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Nucleation and growth of thin gold films on NaCl(100) cleavage planes under carefully controlled conditions
Thin Solid Films, 192 (1990) 163 171
163
PREPARATION AND CHARACTERIZATION
N U C L E A T I O N A N D G R O W T H OF T H I N G O L D FILMS ON NaCI(100) C L E A V A G E PLANES U N D E R C A R E F U L L Y C O N T R O L L E D CONDITIONS R. CONRAD AND M. HARSDORFF lnstitut fffr A ngewandte Physik, Universitiit Hamburg, Jungiusstrafle 1, D 2000 Hamburg 36 ( F. R.G. ) (Received March 19, 1990; accepted May 14, 1990)
In the past, in different research groups, the nucleation and growth of thin metal films on different substrates have been studied. The results can be discussed on the basis of the kinetic nucleation model. Velfe e t al. and Robins demonstrated a reduction in the number density of crystallites if the bombardment of the substrate surface with charged particles during condensation is strictly avoided. In the present paper the trend and results of these investigations are confirmed. Additionally the behaviour of condensation coefficients, average diameters and cluster size distributions under these ultraclean conditions has been studied.
l. INTRODUCTION
The experimental results published by Velfe e t al. 1 in 1982 revealed a basically different behaviour of nucleation and growth than obtained in preceding investigations by other workers. The cluster densities were lower by a factor of about 25 under comparable experimental conditions, and a different dependence on time was observed. In contrast with previous investigations the initial cluster density did not increase linearly with the deposition time, but the measured dependence could be described by a t 1/3 law within the whole studied range. These discrepancies led to further investigations by other groups; these investigations show an influence of substrate damage by charged particles during nucleation experiments, which had been previously disregarded 2' 3. Two consequences arise at the theoretical level. The interpretations of the experiments carried out before 1982, by the use of the rate equations evaluated by Zinsmeister 4 and Venables 5 under the assumption of an ideal and defect-free condition of the substrate should be reconsidered. A first attempt to do this has been made by Usher and Robins 2. The theoretical model of Zinsmeister can be summarized as follows. The behaviour of single atoms striking the surface is determined by the energies of adsorption and of surface diffusion. It is assumed that the surface is homogeneous and isotropic. In the simplest case, only single atoms are 0040-6090/90/$3.50
~? Elsevier Sequoia/Printed in The Netherlands
]64
R. ('()NRAI), M. HARSI)ORFf"
able to diffuse and re-evaporate. The nucleation and growth of clusters are caused by collisions of diffusing single atoms with other atoms or larger clusters. The rate equations describe the temporal changes in concentrations of single atoms, dimers, trimers etc. on the surlace. The solution of these equations shows a dependence of n x ~ t (nx is the cluster density and t the evaporation time) for low evaporation times. This theoretical treatment does not lead to a correct description of the experiments as observed by Velfe et al.t. The nucleation and growth on highly purified NaC1 crystals are therefore determined by other basic processes than supposed previously. An interpretation of the experimental results of ref. I has been given by Velfe and Krohn ~ and by Gates and Robins 7 in different ways. A short rasum6 of the statements and results is given in Section 3. In the present experimental study the reproducibility of the results published by Velfe et al. 1 should be tested under carefully controlled experimental conditions. Additional evaluations of the cluster growth should give further information for the theoretical discussion. 2. EXPERIMENTAL RESULTS
Two sequential series of depositions were produced, showing the temporal development of the condensation process and its dependence on deposition rate and substrate temperature in order to compare the observed behaviour with the data of Velfe etal. (The range of deposition rate variation at T = 423K is 8.4x 10tlcm 2s t ~< R ~<2.5× 1014cm 2s l: the range oftemperature variation a t R = 1.7x1013cm 2s t i s 2 9 8 K ~< T~<473K.) The specimens were prepared under clean ultrahigh vacuum conditions to reduce the influence of residual gases. The b o m b a r d m e n t of the substrate surface with charged particles was avoided by shielding the ionization gauge and the quadrupole mass spectrometer used for flux regulation. Furthermore a newly constructed irradiation-heated Knudsen cell was used for the gold evaporation. An electrostatic field in front of the surface deflects the rest of the electrons and ions. The gold films were analysed using transmission electron microscopy (Philips CM 12), quantitative image analysis (Quantimet 720, Cambridge) and energydispersive X-ray microanalysis in a scanning electron miscroscope (Philips PSEM 500+ EDAX 9100). The experimental results are as follows. 2.1. Dependences ql'cluster density on deposition p a r a m e t e r s
In Fig. I the dependence of the cluster density on deposition time and rate is shown. The observed temporal developments were congruent with regression lines describing a power law n x ,~c t s (n~ is the cluster density, and t the deposition time). In Fig. l(b) the slopes S are plotted vs. deposition rate in comparison with the dependence measured by Velfe et al., which is plotted as a broken line. The data do not confirm the curve exactly but tend to higher values. The determined slopes are within the interval 0.33 ~< S ~< 0.51. In Fig. l(c) the dependence of cluster density on deposition rate is shown. The plotted line reveals a power law with an exponent of 0.34_+ 0.01. So the dependence
NUCLEATION AND G R O W T H OF A u ON
NaCI(100)
165
N
cn~z
j~
S
SUBSTR ATE TEMPERATURE TIKI: /.23
J
DEPOSITIONRATE
10 ~°
~
10 9
(a)
1'0
100
8,/-1011
1000
0,5 .
.
.
.
.
.
. . . .
l
i
1012
i
1013
10lt"
(b)
R
cm2[
N {,]" ~cm
10 9
4.--0"i
1012
(c)
i
1013
i
101.'
R c~;2~ )
Fig. I. Dependence of the duster density on deposition time and rate: (a) temporal development of the cluster density at variable deposition rate; (b) slopes S of the regression lines plotted in (a) vs. deposition rate; (c) Nit s as a function of deposition rate. published by Velfe et al., nx ~- R m with m ~ ½is confirmed. I n a d d i t i o n the position of the curves, which were observed in b o t h investigations, are f o u n d to be identical. T h u s the cluster densities agree sufficiently, a l t h o u g h the e x p o n e n t s of the time d e p e n d e n c e are different, as m e n t i o n e d above.
]66
R. ( ( ) N R A I ) ,
M. I I A R S I ) ( ) R H
The clear deviation of the cluster densities determined at the two lowest deposition rates from lhe plotted curvc in Fig. Ilc} can probably bc cxplamed by a decreased influence of adsorbates. Owing to a lower temperaturc in the gokl evaporator, lhe pressure oflhe residual gases was reduced during nucleation in these cascs.
In I-ig. 2(a) the dependence of cluster density on substrate temperature i> shown. To test reproducibility, several series were produced at at constant substratc temperature. The plotted lines with slopes olJ~ should approach {tic observed dependence, taking all data into consideration. (Only the last broken lmc of stope J~ does not lit the data observed at 473 K: the regression line has a slopc of 0,7,1 It can be seen that the fluctuation of the data obtained from different scries under the same experimental condilions is greater than the expected statistical variation of about
N m~
J ,L
Jf
A
j JJ ~A v
]
• j -
)
Ik:b" P :,:i} "
1FI
~
v
" F~,a P E a
qll,
2~ "iJ ,<~
2';8
/:
10~ 100
10 Ia I
!000
:::<
T /-73
~23
373
323
298
<
A
q-
g
s~o
i 21o
(hi
'
'
2',s
3;0 T
Fig. 2. D e p e n d e n c e of the cluster density on d e p o s i t i o n time ~.llld temperature: I~.l) d u s t e r densil',, as a ['unction of d e p o s i t i o n time at xariable s u b s l r a t e temperatures: Ibl l o g a r i t h m i c plot of N t s ~,s. reciprocal lcnaperal
tire.
NUCLEATION AND GROWTH OF A u ON
NaCI(100)
167
+_lO'~/o.This complication concerning the interpretation of the experimental results has already been mentioned by Velfe et al. A large fluctuation in the data is also visible in Fig. 2(b), where Nit s is plotted vs. 1/T. Further, the cluster densities observed at 373 K are unexpectedly low. Many of the data plotted in Fig. 2(a) are less than the densities determined at 423 K. The reason for this behaviour, which cannot be explained with thermodynamical arguments, is not yet understood. Nevertheless, the energy of 0.10 eV calculated by Velfe et al. could be determined with a least-squares fit. The slope of the broken line indicates an activation energy E of 0.12 +0.01 eV. 2.2. Dependence of condensation coefficient on deposition parameters In Fig. 3 the temporal developments of the integral condensation coefficients which were calculated from the average mass coverages measured by X-ray microanalysis are shown. The curves determined at 423 K with various deposition rates (Fig. 3(a)) show that the condensation is incomplete. It can be seen that the integral condensation coefficients observed at deposition times of up to 1000s with rates below 2 x 1013cm 2 s-1 are not higher than 0.2. If the deposition rates are higher, the condensation coefficients increase quickly at the beginning of nucleation. This behaviour is caused by the quicker increase in the relative covered area. In Fig. 3(b) the dependence of the condensation coefficient on temperature is shown. It should be mentioned that the determined condensation coefficients of the deposits produced at 298 K and 323 K are nearly 1 for relatively short deposition times (100 s and 200 s respectively). On the contrary, less than 40~o of the available material condensed at the highest deposition times if the substrate temperature was higher than 373 K. It can be stated that the experimental results published by other research groups 1,8,9 are in rough agreement with the present results. 2.3. Investigations concerning the growth behaviour Cluster growth can be caused by the capture of diffusing single atoms, by the direct impact of atoms from the vapour and by coalescence caused by cluster mobility and growth. The predominance of one of these processes can be recognized in the shapes of the cluster size distributions of the deposits 1° In Fig. 4 the temporal developments of the cluster size distributions are shown. The distributions determined at short deposition times have a nearly symmetrical shape around the maximum. Island growth which is caused predominantly by the capture of diffusing single atoms, on the contrary, shows a relatively slow increase followed by a sharp maximum and a sharp decrease. At the very beginning of condensation the influence of the direct impact of atoms from the vapour can be neglected, as well as growth coalescence, so that a noticable influence of coalescence caused by cluster mobility can possibly explain the observed shape of the curves. The increasing flanks of the cluster size distributions become flatter with increasing deposition times. In addition the distributions have only one maximum up to the longest deposition time of 1000s. A shape with two local maxima, from which the absolute maximum appears at the smaller diameter (to be expected if
168
R. ('()NRAI), M. HARSDORFF
,/
Off
/ !
0,4 t
SUB STRA1 E TEMPERATURE
./
0,3
DEPOSI TION R A I E
m
0,2
~/
0,1 /// 500
(a) *
1000
e ~
)C '3
29
lO !3
•
I'
12 '3
o
~. f)
:012
22
~012
Lt sec
[
DEPOSITION [¢m2s I'
RATE ' 7 ~013
SUBSIRATE
TEMPERATURE
" LK 1
298
v4
: :
J
)/, 500
]27 I
373
~
.~23
i~
~73
!000 't
Fig. 3. Dependence of the integral condensation coetticients
ondeposition time.
growth coalescence is dominant), was not observed. According to Venables 5 a single maximum is caused by mobility coalescence. In order to study the temporal development of growth as a function of deposition rate and temperature, the diameters dM associated with the maxima in the size distributions were evaluated. The experimental results plotted in Figs. 5 and 6
NUCLEATION AND GROWTH OF A u ON
NaCI(100)
169
bd 108cm2~ I
1000 sec
;000s; 7 100
200
300
d .7_ A
Fig. 4. Temporal developments of the cluster size distributions (substrate temperature, 423 K; deposition rate, 1.7x 10~3cm-Zs i).
SUBSTRATE TEMPERATURE T[K] ~23
dM
A
OEPOSITION RATE [3 7,5 1013
100
•,
2,g 1013
,c,
1,7
•
1,1 .1013
o
4,01012
,L
1013
2,2 1012 8,4.1011
~b
~6o
~o'oo
t sec
Fig. 5. Diameter dMobserved at the maximum of the size distributions as a function of time at various deposition rates.
can be d e s c r i b e d w i t h an e q u a t i o n of the f o r m dM oc t"' R m' exp ~-7= w i t h n' ~ ], ~ ½ a n d E = 0.03 + 0.01 eV. T h i s result c o u l d not be c o m p a r e d w i t h p r e v i o u s results, b e c a u s e of m i s s i n g e x p e r i m e n t a l data.
170
I~. ( ' ( ) N R A I ) , M. IIARSI)ORFI-
°v I
~a,7;c:. i t , 7 N ~ A ' ~
r Ii 50
.
:
}
i I'0 I lg 6
~.
100
Dcpcl/dencc
ofdi:lnlClcf
1000
t
l].q tttl dcpll-;lliOll [llllC ~1t \¢lllOUN Sl.lhMratc |ClllpCF~tlulc'~
('()?",( 1 [ S [ ( ) N
The dependence of the cluster densit~ on lhc deposition parameters, i.~~ ~
s l"R"exp
1,7
\~ith n ~ ~. nz -.- !~and E -= O. 1 c\". lirst observed b', Velfc el a/. could bc csseniiall} confirmed in this investigation. The ~alucs of m and Is could be reproduced tihc value of E here is 0.12~O.OleVi: the determined exponents n of the temporal dependence were bet'a een 0.3 and 0.5. A theoretical discussion of line process should therefore explain lids dependencc. In addition it should be considered that condensation is incomplete, as demonstrated by a condensation coelticient well below unit5. ('oncerning the investigations of the growth behaviour, it should be mentioned that the cluster size distributions obtained from the deposits have a broad, nearl~ symmetrical shape a r o u n d the maximum, and also ~_ll the smallest deposition times. This v~as interpreted as a possible indication of the influence of coalescence causcd b ; cluster mobilii\. The theoretical discussions published by Vellie and K r o h n " and bx Gates and Robins- both proceed from a mobility of small clusters which is not negligible. Krohn and Voile extcndcd the rate equations o f Zinsmeister by expressions which describe the mobility coalescencc of small submicroscopic clusters under the assumption of a monotonicall,, decreasing diffusion coelticient with increasing cluster size. In the case of mobilc dimers and trimcrs the experimentally observed dcpendencc of the cluster density on time and temperalurc could bc explained. However, the dependence n, ,' R ~ -~(for a not too high R) does nol coincide with the theoretical cxpression. Gates and Robins discussed a completely ne,a approach. According to their model, nucleation only occurs at surtace point defects. Concerning the experimental rcsuhs obtained bv rise of'ultraclean substrate crystals. a reasonable number of poinl defects arc present. Refcrrmg to the theoretical
NUCLEATION AND GROWTH OF AU ON NaCI(100)
171
discussions of the binding energies of small gold clusters on N a C ! surfaces given in refs. 11 and 12, Gates and Robins do not assume a m o n o t o n i c decrease in the diffusion coefficient with increasing cluster size. According to ref. 12, a range of cluster sizes exists where rigid base shapes for obtaining the potential m i n i m u m lead to high diffusion coefficients. If a cluster nucleating at a defect site exceeds this size, then it breaks away from the point defect and becomes mobile. The defect site is "reusable" for a further process of nucleation. The mobile microclusters grow owing to coalescence to form stable visible immobile clusters. In the desorption-controlled case the cluster density as a function of process parameters is given by nx _~ Gtl/3 R1/3 ex~{ Ea
Ed'~
with n x the cluster density, t the deposition time, G a constant depending only on atomic parameters, R the deposition rate, E a the energy of adsorption and E d the energy of diffusion. Therefore this model can explain the experimental observed dependences of the cluster density on all deposition parameters including the rate, Complete verification of the assumptions of this model by experimental results has not been done yet. ACKNOWLEDGMENTS We would like to thank the Deutsche Forschungsgemeinschaft for their support o f this research by providing parts o f the experimental equipment and personal funds. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
H. D, Velfe, H. Stenzel and M. Krohn, Thin Solid Films, 98 (1982) 115. B.F. Usher and J. L. Robins, Thin Solid Films, 149 (1987) 351,363. R. Conrad and M. Harsdorff, to be published. G. Zinsmeister, Thin Solid Films, 2 (1968) 497; 4 (1969) 363. J.A. Venables, Philos. Mag., 27(1973) 697. H. D, Velfe and M. Krohn, Thin Solid Films, 98 (1982) 125. A. D, Gates and J. L. Robins, Thin Solid Films, 149 (1987) 113. H. Stenzel, H. D. Velfeand M. Krohn, Krist. Tech., 15 (1980) 255. B.F. Usher and J. L. Robins, Thin Solid Films, 155 (1987) 267. J.A. Venables, G. D. T. Spiller and M. Hanbiicken, Rep. Prog. Phys., 47 (1984) 399. E.M. Chan, M. J. Buckingham and J. L. Robins, Surf. Sci., 67 (1977) 285. A. D, Gates and J. L. Robins, Surf Sci., 194 (1988) 13.
163
PREPARATION AND CHARACTERIZATION
N U C L E A T I O N A N D G R O W T H OF T H I N G O L D FILMS ON NaCI(100) C L E A V A G E PLANES U N D E R C A R E F U L L Y C O N T R O L L E D CONDITIONS R. CONRAD AND M. HARSDORFF lnstitut fffr A ngewandte Physik, Universitiit Hamburg, Jungiusstrafle 1, D 2000 Hamburg 36 ( F. R.G. ) (Received March 19, 1990; accepted May 14, 1990)
In the past, in different research groups, the nucleation and growth of thin metal films on different substrates have been studied. The results can be discussed on the basis of the kinetic nucleation model. Velfe e t al. and Robins demonstrated a reduction in the number density of crystallites if the bombardment of the substrate surface with charged particles during condensation is strictly avoided. In the present paper the trend and results of these investigations are confirmed. Additionally the behaviour of condensation coefficients, average diameters and cluster size distributions under these ultraclean conditions has been studied.
l. INTRODUCTION
The experimental results published by Velfe e t al. 1 in 1982 revealed a basically different behaviour of nucleation and growth than obtained in preceding investigations by other workers. The cluster densities were lower by a factor of about 25 under comparable experimental conditions, and a different dependence on time was observed. In contrast with previous investigations the initial cluster density did not increase linearly with the deposition time, but the measured dependence could be described by a t 1/3 law within the whole studied range. These discrepancies led to further investigations by other groups; these investigations show an influence of substrate damage by charged particles during nucleation experiments, which had been previously disregarded 2' 3. Two consequences arise at the theoretical level. The interpretations of the experiments carried out before 1982, by the use of the rate equations evaluated by Zinsmeister 4 and Venables 5 under the assumption of an ideal and defect-free condition of the substrate should be reconsidered. A first attempt to do this has been made by Usher and Robins 2. The theoretical model of Zinsmeister can be summarized as follows. The behaviour of single atoms striking the surface is determined by the energies of adsorption and of surface diffusion. It is assumed that the surface is homogeneous and isotropic. In the simplest case, only single atoms are 0040-6090/90/$3.50
~? Elsevier Sequoia/Printed in The Netherlands
]64
R. ('()NRAI), M. HARSI)ORFf"
able to diffuse and re-evaporate. The nucleation and growth of clusters are caused by collisions of diffusing single atoms with other atoms or larger clusters. The rate equations describe the temporal changes in concentrations of single atoms, dimers, trimers etc. on the surlace. The solution of these equations shows a dependence of n x ~ t (nx is the cluster density and t the evaporation time) for low evaporation times. This theoretical treatment does not lead to a correct description of the experiments as observed by Velfe et al.t. The nucleation and growth on highly purified NaC1 crystals are therefore determined by other basic processes than supposed previously. An interpretation of the experimental results of ref. I has been given by Velfe and Krohn ~ and by Gates and Robins 7 in different ways. A short rasum6 of the statements and results is given in Section 3. In the present experimental study the reproducibility of the results published by Velfe et al. 1 should be tested under carefully controlled experimental conditions. Additional evaluations of the cluster growth should give further information for the theoretical discussion. 2. EXPERIMENTAL RESULTS
Two sequential series of depositions were produced, showing the temporal development of the condensation process and its dependence on deposition rate and substrate temperature in order to compare the observed behaviour with the data of Velfe etal. (The range of deposition rate variation at T = 423K is 8.4x 10tlcm 2s t ~< R ~<2.5× 1014cm 2s l: the range oftemperature variation a t R = 1.7x1013cm 2s t i s 2 9 8 K ~< T~<473K.) The specimens were prepared under clean ultrahigh vacuum conditions to reduce the influence of residual gases. The b o m b a r d m e n t of the substrate surface with charged particles was avoided by shielding the ionization gauge and the quadrupole mass spectrometer used for flux regulation. Furthermore a newly constructed irradiation-heated Knudsen cell was used for the gold evaporation. An electrostatic field in front of the surface deflects the rest of the electrons and ions. The gold films were analysed using transmission electron microscopy (Philips CM 12), quantitative image analysis (Quantimet 720, Cambridge) and energydispersive X-ray microanalysis in a scanning electron miscroscope (Philips PSEM 500+ EDAX 9100). The experimental results are as follows. 2.1. Dependences ql'cluster density on deposition p a r a m e t e r s
In Fig. I the dependence of the cluster density on deposition time and rate is shown. The observed temporal developments were congruent with regression lines describing a power law n x ,~c t s (n~ is the cluster density, and t the deposition time). In Fig. l(b) the slopes S are plotted vs. deposition rate in comparison with the dependence measured by Velfe et al., which is plotted as a broken line. The data do not confirm the curve exactly but tend to higher values. The determined slopes are within the interval 0.33 ~< S ~< 0.51. In Fig. l(c) the dependence of cluster density on deposition rate is shown. The plotted line reveals a power law with an exponent of 0.34_+ 0.01. So the dependence
NUCLEATION AND G R O W T H OF A u ON
NaCI(100)
165
N
cn~z
j~
S
SUBSTR ATE TEMPERATURE TIKI: /.23
J
DEPOSITIONRATE
10 ~°
~
10 9
(a)
1'0
100
8,/-1011
1000
0,5 .
.
.
.
.
.
. . . .
l
i
1012
i
1013
10lt"
(b)
R
cm2[
N {,]" ~cm
10 9
4.--0"i
1012
(c)
i
1013
i
101.'
R c~;2~ )
Fig. I. Dependence of the duster density on deposition time and rate: (a) temporal development of the cluster density at variable deposition rate; (b) slopes S of the regression lines plotted in (a) vs. deposition rate; (c) Nit s as a function of deposition rate. published by Velfe et al., nx ~- R m with m ~ ½is confirmed. I n a d d i t i o n the position of the curves, which were observed in b o t h investigations, are f o u n d to be identical. T h u s the cluster densities agree sufficiently, a l t h o u g h the e x p o n e n t s of the time d e p e n d e n c e are different, as m e n t i o n e d above.
]66
R. ( ( ) N R A I ) ,
M. I I A R S I ) ( ) R H
The clear deviation of the cluster densities determined at the two lowest deposition rates from lhe plotted curvc in Fig. Ilc} can probably bc cxplamed by a decreased influence of adsorbates. Owing to a lower temperaturc in the gokl evaporator, lhe pressure oflhe residual gases was reduced during nucleation in these cascs.
In I-ig. 2(a) the dependence of cluster density on substrate temperature i> shown. To test reproducibility, several series were produced at at constant substratc temperature. The plotted lines with slopes olJ~ should approach {tic observed dependence, taking all data into consideration. (Only the last broken lmc of stope J~ does not lit the data observed at 473 K: the regression line has a slopc of 0,7,1 It can be seen that the fluctuation of the data obtained from different scries under the same experimental condilions is greater than the expected statistical variation of about
N m~
J ,L
Jf
A
j JJ ~A v
]
• j -
)
Ik:b" P :,:i} "
1FI
~
v
" F~,a P E a
qll,
2~ "iJ ,<~
2';8
/:
10~ 100
10 Ia I
!000
:::<
T /-73
~23
373
323
298
<
A
q-
g
s~o
i 21o
(hi
'
'
2',s
3;0 T
Fig. 2. D e p e n d e n c e of the cluster density on d e p o s i t i o n time ~.llld temperature: I~.l) d u s t e r densil',, as a ['unction of d e p o s i t i o n time at xariable s u b s l r a t e temperatures: Ibl l o g a r i t h m i c plot of N t s ~,s. reciprocal lcnaperal
tire.
NUCLEATION AND GROWTH OF A u ON
NaCI(100)
167
+_lO'~/o.This complication concerning the interpretation of the experimental results has already been mentioned by Velfe et al. A large fluctuation in the data is also visible in Fig. 2(b), where Nit s is plotted vs. 1/T. Further, the cluster densities observed at 373 K are unexpectedly low. Many of the data plotted in Fig. 2(a) are less than the densities determined at 423 K. The reason for this behaviour, which cannot be explained with thermodynamical arguments, is not yet understood. Nevertheless, the energy of 0.10 eV calculated by Velfe et al. could be determined with a least-squares fit. The slope of the broken line indicates an activation energy E of 0.12 +0.01 eV. 2.2. Dependence of condensation coefficient on deposition parameters In Fig. 3 the temporal developments of the integral condensation coefficients which were calculated from the average mass coverages measured by X-ray microanalysis are shown. The curves determined at 423 K with various deposition rates (Fig. 3(a)) show that the condensation is incomplete. It can be seen that the integral condensation coefficients observed at deposition times of up to 1000s with rates below 2 x 1013cm 2 s-1 are not higher than 0.2. If the deposition rates are higher, the condensation coefficients increase quickly at the beginning of nucleation. This behaviour is caused by the quicker increase in the relative covered area. In Fig. 3(b) the dependence of the condensation coefficient on temperature is shown. It should be mentioned that the determined condensation coefficients of the deposits produced at 298 K and 323 K are nearly 1 for relatively short deposition times (100 s and 200 s respectively). On the contrary, less than 40~o of the available material condensed at the highest deposition times if the substrate temperature was higher than 373 K. It can be stated that the experimental results published by other research groups 1,8,9 are in rough agreement with the present results. 2.3. Investigations concerning the growth behaviour Cluster growth can be caused by the capture of diffusing single atoms, by the direct impact of atoms from the vapour and by coalescence caused by cluster mobility and growth. The predominance of one of these processes can be recognized in the shapes of the cluster size distributions of the deposits 1° In Fig. 4 the temporal developments of the cluster size distributions are shown. The distributions determined at short deposition times have a nearly symmetrical shape around the maximum. Island growth which is caused predominantly by the capture of diffusing single atoms, on the contrary, shows a relatively slow increase followed by a sharp maximum and a sharp decrease. At the very beginning of condensation the influence of the direct impact of atoms from the vapour can be neglected, as well as growth coalescence, so that a noticable influence of coalescence caused by cluster mobility can possibly explain the observed shape of the curves. The increasing flanks of the cluster size distributions become flatter with increasing deposition times. In addition the distributions have only one maximum up to the longest deposition time of 1000s. A shape with two local maxima, from which the absolute maximum appears at the smaller diameter (to be expected if
168
R. ('()NRAI), M. HARSDORFF
,/
Off
/ !
0,4 t
SUB STRA1 E TEMPERATURE
./
0,3
DEPOSI TION R A I E
m
0,2
~/
0,1 /// 500
(a) *
1000
e ~
)C '3
29
lO !3
•
I'
12 '3
o
~. f)
:012
22
~012
Lt sec
[
DEPOSITION [¢m2s I'
RATE ' 7 ~013
SUBSIRATE
TEMPERATURE
" LK 1
298
v4
: :
J
)/, 500
]27 I
373
~
.~23
i~
~73
!000 't
Fig. 3. Dependence of the integral condensation coetticients
ondeposition time.
growth coalescence is dominant), was not observed. According to Venables 5 a single maximum is caused by mobility coalescence. In order to study the temporal development of growth as a function of deposition rate and temperature, the diameters dM associated with the maxima in the size distributions were evaluated. The experimental results plotted in Figs. 5 and 6
NUCLEATION AND GROWTH OF A u ON
NaCI(100)
169
bd 108cm2~ I
1000 sec
;000s; 7 100
200
300
d .7_ A
Fig. 4. Temporal developments of the cluster size distributions (substrate temperature, 423 K; deposition rate, 1.7x 10~3cm-Zs i).
SUBSTRATE TEMPERATURE T[K] ~23
dM
A
OEPOSITION RATE [3 7,5 1013
100
•,
2,g 1013
,c,
1,7
•
1,1 .1013
o
4,01012
,L
1013
2,2 1012 8,4.1011
~b
~6o
~o'oo
t sec
Fig. 5. Diameter dMobserved at the maximum of the size distributions as a function of time at various deposition rates.
can be d e s c r i b e d w i t h an e q u a t i o n of the f o r m dM oc t"' R m' exp ~-7= w i t h n' ~ ], ~ ½ a n d E = 0.03 + 0.01 eV. T h i s result c o u l d not be c o m p a r e d w i t h p r e v i o u s results, b e c a u s e of m i s s i n g e x p e r i m e n t a l data.
170
I~. ( ' ( ) N R A I ) , M. IIARSI)ORFI-
°v I
~a,7;c:. i t , 7 N ~ A ' ~
r Ii 50
.
:
}
i I'0 I lg 6
~.
100
Dcpcl/dencc
ofdi:lnlClcf
1000
t
l].q tttl dcpll-;lliOll [llllC ~1t \¢lllOUN Sl.lhMratc |ClllpCF~tlulc'~
('()?",( 1 [ S [ ( ) N
The dependence of the cluster densit~ on lhc deposition parameters, i.~~ ~
s l"R"exp
1,7
\~ith n ~ ~. nz -.- !~and E -= O. 1 c\". lirst observed b', Velfc el a/. could bc csseniiall} confirmed in this investigation. The ~alucs of m and Is could be reproduced tihc value of E here is 0.12~O.OleVi: the determined exponents n of the temporal dependence were bet'a een 0.3 and 0.5. A theoretical discussion of line process should therefore explain lids dependencc. In addition it should be considered that condensation is incomplete, as demonstrated by a condensation coelticient well below unit5. ('oncerning the investigations of the growth behaviour, it should be mentioned that the cluster size distributions obtained from the deposits have a broad, nearl~ symmetrical shape a r o u n d the maximum, and also ~_ll the smallest deposition times. This v~as interpreted as a possible indication of the influence of coalescence causcd b ; cluster mobilii\. The theoretical discussions published by Vellie and K r o h n " and bx Gates and Robins- both proceed from a mobility of small clusters which is not negligible. Krohn and Voile extcndcd the rate equations o f Zinsmeister by expressions which describe the mobility coalescencc of small submicroscopic clusters under the assumption of a monotonicall,, decreasing diffusion coelticient with increasing cluster size. In the case of mobilc dimers and trimcrs the experimentally observed dcpendencc of the cluster density on time and temperalurc could bc explained. However, the dependence n, ,' R ~ -~(for a not too high R) does nol coincide with the theoretical cxpression. Gates and Robins discussed a completely ne,a approach. According to their model, nucleation only occurs at surtace point defects. Concerning the experimental rcsuhs obtained bv rise of'ultraclean substrate crystals. a reasonable number of poinl defects arc present. Refcrrmg to the theoretical
NUCLEATION AND GROWTH OF AU ON NaCI(100)
171
discussions of the binding energies of small gold clusters on N a C ! surfaces given in refs. 11 and 12, Gates and Robins do not assume a m o n o t o n i c decrease in the diffusion coefficient with increasing cluster size. According to ref. 12, a range of cluster sizes exists where rigid base shapes for obtaining the potential m i n i m u m lead to high diffusion coefficients. If a cluster nucleating at a defect site exceeds this size, then it breaks away from the point defect and becomes mobile. The defect site is "reusable" for a further process of nucleation. The mobile microclusters grow owing to coalescence to form stable visible immobile clusters. In the desorption-controlled case the cluster density as a function of process parameters is given by nx _~ Gtl/3 R1/3 ex~{ Ea
Ed'~
with n x the cluster density, t the deposition time, G a constant depending only on atomic parameters, R the deposition rate, E a the energy of adsorption and E d the energy of diffusion. Therefore this model can explain the experimental observed dependences of the cluster density on all deposition parameters including the rate, Complete verification of the assumptions of this model by experimental results has not been done yet. ACKNOWLEDGMENTS We would like to thank the Deutsche Forschungsgemeinschaft for their support o f this research by providing parts o f the experimental equipment and personal funds. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
H. D, Velfe, H. Stenzel and M. Krohn, Thin Solid Films, 98 (1982) 115. B.F. Usher and J. L. Robins, Thin Solid Films, 149 (1987) 351,363. R. Conrad and M. Harsdorff, to be published. G. Zinsmeister, Thin Solid Films, 2 (1968) 497; 4 (1969) 363. J.A. Venables, Philos. Mag., 27(1973) 697. H. D, Velfe and M. Krohn, Thin Solid Films, 98 (1982) 125. A. D, Gates and J. L. Robins, Thin Solid Films, 149 (1987) 113. H. Stenzel, H. D. Velfeand M. Krohn, Krist. Tech., 15 (1980) 255. B.F. Usher and J. L. Robins, Thin Solid Films, 155 (1987) 267. J.A. Venables, G. D. T. Spiller and M. Hanbiicken, Rep. Prog. Phys., 47 (1984) 399. E.M. Chan, M. J. Buckingham and J. L. Robins, Surf. Sci., 67 (1977) 285. A. D, Gates and J. L. Robins, Surf Sci., 194 (1988) 13.