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Thermal strain in thin lead films III: Dependences of the strain on film thickness and on grain size
Thin SolidFilms, 59 (1979) 105-116
Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands
105
THERMAL STRAIN IN THIN LEAD FILMS III: D E P E N D E N C E S OF T H E S T R A I N O N F I L M T H I C K N E S S A N D O N G R A I N SIZE MASANORI MURAKAMI IBM Thomas J. Watson Research Center, Yorktown Heights, N. Y. 10598 (U.S.A.)
( Received June 1, 1978 : accepted August 24, 1978)
The effects of film thickness h or of average grain size g on strains e 33' due to the mismatch of thermal expansion coefficients were studied by an X-ray diffraction technique for thin lead films 0.03-1.0 gm thick evaporated onto silicon substrates. Films with the same average grain size and with different film thicknesses were prepared by a sputter-etch-thinning technique after the film depositions had been completed. Films with small grain sizes were prepared by deposition at liquid nitrogen temperature or by seeding a very thin layer of gold or palladium before the lead deposition. These films were cooled from 300 to 4.2 K using a cold stage attached to an X-ray diffractometer. For films with h < g/5, the ~333' levels were found to be determined by h. The critical film thickness h e was 0.15 gm. he was defined so that for h < h c no strain relaxation was observed, independent of grain sizes. F o r h > he the g33' values were found to be proportional to I/h. The h dependence on the g33' values was analyzed based on an assumption that dislocation glide was the dominant strain relaxation mechanism. It was found that the dislocation pinning distance was about four times smaller than the film thickness, which agrees with the previous result obtained by a cantilever beam technique. F o r films with h > g/5 the critical grain size g~ was determined to be about 1 lam. When g > g¢ the ~33 t levels decreased with increasing g. When g < g~ the ca3' values were found to be independent of g and also of h. However, e33' did not reach the calculated m a x i m u m strain value. We propose that the difference between the calculated strain and the measured strain was due to an absorption of the strain at grain boundaries. The fact that g¢ was about six times larger than he means that g exerted a stronger effect than h did on the inhibition of strain relaxation during cooling to 4.2 K. It was found that the intermetallic compounds Pb3Au or Pb2Pd which were formed in the binary films did not greatly affect the inhibition of strain relaxation. The e33' levels in these binary films were also determined by the grain sizes.
1. INTRODUCTION
When a thin film which has been deposited on a substrate with a different thermal expansion is cooled or heated, a strain is introduced into the film. This strain often leads to plastic deformations, film fracture or peeling. In previous papers 1' 2 studies on the strain have been carried out using an X-ray
106
M. MURAKAMI
diffraction technique. Lead films were deposited at various thicknesses on oxidized silicon substrates at room temperature and were then cooled to 4.2 K. In these previous studies it was found that the strains at 4.2 K depended strongly on the film thickness I and on the grain orientation 2. For films 0.1-0.2 lam thick the strain was found to reach almost the maximum value which was calculated using the thermal expansion coefficients of lead and silicon and a biaxial strain model. The strains for films thicker than 0.2 lam were found to be partially relaxed concurrently with cooling. More strain relaxation was observed for thicker films. The relaxation mechanism is believed to be dislocation glide, because many slip bands were observed for lead films which were thermally cycled between room temperature and 4.2 K many times 3-6. This strong dependence of the strain (or stress) on film thickness has also been observed by Caswell et al. 3 using a cantilever beam technique. Since the films with different thicknesses h had different grain sizes g, we could not conclude from only the measured strain versus thickness plot whether h o r g effectively contributed to an increase in the strains at low temperature. The purpose of the present experiment was to find out whether g or h has more effect on the inhibition of strain relaxation at 4.2 K. To study the dependence of the strain on the film thickness alone, lead films with constant average grain size but with different film thicknesses were used. These films were prepared by a sputteretch-thinning technique. To study the dependence of the strain on grain size, films with constant thickness but with different grain sizes were used. These films were prepared by changing the substrate temperature during film deposition. Also, to prepare films with small grain sizes, a very thin layer of gold or palladium was seeded before the succeeding lead deposition ~. The strains of these films were measured by a conventional X-ray diffraction technique 1' 2, 5. The mechanism of the thin film strength is discussed by comparing the measured dependence of the strains on the film thickness with'the existing models 8. A dependence of the maximum strain on the grain size is explained very well by assuming that large strains occur at the grain boundaries. Finally all the measured strain values were plotted on a g versus h map, which made it very easy to see at a glance the dependence of the strain on g or on h. 2. EXPERIMENTAL PROCEDURES
2.1. Preparation o f samples
Oxidized (111) Si wafers 0.2 gm thick were used as substrates. The substrates were kept 50 cm above the material sources in order to minimize the non-uniformity of film thickness across the substrate. The substrate temperature was kept at room temperature or at 77 K. The substrates were precleaned using an oxygen glow discharge before film depositions except when the deposition was made on the substrate which was kept at 77 K. Films of lead, Au/Pb, Pb/Au/Pb or P d / P b (the solidus will be used to denote the sequence of evaporation) with various lead film thicknesses were prepared by an evaporation method in a vacuum of better than 1 x 10- 7 Torr. The deposition rate of lead was about 30/~ s- 1. The thickness of the gold or palladium layer was 40 A. Films with total thicknesses ranging from 0.05 to 2 gm were thus prepared. The thicknesses were measured using a calibrated quartz thickness monitor placed near
THERMAL
STRAIN IN THIN
Pb
107
FILMS. III
the substrates. After the deposition had been completed, dry oxygen gas was leaked into the v a c u u m c h a m b e r at the deposition temperature. The oxide film (about 25 A thick) should prevent grain growth at r o o m temperature 9. Some of the films were sputter etch thinned by using an argon glow discharge at 1000 V and 10 mTorr. An average sputter-thinning rate was approximately 300 A min -1. The thickness of each sputtered film was accurately measured by interferometry. D a t a for the samples used in the present experiment are given in Table I. Hereafter, for simplicity Pb(A) denotes the lead films deposited at r o o m temperature, Pb(B) denotes the lead films deposited at r o o m temperature and then sputter etch thinned to the desired thickness and Pb(C) denotes the lead films deposited at 77 K. TABLE I THIN FILMS USED IN THE PRESENT EXPERIMENT
Fihns
Pb
Pb
Substrate temperature (K)
Totalfilm thickness(lam)
(lam)
300
0.1 0.2 0.3 0.5 1.0
0.10 0.20, 0.10 0.41, 0.28, 0.19, 0.12 0.57, 0.51, 0.37, 0.11
77
Thickness of sputter-etch-thinnedfilms
0.03 0.07 0.1
0.2 0.3 0.5 1.0
Au/Pb a
300
0.1 0.2 0.4 0.5 1.0
0.30, 0.20 0.80, 0.50
Pb/Au/Pb b
300
0.4
--
Pd/Pb a
300
0.1 0.2 0.3 0.5 1.0
--
a The gold or palladium layer is 40 A. bThe first lead layer is 0.24 IJm and the second lead layer is 0.16 gm; the gold layer between the two lead layers is 40 ~. 2.2. Grain size measurement
Average grain sizes in the films were measured by various m e t h o d s depending on the film thickness ranges. F o r very thick films with large grain sizes the film surfaces were slightly chemically etched by a solution of dilute nitric acid (1 H N O 3 + 6 H 2 0 ) and grain boundaries were observed by optical microscopy
108
M. M U R A K A M I
(OM). For very thin films the grain sizes were observed by transmission electron microscopy (TEM). The T E M samples were prepared as follows: firstly photo resist was coated onto the silicon substrate, then SiO 0.05 gm thick was deposited on dried photo resist and finally a lead film was deposited at the desired thickness. For TEM observation the photo resist was desolved in acetone and the grain size observation for the lead film was carried out through the thin SiO layer. For relatively thick films with very fine grains the grain boundaries were observed without etching by scanning electron microscopy (SEM). The agreement of grain sizes measured by these methods was reasonable. 2.3. Thermal treatments and X-ray intensity measurements Thermal treatments of specimens were carried out using a liquid-helium-cooled X-ray diffraction stage. To improve thermal conductivity between the specimen and the specimen holder, a copper grease (Cry-con grease supplied by Air Products and Chemicals) was used. The environment of a specimen was evacuated to 4 x 1 0 - 6 Torr before cooling by using an 8 1 s-1 ion pump. X-ray diffraction intensity measurements were made through a beryllium window in the refrigerator housing. A computer-controlled G E XR-5 diffractometer was used with Cu K~ radiation (operated at 40 kV and 20 mA) with soller slits. Using a proportional counter the intensities were step scanned for sufficient times (10-40 s) to obtain enough measurable intensity at an interval of 20 = 0.01 ° or 0.02 ° for predetermined diffraction angle ranges.
3.
E X P E R I M E N T A L RESULTS
3.1. Grain sizes Average grain sizes were measured by the different techniques described in Section 2.2 for Pb, Au/Pb and Pd/Pb films. In Fig. 1 typical examples of micrographs obtained by SEM, OM or T E M are shown. Figure l(a) shows the SEM micrograph for the Pb(A) film 1.0 lam thick. Figure l(b) is the OM micrograph for the Pb(A) film 0.5 gm thick; the surface of the film was slightly etched by the dilute nitric acid solution just before the observation. Figure 1(c) is the T E M micrograph for the Pb(C) film 0.1 gm thick deposited on SiO 500 ~ thick at 77 K. The micrograph was taken through the film and the SiO substrate. In the T E M micrograph a high density of twin faults was observed; these might be formed during heating from 77 K to room temperature. Although holes about 0.5 gm in diameter (the density of the holes was 7 x 10 l° cm -2) were observed by SEM in the Pb(A) film 0.1 p.m thick which was deposited at room temperature, no holes were observed in the present 0.1 gm Pb(C) film. It should be noted that grains whose sizes are comparable with the film thickness are observed to be columnar. F r o m the micrographs the average grain sizes g were measured and they are plotted against film thicknesses h in Fig. 2. As seen in the micrographs, the grain sizes are widely distributed. The vertical bars in the figure represent the roughly estimated grain size ranges measured in the micrographs. It was very difficult to obtain the statistical distribution of the grain sizes for these films. Since the Pd/Pb films showed the same grain sizes as those of the Au/Pb films, they were not indicated in the figure. Compared with the Pb(A) films the grain sizes are about a factor of 2 or 3 smaller for
THERMAL STRAIN IN THIN
(a)
Pb
109
FILMS. Ill
{b)
(c) Fig. 1. (a) An SEM micrograph for a Pb(A) film 1.0 l~m thick; (b) an O M micrograph for a Pb(A) film 0.5 pm thick; (c) a T E M micrograph for a Pb(C) film 0.1 pm thick.
the Au/Pb and the Pd/Pb samples and are about a factor of 5 smaller for the Pb(C) samples. The ratios R defined by g/h are as follows: R ~ 5 for the Pb(A) films; R .~ 1 for the Pb(C) films; R ~ 2 for the Au/Pd and the P d / P b films. These results indicate that the films used in the present experiment are typically one grain thick. We observed that the grain sizes of the sputter-etch-thinned films did not change by the sputtering process. The broken lines with arrows shown in Fig. 2 indicate the directions of the sputter etch thinning. The surface of a sputter-etchthinned film was observed to be rougher than that of the as-deposited film. Some grain boundaries were observed to be preferentially etch thinned when the thickness etched was great. The film thicknesses given in Table I were measured by an interferometric technique and they represent the average thickness.
3.2. Strain at 4.2 K The strain that was introduced into a film on cooling from 300 to 4.2 K was measured. (To relax the intrinsic strain in as-deposited films, samples were kept in a vacuum desiccator at least 1 day before cooling to 4.2 K.) The strain e33' normal to the film surface was obtained from e33t =
(d-do)/do
(1)
where d is the measured interplanar spacing normal to the film surface and d o is a
110
M. MURAKAMI
strain-free value which is calculated using the reported thermal expansion coefficients1°. (The subscripts ij denote the directions of the orthogonal axes: 11 and 22 are directions parallel to the film surface and 33 is the direction normal to the film surface.) Since lead, Au/Pb and P d / P b films all have a strong (111) fiber structure, accurate d measurements were carried out from (222) and/or (333) diffraction peaks. Thus the ea3' value calculated from eqn. (1) represents the average elastic strain normal to (111) interplanar spacing within the grains. In Fig. 3 the e3a' values (the absolute values) measured for the lead films are shown as a function of film thickness. In this figure the open circles are the e33' values for Pb(B) films which were deposited at a thickness of 1 pm at room temperature and were then sputter etch thinned to the desired thicknesses, and the open squares are the values for the Pb(C) films which were deposited at 77 K. The broken curve indicates the e3a' values for the Pb(A) films which were deposited at room temperature. (The esa' values of the Pb(A) films have been given in a previous paper 1 and are reproduced here for comparison with the other films.) The theoretical m a x i m u m strain emax' is shown by a broken line calculated 1 using a biaxial strain model 11, 12. This is the strain level that is expected if the (11 D-oriented grains can support elastically the full thermal expansion mismatch.
,oF -.-6.0 5.0 4.0
::k
w ~3.0
I----!
I0
0
0.2
I I 0.4 0.6 0.8 FILM THICKNESS(/~ra)
I 1.0
0
I
0.2
I
I
I
0.4 0.6 0.8 FILM THICKNESS (k~m)
I
1,0
Fig. 2. The grain sizes of lead and Au/Pb films: ~ - - , direction of sputter etch thinning; C), Pb(A); ?., Pb(C); [Z, Au/Pb; O, Pb/Au/Pb. Fig. 3. The strains e33' for lead films of various thicknesses measured at 4.2 K: ,.%- ~, Pb(A); C) C), Pb(B); U]--.--V1, Pb(C). It should be noted that the ~ 3 3 ' values of both the Pb(A) and the Pb(B) films have strong film thickness dependences. (These dependences will be discussed in Section 4.1.) The e33' value reaches emax' at h = 0.15 ~m for the Pb(A) films. However, the e33' values for the Pb(C) films do not depend on h in the thickness range 0.03-1 pm within experimental errors. Moreover, it can be seen that the e33' values at h = 0.1 p.m decrease in the order Pb(A), Pb(B) and Pb(C). This will be discussed in Section 4.2.
THERMAL STRAIN IN THIN Pb FILMS. III
11 l
The/333' values for Au/Pb (open circles), Pd/Pb (open squares) and Pb/Au/Pb (open triangles) films are plotted against total film thickness in Fig. 4. In this figure it should be noted that both the Au/Pb and Pd/Pb films show similar strain behaviors. The e33' values were observed to have almost no h dependence at thicknesses less than h = 0.4 p.m. Compared with the/333' values for the Pb(A) films (Fig. 3), the/333' values for the Au/Pb or the Pd/Pb fihns are larger when h > 0.2 lam and are smaller when h < 0.2 p.m. It should be noted that the e33' value for the Pb/Au/Pb film (h = 0.4 p.m) is about three times smaller than that for the Au/Pb film (h = 0.4 jam). These features will be discussed in Section 4.2. 4. DISCUSSION 4.1. The mechanism of strength in thin films From Fig. 3 it can be seen that the measured/333' values depend strongly on the film thickness for lead films. This dependence will be discussed in this section using the existing thin film strength models. Menter and Pashley 13 and Blumberg and Seraphin 14 havedeveloped a simple model in which it was assumed that plastic flow occurs by the motion of dislocations whose ends are pinned at grain boundaries or at the upper and lower surfaces of the film. For such a model the critical resolved shear stress o-3a" for dislocation slip is given by the relation 14 o-3 l" = o-o" + ~pb/I
(2)
where ao" is the critical resolved shear stress of a lead single crystal, p is the shear modulus, b is the Burgers vector for the slip, I is the distance between the dislocation pinning points and ~ is a constant of magnitude near 0.5-1.0. Satisfactory agreement was observed between theoretical and experimental values for indium and tin 15 when it was assumed that l ~ h. However, Caswell et al. 3 found that experimental a31" values were as much as four times larger than theoretical values for lead films. In the present experiment the dependence of the strain on the film thickness was analyzed based on this model. To eliminate the grain size effect on the stress, an analysis was carried out for the Pb(B) films (Fig. 3) which had a constant average lateral grain size of about 4.5 p.m. The 0 31" values were calculated from the measured ~;33' values. The calculation procedure has been described in ref. 2, Appendix. In Fig. 5 the 0"31"values ar e plotted as a function of 1/h. Excellent linearity is observed in the film thickness range 0.1-1.0 p.m. The theoretical o31" values calculated from eqn. (2) are indicated by the broken line where it was assumed that l = h,/t = 1.00 × 1011 dyn cm -2 (ref. 16), b = 3.5/~, o-0" = 2.66 × 107 dyn cm -2 (ref. 17) at 4.2 K and a = 1. It should be noted that the experimental 0"31" values are 3-4 times larger than the theoretical values in the film thickness range studied. The results agree with those of Caswell et al. 3 This result suggests that the average dislocation pinning distance could be much smaller than the film thickness h if dislocation glide is the dominant strain relaxation mechanism at 4.2 K. The direct observation of the pinning sites has not yet been carried out but it is under way at present using TEM. It seems unreasonable to explain the results based on a hypothesis that the/z values in lead films are 3-4 times larger than those of the bulk material, because the/333' values observed at different crystal orientations were found to agree with those calculated using the
112
M. MURAKAM!
bulk elastic constants 2. The most probable reason for our results is that we used an oversimplified model. However, this model is the most reasonable one currently available for explaining thin film strength but unfortunately it does not take into account dislocation interactions which m a y play an important role in strengthening the films. An improved model is at present being developed to explain the present results 18 1.0-i E ITl~lX
0.5
1.4]
g
1.0 0 5
Q3
__
0.I
J
I0 i 1"2 0.8 0
L
0.1
:~o.4i _
1 0,2
1 0.4. FILM
I 0.6
THICKNESS
I 0,8 (/a.ml
I 1.0
0
2
4 llh
15 (,u.m-I)
8
IO
Fig. 4. The strains %s' for Au/Pb (O), Pd/Pb ([~), and Pb/Au/Pb (:_) films of various thicknesses measured at 4.2 K. Fig. 5. The resolved shear stresses ~z33"for dislocation slip direction of Pb(B) films which were deposited at a thickness of 1.0 p.m and were then sputter etch thinned to the various thicknesses h: - - , experiment: ,calculation. The strain value of a sputter-etch-thinned film (Pb(B)) was observed to be smaller than that of a Pb(A) film with the same film thickness, especially when h < 0.5 pm (Fig. 3). This m a y be interpreted by differences in defect densities and in average grain sizes between the two samples. The Pb(A) films are believed to have higher densities of defects introduced during vapor deposition. The defects are considered to contribute to the film strength ~9' 2o. Also the Pb(A) films have grain sizes that are smaller by a factor of 5-10 than those of the Pb(B1 films when h = 0.10.2 gm. The high defect density and finer grains in Pb(A) films are considered to contribute to the increase in the strain at 4.2 K.
4.2. Strain at grain boundaries In Figs. 3 and 4 we observed that the %3' values for films with fine grains (i.e. the Pb(C), A u / P b or P d / P b films) did not reach the calculated m a x i m u m strain value e,max'. This m a y be due to the occurrence of strain at the grain boundaries. Based on an assumption that there is strain at grain boundaries, the a m o u n t of strain is calculated below. In a film with a lateral grain size go and with a grain b o u n d a r y width 6o at 4.2 K the m a x i m u m strain ~;~i max parallel to the film surface at
T H E R M A L STRAIN IN THIN
Pb
FILMS. III
113
this temperature is expressed by
Ag+ A,5
- - E l l max
go + 6o where Ag - g ' - g o and A6 -- 6 ' - 6 0 (where g' and 6' are the strained grain size and boundary width respectively). This equation is rewritten as A ggo ~ / 3 1 1 m a x
"~g~(/311max -- A7o6)
(3)
The value of Ag/g o corresponds to the strain/311' inside grains parallel to the film surface. In the present X-ray diffraction technique we measured the elastic strains e33' (inside grains) normal to the film surface. However, since /333'/811' is 0.96 for (111)-oriented grains 2,/311' = 1.04/333'. As seen in Figs. 3 and 4, the eaa' value has a maximum value at h = 0.1 ixm for each specimen. Grains in the 0.1 ~tm films are considered to be completely elastically strained, although the grain sizes are different. Based on eqn. (3), the strain values /311' which were calculated from the measured/333' values are plotted against the inverse of the average grain size in Fig. 6. The approximate g values at this film thickness are read from Fig. 2 and are 1.0 lam for the Pb(A) film, 0.45 ~tm for the Au/Pb and the P d / P b films and 0.15 ktm for the Pb(C) film. Reasonable linearity was obtained for this plot. The intersection on the axis 1/g = 0 should be 0.7~o. This value which corresponds to the strain in a single crystal was calculated assuming that there was no strain relaxation on cooling from 300 to 4.2 K. From eqn. (3) the slope 4' of this plot is given by
Thus the strainA6/6 o at grain boundaries is
A,~
--
6o
4'
= ~11 max - - - -
(5)
6o
If we substitute the values'of e 11max = 0.70~, 6 ~ 2b = 7 A and 4' ~ - 2 ,~ into eqn. (5), we calculate A6/6 o to be about 28Y/o. This result suggests that, if we assume the occurrence of strain only at grain boundaries and inside grains, the strain at grain boundaries can be calculated to be as large as about 28~o. 4.3. The dependence of strains on film thickness and on grain size Blakely 2° found that in gold thin films tensile strain-stress behavior showed very little differences between polycrystalline and single-crystal films. This suggests that grain size was not an important factor in the thin film strength. However, the present experiment indicates that the grain size of the lead films is important as well as the film thickness in inhibiting the strain relaxation during cooling to a low temperature. In Fig. 7 the strain ratios ~ of all samples are indicated on a grain size versus film thickness plot. The ~ values represent the measured strains for each sample type normalized by the strain values at h = 0.1 ~tm observed for that type which were
114
M. MURAKAMI
shown in Fig. 6. In this figure the notations of Au/Pb(A) and Au/Pb(B) denote Au/Pb films without and with sputter etch thinning respectively. Although there are not enough data points to draw accurate constant strain contour curves, the approximate contour curves are shown by the full curves. It is obvious from this plot that for h < g/5 the film thickness limits the strain relaxation and that for h > g/5 the grain size limits the relaxation. No significant strain relaxation was observed in the films when g < 1 jam or when h <'0.15 jam within the limits of grain sizes and of film thicknesses studied in the present experiment. It should be noted that the critical sizes for inhibiting strain relaxation are about six times smaller for the film thickness than for the average grain size. This indicates that the strain relaxation was limited more efficiently by the grain size than by the film thickness. The region in which the films can support elastically the thermal strain at 4.2 K is shaded in Fig. 7. 5.0 ~'+~1
014 0.3 ~0.2 o\ ° \ ° / a =0.2 \ ~" tl =0.4
I,~Lot
0.7
~'-:o
,03
o2\J
.=0.6
Vo\ ; 7 \ /
\
0.6
z 3.0~
k/~><
0.~
0.1 •
/
o:o.s
:.~.o
\%1
0.5 1.0
,oFT ,
0.4 -
!ii: ~'°~
I 2
I
I
4 6 I/g {~m "1)
I
8
0~'/, 0
~
0.4 0.6 0.8 0.2 FILM THICKNESS (Fro)
~ 1.0
Fig. 6. The maximum strains which were observed at h = 0.1 ~tm for Pb(A) (O), Pb(C) (V), Au/Pb (±) and Pd/Pb ([]) films with various grain sizes g: - - , e 1ma,. Fig. 7. The strain ratios ct plotted on a film thickness v s . grain size map: e, Pb(A); O, Pb(B); C], Pb(C); A, Au/Pb(A); ~, Au/Pb(B); O, Pb/Au/Pb.
4.4. Role of intermetallic compounds It is evident in Figs. 3 and 4 that gold- or palladium-seeded lead films support larger strains than the Pb(A) films do when h > 0.2 jam. In lead-rich Pb-Au alloys intermetallic compounds of PbaAu are found to be formed at room temperature by X-ray diffraction. Also, as in Fig. 2, the average grain sizes were smaller in the seeded films than in the Pb(A) films. The strain increase observed in the seeded films could be due to finer grains or to intermetallic compounds. These two possibilities could be differentiated by comparing the strains and average grain sizes in the Au/Pb and Pb/Au/Pb films with h = 0.4 jam. The average grain size (Fig. 2) and the strain valu e (Fig. 4) in the Pb/Au/Pb film were observed to be very close to those of the Pb(A) film (h = 0.4 jam). The g value of the Au/Pb film was observed to be about 2.5 times smaller than that of the Pb(A) film and the ~33' value of the Au/Pb film was found to be about three times larger than that of the Pb(A) film. The PbaAu compounds were observed to be distributed uniformly in both the Pb/Au/Pb and the Au/Pb films 21. Thus it may be concluded that g is more
THERMAL STRAIN IN THIN
Pb
FILMS. III
115
important than the intermetallic compounds are in determining the strain levels at 4.2 K. 5. SUMMARIZING REMARKS
The dependences of the thermal strain e33' introduced by the thermal mismatch between film and substrate on film thickness h and on grain size g were studied for lead films with various g and/or h values. The films were prepared by deposition at room temperature or low temperature, by sputter etch thinning after the depositions or by seeding small amounts of gold or palladium layers before the lead depositions. The e33' measurements were carried out by an X-ray diffraction technique for the films which were cooled from 300 to 4.2 K. The experimental results are summarized as follows. (1) In films with h ~ g, the ~33' level was determined by h. The resolved shear stress a 31" for dislocation slip which was calculated from the measured e33' value can be expressed by a31" = ao" + ~/h The magnitude of c~was found to be about four times larger than the product of/zb (where/z is the shear modulus at 4.2 K and b is the Burgers vector). This result suggests that the dislocation pinning distance could be about four times smaller than h if dislocation glide was the dominant strain relaxation mechanism. The critical film thickness hc was determined to be 0.15 pm (he was defined so that for h < hc the strain in the films support the maximum strain, independent of the grain sizes). (2) In films with h > g/5, the critical grain size g¢ was determined to be about 1 gm where g~ was defined so that for g < g¢ the films support the maximum strain, independent of h. However, the e33' levels in the films with g < g~ did not reach the calculated maximum value. We proposed that the difference in the e33' values is due to an absorption of the strain at grain boundaries. (3) Because g~ > hc it is indicated that a reduction in average grain size rather than in film thickness is more effective in inhibiting the strain relaxation at 4.2 K. (4) The strain levels were not influenced by the existence of intermetallic compounds of Pb3Au or Pb2Pd in lead alloy films. (5) Fine-grained lead films prepared by deposition at 77 K or by seeding a thin gold or a thin palladium layer before lead deposition exhibited significantly less strain relaxation during cooling to 4.2 K. ACKNOWLEDGMENTS
The author would like to express his gratitude to C. J. Kircher, P. Chaudhari and K. N. Tu for stimulating discussions, to A. Segmuller for assistance with X-ray diffraction technique, to V. Tom for sample preparation and to the late J. W. Matthews, A. L. Ginzburg and C. M. Serrano for grain size measurements. REFERENCES 1
M. Murakami, Acta Metall., 26 (1978) 175.
1 16
M. M U R A K A M I
2 M. Murakami and P. Chaudhari, Thin Solid Films, 46 (1977) 109. 3 H.L. Caswell, J. R. Priest and Y. Boko, J. Appl. Phys., 34 (1963~ 3261. 4 S.K. Lahiri, J. Appl. Phys., 46 (1975) 2791. 5 M. Murakami, Thin SolidFilms, 55 (1978) 101. 6 H.-C. Huang, personalcommufiication, 1978. 7 R.H. Jeppesen and H. L. Caswell, IBM J. Res. Dev., 7 ( 1963~ 297. 8 R . W . Hoffman, Phys. ThinFilms, 3(1966)211. 9 H.L. Caswell and Y. Budo, J. Appl. Phys., 35 ( 19641 644. 10 D.E. Gray, American Institute of Physics Handbook, McGraw-Hill, New York, 1972. 11 R . W . V o o k a n d F . Witt, J. Appl. Phys.,36(1965~2169. 12 F. Witt and 1~. W. Vook, J. Appl. Phys., 39 (1968~ 2773. 13 J . W . Menter and D. W. Pashley, Proc. Int. Conf. on the Structure and Properties of Thin Films, Bolton Landing, New York, Wiley, New York, 1959, 14 R.H. Blumberg and D. P. Seraphim, J. Appl. Phys., 33 (1962) 163. 15 A . M . Toxen, Phys. Rev., 123 ( 1961 ) 442. 16 D.L. Waldorf and G. A. Alers, J. Appl. Phys., 33 (1962) 3266. 17 V.I. Startsev, V. V. Pustovalov and V. S. Fomenko, Trans. Jpn Inst. Met., 9 (1968) 843. 18 M. Ronay, personal communication, 1978. 19 L.A. Tarshis, M.S. Thesis, Polytechnic Institute of Brooklyn, 1963. 20 J.M. Blakely, J. Appl. Phys., 35 (1964) 1756. 21 S.K. Lahiri, J. Vac. Sci. Teehnol., 13 (1976) 148.
Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands
105
THERMAL STRAIN IN THIN LEAD FILMS III: D E P E N D E N C E S OF T H E S T R A I N O N F I L M T H I C K N E S S A N D O N G R A I N SIZE MASANORI MURAKAMI IBM Thomas J. Watson Research Center, Yorktown Heights, N. Y. 10598 (U.S.A.)
( Received June 1, 1978 : accepted August 24, 1978)
The effects of film thickness h or of average grain size g on strains e 33' due to the mismatch of thermal expansion coefficients were studied by an X-ray diffraction technique for thin lead films 0.03-1.0 gm thick evaporated onto silicon substrates. Films with the same average grain size and with different film thicknesses were prepared by a sputter-etch-thinning technique after the film depositions had been completed. Films with small grain sizes were prepared by deposition at liquid nitrogen temperature or by seeding a very thin layer of gold or palladium before the lead deposition. These films were cooled from 300 to 4.2 K using a cold stage attached to an X-ray diffractometer. For films with h < g/5, the ~333' levels were found to be determined by h. The critical film thickness h e was 0.15 gm. he was defined so that for h < h c no strain relaxation was observed, independent of grain sizes. F o r h > he the g33' values were found to be proportional to I/h. The h dependence on the g33' values was analyzed based on an assumption that dislocation glide was the dominant strain relaxation mechanism. It was found that the dislocation pinning distance was about four times smaller than the film thickness, which agrees with the previous result obtained by a cantilever beam technique. F o r films with h > g/5 the critical grain size g~ was determined to be about 1 lam. When g > g¢ the ~33 t levels decreased with increasing g. When g < g~ the ca3' values were found to be independent of g and also of h. However, e33' did not reach the calculated m a x i m u m strain value. We propose that the difference between the calculated strain and the measured strain was due to an absorption of the strain at grain boundaries. The fact that g¢ was about six times larger than he means that g exerted a stronger effect than h did on the inhibition of strain relaxation during cooling to 4.2 K. It was found that the intermetallic compounds Pb3Au or Pb2Pd which were formed in the binary films did not greatly affect the inhibition of strain relaxation. The e33' levels in these binary films were also determined by the grain sizes.
1. INTRODUCTION
When a thin film which has been deposited on a substrate with a different thermal expansion is cooled or heated, a strain is introduced into the film. This strain often leads to plastic deformations, film fracture or peeling. In previous papers 1' 2 studies on the strain have been carried out using an X-ray
106
M. MURAKAMI
diffraction technique. Lead films were deposited at various thicknesses on oxidized silicon substrates at room temperature and were then cooled to 4.2 K. In these previous studies it was found that the strains at 4.2 K depended strongly on the film thickness I and on the grain orientation 2. For films 0.1-0.2 lam thick the strain was found to reach almost the maximum value which was calculated using the thermal expansion coefficients of lead and silicon and a biaxial strain model. The strains for films thicker than 0.2 lam were found to be partially relaxed concurrently with cooling. More strain relaxation was observed for thicker films. The relaxation mechanism is believed to be dislocation glide, because many slip bands were observed for lead films which were thermally cycled between room temperature and 4.2 K many times 3-6. This strong dependence of the strain (or stress) on film thickness has also been observed by Caswell et al. 3 using a cantilever beam technique. Since the films with different thicknesses h had different grain sizes g, we could not conclude from only the measured strain versus thickness plot whether h o r g effectively contributed to an increase in the strains at low temperature. The purpose of the present experiment was to find out whether g or h has more effect on the inhibition of strain relaxation at 4.2 K. To study the dependence of the strain on the film thickness alone, lead films with constant average grain size but with different film thicknesses were used. These films were prepared by a sputteretch-thinning technique. To study the dependence of the strain on grain size, films with constant thickness but with different grain sizes were used. These films were prepared by changing the substrate temperature during film deposition. Also, to prepare films with small grain sizes, a very thin layer of gold or palladium was seeded before the succeeding lead deposition ~. The strains of these films were measured by a conventional X-ray diffraction technique 1' 2, 5. The mechanism of the thin film strength is discussed by comparing the measured dependence of the strains on the film thickness with'the existing models 8. A dependence of the maximum strain on the grain size is explained very well by assuming that large strains occur at the grain boundaries. Finally all the measured strain values were plotted on a g versus h map, which made it very easy to see at a glance the dependence of the strain on g or on h. 2. EXPERIMENTAL PROCEDURES
2.1. Preparation o f samples
Oxidized (111) Si wafers 0.2 gm thick were used as substrates. The substrates were kept 50 cm above the material sources in order to minimize the non-uniformity of film thickness across the substrate. The substrate temperature was kept at room temperature or at 77 K. The substrates were precleaned using an oxygen glow discharge before film depositions except when the deposition was made on the substrate which was kept at 77 K. Films of lead, Au/Pb, Pb/Au/Pb or P d / P b (the solidus will be used to denote the sequence of evaporation) with various lead film thicknesses were prepared by an evaporation method in a vacuum of better than 1 x 10- 7 Torr. The deposition rate of lead was about 30/~ s- 1. The thickness of the gold or palladium layer was 40 A. Films with total thicknesses ranging from 0.05 to 2 gm were thus prepared. The thicknesses were measured using a calibrated quartz thickness monitor placed near
THERMAL
STRAIN IN THIN
Pb
107
FILMS. III
the substrates. After the deposition had been completed, dry oxygen gas was leaked into the v a c u u m c h a m b e r at the deposition temperature. The oxide film (about 25 A thick) should prevent grain growth at r o o m temperature 9. Some of the films were sputter etch thinned by using an argon glow discharge at 1000 V and 10 mTorr. An average sputter-thinning rate was approximately 300 A min -1. The thickness of each sputtered film was accurately measured by interferometry. D a t a for the samples used in the present experiment are given in Table I. Hereafter, for simplicity Pb(A) denotes the lead films deposited at r o o m temperature, Pb(B) denotes the lead films deposited at r o o m temperature and then sputter etch thinned to the desired thickness and Pb(C) denotes the lead films deposited at 77 K. TABLE I THIN FILMS USED IN THE PRESENT EXPERIMENT
Fihns
Pb
Pb
Substrate temperature (K)
Totalfilm thickness(lam)
(lam)
300
0.1 0.2 0.3 0.5 1.0
0.10 0.20, 0.10 0.41, 0.28, 0.19, 0.12 0.57, 0.51, 0.37, 0.11
77
Thickness of sputter-etch-thinnedfilms
0.03 0.07 0.1
0.2 0.3 0.5 1.0
Au/Pb a
300
0.1 0.2 0.4 0.5 1.0
0.30, 0.20 0.80, 0.50
Pb/Au/Pb b
300
0.4
--
Pd/Pb a
300
0.1 0.2 0.3 0.5 1.0
--
a The gold or palladium layer is 40 A. bThe first lead layer is 0.24 IJm and the second lead layer is 0.16 gm; the gold layer between the two lead layers is 40 ~. 2.2. Grain size measurement
Average grain sizes in the films were measured by various m e t h o d s depending on the film thickness ranges. F o r very thick films with large grain sizes the film surfaces were slightly chemically etched by a solution of dilute nitric acid (1 H N O 3 + 6 H 2 0 ) and grain boundaries were observed by optical microscopy
108
M. M U R A K A M I
(OM). For very thin films the grain sizes were observed by transmission electron microscopy (TEM). The T E M samples were prepared as follows: firstly photo resist was coated onto the silicon substrate, then SiO 0.05 gm thick was deposited on dried photo resist and finally a lead film was deposited at the desired thickness. For TEM observation the photo resist was desolved in acetone and the grain size observation for the lead film was carried out through the thin SiO layer. For relatively thick films with very fine grains the grain boundaries were observed without etching by scanning electron microscopy (SEM). The agreement of grain sizes measured by these methods was reasonable. 2.3. Thermal treatments and X-ray intensity measurements Thermal treatments of specimens were carried out using a liquid-helium-cooled X-ray diffraction stage. To improve thermal conductivity between the specimen and the specimen holder, a copper grease (Cry-con grease supplied by Air Products and Chemicals) was used. The environment of a specimen was evacuated to 4 x 1 0 - 6 Torr before cooling by using an 8 1 s-1 ion pump. X-ray diffraction intensity measurements were made through a beryllium window in the refrigerator housing. A computer-controlled G E XR-5 diffractometer was used with Cu K~ radiation (operated at 40 kV and 20 mA) with soller slits. Using a proportional counter the intensities were step scanned for sufficient times (10-40 s) to obtain enough measurable intensity at an interval of 20 = 0.01 ° or 0.02 ° for predetermined diffraction angle ranges.
3.
E X P E R I M E N T A L RESULTS
3.1. Grain sizes Average grain sizes were measured by the different techniques described in Section 2.2 for Pb, Au/Pb and Pd/Pb films. In Fig. 1 typical examples of micrographs obtained by SEM, OM or T E M are shown. Figure l(a) shows the SEM micrograph for the Pb(A) film 1.0 lam thick. Figure l(b) is the OM micrograph for the Pb(A) film 0.5 gm thick; the surface of the film was slightly etched by the dilute nitric acid solution just before the observation. Figure 1(c) is the T E M micrograph for the Pb(C) film 0.1 gm thick deposited on SiO 500 ~ thick at 77 K. The micrograph was taken through the film and the SiO substrate. In the T E M micrograph a high density of twin faults was observed; these might be formed during heating from 77 K to room temperature. Although holes about 0.5 gm in diameter (the density of the holes was 7 x 10 l° cm -2) were observed by SEM in the Pb(A) film 0.1 p.m thick which was deposited at room temperature, no holes were observed in the present 0.1 gm Pb(C) film. It should be noted that grains whose sizes are comparable with the film thickness are observed to be columnar. F r o m the micrographs the average grain sizes g were measured and they are plotted against film thicknesses h in Fig. 2. As seen in the micrographs, the grain sizes are widely distributed. The vertical bars in the figure represent the roughly estimated grain size ranges measured in the micrographs. It was very difficult to obtain the statistical distribution of the grain sizes for these films. Since the Pd/Pb films showed the same grain sizes as those of the Au/Pb films, they were not indicated in the figure. Compared with the Pb(A) films the grain sizes are about a factor of 2 or 3 smaller for
THERMAL STRAIN IN THIN
(a)
Pb
109
FILMS. Ill
{b)
(c) Fig. 1. (a) An SEM micrograph for a Pb(A) film 1.0 l~m thick; (b) an O M micrograph for a Pb(A) film 0.5 pm thick; (c) a T E M micrograph for a Pb(C) film 0.1 pm thick.
the Au/Pb and the Pd/Pb samples and are about a factor of 5 smaller for the Pb(C) samples. The ratios R defined by g/h are as follows: R ~ 5 for the Pb(A) films; R .~ 1 for the Pb(C) films; R ~ 2 for the Au/Pd and the P d / P b films. These results indicate that the films used in the present experiment are typically one grain thick. We observed that the grain sizes of the sputter-etch-thinned films did not change by the sputtering process. The broken lines with arrows shown in Fig. 2 indicate the directions of the sputter etch thinning. The surface of a sputter-etchthinned film was observed to be rougher than that of the as-deposited film. Some grain boundaries were observed to be preferentially etch thinned when the thickness etched was great. The film thicknesses given in Table I were measured by an interferometric technique and they represent the average thickness.
3.2. Strain at 4.2 K The strain that was introduced into a film on cooling from 300 to 4.2 K was measured. (To relax the intrinsic strain in as-deposited films, samples were kept in a vacuum desiccator at least 1 day before cooling to 4.2 K.) The strain e33' normal to the film surface was obtained from e33t =
(d-do)/do
(1)
where d is the measured interplanar spacing normal to the film surface and d o is a
110
M. MURAKAMI
strain-free value which is calculated using the reported thermal expansion coefficients1°. (The subscripts ij denote the directions of the orthogonal axes: 11 and 22 are directions parallel to the film surface and 33 is the direction normal to the film surface.) Since lead, Au/Pb and P d / P b films all have a strong (111) fiber structure, accurate d measurements were carried out from (222) and/or (333) diffraction peaks. Thus the ea3' value calculated from eqn. (1) represents the average elastic strain normal to (111) interplanar spacing within the grains. In Fig. 3 the e3a' values (the absolute values) measured for the lead films are shown as a function of film thickness. In this figure the open circles are the e33' values for Pb(B) films which were deposited at a thickness of 1 pm at room temperature and were then sputter etch thinned to the desired thicknesses, and the open squares are the values for the Pb(C) films which were deposited at 77 K. The broken curve indicates the e3a' values for the Pb(A) films which were deposited at room temperature. (The esa' values of the Pb(A) films have been given in a previous paper 1 and are reproduced here for comparison with the other films.) The theoretical m a x i m u m strain emax' is shown by a broken line calculated 1 using a biaxial strain model 11, 12. This is the strain level that is expected if the (11 D-oriented grains can support elastically the full thermal expansion mismatch.
,oF -.-6.0 5.0 4.0
::k
w ~3.0
I----!
I0
0
0.2
I I 0.4 0.6 0.8 FILM THICKNESS(/~ra)
I 1.0
0
I
0.2
I
I
I
0.4 0.6 0.8 FILM THICKNESS (k~m)
I
1,0
Fig. 2. The grain sizes of lead and Au/Pb films: ~ - - , direction of sputter etch thinning; C), Pb(A); ?., Pb(C); [Z, Au/Pb; O, Pb/Au/Pb. Fig. 3. The strains e33' for lead films of various thicknesses measured at 4.2 K: ,.%- ~, Pb(A); C) C), Pb(B); U]--.--V1, Pb(C). It should be noted that the ~ 3 3 ' values of both the Pb(A) and the Pb(B) films have strong film thickness dependences. (These dependences will be discussed in Section 4.1.) The e33' value reaches emax' at h = 0.15 ~m for the Pb(A) films. However, the e33' values for the Pb(C) films do not depend on h in the thickness range 0.03-1 pm within experimental errors. Moreover, it can be seen that the e33' values at h = 0.1 p.m decrease in the order Pb(A), Pb(B) and Pb(C). This will be discussed in Section 4.2.
THERMAL STRAIN IN THIN Pb FILMS. III
11 l
The/333' values for Au/Pb (open circles), Pd/Pb (open squares) and Pb/Au/Pb (open triangles) films are plotted against total film thickness in Fig. 4. In this figure it should be noted that both the Au/Pb and Pd/Pb films show similar strain behaviors. The e33' values were observed to have almost no h dependence at thicknesses less than h = 0.4 p.m. Compared with the/333' values for the Pb(A) films (Fig. 3), the/333' values for the Au/Pb or the Pd/Pb fihns are larger when h > 0.2 lam and are smaller when h < 0.2 p.m. It should be noted that the e33' value for the Pb/Au/Pb film (h = 0.4 p.m) is about three times smaller than that for the Au/Pb film (h = 0.4 jam). These features will be discussed in Section 4.2. 4. DISCUSSION 4.1. The mechanism of strength in thin films From Fig. 3 it can be seen that the measured/333' values depend strongly on the film thickness for lead films. This dependence will be discussed in this section using the existing thin film strength models. Menter and Pashley 13 and Blumberg and Seraphin 14 havedeveloped a simple model in which it was assumed that plastic flow occurs by the motion of dislocations whose ends are pinned at grain boundaries or at the upper and lower surfaces of the film. For such a model the critical resolved shear stress o-3a" for dislocation slip is given by the relation 14 o-3 l" = o-o" + ~pb/I
(2)
where ao" is the critical resolved shear stress of a lead single crystal, p is the shear modulus, b is the Burgers vector for the slip, I is the distance between the dislocation pinning points and ~ is a constant of magnitude near 0.5-1.0. Satisfactory agreement was observed between theoretical and experimental values for indium and tin 15 when it was assumed that l ~ h. However, Caswell et al. 3 found that experimental a31" values were as much as four times larger than theoretical values for lead films. In the present experiment the dependence of the strain on the film thickness was analyzed based on this model. To eliminate the grain size effect on the stress, an analysis was carried out for the Pb(B) films (Fig. 3) which had a constant average lateral grain size of about 4.5 p.m. The 0 31" values were calculated from the measured ~;33' values. The calculation procedure has been described in ref. 2, Appendix. In Fig. 5 the 0"31"values ar e plotted as a function of 1/h. Excellent linearity is observed in the film thickness range 0.1-1.0 p.m. The theoretical o31" values calculated from eqn. (2) are indicated by the broken line where it was assumed that l = h,/t = 1.00 × 1011 dyn cm -2 (ref. 16), b = 3.5/~, o-0" = 2.66 × 107 dyn cm -2 (ref. 17) at 4.2 K and a = 1. It should be noted that the experimental 0"31" values are 3-4 times larger than the theoretical values in the film thickness range studied. The results agree with those of Caswell et al. 3 This result suggests that the average dislocation pinning distance could be much smaller than the film thickness h if dislocation glide is the dominant strain relaxation mechanism at 4.2 K. The direct observation of the pinning sites has not yet been carried out but it is under way at present using TEM. It seems unreasonable to explain the results based on a hypothesis that the/z values in lead films are 3-4 times larger than those of the bulk material, because the/333' values observed at different crystal orientations were found to agree with those calculated using the
112
M. MURAKAM!
bulk elastic constants 2. The most probable reason for our results is that we used an oversimplified model. However, this model is the most reasonable one currently available for explaining thin film strength but unfortunately it does not take into account dislocation interactions which m a y play an important role in strengthening the films. An improved model is at present being developed to explain the present results 18 1.0-i E ITl~lX
0.5
1.4]
g
1.0 0 5
Q3
__
0.I
J
I0 i 1"2 0.8 0
L
0.1
:~o.4i _
1 0,2
1 0.4. FILM
I 0.6
THICKNESS
I 0,8 (/a.ml
I 1.0
0
2
4 llh
15 (,u.m-I)
8
IO
Fig. 4. The strains %s' for Au/Pb (O), Pd/Pb ([~), and Pb/Au/Pb (:_) films of various thicknesses measured at 4.2 K. Fig. 5. The resolved shear stresses ~z33"for dislocation slip direction of Pb(B) films which were deposited at a thickness of 1.0 p.m and were then sputter etch thinned to the various thicknesses h: - - , experiment: ,calculation. The strain value of a sputter-etch-thinned film (Pb(B)) was observed to be smaller than that of a Pb(A) film with the same film thickness, especially when h < 0.5 pm (Fig. 3). This m a y be interpreted by differences in defect densities and in average grain sizes between the two samples. The Pb(A) films are believed to have higher densities of defects introduced during vapor deposition. The defects are considered to contribute to the film strength ~9' 2o. Also the Pb(A) films have grain sizes that are smaller by a factor of 5-10 than those of the Pb(B1 films when h = 0.10.2 gm. The high defect density and finer grains in Pb(A) films are considered to contribute to the increase in the strain at 4.2 K.
4.2. Strain at grain boundaries In Figs. 3 and 4 we observed that the %3' values for films with fine grains (i.e. the Pb(C), A u / P b or P d / P b films) did not reach the calculated m a x i m u m strain value e,max'. This m a y be due to the occurrence of strain at the grain boundaries. Based on an assumption that there is strain at grain boundaries, the a m o u n t of strain is calculated below. In a film with a lateral grain size go and with a grain b o u n d a r y width 6o at 4.2 K the m a x i m u m strain ~;~i max parallel to the film surface at
T H E R M A L STRAIN IN THIN
Pb
FILMS. III
113
this temperature is expressed by
Ag+ A,5
- - E l l max
go + 6o where Ag - g ' - g o and A6 -- 6 ' - 6 0 (where g' and 6' are the strained grain size and boundary width respectively). This equation is rewritten as A ggo ~ / 3 1 1 m a x
"~g~(/311max -- A7o6)
(3)
The value of Ag/g o corresponds to the strain/311' inside grains parallel to the film surface. In the present X-ray diffraction technique we measured the elastic strains e33' (inside grains) normal to the film surface. However, since /333'/811' is 0.96 for (111)-oriented grains 2,/311' = 1.04/333'. As seen in Figs. 3 and 4, the eaa' value has a maximum value at h = 0.1 ixm for each specimen. Grains in the 0.1 ~tm films are considered to be completely elastically strained, although the grain sizes are different. Based on eqn. (3), the strain values /311' which were calculated from the measured/333' values are plotted against the inverse of the average grain size in Fig. 6. The approximate g values at this film thickness are read from Fig. 2 and are 1.0 lam for the Pb(A) film, 0.45 ~tm for the Au/Pb and the P d / P b films and 0.15 ktm for the Pb(C) film. Reasonable linearity was obtained for this plot. The intersection on the axis 1/g = 0 should be 0.7~o. This value which corresponds to the strain in a single crystal was calculated assuming that there was no strain relaxation on cooling from 300 to 4.2 K. From eqn. (3) the slope 4' of this plot is given by
Thus the strainA6/6 o at grain boundaries is
A,~
--
6o
4'
= ~11 max - - - -
(5)
6o
If we substitute the values'of e 11max = 0.70~, 6 ~ 2b = 7 A and 4' ~ - 2 ,~ into eqn. (5), we calculate A6/6 o to be about 28Y/o. This result suggests that, if we assume the occurrence of strain only at grain boundaries and inside grains, the strain at grain boundaries can be calculated to be as large as about 28~o. 4.3. The dependence of strains on film thickness and on grain size Blakely 2° found that in gold thin films tensile strain-stress behavior showed very little differences between polycrystalline and single-crystal films. This suggests that grain size was not an important factor in the thin film strength. However, the present experiment indicates that the grain size of the lead films is important as well as the film thickness in inhibiting the strain relaxation during cooling to a low temperature. In Fig. 7 the strain ratios ~ of all samples are indicated on a grain size versus film thickness plot. The ~ values represent the measured strains for each sample type normalized by the strain values at h = 0.1 ~tm observed for that type which were
114
M. MURAKAMI
shown in Fig. 6. In this figure the notations of Au/Pb(A) and Au/Pb(B) denote Au/Pb films without and with sputter etch thinning respectively. Although there are not enough data points to draw accurate constant strain contour curves, the approximate contour curves are shown by the full curves. It is obvious from this plot that for h < g/5 the film thickness limits the strain relaxation and that for h > g/5 the grain size limits the relaxation. No significant strain relaxation was observed in the films when g < 1 jam or when h <'0.15 jam within the limits of grain sizes and of film thicknesses studied in the present experiment. It should be noted that the critical sizes for inhibiting strain relaxation are about six times smaller for the film thickness than for the average grain size. This indicates that the strain relaxation was limited more efficiently by the grain size than by the film thickness. The region in which the films can support elastically the thermal strain at 4.2 K is shaded in Fig. 7. 5.0 ~'+~1
014 0.3 ~0.2 o\ ° \ ° / a =0.2 \ ~" tl =0.4
I,~Lot
0.7
~'-:o
,03
o2\J
.=0.6
Vo\ ; 7 \ /
\
0.6
z 3.0~
k/~><
0.~
0.1 •
/
o:o.s
:.~.o
\%1
0.5 1.0
,oFT ,
0.4 -
!ii: ~'°~
I 2
I
I
4 6 I/g {~m "1)
I
8
0~'/, 0
~
0.4 0.6 0.8 0.2 FILM THICKNESS (Fro)
~ 1.0
Fig. 6. The maximum strains which were observed at h = 0.1 ~tm for Pb(A) (O), Pb(C) (V), Au/Pb (±) and Pd/Pb ([]) films with various grain sizes g: - - , e 1ma,. Fig. 7. The strain ratios ct plotted on a film thickness v s . grain size map: e, Pb(A); O, Pb(B); C], Pb(C); A, Au/Pb(A); ~, Au/Pb(B); O, Pb/Au/Pb.
4.4. Role of intermetallic compounds It is evident in Figs. 3 and 4 that gold- or palladium-seeded lead films support larger strains than the Pb(A) films do when h > 0.2 jam. In lead-rich Pb-Au alloys intermetallic compounds of PbaAu are found to be formed at room temperature by X-ray diffraction. Also, as in Fig. 2, the average grain sizes were smaller in the seeded films than in the Pb(A) films. The strain increase observed in the seeded films could be due to finer grains or to intermetallic compounds. These two possibilities could be differentiated by comparing the strains and average grain sizes in the Au/Pb and Pb/Au/Pb films with h = 0.4 jam. The average grain size (Fig. 2) and the strain valu e (Fig. 4) in the Pb/Au/Pb film were observed to be very close to those of the Pb(A) film (h = 0.4 jam). The g value of the Au/Pb film was observed to be about 2.5 times smaller than that of the Pb(A) film and the ~33' value of the Au/Pb film was found to be about three times larger than that of the Pb(A) film. The PbaAu compounds were observed to be distributed uniformly in both the Pb/Au/Pb and the Au/Pb films 21. Thus it may be concluded that g is more
THERMAL STRAIN IN THIN
Pb
FILMS. III
115
important than the intermetallic compounds are in determining the strain levels at 4.2 K. 5. SUMMARIZING REMARKS
The dependences of the thermal strain e33' introduced by the thermal mismatch between film and substrate on film thickness h and on grain size g were studied for lead films with various g and/or h values. The films were prepared by deposition at room temperature or low temperature, by sputter etch thinning after the depositions or by seeding small amounts of gold or palladium layers before the lead depositions. The e33' measurements were carried out by an X-ray diffraction technique for the films which were cooled from 300 to 4.2 K. The experimental results are summarized as follows. (1) In films with h ~ g, the ~33' level was determined by h. The resolved shear stress a 31" for dislocation slip which was calculated from the measured e33' value can be expressed by a31" = ao" + ~/h The magnitude of c~was found to be about four times larger than the product of/zb (where/z is the shear modulus at 4.2 K and b is the Burgers vector). This result suggests that the dislocation pinning distance could be about four times smaller than h if dislocation glide was the dominant strain relaxation mechanism. The critical film thickness hc was determined to be 0.15 pm (he was defined so that for h < hc the strain in the films support the maximum strain, independent of the grain sizes). (2) In films with h > g/5, the critical grain size g¢ was determined to be about 1 gm where g~ was defined so that for g < g¢ the films support the maximum strain, independent of h. However, the e33' levels in the films with g < g~ did not reach the calculated maximum value. We proposed that the difference in the e33' values is due to an absorption of the strain at grain boundaries. (3) Because g~ > hc it is indicated that a reduction in average grain size rather than in film thickness is more effective in inhibiting the strain relaxation at 4.2 K. (4) The strain levels were not influenced by the existence of intermetallic compounds of Pb3Au or Pb2Pd in lead alloy films. (5) Fine-grained lead films prepared by deposition at 77 K or by seeding a thin gold or a thin palladium layer before lead deposition exhibited significantly less strain relaxation during cooling to 4.2 K. ACKNOWLEDGMENTS
The author would like to express his gratitude to C. J. Kircher, P. Chaudhari and K. N. Tu for stimulating discussions, to A. Segmuller for assistance with X-ray diffraction technique, to V. Tom for sample preparation and to the late J. W. Matthews, A. L. Ginzburg and C. M. Serrano for grain size measurements. REFERENCES 1
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