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Experimental problems of studying thin film nucleation
Thin Solid Films, 32 (1976) 103-115 © Elsevier Sequoia S.A., L a u s a n n e - P r i n t e d in Switzerland
103
EXPERIMENTAL PROBLEMS OF STUDYING THIN FILM NUCLEATION*
M. H A R S D O R F F lnstitut fi~r A ngewandte Physik, Universitiit Hamburg, 2 Hamburg 36, Jungiusstrafle 11 (Germany) (Received August 25, 1975)
1. INTRODUCTION Investigations of heterogeneous nucleation on substrates have been carried out for several decades and modern theoretical concepts of the problem are more than fifty years old. Nevertheless the full understanding of the mechanisms needed for an interpretation of all experimental results is still lacking. This is particularly evident in the case of oriented overgrowth. In many cases experiments were performed in a high vacuum environment with pressures of about 10 -5 Torr without any control of the composition of the residual gases. Now we know that successful investigations of highly surface-dependent processes are not possible under such conditions. In the recent past, some progress has been achieved towards a better understanding of the most important processes involved in the condensation of materials on substrates. Theoretical efforts have been concentrated on heterogeneous nucleation 1-3, atom migration and capture processes on substrate surfaces 4-6, and on the mobility of small crystallites 3,7-9. Experimentally, the introduction of ultrahigh vacuum (UHV) techniques was the decisive condition to obtain reproducible data. Furthermore UHV techniques permit the application of powerful surface analytical tools such as low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). With these methods it is possible to control the structure, chemical composition and cleanness of substrate surfaces before any deposition of material. Furthermore the orientation and quantity of deposited material can be monitored with a sensitivity and accuracy to a fraction of a monolayer. Besides these new experimental methods, the classical high resolution transmission electron microscope plays an important role in giving accurate data about the morphology and structure of the crystallites forming the deposit. The electron microscope has two advantages over many other averaging analytical instruments: firstly a resolving power of a few ~ingstr6ms, and secondly the possibility of obtaining crystallographic data by selected area electron diffraction from areas of about 1/~m 2. In investigations of epitaxy it is possible to get quantitative information about the degree of orientation by using the instrument in a high resolution dark field mode 1°.
* Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 2-I-1.
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If the dynamical behaviour of individual crystallites, e.g. the growth, mobility and changes in crystallographic orientation, is under study, the use of in situ transmission electron microscopy under UHV conditions is the only way to get reliable data t 1-13 Because of the statistical character of the effects being studied in nucleation experiments, only results based on a large number of individual measurements are meaningful. With the methods used up to now this involves a large amount of time-consuming work. The problem of obtaining statistically significant results is easily overcome by the technique of quantitative electronic image analysis. With an inrage analysing computer one can obtain data from electron micrographs or on-line from the screen of an electron microscope, e.g. cluster size distributions or spatial distributions of crystallites 14, which are rarely obtained by other techniques. The examples of nucleation and growth processes discussed later will be limited to combinations of materials with weak relative bonding. In this case we expect nucleation and growth of discrete deposited particles on the substrate. The film formation is characterized by three well-known steps: (1) nucleation and growth, (2) coalescence and (3) a filling-in stage. Only tile first and to some extent the second step will be discussed in this paper. 2. EXPERIMENTAL TECHNIQUES 2.1. UHV L E E D - A E S system
Figure 1 shows schematically an UHV chamber for controlled thin film nucleation and growth studies. For LEED and AES investigations three-grid optics are provided. Facilities for the evaporation of different materials and the control of flux density and residual gas composition, as well as a crystal oven and a crystal multiple cleavage and specimen storage device, are available (see also ref. 15).
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Fig. 1. UHV chamber for controlled thin film nucleation and growth studies: A, crystal oven; a, heater; b, axis of the manipulator; c, crystal; d, Knudsen cell; e, shutter; f, quadrupole mass spectrometer with cross beam ion source; h, crystal cleaving device; i, specimen storage device; k, three-grid optics.
EXPERIMENTALPROBLEMSIN THIN HLM NUCLEATION
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Normally bulk single crystals are used as substrates. To obtain contamination-free surfaces, the crystals are cleaved under UHV prior to the deposition of material. The following crystals are suitable for this purpose: the alkali halides, magnesium oxide, graphite, mica, lead sulphide and lead selenide, to list only the most frequently used materials. Another way to obtain reproducible substrates is to deposit amorphous substances, e.g. carbon 12,16 or silicon monoxide, onto cleavage planes of crystals. If possible, surfaces should be investigated by LEED and AES prior to the deposition of material to check for contamination. However, in some cases it must be borne in mind that surface bombardment with low energy electrons can cause severe defects 17. These defects are sites of preferred nucleation and the statistical nucleation process is then no longer detectable. Also the epitaxial orientation of deposits can be altered by this effect, as was recently demonstrated by Lord and Prutton 18 in the case of f.c.c. metals on alkali halides. Crystals with ionic binding seem to be particularly sensitive to electron bombardment, but even in cases where materials with weaker sensitivity to electron irradiation are used, irradiated and unexposed parts of the surface should be inspected to spot any artefacts in good time. In all investigations of nucleation and crystal growth on substrates two parameters, the substrate temperature and the deposition rate, play an important role. The substrate temperature is usually controlled by an electronic device which should be designed to limit temperature deviations to less than one degree. The deposition rateis frequently monitored and controlled by a quartz crystal oscillator. The limitation of this instrument is due to its measuring the mass of deposited material instead of the particle flux. The use of a quadrupole mass spectrometer tuned to the mass of the deposited material has the great advantage that the output signal can be used for vapour flux control by adjusting the temperature of a Knudsen cell source 19. The experimental arrangement is shown in Fig. 2. With this device the vapour flux can be held constant to -+2% for several hours. Knudsen cells are useful for evaporation sources and, at least for low vapour flux densities, should be preferred because of their stability. 133ats and ribbons show instabilities in the flux density caused by fluctuations of the evaporating area. The application of conventional electron guns is also difficult if the vapour beam and the electron beam are not separated by a crucible. In the usual mode of operation part of the material will be ionized, so that alterations in the condensation process are possible 2°. Prior to the electron microscope investigation any discontinuous deposits must be backed with protective layers. Evaporated layers of silicon monoxide or carbon are used for backing. Whereas layers of SiO often show insufficient protection of the deposit 21 , deposits fixed by thin carbon layers have a remarkable stability. Even the relative position of the crystallites, important for the measurement of epitaxial order, is undisturbed if the carbon layer has a minimum thickness of about 200 A. 2.2. In situ electron microscopy The first thin film depositions inside an electron microscope for in situ studies of nucleation and growth processes were performed by Bassett 22 . A major problem was the contamination of the substrates caused by poor vacuum conditions. To avoid this difficulty Poppa 11'12 and Barna et al. 13 improved the vacuum in the vicinity of the specimen by differential pumping. In Fig. 3 the system used by Moorhead and Poppa
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is shown 15 . The specimen chamber is evacuated by two 400 1 s -1 Orb ion pumps to give a pressure of about 10 -9 Tort. The vapour source for the in situ deposition is heated by electron bombardment, and the vapour flux rate is monitored by a quartz oscillator. Several substrates can be used without breaking the vacuum and devices are available for electronic image intensification and video recording. A great advantage of this technique is the continuous observation and recording of the growth process. It is possible to observe individual crystal growth, thus no averaging over the growth of many crystallites is necessary as in the technique described before. The development of the nucleation process can be observed on the same substrate, whereas with the indirect technique the analysis o f the nucleation process is only possible by preparation of many specimens with different deposition times, each deposited on another cleavage plane. However, numerous limitations of the in situ technique have to be considered. First, the substrate has to be a thin electron-transparent film. Molybdenite, graphite and mica can be cleaved down to a suitable thickness. As shown by Honjo and Shinozaki 23-2s the in situ preparation of electron-transparent areas by thermal cleavage of magnesium oxide, zinc sulphide and lead sulphide is possible using a high intensity electron beam. Another way is to deposit the substrate material onto single-crystal films of the same material prepared outside the microscope. This technique was used by Stowell for gold films on gold 26. However, the selection of a suitable substrate is the major limitation of the in situ technique. Another disadvantage of in situ microscopy is the difficulty of measuring the deposition parameters with the desired accuracy. The measurement of the substrate temperature is particularly difficult because of the poor heat conductivity of thin substrate films.
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
107
2. 3. Evaluation by electronic image analysis A great number of micrographs must be taken from the specimens, prepared as described above, to get reliable data because of the statistical nature of the nucleation process. To get even the simplest result like the number of clusters as a function of deposition time, a large number of crystallites must be counted to achieve statistical significance. It is almost impossible to do by hand an evaluation which requires the measurement of individual crystallites (e.g. their diameters) or the determination of all x, y coordinates. A better solution is the use of a quantitative electronic image analyser 27. A block diagram of the Quantimet 720 system (Imanco) is shown in Fig. 4. The scanner, a television camera, receives the input picture from an electron micrograph or the fluorescent screen of a microscope. The image is divided into 625 lines wlfich are scanned sequentially, and each line is divided into 800 points. The whole image is thus covered by a matrix of about 500 000 square-shaped points. Digitally controlled the video signal reaches the detector point by point. Here a yes-no decision is made of whether the
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2.3.1. Basic measurements The simplest measurement which is important for nucleation kinetics is the coverage of the surface by crystallites. This measurement is done by simply counting those points for which the detector decided that they belong to clusters. Dividing the result of this count by the total number of points gives the relative coverage. The second basic measurement is the counting of the intersections of scanning lines with the right edge of all counted clusters. The result g,ves the sum of all particle diameters in the vertical direction. If the sum is divided by the total number of particles obtained in a third operational mode of the instrument the mean particle diameter for one direction is calculated. In the case of sphere-shaped particles the value is obviously independent of the direction. The superiority of electronic image analysis becomes obvious if the size of a large number of individual crystallites must be determined. The Quantimet is able to suppress the counting of particles that do not satisfy the chosen criterion for size. This criterion may be that the particle's longest chord in the scanning direction is longer than the number of points given by a digi-switch. Successive counts with different pre-seleclions
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of the longest chord give the distribution function of particle diameters. Subtracting these values from each other yields the distribution density. 2. 3.2. System extensions For the special requirements of nucleation work the image analyser was upgraded to drive a paper tape punch to output the results of the basic measurements described, which were usually displayed on the video monitor. In this way the results were prepared for further processing on an external computer. Furthermore the analvser is able to punch all coordinates of detected crystallites onto paper tape. Using x, 3' coordinates it is possible to obtain data about the distribution of nearest neighbours by using an external computer for calculating the relevant distances. 3. EXAMPLES AND RESULTS
A short review will be given of the data obtainable by the techniques described above as far as such data are comparable with predictions of existing condensation theories. 3.1. Condensation coefficient One of the most important parameters is the condensation coefficient ~, defined as the condensed mass divided by the product of flux rate and deposition time. The knowledge of c~ is important for any decision about complete or incomplete deposition taking place, and what approximations to the well-known rate equations are applicable in a special case 2. In the range of more than one monolayer of condensed material measurements by quantitative X-ray analysis are possible 28'29. In heterogeneous nucleation experiments the condensation coefficient is a function of the deposition time since only part of the material is condensing on the substrate, the remainder being directly captured by clusters of deposited material. The latter part is negligible if the condensation coefficient is measured at short deposition times (low coverages). At very low coverages it is possible, as shown by Anton 3°, to measure the condensation coefficient with a calibrated Auger electron spectrometer. The variation of the AES signal versus deposition time is shown in Fig. 5 for gold on amorphous carbon. At short deposition times the signal varies in proportion to the deposition time. Considering the very small escape depth of Auger electrons (~4 A), one can see that there must be a large number of very sm',dl clusters at the beginning of deposition; thus in this region no crystallites are visible in high resolution micrographs. Above a mean thickness of about 2.5 A the AES signal increases in proportion to t z/3. This behaviour is to be expected if the deposits consist of discrete hemispherical crystallites whose diameters are larger than the escape depth of the Auger electrons. In this case a quadratic time-dependent increase of the surface coverage is measured. A confirmation of this result by image analysis of micrographs is shown in Fig. 6. A plot of surface coverage versus deposition time shows the predicted quadratic dependence up to the time of coalescence. 3. 2. Mean particle diameter Kinetic nucleation theory predicts a dependence of the individual crystallite diameter
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on the square root of the deposition time. If we are using data obtained by the AES-EM system, we can only evaluate the mean particle diameter versus deposition time by using the image analysing computer. An example for gold and carbon is shown in Fig. 7. The predictions of the theory seem to be confirmed. In Fig. 8, however, for silver on silicon monoxide two different modes of growth are visible. The results were obtained by Poppa is using in situ electron microscopy. Although the results were obtained in the coalescence stage of film growth, which is not comparable with the nucleation stage, it is indisputable that averaging methods can lead to a loss of information. 3.3. Cluster size d i s t r i b u t i o n s
Cluster size distributions in micrographs taken from gold-rocksalt specimens were evaluated by Schmeisser 31 . All distributions show qualitatively the same shape, inde-
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pendent of experimental parameters: a sharp m a x i m u m at large diameters f o l l o w e d by an abrupt drop; the increase is shallower and depends on the position of the m a x i m u m . This result agrees with that reported by D o n o h o e and Robins a2, w h o also found a single peak in the size distributions at elevated temperatures. A typical example is shown in Fig. 9. In this figure the whole development o f the nucleation, growth and coalescence process can be seen. The increase in crystal density with time is given by the m o n o -
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
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tonically increasing shaded total area under the distribution functions. With increasing deposition time the crystal diameter grows too. This is described by the shift o f the steep increase of the distribution on the d-axis. The flattening of the decreasing branch is caused by severe coalescence at times above 45 s. A more detailed study shows the unexpected result that, besides the shifting of the maximum due to cluster growth, the
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3. 4. Spatial distribution o f clusters In order to describe the spatial distribution of crystallites, a correlation function is defined as the ratio of the actually measured number density of clusters at a distance
112
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from a given cluster to the macroscopically measured concentration 34. The correlation function can be calculated from the x, y coordinates of crystallites using a computer. A typical result is shown in Fig. 11. It can be seen that there is a sharp decrease of the correlation function at small distances. This means that the probability of finding closely neighbouring crystallites is less than would be expected in the case of a random distribution, which corresponds to a correlation function equal to one. There are two possible explanations: (1) the clusters are sinks for single atoms, leading to a reduction of the nucleation rate; (2) coalescence of small clusters reduces the crystallite density. If the first explanation is valid, a very strong dependence of the correlation function on the substrate temperature should be observed, in contradiction to the experiments. For { Korr (r, Ar)
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3.5. Epitaxial nucleation There are marked disagreements between different authors about the processes which lead to a completely oriented continuous epitaxial film. At one extreme there is the opinion that particles develop epitaxial orientation during growth which can be destroyed when coalescence occurs 3s. At the other extreme there is the opinion that the final orientation is determined by the most favourable orientation of critical nuclei 36'37. For gold on potassium chloride Puskeppel showed that part of the material is deposited epitaxially in the nucleation stage 1°. The degree of epitaxial (parallel) orientation was defined by the number of parallelly oriented crystallites, counted with a Quantimet in 100 dark field micrographs, divided by the total number of crystallites, obtained by counting all crystallites in correlated bright field images. The evaluation procedure is demonstrated in Fig. 12. In the upper part of the graph the dependence of the crystallite density of oriented material and the total number density of crystallites are plotted against the deposition time. The quotient of these curves, the degree of orientation, is plotted in the lower part of the graph. The extrapolation to zero deposition time leads to an initial orientation, caused by epitaxial nucleation. This initial degree of orientation shows a characteristic dependence on the deposition rate and the substrate temperature, as predicted by theory 38.
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The graph of cluster size distribution versus deposition time shown in Fig. 13 gives a qualitative insight into the process of epitaxial nucleation, growth, alignment and coalescence. The solid curves show the size distributions of all crystallites, oriented and random, whilst the broken lines show the distributions of the (100)-oriented crystallites, assuming the epitaxial order to be independent of particle diameter. The hatched area is the measured distribution of oriented material. In the nucleation stage (0-150 s) the observed distributions are shifted towards larger diameters. In epitaxial growth the mobility of small clusters leads not only to an alignment of crystallites but also to a formation of larger clusters by mobility coalescence. In the later growth coalescence region all large crystallites are parallelly oriented. This shows that the growth coalescence of differently oriented crystallites leads in this case to large (100)oriented crystallites. Obviously we have to distinguish between three different stages of formation of an epitaxial layer: (1) oriented nucleation with a definite dependence of the epitaxial order on substrate temperature and deposition rate; (2) alignment of small crystallites after nucleation and the formation of larger oriented clusters by coalescence of migrating particles; (3) orientation changes during growth coalescence, perhaps under the in fluence of the recrystallization energy. 4. CONCLUSIONS It is well known that nucleation and cluster growth are dominated by single atom processes and can be described by the rate equation approach 2. The systematic investigation of cluster size distributions, spatial cluster distributions and epitaxial growth suggests that corrections to the coalescence caused by the mobility of small clusters and the growth of crystallites are necessary. In the present situation a further refinement of the theoretical description seems to be desirable because up to now only a qualitative agreement with experimental results is obtainable. In the past only a few combinations of substances have been investigated, e.g.f.c.c. metals on alkali halides and on amorphous carbon. Evidently experiments should be extended to other substrates and deposition materials. The combination of different investigation methods should be continued and extended. The advanced technique of in situ electron microscopy combined with LEED-AES studies and electronic image computation seems to be an effective tool to attack the outstanding problems of random and epitaxial nucleation and growth kinetics. REFERENCES
1 D. Walton, J. Chem. Phys., 37 (1962)2182. 2 G. Zinsmeister, Vacuum, 16 (1966) 529; Thin Solid Films, 2 (1968) 497; 4 (1969) 363; 7 (1971) 51. 3 J. A. Venables, Philos. Mag., 27 (1973) 697. 4 B. Lewis, Surf. Sci., 21 (1970) 273,289. 5 V. Halpcrn, J. Appl. Phys., 40 (1969) 4627. 6 K. I. Routledge and M. J. Stowell, Thin Solid Films, 6 (1970) 401.
EXPERIMENTAL PROBLEMS 1N THIN FILM NUCLEATION 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
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R. Kern, A. Masson and J. J. Metois, Surf. ScL, 27 (1971) 463. J. J. Metois, M. Gauch, A. Masson and R. Kern, Thin Solid Films, 11 (1972) 205. J. J. Metois, Surf. Sci., 36 (1973) 269. M. Harsdorff and A. Puskeppel, submitted to Thin Solid Films. H. Poppa, J. Vac. Sci. Technol., 2 (1965) 42. H. Poppa, J. Appl. Phys., 38 (1967) 3883. A. Barna, P. B. Barna and 1. F. Pocza, Vacuum, 17(1967) 219. H. Schmeisser and M. Harsdorff, Thin Solid Films, 14 (1972) 321. H. Po,ppa, R. D. Moorhead and K. Heinemann, Nucl. Instrum. Methods, 102 (1972) 521. M. Paunov and M. Harsdorff, Z. Naturforsch., 29a (1974) 1311. T. N. Rhodin, P. W. Palmberg and C. J. Todd, J. Vac. Sci. Technol., 6 (1969) 467. D.G. Lord and M. Prutton, Thin Solid Films, 21 (1974) 341. H. Schmeisser, Vak.-Tech., 21 (1972) 165. D. I. Stirland, Appl. Phys. Lett., 8 (1966) 326. J. L. Robins and V. N. E. Robinson, Vacuum, 18 (1968) 641. G. A. Basset, in E. Rutner, P. Goldfinger and I. P. Hirth (eds.), Proc. Int. Symp. on Condensation and Evaporation of Solids, Gordon and Breach, New York, 1964, p. 599. G. Honjo, S. Shinozaki and H. Sato, Appl. Phys. Lett., 9 (1966) 23. S. Shinozaki and H. Sato, J. AppL Phys., 43 (1972) 701. G. Honjo and K. Yagi, J. Vac. ScL Technol., 6 (1969) 576. M. Valdr~, E. A. Robinson, D. W. Pahley, M. J. Stowell and T. I. Law, J. Phys. E, 3 (1970) 501. C. F. Fisher, Microscope, 19 (1971) 1. T. N. Rhodin, Anal Chem., 27 (1955) 1857. R. Weyl, Z. Angew. Phys., 13 (1961) 283. R. Anton and M. Harsdorff, Thin Solid Films, 22 (1974) 23. H. Schmeisser, Thin Solid Films, 22 (1974) 83. A. J. Donohoe and J. L. Robins, J. Cryst. Growth, 17 (1972) 70. J. L. Robins, A. J. Donohoe and B. F. Usher, Proc. 6thlnt. Vac. Congr. 1974, inJpn. J. Appl. Phys., Suppl. 2, Part 1 (1974) 559. H. Schmeisser, Thin Solid Films, 22 (1974) 99. E. Bauer and H. Poppa, Thin Solid Films, 12 (1972) 167. B. Lewis, Thin Solid Films, 7 (1971) 179. C. A. Henning and J. S. Vermaak, Philos. Mag., 22 (1970) 281. M. Harsdorff, Z. Naturforsch., 23a (1968) 1253.
103
EXPERIMENTAL PROBLEMS OF STUDYING THIN FILM NUCLEATION*
M. H A R S D O R F F lnstitut fi~r A ngewandte Physik, Universitiit Hamburg, 2 Hamburg 36, Jungiusstrafle 11 (Germany) (Received August 25, 1975)
1. INTRODUCTION Investigations of heterogeneous nucleation on substrates have been carried out for several decades and modern theoretical concepts of the problem are more than fifty years old. Nevertheless the full understanding of the mechanisms needed for an interpretation of all experimental results is still lacking. This is particularly evident in the case of oriented overgrowth. In many cases experiments were performed in a high vacuum environment with pressures of about 10 -5 Torr without any control of the composition of the residual gases. Now we know that successful investigations of highly surface-dependent processes are not possible under such conditions. In the recent past, some progress has been achieved towards a better understanding of the most important processes involved in the condensation of materials on substrates. Theoretical efforts have been concentrated on heterogeneous nucleation 1-3, atom migration and capture processes on substrate surfaces 4-6, and on the mobility of small crystallites 3,7-9. Experimentally, the introduction of ultrahigh vacuum (UHV) techniques was the decisive condition to obtain reproducible data. Furthermore UHV techniques permit the application of powerful surface analytical tools such as low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). With these methods it is possible to control the structure, chemical composition and cleanness of substrate surfaces before any deposition of material. Furthermore the orientation and quantity of deposited material can be monitored with a sensitivity and accuracy to a fraction of a monolayer. Besides these new experimental methods, the classical high resolution transmission electron microscope plays an important role in giving accurate data about the morphology and structure of the crystallites forming the deposit. The electron microscope has two advantages over many other averaging analytical instruments: firstly a resolving power of a few ~ingstr6ms, and secondly the possibility of obtaining crystallographic data by selected area electron diffraction from areas of about 1/~m 2. In investigations of epitaxy it is possible to get quantitative information about the degree of orientation by using the instrument in a high resolution dark field mode 1°.
* Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 2-I-1.
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If the dynamical behaviour of individual crystallites, e.g. the growth, mobility and changes in crystallographic orientation, is under study, the use of in situ transmission electron microscopy under UHV conditions is the only way to get reliable data t 1-13 Because of the statistical character of the effects being studied in nucleation experiments, only results based on a large number of individual measurements are meaningful. With the methods used up to now this involves a large amount of time-consuming work. The problem of obtaining statistically significant results is easily overcome by the technique of quantitative electronic image analysis. With an inrage analysing computer one can obtain data from electron micrographs or on-line from the screen of an electron microscope, e.g. cluster size distributions or spatial distributions of crystallites 14, which are rarely obtained by other techniques. The examples of nucleation and growth processes discussed later will be limited to combinations of materials with weak relative bonding. In this case we expect nucleation and growth of discrete deposited particles on the substrate. The film formation is characterized by three well-known steps: (1) nucleation and growth, (2) coalescence and (3) a filling-in stage. Only tile first and to some extent the second step will be discussed in this paper. 2. EXPERIMENTAL TECHNIQUES 2.1. UHV L E E D - A E S system
Figure 1 shows schematically an UHV chamber for controlled thin film nucleation and growth studies. For LEED and AES investigations three-grid optics are provided. Facilities for the evaporation of different materials and the control of flux density and residual gas composition, as well as a crystal oven and a crystal multiple cleavage and specimen storage device, are available (see also ref. 15).
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f/ LJ_I di A
Fig. 1. UHV chamber for controlled thin film nucleation and growth studies: A, crystal oven; a, heater; b, axis of the manipulator; c, crystal; d, Knudsen cell; e, shutter; f, quadrupole mass spectrometer with cross beam ion source; h, crystal cleaving device; i, specimen storage device; k, three-grid optics.
EXPERIMENTALPROBLEMSIN THIN HLM NUCLEATION
105
Normally bulk single crystals are used as substrates. To obtain contamination-free surfaces, the crystals are cleaved under UHV prior to the deposition of material. The following crystals are suitable for this purpose: the alkali halides, magnesium oxide, graphite, mica, lead sulphide and lead selenide, to list only the most frequently used materials. Another way to obtain reproducible substrates is to deposit amorphous substances, e.g. carbon 12,16 or silicon monoxide, onto cleavage planes of crystals. If possible, surfaces should be investigated by LEED and AES prior to the deposition of material to check for contamination. However, in some cases it must be borne in mind that surface bombardment with low energy electrons can cause severe defects 17. These defects are sites of preferred nucleation and the statistical nucleation process is then no longer detectable. Also the epitaxial orientation of deposits can be altered by this effect, as was recently demonstrated by Lord and Prutton 18 in the case of f.c.c. metals on alkali halides. Crystals with ionic binding seem to be particularly sensitive to electron bombardment, but even in cases where materials with weaker sensitivity to electron irradiation are used, irradiated and unexposed parts of the surface should be inspected to spot any artefacts in good time. In all investigations of nucleation and crystal growth on substrates two parameters, the substrate temperature and the deposition rate, play an important role. The substrate temperature is usually controlled by an electronic device which should be designed to limit temperature deviations to less than one degree. The deposition rateis frequently monitored and controlled by a quartz crystal oscillator. The limitation of this instrument is due to its measuring the mass of deposited material instead of the particle flux. The use of a quadrupole mass spectrometer tuned to the mass of the deposited material has the great advantage that the output signal can be used for vapour flux control by adjusting the temperature of a Knudsen cell source 19. The experimental arrangement is shown in Fig. 2. With this device the vapour flux can be held constant to -+2% for several hours. Knudsen cells are useful for evaporation sources and, at least for low vapour flux densities, should be preferred because of their stability. 133ats and ribbons show instabilities in the flux density caused by fluctuations of the evaporating area. The application of conventional electron guns is also difficult if the vapour beam and the electron beam are not separated by a crucible. In the usual mode of operation part of the material will be ionized, so that alterations in the condensation process are possible 2°. Prior to the electron microscope investigation any discontinuous deposits must be backed with protective layers. Evaporated layers of silicon monoxide or carbon are used for backing. Whereas layers of SiO often show insufficient protection of the deposit 21 , deposits fixed by thin carbon layers have a remarkable stability. Even the relative position of the crystallites, important for the measurement of epitaxial order, is undisturbed if the carbon layer has a minimum thickness of about 200 A. 2.2. In situ electron microscopy The first thin film depositions inside an electron microscope for in situ studies of nucleation and growth processes were performed by Bassett 22 . A major problem was the contamination of the substrates caused by poor vacuum conditions. To avoid this difficulty Poppa 11'12 and Barna et al. 13 improved the vacuum in the vicinity of the specimen by differential pumping. In Fig. 3 the system used by Moorhead and Poppa
106
M. HARSDORF]:
i I I I I I I I I I
I
If Ii iI/ I
,:,,'
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~ E R ~E~TU~U ~APHRA~
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Fig. 2. Regulation of the vapour flux by use of a quadrupole mass spectrometer: a, substrate; b, vapour beam; c, cross beam ion source; d, quadrupole filter; e, Faraday cage. Fig. 3. Specimen chamber for in situ nucleation experiments, constructed by Moorhead and Poppa.
is shown 15 . The specimen chamber is evacuated by two 400 1 s -1 Orb ion pumps to give a pressure of about 10 -9 Tort. The vapour source for the in situ deposition is heated by electron bombardment, and the vapour flux rate is monitored by a quartz oscillator. Several substrates can be used without breaking the vacuum and devices are available for electronic image intensification and video recording. A great advantage of this technique is the continuous observation and recording of the growth process. It is possible to observe individual crystal growth, thus no averaging over the growth of many crystallites is necessary as in the technique described before. The development of the nucleation process can be observed on the same substrate, whereas with the indirect technique the analysis o f the nucleation process is only possible by preparation of many specimens with different deposition times, each deposited on another cleavage plane. However, numerous limitations of the in situ technique have to be considered. First, the substrate has to be a thin electron-transparent film. Molybdenite, graphite and mica can be cleaved down to a suitable thickness. As shown by Honjo and Shinozaki 23-2s the in situ preparation of electron-transparent areas by thermal cleavage of magnesium oxide, zinc sulphide and lead sulphide is possible using a high intensity electron beam. Another way is to deposit the substrate material onto single-crystal films of the same material prepared outside the microscope. This technique was used by Stowell for gold films on gold 26. However, the selection of a suitable substrate is the major limitation of the in situ technique. Another disadvantage of in situ microscopy is the difficulty of measuring the deposition parameters with the desired accuracy. The measurement of the substrate temperature is particularly difficult because of the poor heat conductivity of thin substrate films.
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
107
2. 3. Evaluation by electronic image analysis A great number of micrographs must be taken from the specimens, prepared as described above, to get reliable data because of the statistical nature of the nucleation process. To get even the simplest result like the number of clusters as a function of deposition time, a large number of crystallites must be counted to achieve statistical significance. It is almost impossible to do by hand an evaluation which requires the measurement of individual crystallites (e.g. their diameters) or the determination of all x, y coordinates. A better solution is the use of a quantitative electronic image analyser 27. A block diagram of the Quantimet 720 system (Imanco) is shown in Fig. 4. The scanner, a television camera, receives the input picture from an electron micrograph or the fluorescent screen of a microscope. The image is divided into 625 lines wlfich are scanned sequentially, and each line is divided into 800 points. The whole image is thus covered by a matrix of about 500 000 square-shaped points. Digitally controlled the video signal reaches the detector point by point. Here a yes-no decision is made of whether the
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.
.
.
.
.
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current point represents a grey level between two thresholds. The sequence of pulses representing the individual decisions is fed into the computer, where the measurements are done.
2.3.1. Basic measurements The simplest measurement which is important for nucleation kinetics is the coverage of the surface by crystallites. This measurement is done by simply counting those points for which the detector decided that they belong to clusters. Dividing the result of this count by the total number of points gives the relative coverage. The second basic measurement is the counting of the intersections of scanning lines with the right edge of all counted clusters. The result g,ves the sum of all particle diameters in the vertical direction. If the sum is divided by the total number of particles obtained in a third operational mode of the instrument the mean particle diameter for one direction is calculated. In the case of sphere-shaped particles the value is obviously independent of the direction. The superiority of electronic image analysis becomes obvious if the size of a large number of individual crystallites must be determined. The Quantimet is able to suppress the counting of particles that do not satisfy the chosen criterion for size. This criterion may be that the particle's longest chord in the scanning direction is longer than the number of points given by a digi-switch. Successive counts with different pre-seleclions
108
M. HARSDORFF
of the longest chord give the distribution function of particle diameters. Subtracting these values from each other yields the distribution density. 2. 3.2. System extensions For the special requirements of nucleation work the image analyser was upgraded to drive a paper tape punch to output the results of the basic measurements described, which were usually displayed on the video monitor. In this way the results were prepared for further processing on an external computer. Furthermore the analvser is able to punch all coordinates of detected crystallites onto paper tape. Using x, 3' coordinates it is possible to obtain data about the distribution of nearest neighbours by using an external computer for calculating the relevant distances. 3. EXAMPLES AND RESULTS
A short review will be given of the data obtainable by the techniques described above as far as such data are comparable with predictions of existing condensation theories. 3.1. Condensation coefficient One of the most important parameters is the condensation coefficient ~, defined as the condensed mass divided by the product of flux rate and deposition time. The knowledge of c~ is important for any decision about complete or incomplete deposition taking place, and what approximations to the well-known rate equations are applicable in a special case 2. In the range of more than one monolayer of condensed material measurements by quantitative X-ray analysis are possible 28'29. In heterogeneous nucleation experiments the condensation coefficient is a function of the deposition time since only part of the material is condensing on the substrate, the remainder being directly captured by clusters of deposited material. The latter part is negligible if the condensation coefficient is measured at short deposition times (low coverages). At very low coverages it is possible, as shown by Anton 3°, to measure the condensation coefficient with a calibrated Auger electron spectrometer. The variation of the AES signal versus deposition time is shown in Fig. 5 for gold on amorphous carbon. At short deposition times the signal varies in proportion to the deposition time. Considering the very small escape depth of Auger electrons (~4 A), one can see that there must be a large number of very sm',dl clusters at the beginning of deposition; thus in this region no crystallites are visible in high resolution micrographs. Above a mean thickness of about 2.5 A the AES signal increases in proportion to t z/3. This behaviour is to be expected if the deposits consist of discrete hemispherical crystallites whose diameters are larger than the escape depth of the Auger electrons. In this case a quadratic time-dependent increase of the surface coverage is measured. A confirmation of this result by image analysis of micrographs is shown in Fig. 6. A plot of surface coverage versus deposition time shows the predicted quadratic dependence up to the time of coalescence. 3. 2. Mean particle diameter Kinetic nucleation theory predicts a dependence of the individual crystallite diameter
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
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Fig. 5. Dependence of the AES signal on the deposition time for gold on carbon. Substrate temperature T = 298 K; deposition rate ND = 3.7 × 1013 cm -2 s -1 . Fig. 6. Relative coverage of the substrate surface vs. deposition time for gold on carbon. Substrate temperature T = 916 K; deposition rates: (a) 1013 cm -2 s-], (b) 2 x 1013 cm -2 s-], (c) 4 x 1013 cm-2 s-1 . The arrows mark the beginning of growth coalescence.
on the square root of the deposition time. If we are using data obtained by the AES-EM system, we can only evaluate the mean particle diameter versus deposition time by using the image analysing computer. An example for gold and carbon is shown in Fig. 7. The predictions of the theory seem to be confirmed. In Fig. 8, however, for silver on silicon monoxide two different modes of growth are visible. The results were obtained by Poppa is using in situ electron microscopy. Although the results were obtained in the coalescence stage of film growth, which is not comparable with the nucleation stage, it is indisputable that averaging methods can lead to a loss of information. 3.3. Cluster size d i s t r i b u t i o n s
Cluster size distributions in micrographs taken from gold-rocksalt specimens were evaluated by Schmeisser 31 . All distributions show qualitatively the same shape, inde-
110
M. HARSDORFF
T A
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,0
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Fig. 7. Mean particle diameter vs. deposition time for gold on carbon. Substrate temperature T = 916 K; deposition rates: (a) 4 x 1013 cm -2 s -1 , (b) 2 x 1013 cm -2 s -I , (c) 1013 cm "2 s -1
CRY~ALLITES
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Fig. 8. Growth of silver on amorphous SiO. Left, electron micrograph showing two different growth modes; right, particle diameter vs. deposition time.
pendent of experimental parameters: a sharp m a x i m u m at large diameters f o l l o w e d by an abrupt drop; the increase is shallower and depends on the position of the m a x i m u m . This result agrees with that reported by D o n o h o e and Robins a2, w h o also found a single peak in the size distributions at elevated temperatures. A typical example is shown in Fig. 9. In this figure the whole development o f the nucleation, growth and coalescence process can be seen. The increase in crystal density with time is given by the m o n o -
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
111
tonically increasing shaded total area under the distribution functions. With increasing deposition time the crystal diameter grows too. This is described by the shift o f the steep increase of the distribution on the d-axis. The flattening of the decreasing branch is caused by severe coalescence at times above 45 s. A more detailed study shows the unexpected result that, besides the shifting of the maximum due to cluster growth, the
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Fig. 9. Comprehensive description of the complete nucleation process for gold on rocksalt by means of cluster size distributions. Fig. 10. Time dependence of cluster size distributions (gold/rocksalt). left branch of the distributions drops with increasing deposition times even in the nucleation stage. This is shown in detail in Fig. 10. It should be noted that a reduction of the small cluster population takes place at constant nucleation rate. Zinsmeister 2 has shown that at a constant nucleation rate without coalescence the distribution curves would coincide with each other in the lower region. Either growth coalescence or cluster mobility must therefore be taken into account. Using Venables' calculations 3 for the determination of the maximum cluster density that is caused by growth coalescence, it is found that the experimental values differ systematically from these theoretical estimations. The theory leads to results which are larger than the measured data. Similar results were reported by Robins et al. 33 Hence the mobility of small clusters is thought to be the most important effect causing coalescence.
3. 4. Spatial distribution o f clusters In order to describe the spatial distribution of crystallites, a correlation function is defined as the ratio of the actually measured number density of clusters at a distance
112
M. HARSDORFF
from a given cluster to the macroscopically measured concentration 34. The correlation function can be calculated from the x, y coordinates of crystallites using a computer. A typical result is shown in Fig. 11. It can be seen that there is a sharp decrease of the correlation function at small distances. This means that the probability of finding closely neighbouring crystallites is less than would be expected in the case of a random distribution, which corresponds to a correlation function equal to one. There are two possible explanations: (1) the clusters are sinks for single atoms, leading to a reduction of the nucleation rate; (2) coalescence of small clusters reduces the crystallite density. If the first explanation is valid, a very strong dependence of the correlation function on the substrate temperature should be observed, in contradiction to the experiments. For { Korr (r, Ar)
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Fig. 11. Correlation functions at different number densities of clusters (gold/rocksalt). the second case Venables 3 has described a diffusion formalism for small clusters. The correlation function should only depend weakly on the surface coverage and not on substrate temperature and impinging flux, as confirmed by experiment.
3.5. Epitaxial nucleation There are marked disagreements between different authors about the processes which lead to a completely oriented continuous epitaxial film. At one extreme there is the opinion that particles develop epitaxial orientation during growth which can be destroyed when coalescence occurs 3s. At the other extreme there is the opinion that the final orientation is determined by the most favourable orientation of critical nuclei 36'37. For gold on potassium chloride Puskeppel showed that part of the material is deposited epitaxially in the nucleation stage 1°. The degree of epitaxial (parallel) orientation was defined by the number of parallelly oriented crystallites, counted with a Quantimet in 100 dark field micrographs, divided by the total number of crystallites, obtained by counting all crystallites in correlated bright field images. The evaluation procedure is demonstrated in Fig. 12. In the upper part of the graph the dependence of the crystallite density of oriented material and the total number density of crystallites are plotted against the deposition time. The quotient of these curves, the degree of orientation, is plotted in the lower part of the graph. The extrapolation to zero deposition time leads to an initial orientation, caused by epitaxial nucleation. This initial degree of orientation shows a characteristic dependence on the deposition rate and the substrate temperature, as predicted by theory 38.
113
EXPERIMENTAL PROBLEMS IN THIN FILM NUCLEATION
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&tt A e 10|114
/
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Fig. 13. Description of the complete process of epitaxial nucleation, growth and alignment by means of cluster size distributions (gold/potassium chloride).
114
M. HARSDORFF
The graph of cluster size distribution versus deposition time shown in Fig. 13 gives a qualitative insight into the process of epitaxial nucleation, growth, alignment and coalescence. The solid curves show the size distributions of all crystallites, oriented and random, whilst the broken lines show the distributions of the (100)-oriented crystallites, assuming the epitaxial order to be independent of particle diameter. The hatched area is the measured distribution of oriented material. In the nucleation stage (0-150 s) the observed distributions are shifted towards larger diameters. In epitaxial growth the mobility of small clusters leads not only to an alignment of crystallites but also to a formation of larger clusters by mobility coalescence. In the later growth coalescence region all large crystallites are parallelly oriented. This shows that the growth coalescence of differently oriented crystallites leads in this case to large (100)oriented crystallites. Obviously we have to distinguish between three different stages of formation of an epitaxial layer: (1) oriented nucleation with a definite dependence of the epitaxial order on substrate temperature and deposition rate; (2) alignment of small crystallites after nucleation and the formation of larger oriented clusters by coalescence of migrating particles; (3) orientation changes during growth coalescence, perhaps under the in fluence of the recrystallization energy. 4. CONCLUSIONS It is well known that nucleation and cluster growth are dominated by single atom processes and can be described by the rate equation approach 2. The systematic investigation of cluster size distributions, spatial cluster distributions and epitaxial growth suggests that corrections to the coalescence caused by the mobility of small clusters and the growth of crystallites are necessary. In the present situation a further refinement of the theoretical description seems to be desirable because up to now only a qualitative agreement with experimental results is obtainable. In the past only a few combinations of substances have been investigated, e.g.f.c.c. metals on alkali halides and on amorphous carbon. Evidently experiments should be extended to other substrates and deposition materials. The combination of different investigation methods should be continued and extended. The advanced technique of in situ electron microscopy combined with LEED-AES studies and electronic image computation seems to be an effective tool to attack the outstanding problems of random and epitaxial nucleation and growth kinetics. REFERENCES
1 D. Walton, J. Chem. Phys., 37 (1962)2182. 2 G. Zinsmeister, Vacuum, 16 (1966) 529; Thin Solid Films, 2 (1968) 497; 4 (1969) 363; 7 (1971) 51. 3 J. A. Venables, Philos. Mag., 27 (1973) 697. 4 B. Lewis, Surf. Sci., 21 (1970) 273,289. 5 V. Halpcrn, J. Appl. Phys., 40 (1969) 4627. 6 K. I. Routledge and M. J. Stowell, Thin Solid Films, 6 (1970) 401.
EXPERIMENTAL PROBLEMS 1N THIN FILM NUCLEATION 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
115
R. Kern, A. Masson and J. J. Metois, Surf. ScL, 27 (1971) 463. J. J. Metois, M. Gauch, A. Masson and R. Kern, Thin Solid Films, 11 (1972) 205. J. J. Metois, Surf. Sci., 36 (1973) 269. M. Harsdorff and A. Puskeppel, submitted to Thin Solid Films. H. Poppa, J. Vac. Sci. Technol., 2 (1965) 42. H. Poppa, J. Appl. Phys., 38 (1967) 3883. A. Barna, P. B. Barna and 1. F. Pocza, Vacuum, 17(1967) 219. H. Schmeisser and M. Harsdorff, Thin Solid Films, 14 (1972) 321. H. Po,ppa, R. D. Moorhead and K. Heinemann, Nucl. Instrum. Methods, 102 (1972) 521. M. Paunov and M. Harsdorff, Z. Naturforsch., 29a (1974) 1311. T. N. Rhodin, P. W. Palmberg and C. J. Todd, J. Vac. Sci. Technol., 6 (1969) 467. D.G. Lord and M. Prutton, Thin Solid Films, 21 (1974) 341. H. Schmeisser, Vak.-Tech., 21 (1972) 165. D. I. Stirland, Appl. Phys. Lett., 8 (1966) 326. J. L. Robins and V. N. E. Robinson, Vacuum, 18 (1968) 641. G. A. Basset, in E. Rutner, P. Goldfinger and I. P. Hirth (eds.), Proc. Int. Symp. on Condensation and Evaporation of Solids, Gordon and Breach, New York, 1964, p. 599. G. Honjo, S. Shinozaki and H. Sato, Appl. Phys. Lett., 9 (1966) 23. S. Shinozaki and H. Sato, J. AppL Phys., 43 (1972) 701. G. Honjo and K. Yagi, J. Vac. ScL Technol., 6 (1969) 576. M. Valdr~, E. A. Robinson, D. W. Pahley, M. J. Stowell and T. I. Law, J. Phys. E, 3 (1970) 501. C. F. Fisher, Microscope, 19 (1971) 1. T. N. Rhodin, Anal Chem., 27 (1955) 1857. R. Weyl, Z. Angew. Phys., 13 (1961) 283. R. Anton and M. Harsdorff, Thin Solid Films, 22 (1974) 23. H. Schmeisser, Thin Solid Films, 22 (1974) 83. A. J. Donohoe and J. L. Robins, J. Cryst. Growth, 17 (1972) 70. J. L. Robins, A. J. Donohoe and B. F. Usher, Proc. 6thlnt. Vac. Congr. 1974, inJpn. J. Appl. Phys., Suppl. 2, Part 1 (1974) 559. H. Schmeisser, Thin Solid Films, 22 (1974) 99. E. Bauer and H. Poppa, Thin Solid Films, 12 (1972) 167. B. Lewis, Thin Solid Films, 7 (1971) 179. C. A. Henning and J. S. Vermaak, Philos. Mag., 22 (1970) 281. M. Harsdorff, Z. Naturforsch., 23a (1968) 1253.