Investigation of the elastic modulus of thin films using simple biaxial bending techniques

Thin Solid Films 308–309 (1997) 304–309

Investigation of the elastic modulus of thin films using simple biaxial bending techniques ˚ .K. Ja¨mting a ,*, J.M. Bell a, M.V. Swain b, N. Schwarzer c A a

Queensland University of Technology, Department of Mechanical, Manufacturing and Medical Engineering, Brisbane, Australia b CSIRO; Division of Telecommunications and Industrial Physics, Lindfield, Australia c Institute of Physics, Technische Universita¨t, Chemnitz-Zwickau, Germany

Abstract The increasing use of thin films in numerous applications has raised the interest in the mechanical behavior of thin films; particularly the hardness and the elastic modulus of these films. The aim of the present study is to evaluate a simple biaxial bending technique to measure the elastic modulus of films with thicknesses ranging from 0.1 to 2 mm. In this range, it can be difficult to use simple indentation techniques owing to the influence of the substrate, and in order to determine the performance of these systems it is often essential to be able to determine the elastic modulus unambiguously. Tests have been carried out on glass substrates, and magnetron sputtered metal films (copper and aluminium) have been deposited on glass discs to evaluate the film properties. The samples were loaded in biaxial flexure using a point load on the disc supported by three point supports. The bending apparatus uses a commercially available micromechanical probe (UMIS 2000) that enables the measurement of very low loads and small displacements. Comparison is made between the force-displacement response of the disc with and without the sputtered film. Analysis of the bending response gave values of the elastic modulus for the glass discs of E = 54.7 ± 0.4 GPa, while E = 116 ± 8 GPa for the copper films and E = 84 ± 5 GPa for the aluminium films.  1997 Elsevier Science S.A. Keywords: Elastic modulus; Biaxial bending; Thin films; Magnetron sputtering

1. Introduction In recent years, the market for high performance thin film materials has increased enormously. Performance demands have also increased, and so has the necessity to establish different properties of thin films, including the hardness and the elastic modulus of thin films. The latter is commonly used in other investigations, such as determination of the stresses in the films [1,2]. During the last few years the development of highly sensitive microindentation techniques [3] has enabled the monitoring of the response of very thin films during nano-scale indentation. Using diamond tipped indenters of various shapes, both these properties can be determined [4]. The elastic response of different coatings during indentation has been presented in several recent reports [5,6]. Recently Field et al. [7] have developed a model to establish the elastic modulus of thin films and near surface materials using spherical indenters. Spherical * Corresponding author. Tel: +61 2 9413 7379; fax: +61 2 9413 7161; e-mail: [email protected]

0040-6090/97/$17.00  1997 Elsevier Science S.A. All rights reserved PII S0040-6090 (97 )0 0559-2

indenters also enables the transition from elastic to plastic penetration to be studied. Mencı´k et al. [8] have further evaluated different approaches for estimating the modulus of thin films from indentation data. Indentation techniques have proved to be quite successful, but for very thin films there are limitations in the accuracy due to limited film thickness. Different criteria are used to decide when the influence of the substrate material affects the measured properties. These vary between a depth of penetration from 25% [9] of the overall thickness to as little as 10% [10]. When indenting films less than a few hundred nanometers thick, this constraint can severely limit the range of experimental parameters. This difficulty prompted our interest in different methods for the determination of the elastic modulus of thin films. Methods which have been proposed include bending tests [11,12], X-ray methods [13,14] and surface acoustic waves [15–17]. Recent work by Rouzaud et al. [18] describes measurement of the elastic modulus using a three-point bending apparatus and very low loads, and Mencı´k et al. [19] incorporates results from a cantilever beam bending

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arrangement applied to coated systems. These approaches have problems with biaxial curvature of thin beams resulting from residual stresses and the difficulty of uniform loading of these beams at the contact points. We present a novel approach to the more common threepoint bending technique which overcomes some of the problems associated with the bending of thin coated systems. The set-up used for these experiments is based on a simply supported circular plate in biaxial bending. The theory is based on Timoshenko’s [20,21] equations. The maximum deflection, d, of a simply supported disc can be expressed as: d=

Fa2 ⋅y 16pD

(1)

where F is the applied force, a is the radial distance from point of loading to the supporting balls and y=

3+n 1+n

(2)

where u is Poisson’s ratio. The flexural rigidity D for a homogeneous disc is given by: D=

Et3 12(1 − n2 )

(3)

where E is the elastic modulus and t is the thickness of the disc. The deflection of the disc is directly related to the elastic modulus and the thickness of the disc. To compensate for the difference in flexural rigidity caused by the influence of the thin film, the following integral must be solved [21]: … …ts + tf †=2 E(z) 2 z dz (4) D= 2 …t2 − tf †=2 1 − n(z) For a substrate with a single layer we obtain:  1 E {(ts + tf )3 + (ts − tf )3 } s 2 D= 24 1 − ns + {(ts + tf )3 − (ts − tf )3 }

(5)

Ef Š 1 − n2f

where subscripts s and f denote the substrate and the film, respectively. For cases where the film is much thinner than the substrate, the influence of u is not significant since the differences are usually small and therefore the approximation of Eq. (2) using the Poisson’s ratio for the substrate has been used in the present study. This gives the final expression for the deflection of a coated substrate. The effect of this assumption is discussed further in Section 4. By monitoring the force and deflection before and after coating, the difference in bending response should give a clear indication of the elastic modulus of the film. To evaluate this particular method, magnetron sputtered metal films were deposited on glass substrates. These thin, ductile films were likely to withstand the bending moment without cracking, which would create complications in the analysis.

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2. Experimental The precise measurements of the force and deflection during the biaxial loading of the discs are achieved using a UMIS 2000, a commercially available micromechanical probe [22], where the force is applied and recorded stepwise and the deflection of the disc is measured for each step of the applied force. The loading cycle was divided into 20 steps which enables a close monitoring of the bending response of the tested discs. The test set-up is schematically described in Fig. 1. The force is applied using a blunt indenter (a ruby ball, diameter = 500 mm) on a brass shaft. The supporting balls were 4.04-mm diameter steel ball bearings. The loads used were 5, 10 and 15 mN, giving deflections up to approximately 2300 nm for the thinnest discs. To ensure statistical reliability, each disc was tested three times, with a rotation of 120° between measurements. The difference in deflection between positions are small (,0.1% for the uncoated discs and about 0.6% for the coated ones). Each load cycle was repeated five times and the values were then averaged for the analysis. The substrates used were glass cover slips, 15 mm in diameter and with a thickness of 151–155 mm. Thickness measurements were carried out using a Tesa Module Gauge Block comparator. The results from these measurements are shown in the graph in Fig. 3. Two different metal films, copper and aluminium, were deposited on the glass discs using magnetron sputtering. These metals were chosen to provide values of elastic modulus that differed significantly. The deposition system used a 90-mm diameter target with a substrate-target distance of 60 mm. The argon pressure during deposition was 0.2 Pa, and a DC power of 80 W and a bias voltage of 350–370 V. The deposition rates were 105 nm/min for copper and 64 nm/min for aluminium. The values found in the literature for the elastic modulus of bulk material of copper and aluminium are 71 GPa and 130 GPa [23], respectively. These are also relatively ductile materials, so that problems of cracking and delamination should be eliminated. The film thickness was measured using a Dektak surface profilometer and later confirmed using atomic force micro-

Fig. 1. A schematic picture of the set-up configuration.

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• •

Table 1 Results from the film thickness measurements Aluminium films (mm) Disc A1, disc B1 and disc C1 Disc B2, disc C2 and disc C4 Disc A3, disc B3 and disc C3 Disc A4, disc B4 and disc B5

l = 0.345

Copper films (mm)

1.59 ± 0.01

3. Results

0.76 ± 0.01 0.81 ± 0.02 0.45 ± 0.02

scopy (AFM). The results from these measurements are presented in Table 1. Four samples were coated during each coating run. Three of these samples were used for the bending tests, while the fourth sample was a sacrificial one to be used for thickness measurements. To estimate the density of the films, the weight of the discs to be coated with aluminium were measured before and after coating using a set of scales with 1 mg resolution (Sartorius). The density of the glass was found to be 2.492 ± 0.004 g/cm3. The results for the Al-coated samples are presented in Table 2 and the very small differences between films also justified the assumption of equal thickness. The samples were also studied after deposition using AFM. The AFM scans revealed that the copper films were very smooth, with 100-mm line scans giving an average surface roughness of R a = 8 nm. The microstructure showed an average grain size of about 120 nm. The aluminium films were even smoother with an average roughness of R a = 4 nm, but with an average grain size of 300 nm. In Fig. 2, a 5mm scan of the 0.76-mm thick aluminium film shows the smooth and even surface, with the grain structure clearly showing. After film deposition the samples were again inserted into the test set-up and tested under the same conditions as the uncoated discs. For the theoretical analysis, the following material constant values were assumed: •

Poisson’s ratio for the copper film [23], uCu = 0.343 Poisson’s ratio for the aluminium film [23], \ DuA-

Poisson’s ratio for the substrate [24], us = 0.21

The bending response of the glass discs was very consistent. A large number of glass discs were tested and the measured force and deflection data were very consistent. Substituting the data into Eq. (1) using the constants above yields an elastic modulus of 54.7 ± 0.4 GPa. The scatter in the results is small, as can be seen in Fig. 3. For the bending tests six samples were coated with copper and six with aluminium. To study the influence of the film thickness, three samples were coated in the same batch and two different thicknesses were deposited for each material: approximately 1 and 0.5 mm copper films, and 2 and 1 mm aluminium films. The films turned were slightly thinner than expected with the measured thicknesses found in Table 1. The difference in bending response between the coated and uncoated samples was obvious, as can be seen in Fig. 4 which shows the results from the bending of an aluminium coated disc, with the three different loads superimposed, demonstrating the reproducibility of the response. This response was very typical, for both copper and aluminium and for all the different thicknesses. Altogether 6 discs were tested in this biaxial bending setup. As described earlier, different loads were applied and the discs were rotated between tests. The data from these tests were analysed using Eq. (5). The results from the bending tests for both the copper and aluminium coated samples are summarised in Table 3. Analysis of this data yielded a modulus for the films that was higher than for bulk aluminium (E = 71 GPa), as can be seen in Table 3.

4. Discussion The results from the bending tests on the glass substrates were very encouraging. The results were very reproducible (Fig. 2) and gave values of E-modulus that corresponds well with the literature [24].

Table 2 Mass and density measurements for the aluminium films Aluminium films Film thickness (mm) Disc Disc Disc Disc Disc Disc

B2 C2 C4 A3 B3 C3

0.76 0.76 0.76 1.59 1.59 1.59

± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.01

Mass of substrate (mg) 67.9665 66.9173 67.8983 66.8789 67.1576 67.8236

± ± ± ± ± ±

0.0012 0.0004 0.0017 0.0003 0.0018 0.0001

Mass substrate + coating (mg) 68.3418 67.2923 68.2632 67.6383 67.9110 68.5615

± ± ± ± ± ±

0.0003 1.42E-14 0.0001 0.0011 0.0013 0.0005

Mass of film (mg) 0.3753 0.3750 0.3649 0.7565 0.7534 0.7379

± ± ± ± ± ±

0.0003 0.0003 0.0003 0.0014 0.0031 0.0006

Density of film (g/cm3) 2.794 2.792 2.717 2.692 2.681 2.626

± ± ± ± ± ±

0.048 0.040 0.049 0.022 0.028 0.019

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Fig. 2. A 5-mm AFM scan of an 0.76-mm thick aluminium film. Note the vertical scale.

When analysing the force-deflection data using Eqs. (1)– (4), it is obvious that the calculated values of E-modulus are dependent on the thickness measurements of both substrate and film as well as material constants. A sensitivity analysis of the bending allowing for the variations in the substrate thickness (±1 SD) showed variations in the calculated value of Es of less than 2%. A similar analysis was made for the bending data of the substrate + film system and it was found that the influence of the thickness variation for the substrate gave rise to ,3% variations in the film modulus. Similarly, the uncertainty in the film thickness also resulted in a variation in the final film modulus of ,3%. Another factor that could influence the modelling was the values of the material constants used, in particular the Pois-

son’s ratio of the substrate material. A change of ±5% (±0.01) in the value of the Poisson’s ratio for the substrate leads to variations in the substrate modulus of about ±1% (±0.5 GPa). The effect of this variation on the Poisson’s ratio of the substrate on the film modulus gives a variation of ,0.7% in the elastic modulus of the film. The sensitivity of the results to the Poisson’s ratio is not seen as a problem with this method. The largest source of uncertainty in these experiments arises from the uncertainty in the force displacement data obtained from the bending tests. Small variations in the slope of the bending response curve are the dominant contribution to the relatively large uncertainties (of several tens of GPa - up to 20%) in the final film moduli, as can be seen

Fig. 3. The results from bending tests of the glass substrates (left axis) and their thickness variation (right axis).

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Fig. 4. The difference in bending response for an 0.81-mm thick aluminium film compared with the uncoated glass disc, with the three loads of 5, 10 and 15 mN superimposed. The reproducibility in response, independent of load, is clearly shown in the perfect superposition of the curves.

in Table 3. The UMIS 2000 used in this experiment is very sensitive, so the measurement itself is not seen as the most probable source of this uncertainty. We believe that the most likely source of this high sensitivity is the differences in stiffness caused by only slight variations in thickness (of either the substrate or, more likely, the film). It is also believed that the larger variation in uncertainty for the thinner films may be enhanced by the relative greater importance of a small thickness non-uniformity in the film when the film thickness is smaller. This could possibly be improved with a more controlled deposition and more carefully chosen substrates. When studying the results for copper in Table 3, it can be seen that apart from one set of values, the films modulus is approximately 116 GPa which is in agreement with the expected value considering that sputtered films are not expected to be fully dense. Weight measurements similar to those conducted with the aluminium samples will be performed to determine the porosity in these films. The results for the copper film could also be somewhat affected

by the adhesion of the films to the glass. We did not experience obvious peeling of the Cu-films during the bending tests but studies of the sacrificial discs indicated that the films have a tendency to delaminate when exposed to mechanical damage. The values of elastic modulus for aluminium in Table 3 are rather high for a pure aluminium film. These results, together with density measurements, suggest that these films may be slightly contaminated. The density of the thinner films is about 2.78 g/cm3 and for the thicker ones about 2.67 g/cm3 (Table 2) which is slightly higher than the density of pure aluminium (2.7 g/cm3). This behaviour is most likely to be caused by a thin surface layer of native oxide forming in the aluminium film. The tests with the thicker aluminium films gave some results that lacked the reproducibility of the previous ones, but this could possibly be explained by their appearance. AFM scans of the thicker films revealed that they were slightly rougher than the thinner ones (Ra = 17 nm) and showed a random formation of grains that were about 150 nm higher than the surrounding ones.

Table 3 The values of elastic modulus from the bending tests with the copper and aluminium films Elastic modulus for Cu-films (GPa) Disc Disc Disc Disc Disc Disc

A1 B1 C1 A4 B4 B5

117.2 116.4 114.1 111.1 116.5 120.8

± ± ± ± ± ±

1.2 3.1 9.1 30.5 3.2 2.0

Elastic modulus for Al-films (GPa) Disc Disc Disc Disc Disc Disc

B2 C2 C4 A3 B3 C3

88.4 84.9 89.4 83.2 75.6 62.4

± ± ± ± ± ±

8.6 7.0 4.4 4.6 2.9 2.7

5. Conclusions The biaxial flexure test set-up used was found to give very reproducible results. This technique seems to be less susceptible to distortion by biaxial curvature, caused by residual stress in the samples, than the more common three- and four-point bending set-ups. The results from the bending of the substrate gave very reproducible results with an elastic modulus of 54.7 ± 0.4 GPa. The results from the bending of the coated samples were also very consistent but

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the analysis revealed a rather large uncertainty in the individual results. The average values of elastic modulus for the magnetron sputtered copper films with their uncertainties were 116 ± 8 GPa and for the aluminium films 84 ± 5 GPa. A rather large scatter in the results was found but this could possibly be due to factors such as delamination of the films during bending, surface oxide layers and nonuniform thickness of the films. For future work, a wider range of films with a larger difference in both the thickness and in the values of elastic modulus between substrate and coating is planned.

Acknowledgements This project was sponsored by Sustainable Technologies Australia. The authors would like to thank Dr. Geoffrey Harding, who deposited the magnetron sputtered films, Frank Lesha, who performed the AFM analysis and Kitty Fen, who performed the weight measurements, all of the above at DTIP, CSIRO, Australia.

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