2 464-8602 1 2 2 2 N ΔμN ( N 2/3 ) N - (seed) (nucleation) 1.4 2 2.1 1 Makio Uwaha. E-mail:uwaha@nagoya-u.jp; http://slab.phys.nagoya-u.ac.jp/uwaha/ 2 [1] [2] [3](e) 3
2.1: [1] 2.1 ( ) 1 (cluster) ( N S ) 2 ( ) 2.1(a) e δg/kbt 2.1(b) 1 N S N S (thermodynamical critical nucleus) 1. δn S δg < 0 2.
3. N S α R δg(r) = 4π 3 R3 n S Δμ +4πR 2 α (2.1) n S =1/v S Δμ = μ L (T L,P L ) μ S (T L,P L ) (2.2) L T L P L ( ) ((1.5) ) μ S (T L,P L ) μ S (T L,P S ) μ L (T L,P L )=μ S (T L,P S ) P S P L R c δg (2.1) R R c = 2α (2.3) n S Δμ δg c δg(r c ) = 16π 3 = 4π 3 R2 cα α 3 n 2 S (Δμ)2 = 2π 3 R3 cn S Δμ (2.4) 2 δg c 1/3 3 Δμ 1/2 2.2
2.2: ( ) ( ) ( ) (a) (b) (c) [2] N 2.2 Δμ <0 2.2(a) (1.27) (2.1) Δμ eff = (δg) N S =Δμ 2α Rn S (2.5) N S =(4π/3)R 3 n S (4πR 2 )/ N S =2/Rn S Δμ <0 Δμ eff Δμ =0 2.2(b) Δμ >0 2.2(c) N c
(a) (b) 2.3: (a) (b) N 2.2(a) N n N (t) ( 2.2(a)) N =1 ( monomer) N : n N (t) t = n 1 (t)n N 1 (t)σ N 1 n 1 (t)n N (t)σ N +n N+1 (t)λ N+1 n N (t)λ N. (2.6) σ N N N =1 λ N N (Becker-Döring theory) ( 2.3) ( ) λ N N n N (t) = j N 1 (t) j N (t), t (2.7) j N (t) =n 1 (t)n N (t)σ N n N+1 (t)λ N+1 (2.8)
2.4: 4 Nn N (t) [4] ( 2.3(b)) j N (t) N N +1 (2.8) N 1 (2.6) (2.7) N 2 n 1 (t) t = f 2n 2 1 (t)σ 1 n 1 (t) n N (t)σ N +2n 2 (t)λ 2 + N=2 N=3 n N (t)λ N (2.9) f 2 f =0 ( [2] ) 1. N c 2. n 1 j st n 1 σ Nc n 1 e δg Nc /k BT (2.10) n 1 n 1 e δg Nc /k BT n 1 2.4 4 Nn N (t)
2.5: 50 Nn N (t) [4] Nn N (t) ( 2.5) 50 1 N c (t) N c (t) (Ostwald ripening) n N (t) = N c(0) N 2 c (t) ν(n/n c(t)), (2.11) ν(x) ( ) - - (2.3) 2 (1.29) R 2c = Ω 2β (2.12) Δμ ( )Δμ R c t 1/2 R c t 1/3
2.3 2 MBE 2 MBE (molecular beam epitaxy: MBE) ( ) 2 2 MBE N c =1 N c ( 2,3 ) n 1 (t) N c 2 (stable island) n si (t) = N=N c+1 n N (t) (2.13) N c =1 N 2 (2.6) (2.9) n 1 (t) t n si (t) t = f 2D s σ 1 n 2 1 (t) D sσ(t)n 1 (t)n si (t), (2.14) = D s σ 1 n 2 1(t), (2.15) 1 2 N =2 3 D s σ N σ N (capture number) σ(t) σ(t) = 1 n si (t) N=N c+1 σ N n N (t) (2.16)
(2.14) (2.15) n 1 (t) n si (t) (2.16) ( [5]) 2 n 1 (t) ft Ω 2 1 Θ(t) =Ω 2 N=1 Nn N (t) =Ω 2 ft (2.17) 2 (2.14) 2 3 (2.15) n si (t) 1 3 D sσ 1 f 2 t 3 D s Ω 3 2 f σ 1Θ 3 (2.18) 3 (2.14) 2 3 n 1 (t)/ t 0 n si (t) 2 n 1 (t) f D s σ(t)n si (t) (2.19) (2.15) σ(t) n si (t) ( ) f 2/3 (3D s σ 1 t) 1/3 D s σ 1 σ 1/3 ( ) 1 Ω 2 1/3 2 f Ω 2 σ 2/3 Θ 1/3. (2.20) D s 1/3 (f/d s ) 1/3
2.6: 2.4 (homogeneous necleation) (heterogeneous necleation) (epitaxial growth) 2.6 θ α gw = α lw + α lg cos θ (2.21) ( gass wall liquid ) θ α gw α lw α lg cos θ = α gw α lw s (2.22) α lg (wetting) 1. α lw >α gw + α lg : ( 2.6(a)) 2. α lg <α gw α lw <α lg : (2.3) n S n L
2.7: [2] (a) (d) α lw θ ( 2.6(b)) 3. α gw >α lw + α lg : θ =0 δg c =0 ( 2.6(c)) α lw α gw α lw <α gw α gw <α lw ( 2.7) ( ) (a) 1 2 ( 2.6 (c) ) (d) ( 2.6 (a) ) (b) (c) ( 2.6 (b) )
(W) (S) α SW α SW α W α SW α W α(001) <α SW α W α(001) >α SW α W α(ˆn) α S δg c = 1 2 ΔμN c. (2.23) [2] δg c δg c 2.7 (a) (b) (c) (d) [1], 2 ( 2002). [2], 2 ( 2008). [3] : (a), (,, 1984) (b), ( 2002) (c), ( 2003) (d) 7 ( 2002) (e), ( 1997). [4] (2007 1 ) [5] T. Michely and J. Krug, Islands, Mounds, and Atoms: Patterns and Processes in Crystal Growth Far from Equilibrium, (Springer, Berlin, 2004).