シリコン結晶化過程の分子動力学

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2 CVD SPE Tesoff 14.. Lennad-Jones Langevn SPE SPE [111] SPE K K K [001] SPE K 39

3 A Tesoff 61

4 1 4

5 S 1.1. (1690K 1400 S 500 TFT Table 1-1 Slcon cystal and devces. CVD + CVD TFT (Slcon On Glass TFT (a CZ (Fg m

6 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 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 CVD 0.1m (=100nm MOS 1 nm (=10 Å 3 4 CVD Cu CVD CVD CVD

8 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 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 10 (c Tght-Bndng Tght-Bndng Hückel Self-Consstent ab-nto N O(NN Tght-Bndng 1.. SPE Tesoff [001] SPE (Sold Phase Eptaxy / ( K ( K [4] (Fg. 1-4 Fg. 1-4 Ahenus plot of SPE gowth.

11 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] ( CVD S (111

12 1

13 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 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 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 Dstance [Å] Fg. - Bond-ode vaaton by θ k.

16 16 Potental Enegy (ev 1 =.4Å =.6Å =.Å θ (degee Fg. -3 Potental enegy vs. θ. (a Tesoff Table -1S(C S(C S(B S(C S(B S(C K Tesoff S(C 600K Table -1 Paametes of Tesoff potental model. S(B S(C S(B S(C A (ev c B (ev d λ 1 (Å h λ (Å R (Å β D (Å n

17 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 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 ( t 1/ t t t t t = 0.4fs

19 Fg. -6 j' j ' Fg. -6 Peodc bounday condton. j lv j lv/ lv Fg. -6 j j j Tesoff lv

20 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

21 1 6 O(N Book Keepng

22 .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

23 3.7 [111][001] Sold Phase Eptaxy (SPE 1..[111][001].7.1 SPE Fg atoms (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

24 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

25 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] z 1 z F ( z = 4πρεσ (.17 5 σ σ σ = 3.3Å 90 ρε = (J/m z = σ 0.14eV S-S 10 1 z = 4σ z < 4σ Langevn

26 6 (a Fg. -10 Fg ns 816 atoms 816 atoms 100 m/s 1D Potental Wall Fxed Seed Atoms Fg. -11 Intal Condton fo nucle gowth calculatons eV Tesoff 1/

27 7 Fg seed Fg. -1 Vsualzaton of cystallzed atoms.

28 3SPE 8

29 9 3.1 [111][001] Sold Phase EptaxySPE; 3. [111] SPE [111] SPE K K (a Snapshots 000KFg. 3-1Fg

30 Fg. 3-1 Snapshots of SPE [111] at 000K. 30

31 31 Fg. 3- Detal of [111] laye-by-laye gowth pocess. 1000ps a/c ps ps, 3 Fg. 3- (b a/c Fg m/s SPE 1cm/s 100 Tesoff S(C1700K

32 3 a/c Inteface Poston (Å m/s a/c Inteface Potental Enegy 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 33 Stackng Faults Fg. 3-4 Stackng faults of [111] SPE gowth K 400K Fg. 3-5, Fg K 3.57m/s

34 34 Fg. 3-5 Snapshots of SPE [111] at 400K. a/c Inteface Poston (Å a/c Inteface 3.57 m/s Potental Enegy Potental Enegy (ev/atom Tme (ps Fg. 3-6 Tme pofle of SPE gowth at 400K.

35 K 600K Fg. 3-7, Fg. 3-8 Tesoff S(C Fg. 3-7 Snapshots of cystal-lqud equlbum. 35 a/c Inteface Poston (Å a/c Inteface Potental Enegy Potental Enegy (ev/atom Tme (ps Fg. 3-8 Tme pofle of nteface poston and potental enegy nea meltng pont K-500K a/c Fg. 3-9

36 a/c Inteface Poston Tme (ps a/c Inteface Poston a/c Inteface Poston Tme (ps Tme (ps Fg. 3-9 [111] SPE gowth at vaous tempeatue.

37 37 Fg Inteface Velocty (m/s Ea = 1.eV /T (K 1 Fg Ahenus plot of cystal gowth speed K 500K k Ahenus k = Ea Aexp (3.1 k BT A E a T Ea log k = + C (3. k T B

38 38 Fg K 1.eV [001] 1.. Fg. 3-1.eV (111 a/c S

39 [001] SPE [001] K 000K Fg. 3-11, Fg. 3-1 Fg Snapshots of [001] SPE gowth at 000K.

40 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 m/s a/c Inteface Poston (Å a/c Inteface Potental Enegy Potental Enegy (ev/atom Tme (ps Fg Tme pofle of [001] SPE gowth at 000K K (Fg Fg Plane defects of cystal.

42 4 Fg Snapshots of defect ntoducton pocess. (111Fg V 1800K Fg. 3-15( (c 1900K Fg. 3-16

43 43 Fg Dffeence of cystal oentaton. 3..1(c K a/c Fg. 3-17[111] Aehnus Plot Fg. 3-18[111] [001] [111][001]

44 a/c Inteface Poston Tme (ps a/c Inteface Poston Tme (ps Fg [001] SPE gowth at vaous tempeatue.

45 45 Inteface Velocty (m/s Ea[111] = 1.eV Ea[001] = 1.34eV /T (K 1 Fg Ahehnus plot of SPE gowth velocty.

46 [111][001] [001](111 [111] laye-by-laye (as-gown defects [111][001](111 Tesoff (111 a/c 1.eV

47 47 4

48 K 4. Fg. 4-1 (111 oented A13 A16 A4 (001 oented B15 B8 Fg. 4-1 Sets of seed atoms fo cystal nucleaton. (111( Table 4-1(111 A 16 (001 B 8 Table 4-1 Smulaton esults of cystal nucleaton. A13 A16 A4 B15 B A16, A4, B8

49 49 (a A16 11ns 50 Fg ns 6ns 6.6ns ns 1ns 17.9ns Fg. 4- Snapshots of A16. (b A4 Fg. 4-4(111 (001[111] (001(111 [111]

50 50 Fg. 4-3 Snapshots of A4 3.ns 3.9ns 4.ns 5.ns Fg. 4-4 Gowth decton. (c B8 8ns

51 51 Fg. 4-5 Snapshots of B (a A Cystal Nucleus Sze (numbe of atoms Potental Enegy Nucleus Sze Potental Enegy (ev/atom Tme (ps 4 Fg. 4-6 Tme pofle of A13.

52 5 (b A Cystal Nucleus Sze (numbe of atoms Potental Enegy Nucleus Sze Potental Enegy (ev/atom Tme (ps 4 Fg. 4-7 Tme pofle of A16. (c A Cystal Nucleus Sze (numbe of atoms Nucleus Sze Potental Enegy Potental Enegy (ev/atom Tme (ps 4 Fg. 4-8 Tme pofle of A4.

53 53 (d B Cystal Nucleus Sze (numbe of atoms Potental Enegy Nucleus Sze Potental Enegy (ev/atom Tme (ps 4 Fg. 4-9 Tme pofle of B15 (e B Cystal Nucleus Sze (numbe of atoms Potental Enegy Nucleus Sze Potental Enegy (ev/atom Tme (ps 4 Fg Tme pofle of B8.

54 Fg Fg Fg A13 B Cystal Nucleus Sze (numbe of atoms Ctcal Sze A4 B Tme (ps Fg Ctcal sze of cystal nucle. A16 A13 B15

55 (111(001 [111](001(111(111 (111 (001 a/c (

56 5 56

57 Tesoff S(C [111] (001 (111[001] SPE (111 [111], [001] SPE SPE

58 58

59 59 [1] Stllnge, F. & Webe, T., Compute smulaton of local ode n condensed phase of slcon, Phys. Rev. B, 31-8, p. 56, [] Gong, G., Empcal-potental studes on the stuctual popetes of small slcon clustes, Phys. Rev. B, 47-4, p. 39, [3] Tesoff, J., Empcal nteatomc potental fo slcon wth mpoved popetes, Phys. Rev. B, 38-14, p. 990, [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 60

61 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

62 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 ( 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 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 (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 64 dg( θ = d(cosθ c (cosθ h { d + ( h cosθ } (A.13

65

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