, θ = k h k k a k a 0, ( a o k k < a a (1.3 1 g ( θ = λcos θ + (1.4 3,, θ k I j -j -k (1.4 (cosθ = -1/3 Gong (1.4 (1.5 S-W [] {( θ + C } 1 g Gong ( θ = λ1cosθ + cos + C 1 (1.5 3 (b Tesoff Tesoff [3] j { f ( + b f ( } 1 E s = f C ( R A (1.6 f R (f A (f C ( b Tesoff S-C S-Ge (1.6Petfo Tght-Bndng Tesoff..1
10 (c Tght-Bndng Tght-Bndng Hückel Self-Consstent ab-nto N O(NN Tght-Bndng 1.. SPE Tesoff [001] SPE (Sold Phase Eptaxy / (1600-000K (1450-1550K [4] (Fg. 1-4 Fg. 1-4 Ahenus plot of SPE gowth.
11 (a lowe tempeatue (001 (b hghe tempeatue (111 knk (001 Fg. 1-5 Rate lmtng steps of SPE gowth. (001 (Fg. 1-5 a(111 S (Fg. 1-5 b.6ev (0011.eV (111 S [001] (111 1.3 CVD S (111
1
13.1 E Newton E F = = m d d t (.1 Taylo Velet t Taylo ( t + t = ( t + tv ( t + ( t ( t t = ( t tv ( t + ( t ( t F m ( t F m (. ( t t + ( t t = ( t + ( t F ( t + (.3 m ( t t ( t t = t v ( t + (.4 t + t t v ( t t = ( t ( t t + ( t F ( t + (.5 m 1 t ( t = { ( t + t ( t t } (.6 Velet t ( t t = ( t + t v ( t + ( t F ( t + (.7 m t v + m ( t + t = v ( t + { F ( t + t F ( t } (.8 Velet (Velocty Velet
14. 1..1 Tesoff Lennad-Jones..1 Tesoff Tesoff E s j { a f ( + b f ( } 1 E s = f C ( R A (.9 f R (f A ( Mose f f R A ( = Aexp( λ ( = B exp( λ 1 (.10 f C ( 1, < R D 1 1 π f C ( = sn ( R / D, R D < < R + D (.11 0, > R + D f R (f A ( a b (Bond Ode a b ζ = 1 = = n n ( 1+ β ζ C k (, j c g( θ = 1+ d f ( k d 1/ n g( θ k c + ( h cosθ (.1 -j -k (Fg. -1θ k
15 S(CFg. -Fg. -3 k θ k j Fg. -1 Bond.envonment. Potental Enegy [ev] 4 0 θ = 45 θ = 90 θ = 180 θ = 135 body 1.5.5 3 Dstance [Å] Fg. - Bond-ode vaaton by θ k.
16 Potental Enegy (ev 1 =.4Å =.6Å =.Å 0 60 10 180 θ (degee Fg. -3 Potental enegy vs. θ. (a Tesoff Table -1S(C S(C S(B S(C S(B S(C 109.5 1700K Tesoff S(C 600K Table -1 Paametes of Tesoff potental model. S(B S(C S(B S(C A (ev 3.647 10 3 1.8308 10 3 c 4.8381 1.0039 10 5 B (ev 9.5373 10 1 4.7118 10 d.0417 1.617 10 1 λ 1 (Å -1 3.394.4799 h 0.0-5.985 10-1 λ (Å -1 1.358 1.73 R (Å 3.0.85 β 3.3675 10-1 1.1000 10-6 D (Å 0. 0.15 n.956 10 1 7.8734 10-1
17.. Lennad-Jones φ L J σ = 4ε 1 6 σ (.13 ε L-J σ = σ L-J = 0 Fg. -4 φ 0 σ 1/6 σ σ ε Fg. -4 Lennad-Jones potental. ε, σ.7. (a Fg. -5 l z dr R Fg. -5 L-J potental on nfnte wall.
18 ρ f ( F (z z F ( z = ρ f ( x + y + z = ρ π 0 0 = πρ = πρ 0 Rf z Rf lf ( R + z ( R + z ( l dl dθdr dr dxdy (.14 Lennad-Jones F (z F ( z = πρ f ( z = 8πρεσ d σ 11 1 z = 4πρεσ 5 σ z 10 σ 5 1 z σ d 4 (.15.3 1 t 1/ t t t t t = 0.4fs
19.4 10 3 Fg. -6 j' j ' Fg. -6 Peodc bounday condton. j lv j lv/ lv Fg. -6 j j j Tesoff lv
0.5 j Book Keepng Book Keepng N Book Keepng O(N Book Keepng Tesoff L Fg. -7 Doman dvson method. Fg. -7 L Book Keepng
1 6 O(N Book Keepng
.6 Langevn Langevn [5] Langevn Langevn m x = f σ = Potental αk T B π α = m ω 6 k Bθ ωd = t D S + f Contol Random ( σ α x (.16 f Potental f Random (σ m, α, T Contol, t s, ω D NVE α σ f Random 3 1 t S phonon T Contol T Contol θ [6] θ = 645K
3.7 [111][001] Sold Phase Eptaxy (SPE 1..[111][001].7.1 SPE Fg. -8 3456 13 atoms 6.75 7 50Å @000K (Peodc Bounday [111] amophous/cystal Inteface Tempeatue Contolled Laye Fxed Atoms: (111 suface Fg. -8 MD system fo SPE calculaton. [111] SPE 13 S a/c (111(001.6
4 (a 1.. Langevn 1ns 3000K 3. 50ps [111][001] 00K [111] 13 [001] 1176 (111 (001 Fg. -9 Intal condtons of SPE calculatons..7. SPE
5 Fg. -10 z 816 atoms Potental Enegy fom Wall 1D Potental Wall Tempeatue Contolled Regon Fxed Seed Atoms Fg. -10 MD system fo cystal nucleus gowth. 1 SO..[(.17] 10 4 1 z 1 z F ( z = 4πρεσ (.17 5 σ σ σ = 3.3Å 90 ρε = 0.0578 (J/m z = σ 0.14eV S-S 10 1 z = 4σ z < 4σ Langevn
6 (a Fg. -10 Fg. -11 1ns 816 atoms 816 atoms 100 m/s 1D Potental Wall Fxed Seed Atoms Fg. -11 Intal Condton fo nucle gowth calculatons..7.3 1. -4.5eV. 1. 4 Tesoff 1/
7 Fg. -1 1. seed Fg. -1 Vsualzaton of cystallzed atoms.
3SPE 8
9 3.1 [111][001] Sold Phase EptaxySPE; 3. [111] SPE [111] SPE 1800-600K 3..1 000K (a Snapshots 000KFg. 3-1Fg. 3-.7.3
Fg. 3-1 Snapshots of SPE [111] at 000K. 30
31 Fg. 3- Detal of [111] laye-by-laye gowth pocess. 1000ps a/c 1000-1400ps 1600-000ps, 3 Fg. 3- (b a/c Fg. 3-3 1.74m/s SPE 1cm/s 100 Tesoff S(C1700K
3 a/c Inteface Poston (Å 35 30 1.74 m/s a/c Inteface 5 0 15 10 Potental Enegy 4.1 4. 4.3 5 0 1000 000 3000 4000 Tme (ps Fg. 3-3 Tme pofle of a/c nteface poston and potental enegy at 000K. Potental Enegy (ev/atom (c 000K Fg. 3-4Tesoff [111] SPE
33 Stackng Faults Fg. 3-4 Stackng faults of [111] SPE gowth. 3.. 400K 400K Fg. 3-5, Fg. 3-6000K 3.57m/s
34 Fg. 3-5 Snapshots of SPE [111] at 400K. a/c Inteface Poston (Å 30 0 10 a/c Inteface 3.57 m/s Potental Enegy 4 4.1 4. Potental Enegy (ev/atom 0 500 1000 Tme (ps Fg. 3-6 Tme pofle of SPE gowth at 400K.
35 3..3 600K 600K Fg. 3-7, Fg. 3-8 Tesoff S(C Fg. 3-7 Snapshots of cystal-lqud equlbum. 35 a/c Inteface Poston (Å 30 5 0 15 10 a/c Inteface Potental Enegy 3.9 4 Potental Enegy (ev/atom 5 0 1000 000 3000 4000 Tme (ps Fg. 3-8 Tme pofle of nteface poston and potental enegy nea meltng pont. 3..4 1800K-500K a/c Fg. 3-9
36 35 1900 30 a/c Inteface Poston 5 0 15 000 1950 1800 10 5 0 10000 0000 Tme (ps 35 30 00 100 150 000 a/c Inteface Poston 5 0 15 050 10 a/c Inteface Poston 35 30 5 0 15 10 5 0 1000 000 400 Tme (ps 300 00 500 5 0 1000 000 Tme (ps Fg. 3-9 [111] SPE gowth at vaous tempeatue.
37 Fg. 3-10 Inteface Velocty (m/s 5 4 3 0.9 1 0.8 0.7 0.6 600 400 00 000 1800 Ea = 1.eV 0.4 0.45 0.5 0.55 1000/T (K 1 Fg. 3-10 Ahenus plot of cystal gowth speed. 1800-50K 500K k Ahenus k = Ea Aexp (3.1 k BT A E a T Ea log k = + C (3. k T B
38 Fg. 3-1050K 1.eV [001] 1.. Fg. 3-1.eV (111 a/c S
39 3.3 [001] SPE [001] 3.3.1 000K 000K Fg. 3-11, Fg. 3-1 Fg. 3-11 Snapshots of [001] SPE gowth at 000K.
40 Fg. 3-1 Detal of [001] SPE gowth. [111] SPE (111 laye-by-laye [001] 3 (111 (Fg. 3-1(111(001(111 S (001 (001(111 Fg. 3-13[111]
41 35 4 30 1.60 m/s a/c Inteface Poston (Å 5 0 15 10 a/c Inteface Potental Enegy 4.1 4. Potental Enegy (ev/atom 5 0 1000 000 3000 4000 Tme (ps Fg. 3-13 Tme pofle of [001] SPE gowth at 000K. 3.3. 100K (Fg. 3-14 Fg. 3-14 Plane defects of cystal.
4 Fg. 3-15 Snapshots of defect ntoducton pocess. (111Fg. 3-14 V 1800K Fg. 3-15(111 3..1(c 1900K Fg. 3-16
43 Fg. 3-16 Dffeence of cystal oentaton. 3..1(c 3.3.3 1800-500K a/c Fg. 3-17[111] Aehnus Plot Fg. 3-18[111] [001] [111][001]
44 35 000 30 a/c Inteface Poston 5 0 15 100 1950 1900 1800 10 5 0 000 4000 6000 8000 35 Tme (ps a/c Inteface Poston 30 5 0 15 400 300 00 500 10 5 0 500 1000 1500 Tme (ps Fg. 3-17 [001] SPE gowth at vaous tempeatue.
45 Inteface Velocty (m/s 600 400 00 000 1800 5 4 Ea[111] = 1.eV 3 0.9 1 0.8 0.7 0.6 0.5 0.4 0.3 Ea[001] = 1.34eV 0.4 0.45 0.5 0.55 1000/T (K 1 Fg. 3-18 Ahehnus plot of SPE gowth velocty.
46 3.4 [111][001] [001](111 [111] laye-by-laye (as-gown defects [111][001](111 Tesoff (111 a/c 1.eV
47 4
48 4.1 000K 4. Fg. 4-1 (111 oented A13 A16 A4 (001 oented B15 B8 Fg. 4-1 Sets of seed atoms fo cystal nucleaton. (111(001 5 4.3 Table 4-1(111 A 16 (001 B 8 Table 4-1 Smulaton esults of cystal nucleaton. A13 A16 A4 B15 B8 4.3.1 A16, A4, B8
49 (a A16 11ns 50 Fg. 4-5.5ns 6ns 6.6ns 15 51 11 11.5ns 1ns 17.9ns 56 95 08 Fg. 4- Snapshots of A16. (b A4 Fg. 4-4(111 (001[111] (001(111 [111]
50 Fg. 4-3 Snapshots of A4 3.ns 3.9ns 4.ns 5.ns Fg. 4-4 Gowth decton. (c B8 8ns
51 Fg. 4-5 Snapshots of B8 4.3. (a A13 300 3.7 Cystal Nucleus Sze (numbe of atoms 00 100 Potental Enegy Nucleus Sze 3.8 3.9 Potental Enegy (ev/atom 0 0 4000 8000 1000 Tme (ps 4 Fg. 4-6 Tme pofle of A13.
5 (b A16 300 3.7 Cystal Nucleus Sze (numbe of atoms 00 100 Potental Enegy Nucleus Sze 3.8 3.9 Potental Enegy (ev/atom 0 0 4000 8000 1000 Tme (ps 4 Fg. 4-7 Tme pofle of A16. (c A4 300 3.7 Cystal Nucleus Sze (numbe of atoms 00 100 Nucleus Sze Potental Enegy 3.8 3.9 Potental Enegy (ev/atom 0 0 4000 8000 1000 Tme (ps 4 Fg. 4-8 Tme pofle of A4.
53 (d B15 300 3.7 Cystal Nucleus Sze (numbe of atoms 00 100 Potental Enegy Nucleus Sze 3.8 3.9 Potental Enegy (ev/atom 0 0 4000 8000 1000 Tme (ps 4 Fg. 4-9 Tme pofle of B15 (e B8 300 3.7 Cystal Nucleus Sze (numbe of atoms 00 100 Potental Enegy Nucleus Sze 3.8 3.9 Potental Enegy (ev/atom 0 0 4000 8000 1000 Tme (ps 4 Fg. 4-10 Tme pofle of B8.
54 4.4 4.3. Fg. 4-11 110 Fg. 4-11 Fg. 4-11 110 A13 B15 110 Cystal Nucleus Sze (numbe of atoms 300 00 100 Ctcal Sze A4 B8 0 0 4000 8000 1000 Tme (ps Fg. 4-11 Ctcal sze of cystal nucle. A16 A13 B15
55 4.5 (111(001 [111](001(111(111 (111 (001 a/c (111 110
5 56
57 5.1 Tesoff S(C [111] (001 (111[001] SPE (111 [111], [001] 110 5. SPE SPE
58
59 [1] Stllnge, F. & Webe, T., Compute smulaton of local ode n condensed phase of slcon, Phys. Rev. B, 31-8, p. 56, 1985. [] Gong, G., Empcal-potental studes on the stuctual popetes of small slcon clustes, Phys. Rev. B, 47-4, p. 39, 1993. [3] Tesoff, J., Empcal nteatomc potental fo slcon wth mpoved popetes, Phys. Rev. B, 38-14, p. 990, 1988. [4] Motooka, T., at al., Molecula-dynamcs smulatons of sold-phase eptaxy of S: Gowth mechansms, Phys. Rev. B, 61-1, p. 8537, 000. [5] Blöme, J. & Beylch, A., Suface Scence, 43, p. 17., 1999 [6],, p. 139
60
61 A Tesoff j { f ( + b f ( } 1 E s = fc ( R A (A.1 f f R A ( = Aexp( λ ( = Bexp( λ 1 (A. 1, < R D 1 1 π f C ( = sn ( R / D, R D < < R + D (A.3 0, > R + D b ζ = = n n ( 1+ β ζ C k (, j c g( θ = 1+ d f ( k d 1/ n g( θ k c + ( h cosθ (A.4 (1 -j -k k Fg. A-1 -j -k k k θ k j m Fg. A-1 -j
6 E b * b ζ = f b = = = C b + b ( f R ( + + b n n ( 1+ β ζ f j C m(, j ( m 1/ n g( θ m j f A ( = f C ( f R ( + b * f C ( f A ( (A.5 (A.5 F F F j k E = E = E = j k = = = f C d d d d ( * d ( f ( f ( b ( f ( f ( C * d ( f ( f ( b ( f ( f ( C f A ( R R k b * d d C C A A j f f C C ( ( f f A A ( ( b (A.6 j b * * F, F j -j -j k k n b * 1 b = n b + j n ( n =, j, k (A.7 k b n b j n jm b b j b k 1 = n 1 = n 1 = n n n n n ( 1 1 1 + β ζ n ( 1 + β ζ 1 n n 1 n n ( 1 + β ζ n ( 1 + β ζ 1 n n 1 n n ( 1 + β ζ n ( 1 + β ζ j k (A.8
63 ( ( ( k n n n n k j n n n n j n n n n n n n ζ ζ β = ζ + β ζ ζ β = ζ + β ζ ζ β = ζ + β 1 1 1 1 1 1 (A.9 = θ = θ = ζ, (, (,, ( ( ( ( ( j m m m C n j m m m C n n k j n g f g f (A.10 k ( ( k k C n g f θ ( ( ( k m g f m m C n θ m ( ( k k C k g f θ ζ k k C k k k k C k k j k C j k k C k k k k C k d dg f d df g d dg f d dg f d df g θ θ θ + θ = ζ θ θ θ = ζ θ θ θ + θ = ζ cos (cos ( ( ( ( cos (cos ( ( cos (cos ( ( ( ( (A.11 + θ = θ + θ = θ + θ + + θ = θ k k k k k k k k j k k k k j k k 1 cos cos 1 cos cos 1 cos 1 cos cos (A.1
64 dg( θ = d(cosθ c (cosθ h { d + ( h cosθ } (A.13
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