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Interface fracture properties of thin films studied by using the micro-cantilever deflection technique
Surface & Coatings Technology 204 (2009) 878–881
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Interface fracture properties of thin films studied by using the micro-cantilever deflection technique Kurt Matoy a,b,c,⁎, Thomas Detzel d, Matthias Müller d, Christian Motz b, Gerhard Dehm b,c a
Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, A-9524 Villach, Austria Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, A-8700 Leoben, Austria Department Materials Physics, University of Leoben, A-8700 Leoben, Austria d Infineon Technologies Austria AG, A-9500 Villach, Austria b c
a r t i c l e
i n f o
Available online 11 September 2009 Keywords: Interface toughness Micro-cantilever Ion beam processing
a b s t r a c t The mechanical behavior of interfaces between silicon oxide and metallic thin films is investigated using an alternative approach which is based on the miniaturized cantilever deflection technique (Weihs et al., 1988 [1]). The critical energy release rates for three different silicon oxide/metal systems are determined and the results are discussed in this paper. The technique suggested may be applicable with high spatial resolution for a wide variety of structured thin film systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In microelectronic devices the interfaces between thin film materials are common sources of mechanical failure. Their probability to fail can be estimated by finite element simulations if the interface properties are well known. Due to the small dimensions, measuring those quantities poses a challenge to the experimentalists, especially when the interface of interest is buried. The possibility to fabricate miniaturized fracture mechanic specimens of buried interfaces by using focused ion beam machining is demonstrated in this paper. The approach described here complements classical interface characterization techniques such as indentation or scratch testing of thin film systems [2,3], which also provide a high local spatial resolution. In recent studies, fracture toughness values of monolithic materials were successfully determined with micro-cantilevers [1] using pre-notched specimens [4]. For thin film systems very few studies concerning the measurement of the fracture properties of interfaces using micro-cantilevers exist. While Hwang et al. [5] produced pre-cracks between a polymer film and silicon to measure the interface fracture toughness, Kitamura et al. determined the critical stress intensity at the delamination load, KC in MPa m− λ (λ = 0.5 for a pre-existing crack), without introducing a pre-crack [6,7]. Encouraged by these studies, we extended the cantilever deflection method to evaluate the critical energy release rates, GC, for interface fracture of metal films sandwiched between silicon oxide. Due to the small dimensions it is challenging to introduce a defined defect (pre-crack) at the free edge of the interface with the focused ion beam microscope. In addition, fatigue pre-cracking at the
⁎ Corresponding author. Tel.: +004 3 (0)6504959903; fax: +004 3 (0)3842804116. E-mail address: [email protected] (K. Matoy). 0257-8972/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2009.09.013
sub-micrometer scale for thin film interfaces is difficult to realize. Hence, an alternative defect introduction technique (pre-cracking) is proposed, which is based on the natural crack deflection at weak interfaces during a simple macroscopic 4-point bending test similar to that described in the studies of Dauskardt et al. [8]. This technique does not necessarily allow for the design of a defined pre-crack, however, surface defects are produced at the free edge of the interface and their dimensions can be measured with the atomic force microscope. The paper outlines the cantilever preparation, the fracture experiment and the data analysis in order to determine the critical energy release rates of interfaces between copper (Cu), tungsten (W), tungsten titanium (W(Ti)) films and silicon oxide (SiOx). 2. Experimental 2.1. Sample preparation In order to prepare a cantilever which exhibits a silicon oxide/metal thin film interface that is perpendicular to the axis of maximum normal stress, silicon oxide with a thickness of 80 nm is deposited by plasma enhanced chemical vapor deposition on a 725 μm thick (100) silicon substrate. Subsequently, a 50 nm thick metal layer is sputtered onto the silicon oxide layer and covered with a 2300 nm thick silicon oxide layer. By this technique a stack consisting of silicon substrate/silicon oxide/ metal/silicon oxide is created as illustrated in Fig. 1 (step I). Three different silicon oxide/metal systems were prepared: SiOx/ Cu, SiOx/W and SiOx/W(Ti), where W(Ti) is a co-sputtered W film containing Ti (W(70 at.%)–Ti(30 at.%) target). In order to determine the critical energy release rate a pre-crack must be introduced at the free edge of the interface. We utilize the natural crack deflection at weak interfaces during a 4-point bending
K. Matoy et al. / Surface & Coatings Technology 204 (2009) 878–881
879
Fig. 1. Schematic diagram of the cantilever preparation process. After notching the material stack (I + II), the stack is broken by 4-point bending in two parts (III + IV). Finally the cantilevers are produced through rotating one part and utilizing focused ion beam (V + VI).
experiment to produce a surface defect at the free edge of the interface. To achieve this, the silicon substrate with the material stack is cut into small pieces of 10 × 10 mm2 in size. These pieces are then notched (Fig. 1 (step II)) and subsequently loaded macroscopically in a 4-point bending mode as it is illustrated in Fig. 1 (step III). The <100> direction of the silicon substrate is aligned parallel to the loading direction. By using this technique the silicon frequently breaks along the (100) lattice plane, creating smooth (100) silicon fracture surfaces (root mean square roughness: <1 nm) and nanometer-sized defects (<18 nm) at the free edge of the interfaces (Fig. 1 (step IV)). In order to produce cantilevers containing the interface with the surface defect, focused ion beam machining is used (FIB, Ga+-ions, 30 keV, 5–50 pA ion current on a dual beam LEO XB 1540 workstation), as illustrated in Fig. 1 (step VI). To prepare a freestanding cantilever, the sample has to be rotated in the focused ion beam workstation twice. To minimize the Ga+ implantation dose, grazing incidence ion milling with currents of 50 pA is used for final polishing. Additionally, position-marks are made on the top surface of the cantilevers at the free end with the FIB for easier positioning of the nanoindenter tip. After beam preparation the cantilever's top surface, which is formerly the fracture surface created by the 4-point bending procedure, is profiled using an atomic force microscope (Digital Instruments 3100) to measure the size of the surface defects created at the free edge of the interface. Examples of the atomic force microscopy images of the three systems, containing the surface defect at the free edge of interface, are illustrated in Fig. 2. Six cantilevers are prepared by this technique. The cantilevers' dimensions and measured maximum defect sizes are summarized in Table 1. In Table 1, t, represents the cantilever thickness, l, the distance between the metal layer and the point of loading, h, the length of the silicon junction, w, the cantilever's width, a, the defect size and E the Young's modulus of the metal layer.
Fig. 2. Atomic force microscopy height images reveal that major grooves are created at the free edges of the SiOx/Cu (a), SiOx/W (b) and SiOx/W(Ti) (c) interfaces. In (a), excess copper due to the 4-point bending process broadens the associated 50 nm copper line.
As the maximum load observed for the different material sandwiches are more or less identical for identical material combinations, it can be concluded that the defects introduced earlier by the 4-point bending procedure are similar in size. 3. Data evaluation
2.2. Cantilever loading and loading response The loading of the cantilever beams (see Fig. 3(a)) is performed exsitu with a nanoindentation system (Hysitron Triboscope) attached to an atomic force microscope (Digital Instruments 3100). A conospherical tip is used as a deflection tool (tip-radius 550 nm, determined by Hertzian contact on fused silica). The indentation equipment is capable of imaging the scanned surface with the indenter-tip, which makes it possible to position the tip with an accuracy of a few nanometers. Load and displacement are recorded during the deflection experiment. All cantilever deflection experiments are performed under ambient conditions with a load rate of 1 mN/s. The load versus deflection curves are linear elastic until fracture occurs, as illustrated in Fig. 4. Due to the fact that the cantilevers probed are approximately equal in size, the slope of the load versus deflection response is similar for all samples.
Due to the fact that the load–deflection curves show purely brittle behavior, we believe that the contribution of plasticity to the energy release rates is small. Thus, linear elastic fracture mechanics is applied. Table 1 Summary of the cantilever dimensions, the metal layer and its Young's modulus.
a
Number
Metal
E [GPa]
t [nm]
l [nm]
h [nm]
w [nm]
a [nm]
1 2 3 4 5 6
Cu Cu Cu W W(Ti) W(Ti)
121 121 121 411 324a 324a
1000 1000 1000 850 980 980
1820 1930 1800 1880 1850 1850
330 310 330 380 330 350
810 880 850 833 770 800
13 17 18 9 7 5
For simple estimation the following rule of mixture is used to calculate the modulus of W(Ti): 0.7 × 411 GPa + 0.3 × 120 GPa (W(70 at.%)–Ti(30 at.%) target), where the Young's modulus of Ti is 120 GPa.
880
K. Matoy et al. / Surface & Coatings Technology 204 (2009) 878–881
In this equation E1 represents the Young's modulus of SiOx and E2 the Young's modulus of the metal layer. The critical stress intensity is given by pffiffiffiffiffiffi K = 1:12σ πa [10] with 2
σ = 6Fl = wt ;
Fig. 3. Scanning electron microscope images of a micro-cantilever containing a silicon oxide/W interface before (a) and after fracture (b).
Both, finite element (FE) simulations and analytical energy release rate calculations are provided. For the simple analytical solution the energy release rate is determined by making use of 2
G = K =E
⁎
with ⁎
1 = E = 1 = 2ð1 = E1 + 1 = E2 Þ [9].
Fig. 4. The load–deflection curves of the cantilevers tested show linear elastic behavior. It should be noted that the cantilevers with W(Ti) fracture at much higher loads than the other oxide/metal systems. The curves for the cantilevers containing W(Ti) are almost overlapping.
where F denotes the maximum load and the factor 1.12 expresses the shape factor for a half-circular surface crack in a semi-infinite body. In order to determine the critical energy release rate by finite element simulation the J-integral is employed. A requirement for using the J-integral to determine a critical value for crack initiation is linear or non linear elastic material behavior. A further condition is the path independency of the J-integral. The self-similarity of the employed geometry with the defect located at the interface fulfils the requirement. To ensure that there is no path dependency 20 contour integrals for each pre-crack were calculated and checked for agreement. It is shown elsewhere that the energy release rate, G, can be determined from the J-integral (G = J) [11]. For data evaluation the critical J-integral is computed using two dimensional ABAQUS finite element simulation. CPS8 (8-node biquadratic plane stress quadrilateral) and CPE8 (8-node biquadratic plane strain quadrilateral) elements are used and an isotropic and linear elastic material behavior is utilized for the materials building the sandwich cantilever. Critical J-integral values determined using plane strain elements are, at the most 4.5%, smaller than those determined with plane stress elements. In the subsequent discussion the plane stress FE results are shown. The region close to the defect on the free edge of the interface is meshed with a mesh size of ~ 1 nm. The total number of elements for each cantilever deflection simulation is ~11,000. The elastic constants of the metallic materials used are listed in Table 1 [12]. For silicon oxide and silicon Young's moduli of 65 GPa (nanoindentation considering a Poisson ratio of 0.2) and 163 GPa [13], respectively, are used. Scanning electron microscope images reveal that the cantilevers fail at the silicon oxide/metal interface which is closer to the silicon substrate (see Fig. 3(b)). This interface exhibits more pronounced defects in our method and experiences a higher bending moment. As we are principally interested in the determination of critical energy release rates for crack initiation by utilizing a fracture mechanical experiment, we want to refer the reader to an article by Chen and Bull [14] for deeper understanding of the failure mechanism observed in multi layer systems. Smooth fracture surfaces imply that no plastic deformation occurs at the interface with no metal remaining on the silicon oxide layer on top of the silicon wafer. Cantilever interface fracture experiments on the system silicon/SiOx show crack initiation in the silicon [15]. For data evaluation, the beam geometries are determined from the scanning electron microscope images (Fig. 3) and the size of the surface defect (depth of the grooves at the interface) is determined with the atomic force microscope and implemented into the simulation by a sharp crack. The maximum measured defect size, a, underestimates the actual defect size, as the tip of the atomic force microscope is not infinitesimally small (typical tip-radius of <7 nm). Hence, the apparent critical energy release rate might underestimate the actual energy release rate. The maximum critical energy release rates determined analytically and with finite element simulation reveal that the silicon oxide/Cu interface is the weakest (FE: 0.65 J/m2, analytically: 0.57 J/m2), whereas the silicon oxide/W(Ti) interfacial adhesion is seven times higher (FE: 4.8 J/m2, analytically: 4.3 J/m2). The critical energy release rate determined for the system silicon oxide/W by FE simulation is 2.86 J/m2, and 2.84 J/m2 determined analytically. The results are
K. Matoy et al. / Surface & Coatings Technology 204 (2009) 878–881
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that such small values, which are reported in the literature, can only be obtained in the cantilever experiments if the size of the defect is in the range of a few nanometers, one might conclude that the actual defect size almost corresponds to the measured surface-defect size. Moreover, taking into account that the cantilever deflection experiment is extremely sensitive to defects on the beam's top surface it is reasonable to assume that the natural defect produced by the 4-point bending procedure represents the critical defect. 4. Conclusion
Fig. 5. Comparison between the maximum critical energy release rates determined analytically and by FE plane stress analysis. The energy release rates obtained deviate by ~ 10%.
summarized in Fig. 5. Discrepancies between FE and analytical results may be attributed to the fact that the analytical solution considers a half-circular surface crack while the FE simulation assumes a uniform defect over the full width of the cantilever. The actual energy release rates will be somewhere in between the analytical and the FE solution as both crack geometries describe limits of the crack shapes observed in Fig. 2. The error bar in Fig. 5 is ±30% and considers an error of 30% in the defect size measured. Comparing energy release rates with literature values reveals that the data obtained give reasonable results for metal films of similar thickness. Typical reported adhesion energies are 0.6–100 J/m2 for the silicon oxide/copper interface (determined for a copper thickness of 40–3000 nm) [3], 5–9 J/m2 for the silicon oxide/ tungsten interface (tungsten thickness: 530–760 nm) [3] while for the silicon oxide/W(Ti) interface no data are available. For the system silicon oxide/W a discrepancy of ~50% between the smallest reported and the measured value exists. Generally, thicker metal layers increase the critical energy release rate, due to energy dissipation by plastic deformation. The tungsten thin films investigated in our systems are ten times thinner than that in [3], which might result in a smaller value of GC in this study. The fact that GC is higher for the system containing W (Ti) in comparison to that containing W is supported by the observation that the addition of titanium to tungsten increases the adhesive strength to silicon oxide [16]. Due to the fact that energy dissipation by plastic deformation in the load deflection curves is not noticeable, the values for our systems are expected to be on the lower limit of the literature values, besides the fact of underestimating the actual defect size. Considering further
A micro-cantilever approach to determine the critical energy release rate for crack initiation at small length scales was developed. The critical energy release rates determined by this method range between 0.65 J/m2, 2.86 J/m2 and 4.8 J/m2 for SiOx/Cu, SiOx/W and SiOx/W(Ti) interfaces. These values agree with the data reported in the literature. Moreover, a possibility to introduce a pre-crack at the free edge of the interface in a micro-scaled fracture mechanical specimen is suggested. Acknowledgements The authors want to thank O. Kolednik and R. Pippan for stimulating and helpful discussions and T. Schöberl for assistance with the atomic force microscopy measurements. This work was jointly funded by the Federal Ministry of Economics and Labour of the Republic of Austria (contract 98.362/0112-C1/10/2005) and the Carinthian Economic Promotion Fund (KWF) (contract 98.362/ 0112-C1/10/2005). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
T.P. Weihs, S. Hong, J.C. Bravman, W.D. Nix, J. Mater. Res. 3/5 (1988) 931. J. Chen, S.J. Bull, J. Phys., D, Appl. Phys. 40 (2007) 5401. A.A. Volinsky, N.R. Moody, W.W. Gerberich, Acta Mater. 50/3 (2002) 441. D. Di Maio, S.G. Roberts, J. Mater. Res. 20/2 (2005) 299. S.-F. Hwang, J.-H. Yu, B.-J. Lai, H.-K. Liu, Mech. Mater. 40/8 (2008) 658. T. Kitamura, T. Shibutani, T. Ueno, Eng. Fract. Mech. 69/12 (2002) 1289. H. Hirakata, T. Hirako, Y. Takahashi, Y. Matsuoka, T. Kitamura, Eng. Fract. Mech. 75/10 (2008) 2907. R. Dauskardt, M. Lane, Q. Ma, N. Krishna, Eng. Fract. Mech. 61/1 (1998) 141. J.W. Hutchinson, Z. Suo, Adv. Appl. Mech. 29 (1992) 63. H. Tada, P.C. Paris, G.R. Irwin, The Stress Analysis of Cracks Hand Book, ASME Pr, New York, 2000. D. Gross, T. Seelig, Fracture Mechanics, third ed., Springer, Berlin, 2001, p. 121. T.H. Courtney, Mechanical Behavior of Materials, 2nd ed., McGraw-Hill, Boston, 2000, p. 60. J. Mencik, E. Quandt, J. Mater. Res. 14/5 (1999) 2152. J. Chen, S.J. Bull, Thin Solid Films 517 (2009) 3704. K. Matoy, PhD Thesis, University of Leoben, 2009 in preparation. J. Valldorf, W. Gessner, Advanced Microsystems for Automotive Applications, Springer Berlin, Heidelberg, 2008, p. 181.
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Interface fracture properties of thin films studied by using the micro-cantilever deflection technique Kurt Matoy a,b,c,⁎, Thomas Detzel d, Matthias Müller d, Christian Motz b, Gerhard Dehm b,c a
Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, A-9524 Villach, Austria Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, A-8700 Leoben, Austria Department Materials Physics, University of Leoben, A-8700 Leoben, Austria d Infineon Technologies Austria AG, A-9500 Villach, Austria b c
a r t i c l e
i n f o
Available online 11 September 2009 Keywords: Interface toughness Micro-cantilever Ion beam processing
a b s t r a c t The mechanical behavior of interfaces between silicon oxide and metallic thin films is investigated using an alternative approach which is based on the miniaturized cantilever deflection technique (Weihs et al., 1988 [1]). The critical energy release rates for three different silicon oxide/metal systems are determined and the results are discussed in this paper. The technique suggested may be applicable with high spatial resolution for a wide variety of structured thin film systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In microelectronic devices the interfaces between thin film materials are common sources of mechanical failure. Their probability to fail can be estimated by finite element simulations if the interface properties are well known. Due to the small dimensions, measuring those quantities poses a challenge to the experimentalists, especially when the interface of interest is buried. The possibility to fabricate miniaturized fracture mechanic specimens of buried interfaces by using focused ion beam machining is demonstrated in this paper. The approach described here complements classical interface characterization techniques such as indentation or scratch testing of thin film systems [2,3], which also provide a high local spatial resolution. In recent studies, fracture toughness values of monolithic materials were successfully determined with micro-cantilevers [1] using pre-notched specimens [4]. For thin film systems very few studies concerning the measurement of the fracture properties of interfaces using micro-cantilevers exist. While Hwang et al. [5] produced pre-cracks between a polymer film and silicon to measure the interface fracture toughness, Kitamura et al. determined the critical stress intensity at the delamination load, KC in MPa m− λ (λ = 0.5 for a pre-existing crack), without introducing a pre-crack [6,7]. Encouraged by these studies, we extended the cantilever deflection method to evaluate the critical energy release rates, GC, for interface fracture of metal films sandwiched between silicon oxide. Due to the small dimensions it is challenging to introduce a defined defect (pre-crack) at the free edge of the interface with the focused ion beam microscope. In addition, fatigue pre-cracking at the
⁎ Corresponding author. Tel.: +004 3 (0)6504959903; fax: +004 3 (0)3842804116. E-mail address: [email protected] (K. Matoy). 0257-8972/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2009.09.013
sub-micrometer scale for thin film interfaces is difficult to realize. Hence, an alternative defect introduction technique (pre-cracking) is proposed, which is based on the natural crack deflection at weak interfaces during a simple macroscopic 4-point bending test similar to that described in the studies of Dauskardt et al. [8]. This technique does not necessarily allow for the design of a defined pre-crack, however, surface defects are produced at the free edge of the interface and their dimensions can be measured with the atomic force microscope. The paper outlines the cantilever preparation, the fracture experiment and the data analysis in order to determine the critical energy release rates of interfaces between copper (Cu), tungsten (W), tungsten titanium (W(Ti)) films and silicon oxide (SiOx). 2. Experimental 2.1. Sample preparation In order to prepare a cantilever which exhibits a silicon oxide/metal thin film interface that is perpendicular to the axis of maximum normal stress, silicon oxide with a thickness of 80 nm is deposited by plasma enhanced chemical vapor deposition on a 725 μm thick (100) silicon substrate. Subsequently, a 50 nm thick metal layer is sputtered onto the silicon oxide layer and covered with a 2300 nm thick silicon oxide layer. By this technique a stack consisting of silicon substrate/silicon oxide/ metal/silicon oxide is created as illustrated in Fig. 1 (step I). Three different silicon oxide/metal systems were prepared: SiOx/ Cu, SiOx/W and SiOx/W(Ti), where W(Ti) is a co-sputtered W film containing Ti (W(70 at.%)–Ti(30 at.%) target). In order to determine the critical energy release rate a pre-crack must be introduced at the free edge of the interface. We utilize the natural crack deflection at weak interfaces during a 4-point bending
K. Matoy et al. / Surface & Coatings Technology 204 (2009) 878–881
879
Fig. 1. Schematic diagram of the cantilever preparation process. After notching the material stack (I + II), the stack is broken by 4-point bending in two parts (III + IV). Finally the cantilevers are produced through rotating one part and utilizing focused ion beam (V + VI).
experiment to produce a surface defect at the free edge of the interface. To achieve this, the silicon substrate with the material stack is cut into small pieces of 10 × 10 mm2 in size. These pieces are then notched (Fig. 1 (step II)) and subsequently loaded macroscopically in a 4-point bending mode as it is illustrated in Fig. 1 (step III). The <100> direction of the silicon substrate is aligned parallel to the loading direction. By using this technique the silicon frequently breaks along the (100) lattice plane, creating smooth (100) silicon fracture surfaces (root mean square roughness: <1 nm) and nanometer-sized defects (<18 nm) at the free edge of the interfaces (Fig. 1 (step IV)). In order to produce cantilevers containing the interface with the surface defect, focused ion beam machining is used (FIB, Ga+-ions, 30 keV, 5–50 pA ion current on a dual beam LEO XB 1540 workstation), as illustrated in Fig. 1 (step VI). To prepare a freestanding cantilever, the sample has to be rotated in the focused ion beam workstation twice. To minimize the Ga+ implantation dose, grazing incidence ion milling with currents of 50 pA is used for final polishing. Additionally, position-marks are made on the top surface of the cantilevers at the free end with the FIB for easier positioning of the nanoindenter tip. After beam preparation the cantilever's top surface, which is formerly the fracture surface created by the 4-point bending procedure, is profiled using an atomic force microscope (Digital Instruments 3100) to measure the size of the surface defects created at the free edge of the interface. Examples of the atomic force microscopy images of the three systems, containing the surface defect at the free edge of interface, are illustrated in Fig. 2. Six cantilevers are prepared by this technique. The cantilevers' dimensions and measured maximum defect sizes are summarized in Table 1. In Table 1, t, represents the cantilever thickness, l, the distance between the metal layer and the point of loading, h, the length of the silicon junction, w, the cantilever's width, a, the defect size and E the Young's modulus of the metal layer.
Fig. 2. Atomic force microscopy height images reveal that major grooves are created at the free edges of the SiOx/Cu (a), SiOx/W (b) and SiOx/W(Ti) (c) interfaces. In (a), excess copper due to the 4-point bending process broadens the associated 50 nm copper line.
As the maximum load observed for the different material sandwiches are more or less identical for identical material combinations, it can be concluded that the defects introduced earlier by the 4-point bending procedure are similar in size. 3. Data evaluation
2.2. Cantilever loading and loading response The loading of the cantilever beams (see Fig. 3(a)) is performed exsitu with a nanoindentation system (Hysitron Triboscope) attached to an atomic force microscope (Digital Instruments 3100). A conospherical tip is used as a deflection tool (tip-radius 550 nm, determined by Hertzian contact on fused silica). The indentation equipment is capable of imaging the scanned surface with the indenter-tip, which makes it possible to position the tip with an accuracy of a few nanometers. Load and displacement are recorded during the deflection experiment. All cantilever deflection experiments are performed under ambient conditions with a load rate of 1 mN/s. The load versus deflection curves are linear elastic until fracture occurs, as illustrated in Fig. 4. Due to the fact that the cantilevers probed are approximately equal in size, the slope of the load versus deflection response is similar for all samples.
Due to the fact that the load–deflection curves show purely brittle behavior, we believe that the contribution of plasticity to the energy release rates is small. Thus, linear elastic fracture mechanics is applied. Table 1 Summary of the cantilever dimensions, the metal layer and its Young's modulus.
a
Number
Metal
E [GPa]
t [nm]
l [nm]
h [nm]
w [nm]
a [nm]
1 2 3 4 5 6
Cu Cu Cu W W(Ti) W(Ti)
121 121 121 411 324a 324a
1000 1000 1000 850 980 980
1820 1930 1800 1880 1850 1850
330 310 330 380 330 350
810 880 850 833 770 800
13 17 18 9 7 5
For simple estimation the following rule of mixture is used to calculate the modulus of W(Ti): 0.7 × 411 GPa + 0.3 × 120 GPa (W(70 at.%)–Ti(30 at.%) target), where the Young's modulus of Ti is 120 GPa.
880
K. Matoy et al. / Surface & Coatings Technology 204 (2009) 878–881
In this equation E1 represents the Young's modulus of SiOx and E2 the Young's modulus of the metal layer. The critical stress intensity is given by pffiffiffiffiffiffi K = 1:12σ πa [10] with 2
σ = 6Fl = wt ;
Fig. 3. Scanning electron microscope images of a micro-cantilever containing a silicon oxide/W interface before (a) and after fracture (b).
Both, finite element (FE) simulations and analytical energy release rate calculations are provided. For the simple analytical solution the energy release rate is determined by making use of 2
G = K =E
⁎
with ⁎
1 = E = 1 = 2ð1 = E1 + 1 = E2 Þ [9].
Fig. 4. The load–deflection curves of the cantilevers tested show linear elastic behavior. It should be noted that the cantilevers with W(Ti) fracture at much higher loads than the other oxide/metal systems. The curves for the cantilevers containing W(Ti) are almost overlapping.
where F denotes the maximum load and the factor 1.12 expresses the shape factor for a half-circular surface crack in a semi-infinite body. In order to determine the critical energy release rate by finite element simulation the J-integral is employed. A requirement for using the J-integral to determine a critical value for crack initiation is linear or non linear elastic material behavior. A further condition is the path independency of the J-integral. The self-similarity of the employed geometry with the defect located at the interface fulfils the requirement. To ensure that there is no path dependency 20 contour integrals for each pre-crack were calculated and checked for agreement. It is shown elsewhere that the energy release rate, G, can be determined from the J-integral (G = J) [11]. For data evaluation the critical J-integral is computed using two dimensional ABAQUS finite element simulation. CPS8 (8-node biquadratic plane stress quadrilateral) and CPE8 (8-node biquadratic plane strain quadrilateral) elements are used and an isotropic and linear elastic material behavior is utilized for the materials building the sandwich cantilever. Critical J-integral values determined using plane strain elements are, at the most 4.5%, smaller than those determined with plane stress elements. In the subsequent discussion the plane stress FE results are shown. The region close to the defect on the free edge of the interface is meshed with a mesh size of ~ 1 nm. The total number of elements for each cantilever deflection simulation is ~11,000. The elastic constants of the metallic materials used are listed in Table 1 [12]. For silicon oxide and silicon Young's moduli of 65 GPa (nanoindentation considering a Poisson ratio of 0.2) and 163 GPa [13], respectively, are used. Scanning electron microscope images reveal that the cantilevers fail at the silicon oxide/metal interface which is closer to the silicon substrate (see Fig. 3(b)). This interface exhibits more pronounced defects in our method and experiences a higher bending moment. As we are principally interested in the determination of critical energy release rates for crack initiation by utilizing a fracture mechanical experiment, we want to refer the reader to an article by Chen and Bull [14] for deeper understanding of the failure mechanism observed in multi layer systems. Smooth fracture surfaces imply that no plastic deformation occurs at the interface with no metal remaining on the silicon oxide layer on top of the silicon wafer. Cantilever interface fracture experiments on the system silicon/SiOx show crack initiation in the silicon [15]. For data evaluation, the beam geometries are determined from the scanning electron microscope images (Fig. 3) and the size of the surface defect (depth of the grooves at the interface) is determined with the atomic force microscope and implemented into the simulation by a sharp crack. The maximum measured defect size, a, underestimates the actual defect size, as the tip of the atomic force microscope is not infinitesimally small (typical tip-radius of <7 nm). Hence, the apparent critical energy release rate might underestimate the actual energy release rate. The maximum critical energy release rates determined analytically and with finite element simulation reveal that the silicon oxide/Cu interface is the weakest (FE: 0.65 J/m2, analytically: 0.57 J/m2), whereas the silicon oxide/W(Ti) interfacial adhesion is seven times higher (FE: 4.8 J/m2, analytically: 4.3 J/m2). The critical energy release rate determined for the system silicon oxide/W by FE simulation is 2.86 J/m2, and 2.84 J/m2 determined analytically. The results are
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that such small values, which are reported in the literature, can only be obtained in the cantilever experiments if the size of the defect is in the range of a few nanometers, one might conclude that the actual defect size almost corresponds to the measured surface-defect size. Moreover, taking into account that the cantilever deflection experiment is extremely sensitive to defects on the beam's top surface it is reasonable to assume that the natural defect produced by the 4-point bending procedure represents the critical defect. 4. Conclusion
Fig. 5. Comparison between the maximum critical energy release rates determined analytically and by FE plane stress analysis. The energy release rates obtained deviate by ~ 10%.
summarized in Fig. 5. Discrepancies between FE and analytical results may be attributed to the fact that the analytical solution considers a half-circular surface crack while the FE simulation assumes a uniform defect over the full width of the cantilever. The actual energy release rates will be somewhere in between the analytical and the FE solution as both crack geometries describe limits of the crack shapes observed in Fig. 2. The error bar in Fig. 5 is ±30% and considers an error of 30% in the defect size measured. Comparing energy release rates with literature values reveals that the data obtained give reasonable results for metal films of similar thickness. Typical reported adhesion energies are 0.6–100 J/m2 for the silicon oxide/copper interface (determined for a copper thickness of 40–3000 nm) [3], 5–9 J/m2 for the silicon oxide/ tungsten interface (tungsten thickness: 530–760 nm) [3] while for the silicon oxide/W(Ti) interface no data are available. For the system silicon oxide/W a discrepancy of ~50% between the smallest reported and the measured value exists. Generally, thicker metal layers increase the critical energy release rate, due to energy dissipation by plastic deformation. The tungsten thin films investigated in our systems are ten times thinner than that in [3], which might result in a smaller value of GC in this study. The fact that GC is higher for the system containing W (Ti) in comparison to that containing W is supported by the observation that the addition of titanium to tungsten increases the adhesive strength to silicon oxide [16]. Due to the fact that energy dissipation by plastic deformation in the load deflection curves is not noticeable, the values for our systems are expected to be on the lower limit of the literature values, besides the fact of underestimating the actual defect size. Considering further
A micro-cantilever approach to determine the critical energy release rate for crack initiation at small length scales was developed. The critical energy release rates determined by this method range between 0.65 J/m2, 2.86 J/m2 and 4.8 J/m2 for SiOx/Cu, SiOx/W and SiOx/W(Ti) interfaces. These values agree with the data reported in the literature. Moreover, a possibility to introduce a pre-crack at the free edge of the interface in a micro-scaled fracture mechanical specimen is suggested. Acknowledgements The authors want to thank O. Kolednik and R. Pippan for stimulating and helpful discussions and T. Schöberl for assistance with the atomic force microscopy measurements. This work was jointly funded by the Federal Ministry of Economics and Labour of the Republic of Austria (contract 98.362/0112-C1/10/2005) and the Carinthian Economic Promotion Fund (KWF) (contract 98.362/ 0112-C1/10/2005). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
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