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506 Applications of Surface Science 22/23 (1985) 50e~-5l 1 North-Holland, Amsterdam THE CONTRIBUTION OF KINETIC NUCLEATION THEORIES TO STUDIES OF VOLMER-WEBER THIN FILM GROWTH B.F. USHER Telecom Research Laboratories, 770 Blackburn Road, Clayton, Victoria 31(x% Australia Received 27 August 1984; accepted for publication 31 October 1984 Extensive study of the vapour deposition of noble metals onto UHV cleaved alkali halide crystal surfaces has made an important contribution to the development of time-dependent nucleation theory. There nevertheless remain significant inconsistencies between results obtained from different studies of identical systems. The role which the time-dependent kinetic approach to nucleation theory has played in the past and that which it might take in the futurc are discussed. 1. Introduction The technological importance of a vast family of solid thin films has been clear for many decades. The relatively recent utilization of thin films in electronics has led to very large scale integration and the associated decrease in size and cost has been one of the most prominent successes of thin film technology. The development of the transmission electron microscope pro- vided the first powerful technique with which to investigate fundamental aspects of the initial nucleation and growth of thin films. Since this development the main subjects of attempts to test thin film nucleation and growth theory, in the case of the island growth mode, have been those of noble metals vacuum evaporated onto UHV cleaved alkali halide crystals. Despite considerable efforts over nearly three decades, investigations of these systems have revealed a conspicuous lack of agreement between different studies of identical deposit/substrate systems. The intention here is to examine the reasons for this disagreement and in particular to examinc the role kinetic nucleation theories have played in the past and might play in the future in contributing to our understanding of the initial stages of thin film nucleation and growth. 0378-5963/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

The contribution of kinetic nucleation theories to studies of Volmer-Weber thin film growth

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Page 1: The contribution of kinetic nucleation theories to studies of Volmer-Weber thin film growth

506 Applications of Surface Science 22/23 (1985) 50e~-5l 1 North-Holland, Amsterdam

T H E C O N T R I B U T I O N O F K I N E T I C N U C L E A T I O N T H E O R I E S T O S T U D I E S OF V O L M E R - W E B E R T H I N FILM G R O W T H

B.F. U S H E R

Telecom Research Laboratories, 770 Blackburn Road, Clayton, Victoria 31(x% Australia

Received 27 August 1984; accepted for publication 31 October 1984

Extensive study of the vapour deposition of noble metals onto UHV cleaved alkali halide crystal surfaces has made an important contribution to the development of time-dependent nucleation theory. There nevertheless remain significant inconsistencies between results obtained from different studies of identical systems. The role which the time-dependent kinetic approach to nucleation theory has played in the past and that which it might take in the futurc are discussed.

1. Introduct ion

The t echno log ica l i m p o r t a n c e of a vast family of sol id thin films has been c lear for many decades . The re la t ive ly recen t u t i l iza t ion of thin films in e lec t ron ics has led to very large scale in teg ra t ion and the assoc ia ted dec rease in size and cost has been one of the most p r o m i n e n t successes of thin film technology . The d e v e l o p m e n t of the t r ansmiss ion e lec t ron mic roscope pro- v ided the first power fu l t echn ique with which to inves t iga te f u n d a m e n t a l aspec ts of the initial nuc lea t ion and growth of thin films. Since this d e v e l o p m e n t the main sub jec t s of a t t e m p t s to test thin film nuc lea t ion and g rowth theory , in the case of the i s land g rowth mode , have been those of nob le meta l s vacuum e v a p o r a t e d on to U H V c leaved alkal i ha l ide crystals . Desp i t e cons ide r ab l e efforts ove r nea r ly th ree decades , inves t iga t ions of these sys tems have r evea l ed a consp icuous lack of a g r e e m e n t be tw e e n di f ferent s tudies of ident ica l d e p o s i t / s u b s t r a t e systems. The in ten t ion here is to e x a m i n e the r easons for this d i s a g r e e m e n t and in pa r t i cu la r to e xa minc the role k inet ic nuc lea t ion theor ies have p l ayed in the past and might play in the fu ture in con t r ibu t ing to o u r u n d e r s t a n d i n g of the initial s tages of thin film nuc lea t ion and growth.

0378-5963/85/$03.30 © Elsev ie r Science Publ i shers B.V. ( N o r t h - H o l l a n d Physics Publ i sh ing Divis ion)

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B.F. Usher / Volmer-Weber thin film growth 507

2. Theoretical developments

The noble metals on alkali halide systems are the most extensively studied examples of the Vo lmer -Weber [1] or island growth mode in which ~:he deposit material is more strongly bound to itself than to the substrate. In this, the most common growth mode, deposit material arrives from the vapour and is thermally accommodated on the surface. Subsequent migra- tion and mutual capture creates stable clusters which consume material migrating on the surface or arriving direct from the vapour. Clusters may participate in a number of processes such as growth or mobility coalescence and may in certain circumstances interact with each other on the surface. As clusters grow the fractional surface coverage increases until a continuous film is eventually formed.

Theoretical descriptions of the island growth mode began with classical thermodynamic models; however, atomistic theories were subsequently developed when it was found that for many deposit substrate systems of interest the critical cluster contained at most a few atoms. In 1966 Zins- meister [2] pioneered the development of t ime-dependent nucleation theory by extending earlier work by Frenkel [3]. He used a rate equation approach to describe the time dependence of adatom and dus te r popu- lations. Eqs. (1) and (2) represent examples of a relatively simple rate equation representat ion which might be used to model the nucleation and initial growth kinetics of noble metals vacuum evaporated onto U H V cleaved alkali halide crystals:

d U ~ _ R - N ~ _ 2 J - D N 1 ~ o- .~i , (1) d t "/'a i

dU,dt - dNxdt - j - R m .

In these equations NI is the adatom density, N~ is the density of stable clusters containing i atoms and N x is the total stable cluster density, o- i is the single atom capture number appropriate to a cluster containing i atoms, J is the rate of nucleation of clusters, ~'a is thc mean stay time before reevapora- tion and D is the adatom diffusion coefficient. Eq. (1) describes the time rate of change of the adatom population N~. The terms on the right-hand side of eq. (1) describe the rate of arrival, R, of single atoms at the substrate from the vapour, the rate of thermal desorption of adatoms from the surface, the rate of loss of adatoms as a result of the formation of a new cluster and the rate of incorporation of adatoms into stable clusters of all sizes, respectively. Eq. (2) describes the time rate of change of the total stable cluster density, N x. The first term on the right-hand side of this equation describes the rate of formation of pairs, while the second and third describe the rates of cluster

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5(18 B.F. Usher / Volmer-Weber thin film growth

growth and mobility coalescence respectively. The particular form and complexity of a chosen set of rate equations depend on the purpose to which they are to be put; however, eqs. (1) and (2) adequately represent the spirit of the rate equation representation.

3. Analysis of experimental results

The analysis of experimental results from a number of studies [4-14] of gold vapour deposited onto U H V cleaved sodium chloride, using rate equations similar to eqs. (1) and (2), has yielded values for the energy barriers to adatom surface diffusion, E a, and adatom reevaporat ion, E,, which are displayed in table 1. These parameters are fundamental to any description of the island growth mode of thin film nucleation. The wide variability in their experimentally determined values reflects variations of as much as an order of magnitude in the raw experimental data (such as cluster densities or sticking coefficients) from which these parameters were deter- mined. It is clear that while the application of t ime-dependent rate equations to the analysis of experimental studies of island growth has been shown to be appropriate , the disparate results suggest that significant problems remain to be resolved. Factors relating to experimental conditions such as surface contamination or the presence of preferred sites would probably account for these variations. However , if the intention is to perform an appropriate analysis of experimental results, then it does not mat ter that the kinetics are being influenced by such effects if terms describing all relevant processes are included self-consistently in a set of appropriate rate equations. Indeed a considerable number of workers have intentionally studied the initial

Table I Values for E. (adatom adsorption energy) and/or Ea (adatom surface diffusion energy) de termined by various studies; the figures underl ined represent values derived from the results originally published

Author(s) Year E. Ed 2E.-Ea Ea-Ed Refs.

Lewis and Campbell 1967 (I.36 [4] Inuzuka and Ueda 1968 0.66 0.52 0.80 0.14 [5] Robinson and Robins 1970 (I.68 (1.27 1.09 0.41 [61 Schmeisser and Harsdorff 1970 0.85 (I.52 1.18 (t.33 [7] Donohoe and Robins 1972 0.56 0.17 (I.95 (I.39 [8] Schmeisser 1974 (I.38 [9,1()] An ton et al. 1974 1.12 [ 11 ] Lane and Anderson 1975 (I.67 (I.31 1.(13 0.3~ [12] Stenzel et al. 198(I (I.31 [13] Usher and Robins 1984 0.48 (I.15 (I.81 0.33 [t4,17]

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B.F. Usher / Volmer-Weber thin film growth 509

nucleation and growth of thin films in the presence of a variety of dis- tributions of surface defects, and considerable useful information can be obtained from such studies. Where then does the problem lie?

Any physical system can be treated mathematically in many different ways. Even within the context of the rate equation formulation of the initial stages of thin film nucleation and growth there exists a family of equations which, while each represents a different interpretation of the mechanics of the system, are equivalent in the sense that agreement with experiment is possible if parameters are chosen appropriately. It is easy, however, to be so familiar with one conventional mathematical formulation that particular terms within a set of particular equations become identified with the real system. In this case the physical system may to a certain extent be forgotten and fundamental questions can be overlooked in favour either of develop- ment of the mathematical abstraction or achieving in effect no more than empirical agreement between theory and experiment. The rate equation approach can at the moment best serve in the analysis of experimental results as a simple, versatile and powerful means of determining which adatom and cluster processes are relevant to the description of the initial nucleation and growth of the particular thin film in question. The consider- able uncertainty which presently exists as to the specific conditions under which different experimental results have and in some cases still are being collected, suggests that it is premature to use experimental studies of the nucleation and growth of noble metals on alkali halide crystals as a testing ground for the more detailed aspects of t ime-dependent nucleation and growth theory.

Space considerations preclude detailed discussion of how best to ap- proach the task of identifying adatom and cluster processes using the rate equation approach. Suffice it to say that a recent study [14] applied a range of mathematical formulations (within the rate equation context) to the task of developing a self-consistent description of two earlier comprehensive studies [8,15] of the gold on sodium chloride system. It had been found there were a number of severe inconsistencies both within [16] and between [17] the original interpretations. Despite the original assumption of free surface nucleation, the outcome of this work revealed the dominant role of pre- ferred sites in the substrate surface. While the inclusion of additional processes necessarily added additional free parameters , the model was successful in removing the inconsistencies which had rendered the original analyses inappropriate.

4. Conclusions

Despite the problems which have in the past been encountered in studies of noble metal deposition onto alkali halide crystals, there are several

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51(J B.F Usher I Volmer-Weber thin .film growth

reasons to expect further progress in the coming years. First, it would seem that for these systems at least, most of the processes involved in thin film nucleation and growth have now been identified. Second, there is a growing awareness of the involvement of preferred sites in studies associated with the alkali halides. It is now important that extensive experimental data from experiments performed under as near ideal conditions as possible be collec- ted in order to clearly establish the validity of our present understanding of the growth of noble metals on alkali halide crystals. In applying time- dependent nucleation theory to systems such as gold on sodium chloride, agreement must first be obtained between primary experimental data and the broad features of the model. Attention should then be given to demon- strating consistency with more detailed data. Measurement of the sticking coefficient, for example, may or may not confirm initial estimates of the single a tom diffusion and evaporat ion probabilities obtained from nucleation rate or maximum density measurements . Disagreement at this level requires recursive modification of the starting model to retain consistency with all available data. More detailed data can also play a significant role in the initial development of appropriate theoretical models. Qualitative inspection of cluster size distributions, for example, can often provide strong clues as to whether growth or mobility coalescence is predominant or whether defect- induced nucleation is significant.

One of the strengths of the rate equation formulation is that even with seemingly gross approximations for some of the terms appearing in those equations, a meaningful comparison between experiment and theory is possible. For example, the assumption of a time- and size-independent cluster capture number does not alone prevent obtaining adequate agreement between theory and experiment and is not unreasonable when an analysis is directed primarily to determining whether growth or mobility coalescence is predominant . Simplifications such as these can be particularly advantageous since they allow rapid development of equations, frequently analytical, with which the consequences of a broad spectrum of possible mechanisms can be explored and compared with experiment. Additional mechanisms such as the diffusion of deposit atoms into the substrate or the nucleation of clusters from dimers or trimers present in the incident beam can also be included in a straightforward way. It is thus possible to quickly assess the compatibility of any reasonably simple mechanism with a range of experimental data.

As efforts are made to identify the processes influencing thin film nuclea- tion and growth, work needs to be undertaken to separately investigate (from both the experimental and theoretical points of view), some of the more elusive adatom and cluster processes. A good deal of information can be provided by kinetic studies themselves; however, mechanisms such as cluster-cluster forces demand independent study. There also remains the

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B.F.. Usher / Volmer-Weber thin film growth 511

need to make independent measurements, where possible, of some of the fundamental material parameters involved in the nucleation and growth process, such as the energy barriers to adatom diffusion and reevaporation.

Acknowledgement

The permission of the Director, Research, Telecom Australia, to publish the above paper is hereby acknowledged.

References

[1] E. Bauer, Z. Krist. 110 (1958) 372. [2] G. Zinsmeister, Vacuum 16 (1966) 529. [3] J. Frenkel, Z. Physik 26 (1924) 117. [4] B. Lewis and D.S. Campbell, J. Vacuum Sci. Technol. 4 (1967) 209. [5] T. Inuzuka and R. Ueda, J. Phys. Soc. Japan 25 (1968) 1299. [6] V.N.E. Robinson and J.L. Robins, Thin Solid Films 5 (1970) 313. [7] H. Schmeisser and M. Harsdorff, Z. Naturforsch. 25a (1970) 1896. [8] A.J. Donohoe and J.L. Robins, J. Crystal Growth 17 (1972) 70. [9] H. Schmeisser, Thin Solid Films 22 (1974) 83.

[10] H. Schmeisser, Thin Solid Films 22 (1974) 99. [11] R. Anton, M. Harsdorfl, M. Paunov and H. Schmeisser, Japan. J. Appl. Phys. Suppl. 2, Pt.

1 (1974) 563. [12] G.E. Lane and J.C. Anderson, Thin Solid Films 26 (1975) 5. [13] H. Stenzel, H.D. Velfe and M. Krohn, Kristall Tech. 15 (1980) 255. [14] B.F. Usher and J.L. Robins, in press. [15] V.N.E. Robinson and J.L. Robins, Thin Solid Films 20 (1974) 155. [16] J.L. Robins, A.J. Donohoe and B.F. Usher, Japan. J. Appl. Phys. Suppl. 2, Pt. 1 (1974)

559. [17] B.F. Usher, PhD Thesis, University of Western Australia (1981).