Recent developments in the study of mechanical properties of thin films

Thin Solid Films - Elsevier Sequoia S.A., Lausanne - Printed in Switzerland

17

RECENT DEVELOPMENTS IN THE STUDY OF MECHANICAL PROPERTIES OF THIN FILMS

KOREO KINOSITA Department o f Physics, Gakushuin University, Mejiro, Tokyo (Japan) (Received May 15, 1972)

Recent activities in the study of film stress are described. After a brief survey of the stress versus film thickness relations, an analysis of the t h e r m a l stress is given, and the difficulties in thermal stress corrections are pointed out. The models for the origin of the intrinsic stress that have been proposed recently are critically reviewed, and future steps to construct better models are discussed. The complicated stress behaviours observed with Ag films that have been deposited on baked or unbaked mica substrates and kept in a vacuum of 10- 8 torr or 10- 5 torr are described; they present novel problems to the existing models. A Vickers type ultra-microhardness tester for thin films is described. With this instrument, any load between 1 and 100 mg-wt can be applied to a diamond triangular pyramid indenter and its penetration depth determined to + 100 A. The results with LiF, MgF2, Cr and Ag films are briefly discussed.

1. INTRODUCTION The internal stresses in thin films grown on a substrate have been investigated extensively for many years. A concise review of the studies up to 1965 was presented by Campbell 1 at the Symposium on Basic Problems in Thin Film Physics, Clausthal, 1965. Excellent reviews can also be found in Hoffman's articles 2-4, which cover a wider a r e a - the mechanical properties of thin films in general. At the International Conference on Thin Films, Boston, 1969, Buckel 5 gave a paper entitled "Internal Stresses ", which was partly a review of more recent results; in essence, however, he concentrated on the study carried out in his laboratory of the stresses in films of some metals and alloys at low temperatures, concluding that the stress is developed in the amorphous-crystalline phase change that takes place during the condensation. In the present paper, an attempt is made to clarify where the unsettled or unexplored problems lie rather than to give an exhaustive review of what has been done. Section 2 is devoted to film stress. The reader is introduced to basic quantities relevant to film stress in Sections 2.1 and 2.2. The so-called thermal stress is discussed in 2.3. In Section 2.4 the models proposed for the origin of the intrinsic stress are critically reviewed, and some new experiments are described in 2.5 which present problems to the existing models. In Section 3, a newly developed Thin Solid Films, 12 (1972) 17-28

18

K. KINO$ITA

ultra-microhardness tester for thin films is described, with some preliminary results that may seem challenging to the workers in this area. Only vacuum deposited films will be considered in the following, unless otherwise stated. 2.

FILM STRESS

2.1. The measurement o f f i l m stress

The stress formulae and the techniques for the determination of film stress have been reviewed by Campbell x and Hoffman 2-4. For more recent developments the reader is referred, for example, to Ennos 6, Klokholm 7' s, Wilcock and Campbell9, Rottmayer 1° and Doljack 11. The most common method of observing stress is to deposit the film on one side of a long, thin, rectangular substrate rigidly clamped at one end and observe the deflection of the free end 6. This is proportional to the bending force per unit width S:

s =

+3~

~

(1)

Here E and v stand for Young's modulus and Poisson's ratio, suffixes s and f represent the substrate and film respectively, D is the thickness and 1 the unclamped length of the substrate, and dis the film thickness. The second term in the braces, originally due to Brenner and Senderoff12, can be neglected if d ~ : D and E l V E s . The (1 - v ) correction, which for brevity was omitted in the second term, was introduced by Finegan and Hoffman ~3 considering the biaxial nature of the stress in a plate. The average stress in the film is given by

(2)

= S/d

It is usual to assign positive or negative values for 6, S and a according as the stress is tensile* or compressive. 2.2. S versus d and a versus d relations In 1960 Kinosita et al. t* investigated the a versus d relation for silver films 30-2500 A in thickness. A large number of papers on the S versus d or a versus d

relations for metal and non-metal films have since been published, some of themlS-19, 10 paying particular attention to the relation with the film structure and growth processes. It is preferable to present the data in the S versus d diagram, because (a) it is S that is directly observed and (b) a knowledge of the incremental (or instantaneous) stress, equal to the local slope at a point on the S versus d curve, is useful. The incremental stress a (z) is the stress present in a layer of thickness dz at a distance z from the film/substrate interface. Thus d

S = ~ a(z)dz

or

a(z) = dS/dz

o * I f the stress is tensile, the film is trying to contract.

Thin Solid Films, 12 (1972) 17-28

(3)

19

MECHANICAL PROPERTIES OF THIN FILMS

Most measurements carried out so far pertain to metal films. Ennos’s work6 on the stresses in optical lilm coatings is worth quoting in that a wide variety of dielectric films were covered, including lesser known ones such as ThOF2, PbF,, SNaF-3AlF,, CeF,, PbCl,, TlCl, TlI etc. Figure l(a), part of the results obtained by Klokhohn and Berry”, gives typical S uersus drelations for metal films. In Fig. l(b) the values of cr at d = 1000 A

22 23242526272822 Film

thickness

(1)

47 (b)

(a)

Fig. 1. (a) S us. d relations for metal films. Glass substrates. 10-6-10-’ torr. 2-5 A s-r deposition rates. Electron gun evaporation source. (b) The average stress at 1000 A thickness a(1000 A),rigidity G and melting point T,. The abscissa gives the atomic number. After Klokholm and Berry”. for the transition metals they studied are given, together with the rigidity G and the melting point T, of each metal. We observe that (a) metal films exhibit tensile stress with few exceptions; (b) the values of a(1000 A) in films of harder, more refractory metals are very large, x 10l Odyn cme2, while in films of softer, more fusible metals they are much smaller; and (c) with the former class of metals S increases almost linearly with d, while with the latter S rises from a very small value to attain a broad maximum or to approach a constant value.

2.3. The thermal stress With a film deposited on a substrate at a temperature above or below the temperature of the measurement, the observed film stress consists of two terms: the thermal stress due to the difference in thermal expansion (DTE) between the film and the substrate, and the intrinsic stress which is a result of the manner of growth of the film. The interest of physicists centres in the latter, but there is no way of determining the intrinsic stress without evaluating the thermal stress*. The correction for thermal stress is not of vital importance with films exhibiting large intrinsic stress, Fe, Ni, MgF, etc., but it is essential in determining the small intrinsic stress in films of Ag, Cu, PbCl, etc. Unless the temperature deposition.

l

of the measurement

Thin Solid Films, 12 (1972) 17-28

is equal to the substrate temperature

during the

20

K. KINOSITA

The deflection of a cantilevered substrate caused by thermal and momentum transfer effects has been recently analysed by Maki and Kinosita (to be published; see also Kinosita21). Some of their points are given below. Figure 2(a) illustrates for example the free end deflection 6" of a cantilevered mica substrate, 3.5 cm x0.7 cm x0.001 cm, during and after the deposition of a d (A) 450

0 4

go0

i

6

~""''~~'\

4O

~o

j'{

u

3

i

~4 E u

'o

"U

:~" ~o 2 0 ~-~

/ -2

0

i ,

j

20

40

t(s) (a)

0

0 0.1

1

tCh)

10

I

-1.5

0

300

I

d(~)

600

900

(b)

Fig. 2. (a) Free end deflection 6", rise in substrate temperature T~- T, deflection due to differential thermal expansion (DTE) 6*m-E,and deflection due to intrinsic stress 6~ as functions of time t. (b) Force per unit width S corresponding to 6o, residual deflection due to DTE 6I~TEand deflection due to residual intrinsic stress 61 as functions of film thickness d. Ag films deposited on cantilevered mica substrates. 10- s torr. 20 A s- t. After Maki and Kinosita.

Ag film at a rate of 20 A s-1 in a vacuum of 1 x 10-s torr in an oil pumped, liquid nitrogen trapped evaporator. The source-to-substrate distance was 20 crn. Here, and hereafter, the superscript * to a symbol indicates transitional values of the quantity represented by that symbol observed during (and after) the deposition. In the S versus d curve in Fig. 2(b), each of the experimental points (not shown) has been obtained by depositing the film on a new substrate, observing 6o (Fig. 2(a)) and substituting into eqn. (1). It will be seen that, when the intrinsic stress is small, a film which shows tension after the deposition does not necessarily bend the substrate toward the tension side during the deposition. A momentary negative deflection at the beginning (Fig. 2(a)) can be explained quantitatively by the momentum transfer from the impinging evaporant atoms. Such deflection has often been attributed to the temperature gradient across the substrate, but with very thin substrates the momentum transfer effect is predominant. With the common metal films that exhibit tensile intrinsic stress, this negative deflection is soon overcome by the rapid increase in the intrinsic stress which causes a positive deflection. Hence the deflection 6* is the algebraic sum of three components: 61 "[- 6DT E "q" 6 p

(4)

Here 6r is due to the intrinsic stress, 6~)TE to the difference in the thermal expansion coefficients of the film and the substrate, ~f-~s, and 6~ to the momentum transfer effect. Thin Solid Films,' 12 (1972) 17-28

MECHANICAL PROPERTIES OF THIN FILMS

21

Let us assume, for a first approximation, that (a) no stress other than the intrinsic incremental stress th(z ) is present in a layer dz when it is deposited on top of a film of thickness z at temperaturet T,(z); and (b) the layer dz undergoes constrained expansion or contraction, without stress relief, as its temperature is changed by further deposition of film. Then, at the moment the film reaches d in thickness and T~ in temperature, 6~TE =

3/2El(1 - v s ) d E~(I_vf)D2 (~f--~) (T~- < T~>)

(5)

with

1 i T~(z)dz < ~ > =d0

(6)

If the deposition is interrupted here and the substrate allowed to cool, the residual deflection due to DTE is given by 3/2El(1 - vs)d 6I)TE = E~(1-- vf)D2 (ctf- ~q) ( < T~> - Tr)

(7)

where T~ is room temperature. In so far as the assumption (b) is valid, the residual deflection due to the intrinsic stress is 3/2(1

6~ = 6T =

EsD2

Vs)

d_ ~ ~(z)dz o

(8)

Accordingly, the deflection observed after the deposition is finished, 60, from which S in Fig. 2(b) has been calculated, is given by ~o = ~i +~orE

(9)

Thus if we know < T~> we can make the thermal stress correction and obtain 6t, from which the intrinsic force per unit width Sx, and hence the average intrinsic stress a~, can be calculated at once. The thermal stress correction has quite often been mentioned but scarcely ever been made properly, primarily due to the difficulties in determining < T~>. Some authors 1°' 19,20 tried to avoid the trouble by keeping T~ constant and/or choosing a substrate whose expansion coefficient was practically equal to that of the f i l l , but such techniques are only applicable in limited cases. Maki and Kinosita made continuous measurements of T~ in their experiment quoted above. They evaluated the values of < T~> from the (T~- T~) curve* given in Fig. 2(a), and from these they calculated ~a-E and 6~, and 6m-~ and 6r (6~ was evaluated from the first minimum in the ~ versus d curve.) The results, given in Fig. 2 (a) and (b), show that we are approaching, but have not arrived at, a clear t T~(z) is the substrate temperature, which is practically equal to the film temperature, at the instant the film thickness reaches z. * For the characteristics of T~- T~ curves, the reader is referred to Yoda a2, 23 and N a m b a z4. Thin Solid Films, 12 (1972) 17-28

22

K. KINOSITA

understanding o fthe thermal effectinherent in the cantilevered substrate technique. The negative values of (di~ and) 6t at larger thicknesses are inexplicable. The features of the ~ and ~ curves indicate that a considerable stress relief takes place during the film deposition, contrary to our assumption (b).

2.4. Models for the origin of intrinsic stress The earlier models have been reviewed by Campbell x, Hoffman2-4 and very briefly by Buckel s. The more recent ones only will be discussed here. Based on their low temperature experiments on Ga, Bi, Sn-Cu and Pb-Bi alloys etc., Bauer and Buckel 2~27 (see also Buckel 5) proposed a model as follows. (a) Even in the temperature range where the crystalline phases are stable, the film is at first condensed in a metastable solid phase with a short range order like that of a liquid, It is free of stress at this stage. (b) When the metastable phase is transformed into a stable, crystalline phase, the intrinsic stress arises from the difference in density of the two phases. Klokholm and Berry 2° claimed that the tensile intrinsic stress in common metal films at higher temperatures (see Fig. 1) are developed by a similar mechanism, i.e. by the rearrangement and shrinkage of disordered material buried under the advancing surface of a growing film. According to these authors, the arriving atoms can move about to improve the crystalline order while they are exposed on the surface, but are frozen up as soon as they are buried, later to be rearranged at a slower rate resulting in a shrinkage. Assuming that the annealing on the surface is a thermally activated process, they reasoned that, for deposition rates of the order of a few /~ngstrfms per second, a high (low) stress will be developed if Tm/T~ >4.5 (<4.5). Here Tmis the melting point of the metal. This reasoning has been confirmed2s. These theories are attractive in their simplicity. However, the presence of a transitional disordered layer is a hypothesis which is not based on experimental grounds*. According to Klokholm and Berry's model the tensile force per unit width S should be proportional to d. This is not the case at small film thickfiesses, even with films such as Fe and Cr in which S does increase linearly with d at larger thicknesses. Granted that the model indicates the vital point, it does not apply to very thin films. Blackburn and Campbell 15 found that stress exists in the thinnest films consisting of separate islands. For such stress, no models seem to have been proposed that are very convincing. KJnosita and co-workers 16' iT, ao. at established that, with very thin films of Ag and similar metals, S increases sigmoidally with d, the steep slope of the sigmoid being located in the thickness range where the film is in the late coalescence stage and the channel stage.The average stress a increases sharply to assume a maximum at a thickness~f dm around 200 A, where the film is continuous but * Sb is an exception; it is deposited as an amorphous film at room temperature but suddenly crystallizes when a critical thickness is reached, developing a large stress 29. I" If a tangent is drawn through the origin to the S versus d curve, the abscissa o f the contact point is equal to d m (ref. 16). Thin Solid Films, 12 (1972) 17-28

MECHANICAL PROPERTIES OF THIN FILMS

23

contains some small irregular holes. They concluded that the stress build-up in this thickness range is due to the coalescence of islands, in which the area occupied by the compound island is observed to be smaller than the sum of the areas occupied by the primary ones. Wilcock et al. 1s also studied the S versus d relations for Ag and Au films and obtained much the same results. Based on the scanning electron diffraction work of Grigson and Dove 32 and Heritage 33, which demonstrated that an electron microscopically observed "island" consists of smaller crystallites, these authors attributed the marked increase in S before the film becomes continuous to the annealing of the crystallite boundaries, which they claim results in a decrease in the void content per island. This might be a possible mechanism responsible for the stress build-up in the thinnest metal films, but their calculation of the magnitude of the stress is not very convincing. Hoffman and co-workers 1°' 11,13, 19 developed a model* for the intrinsic stress in metal films on the following lines. (a) As the grains (islands) grow together, the interatomic forces acting across the gap between the two grains cause an elastic relaxation of the grain walls toward each other, the grains being constrained to the substrate. The average decrease in the gap spacing is denoted by A. (b) Such relaxation induces an elastic stress in the grains which on the average is equal to {El/(1- vf)}A/~, if q~ is the average grain diameter measured parallel to the plane of the film. (c) If the grains recrystallize to form larger ones during the film growth, a three-dimensional rearrangement of the atoms during this process eliminates the strains due to the former gaps. Thus, the film stress is determined by the forces acting at the boundaries of the final grains. Doljack 11, who studied the stress in Ni fills, constructed a grain boundary potential, calculated A(~0.9 A), and compared the values of {El/(1-vf)}A/dp with the incremental stress observed in films of various grain sizes, which were obtained by depositions at different substrate temperatures. The results seem to be fairly satisfactory. However, the grain boundary relaxation model does not apply to silver films, as will be shown in Section 2.5. To sum up, it does not seem likely that we may construct a model which explains all the observations. This is only to be expected if we consider the developments of stresses in bulk materials. Nevertheless, it is worthwhile working out a good model for the intrinsic f i l l stress, because it helps towards an understanding of the film growth. In improving the models, the following points would seem helpful. Consider first the stress in metal films. (1) The stress in very thin, discontinuous or partly discontinuous films and the stress in thicker, continuous films should be treated separately. Klokholm's and Hoffman's models apply to the latter, and Kinosita's and Wilcock's to the former, exclusively. (2) The correlation between the stress and recrystallization temperature 34, the correlations among the stress, melting point and rigidity (Fig. l(b)) 2° and * A detailed description o f the model can be found iri Doljack 11.

Thin Solid Films, 12 (1972) 17-28

24

K. KINOSITA

the Tm/T~ criterion proposed by Klokholm 2°" 2s probably indicate an important strategic point. (3) It is desirable that the proposed model applies to electroplated films as well. If we enlarge our horizon, (4) more work should be done on the stresses in dielectric films, especially on their relation to the film structure and growth processes; and (5) a search of convincing models for the compressive stress in dielectric films is urgently demanded.

2.5. New experiments in stress in Ag films A preliminary note has been published by Nakajima and Kinosita al on the stress in Ag f i l l s deposited on mica at 10-8 tort. They have extended the work to cover the stress behaviours in all the combinations of the following deposition parameters (an ion pumped evaporator was employed unless otherwise stated): surface condition of mica (baked at 10 -8 torr/unbaked), vacuum before deposition (10-a torr/10-5 torr), vacuum during deposition (10-8 torr/ 10 -s torr) and vacuum after deposition (10 -8 torr/10 -5 torr). Some of their points are given belowt. (a) The stress behaviour before the film becomes continuous, which was studied in detail previously 16' 17, is not greatly influenced by the deposition parameters. (b) The residual gas pressure during the deposition has no appreciable influence on the stress behaviour. (c) If, after the deposition, the film is kept in a vacuum of 10 -a torr, the free end deflection slightly increases with time (fills on baked mica) or remains constant (fills on unbaked mica). If kept in a vacuum of 10- 5 torr, it decreases with time. The value of S was calculated from the deflection observed 3 h after the deposition. (d) With f i l l s deposited on mica substrates thoroughly cleaned beforehand by baking the evaporator, S does not increase at larger film thicknesses: with films kept in a vacuum of 10-8 torr, S exhibits no change with d; with those kept in a vacuum of 10-s torr, S decreases slightly with increase in d. (e) With films deposited on unbaked mica substrates, S increases with d. The increase is more marked with f i l l s kept at 10-a torr after the deposition than with those kept at 10 -5 torr. The changes in the free end deflection and those in the residual force per unit width S described above are qualitatively illustrated in Fig. 3(a) and (b). We note that the S versus d curve for f i l l s deposited and kept at 10-s torr in an oil pumped, liquid nitrogen trapped evaporator (the broken line in Fig. 3(b)) is between the curve for films deposited on baked substrates and the curve for films deposited on unbaked substrates in an ion pumped evaporator. Electron diffraction and electron microscopic observations proved that t In the following, what is referred to as S is the force per unit width calculated from the as-observed free end deflection. No thermal stress correction has been made, because the substrate temperature was not measured.

Thin Solid Films, 12 (1972) 17-28

25

MECHANICAL PROPERTIES OF THIN FILMS

I'

"i

So

I l

~o I / / X

i

'~ " ~

,

, 4

lO'Storr

2 =---

'

~'o

.....

10 -8 t o r r

:---

~; i

10" t o r t i

¢,,0

.... i

/

7

-

/ I

0

1000

(b)

dCA)

!

2000

Fig. 3. (a) Free end deflections ~ during and after deposition of Ag films on baked (B) and unbaked (UB) mica substrates. Arrows indicate interruption of deposition. (b) S vs. d relations for Ag films on baked (B) and unbaked (UB) mica substrates. For the broken curve, see text. Deposited in an ion pumped evaporator unless otherwise stated. After Nakajima and Kinosita.

(f) the films deposited in an ion pumped evaporator on baked, thoroughly clean mica substrates are polycrystalline films with poor* (111) epitaxy and consist of small grains. Those deposited in the same evaporator on unbaked substrates are (111) single-crystal films (when kept at 10 -5 torr before the evaporation) or (111) single-crystal films with some polycrystalline areas (when kept at 10-s torr before the evaporation), both consisting of larger grains. With f i l l s deposited in an oil pumped, liquid nitrogen trapped evaporator on unbaked substrates, the degree of orientation increases with film thickness. The points (d), (e) and (f) show that the stress is developed at larger thicknesses in epitaxial films that consist of larger grains, and not in polycrystalline f i l l s that consist of smaller grains. We note that, with epitaxial fills, there are tendencies for the grain size to become larger with the film thickness. These observations are contrary to the grain boundary relaxation theory. As for the point (c), there is evidence that the decrease with time of the free end deflection after the shutter is put in is caused by the sorption in the film of residual gases. If we deposit a film at 10 -a torr on an unbaked substrate and keep it in the same vacuum, the deflection remains constant. If we allow the pressure to rise to 10 -5 torr by introducing air through a needle valve, the deflection gradually decreases with a simultaneous increase in the electrical resistivity of the f i l l . If we again pump the system to 10 -8 torr, the changes in deflection and resistivity recover with a time constant of the order of hours. Further details will be published in the near future. 3. ULTRA-MICROHARDNESS MEASUREMENT Nishibori and Kinosita 36 have developed a Vickers type ultra-microhardness tester for thin films, by means of which they are exploiting a new area. * The "degree of orientation "' is about 20 % according to Ino's scale35; he was the first to find that films of Ag and similar metals exhibit inferior epitaxy when deposited on a cleavage face of NaC1 cleaved in an ultra-high vacuum. Thin Solid Films, 12 (1972) 17-28

26

K. KINOSITA

Figure 4(a) illustrates schematically the construction of this instrument. A diamond triangular pyramid indenter with 100° apex angle and 1200 A tip

4000F d=9200~ tLiFfilrn / / -/ o=296o 5o "o .... jp._d=25 8

w

G

=..3ooo[..........

.;,

~

L

o_ 1 0 0 0 1 [ / / sl

yst

I

0 (a)

5 10 Load (rag-wt) (b)

15

Fig. 4. (a) Ultra-microhardness tester. M metal arm (vertically movable); G unbonded type strain gauge; L link arm; H indenter holder; B balance beam; C capacitor; and S specimen. (b) Measurement of penetration depth t for LiF crystal and LiF films deposited at 5 x 10-6 torr at a rate of 15 A s - t . After Nishibori and Kinosita.

radius is mounted in a holder H. The holder H is fixed to the link arm L of an unbonded type strain gauge G, which is fitted to a metal arm M that can be vertically displaced very smoothly, to an accuracy of 100 A, by a hydraulic system. One end of the beam B of a very light balance rests on top of H. Any load W between 1 and 100 mg-wt can be applied to H by allowing the pointer of a d'Arsonval meter, which is fixed to M, to push this end of B. By adjusting the current, the load W can be regulated to _ 0.1 mg-wt. Let us consider first the case when H is freely suspended (W = 0 ) t , the indenter tip floating somewhere above the specimen surface. Let us assume, for simplicity, that the beam B is horizontal at this stage (Stage I). The output of the strain gauge E at Stage I will be denoted by Eo. If a load W is applied, the beam B is inclined by an angle ~t, the indenter tip being shifted downward by x0 but still floating (Stage II). The shift Xo is measured by a capacitor C, one of the electrodes of which is attached to the other end of B. Now, let the metal arm M be displaced downward until the indenter tip barely touches the specimen S (Stage III). If M is further displaced and the indenter tip is allowed to penetrate into the specimen, the beam angle ~, and hence the output E, will decrease owing to the resistive force exerted by the specimen. When E becomes equal to Eo the beam B is again horizontal (Stage IV). The displacement b of M between Stage III and Stage IV will give the depth e to which the indenter tip has penetrated as 8 = b - x 0 . In practice, the displacement x of the other end of B between Stages III t Here L is more or less inclined by the weight of H. Thin Solid Films, 12 (1972) 17-28

MECHANICAL PROPERTIES OF THIN FILMS

27

and IV is measured. It can be shown that e = x - 2x0. Thus the penetration depth e under a given load W can be determined to + 100 A. Figure 4(b) shows the results for a cleavage face of a LiF crystal and films prepared by evaporating the same crystal onto glass substrates 2550, 2960 and 9200 A in thickness. The sharp bends observed in the curves for films 2550 and 2960 A thick are due to the indenter tip reaching the glass surface. The proportionality between the applied load W and the penetration depth e is rather surprising, because in ordinary Vickers hardness measurements the ratio of the load to the indentation a r e a would be constant. It is another surprise that, for the cleavage face, e remains practically equal to zero until W reaches 7 mg-wt, when e starts to rise again linearly. The apparent rigidity observed for W< 7 mg-wt can be fairly well understood by taking into account the spherical shape of the indenter tip, but the linear increase of e remains unexplained. The results for a MgF 2 crystal and films obtained by evaporating the same crystal showed similar features. With Cr and Ag films the e v e r s u s W curves were found to be more like a parabola (eoc W1/2) than a straight line (eoc W). It is hoped that an accumulation of such data will help towards the understanding of the structure and mechanical properties of evaporated films as well as of the surface layers of solids. REFERENCES 1 D.S. Campbell, in R. Niedermayer and H. Mayer (eds.), Basic Problems in Thin Film Physics, Vandenhoeck and Ruprecht, G6ttingen, 1966, p. 223. 2 R . W . Hoffman, in H. G. F. Wilsdorf (ed.), Thin Films, Am. Soc. Metals, Metals Park, Ohio, 1964, p. 99. 3 R.W. Hoffman, in G. Hass and R. E. Thun (eds.), Physics o f Thin Films, Vol. 3, Academic Press, New York, 1966, p. 211. 4 R. W. Hoffman, in J. C. Anderson (ed.), The Use o f Thin Films in Physical Investigations, Academic Press, New York, 1966, p. 261. 5 W. Buckel, J. Vac. Sci. Technol., 6 (1969) 606. 6 A.E. Ennos, Appl. Optics, 5 (1966) 51. 7 E. Klokhohn, Thin Solid Films, 4 (1969) R9. 8 E. Klokholm, Rev. Sci. Instr., 40 (1969) 1054. 9 J . D . Wilcock and D. S. Campbell, Thin Solid Films, 3 (1969) 3. 10 R.E. Rottmayer, AEC Tech. Rept 64, Case Western Reserve Univ., Cleveland, 1970. 11 F . A . Doljack, AEC Tech. Rept 76, Case Western Reserve Univ., Cleveland, 1971. 12 A. Brenner and S. Senderoff, J. Res. Nat. Bur. Stand., 42 (1949) 105. 13 J.D. Finegan and R. W. Hoffman, AEC Teeh. Rept 15, Case Inst. Technol., Cleveland, 1961. 14 K. Kinosita, H. Kondo and I. Sawamura, J. Phys. Soc. Japan, 15 (1960) 942. 15 H. Blackburn and D. S. Campbell, Phil. Mag., 8 (1963) 823. 16 K. Kinosita, K. Maki, K. Nakamizo and K. Takeuchi, Japan. J. Appl. Phys., 6 (1967) 42. 17 K. Kinosita, K. Maki and K. Takeuchi, in E. Hahn (ed.), Proc. 2nd Coll. on Thin Films, Budapest, 1967, Vandenhoek and Ruprecht, G6ttingen, 1968, p. 118. 18 J.D. Wileock, D. S. Campbell and J. C. Anderson, Thin Solid Films, 3 (1969) 13. 19 R.E. Rottmayer and R. W. Hoffman, J. Vac. Sci. Technol., 8 (1971) 151. 20 E. Klokholm and B. S. Berry, J. Electrochem. Soc., 115 (1968) 823. 21 K. Kinosita, in E. Hahn (eel.), Proe. 2nd Coll. on Thin Films, Budapest, 1967, Vandenhoek and Ruprecht, G6ttingen, 1968, p. 31. 22 E. Yoda, Japan. J. Appl. Phys., 8 (1969) 191. 23 E. Yoda, Japan. J. Appl. Phys., 8 (1969) 1355. Thin Solid Films, 12 (1972) 17-28

28 24 25 26 27 28 29 30 31 32 33 34 35 36

K. KINOSITA Y. Namba, Oyo Buturi, 38 (1969) 411. H.J. Bauer and W. Buckel, Z. Physik, 216 (1968) 507. H.J. Bauer and W. Buckel, Helv. Phys. Acta, 41 (1968) 674. H.J. Bauer and W. Buckel, Z. Physik, 220 (1969) 293. E. Klokholm, J. Vac. Sci. Technol., 6 (1969) 138. H. Horikoshi and N. Tamura, Japan. J. AppL Phys., 2 (1963) 328. K. Maki, Y. Nakajima and K. Kinosita, J. Vac. Sci. Technol., 6 (1969) 622. Y. Nakajima and K. Kinosita, Thin Solid Films, 5 (1970) R5. C.W.B. Grigson and D. B. Dove, J. Vac. Sci. Technol., 3 (1966) 120. M.B. Heritage, Ph.D. Dissertation, Univ. of Cambridge, 1968; through Wilcock et aL 1~ H.P. Murbach and H. Wilman, Proc. Phys. Soc. (London), B66 (1953) 905. S. Ino, D. Watanabe and S. Ogawa, J. Phys. Soc. Japan, 19 (1964) 155. M. Nishibori and K. Kinosita, Japan. J. AppL Phys., 11 (1972) 758.

Thin Solid Films, 12 (1972) 17-28