one-dimensional ostwald ripening on island growth an-li chin ( 秦安立 ) department of physics...

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