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Evaluation of the mechanical properties of thin metal films
Surface and Coatings Technology 116–119 (1999) 128–132 www.elsevier.nl/locate/surfcoat
Evaluation of the mechanical properties of thin metal films Dejun Ma a, *, Kewei Xu a, Jiawen He a, Jian Lu b a State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China b Universite de Technologie de Troyes, BP 2060-10010, Troyes Cedex, France
Abstract The nano-indentation method has been developed to evaluate the mechanical properties of metal films. In this study an indentation loading curve is employed to determine the yield strength and hardening index of an Al film on a Si substrate. The result is compared with that measured by a uniaxial tensile test with an Al film deposited on an Al foil. The yield strength of the Al film can be determined according to the testing results of this compound material and it agrees reasonably with that evaluated by the nano-indentation method. In addition, X-ray diffraction measurements of the four point bending specimen is used to measure the stress–strain curve of Cu films on steel substrate. The samples are prepared by ion beam enhanced deposition and magnetron-sputtering deposition. The results show that the strength of Cu film depends on the deposition technology and is much higher than that of the bulk material. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Hardening index; Metal films; Nano-indentation; X-ray diffraction; Yield strength
1. Introduction Aluminum, copper and their alloy films have been widely used in integrated circuits, and their mechanical properties are important in the design. Their service properties such as thermal fatigue strength and stress relaxation are closely related to their fundamental mechanical parameters. According to Blech [1] and Arzt and Nix [2], the mechanical strengths of metal films can play an important role in the failure of the interconnect lines. It is crucial to determine its mechanical properties. Several methods have been used for this purpose. Reed and Dally [3] used the uniaxial tensile testing method for free standing films. The films should be removed from the substrate prior to testing. In this case the effect of the substrate is not included and the removed films are vulnerable, thus the tested mechanical properties may differ from those of the attached films. Using the difference in the thermal expansion coefficients between film and substrate, Shute and Cohen [4] used the X-ray diffraction method to examine the yield strength of Al films through cooling. Bader et al. [5] used the curvature technique to study the mechanical * Corresponding author. E-mail address: [email protected] (D. Ma)
properties of Al films by heating the samples. However, when a thermal effect is involved, annealing and re-crystallization may take place. This will significantly influence the mechanical parameters. In recent years, the nano-indentation technique has been used to determine the hardness and Young’s modulus of thin films, but little work has been conducted on the evaluation of its yield strength and hardening index. In this paper, the nano-indentation method is used to determine the yield strength and hardening indices of Al films on Si substrate. The X-ray diffraction method with four-point bending loading is used to measure the stress–strain curves of Cu films on a steel substrate.
2. The mechanical property measurement model using the nano-indentation method 2.1. Basic equations The finite element method for large scale elastoplastic strain was employed to simulate the indentation test of thin metal films on ceramic substrates using a rigid Berkovich indentor. A power law function is used to fit the load–displacement curve as follows: P=P
0257-8972/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S0 2 5 7- 8 9 7 2 ( 9 9 ) 0 0 21 8 - 2
A B h
max h max
x
,
(1)
129
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
Fig. 1. Sketch of the blunting Berkovich indentor. Table 1 Blunting ratio r and fitting exponent x for bulk material b b 0 2.0
r b x b
0.02 1.93
0.06 1.83
0.10 1.74
film/substrate, the fitting exponent and the maximum load from the indentation loading curve as follows:
0.15 1.65
0.20 1.57
Table 2 Coefficients x (i=0, 1, 2) with r i b x i
r =0 b
r =0.02 b
r =0.06 b
r =0.10 b
r =0.15 b
r =0.20 b
x 0 x 1 x 2
2.03 1.47 −1.33
2.00 1.40 −1.33
1.88 1.37 −1.18
1.80 1.27 −0.89
1.72 1.20 −0.89
1.65 1.13 −0.89
0 0.15 0.3
P
max
=
A B t
t
f
f0
2
(2)
A B
s i 2 2 k (r , n ) ∑ ∑ P (E , E )nj fs , p b f ij f s f s i=0 j=0 0 (3)
Table 3 Coefficients k (r , n ) with r and n p b f b f n f
2 x= ∑ x (r , E )ni i b s f i=0
k (r , n ) p b f r =0 b
r =0.02 b
r =0.06 b
r =0.10 b
r =0.15 b
r =0.20 b
1 1 1
1.04 1.05 1.05
1.11 1.14 1.15
1.21 1.24 1.26
1.32 1.38 1.40
1.47 1.53 1.57
where P and h are the maximum indentation load max max and depth, respectively. x is the fitting exponent. For bulk materials with no limitation of indentation depth, h can be selected arbitrarily and x is expressed in max x . For the film–substrate system, h is selected to be b max equal to half of the film thickness t , and the P is the f max value corresponding to h =t /2. max f Blunting of the indentor tip is inevitable, and should be corrected. A simple way of describing the bluntness is shown in Fig. 1, Dh is defined as the bluntness value, and r =Dh/h is defined as the relative blunting ratio. b max By FEM simulation, r of the Berkovich indentor can b be determined from the fitting exponent x of the bulk b material [6 ]. The relation between r and x is given b b in Table 1. Eqs. (2) and (3) have been developed to establish the relation among the mechanical properties of
where, s is the yield strength of the film, n and t are fs f f the hardening index and the thickness of the film, respectively, E and E are the elastic moduli of the film f s and the substrate, respectively; t =1 mm and f0 s =100 MPa are presumed to be constants; and x , P 0 i ij and k are coefficients, and for Al films on Si substrates p their values are given in Table 2. Thus the hardening index n and the yield strength f s of the film can be derived through the fitting exponent fs x and the maximum load P from the indentation max loading curve for a film/substrate combination system, that is: n= f
앀x2 +4x (x−x )−x 1 2 0 1 2x 2
s =s fs 0
(4)
앀s2 +4s {P /[k (t /t )2]−s }−s 1 2 max p f f0 0 1, 2s 2
(5)
where: 2 s = ∑ P nj , i=0, 1, 2. i ij f j=0 2.2. The nano-indentation test The nano-indentation loading curves for the Al films with the three thicknesses of 1.0, 2.0 and 4.0 mm on the Si substrate are similar, and the 4.0 mm one is shown in
Table 4. Coefficients P (i, j=0, 1, 2) ij P (mN ) 22
P (mN ) 21
P (mN ) 20
P (mN ) 12
P (mN ) 11
P (mN ) 10
P (mN ) 02
P (mN ) 01
P (mN ) 00
−2.349
−0.327
−0.049
8.958
7.449
2.531
43.34
−1.341
0.456
130
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
Fig. 2. Nano-indentation loading curves for Al films on the Si substrate.
Fig. 2. The maximum indentation depth for the 4.0 mm film is kept at one-tenth of the film thickness, thus this curve can be taken as the load–displacement relation of the bulk Al material free of substrate effect. The relative blunting ratio r of the indentor can be determined from b this curve. By fitting the curve, an exponent of x =1.571 is obtained. From Table 1 r =0.198 and Dh= b b 79.2 nm are achieved. The correlation coefficient of the curve fit in this study is better than 0.98. For the other three curves with h =t /2, the fitting max f exponent x, the relative blunting ratio r , and the b maximum load P can also be obtained. Using these max values in Tables 2–4, and Eqs. (4) and (5), the hardening indices and yield strengths of the Al films with three thicknesses can be determined, as shown in Table 5. In order to calibrate the nano-indentation results, the stress–strain curve of an uniaxial tensile test was performed. Films 4.0 mm thick were deposited on two sides of a 70 mm thick Al foil to form a compound. The yield strength and hardening index of the Al film can be evaluated from the compound stress–strain curve. Curve 1 in Fig. 3 is just from Al foil, curve 2 is from the compound film and curve 3 is derived from curves 1 and 2 gives the stress–strain curve of the pure Al film. Curve 4 is achieved by nano-indentation. The difference in curves 3 and 4 may be due to the following reasons: 1. the friction force between the indentor and the film is neglected; and 2. the Al film on the Al foil was prepared by evaporation in the vacuum. For 4 mm film deposition, it took >2 h, even the foil was attached with a cooling stage, its temperature might be increased and would result in the recovering or even Table 5 s and n for 1.0, 2.0 and 4.0 mm Al films fs f t (mm) f
x
r b
P
(mN ) max
1.0 2.0 4.0
1.800 1.955 2.070
0.1584 0.0792 0.0396
8.583 26.77 89.56
n f
s (MPa) fs
0.0826 0.0925 0.1030
183.70 158.84 133.62
Fig. 3. The uniaxial tensile stress–strain curves.
annealing of the film. If we notice that the difference of curves 3 and 4 is only slight, but both of them are much higher than the curve of the Al foil, it can be seen that mechanical property measurement of a metal film on the ceramic substrate can be done by nano-indentation testing.
3. X-ray diffraction measurement 3.1. Fundamental procedures By X-ray stress analysis the internal stress calculation formula for the y-goniometer method can be described as: p ∂(2h ) −E y , ctgh sec2(90°−h°) s = 0 w 2(1+n) 180 ∂(sin2 y)
(6)
where 2h is the stress free diffraction angle, y is the tilt 0 angle. For Fe Ka and Cu (311), 2h equals 125.4°. The 0 elastic constants for bulk copper E=119 GPa and n= 0.33 were used to calculate the stress. The strain values in four-point bending loading were measured by a strain gauge on the steel substrate side. The error bar of this testing method is ca 20 MPa. The experiment was detailed in Ref. [7]. 3.2. Experimental results Two different deposition technologies, IBED (ion beam enhanced deposition) and MSD (magnetron sputtering deposition) were employed to deposit the Cu films. Fig. 4 shows the stress–strain curves of Cu films with three different thicknesses (0.5, 1.0 and 1.5 mm) prepared by IBED. From these curves, the yield strengths and the hardening indices of the Cu films can be determined, their yield strengths s are the same as fs
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
131
Fig. 5. Stress–strain curves measured by XRD for MSD Cu films.
4. Conclusions
Fig. 4. Stress–strain curves measured by XRD for IBED Cu films.
for magnitude of ca 450 MPa, and the hardening indices n are also nearly the same as 0.4. They are independent f on the film thickness. Fig. 5 shows the stress–strain curves of Cu films with two different thicknesses (1.5 and 2.5 mm) prepared by MSD, their yield strengths are nearly equal to 280 MPa, but the hardening indices are different. For the 1.5 mm film, n =0.5 and for the 2.5 mm f film, n =0.44. f The results above indicate that the strength levels of the Cu films are strongly dependent on the deposition technology of the film. Yet the dependence of the film thickness with yield strength is different for different processes. It can also be seen that the measured strengths for Cu films are all higher than that of the bulk material.
Two different methods were used to determine the mechanical properties of thin metal films. The yield strength of the Al film measured by the nano-indentation method are in fairly good agreement with that measured by the conventional tensile test. The yield strengths of the Cu films measured by X-ray diffraction show that the strengths of the films are much higher than those of the bulk material, and they are strongly dependent on the deposition technology of the films.
Acknowledgements The authors are grateful to the China Natural Science Foundation for the support provided by Grants Nos 59571031 and 59731020 and the Sino–French collaboration project.
References [1] A.I. Blech, Electromigration in thin aluminum films on titanium nitride, J. Appl. Phys. 47 (4) (1976) 1203.
132
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
[2] E. Arzt, W.D. Nix, A model for the effect of line width and mechanical strength on electromigration failure of interconnects with ‘‘near-bamboo’’ grain structures, J. Mater. Res. 6 (4) (1991) 731. [3] D.T. Read, J.W. Dally, A new method for measuring the strength and ductility of thin films, J. Mater. Res. 8 (7) (1993) 1542. [4] C.J. Shute, J.B. Cohen, Determination of yielding and debonding in Al–Cu thin films from residual stress measurements via diffraction, J. Mater. Res. 6 (5) (1991) 950.
[5] S. Bader, E.M. Dalaugher, E. Arzt, Comparison of mechanical properties and microstructure of Al (1 wt.%Si) and Al (1 wt.%Si, 0.5 wt.%Cu), Thin Solid Films 263 (2) (1995) 175. [6 ] Y.T. Cheng, C.M. Cheng, Scaling approach to conical indentation in elastic–plastic solids with work hardening, J. Appl. Phys. 84 (3) (1998) 1284–1291. [7] J. He, H. Wang, J. Nan, Fatigue strength evaluation from surface yielding data, Fatigue Fract. Eng. Struct. 16 (6) (1993) 591.
Evaluation of the mechanical properties of thin metal films Dejun Ma a, *, Kewei Xu a, Jiawen He a, Jian Lu b a State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China b Universite de Technologie de Troyes, BP 2060-10010, Troyes Cedex, France
Abstract The nano-indentation method has been developed to evaluate the mechanical properties of metal films. In this study an indentation loading curve is employed to determine the yield strength and hardening index of an Al film on a Si substrate. The result is compared with that measured by a uniaxial tensile test with an Al film deposited on an Al foil. The yield strength of the Al film can be determined according to the testing results of this compound material and it agrees reasonably with that evaluated by the nano-indentation method. In addition, X-ray diffraction measurements of the four point bending specimen is used to measure the stress–strain curve of Cu films on steel substrate. The samples are prepared by ion beam enhanced deposition and magnetron-sputtering deposition. The results show that the strength of Cu film depends on the deposition technology and is much higher than that of the bulk material. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Hardening index; Metal films; Nano-indentation; X-ray diffraction; Yield strength
1. Introduction Aluminum, copper and their alloy films have been widely used in integrated circuits, and their mechanical properties are important in the design. Their service properties such as thermal fatigue strength and stress relaxation are closely related to their fundamental mechanical parameters. According to Blech [1] and Arzt and Nix [2], the mechanical strengths of metal films can play an important role in the failure of the interconnect lines. It is crucial to determine its mechanical properties. Several methods have been used for this purpose. Reed and Dally [3] used the uniaxial tensile testing method for free standing films. The films should be removed from the substrate prior to testing. In this case the effect of the substrate is not included and the removed films are vulnerable, thus the tested mechanical properties may differ from those of the attached films. Using the difference in the thermal expansion coefficients between film and substrate, Shute and Cohen [4] used the X-ray diffraction method to examine the yield strength of Al films through cooling. Bader et al. [5] used the curvature technique to study the mechanical * Corresponding author. E-mail address: [email protected] (D. Ma)
properties of Al films by heating the samples. However, when a thermal effect is involved, annealing and re-crystallization may take place. This will significantly influence the mechanical parameters. In recent years, the nano-indentation technique has been used to determine the hardness and Young’s modulus of thin films, but little work has been conducted on the evaluation of its yield strength and hardening index. In this paper, the nano-indentation method is used to determine the yield strength and hardening indices of Al films on Si substrate. The X-ray diffraction method with four-point bending loading is used to measure the stress–strain curves of Cu films on a steel substrate.
2. The mechanical property measurement model using the nano-indentation method 2.1. Basic equations The finite element method for large scale elastoplastic strain was employed to simulate the indentation test of thin metal films on ceramic substrates using a rigid Berkovich indentor. A power law function is used to fit the load–displacement curve as follows: P=P
0257-8972/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S0 2 5 7- 8 9 7 2 ( 9 9 ) 0 0 21 8 - 2
A B h
max h max
x
,
(1)
129
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
Fig. 1. Sketch of the blunting Berkovich indentor. Table 1 Blunting ratio r and fitting exponent x for bulk material b b 0 2.0
r b x b
0.02 1.93
0.06 1.83
0.10 1.74
film/substrate, the fitting exponent and the maximum load from the indentation loading curve as follows:
0.15 1.65
0.20 1.57
Table 2 Coefficients x (i=0, 1, 2) with r i b x i
r =0 b
r =0.02 b
r =0.06 b
r =0.10 b
r =0.15 b
r =0.20 b
x 0 x 1 x 2
2.03 1.47 −1.33
2.00 1.40 −1.33
1.88 1.37 −1.18
1.80 1.27 −0.89
1.72 1.20 −0.89
1.65 1.13 −0.89
0 0.15 0.3
P
max
=
A B t
t
f
f0
2
(2)
A B
s i 2 2 k (r , n ) ∑ ∑ P (E , E )nj fs , p b f ij f s f s i=0 j=0 0 (3)
Table 3 Coefficients k (r , n ) with r and n p b f b f n f
2 x= ∑ x (r , E )ni i b s f i=0
k (r , n ) p b f r =0 b
r =0.02 b
r =0.06 b
r =0.10 b
r =0.15 b
r =0.20 b
1 1 1
1.04 1.05 1.05
1.11 1.14 1.15
1.21 1.24 1.26
1.32 1.38 1.40
1.47 1.53 1.57
where P and h are the maximum indentation load max max and depth, respectively. x is the fitting exponent. For bulk materials with no limitation of indentation depth, h can be selected arbitrarily and x is expressed in max x . For the film–substrate system, h is selected to be b max equal to half of the film thickness t , and the P is the f max value corresponding to h =t /2. max f Blunting of the indentor tip is inevitable, and should be corrected. A simple way of describing the bluntness is shown in Fig. 1, Dh is defined as the bluntness value, and r =Dh/h is defined as the relative blunting ratio. b max By FEM simulation, r of the Berkovich indentor can b be determined from the fitting exponent x of the bulk b material [6 ]. The relation between r and x is given b b in Table 1. Eqs. (2) and (3) have been developed to establish the relation among the mechanical properties of
where, s is the yield strength of the film, n and t are fs f f the hardening index and the thickness of the film, respectively, E and E are the elastic moduli of the film f s and the substrate, respectively; t =1 mm and f0 s =100 MPa are presumed to be constants; and x , P 0 i ij and k are coefficients, and for Al films on Si substrates p their values are given in Table 2. Thus the hardening index n and the yield strength f s of the film can be derived through the fitting exponent fs x and the maximum load P from the indentation max loading curve for a film/substrate combination system, that is: n= f
앀x2 +4x (x−x )−x 1 2 0 1 2x 2
s =s fs 0
(4)
앀s2 +4s {P /[k (t /t )2]−s }−s 1 2 max p f f0 0 1, 2s 2
(5)
where: 2 s = ∑ P nj , i=0, 1, 2. i ij f j=0 2.2. The nano-indentation test The nano-indentation loading curves for the Al films with the three thicknesses of 1.0, 2.0 and 4.0 mm on the Si substrate are similar, and the 4.0 mm one is shown in
Table 4. Coefficients P (i, j=0, 1, 2) ij P (mN ) 22
P (mN ) 21
P (mN ) 20
P (mN ) 12
P (mN ) 11
P (mN ) 10
P (mN ) 02
P (mN ) 01
P (mN ) 00
−2.349
−0.327
−0.049
8.958
7.449
2.531
43.34
−1.341
0.456
130
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
Fig. 2. Nano-indentation loading curves for Al films on the Si substrate.
Fig. 2. The maximum indentation depth for the 4.0 mm film is kept at one-tenth of the film thickness, thus this curve can be taken as the load–displacement relation of the bulk Al material free of substrate effect. The relative blunting ratio r of the indentor can be determined from b this curve. By fitting the curve, an exponent of x =1.571 is obtained. From Table 1 r =0.198 and Dh= b b 79.2 nm are achieved. The correlation coefficient of the curve fit in this study is better than 0.98. For the other three curves with h =t /2, the fitting max f exponent x, the relative blunting ratio r , and the b maximum load P can also be obtained. Using these max values in Tables 2–4, and Eqs. (4) and (5), the hardening indices and yield strengths of the Al films with three thicknesses can be determined, as shown in Table 5. In order to calibrate the nano-indentation results, the stress–strain curve of an uniaxial tensile test was performed. Films 4.0 mm thick were deposited on two sides of a 70 mm thick Al foil to form a compound. The yield strength and hardening index of the Al film can be evaluated from the compound stress–strain curve. Curve 1 in Fig. 3 is just from Al foil, curve 2 is from the compound film and curve 3 is derived from curves 1 and 2 gives the stress–strain curve of the pure Al film. Curve 4 is achieved by nano-indentation. The difference in curves 3 and 4 may be due to the following reasons: 1. the friction force between the indentor and the film is neglected; and 2. the Al film on the Al foil was prepared by evaporation in the vacuum. For 4 mm film deposition, it took >2 h, even the foil was attached with a cooling stage, its temperature might be increased and would result in the recovering or even Table 5 s and n for 1.0, 2.0 and 4.0 mm Al films fs f t (mm) f
x
r b
P
(mN ) max
1.0 2.0 4.0
1.800 1.955 2.070
0.1584 0.0792 0.0396
8.583 26.77 89.56
n f
s (MPa) fs
0.0826 0.0925 0.1030
183.70 158.84 133.62
Fig. 3. The uniaxial tensile stress–strain curves.
annealing of the film. If we notice that the difference of curves 3 and 4 is only slight, but both of them are much higher than the curve of the Al foil, it can be seen that mechanical property measurement of a metal film on the ceramic substrate can be done by nano-indentation testing.
3. X-ray diffraction measurement 3.1. Fundamental procedures By X-ray stress analysis the internal stress calculation formula for the y-goniometer method can be described as: p ∂(2h ) −E y , ctgh sec2(90°−h°) s = 0 w 2(1+n) 180 ∂(sin2 y)
(6)
where 2h is the stress free diffraction angle, y is the tilt 0 angle. For Fe Ka and Cu (311), 2h equals 125.4°. The 0 elastic constants for bulk copper E=119 GPa and n= 0.33 were used to calculate the stress. The strain values in four-point bending loading were measured by a strain gauge on the steel substrate side. The error bar of this testing method is ca 20 MPa. The experiment was detailed in Ref. [7]. 3.2. Experimental results Two different deposition technologies, IBED (ion beam enhanced deposition) and MSD (magnetron sputtering deposition) were employed to deposit the Cu films. Fig. 4 shows the stress–strain curves of Cu films with three different thicknesses (0.5, 1.0 and 1.5 mm) prepared by IBED. From these curves, the yield strengths and the hardening indices of the Cu films can be determined, their yield strengths s are the same as fs
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
131
Fig. 5. Stress–strain curves measured by XRD for MSD Cu films.
4. Conclusions
Fig. 4. Stress–strain curves measured by XRD for IBED Cu films.
for magnitude of ca 450 MPa, and the hardening indices n are also nearly the same as 0.4. They are independent f on the film thickness. Fig. 5 shows the stress–strain curves of Cu films with two different thicknesses (1.5 and 2.5 mm) prepared by MSD, their yield strengths are nearly equal to 280 MPa, but the hardening indices are different. For the 1.5 mm film, n =0.5 and for the 2.5 mm f film, n =0.44. f The results above indicate that the strength levels of the Cu films are strongly dependent on the deposition technology of the film. Yet the dependence of the film thickness with yield strength is different for different processes. It can also be seen that the measured strengths for Cu films are all higher than that of the bulk material.
Two different methods were used to determine the mechanical properties of thin metal films. The yield strength of the Al film measured by the nano-indentation method are in fairly good agreement with that measured by the conventional tensile test. The yield strengths of the Cu films measured by X-ray diffraction show that the strengths of the films are much higher than those of the bulk material, and they are strongly dependent on the deposition technology of the films.
Acknowledgements The authors are grateful to the China Natural Science Foundation for the support provided by Grants Nos 59571031 and 59731020 and the Sino–French collaboration project.
References [1] A.I. Blech, Electromigration in thin aluminum films on titanium nitride, J. Appl. Phys. 47 (4) (1976) 1203.
132
D. Ma et al. / Surface and Coatings Technology 116–119 (1999) 128–132
[2] E. Arzt, W.D. Nix, A model for the effect of line width and mechanical strength on electromigration failure of interconnects with ‘‘near-bamboo’’ grain structures, J. Mater. Res. 6 (4) (1991) 731. [3] D.T. Read, J.W. Dally, A new method for measuring the strength and ductility of thin films, J. Mater. Res. 8 (7) (1993) 1542. [4] C.J. Shute, J.B. Cohen, Determination of yielding and debonding in Al–Cu thin films from residual stress measurements via diffraction, J. Mater. Res. 6 (5) (1991) 950.
[5] S. Bader, E.M. Dalaugher, E. Arzt, Comparison of mechanical properties and microstructure of Al (1 wt.%Si) and Al (1 wt.%Si, 0.5 wt.%Cu), Thin Solid Films 263 (2) (1995) 175. [6 ] Y.T. Cheng, C.M. Cheng, Scaling approach to conical indentation in elastic–plastic solids with work hardening, J. Appl. Phys. 84 (3) (1998) 1284–1291. [7] J. He, H. Wang, J. Nan, Fatigue strength evaluation from surface yielding data, Fatigue Fract. Eng. Struct. 16 (6) (1993) 591.