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Surface properties important for film formation
Thin Solid Films, 32 (1976) 117-126
© Elsevier Sequoia S.A. Lausanne-Printed in Switzerland
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SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION* O. S. HEAVENS University o f York, York [Gt. Britain)
(Received August 25, 1975)
1. INTRODUCTION A considerable amount of experimental data has now been accumulated which has been obtained under clean vacuum conditions. The new experimental techniques of the past ten years have yielded invaluable information on such matters as substtate surface structures, adsorbate structures, deposit structures and orientation, nucleation features and post-deposition phenomena. In some cases this has led to the emergence of "recipes" for the preparation of single-crystal films of remarkable perfection (e.g. the II-IV compoundsl). The role o f the substrate in determining the crystal structure of films is often reasonably well understood. Crystallite orientations can be successfully interpreted in terms of misfit dislocations at grain boundaries 2. The role of contaminants in influencing growth is often appreciated, if not actually understood. While still lacking a complete all-embracing theory of epitaxial growth, we are in a stronger position now than ever before for making plausible predictions on which depositsubstrate pairs are likely to yield epitaxial films. One of the more severe present limitations, however, is our inability to observe the orientation of very small (~ten atom) clusters during the early condensation stage. The lively controversies which have emerged in recent years on cluster behaviour and mobility remain as yet unresolved. In this paper, recent work will be reviewed which contributes to our present understanding of the role of the substrate in determining the structure and behaviour of films. 2. SURFACE STRUCTURES The combination of LEED and Auger spectroscopy (AES) has enabled a much more precise idea of the true nature of single-crystal surfaces than had hitherto been available. Under the best conditions, AES enables quite small fractions of a monolayer of impurity to be detected on a surface, whilst LEED may give a reasonably accurate idea of the geometrical disposition of surface atoms. In principle, LEED should be able to detect distortions from normal interatomic spacings and small displacements from normal "bulk" sites for surface atoms. Thus the results of Martin and Somorjai 3 and others 4,s on the (100), (110) and (111) faces of aluminium suggest a significant * Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 2-I-2.
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contraction of about 10% of the spacing of the (110) planes on the dodecahedral face, but with no detectable changes on the cube or octahedral faces. This behaviour has been accounted for in a simple way by Heine 6 who points out that the free electron distribution around the aluminium ions on a (110) face will tend to "flatten" at the metal-vacuum interface in such a way that the electrostatic centre of the free electron distribution moves in towards the bulk. The surface ions are then pulled in by the electrostatic forces involved. No such argument applies to the (111) face of AI, so that the observed bulk spacing for these planes is not surprising. In similar LEED studies of the (111) face of Pt, Kesmodel and Somorjai 7 conclude that there is no reason for expecting a departure from bulk spacing in this case. The extraction of structural information from LEED data is more involved than, for example, in the X-ray or high energy electron diffraction cases, since the effects of multiple scattering are large. Kinematic theory is inadequate. In some circumstances, the effects of multiple scattering can be reduced by averaging processes (e.g. ref. 8) and the single-scattering data extracted. For close-packed surfaces, the angular distribution of scattered intensity (other than in the near-forward scattering direction) for the averaged data is found to agree reasonably well with that based on a kinematic calculation. This method, known as the constant-momentum-transfer averaging method, appears to be capable of detecting small displacements from normal atomic positions. Thus in studies of W (110) surfaces Buchholz et al. 9 deduce that the W atoms cannot be displaced by more than 0.06 N from the "bulk" position. Moreover, in the case of adsorbed O, forming the structure W (110) p(2 x 1)-O, no significant displacement (< 0.05 A) of the W atoms from the surface plane is indicated. There are difficulties, however, in averaging methods such as these. The scattering cross sections and mean free paths which need to be inserted in the kinematic expressions differ significantly from those determined by other methods, so that the physical significance of these factors is obscure. On account of the very large amount of computing effort required for full-scale LEED calculations in which multiple scattering effects are included, the number of crystal surfaces studied so far in this way is small. Less detailed information-e.g, on the form of the many superstructures commonly observed on crystal surfaces-can be obtained without the full-scale analysis required for precision location of atomic positions. Such results require an examination of the position of LEED spots, which readily indicate the nature of any superlattices present. It should be emphasized, however, that reliable information on surface structures requires the study of diffracted intensities as well as of directions. The usual way in which this is obtained is by deriving intensity versus energy (I-V) profiles and comparing with experimental values. When, as is often the case, experiments are carried out over only a limited range of angles of incidence, this method is of limited reliability. Thus two independent analyses aimed at determining the spacing between sulphur and nickel layers in Ni(001)-S-c(2 x 2) give (a) 1.7 -+ 0.1 ~ and (b) 1.3 -+ 0.1 A. The Group d'Etude des Surfaces ~° has shown that a more satisfactory approach is to examine iso-intensity contours in (E, 0) and (0, O) coordinates. Not only does this method improve sensitivity, but the computing effort required is less than that for I- V comparisons.
SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION
119
The importance of the types of superlattice structure which are known to form on crystal surfaces for the structures of a growing film can be illustrated by the example of the growth of Si crystals from the melt. LEED studies of freshly cleaved Si reveal a (2 x 1) structure on the (111) cleavage face which, on annealing, is transformed to the classic (7 x 7) structure. Whereas the (2 x 1) structure is believed to arise from a simple displacement of surface atoms, the (7 x 7) results from a major reorganization of the surface which leaves 26.5% of the normal lattice sites vacant. The character of the crystal grown on such a surface will depend on whether the (2 x 1) structure is present or whether sufficient time has passed for the (7 x 7) structure to form. The former would be expected under conditions of rapid growth and the latter by slow growth, where the time reference is related to the (2 x 1) to (7 x 7) transformation time. On the above argument, slower growth would be expected to produce crystals with a high vacancy concentration. The results of Van Vechten ~1 confirm this dramatically. For growth rates up to 4 mm min -1 , 106-10 a vacancy clusters per cubic centimetre are observed. Beyond this growth rate, the vacancy concentration falls to about 1 c m -3. Although this represents a very high growth rate in relation to that for films grown by, for example, vapour deposition or sputtering, the lower growing temperature would imply a slower rate of surface reconstruction. Thus the present situation over surface structures is (i) that a complete LEED study should, at the expense of major computing routines, enable reasonably accurate analysis to be made of the location of surface atoms, (ii) that through suitable averaging processes, involving far less computing time, reliable results can be expected in some cases, particularly for close-packed planes, and (iii) that accurate information on surface structures, including that on superlattices and surface reconstructions, is likely to provide an invaluable guide to the form taken by a depositing film. The main remaining uncertainty is the role of impurities at concentrations below those detectable by Auger spectroscopy. 3. EPITAXIAL GROWTH It is sometimes suggested that, despite the many square metres of gold which have been grown epitaxially on rocksalt, we remain sadly lacking in a unified theory of epitaxy. Even supposing that all the factors which can influence epitaxial growth were always under control, and all the relevant parameters known, it would seem unlikely that any compact single description could apply to any deposit-substrate pair regardless of the widely varying relative binding energies involved. Epitaxial growth situations are often further complicated by a marked dependence on impurities, by the uncertainties of the roles of re-evaporation, surface diffusion or diffusion into the substrate and by our inability to observe the precise behaviour of sub-electronmicroscopic clusters at a critical stage in the film growth. Furthermore, one is often uncertain of the extent to which the processes under study are influenced by the method of examination. Electron-stimulated desorption is an interesting topic in its own right but can be an embarrassment. Despite the above limitations, the major factors w ~ c h govern many epitaxial processes are beginning to be understood. Although there are as yet few generalizations, some growth features follow the expected
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behaviour in relation to relative binding energies. Thus the initial stage of deposition of metals on non-metals often takes the form of three-dimensional nuclei. Although nucleation effects are observed on some metal-metal systems, there is evidence that the substrate regions between crystallites may be covered by monolayer deposit.
3.1. Significance of lattice misfit Since a monocrystalline substrate is essential for the occurrence of epitaxial growth, it is to be expected that, for deposits which bond strongly to the substrate, lattice misfit will be an important parameter. Two examples suffice to illustrate the way in which f'tlm structure and properties are so dependent. In order to grow films of Gaxlnl_xAs epitaxially, over the range 1.0 > x > 0.43, Nagai and Noguchi 12 prepared crystals of Gaxlnl_xASyPl_y in which a continuous range of lattice parameters could be obtained by adjusting the values of y. When the lattice parameter of the substrate crystal matched that of Gaxlnl _xAs, good epitaxial films could be grown. Similarly, Enstrom and Fisher 13 adjusted the composition of InxGal _x P until its lattice parameter matched that of GaAs, under which condition the quantum of the GaAs layers increased considerably. Theories of the effects of mismatch on the stability of an oriented overgrowth date from the earliest days of epitaxy. From a variety of potential models of the substrate surface, the general conclusion emerges that limiting misfits for stability can be tolerated and the limited misfit decreases with increasing number of layers of the deposit crystal (assuming layered growth). Figure 1 compares the results for a number of such models 14. These results suggest that pseudomorphic growth should occur in some circumstances. Although some doubt exists about the earliest observations of abnormal spacings of deposit layers, there is now considerable evidence in support of this phenomenon (see, for example, refs. 19 and 20). In studies of copper grown in ultrahigh vacuum on single-crystal nickel, Chambers and Jackson 21 extract misfit data from measurements of the spacing of moir6 fringes and compare the lattice strain as a function of thickness with the theoretical predictions of Jesser and Kuhlmann-Wilsdorf 16, obtaining excellent agreement for film thicknesses up to 10 nm. The films were deposited at room temperature and annealed at 300 ° C. Alloy formation would not be
E i h
Fig. 1. Limiting misfit as a function of the number of layers: A, parabolic pertodlc potential ; B, refined model of Jesser and Kuhlmann-Wilsdorfl6;C, Stoop-van der Merwe model14,17'; D, Peierls-Nabarro model Is . •
"
"
15
SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION
121
expected at this temperature. Evidence suggesting that this does not occur comes from Auger studies in which no decrease in the amplitude of the copper peak is observed. If significant alloying occurred on annealing, the Cu signal would fall significantly. The results suggest that the form of growth is that of a monolayer formation followed by crystallite nucleation (Stranski-Krastanov). 3.2. Nucleation p h e n o m e n a
Although the foregoing treatment indicates the likely stability of layered structures once they have formed, it gives no indication of the process of formation. In the case of metals on alkali halides, f'dms do not in fact grow by the successive deposition of extensive layers, but by the formation, through surface diffusion processes, of nuclei. Information on the orientation of very small (few atom) nuclei is not generally available, but it is likely that the orientations adopted in the initial stages will bear some simple relationship to the substrate orientation. When the nuclei have grown to the size at which observations may be made, it becomes possible to apply the ideas of classical nucleation theory. Considerable progress in these studies 22 has enabled many features of nucleation behaviour to be reasonably well understood, although the observed initial development of the nucleation versus time curve remains a mystery. Although a variety of detailed growth and coalescence phenomena, involving diffusion of both individual atoms and dusters, are known to occur, the problems of including all these effects in a single description are formidable. From the experimental point of view it is known that defects on the substrate surface can play a significant role in determining the perfection and structure of an epitaxial film. Nucleation theory can be extended to include such heterogeneous effects. It is necessary not simply to postulate nucleus formation on each defect site, but to take account of the fact that a growing nucleus acts as an effective sink for atoms arriving within a certain distance (nucleation exclusion zones). The size of such zones increases with time; if they include active sites on which nucleation has not yet started then these sites become ineffective for initiating further nucleation 23'~. In some cases, there appears to be evidence that atoms which do not strike an active adsorption site on a surface may diffuse into the substrate 2s. One important feature of the last-mentioned work is that experiments were carried out over a range of two orders of magnitude in background pressure with no detectable effect on the form of deposits obtained, suggesting that reactions with residual gas26 are of little importance in these experiments (Au, Ag, Pd on C, SiO2). On the other hand, there have been reports indicating residual gas effects on the epitaxial growth of films on, particularly, alkali halides 27-29. In some respects therefore the role of the residual gas remains an open question. The role of surface defects created by electron bombardment in influencing fdm structure is now well established. The creation of F-centres in the surfaces of alkali halides is reasonably established by the work of Lord and Gallon a° in Auger studies on LiF. The effect of F-centre formation on the epitaxial growth of Ag on KC1 (Fig. 2) is illustrated by the work of Lord and Prutton 31. Similarly, the role of colloidal centres formed electrolytically in NaC1 on the epitaxy of UO2 has been established by Vasilu et al. 32 and of diffused Mn 2+ ions (impurities in NaC1, KCI, LiF and LiC1 crystals) on the epitaxy of Au and Ag by Pedrero et aL 33
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(a)
(b)
(c)
(d)
Fig. 2. (a), (c) Electron micrograph/diffraction pattern for 4 nm Ag on cleaved KCI. (b), (d) Corresponding figures for KCI irradiated by 500 eV electrons, 25/~A c m - 2 for 6 s at 50°C. Density of F-centres 7 x 1013 cm -2. (After Lord and Prutton 31.) 3.3. Prediction o f e p i t a x y
Although, as mentioned above, the existence of zero misfit between substrate and deposit lattice enables films of high structural perfection to be obtained (between materials of similar bonding types), epitaxial growth is often observed in the face of substantial misfits. In some cases this can be reasonably well understood by considertng the vernier effect of coincidences between adjacent lattice atoms. If n spacings of lattice a correspond to m spacings of lattice b, then the misfit w = (b - a)/a is given by n / m - 1. For certain values of misfit, n and m will be small integers, indicating frequent coincidences between atoms in adjacent layers. Kotz6 et al. 34 define the first coincidence number N * as N* = 1 ~ 1/W
where W = Iwl and N * is rounded to the nearest integer. For low values of N * , nearcoincidences will occur frequently along lattice rows and this might be expected to encourage epitaxy. The results of a survey of metal-alkali halide systems is shown in Table I, where a description of the "degree" of epitaxy (N, none; G, good; M, moderate; W, weak) is given. Although many factors other than simple misfit may influence the degree of epitaxy, the above results indicate generally good epitaxy for low N * values and poor (or absence of) epitaxy for large values. Kenty 35 has examined the extent to which an elaboration of misfit ideas treats the problem two-dimensionally, by defining a figure of merit related to the strain energy involved in two-dimensional deformation to produce matching. In studies of the epitaxial growth of GaAs on a large number of BeO planes, he finds such an elaboration of very little predictive value. It is clear that simple misfit criteria can be expected to be only a somewhat general guide. The question of fitting between deposit and substrate lattices has been considered from another standpoint by Henning and Vermaak 27, who consider the concept of
SURFACE
PROPERTIES
IMPORTANT
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FOR FILM FORMATION
TABLE I
Substrate
NaF NaC1 NaBr NaI KF KC1 KBr KI RbCI RbBr RbI
Deposit Au
Ag
Al
Cu
Ni
Pd
Pt
N*
N*
N*
N*
N*
N*
N*
9 5 4 4 5 4 4 3 4 3 3
N N W G N G G G G G G
10 5 4 4 5 4 4 3 4 3 3
N W M G N W M G W M G
9 5 4 4 5 4 4 3 4 3 3
N M W W -
6 4 4 3 4 3 3 3 3 3 3
N M G G M G G G G G G
5 4 3 3 4 3 3 3 3 3 3
G G G M -
7 4 4 4 5 4 3 3 3 3 3
M M M M -
8 4 4 4 5 4 3 3 3 3 3
G -
critical accommodation centres for four-atom (100) clusters in which each atom lies in a potential minimum on the substrate and where both nearest neighbour and nextnearest neighbour bonding requirements are satisfied. For substrate anion and cation radii r a and rc, the radius r d of a deposit atom which exactly satisfies the critical accommodation condition is given by ra 2 --/.c 2 + d 2
r d = 2(re +x/2d - ra) where d = ra + rc. Provided the radius of the deposit atom exceeds rd, the formation of nuclei satisfying the above conditions is possible (on a "hard-sphere" model) and epitaxy should occur. The extent to which this rule can act as a guide to the occurrence of epitaxy has been examined by Lord and Prutton al, yielding the results given in Table II. Squares indicate the occurrence of good epitaxial growth. Circles correspond to cases where epitaxial growth does not occur, although in some cases the creation of damage sites by electron bombardment results in some measure of preferred orientation. The line in Table II indicates the critical radius of a deposit atom according to the Henning and Vermaak model. Cases above the line should show epitaxy; those below should not. The only exceptional case appears to be A1 on KC1, in which the deposit atom radius and critical value are very close together. It is unlikely that simpl e criteria such as those referred to above could be developed for more complex deposit-substrate combinations. The above models indicate that, for certain systems, reasonable predictions of the likelihood of epitaxy occurring can be made.
3.4. Epitaxy on amorphous layers The results of Distler and his coworkers on the epitaxial growth of films on amorphous overlayers to single crystals caused problems of interpretation at an early stage. Other workers' failure to repeat the experiment led to highly critical comments 36 on the reality of the effect in question. Certainly any discussion of growth in terms of
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O. S. HEAVENS
TABLE II Substrate rd
Deposit Ni(1.24)
Cu(1.28)
A1(1.43)
Ag(1.44)
Au{l.44)
NaV
1.07
[]
[]
[]
[]
LiF
1.25
[]
[]
[]
[]
[]
MgO
1.33
(D
C)
[]
[]
[]
KC1
1.44
C)
(D
[]
(D
[]
NaCl
1.63
0
0
0
0
0
Ultrahigh vacuum conditions; & vacuo cleavage of substrate.
substrate lattice periodicity appears irrelevant to the situation where the crystal is covered with an amorphous layer in excess of 10 nm thick. Although doubts could be raised concerning these experiments (e.g. on the continuity of the amorphous films used), these cannot apply to the later experiments 37 in which epitaxy was demonstrated on a polyvinyl chloride replica of the crystal surface. Electron micrographs show no sign of growth at, for example, steps formed on the replica and the explanation involves recognition that the PVC film displays electret behaviour. Thus the replica forms an "electrical copy" of the surface and the mode of epitaxial growth observed suggests that the features copied are those of charged point defects and defect clusters. From other work on epitaxy it is certainly the case that defects do play a part in the epitaxial process. While sceptics will no doubt remain, there are by now severa! observations 3a'39 which are very difficult to account for by any of the more .conventional explanations for epitaxial growth. 4. PHYSICAL PROPERTIES OF FILMS INFLUENCED BY THE SUBSTRATE The previous discussion shows the extent to which the crystal form of a deposit material may be influenced by that of the substrate. Since the epitaxial film represents a highly ordered state, we could expect such films to be structurally stable. This is illustrated by the studies of lead films on mica4°. Non-epitaxial films are observed to undergo significant recrystallization on temperature cycling, resulting in extensive growth of hillocks. Epitaxial films show no such change. In general, we should expect any of the structure-sensitive physical properties of films to depend on substrate conditions and this is generally observed to be the case. Thus the optical constants of very thin (few nanometres) metal films deposited on glass or crystal substrates tend to be determined largely by the size and shape of the constituent crystallites. The values obtained bear little relationship to the bulk values, as is expected simply on the grounds that surface scattering plays a dominant role. Considerable caution is needed in interpreting the dispersion behaviour of thin film specimens in terms of solid state theory. Thus very thin films of copper (~8 nm thick) are observed to display an abnormal adsorption peak at around hv = 7.5 eV in addition
S U R F A C E PROPERTIES IMPORTANT FOR FILM F O R M A T I O N
125
to peaks associated with interband transitions 4~ . On exposure to nitrogen, the abnormal peak disappears. Such extra peaks can be interpreted in terms of plasma oscillations, which will occur at frequencies depending on the crystallite size and shape. Significant changes are observed in the crystallite size and shape of the Cu grains in these experiments. In contrast with the behaviour of metals, the refractive index of many dielectric materials appears to depend mainly on the proportion of a film occupied by voids. Lower-than-bulk refractive indices can be achieved by deposition under conditions where a large void concentration is obtained. In the case of semiconducting materials, significant effects may arise through the contribution to the polarizability of the material through dangling bonds. A case which has received some attention is that of silicon. It is known that the refractive index of amorphous films is significantly higher than that of the monocrystalline material. From classical dispersion theory the refractive index of a film in which a fraction s of the Si bonds are dangling can be obtained 42 in the form nf 2 - 1 _ pf (dam~dot) s nc 2 - 1 Pc (1 -- $)2 where pf, Pc are the film and single-crystal densities, dcr is the bond length in the single crystal and dam is the mean bond length in the amorphous material, obtained from the radial distribution function. The value of the ratio dam/dcr is a matter of some uncertainty, so that the above expression cannot give nf with great precision. For plausible values ofdam/der , however, differences between nf and n c of only a few per cent are indicated. Recent measurements 4a at photon energies 0.5 eV and 1.75 eV reveal increases of 30-40% over the single-crystal values. (These results help to explain apparently puzzling observations obtained in infrared multilayer optical systems, in which the resultant optical characteristics indicate index values for the semiconducting films significantly different from the bulk values.) Films of thickness approximately 1/am were formed on oxidized silicon at temperatures from 20 °C to 880 °C. Measurements of electron diffraction linewidths gave the sizes of the coherent scattering regions at each temperature, revealing an increase from about 0.8 nm at 20 °C to 10 nm at 880 °C. Spin resonance studies confirmed the presence of free spins (8 x 1020 cm -3) for the 20 °C films and no detectable resonance ( < 0.5 x 1020 spins cm -3) for the 5,5
I
,o
0
/
J/E.
O~ -I,0 Ph~m ~
/
1"5 2.o h~bV)
,c
25
Fig. 3. Dependence of t h e refractive index of silicon films on the deposition conditions: full lines, results of Schwidefsky43; o, from m e a s u r e m e n t s on b a n d w i d t h s of interference filters.
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O. S. HEAVENS
8 8 0 °C fihns. T h e refractive i n d e x fell f r o m 4.5 to 3.5. A f u r t h e r i l l u s t r a t i o n o f the d e p e n d e n c e o f t h e refractive i n d e x o f Si films o n the m e t h o d o f d e p o s i t i o n and o n substrate t e m p e r a t u r e is s h o w n in Fig. 3. T h e p o i n t s o n this diagram refer to Si films in Si-MgF2 multilayers, d e p o s i t e d at a s u b s t r a t e t e m p e r a t u r e o f 2 0 0 °C, f r o m w h i c h the i n d e x o f the Si fihns is d e d u c e d f r o m the o b s e r v e d optical t r a n s m i s s i o n curves. These results lie closer to the 380 °C p o i n t s t h a n m i g h t have b e e n e x p e c t e d , w h i c h may reflect the d i f f e r e n t n u c l e a t i n g c h a r a c t e r i s t i c s for the Si layers o n t h e MgF2 films used in the multilayer. REFERENCES 1 D. B. Holt, Thin Solid Films, 24 (1974) 1-53. 2 0 . lgarashi, J. Appl. Phys., 42 (197l) 4035--43. 3 M. R. Martin and G. A. Somorjai, Phys. Rev. B, 7 (1974) 3607-15. 4 G. E. Laramore and C. B. Duke, Phys. Rev. B,5 (1972) 267-85. 5 D. W. Jepson, P. M. Marcus and F. Jona, Phys. Rev. B,6 (1972) 3684-90; 8 (1973) 1786. 6 V. Heine, Jpn. J. Appl. Phys., SuppL 2, Part 2 (1974) 679. 7 L. L. Kesmodel and G. A. Somorjai, Phys. Rev. B, 1 l (1975) 630-7. 8 T. C. Ngoc, M. G. Lagally and M. B. Webb,Surf SoL, 35 (1973) 117--44. 9 J. C. Buchholz, G.-C. Wang and M. G. Lagally, Surf Sci., 49 (1975) 508. 10 Group d'Etude des Surfaces (D. Aberdam, R. Baudoing, C. Gaubert, Y. Gauthier and V. Hoffgtein), Surf ScL, 48 (1975) 497-508. 11 J. A. Van Vechten, Appl. Phys. Lett., 26 (1975) 593-6. 12 H. Nagai and Y. Noguchi, Appl. Phys. Lett., 26 (1975) 108-10. 13 R. E. Enstrom and D. G. Fisher, J. Appl. Phys., 46 (1975) 1976-82. 14 L. C. A. Stoop, Thin Solid Films, 24 (1974) 229. 15 J. H. van der Merwe, J. Appl. Phys., 41 (1970) 4725. 16 W. A. Jesser and D. Kuhlmann-Wilsdorf, Phys. Status SolidL 19 (1967) 95. 17 L. C. A. Stoop and J. H. van der Merwe, Thin Solid Films, 1 7 (1973) 291-309. 18 See J. H. van tier Merwe, ,L Appl. Phys., 34 (1963) 117-27. 19 R. Kuntze, A. Chambers and M. Prutton, Thin SolMFilms, 4 (1969) 47-60. 20 J. D. Briante, J. M. Corbett and F. W. Boswell, Thin Solid Films, 14 (1972) 305-20. 21 A. Chambers and D. C. Jackson, Philos. Mag., 31 (1975) 1357-71. 22 G. Zinsmeister, Jpn. J. Appl. Phys., Suppl. 2, Part 1 (1974) 545-50. 23 I. Markov and D. Kashchiev, Thin Solid Films, 15 (1973) 181-9. 24 A. Milchev, S. Stoyanov and R. Kaischev, Thin Solid Films, 22 (1974) 255-65. 25 J. F. Hamilton and P. C. Logel, Thin Solid Films, 23 (1974) 89-100. 26 1. A. Venables, Thin Solid Films, 18 (1973) S l l . 27 C. A. O. Henning and J. S. Vermaak,Appl. Phys. Lett., 15 (1969) 3. 28 J. S. Vermaak and C. A. O. Henning, Philos. Mag., 22 (1970) 269-80; 281-9. 29 A. K. Green, E. Bauer and J. Dancy, J. Appl. Phys., 41 (1970) 4736. 30 D.G. Lord and T. E. Gallon, Surf ScL, 36 (1973) 381. 31 D.G. Lord and M. Prutton, Thin SolMFilms, 21 (1974) 341-56. 32 F. Vasilu, V. Topa, N. G. Popescu-Pogrion and M. I. Bi'rjega, Jpn. J. Appl. Phys., SuppL 2, Part 1 (1974) 605. 33 E. Pedrero, T. Oca~a, A. G6mez and M. J. Yacam~in, Thin Solid Films, 27 (1975) 149-53. 34 I. A. Kotz6, J. C. Lombaard and C. A. O. Henning, Thin Solid Films, 23 (1974) 221-32. 35 J. L. Kenty, Thin Solid Films, 26 (1975) 181-95. 36 K. L. Chopra, J. Appl. Phys., 40 (1969) 906. 37 G. I. Distler and E. I. Tokmakova, Soy. Phys. Crystallogr., 17 (1972) 545. 38 A. Barna, P. B. Barna and J. F. Pocza, Thin Solid Films, 4 (1969) R32. 39 L. L. Aksenova, G. I. Distler, A. V. Kovda and E. 1. Kortukova, Soy. Phys. Solid State, 15 (1973) 1100. 40 S. K. Lahiri, J2 AppL Phys., 46 (1975) 2791. 41 F..Payan, Thin Solid Films, 18 (1973) 85-9. 42 J. A. Van Vechten, Phys. Rev., 182 (1969) 891. 43 F. Schwidefsky, Thin Solid Films, 18 (1973) 45-52.
© Elsevier Sequoia S.A. Lausanne-Printed in Switzerland
117
SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION* O. S. HEAVENS University o f York, York [Gt. Britain)
(Received August 25, 1975)
1. INTRODUCTION A considerable amount of experimental data has now been accumulated which has been obtained under clean vacuum conditions. The new experimental techniques of the past ten years have yielded invaluable information on such matters as substtate surface structures, adsorbate structures, deposit structures and orientation, nucleation features and post-deposition phenomena. In some cases this has led to the emergence of "recipes" for the preparation of single-crystal films of remarkable perfection (e.g. the II-IV compoundsl). The role o f the substrate in determining the crystal structure of films is often reasonably well understood. Crystallite orientations can be successfully interpreted in terms of misfit dislocations at grain boundaries 2. The role of contaminants in influencing growth is often appreciated, if not actually understood. While still lacking a complete all-embracing theory of epitaxial growth, we are in a stronger position now than ever before for making plausible predictions on which depositsubstrate pairs are likely to yield epitaxial films. One of the more severe present limitations, however, is our inability to observe the orientation of very small (~ten atom) clusters during the early condensation stage. The lively controversies which have emerged in recent years on cluster behaviour and mobility remain as yet unresolved. In this paper, recent work will be reviewed which contributes to our present understanding of the role of the substrate in determining the structure and behaviour of films. 2. SURFACE STRUCTURES The combination of LEED and Auger spectroscopy (AES) has enabled a much more precise idea of the true nature of single-crystal surfaces than had hitherto been available. Under the best conditions, AES enables quite small fractions of a monolayer of impurity to be detected on a surface, whilst LEED may give a reasonably accurate idea of the geometrical disposition of surface atoms. In principle, LEED should be able to detect distortions from normal interatomic spacings and small displacements from normal "bulk" sites for surface atoms. Thus the results of Martin and Somorjai 3 and others 4,s on the (100), (110) and (111) faces of aluminium suggest a significant * Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 2-I-2.
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O. S. HEAVENS
contraction of about 10% of the spacing of the (110) planes on the dodecahedral face, but with no detectable changes on the cube or octahedral faces. This behaviour has been accounted for in a simple way by Heine 6 who points out that the free electron distribution around the aluminium ions on a (110) face will tend to "flatten" at the metal-vacuum interface in such a way that the electrostatic centre of the free electron distribution moves in towards the bulk. The surface ions are then pulled in by the electrostatic forces involved. No such argument applies to the (111) face of AI, so that the observed bulk spacing for these planes is not surprising. In similar LEED studies of the (111) face of Pt, Kesmodel and Somorjai 7 conclude that there is no reason for expecting a departure from bulk spacing in this case. The extraction of structural information from LEED data is more involved than, for example, in the X-ray or high energy electron diffraction cases, since the effects of multiple scattering are large. Kinematic theory is inadequate. In some circumstances, the effects of multiple scattering can be reduced by averaging processes (e.g. ref. 8) and the single-scattering data extracted. For close-packed surfaces, the angular distribution of scattered intensity (other than in the near-forward scattering direction) for the averaged data is found to agree reasonably well with that based on a kinematic calculation. This method, known as the constant-momentum-transfer averaging method, appears to be capable of detecting small displacements from normal atomic positions. Thus in studies of W (110) surfaces Buchholz et al. 9 deduce that the W atoms cannot be displaced by more than 0.06 N from the "bulk" position. Moreover, in the case of adsorbed O, forming the structure W (110) p(2 x 1)-O, no significant displacement (< 0.05 A) of the W atoms from the surface plane is indicated. There are difficulties, however, in averaging methods such as these. The scattering cross sections and mean free paths which need to be inserted in the kinematic expressions differ significantly from those determined by other methods, so that the physical significance of these factors is obscure. On account of the very large amount of computing effort required for full-scale LEED calculations in which multiple scattering effects are included, the number of crystal surfaces studied so far in this way is small. Less detailed information-e.g, on the form of the many superstructures commonly observed on crystal surfaces-can be obtained without the full-scale analysis required for precision location of atomic positions. Such results require an examination of the position of LEED spots, which readily indicate the nature of any superlattices present. It should be emphasized, however, that reliable information on surface structures requires the study of diffracted intensities as well as of directions. The usual way in which this is obtained is by deriving intensity versus energy (I-V) profiles and comparing with experimental values. When, as is often the case, experiments are carried out over only a limited range of angles of incidence, this method is of limited reliability. Thus two independent analyses aimed at determining the spacing between sulphur and nickel layers in Ni(001)-S-c(2 x 2) give (a) 1.7 -+ 0.1 ~ and (b) 1.3 -+ 0.1 A. The Group d'Etude des Surfaces ~° has shown that a more satisfactory approach is to examine iso-intensity contours in (E, 0) and (0, O) coordinates. Not only does this method improve sensitivity, but the computing effort required is less than that for I- V comparisons.
SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION
119
The importance of the types of superlattice structure which are known to form on crystal surfaces for the structures of a growing film can be illustrated by the example of the growth of Si crystals from the melt. LEED studies of freshly cleaved Si reveal a (2 x 1) structure on the (111) cleavage face which, on annealing, is transformed to the classic (7 x 7) structure. Whereas the (2 x 1) structure is believed to arise from a simple displacement of surface atoms, the (7 x 7) results from a major reorganization of the surface which leaves 26.5% of the normal lattice sites vacant. The character of the crystal grown on such a surface will depend on whether the (2 x 1) structure is present or whether sufficient time has passed for the (7 x 7) structure to form. The former would be expected under conditions of rapid growth and the latter by slow growth, where the time reference is related to the (2 x 1) to (7 x 7) transformation time. On the above argument, slower growth would be expected to produce crystals with a high vacancy concentration. The results of Van Vechten ~1 confirm this dramatically. For growth rates up to 4 mm min -1 , 106-10 a vacancy clusters per cubic centimetre are observed. Beyond this growth rate, the vacancy concentration falls to about 1 c m -3. Although this represents a very high growth rate in relation to that for films grown by, for example, vapour deposition or sputtering, the lower growing temperature would imply a slower rate of surface reconstruction. Thus the present situation over surface structures is (i) that a complete LEED study should, at the expense of major computing routines, enable reasonably accurate analysis to be made of the location of surface atoms, (ii) that through suitable averaging processes, involving far less computing time, reliable results can be expected in some cases, particularly for close-packed planes, and (iii) that accurate information on surface structures, including that on superlattices and surface reconstructions, is likely to provide an invaluable guide to the form taken by a depositing film. The main remaining uncertainty is the role of impurities at concentrations below those detectable by Auger spectroscopy. 3. EPITAXIAL GROWTH It is sometimes suggested that, despite the many square metres of gold which have been grown epitaxially on rocksalt, we remain sadly lacking in a unified theory of epitaxy. Even supposing that all the factors which can influence epitaxial growth were always under control, and all the relevant parameters known, it would seem unlikely that any compact single description could apply to any deposit-substrate pair regardless of the widely varying relative binding energies involved. Epitaxial growth situations are often further complicated by a marked dependence on impurities, by the uncertainties of the roles of re-evaporation, surface diffusion or diffusion into the substrate and by our inability to observe the precise behaviour of sub-electronmicroscopic clusters at a critical stage in the film growth. Furthermore, one is often uncertain of the extent to which the processes under study are influenced by the method of examination. Electron-stimulated desorption is an interesting topic in its own right but can be an embarrassment. Despite the above limitations, the major factors w ~ c h govern many epitaxial processes are beginning to be understood. Although there are as yet few generalizations, some growth features follow the expected
120
o . s . HEAVENS
behaviour in relation to relative binding energies. Thus the initial stage of deposition of metals on non-metals often takes the form of three-dimensional nuclei. Although nucleation effects are observed on some metal-metal systems, there is evidence that the substrate regions between crystallites may be covered by monolayer deposit.
3.1. Significance of lattice misfit Since a monocrystalline substrate is essential for the occurrence of epitaxial growth, it is to be expected that, for deposits which bond strongly to the substrate, lattice misfit will be an important parameter. Two examples suffice to illustrate the way in which f'tlm structure and properties are so dependent. In order to grow films of Gaxlnl_xAs epitaxially, over the range 1.0 > x > 0.43, Nagai and Noguchi 12 prepared crystals of Gaxlnl_xASyPl_y in which a continuous range of lattice parameters could be obtained by adjusting the values of y. When the lattice parameter of the substrate crystal matched that of Gaxlnl _xAs, good epitaxial films could be grown. Similarly, Enstrom and Fisher 13 adjusted the composition of InxGal _x P until its lattice parameter matched that of GaAs, under which condition the quantum of the GaAs layers increased considerably. Theories of the effects of mismatch on the stability of an oriented overgrowth date from the earliest days of epitaxy. From a variety of potential models of the substrate surface, the general conclusion emerges that limiting misfits for stability can be tolerated and the limited misfit decreases with increasing number of layers of the deposit crystal (assuming layered growth). Figure 1 compares the results for a number of such models 14. These results suggest that pseudomorphic growth should occur in some circumstances. Although some doubt exists about the earliest observations of abnormal spacings of deposit layers, there is now considerable evidence in support of this phenomenon (see, for example, refs. 19 and 20). In studies of copper grown in ultrahigh vacuum on single-crystal nickel, Chambers and Jackson 21 extract misfit data from measurements of the spacing of moir6 fringes and compare the lattice strain as a function of thickness with the theoretical predictions of Jesser and Kuhlmann-Wilsdorf 16, obtaining excellent agreement for film thicknesses up to 10 nm. The films were deposited at room temperature and annealed at 300 ° C. Alloy formation would not be
E i h
Fig. 1. Limiting misfit as a function of the number of layers: A, parabolic pertodlc potential ; B, refined model of Jesser and Kuhlmann-Wilsdorfl6;C, Stoop-van der Merwe model14,17'; D, Peierls-Nabarro model Is . •
"
"
15
SURFACE PROPERTIES IMPORTANT FOR FILM FORMATION
121
expected at this temperature. Evidence suggesting that this does not occur comes from Auger studies in which no decrease in the amplitude of the copper peak is observed. If significant alloying occurred on annealing, the Cu signal would fall significantly. The results suggest that the form of growth is that of a monolayer formation followed by crystallite nucleation (Stranski-Krastanov). 3.2. Nucleation p h e n o m e n a
Although the foregoing treatment indicates the likely stability of layered structures once they have formed, it gives no indication of the process of formation. In the case of metals on alkali halides, f'dms do not in fact grow by the successive deposition of extensive layers, but by the formation, through surface diffusion processes, of nuclei. Information on the orientation of very small (few atom) nuclei is not generally available, but it is likely that the orientations adopted in the initial stages will bear some simple relationship to the substrate orientation. When the nuclei have grown to the size at which observations may be made, it becomes possible to apply the ideas of classical nucleation theory. Considerable progress in these studies 22 has enabled many features of nucleation behaviour to be reasonably well understood, although the observed initial development of the nucleation versus time curve remains a mystery. Although a variety of detailed growth and coalescence phenomena, involving diffusion of both individual atoms and dusters, are known to occur, the problems of including all these effects in a single description are formidable. From the experimental point of view it is known that defects on the substrate surface can play a significant role in determining the perfection and structure of an epitaxial film. Nucleation theory can be extended to include such heterogeneous effects. It is necessary not simply to postulate nucleus formation on each defect site, but to take account of the fact that a growing nucleus acts as an effective sink for atoms arriving within a certain distance (nucleation exclusion zones). The size of such zones increases with time; if they include active sites on which nucleation has not yet started then these sites become ineffective for initiating further nucleation 23'~. In some cases, there appears to be evidence that atoms which do not strike an active adsorption site on a surface may diffuse into the substrate 2s. One important feature of the last-mentioned work is that experiments were carried out over a range of two orders of magnitude in background pressure with no detectable effect on the form of deposits obtained, suggesting that reactions with residual gas26 are of little importance in these experiments (Au, Ag, Pd on C, SiO2). On the other hand, there have been reports indicating residual gas effects on the epitaxial growth of films on, particularly, alkali halides 27-29. In some respects therefore the role of the residual gas remains an open question. The role of surface defects created by electron bombardment in influencing fdm structure is now well established. The creation of F-centres in the surfaces of alkali halides is reasonably established by the work of Lord and Gallon a° in Auger studies on LiF. The effect of F-centre formation on the epitaxial growth of Ag on KC1 (Fig. 2) is illustrated by the work of Lord and Prutton 31. Similarly, the role of colloidal centres formed electrolytically in NaC1 on the epitaxy of UO2 has been established by Vasilu et al. 32 and of diffused Mn 2+ ions (impurities in NaC1, KCI, LiF and LiC1 crystals) on the epitaxy of Au and Ag by Pedrero et aL 33
122
O~S. HEAVENS
(a)
(b)
(c)
(d)
Fig. 2. (a), (c) Electron micrograph/diffraction pattern for 4 nm Ag on cleaved KCI. (b), (d) Corresponding figures for KCI irradiated by 500 eV electrons, 25/~A c m - 2 for 6 s at 50°C. Density of F-centres 7 x 1013 cm -2. (After Lord and Prutton 31.) 3.3. Prediction o f e p i t a x y
Although, as mentioned above, the existence of zero misfit between substrate and deposit lattice enables films of high structural perfection to be obtained (between materials of similar bonding types), epitaxial growth is often observed in the face of substantial misfits. In some cases this can be reasonably well understood by considertng the vernier effect of coincidences between adjacent lattice atoms. If n spacings of lattice a correspond to m spacings of lattice b, then the misfit w = (b - a)/a is given by n / m - 1. For certain values of misfit, n and m will be small integers, indicating frequent coincidences between atoms in adjacent layers. Kotz6 et al. 34 define the first coincidence number N * as N* = 1 ~ 1/W
where W = Iwl and N * is rounded to the nearest integer. For low values of N * , nearcoincidences will occur frequently along lattice rows and this might be expected to encourage epitaxy. The results of a survey of metal-alkali halide systems is shown in Table I, where a description of the "degree" of epitaxy (N, none; G, good; M, moderate; W, weak) is given. Although many factors other than simple misfit may influence the degree of epitaxy, the above results indicate generally good epitaxy for low N * values and poor (or absence of) epitaxy for large values. Kenty 35 has examined the extent to which an elaboration of misfit ideas treats the problem two-dimensionally, by defining a figure of merit related to the strain energy involved in two-dimensional deformation to produce matching. In studies of the epitaxial growth of GaAs on a large number of BeO planes, he finds such an elaboration of very little predictive value. It is clear that simple misfit criteria can be expected to be only a somewhat general guide. The question of fitting between deposit and substrate lattices has been considered from another standpoint by Henning and Vermaak 27, who consider the concept of
SURFACE
PROPERTIES
IMPORTANT
123
FOR FILM FORMATION
TABLE I
Substrate
NaF NaC1 NaBr NaI KF KC1 KBr KI RbCI RbBr RbI
Deposit Au
Ag
Al
Cu
Ni
Pd
Pt
N*
N*
N*
N*
N*
N*
N*
9 5 4 4 5 4 4 3 4 3 3
N N W G N G G G G G G
10 5 4 4 5 4 4 3 4 3 3
N W M G N W M G W M G
9 5 4 4 5 4 4 3 4 3 3
N M W W -
6 4 4 3 4 3 3 3 3 3 3
N M G G M G G G G G G
5 4 3 3 4 3 3 3 3 3 3
G G G M -
7 4 4 4 5 4 3 3 3 3 3
M M M M -
8 4 4 4 5 4 3 3 3 3 3
G -
critical accommodation centres for four-atom (100) clusters in which each atom lies in a potential minimum on the substrate and where both nearest neighbour and nextnearest neighbour bonding requirements are satisfied. For substrate anion and cation radii r a and rc, the radius r d of a deposit atom which exactly satisfies the critical accommodation condition is given by ra 2 --/.c 2 + d 2
r d = 2(re +x/2d - ra) where d = ra + rc. Provided the radius of the deposit atom exceeds rd, the formation of nuclei satisfying the above conditions is possible (on a "hard-sphere" model) and epitaxy should occur. The extent to which this rule can act as a guide to the occurrence of epitaxy has been examined by Lord and Prutton al, yielding the results given in Table II. Squares indicate the occurrence of good epitaxial growth. Circles correspond to cases where epitaxial growth does not occur, although in some cases the creation of damage sites by electron bombardment results in some measure of preferred orientation. The line in Table II indicates the critical radius of a deposit atom according to the Henning and Vermaak model. Cases above the line should show epitaxy; those below should not. The only exceptional case appears to be A1 on KC1, in which the deposit atom radius and critical value are very close together. It is unlikely that simpl e criteria such as those referred to above could be developed for more complex deposit-substrate combinations. The above models indicate that, for certain systems, reasonable predictions of the likelihood of epitaxy occurring can be made.
3.4. Epitaxy on amorphous layers The results of Distler and his coworkers on the epitaxial growth of films on amorphous overlayers to single crystals caused problems of interpretation at an early stage. Other workers' failure to repeat the experiment led to highly critical comments 36 on the reality of the effect in question. Certainly any discussion of growth in terms of
124
O. S. HEAVENS
TABLE II Substrate rd
Deposit Ni(1.24)
Cu(1.28)
A1(1.43)
Ag(1.44)
Au{l.44)
NaV
1.07
[]
[]
[]
[]
LiF
1.25
[]
[]
[]
[]
[]
MgO
1.33
(D
C)
[]
[]
[]
KC1
1.44
C)
(D
[]
(D
[]
NaCl
1.63
0
0
0
0
0
Ultrahigh vacuum conditions; & vacuo cleavage of substrate.
substrate lattice periodicity appears irrelevant to the situation where the crystal is covered with an amorphous layer in excess of 10 nm thick. Although doubts could be raised concerning these experiments (e.g. on the continuity of the amorphous films used), these cannot apply to the later experiments 37 in which epitaxy was demonstrated on a polyvinyl chloride replica of the crystal surface. Electron micrographs show no sign of growth at, for example, steps formed on the replica and the explanation involves recognition that the PVC film displays electret behaviour. Thus the replica forms an "electrical copy" of the surface and the mode of epitaxial growth observed suggests that the features copied are those of charged point defects and defect clusters. From other work on epitaxy it is certainly the case that defects do play a part in the epitaxial process. While sceptics will no doubt remain, there are by now severa! observations 3a'39 which are very difficult to account for by any of the more .conventional explanations for epitaxial growth. 4. PHYSICAL PROPERTIES OF FILMS INFLUENCED BY THE SUBSTRATE The previous discussion shows the extent to which the crystal form of a deposit material may be influenced by that of the substrate. Since the epitaxial film represents a highly ordered state, we could expect such films to be structurally stable. This is illustrated by the studies of lead films on mica4°. Non-epitaxial films are observed to undergo significant recrystallization on temperature cycling, resulting in extensive growth of hillocks. Epitaxial films show no such change. In general, we should expect any of the structure-sensitive physical properties of films to depend on substrate conditions and this is generally observed to be the case. Thus the optical constants of very thin (few nanometres) metal films deposited on glass or crystal substrates tend to be determined largely by the size and shape of the constituent crystallites. The values obtained bear little relationship to the bulk values, as is expected simply on the grounds that surface scattering plays a dominant role. Considerable caution is needed in interpreting the dispersion behaviour of thin film specimens in terms of solid state theory. Thus very thin films of copper (~8 nm thick) are observed to display an abnormal adsorption peak at around hv = 7.5 eV in addition
S U R F A C E PROPERTIES IMPORTANT FOR FILM F O R M A T I O N
125
to peaks associated with interband transitions 4~ . On exposure to nitrogen, the abnormal peak disappears. Such extra peaks can be interpreted in terms of plasma oscillations, which will occur at frequencies depending on the crystallite size and shape. Significant changes are observed in the crystallite size and shape of the Cu grains in these experiments. In contrast with the behaviour of metals, the refractive index of many dielectric materials appears to depend mainly on the proportion of a film occupied by voids. Lower-than-bulk refractive indices can be achieved by deposition under conditions where a large void concentration is obtained. In the case of semiconducting materials, significant effects may arise through the contribution to the polarizability of the material through dangling bonds. A case which has received some attention is that of silicon. It is known that the refractive index of amorphous films is significantly higher than that of the monocrystalline material. From classical dispersion theory the refractive index of a film in which a fraction s of the Si bonds are dangling can be obtained 42 in the form nf 2 - 1 _ pf (dam~dot) s nc 2 - 1 Pc (1 -- $)2 where pf, Pc are the film and single-crystal densities, dcr is the bond length in the single crystal and dam is the mean bond length in the amorphous material, obtained from the radial distribution function. The value of the ratio dam/dcr is a matter of some uncertainty, so that the above expression cannot give nf with great precision. For plausible values ofdam/der , however, differences between nf and n c of only a few per cent are indicated. Recent measurements 4a at photon energies 0.5 eV and 1.75 eV reveal increases of 30-40% over the single-crystal values. (These results help to explain apparently puzzling observations obtained in infrared multilayer optical systems, in which the resultant optical characteristics indicate index values for the semiconducting films significantly different from the bulk values.) Films of thickness approximately 1/am were formed on oxidized silicon at temperatures from 20 °C to 880 °C. Measurements of electron diffraction linewidths gave the sizes of the coherent scattering regions at each temperature, revealing an increase from about 0.8 nm at 20 °C to 10 nm at 880 °C. Spin resonance studies confirmed the presence of free spins (8 x 1020 cm -3) for the 20 °C films and no detectable resonance ( < 0.5 x 1020 spins cm -3) for the 5,5
I
,o
0
/
J/E.
O~ -I,0 Ph~m ~
/
1"5 2.o h~bV)
,c
25
Fig. 3. Dependence of t h e refractive index of silicon films on the deposition conditions: full lines, results of Schwidefsky43; o, from m e a s u r e m e n t s on b a n d w i d t h s of interference filters.
126
O. S. HEAVENS
8 8 0 °C fihns. T h e refractive i n d e x fell f r o m 4.5 to 3.5. A f u r t h e r i l l u s t r a t i o n o f the d e p e n d e n c e o f t h e refractive i n d e x o f Si films o n the m e t h o d o f d e p o s i t i o n and o n substrate t e m p e r a t u r e is s h o w n in Fig. 3. T h e p o i n t s o n this diagram refer to Si films in Si-MgF2 multilayers, d e p o s i t e d at a s u b s t r a t e t e m p e r a t u r e o f 2 0 0 °C, f r o m w h i c h the i n d e x o f the Si fihns is d e d u c e d f r o m the o b s e r v e d optical t r a n s m i s s i o n curves. These results lie closer to the 380 °C p o i n t s t h a n m i g h t have b e e n e x p e c t e d , w h i c h may reflect the d i f f e r e n t n u c l e a t i n g c h a r a c t e r i s t i c s for the Si layers o n t h e MgF2 films used in the multilayer. REFERENCES 1 D. B. Holt, Thin Solid Films, 24 (1974) 1-53. 2 0 . lgarashi, J. Appl. Phys., 42 (197l) 4035--43. 3 M. R. Martin and G. A. Somorjai, Phys. Rev. B, 7 (1974) 3607-15. 4 G. E. Laramore and C. B. Duke, Phys. Rev. B,5 (1972) 267-85. 5 D. W. Jepson, P. M. Marcus and F. Jona, Phys. Rev. B,6 (1972) 3684-90; 8 (1973) 1786. 6 V. Heine, Jpn. J. Appl. Phys., SuppL 2, Part 2 (1974) 679. 7 L. L. Kesmodel and G. A. Somorjai, Phys. Rev. B, 1 l (1975) 630-7. 8 T. C. Ngoc, M. G. Lagally and M. B. Webb,Surf SoL, 35 (1973) 117--44. 9 J. C. Buchholz, G.-C. Wang and M. G. Lagally, Surf Sci., 49 (1975) 508. 10 Group d'Etude des Surfaces (D. Aberdam, R. Baudoing, C. Gaubert, Y. Gauthier and V. Hoffgtein), Surf ScL, 48 (1975) 497-508. 11 J. A. Van Vechten, Appl. Phys. Lett., 26 (1975) 593-6. 12 H. Nagai and Y. Noguchi, Appl. Phys. Lett., 26 (1975) 108-10. 13 R. E. Enstrom and D. G. Fisher, J. Appl. Phys., 46 (1975) 1976-82. 14 L. C. A. Stoop, Thin Solid Films, 24 (1974) 229. 15 J. H. van der Merwe, J. Appl. Phys., 41 (1970) 4725. 16 W. A. Jesser and D. Kuhlmann-Wilsdorf, Phys. Status SolidL 19 (1967) 95. 17 L. C. A. Stoop and J. H. van der Merwe, Thin Solid Films, 1 7 (1973) 291-309. 18 See J. H. van tier Merwe, ,L Appl. Phys., 34 (1963) 117-27. 19 R. Kuntze, A. Chambers and M. Prutton, Thin SolMFilms, 4 (1969) 47-60. 20 J. D. Briante, J. M. Corbett and F. W. Boswell, Thin Solid Films, 14 (1972) 305-20. 21 A. Chambers and D. C. Jackson, Philos. Mag., 31 (1975) 1357-71. 22 G. Zinsmeister, Jpn. J. Appl. Phys., Suppl. 2, Part 1 (1974) 545-50. 23 I. Markov and D. Kashchiev, Thin Solid Films, 15 (1973) 181-9. 24 A. Milchev, S. Stoyanov and R. Kaischev, Thin Solid Films, 22 (1974) 255-65. 25 J. F. Hamilton and P. C. Logel, Thin Solid Films, 23 (1974) 89-100. 26 1. A. Venables, Thin Solid Films, 18 (1973) S l l . 27 C. A. O. Henning and J. S. Vermaak,Appl. Phys. Lett., 15 (1969) 3. 28 J. S. Vermaak and C. A. O. Henning, Philos. Mag., 22 (1970) 269-80; 281-9. 29 A. K. Green, E. Bauer and J. Dancy, J. Appl. Phys., 41 (1970) 4736. 30 D.G. Lord and T. E. Gallon, Surf ScL, 36 (1973) 381. 31 D.G. Lord and M. Prutton, Thin SolMFilms, 21 (1974) 341-56. 32 F. Vasilu, V. Topa, N. G. Popescu-Pogrion and M. I. Bi'rjega, Jpn. J. Appl. Phys., SuppL 2, Part 1 (1974) 605. 33 E. Pedrero, T. Oca~a, A. G6mez and M. J. Yacam~in, Thin Solid Films, 27 (1975) 149-53. 34 I. A. Kotz6, J. C. Lombaard and C. A. O. Henning, Thin Solid Films, 23 (1974) 221-32. 35 J. L. Kenty, Thin Solid Films, 26 (1975) 181-95. 36 K. L. Chopra, J. Appl. Phys., 40 (1969) 906. 37 G. I. Distler and E. I. Tokmakova, Soy. Phys. Crystallogr., 17 (1972) 545. 38 A. Barna, P. B. Barna and J. F. Pocza, Thin Solid Films, 4 (1969) R32. 39 L. L. Aksenova, G. I. Distler, A. V. Kovda and E. 1. Kortukova, Soy. Phys. Solid State, 15 (1973) 1100. 40 S. K. Lahiri, J2 AppL Phys., 46 (1975) 2791. 41 F..Payan, Thin Solid Films, 18 (1973) 85-9. 42 J. A. Van Vechten, Phys. Rev., 182 (1969) 891. 43 F. Schwidefsky, Thin Solid Films, 18 (1973) 45-52.