FORMATION AND GROWTH OF CLUSTERS AND ULTRA FINE PARTICLES ON SOLID SURFACES

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HAL Id: jpa-00226895

https://hal.archives-ouvertes.fr/jpa-00226895

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

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FORMATION AND GROWTH OF CLUSTERS AND ULTRA FINE PARTICLES ON SOLID SURFACES

Q. Wu

To cite this version:

Q. Wu. FORMATION AND GROWTH OF CLUSTERS AND ULTRA FINE PARTICLES ON SOLID SURFACES. Journal de Physique Colloques, 1987, 48 (C6), pp.C6-531-C6-536.

�10.1051/jphyscol:1987687�. �jpa-00226895�

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JOURNAL DE PHYSIQUE

Colloque C6, supplkment au n O 1 l , Tome 48, novembre 1987

FORMATION AND GROWTH OF CLUSTERS AND ULTRA FINE PARTICLES ON SOLID SURFACES

Q* WU.

Department of Radio-Electronics, Peking University, Beijing, China

Abstract: A short review of experiments using FIM and STM to investigate clusters and ultra fine particles. and a theory of formation and growth of them in a semiconductor or dielectric matrix or on a substrate are presented. Conditions of epitaxial growth deduced from this theory are also presented in this paper.

I. Introduction

Formation, growth and movement of clusters and ultra fine (small or colloidal) particles belong to a very attractive scientific subject. A cluster contains in the range of 2 to 200 atoms. An ultra fine article is defined as a particle having dimension in the range of 10 to 1000

8 .

Clusters and ultra fine particles on substrate have special properties which are different from the properties described by atomic physics and solid state physics.

There are several simplified theories for nucleation and initial growth of vapor-deposited thin f i lms

.'

Auger Electron Spectroscopy and X-ray Photoelectron Spectroscopy can be usually used for thin film analysis, but they are difficult for investigating cluster nucleation and particle growth. On the contrary.

Field Ion Microscopy (FIR) and Scanning Tunneling Microscopy (STMI can be used for most cases.

11. Review of Experiments Using FIM and STM

FIM can be used to investigate the formation and movement of one or two dimensional clusters, but it is difficult to investigate three dimensional ultra fine particles due to field evaporation. There are a lot of examples. For example, Prof. T. T. Tsong has shown many figures and discussions about atomic processes on metal surfaces."~

It should be emphasized that it is difficult to use FIM to investigate three dimensional particles due to field evaporation.

Fortunately STM can be used to investigate them, both for clusters and small particles.

Results on a Au(ll0) surface have been obtained by Th. Berghaue et alP J. k. Ginzewski et a1.7 finished a comparative study of coldly- and warmly-condensed Ag films by STM. The coldly-condensed films are known to show the surface enhanced Raman effect, while the room temperature condensed films do not. D.W. Abraham et al.8 reported the use of a STM in air to image clusters of Au and As atoms deposited on the surface of highly oriented pyrolitic graphite. The large silver cluster shown in Fig.1C.a) (after Ref. 8 ) is roughly cylindrical with a diameter of 350

A

and a height of about 30

a.

Closer inspection reveals that the particle is composed of several small agglomeration

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987687

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C6-5 32 JOURNAL DE PHYSIQUE

each 30-100

8

in diameter. The presence and shape of the sub- structures suggest that the large cluster was formed by the coalescence or piled together of small clusters after deposition.

These conclusions are quite similar to that of my paper published in 1 9 7 9 P The structure of small silver particles in Ag-0-Cs photocathode (i.e. the small silver particles embedded in cesium oxide) were studied by means of the replica method and direct observation in electron microscope. One of them is shown in Fig.l(b). The behavior of

Fig.1 (a) A large Ag ciuster on graphite by STM (after D. W.

Abraham et ale); (b) Ag cluster in Ag-0-Cs photocathode.9

silver clusters on graphite is quite similar to that in cesium oxide.

These small particles like flowers, but their cause of formation is still mysterious.

111. Theory of Formation and Growth of Clusters and Small Particles

1. Nucleation and Growth in A Matrix of Semiconductor and Dielectric Let us discuss the formation in a matrix first. The idea of free energy has been used in the discussion for the formation of small particles in a matrix.lo

Let N be the number of impurity atoms in unit volume, and

p

^{be the}

number of clusters or small particles, each containing n impurity atoms, in unit volume, then

N = n p t

h(g

:

¹⁾

where ND is impurity atoms per unit volume outside small particles.

Let

F

be the total free energy in unit volume. Using eqution (1) and conditions of unstable equilibrium for free energy

a F / d n = o , a F / a P = o ;

⁽²

we can solve the critical values f o r k and $', i.e.

nc

^and

PC.

Only when f i

> nr

, this system becomes a sol id emdedded with small particles. F c a n be written as

F = E , - E 8 p n + f i ~ n " ~ - R T L ~ N / ~ / N ~ ! - % T ~ ~ N I P / ~ ! ,

₍₃

where

E,, Eg

and E4 are terms related to energies but with different connotationSfor A 0 ionic crystals or covalent crystal with G impurity atom, where A ,

B

and C denote chemical elements; Nt is the number of A and 6 lattice sites in unit volume; 7 is the matrix temperature during preparation;

E4

= a

(2 ~ A B

-

^~ ^A

-

^C

S B C ) ,

( 4 )

and d s

f$

(4~)"' 3* (VC

/ VIC)2/J

^j

(4)

here P A * , gAe

, SBe

denote the bonding energies between A8

.

^AC ^and^{8 C}

pairs respectively;

1IL

denotes the average volume of matrix atom; $ denotes the average volume of C atom; and E . = ( 4 r ) U ( 3 %

PC;

U is the interfacial energy of the small particle.

From the conditions a F / a p s 0 and

aF/an=

^{0 ,} critical conditions

( NL.

P C .

Not at activation temperation

5

can be obtained:

& c a n be solved from the following relation:

then,

n,

= kc ( N I N Q , T A .

E C ,

ES

) .

The physical conditions for the existence of small particles are as follows:

(1) The first physical condition is: E4> 0 , i.e,,

3 4 s

> $ ( g ~ c

⁺

BBCJ .

^{( 8}

It means that for ionic crystal the attractive force between impurity ion and matrix ions must be less than the attractive between matrix ions; and the same for covalent crystal, except that ions are substituted by atoms.

(ii) From formula ( 7 1 , let us keep

7~

unchanged, when MfNt decreades, & increases. There is a critical impurity density N*, then the second condition is

N _> **N * =**

NL ~ Y P C - E ~ / ~ T A ) . ( 9 )

It is a necessary condition, but not a sufficient condition.

It can be proved that the point (

ne,.pc

1 on the surface of free energy

F

is a saddle point. Only when

n > n e ,

the nucleation clusters grow up.

The density N D ~ of impurity atoms at the neighborhood of a particle with

n

atoms can be given by:

N D ~

= & ^expl-

E s / k n ]

QXPC$E'UI-'//~~~J.

₍₁₀₎

This means that the density of impurity atoms at the neighborhood of small particles is greater than that near larger ones, so will be the diffusion. The atoms in smaller particles may diffuse into their surrounding regions, and then the diffusion may maintain. The impurity atoms in the neighborhood of larger particle may deposit onto this particle. There is a-reference particle with Ratoms. After baking.

larser particles [ Y > P ) have grown up, but the smaller ones ( P < F ) have reduced in size, even disappeared. The growth rate was given in Ref. 10.

2. Nucleation and growth on substrate (1). Free energy function

Let

N

be the density of deposited atoms or monomers on unit area;

and

+

is the number of clusters or small particles (aggregates) containing a atoms each on unit area, and No is the monomers deposited on this area outside the aggregates. Then

~ = p n 4 ~ 3

(11) Their free energy can be written as;

L I F = E ~ - E ~ ~ ~ + E ~ ~ ~ ~ - ~ T ~ ~ N , ~ / N ~ ! - k ~ l n ~ ~ ~ / p !

; (12)

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JOURNAL DE PHYSIQUE

where

,alp

is the surface area exposed to vapor phase. U z r * is the contact area between aggregate and substrate. a3r3 is its volume, Ur, A=

,

aj

are geometric constants describing the shape of an aggregate.

ccu and Csc are the surface and interfacial free energies of the aggregate respectively, and Qjvis the surface energy of the substrate;

the bonding energies for substrate atoms and for aggregate atoms are converted to q, and 6,v; Ifo is the potential energy, Eg

.

^,755 ^are

thermal energies; /& is the number of monolayer

c

atoms in unit area;

*rev is the free energy of condensation of the deposited material in

the bulk under the same conditions of supersaturation and is given by

A& S

-

( k r / ~ )

172

& / R ~ _{( 1 6 )}

where Sd is the deposition rate and Re is the evaporation rate of monomers from the bulk at the substrate temperature.

a/&

^{is the}

supersaturation ratio.

( 2 ) Critical conditions for nucleation

The critical conditions can be obtained from a ~ F / a n = o , and W F / B P 10;

We may solve the last equation to get

nc

which is a function of N/l\(d

, . e. ^{E ~ S ,}

^A& etc. The critical radius of aggregate is equal to

(

% / a 3 )vJn:?

The physical conditions for nucleation are:

E i 7 0 ,

and

N ~ N O ~ X ~ [ - E ~ / A ~ A ] .

( 2 0 ) (3). Spherical cap aggregate

Suppose that elements

A

and 6 constitute the substrate. For spherical cap aggregate, related parameters can be written as:

0-cs

= (l/6)V3- f

^{( 2}^{$ A ~}

- ^- ^&),

q,P =

( ' / ~ 4 ) ~ ' 3

iTA6

, ^{( 2 1 )}

q,, =

C ' / 1 / ~ ) ~ ' 3

PFcc

^;

and

2

L

R,=ZX(I-cose), a2=nsjn2e. a , = = 7 ~ [ ~ - ~ c o s e ( s i . % + 4 ~ .

^{( 2 2 ,}

The physical condition (

E i >

⁰⁾^becomes

4 ⁽

¹

⁺ (v,/~)'~(I~~ r P ~ ~ J / Z ~F~~J(IJ.(Y/~I~'YB~+~J/z gCC <

; ( 2 3 )

(6)

where

(%/&tY3(gAC

^-I~ , c ) / z & c

= ws

0

s

I , (24) where 9 is the contact angle of the aggregate with the substrate.

( 4 ) Growth of aggregates

The growth of aggregates relate to surface diffusion. Surface diffusion coefficient3 can be written as

D = DO e ~ p

C- E D / ~ T ) , _{( 2 5 )} where Eo is surface diffusion edergy. The number of diffused monomers onto the aggregate with

n

atoms in unit time is

1. I ₌ $ ^{xv ln} ^(R/~$-N,,

^ex![-

**E ; ~ / * T ~ J**

( e x p l j ~ ~

n'-hh~] - e~p[$G~-~/kTd);

26) here

N, u ~ t - E ~ h ~ e x p [ $ ~ ~ n ' ~ f i / k ~ ~ I = N , .

(27) When

n > % , I

is positive, this aggregate will grow up. When

I Z . < ~ , I

is negative. this aggregate will reduce in size, even disappear. Its growth rate can be written as

2 s b

$ ⁼ PA/*. ^InK/it

^i/n.

^nl ~~~(-E~'/~TAI(&JE~~~~A~I-@R~~'~TA,I.

⁽²⁸⁾

After baking, the total number of asgresates on unit area may decrease.

IV. Conditions for epitaxial growth

Epitaxial growth can be discussed through nucleation theory. For the case of heteroepitaxial growth, following conditions should be satisfied. The first condition is

&'<

^{0, i. e.}

a, (y/@Y3qv z a, **( ~ , / a ~ j * s , ~ + a 2 ( ~ / q J M ~** .

(29) AS discussed in the spherical cap aggregate, when ( I/e

a

?(~~pcf&)/Z

gCc

>

1, the contact angle 8 does not exist. i.e. we can not get nucleation. The second condition is E$

<

0. From formula (18). if Ed J 0, the N w $ N O . This is the second condition of epitaxial growth. From formula (141, it can be expressed as:

k r h

R ~ / R ~

2

(%)"(ajv -%c)

+ W T -

^Ho^; ⁽³⁰⁾

p i e a constant for first order approximation. is the evaporation rate of monomers and is an exponential function of T . For a given temperature. R d should be lower than its upper limit given by this formula. & / R e decreases when the temperature increases. For perfect epitaxial growth, the third condition related to surface diffusion should be considered, since the deposited monomers should move to their proper positions. Therefore there is a lower limit of substrate temperature. The epitaxial temperature depends on Rd and the bonding energy between the deposited atom and the substrate. When the substrate temperature is too high, thermal defects may appear in this film, and even then it may become noncrystallinity.

When

E: >

^{0, but}E:

6

(2/3)&qf&-'/S, N ~ & / i l o . The formula (30) becomes

If this condition is satisfied, and the substrate temperature is within the epitaxial temperacure range, the epitaxial film may also grow up.

V. Discussion and Conclusion

1 Deposition of metal elements on GaAsCllO) surface

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C6-536 JOURNAL DE PHYSIQUE

GaAsCllO) surface is an important surface for Schotky barrier research. The epitaxial growth of A1 on GaAs(ll0) can not be observed, but A1 clusters can. A. zungerJ4 considered that the interaction between A1 atoms must be stronger than that between A1 atom and the substrate atoms. This conclusion coincides with the condition & ( $ h ~ g +

3 n s ~ l )

< ^SAtbt ^for A1 c lusters. The same reason can be used for A g clusters. But Ifor cesium. no cluster can be observed on the same surf ace, since p (3?*&c,

-+

~ A ~ c J )

>

^Jets

.

( 2 ) . Two dimensional silver clusters and epitaxial growth

At very low density of deposited atoms, they form two dimensional clusters easily. It can be believed that the epitaxial growth can be obtained when the silver atoms are slowly deposited onto graphite with suitable temperature.

(3). One dimensional clusters

In Ref.5 and 8, we may find out the experimental results for one dimensional clusters obtained from FIM and STM. It is difficult to dlecuss, since the phenomena are complicated in a microscopic point of view.

Theory of formation and growth of clusters and small particles and conditions for epitaxial growth have been developed and discussed. STM and FIM are useful and powerful tools for investigating clusters and ultra fine particles. The experimental results obtained from STM and FIM would stimulate the theoretical development of clusters, ultra fine particles, and thin films.

References

C.A. Neugebauer, chapter 8 in "Handbook of Thin Films Technology"

edited by L.I. Maissel and R. Glang, 1970.

T.T. Tsong, Progress in Surface Science, 10 (19801, 165.

T.T. Tsong and R. Casanova, Phys. R e v . B 24 (1981). 3046.

T.T. Tsong, Phys. Rev. B 25 (1982). 5234.

Qiaojun Gao and T.T. Tsong, Phys. Rev. Letters, 57 (1986). 452.

Th. Berghaus, N. Neddermeyer, and St. Tosch. IBM J. Res. Develop.

30 ( 5 ) (1986). 520.

J.K. Gimzewski and A.Humbert, IBM J. Res. Develop. 30(4) (19861.472.

D.W. Abraham, K. Sattler. E. Ganz. H.J. Mamin. R.E. Thomson.

J. Clarke, Appl. Phys. Lett. 49(4) (19861, 853.

Wu Quan-De. Acta Physica Sinica. 24 (1979). 553.

Wu Quan-De, Acta Physica Sinica, 22 (1966). 1, 17.

A. Zunger. Thin Solid Films. 104 (19831, 301.

FORMATION AND GROWTH OF CLUSTERS AND ULTRA FINE PARTICLES ON SOLID SURFACES

HAL Id: jpa-00226895

https://hal.archives-ouvertes.fr/jpa-00226895

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.