1. Multi-Site-Correlated Surface Growths with Restricted Solid-on-Solid Condition
Yup Kim, T. S. Kim(Kyung Hee University) and Hyunggyu Park(Inha University)

2. 1
 Abstract
Provided that the heights of randomly chosen k columns are all equal in a surface growth model, then the simultaneous deposition processes are attempted with a probability p and the simultaneous evaporation processes are attempted with the probability q=1-p. The whole growth processes are discarded if any process violates the restricted solid-on-solid (RSOS) condition. If the heights of the chosen k columns are not all equal, then the chosen columns are given up and a new selection of k columns is taken. The recently suggested dissociative k -mer growth is in a sense a special case of the present model.
In the k-mer growth the choice of k columns is constrained to the case of the consecutive k columns. The dynamical scaling properties of the models are investigated by simulations and compared to those of the k-mer growth models. We also discuss the ergodicty problems when we consider the relation of present models and k-mer growth models to the random walks with the global constraints.

3. 2.Model  The growth rule for the -site correlated growth
 P : probability of deposition
 q = 1-p : probability of evaporation
 The growth rule for the -site correlated growth
<1> Select columns { } (  2) randomly.
<2-a> If
then for =1,2..., with a probability p.
for =1,2..., with q =1-p.
With restricted solid-on-solid(RSOS)condition,
<2-b>
then new selection of columns is taken.
 The dissociative -mer growth
▶ A special case of the -site correlated growth.
Select consecutive columns

4.  An arbitrary combination of (2, 3, 4) sites of the same height
Model (k-site)
 The models with extended ergodicity
 An arbitrary combination of (2, 3, 4) sites of the same height q p p q p q
 Nonlocal topological constraint :
All height levels must be occupied by an (2,3,4)-multiple number of sites.
Mod (2,3,4) conservation of site number at each height level.
Dynamical Scaling Law for Kinetic Surface Roughening

5.  Physical Backgrounds for This Study4
 Physical Backgrounds for This Study
Steady state or Saturation regime,
1. Simple RSOS with
Normal Random Walk(1d)
 =-1, nh=even number,
Even-Visiting Random Walk (1d)

6. - mer 3. Simulation results - site (1) 1-dimension ; eff ( )5
3. Simulation results
(1) 1-dimension ; eff ( )
(i) p = q = 1/2
- site
a  1 / 3
( L→ ∞ )
- mer
a  1 / 3
( L→ ∞ )

7. - mer - site (ii) P =0.6 (p > q) & P =0.1 (p < q)
▶ p (growing phase), q (eroding phase)
a  1
( L→ ∞ )
- site
a  1
( L→ ∞ )
- mer

8. Surface Morphology of k-site growth model7
Surface Morphology of k-site growth model
P = 0.6 (p > q) & P = 0.1 (p < q)
Groove formation (relatively Yup-Kim and Jin Min Kim, PRE. (1997))

9. Surface Morphology of k-mer growth model8
Surface Morphology of k-mer growth model
P = 0.6 (p > q) & P = 0.1 (p < q)
Facet structure (J. D. Noh, H. Park, Doochul Kim and M. den Nijs, PRE. (2001))

10. - mer 0.097 4-site 0.14 3-site 0.193 2-site model 0.098 4-mer 0.10
(i) p = q =1/2
eff ( )
- site
0.097
4-site
0.14
3-site
0.193
2-site
model 
- mer
0.098
4-mer
0.10
Trimer
0.108
Dimer
model 

11. - mer 0.214 4-site 0.325 3-site 0.46 2-site model - site 10
(ii) P = 0.6 (p > q)
- site
0.214
4-site
0.325
3-site
0.46
2-site
model 
Groove phase
- mer
Sharp facet

12. Slope a  a values 2-dimension Model N. RSOS 0.174 p = 0.5 0.17411
2-dimension
( )
 a values
Model
Slope a
N. RSOS
0.174
p = 0.5
0.174
Dimer growth
0.16
Two-site growth
0.174

13. 4. Conclusion L   , Ergodicity problem eff eff12
4. Conclusion
L   ,
1. p = q = 1/2
 1/3 ( k-site, 3,4-mer)
? 1/3 (Dimer growth model)
Ergodicity problem
2. p ≠ q
 1 k-mer (faceted)
(J. D. Noh, H. Park, Doochul Kim and M. den Nijs, PRE. (2001))
 1 k-site (groove formation )
 Saturation Regime  Conserved RSOS model(?)
(Yup-Kim and Jin Min Kim, PRE. (1997))
(D. E. Wolf and J. Villain Europhys. Lett. 13, 389 (1990))
eff
eff
eff
eff