Transcript 04년 가을 물리학회

2004년 한국물리학회 가을 학술 논문 발표회
A theoretical suggestion
to make real clean material surface
Sooyeon Yoon and Yup Kim
Kyung Hee Univ. Dept. of Phys.
1
Abstract
Abstract
We study a dynamical scaling property of real two dimensional surface
eroded from the rough surface by an external particle which does biased
random walk. We first prepare the rough surfaces by use of several growth
methods, i.e., the random deposition, the restricted solid-on-solid (RSOS)
model, and conserved RSOS model. We first show that the roughness of
surfaces eroded by unbiased random walking particles in three dimensional
space eventually reaches within mono-layer thickness. We also found
that the dynamical scaling property of the surface satisfies the scaling ansatz
W~f(t/Lz) with the dynamical exponent z=1. When the attractive bias
exists, the surface roughness increases logarithmically with size.
2004년 한국물리학회 가을 학술 논문 발표회
2
Motivation of this study
Motivation of this study
 Theoretical base
Surface evolution models with z = 1
 Biased-Diffusion-Limited-Erosion
(PRE 66, 031105 (2002))
 Time-Reversed Dielectric Breakdown Model
(PRE 67, 05611(2003))
 Surface Growth Model with a Random walk like Nonlocality
(PRE 68, 036221 (2003))
2004년 한국물리학회 가을 학술 논문 발표회
3
Motivation of this study
h(q, t )
  | q | z h(q, t )   (q, t )
t
 (q, t ))  0
 (q, t ) (q' , t )  D qq' (t  t )
white noise
 DLE Model and TDBM (Dynamical Scaling Law : z = 1)
2

W
 f (t / L)
(1D)

2
W 
 0 (2D)

 f (t / L) t
 BDLE Model (Dynamical Scaling Law : z = 2)


 L2 f t / Lz
W 
z
ln
L
f
t
/
L

2
2004년 한국물리학회 가을 학술 논문 발표회


(1D)
(2D)
Motivation of this study
 Experimental base
 Plasma-surface interaction
: A flux of ions emerges from the plasma and a thin film is being
etched by accommodation of incident ions on a substrate.
(Progress in Surface Science 76, 21 (2004))
 Chemical etching
: Boiling silicon wafer in an HCL/H2O2 or NH4OH/H2O2 solution
(RCA review 31, 187 (1970))
 Electropolishing
: Electrochemical etching of silicon in hydrofluoride containing
eletrolytes leads.
(PRE 64, 031604 (2001, theoretical base))
2004년 한국물리학회 가을 학술 논문 발표회
4
5
Model
Model
2-dimensional L x L substrate,
1. First make a rough surface(material) with
restricted solid-on-solid method, random deposition method.
2. Choose randomly one site (x,y,z) at the starting
plane. A particle does the biased random walk with
down probability Pb in the empty space.
3. If the particle gets to the killing plane, the
new one is started from the other randomly selected
site among the starting plane.
Otherwise, if the particle reaches the nearest
neighbor of the rough surface, the incident particle
and material particle are removed together.
Killing plane
zk
Starting plane
zmax
L
※ If the sites which the incident particle is located
are more two, randomly select one of them.
z
x
P( x, y, z  1)  Pb
(0  Pb  1)
P( x  1, y, z )  P( x  1, y, z )  P( x, y  1, z )  P( x, y  1, z )  P( x, y, z  1) 
y
Pb
2004년 한국물리학회 가을 학술 논문 발표회
1  Pb
6
6
Results
Results
1-1. Restricted solid-on-solid(RSOS) type growth & Down probability,Pb=1/6
L=8
L = 16
L = 32
L = 64
L = 128
2.0
L=8
L = 16
L = 32
L = 64
L = 128
2.0
W
W
2
1.5
2
1.5
1.0
1.0
0.5
0.5
0
40
80
120
160
200
0
t
10
15
t/L
W 2  f (t / L) t
 0

2004년 한국물리학회 가을 학술 논문 발표회
5
20
25
30
7
Results
 Morphology change of RSOS surface
t=0
2004년 한국물리학회 가을 학술 논문 발표회
t=
8
Results
1-2. Restricted solid-on-solid(RSOS) type growth & Down probability, Pb=1
5
L=8
L=16
L=32
L=64
L=128
4
1.2
W
2
3
2
1.0
Ws
2
1
0
2
4
2
0.8
L=8
L=16
L=32
L=64
L=128
3
0.6
W 2  A ln L
2
2
3
4
5
2
W - Ws
8
ln t
4
Scaling collapse
with z=2
6
A=0.193(2)
ln L
1
0
-10
-8
-6
-4
-2
z
ln(t/L )
2004년 한국물리학회 가을 학술 논문 발표회
0
2

W 2  ln L f t / Lz

9
Results
※ Confirm of 2D BDLE ( Pb = 1)
Erosion is started from the flat surface ( h = 0 )
0.2
0.9
L=8
L = 16
L = 32
0.8
0.0
A=0.205(1)
2
W
0.8
0.7
2
-0.2
W
2
W -Ws
2
1.0
0.6
0.6
W 2  A ln L
0.4
-0.4
0
2
4
6
8
10
ln t
-6
-4
-2
0
0.5
2
2.0
Dynamic exponent ,
z=2
2004년 한국물리학회 가을 학술 논문 발표회
2.8
ln L
z
ln(t/L )
2.4

W 2  ln L f t / Lz

3.2
3.6
10
Results
2-1. Random deposition(RD) type growth & Down probability, Pb=1/6
L=8
L = 16
L = 32
90
L=8
L = 16
L = 32
90
W
W
2
60
2
60
30
30
0
0
0
200
400
600
t
2004년 한국물리학회 가을 학술 논문 발표회
800
1000
0
50
100
t/L
150
200
11
Results
2-2. Random deposition(RD) type growth & Down probability, Pb=1

W 2  ln L f t / Lz
A=0.205(1)
0.8
W
2
1.0
0.6
W 2  A ln L
2
3
ln L
2004년 한국물리학회 가을 학술 논문 발표회
4

12
Conclusions & Discussions
Conclusions & Discussions
We study a dynamical scaling property of two dimensional surface
eroded from the rough surface by (biased) random walking particles.
1. RSOS type surface eroded by unbiased random walking particles (Pb=1/6)
W 2  f (t / L) t
 0

2. RD type surface eroded by unbiased random walking particles (Pb=1/6)
??
3. The attractive bias exists (Pb=1), the surface roughness increases
logarithmically with size.

W 2  ln L f t / Lz
2004년 한국물리학회 가을 학술 논문 발표회
