Electron-irradiation-stimulated coalescence in discontinuous metallic thin films

Thin Solid Films, 141 (1986) 137-156

137

GENERAL FILM BEHAVIOUR

E L E C T R O N - I R R A D I A T I O N - S T I M U L A T E D C O A L E S C E N C E IN D I S C O N T I N U O U S M E T A L L I C T H I N FILMS B. G. ATABAEV, E. M. DUBININA, S. S. ELOVIKOV AND M. M. SAAD ELDIN

Department of Physics, Moscow State University, Moscow 119899 (U.S.S.R.) (Received May 17, 1984; revised March 28, 1985; accepted January 13, 1986)

Dynamic coalescence and autocoalescence processes were investigated in discontinuous metallic films (gold, silver and indium) on amorphous (SiOx, carbon and MgO) and monocrystalline (KC1, silicon and MgO) substrates under electron irradiation. Effective coefficients DB for the surface diffusion of islands were estimated. It was found that under electron irradiation DB is 10-15-10 16 cm 3 s- 1, which is one to two orders of magnitude higher than D B under thermal annealing. The influence of the degree of orientation of islands on the coalescence process was studied. A theoretical model of the phenomena is presented.

1. INTRODUCTION In recent years a great deal of research has been directed towards the study of discontinuous metallic thin films (DMTFs) owing to their unique properties. Experiments with D M T F s provide important information concerning the physical processes on the surface. This information makes it possible to estimate the coefficients of surface diffusion of adatoms and of migration of film islands. A knowledge of the characteristics and properties of D M T F s is also important for understanding the physics of film deposition from the vapour phase, since a discontinuous film is the fundamental state in the formation process of a continuous condensate. D M T F s have many practical applications. They are used as emitters of hot electrons 1, as optical filters with anomalous absorption spectra in the IR region 2, for increasing second-harmonic generation 3 etc. It is also known that small particles deposited onto bulk samples cause elastic tensions in them, which markedly affect their electrophysical and mechanical properties 4. The wide application of D M T F s produced in vacuum from molecular beams, however, is limited owing to their instability and the poor reproducibility of the required properties. Film properties can be effectively controlled by low energy electron irradiation of the glowing layers 5-7, especially during the earliest stages of its growth. According to previous investigations, such control is achieved because of the generation of point defects on the substrate. However, not all the experimental data can be explained according to this model. 0040-6090/86/$3.50

© Elsevier Sequoia/Printed in The Netherlands

138

B.G. ATABAEVet al.

The aim of the present work is the study of the influence of electron irradiation on the morphology and orientation of D M T F s after deposition, i.e. during the film aging while the condensed mass is conserved. 2. EXPERIMENTAL DETAILS

2.1. Experimental arrangement Experiments were carried out in an ultrahigh vacuum chamber (pressure p = 10 7-10- 8 Pa) equipped with an Auger analyser, a mass spectrometer, a precise manipulator with heated samples and several calibrated evaporation sources (Fig. I). 9

Fig. 1. Schematic re wesentatlon of the experimental arrangement: 1, ultrahigh vacuum chamber; 2, hyperboloid energy analyser; 3, electron gun; 4, metal atom source; 5, mass spectrometer; 6, heated substrate holder; 7, manipulator axis; 8, ion gun; 9, rotary feedthrough; 10, shutter; 11, conic evaporator.

The electron gun for the Auger analyser and film irradiation gave a current density of up to 1 mA c m - 2 with a beam energy of 1-3 keV. The beam radius at the sample surface, situated 20 m m from the gun, could be varied between 1 and 3 mm. Clean surfaces were prepared either by thermal treatment of the surface or by ion etching followed by annealing of defects. In special cases the substrates were thin layers deposited onto bulk samples under the ultrahigh vacuum. Deposition of the D M T F was carried out using calibrated evaporation sources which were heated either by the radiation from the heated cathode alone (if a temperature of 1100 K or less was required) or by bombarding it additionally with accelerated thermal electrons from the cathode (usually at an energy Ep of 1 keV). Sets of thermal screens surrounded the evaporation source to limit the radiation effects on the surroundings and to decrease the power dissipated. The cell temperature was measured with a calibrated W - R e thermocouple with a sensitivity of 16 mV K - 1. Sources were calibrated by measuring the thickness of the deposits obtained. A shutter was used to close the source outlet until the required temperature was reached. An evaporator of similar design was used for the deposition of thin SiO films.

139

STIMULATED COALESCENCE IN DISCONTINUOUS METALLIC FILMS

All the experimental procedures (preparation or deposition of the thin film substrate, deposition of the D M T F , film irradiation and its investigation, deposition of fixing layers etc.) could be carried out with the vacuum chamber hermetically sealed. 2.2. Experimental methods

As amorphous substrates we used films of SiO or carbon deposited onto KC1 surfaces. For the study of orientational and in some cases autocoalescence effects in films, the substrates were single crystals of KC1 and MgO. The materials deposited were gold, silver and indium. For film deposition, substrates were mounted on a holder (Fig. 1, point 6) which ensures the absence of charge leakage. When the required pressure had been attained (p ~ 10 7 Pa), the substrates were annealed for 1 h at 650-700 K. Then they were cooled to room temperature and afterwards an SiOx layer approximately 0.1 ~tm thick was deposited onto them at a rate of 0.5 n m s x from the evaporator 4. Control of the surface contaminations of the prepared SiOx layer was achieved using the Auger spectrometer 2. Metallic films were deposited from the calibrated evaporator 4; using the rotary feedthrough, the shutter 10 was opened for a certain time at a given evaporation rate. After deposition, the layers were successively located at the focus of the energy analyser to obtain Auger spectra of the substrate material (Is) and of the film material (If). Comparing the initial ratios If~1 s of the Auger peaks for different substrates, we were able to estimate the homogeneity of film deposition. In some cases, to prevent the bombardment of non-irradiated samples with scattered electrons, depositions were carried out by a special method using shadowing with a wire (Fig. 2). A sharp boundary (less than 0.1 lam wide) was thus obtained between the non-irradiated and the irradiated films. Under electron irradiation SiOx/KC1 samples that are isolated from the substrate holder by a layer of vacuum cement (Fig. 3) become charged, positively if

[ 3

5 ,',; ¢, ~ ' ~

1

I /-I

2

4 ,,

Fig. 2. Method of obtaining island film boundaries: 1, SiOx evaporator; 2, D M T F evaporator; 3, wire layers; 4, SiO fixing film; 5, D M T F ; 6, substrate without film. Fig. 3. Sample holder: I, sample; 2, vacuum cement; 3, thermocouple contact; 4, ceramic tube; 5, thermocouple; 6, holding base.

B.G. ATABAEVet al.

140

the secondary electron emission coefficient a' > 1 and negatively if a' < 1. The potential to which the surface is charged depends on many factors. Charging of isolated targets has been discussed by Fridrikhov and Schulman s in detail. For 0 ' > 1 the maximum potential is about 10-15V. We estimated it from the displacement of the Auger peaks. Under electron irradiation a change in the surface stoichiometry could take place as well as the growth of an adsorbed carbon layer. In our case, the Auger spectroscopy control of the surface showed that at D < 1 0 2 2 electrons cm -2, the Auger peaks of bound silicon, oxygen and carbon were essentially unchanged. 3.

MIGRATIONAL

METALLIC

COALESCENCE

DURING

ELECTRON

IRRADIATION

OF DISCONTINUOUS

THIN FILMS

3.1. Change in the morphology of discontinuous metallic thin films under electron irradiation Gold films of effective thickness d ,~ 1.5 nm, deposited onto the surface of an SiOx layer, were of fine and uniform structure (Fig. 4(a)). Irradiation of such films to a dose D ~ 1 0 2 2 electrons cm -2 at an electron energy Ep of 3 keV resulted in a marked change in the film morphology. Large islands surrounded by depletion zones appeared (Fig. 4(b)). For films of thickness d ~ 4.5 nm the irradiation resulted in a change in the shape of islands, but their concentration remained the same. Gold films of thickness about 6 nm had a grid-like structure. After irradiation a similar structure remains, but the gold has been redistributed such that wider empty channels are formed. Thus irradiation of the D M T F stimulates the coalescence as well as the autocoalescence processes. For an Au/KC1 film (d = 2.5 nm) (Fig. 5) another structure is observed after irradiation. It is believed that the observed effects are due to surface charging, since we could not detect them when charge leakage was

(a)

I (b) ..........................................

(A) Fig. 4. Morphology

! 100 n m

(B) of a gold DMTF

j - 500 g A c m - 2 ; D = 101 s e l e c t r o n s c m

(C) (a) bcfore and (b) after electron irradiation (Ep = 3 keV; 2): (A) d = 1.5 n m ; (B) d - 4.5 n m ; (C) d = 6.0 n m .

141

S T I M U L A T E D C O A L E S C E N C E IN D I S C O N T I N U O U S M E T A L L I C FILMS

I

I 100nm

(a) (b) Fig. 5. M o r p h o l o g y of a g o l d island film o n KCI (a) before a n d (b) after i r r a d i a t i o n (Ep = 6 0 0 e V ; j - 5 0 0 / a A crn z ; D - 1018 e l e c t r o n s c m - 2 ; d = 2.5 nm).

provided. The secondary electron emission coefficients of the substrate (g'siox) and of the film (a'Au) at energies Epof 3 keV are greater than unity. Hence the substrate and the islands are similarly charged. In the case of Au/C, in spite of the fact that g'c < 1 at Ep = 3 keV, the islands and the substrate are also similarly charged, since the carbon substrate possesses sufficient conductivity. For the KC1 surface or' > 1 but can become less than unity owing to the electron-stimulated desorption of chlorine. In this case it is not easy to determine the sign of the surface charge.

3.2. Changes in the mean film parameters by irradiation To establish the quantitative relationship between the charge effects in the system o f a D M T F on an isolated substrate and the coalescence processes, the effect of the irradiation dose on the film morphology was studied. The changes in morphology enable the mechanism of surface mass transfer to be found and its parameters to be determined. Gold D M T F s of effective thickness d = 2.5 nm were formed on SiOx layers of thickness d = 0.15 nm and were then irradiated with electrons of energy Ep = 3 keV at a current density j -- 1 mA c m - 2. Transmission electron micrographs show that the film morphology changes with the exposure time t (Figs. 6(a) and 6(b)). At t = 5 min the island concentration N decreases more rapidly than the coverage coefficient S (Table I). This is a result of the migrational coagulation of islands. At t = 15 rain large islands of right circular shapes and depletion zones filled with fine islands are observed. In this case migrational coalescence of the islands takes place and the values of N and S decrease. At t = 25 min a further increase in the island mean radius and a decrease in N and S can be seen. To estimate the influence of substrate temperature the film was annealed at higher temperatures and for longer times. Figure 6(c) shows that only slight changes in the D M T F morphology were observed in this case. F r o m a comparison of Figs. 6(a), 6(b) and 6(c) it can be concluded that the prevailing mechanism is the interaction of the islands because of their charges. This is proved by the small influence of irradiation on the Au/C system when charge leakage is ensured. In Fig. 7 the histograms which characterize the island size distribution functions Z(R,t) for different exposure times are presented. The initial function Zo(R,t) with one m a x i m u m is transformed to a function with two maxima as the

142

B.G. ATABAEV et al.

(a) t = 0rain

t = 5rain

t = 15min

t = 25min

t = 0 min

t = 5 min

t = 10 min

r = 20 min

(b)

I

I 400 nm

(c) t - 60 rain Fig. j-

6. M o r p h o l o g i c a l l mAcm

2: T , -

changes

500K;

d=

in a gold 2.5nm)

film o n

SiOx

(a),(b)

under irradiation (Ep = 3 k e V ;

a s a function of time t a n d (c) under thermal annealing

(T, = 880 K).

TABLE

1

CHANGES 1N THE MEAN CHARACTERISTICS OF A DISCONTINUOUS (;.OLD THIN FILM ON g i G x UNDER IRRADIATION a (ROWS 1--5) AND UNDER THERMAL ANNEALING (ROWS 6 - 8 ) t

R

~

NxlO

(K)

(mint

(nm)

(nm)

(cm

-I~

2)

S

(%)

1

400

0

1.7

0.4

27

27

2

400

0.5

2

0.6

12

16

3

400

10

3.5

1.5

2.4

4

400

20

4.4

2.7

0.6

7.6

5

400

30

7.4

4.3

0.2

4.7

6

880

0

3.1

9

0.8

26

7

880

30

3.3

9.8

0.6

25

8

880

180

4.5

0.4

21

aEp=3keV;j=

lmAcm

10

1l

2.

irradiation dose is increased. The second maximum corresponds to a larger island size. A slight shift in both maxima towards higher values of R is also observed. The shift in the first maximum can be explained by the participation of small islands (which are not seen in the transmission electron microscope) in the coalescence processes. Since the mass transfer is provided mainly by the large islands, we consider only the change in the second maximum. It can be assumed that in all cases the more probable mechanism of mass transfer is the displacement of the islands as a whole. There is also a certain probability of a diffusional coalescence by the process of Ostwald ripening. However, this usually takes place at higher substrate temperatures T~ ~ Tin~2, where Tm is the melting temperature of the island material. According to Geguzin and

S T I M U L A T E D C O A L E S C E N C E IN D I S C O N T I N U O U S M E T A L L I C FILMS

143

N.10"~°,cm

L 1o~

t =10 s

103~ II

6

J2

=8

2~

~, nm

Fig. 7. Size distribution histograms of gold islands on SiOx for different irradiation times (Ep = 3 keV; j = 1 mA cm

z; T, = 4 0 0 K).

coworkers 9,1 o, the presence of electrical charges on the islands opposes this type of coalescence. Under electron irradiation, the random migration of an island is mainly due to the influence of a disorderly varying external force, which is a result of the electrostatic interaction between the islands. If it is assumed that each island exists in a field of unpredictable electrostatic forces, formed by the charges on the substrate and the islands, it is possible to introduce a corresponding effective temperature and to apply to the system the formalism developed for the estimation of the island surface migration coefficient, which in our case can be considered as the "effective migration coefficient". Estimation of this value can be achieved either, according to Masson et al. 11, by the time deformation of the condensate sharp boundary or by the change in the size distribution function of the islands proposed by Kashchiev ~2. In our case the second method appeared to be more appropriate.

3.3. Determination of the effective coefficients of the islands' brownian migration by transmission electron microscopy Using transmission electron microscopy (TEM) we studied some combinations of D M T F s and substrates which were irradiated by electrons or annealed. The following notation is used: substrate temperature T~, mean radius R of the islands, dispersion a of their size distribution functions, island concentration N at the substrate, coefficient S of substrate coverage with islands, total exposed area S e. Some of the quantitative estimations as well as experimental conditions and main characteristics are displayed in Table II. To use the models for the calculation of migrational parameters, we consider the time relationships of the averaged characteristics for the system Au/SiOx. Figure 8 shows the histograms for the island size distribution. Figure 8(a) corresponds to the initial structure for which R = 1.72nm, a = 0 . 4 3 n m , N = 1.7×1012cm -z and Se=27~o. For the film irradiated for 10min with a beam of energy Ep = 2 keV and current density

880 400 880 300 500 300

Au/SiOx Au/SiOx Au/C Ag/C In/SiOx Ag/MgO

0 1000 0 40 1000 70

j (mAcm

2)

4.5 7.4 5.6 7.5 17 6

R (nmt

1 4.3 1.4 2.3 9.8 1.8

a (nm)

4.4 0.2 2.4 0.6 0.1 1.9

N × 10 11

21 5 25 11 13 24

S (~i,)

" T h e process is c o n t r o l l e d by c o a l e s c e n c e a n d the l o w e r limit of DB is i n d i c a t e d .

~ (K)

Sample

2 -2 a 0 -1 -2 a -2 a

s

T A B L E II ISLAND MIGRATION COEFFICIENTS AND ACTIVATION ENERGIES FOR VARIOUS SAMPLES

2 × 10 -16 3 x 10 13 3 x 10 14 10 -15 2 x 1 0 13 101~

Dn (cm2s-l)

3 x 10 -11 4 x 1 0 13 3 × 1 0 14

DBAI~s (cm2s-1)

1) 6 x 10 -17 7 x 10 is 3 x 10- 16 2 x 10 12 2 × 1 0 13 2x 10-1s

DBj (cm2s

l0 14 10-~s

10 -16 10 1,* 10 16

D (cmas

1)

0.67

2.3 0.91 2.1 0.66

Ed (eV)

<

,..]

4~

STIMULATED COALESCENCE IN DISCONTINUOUS

METALLIC FILMS

145

j = l m A c m -2 (Fig. 8(b)), R = 3 . 4 n m , a = 1.53nm, N = 2 . 4 × 1 0 1 1 c m -2 and Se = 1 1 ~ at a substrate temperature T~ of 400 K. Figure 8(c) corresponds to the system Au/SiOx annealed at T~ = 400 K for 1 h. Here R = 2.02 nm, a = 0.72 nm, N = 1.6 × 1012cm -2 a n d S e = 23~o. C o m p a r i s o n of the histograms shows that as time elapses R increases and thus the distribution function shifts towards larger values of R and broadens. This is characterized by an increase in tr with time and a corresponding decrease in N and S~. It can be seen (Fig. 8(c)) that thermal annealing for 1 h at T~ = 400 K changes the distribution function less drastically than the 10min irradiation at the same temperature does. N. I0"~f cm ~2

Is

(a)

N. |0-1~ cm-2

(e) u

/ 3

R,nm

(b) ~ i

"

t___.I 3

5"

7

Rnm

Fig. 8. Size distribution histograms of gold islands on SiOx: (a) initial structure; (b) after electron irradiation (Ep=2keV; j = l mAcm-2; t = 10min); (c) after thermal annealing (T~=400K; t = 60 min). The knowledge of R, or, N, S and Se at different times makes it possible to determine the effective coefficient DB of island migration, according to Kashchiev 12, from the following relationships: N(t)

= KoS3(S3Qot

) - 3/(s

+

3)

(l)

B.G. ATABAEVet al.

146

R(t)

~oo(S3Qot) l.'ls+ 3)

=

1

=

(S3Qot) 2 / ( s + 3~

(2)

(3)

S(t) = ~K2S3(S3Qot) ~ 1/t~+3~

(4)

Se(t ) = 4Ttg(O)KzS3(S3Qot) 1/1~+37

(5)

where D B = DoR ~, Qo = 4neDo (e is a factor c o n s i d e r e d to be a n u m b e r between 0.2 a n d 0.5), $3 = 3d/4nf(O), f(O) a n d g(O) are functions of the wetting angle 0 of the islands, and the values of the c o n s t a n t s Ko, K1 a n d K 2 d e p e n d only on s. The p a r a m e t e r s characterizes a process which c o n t r o l s the coalescence: at s > 0 the coalescence is d e t e r m i n e d by island m i g r a t i o n , at s < 0 it is c o n t r o l l e d by island fusion a n d at s = 0 it is c o n t r o l l e d by b o t h processes, s can be d e t e r m i n e d from any of eqns. (!) (5) (in our case for t > t* = 5 min). T h u s we can d e t e r m i n e Do by several m e t h o d s using the change with time in the m e a n characteristics of a D M T F . A m o r e reliable e s t i m a t i o n of D o is achieved by a v e r a g i n g the values o b t a i n e d for Do. C o m p a r i s o n of Da values for A u / S i O x in the case of a n n e a l i n g a n d i r r a d i a t i o n (Table II) shows that the effective m i g r a t i o n coefficient u n d e r electron i r r a d i a t i o n is two o r d e r s of m a g n i t u d e higher than that u n d e r annealing. This indicates the s t i m u l a t i o n of the m i g r a t i o n a l coalescence process by electron irradiation. A n a l o g o u s results were o b t a i n e d for the o t h e r systems. It is also possible to estimate Da using the m o d e l p r o p o s e d by Shiojiri et al. ~3 for the g r o w t h of an island with the average r a d i u s g in an inert gas a t m o s p h e r e for the t h r e e - d i m e n s i o n a l case. C o n s i d e r i n g the t w o - d i m e n s i o n a l case for coalescence on the surface after m o d i f i c a t i o n of expression (1) in ref. 13 we o b t a i n

~3 _

3DBjdt

[_Ro 3-

(6)

1 + 3(o/R) 2 The values of DBj = Do/R c a l c u l a t e d for different systems are listed in T a b l e II. It is interesting to note that, using an even m o r e primitive model, in m o s t cases we o b t a i n the same o r d e r of m a g n i t u d e for DR. A c c o r d i n g to this m o d e l the island m i g r a t i o n is of the b r o w n i a n type, the coalescence is very fast a n d DB = /5 does not d e p e n d on R. In a d d i t i o n , f(t) is essentially c o n s t a n t d u r i n g the time z between the two successive coalescence acts. T h u s for S in the case of unit surface a r e a we have

S(t) = 7z .f rZf(r,t) dr Thus the m a x i m u m a r e a which can be covered by the ensemble of m o v i n g islands will be 1 - S a n d we can write

N AS = 2N R(2Dz) 1/2 = 1 - S where AS is the a r e a covered by one m o v i n g island. The collision frequency will be

STIMULATED COALESCENCE IN D I S C O N T I N U O U S METALLIC FILMS

147

equal to 1

8N2R2/) (1 - S ) 2

The n u m b e r of islands taking part in the coalescence during dt is 1

8 N 3/)1~ 2

- N dt - r

-

(l - - 8 ) 2

dt

If it is assumed that only two islands m a y interact we have for the coalescence rate dN 4N3/)R 2 dt - ( l - S ) 2

(7)

The/15 values estimated according to eqn. (7) are presented in Table II and it can be seen that they coincide sufficiently well with DR and DBs. F o r the system Ag/Si after 20 min of irradiation, islands of radius a b o u t 0.3 gm are formed. These are easily observed even in a scanning electron microscope (Fig. 9). O w i n g to the resolution of the scanning electron microscope it is impossible to consider the role of small particles when calculating D O.

(a) (b) (c) I 0.8 g m ! Fig. 9. M o r p h o l o g i c a l changes in a silver island film on silicon u n d e r electron i r r a d i a t i o n (Ep = 2 keV; j = 350 taA cm 2): (a) t = 0 m i n ; (b) t = 10 rain; (c) t = 20 min.

3.4. Determination of the effective coefficients of brownian migration using Auger electron spectroscopy Shigeta and Maki 14 and A n t o n 15 have concluded that it is possible to use Auger electron spectroscopy (AES) to determine the coefficient S of the surface coverage with islands. Moreover, according to Kashschiev 12, S e ~ 1-48 and it is also possible to determine the total exposed area from the normalized Auger signal I. We found that SAE S = 1.5--2STEM. In the case of AES the islands with R < 1 nm are included in the value of S, and that is why SA~S > STE~. Figure 10 shows the island size distribution functions obtained by T E M and the corresponding relationship Se(t) oc lAg(t) obtained by AES for Ag/C. Approximating the experimental curve Se(t) by the least-squares method, we obtain Se(t ) ~, At-b where b = 1Is + 3 and t > t*. The deviation between the two curves is no m o r e than 10%; thus S can be determined and it is also possible to calculate D o from eqn. (4) as well as from ref. 12, eqn. (3.13). Substituting in eqn. (4) g(O) = f(O) = 0.5, e = 0.2,

B.G. ATABAEVet al.

148

d = 3 n m and k= from ref. 12, Table 1, for each value of s obtained, we can calculate DogEs a n d then DBAES = DOAEs/RS. The results are presented in T a b l e II. In the case of In/SiOx the data almost coincide with those from T E M while for Ag/C and A g / M g O the coefficients D , calculated from AES data are one order of m a g n i t u d e higher. This is because using AES we take into a c c o u n t the islands with R < 1 nm. C o m p a r i n g the b values of Se(t) for various samples, we can estimate the coalescence rate: the greater b is the quicker Se decreases with time (Fig. 10). F o r c o m p a r i s o n , S(t) values for Au/SiO~ o b t a i n e d from T E M studies are presented in Fig. 1 1. N.tu -tO , cm-2

30

60

R,nm

, I N. f 0 9 . . , -~

|0', I

B%

L = t5 rain

(a)

5

tO

R,

,~

20

I 200

~ ......

//i 100

C

~

~

10

C t = f

10

J

r

2O

i

i

3 0 t.,min

(b) tO 20 30 q~o tz, rain Fig. 10. (a) Island size distribution of a silverfilmon carbon for differentirradiation times; (b) Auger peak amplitudes 1 (in arbitrary units) of silver and carbon vs. irradiation time (d ~ 2.5 nm; Ep- 2keV: j - 60 p.A cm - 2). Fig. 11. The coverage coefficientS (determined by TEM) as a function of the irradiation time of a gold film on SiOx(Ep = 3keV;j - 1 mAcm z).

3.5. Estimation of the activation energy Eo of islandmigration The activation energy E a of island m i g r a t i o n can be d e t e r m i n e d according to Philips et al. a6 (eqn. (13')) from the expression

Rv/2=l.82t~Z\~-

/

exp

t+

(8)

where M is the island mass per unit area, p is the density of the film material a n d R o is the initial m e a n radius of the islands. F r o m the E a values presented in Table II it can be seen that the E a value for electron i r r a d i a t i o n of the Au/SiOx system is a b o u t 1 eV less than that for thermal annealing.

3.6. Results and discussion of the migrational coalescence model in an ensemble of interacting islands The results can be explained according to the m i g r a t i o n a l coalescence model in

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149

an ensemble of interacting islands. The random migration of the islands occurs as a result of the action of an external force which varies unpredictably in both direction and magnitude and in our case is a result of the electrostatic interaction between the charged islands on the charged substrate. To determine the value of the fluctuating force F acting on an island having a unit charge in a similarly charged ensemble of particles, we use the statistical methods of a gravitational field, developed by Chandrasekhar 17. It is necessary to distinguish between the action of the whole system on a given island and that due to the local action of the nearest neighbours to the island: the first action is a slowly varying function of the coordinates and time, while the second is a rapidly varying function. The influence of the whole system can be expressed through the Coulomb potential U(r, t), which is a function of N(r,q, t), the mean two-dimensional spatial distribution of islands of different charges q at time t:

U(r,t)=

f; f; qN(r'q't~) l-r[

(9)

The potential U(r,t) characterizes the "smoothed" charge distribution in an ensemble of charged particle. Thus the force acting on an island of unit charge due to the whole system is given as K = - grad{ U(r, t)}

(10)

However, as a result of the fluctuations in the distribution of the nearest islands and their charges, the instantaneous force acting on the island does not correspond to eqn. (10). To determine the nature of such fluctuations, let us consider a given island to be surrounded by an elementary area which is small enough to contain only a few islands. At any m o m e n t this number will not coincide with the mean expected number, i.e. with N, because of the fluctuations, which obey the Poisson distribution for the variable N,. The influence of the nearest surroundings on the given island will vary with time owing to the change in the number of islands in an elementary area. The mean period of such fluctuations is determined by the time T needed for two islands to separate by the mean distance for the system. This time is much less than that required for a change in the island distribution of the whole system to occur. Thus the total force acting on an island of unit charge can be expressed as

= K(r,t)+F(r,t)

(11)

where F is the fluctuating force due to the nearest surroundings. Let At be a time interval larger than T when

At = K A t + f ( t +At, t)

(12)

where

6(t + At, t) =

ft t+AtF(~) d~

For the given conditions of At >> T, the values of6(t + At, t) and 6(t + 2At, t + At), corresponding to two successive time intervals, must not correlate with each other.

B.G. ATABAEVet al.

150

There must be a certain distribution law for the probability of the establishment of different values of6(t + At, t). If we suppose that F is determined mainly by the nearest island, we can determine the stochastic probability distribution W(F) for the particles with a Coulomb potential interaction. Using the distribution law of nearest neighbours (ref. 14, eqn. (671))

W(r) = e x p ( - nrZN)2nrN

(13)

and substituting

r = ( < Q > m ~ 1/2 we obtain

W(V) = exp

t g(Q)m2 x](7~(Q)m2~l:2 ~

]\

e,~f

/

U

(14)

with the most probable value

Fp --

(15)

N(Q)m2

2eoe

where (Q)m is the mean charge on the islands. According to ref. 14, eqn. (595), if the island velocity V = 0, the mean force (F)m acting on it is zero; if V.F > 0, then IFI increases and it can be supposed that the coalescence probability must increase; if V.F < 0, then IFI decreases. In an ensemble of similarly charged islands, pair interactions are also possible but only at large differences in island radii (Marcus-Joyce mechanism) 18 According to Geguzin and Kaganovskii TM the experimentally measured coefficient OBqof island migration under the action of an external force is determined by the excess of the work of the force for an elementary j u m p over the thermal energy and is given by

D.q =

lF

~-DBT

(16)

where DBv is the migration coefficient under thermal activation, I is the length of the elementary jump, which has the physical meaning of the "mean free path" at constant F. In our case F = Fp and

lN~Q~m 2

DBq-- kTf:oe Day Substitutingl= 10-s-10 we obtain

DBq =

10-2-10

(17) 7m19, N =

10 ~Sm Z , T = 4 0 0 K a n d ( Q ) m =

10 18C,

3D,T

which is in good agreement with the experimentally determined migration coefficients. N is determined by T E M and (Q)m is estimated from the shift in the Auger peaks due to surface charging: (Q)m = 4~eoRV (V = 10 V; R = 10 8 m).

STIMULATED COALESCENCE IN DISCONTINUOUS METALLIC FILMS

151

Irradiation of a liquid D M T F in the system In/SiOx is a good illustration of migrational coalescence, where the instantaneous fusion of islands takes place. Electron irradiation results in enlargement of islands, and some of them leave behind tracks that are free of material (Fig. 12). Since the tracks are formed behind the large islands, the latter must have velocities higher than those of the fine particles. This effect cannot be explained on the basis of thermal brownian motion. Obviously, the high velocity of large islands can in our case be explained by additional electrostatic forces due to charging of the islands. Analogous effects were observed when the systems Ag/SiOx, Ag/C and Si/SiOx were irradiated.

I

I

400 n m Fig. 12. Coalescence of i n d i u m islands o n SiOx u n d e r electron i r r a d i a t i o n (T~ = 300 K ; Ep = 2 keV; D = 1018 electrons cm 2).

4.

ORIENTATIONAL

MONOCRYSTALLINE

EFFECTS

KC1

IN

IRRADIATED

DISCONTINUOUS

GOLD

FILMS

ON

SURFACES

4.1. Influence of substrate temperature on the orientation of a discontinuous gold thin film The degree of orientation in the system Au/KCI was estimated using the microdiffraction patterns from regions of size 1 ~m and from the analysis of the dark field image associated with the bright field image. A study of the influence of thermal annealing gave the following results. Annealing at Ts = 480 K for 16 min results not only in enlargement of islands owing to their coalescence but also in their acquiring epitaxial orientation. This is confirmed by the appearance of separate reflections on the 200 and 220 diffraction rings (Fig. 13). The formation of epitaxially oriented islands at this temperature has also been reported by Masson et al. 11 As a result of the migrational coalescence, as the islands fuse they transfer from the non-epitaxial (111) to the epitaxial (100) orientation and lose their mobility. A further temperature increase to T~ = 580 K does not result in noticeable changes in the morphology and orientation of the film. 4.2. Influence o f electron irradiation on orientation o f a discontinuous gold film Weak electron fluxes at Ep = 1 keV a n d j = 50 mA cm -2 were used to prevent surface heating by the beam. To determine the influence of the substrate temperature under irradiation conditions, the samples were fixed on holders with a temperature

152

B.G. ATABAEVet al.

(a)

(b)

(c)

I

!

100 nm

(d) Fig. ! 3. Morphological changes in a gold film on KCI under thermal annealing at various temperatures (t - 16 min): (a) 300 K ; (b) 380 K; (c) 4-80 K ; (d) 580 K.

gradient of 0.1 K m m - I and irradiated with a scanning beam to a dose D ~ (5-10) × 1015 electrons cm 2. The o p t i m u m temperature for irradiation of a D M T F (d = 1.5-2 nm) was found to be about 430 K. Figure |4 shows the micrographs and diffraction patterns from a gold film deposited onto KCI at ~ = 300 K. The initial structure contains islands of mean radius R ~ 2 n m with a preferred orientation of (l l l). Electron irradiation (D ~ 1016 electrons cm 2; Ep = 1 keV; j = 5 0 g A c m -2) for 103s caused a migrational coalescence of the islands, the mean island radius increasing to 10-20 nm, with a preferred orientation of(001) (Fig. 14(b)). This is confirmed by the appearance of the separate reflections 200 and 220. The centre of Fig. 14(b)) shows the dark field image of the film in the reflection 111, which corresponds to the multitwinned islands 11. Thermal annealing at ~ = 430 K for t = 16 min (Fig. 14(c)) leads to less m a r k e d changes. Such a film contains islands of a smaller mean size, and the concentration of those with the non-epitaxial orientation (111) is higher than that in the previous case. To estimate the fraction of islands with the epitaxial orientation, we used the criterion ~ = Nzoo/N111, where N2oo is the island concentration in the dark field

153

STIMULATED COALESCENCE IN DISCONTINUOUS METALLIC FILMS

(a)

(b)

I

I 100 nm

(c) Fig. 14. Morphological and orientational changes in a gold film on KCI: (a) initial structure; (b) after thermal annealing with irradiation (Ep = 1 keV, ~ = 400 K, D ~ 1016 electrons cm 2); (c) after thermal annealing without irradiation (T~ = 400 K, t ~ 15 min). The dark field images correspond to the 111 reflections.

image for the reflection 200, which corresponds to the orientation (100), and N t 11 is the concentration for the reflection 111, which corresponds to the non-epitaxial orientation, particularly the twins. Figure 15 shows the parameter ¢ and the total island concentration N in the bright field image v e r s u s the electron beam dose for a gold film deposited at room temperature. Owing to the migrational coalescence, the island concentration decreases when the irradiation dose is increased. At the same time the parameter increases. At doses D ~ 5 × 1016 electrons cm -z a destruction of the KC1 surface occurs and ¢ decreases. Irradiation of the partially oriented island film deposited at T~ = 430 K improves the orientation, but the migration coalescence process becomes slower than that when the initial film has no preferred orientation. This may be seen from a comparison of curves 5 and 7 in Fig. 15. The island concentration of the non-oriented film decreases by about one order of magnitude when it is irradiated while that of the partially oriented film decreases by only a factor of 2. Thus it can be concluded that the influence of irradiation on the migrational coalescence diminishes if the islands are initially oriented. In analysing expression (15) for the most probable value of the fluctuating force as a function of N and ( Q ) m , we can consider the following cases. (1) At high values of N and (Q)m the force Facting on the island is sufficient to overcome the Coulomb barrier between similarly charged islands. This enhances the migrational coalescence, and the coalescence of two islands of orientation (111) results in an epitaxially oriented island. (2) At lower values of N and ( Q ) m a situation can arise in which Fis sufficient for migration but insufficient for the islands to become close enough for fusion.

B.G. ATABAEVet al.

154

0.8 ~

~

~ o

~

°

1

0.4

\~o 3

(a)

,

0-8/[

/

L

o ~

\ 4

/

"~o (b)

'

0.8

,

•

./

///

5 ,

"\

10 Is 0 D,el cmFig. 15. The parameter ~ and the island concentrations N in the bright and dark field for reflections 111 (Nl~l) and 200 (N2oo) as a function of the irradiation dose (Ts = 400 K ; j = 50 laA cm 2; Ep = l keV): (a), (b) non-oriented films; (c) partially oriented film. Curves 2, 4, 6, ~; curve 1, N 111 x 10- 9 cm 2; curve 3, N2o o x 1.6 x 10-8 c m - 2; curves 5, 7, N x 1012 c m - 2

Hence an island of orientation (111) can transfer to the orientation (100) during migration without coalescence, if it has sufficient mobility. (3) Finally, at low values of N and ( Q ) ~ the migration of islands is improbable. However, because of the long-order coulombic interaction, they can cooperatively transfer to another orientational state at certain critical values of T~and S and under the condition that S = lOT~/3al(r), where al(r ) is the energy of interaction between islands 2°. The appearance of texture or epitaxy is due to the rotation of the islands because of electrostatic interaction. 5. AUTOCOALESCENCE IN IRRADIATED DISCONTINUOUS METALLIC THIN FILMS

We observed that electron irradiation affects the shape of some islands and the channel width in a D M T F of grid-like structure. This indicated a certain role of electron irradiation in autocoalescence processes. In Fig. 5 it can be seen that irradiation of irregularly shaped islands of gold on SiOx promotes their transformation to the equilibrium spherical shape. Irradiation of an Au/SiO~ grid-like film (D ~ 10 TM electrons c m - 2 ; d = 6 nm) results in the appearance of an ensemble of separate islands (Fig. 16). Electron b o m b a r d m e n t of such films with a greater effective thickness leads to the broadening of the channels. In D M T F s on monocrystalline surfaces, as well as a tendency to acquire an equilibrium form the island volume undergoes an intense recrystallization.

STIMULATED COALESCENCE IN D I S C O N T I N U O U S METALLIC FILMS

155

I

4 100nm

(a)

(b)

Fig. 16. A u t o c o a l e s c e n c e in a gold island film (d - 6 nm) on SiOx u n d e r electron i r r a d i a t i o n : (a) initial structure; (b) after i r r a d i a t i o n (Ep = 2 k e V ; j = 1 m A c m - z; D .~ 10 ~s electrons c m - 2 ; Ts = 400 K).

Figure 17 shows micrographs of an Ag/MgO film after annealing for 3 h at T~ = 600 °C. Inhomogeneities are clearly seen; these are due to the boundaries of different orientations in the island volume. These inhomogeneities disappear after electron irradiation because of the recrystallization (Fig. 17(b)). The diffraction patterns of the irradiated film show a smaller number of reflections on the 111,200 and 220 rings than do the non-irradiated films (Table III) and the reflection intensity ratio I 2 o o / I 1 1 1 increases. According to Iwama and Sahashi El, this indicates a decrease in grain boundary disorder of the (! 1 l) planes in b.c.c, metals.

(a)

I

! 200 n m

(b) Fig. 17. A u t o c o a l e s c e n c e in silver islands on M g O : (a) after t h e r m a l a n n e a l i n g (T~ = 873 K ; t = 180 min); (b) after electron i r r a d i a t i o n (Ep = l keV, j = 80 ~A cm 2, T = 880 K, t = 30 min). T A B L E lII NUMBER OF REFLECTIONS IN THE DIFFRACTION RINGS FROM SILVER ISLANDS ON MONOCRYSTALLINE M g O Rmg

Annealing at ~ = 900 K

Irradiation at ~ = 900 K a n d D = 101Selectronscm

lll 200 220 311

200 160 208 280

136 90 120 136

2

156

B.G. ATABAEV et al.

T h e i r r a d i a t i o n effect c a n b e e s t i m a t e d t h r o u g h t h e t i m e ra n e e d e d f o r t h e i s l a n d t o t r a n s f o r m t o t h e e q u i l i b r i u m s h a p e . T h e m a x i m u m v a l u e o f r , in o u r e x p e r i m e n t s is a b o u t 103 s. D r e c h s l e r et al. 22, s t u d y i n g m o r p h o l o g i c a l c h a n g e s in g o l d d e n d r i t e s o n c a r b o n , f o u n d t h a t at ~ ~ 800 K n o t r a n s f o r m a t i o n t o t h e s e m i e q u i l i b r i u m shape was observed. REFERENCES l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

P.G. Borziak and Y. A. Kulyupin, Electronie Processi v Ostrokovikh Metallicheskikh Plenkakh, Naukova dumka, Kiev, 1980, p. 134. B.O. Seraphin and A. B. Meinel, in B. O. Seraphin (ed.), Optical Properties o f Soli& New Developments, North-Holland, Amsterdam, 1975, p. 927. C . K . Chen, A . R . B . d e C ~ s t r o a n d Y . R. Shen, Phys. Rev. Lett.,46(1981) 145. V.M. levlev, L. I. Trusov and V. A. Khalmyanskii, Structurnie Prevrascheniya v Tonkikh Plenkakh, Metallurgiya, Moscow, 1982, p. 248. E.M. Dubinina, S. S. Elovikov and V. P. Novojilov, Thin Solid Fihns, 37 (1976) 7. E.M.Dubinina~S.S.E~vik~vandA.V.Ivan~v~zv.Akad.NaukS.S.S.R.~Ser.Fiz.,24(~979)738. E.M. Dubinina, S. S. Elovikov, A. S. Ovayanitskii, G. P. Netishenskaya and E. P. Kirilenko, Vestn. Mosk. Univ., Fiz., Astron., 20 (1979) 54. S.A. Fridrikhov and A. R. Schulman, Vtoriehno-emissionnie Methodi Issledovaniya Tverdikh Tel, Nauka, Moscow, 1977. Ya. E. Geguzin, Yu. S. Kaganovskii, V. V. Kalinin and V. V. Slyosov, Fiz. Tverd. Tela (Leningrad), 12 (1970) 1953. Ya. E. Geguzin and Yu. S. Kaganovskii, Usp. Fiz. Nauk, 125 (1978) 489. A. Masson, J. J. Metois and R. Kern, Surf Sei., 27 (1971) 463. D. Kashchiev, Sur[] Sci., 55 (1976) 477. M. Shiojiri, C. Kaito, H. Sasaki and K. Fujita, Proc. 6th Int. Con[~ on Crystal Growth, Rasshirennie tezisi, Vol. 1, Rost iz gazovoi fazi, Nauka, Moscow, 1980, p. 149. Y. Shigeta and K. Maki, Jpn. J. Appl. Phys., 18 (1979) 71. R. Anton, Vak.-Tech.,23(1974) 172. W.B. Philips, E. A. Desloge and J. G. Skofronick, J. Appl. Phys., 39 (1968) 3210. S. Chandrasekhar, Rev. Mod. Phys., 15 (1943) 1. R.B. Marcus and W. P. Joyce, Thin Solid Films, 7 (1971) 3. GI.S. JdanovandT. A. Cousova, lsv. Akad. NaukS.S.S.R.,Ser. Fiz.,47(1983) l191. L.I. Trusov, E. I. Kats, V. I. Novikov and M. A. Kusenkovm Kristallografiya, 27 (1982) 566. S. lwama and T. Sahashi, Jpn. J. Appl. Phys., 19 (1980) 1039. M. Drechsler, J. J. Metois and J. C. Heyrand, Surf Sci., 108 ( 1981 ) 549.