4 464-8602 1 [1] 2 (STM: scanning tunneling microscope) (AFM: atomic force microscope) 1 ( ) 4 LPE(liquid phase epitaxy) 4.1 - - - - (Burton Cabrera Frank) BCF [2] P f = (4.1) 2πmkB T 1 Makio Uwaha. E-mail:uwaha@nagoya-u.jp; http://slab.phys.nagoya-u.ac.jp/uwaha/ 2 [3] 1
(P m ) (1.3 1.7) ( ) c(x, y) ( )f τ( E b τ exp (E b /k B T )) c t = D s 2 c c τ + f (4.2) (4.2) c = fτ( c ) v st (1.8) Δμ =(k B T/c 0 eq)(c c 0 eq) ( c 0 eq ) (1.26) (1.27) v st = K st k B T c 0 eq ( c c 0 eq Ω 2c 0 eq β k B TR ) ( =Ω 2 K st c c 0 eq Γ ) R (4.3) (Γ = Ω 2 c 0 β/(k eq B T )) Ω 2 1 R (κ =1/R) - V/Δμ j c K K st =(k B T/Ω 2 c 0 eq)k st (4.2) (4.3) l [3] c c 0 eq v st =Ω 2 Kst 1 + [(2D s /x s ) tanh (l/2x s )] 1 (4.4) ( c eq c s 4.1 ) x s D s τ τ. (c c 0 eq) Kst 1 [(2D s /x s ) tanh (l/2x s )] 1 j l V = v st (a/l) K st l<x s (4.4) Ω 2 (c c 0 eq)(2d s /x s )(l/2x s )=Ω 2 τ(f f eq )(l/τ) 2
4.1: BCF [5] V Ω 2 a(f f eq )=v S (f f eq ) ( f eq = c 0 eq/τ) (4.3) ( ) ( ) v =Ω 2 K c c 0 eq Γκ +Ω 2 K + c + c 0 eq Γκ (4.5) 1 2 (c ± ) K < K + (ES ) 4.4 4.2 T R 3
4.2: [3] (1.25) ξ ( 4.2) R τ dr dt K stω 2 β R (4.6) τ R 2 / βk st t R ( βk st t) 1/2 4.3 n (4.3) R 2c =Γ/(c c 0 eq ) 4
J i J i 1 c i (r) ci 1 (r) R N R i+1 R i R i 1 R 1 c 0 (r) 4.3: R n <R 2c R 2c τ R2 2c (4.7) K st Ω 2 β 2 R f R 0 1 a z ( R f 10 Ω2 2 c0 β ) 1/5 eq k B T D sa z R 0 t (4.8) [3] t 1/5 STM [4] 4.4(a) (111) STM 4.4(b) (c) 5
(a) (b) (c) 4.4: (a) STM (b) (c) ( [4] ) 4.3 - - (MS Mullins-Sekerka instability) ( 4.5(a)) ( 4.5(b)) 4.5(c) (b) (c) 6
4.5: [5] ( ) - λ λ D 3 d c λ λ D d c (4.9) λ 3 d c =(c 0 eq/k BT )v 2 S α (v S 1 ) - (c 0 eq/k BT )v S α/r c S =1/v S R 7
4.6: ES [6] 4.4 MS 2 ( ) MS (Bales-Zangwill instability) 4.6 τ x s ( ) x s ( x s ) ( ) ( 4.6(a)) ( 4.6(b)) 8
( ) y st (x, t) =vst 0 t q y st (x, t) =y st0 (t)+δy st (x, t) =v 0 st t + δy stq e iqx+ωqt, ω q ( 1.7 ) c(x, y, t) = c 0 (y, t)+δc(x, y, t) = c +(c 0 eq c )e (y v0 st t)/xs + δc q e iqx Λq(y v0 st t)+ωqt (4.10). ES c 0 (y, t) 2 2 y Λ q q 2 + x 2 s x q (4.2) ω q ω q = v 0 st(λ q x 1 s ) D s Ω 2 ΓΛ q q 2 (4.11) q ω q ( 1 2 v0 stx s D ) ( sω 2 Γ 1 q 2 x s 8 v0 stx 3 s + 1 ) 2 D sω 2 Γx st q 4 (4.12) 1 vst 0 2D s Ω 2 Γ/x 2 s (4.4) K st l vst 0 =Ω 2τ(f f eq )D s /x s f c ( f f c f eq 1+ 2 βω ) 2 (4.13) x s k B T (4.11) x s Λ q q ω q = v 0 st q D sω 2 Γq 3 (4.14) (4.14) vst 0 q max = 3D s Ω 2 Γ (4.15) 9
4.7: ES [6] Ω 2 Γ l D = D s /vst 0 (4.9) Si(111) 860 C Si(111) 1 1 7 7 7 7 4 1 1 ES [7] Si(111) [8] [9] 4.5 (x ) (y ) (step bunching) 4 1 1 7 7 7 7 10
4.8: ES 1 [10] ( ) ( ) (a) (b) 4.7 (K + > K ) ( ) ( 4.7(a)) ( ) ( 4.7(b)) n l k δy k y n (t) =vn(t)+δy 0 n (t) =vstt 0 + nl + δy k e ω kt+iknl (4.16) ω k (kl 1) 11
(a) t 1000 800 600 400 200 0 0 10 20 30 y (b) t 200 150 100 50 0 0 10 20 30 y 4.9: 1 [11] ( π 2 ω k 2l + 1 ) d d + v 0 2 d + + d stl k 2 π 2 x s 2(d + + d ) k4 + ivst [1 0 1 ] 6 (kl)2 k (4.17) d ± = D s /K ± (4.17) ω k vst 0 ( vst 0 < 0 ) k2 vst 0 ω k > 0 4.8 [9] 5 5 12
4 8 ( 4.9(a)) 1/2 4.8 4.9(a) ( 4.9(b)) [1] Crystal Letters No.40 (2009) 3; No.41 (2009) 3; No.42 (2009) 7. [2] W. K. Burton, N. Cabrera, and F. C. Frank, Phil. Trans. Roy. Soc. London 234A (1951) 299. [3], 2 ( 2008). [4] K. Thürmer, J. E. Reutt-Robey, E. D. Williams, M. Uwaha, A. Emundts and H. P. Bonzel, Phys. Rev. Lett. 87 (2001) 186102. [5], 2 ( 2002). [6], 3 ( 1997). [7] R. Kato, M. Uwaha, Y. Saito and H. Hibino, Surf. Sci. 522 (2003) 64. [8] M. Sato and M. Uwaha, J. Phys. Soc. Jpn. 65 (1996) 2146. [9] K. Yagi, H. Minoda and M. Degawa, Surf. Sci. Rep. 43 (2001) 45. [10] M. Sato and M. Uwaha, Phys. Rev. B 51 (1995) 11172. [11] M. Sato and M. Uwaha, Surf. Sci., 442 (1999) 318. 13