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One-dimensional Ostwald Ripeningon
Island Growth An-Li Chin (秦安立 )
Department of PhysicsNational Chung Cheng University
Chia-Yi 621Taiwan, ROC
Prof. Fu-Kwo Men (門福國 ) Prof. Chin-Rong Lee( 李進榮 )
OutlineIntroduction Growth modes Experimental setupOur works Nucleation and growth of islands Selective growth Coalescence of islands ‘1-D’ island ripeningConclusion
RT-Scanning Tunneling Microscopy
Substrate structure
(7×7)
24×24nm2
(5×2)
10×10nm2
The force equilibrium can be written as γS= γF/S + γF cosφ
φ : the island wetting layerγS : the surface tension of the substrateγF/S : the inter-surface tension of the film/substrateγF : the surface tension of the film substrate
γS ≧ γF/S + γF (layer-by-layer)
γS < γF/S + γF (island growth))
Growth modes
γS γF/S
γF φ
-200
0
200
400
600
Growth of Cobalt on clean Si(111)
0.1ML 0.3ML
• (√7 × √7) structure.
• Steps of double bi- layer height transformed to single bi-layer height.
• CoSi2 islands emerging at Co coverages above 0.3 ML.
500 Å × 500 Å1000 Å × 1000 Å
0
(Å)
620℃
Cobalt on Si(111)-5 × 2/Au0.1ML 0.3ML
0.5ML 0.5ML
• Islands are formed on surface with only 0.1ML Co deposition.
6000 Å × 6000 Å
500℃ 700℃
600℃600℃
2000 Å × 2000 Å
0.0 0.2 0.4 0.6 0.8 1.0
Isla
nd d
ensi
ty
Coverage(ML)
0.0 0.2 0.4 0.6 0.8 1.0
6X6
5X2
7x7
Rec
onst
ruct
ion
Au coverage (ML)
(7×7)
24×24nm2
(5×2)
36×36nm2
Surface structure vs. Au coverage
√3× √3
( 4° )
Controlled structural change via Au deposition
2000 Å × 2000 Å(5 × 2) (7 × 7)
240 Å × 240 Å 240 Å × 240 Å
500 Å × 4000 Å(7 × 7)
(5 × 2)
700℃ 630℃
12000 Å × 4000 Å
• Islands grow only on (5 × 2) terraces.
• No islands grows on (√7 × √7) terraces up to 0.3 ML of Co.
• The island is consisted of Si and Co atoms.
The selective island growth
4000 Å × 4000 Å
500 Å × 500 Å
√7 × √7
5 × 2
Growth Scheme
I. Depositing Au onto a nominally flat Si(111)-(77) surface to induce a (52) reconstruction. (Au coverage 0.443 ML);
II. Depositing Co onto the Si(111)-(52)/Au surface at
room temperature; (A disordered surface results.)
III. Observing surface morphological change as a function
of sample heating time.
Coalescence of islands
0.5 ML Co on Si(111)-(52)/Au at RT followed by 620C heating
30 sec 210 sec90 sec
900 sec510 sec
200200nm2
330 sec
With islands on terrace decreasing gradually in size, atoms diffuse away from edges of terrace islands and feed the growth of islands at step edges.
Islands on step edge and terrace
0 1 2 3 4 5 6 70
5
10
15
20
25
0 1 2 3 4 5 6 70
10
20
Percen
tage (
%)
0 1 2 3 4 5 6 70
10
20
Height (nm)
Heating for 30sec
Heating for 90sec
Heating for 210sec
terracestep edge
Relative populations of two types of islands
Most islands appear at step edges at late stage of ripening process. (note that the number density of the islands at step edges decreases as well.)
0 200 400 600 800 10000
20
40
60
80
100
Per
cen
tag
e (
% )
Time ( sec )
Cluster at step edgeCluster on terrace
0 200 400 600 800 10001x104
2x104
3x104
4x104
5x104
6x104
Sum
of
volu
me
/ 200
x 2
00 n
m2
Heating time(sec)
Conservation of sum of island volume
Total island volume is conserved during the ripening process.
Average island size vs. growth time
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Hig
ht(n
m)
0 200 400 600 800 1000
12
14
16
18
20
22
cros
s-se
ctio
nal
len
gth
( n
m )
Heating time(sec)
2D-adatom gasdiffusion length
low
high
/rkT)νexp(2γcc(r) CMCV
Ripening growthGibbs-Thomson effect:
isla
nd d
ensi
ty
energy (heating time)
Overview of clustering
nucleation
aggregation
late stage growth
Model for island ripening 1/2
Consider the adatom diffusion among neighboring islands resulting from the chemical potential differences in islands of different sizes, the change in island radius, r, can be expressed as
I.M. Lifshitz and V.V. Slyozov (1958)
where rcr is some critical grain radius. A grain in the solution grows (shrinks) if its radius is larger (smaller) than rcr. D is the diffusion coefficient and the S size of the region involved in the adatom exchange process, the concentration of the solution, the grain surface energy per unit area, and the molar volume of the dissolved material.
(1)
where W has the width of a step if the diffusing atoms are confined to move along step edges.
r > rcr, island growsr < rcr, island shrinks
)11
(SD 3
rrr
r
dt
dN
cr
cr
)
11(
D2
)11
(D2
)3
4(
3
3
3
rrr
rW
rrrπ
rπ
dt
d
cr
crline
crcrsurf (i)
(ii)
Model for island ripening 2/2
With the constraint that the number of adatoms on the surface is conserved, we solve equations (1) and (2). The results are
rcr(t) t 1/5
N(t) t -3/5
(Experimental results: )
Let f(r, t) be the number distribution function of island with radius r at time t, from the equation of continuity we have
(2)
rcr(t) t 0.201
N(t) t -0.55
0)(
dt
drf
rt
f
rcr(t) t 01/4
N(t) t -3/4(i) (ii)
3 4 5 6 7
3
4
5
ln(I
slan
d nu
mbe
r)(2
00n
m)2
ln(Time)(sec)
3 4 5 6 7
0.8
1.0
1.2
1.4
1.6
ln(i
slan
d h
eigh
t)(n
m)
ln(Time)(sec)
Island distributions vs. time
Island density decreases as time to the -0.55 power.
Island height increases as time to the 0.2 power.
(Island shape independent of island size.)
Slope = -0.55 Slope = 0.2
Average island density Average island height
Diffusing species diffusion pathway
Single bi-layer-heightstep (3.1 Å)
1. escape from islands on terraces;
2. diffuse toward step edges, which act as sinks;
3. diffuse along step edges(rate-limiting)
4. attach to islands at step edges followed by edge diffusion.
Diffusing species must
Conclusion
We have demonstrated the self-selective growth of CoSi2 islands with narrow size distribution on only one of the two domains by depositing up to 0.3 ML of Co.
We have observed a unique 1D diffusion process leading to the growth of step-edge islands at the expense of terrace islands.
Island distribution
0 1 20.0
0.1
0.2
P
erce
nta
ge
Island height/<island height>
30sec1 90sec11 120sec121 60sec1 150sec1 210sec1 330sec1