Chapter The interfacial adhesion energy for the same 500 nm thickness BD film obtained by using the interfacial energy-strength contour (Γ0=5.58-8.49 J/m2) is slightly higher than the interfacial toughness determined in Section 4.4.3 using the experimental method (Γ0=5.40±0.90 J/m2). The reasons for the differences will be discussed together with the results on the MSQ film in the next section. 5.2.2 MSQ film on Si Substrate Fig. 5.4: The MSQ/Si system’s interfacial energy-strength contour for 90° and 120° wedge indentation showing the intersection of Pc90/(σyf Δo) = 4.52 – 6.78µm and Pc120/(σyf Δo) = 7.24 – 11.31µm. Full lines represent the contour for Pc90/(σyf Δo), while dashed lines represent that for Pc120/(σyf Δo) [1]. 131 Chapter Fig.5.4 shows the interfacial energy-strength contour for MSQ/Si system. According to the fracture-indentation correlation studies on the MSQ/Si system, popin loads for 90° and 120° wedge indentations are 2mN and 3.25mN, respectively; and the interfacial delamination occurred at 3mN and 5mN for the 90° and 120° wedge indentations, respectively. By assuming the later values (3mN and 5mN) are the critical indentation loads, Pc90/(σyfΔ0) and Pc120/(σyfΔ0) for MSQ/Si system (σyf=0.45GPa) can be calculated as 6.78µm and 11.31µm, respectively. From the intersection of these two curves (Pc90/(σyfΔ0)=6.78µm and Pc120/(σyfΔ0) =11.31µm) in the interfacial energy – strength contour, it can be found that the interfacial energy, Γ0 is 2.61J/m2 and interfacial strength, σstrength, is 0.29GPa. These two values can be considered as the higher-bounds for the interfacial properties. On the other hand, the values of the lower-bounds are found as Γ0 = 2.13J/m2 and σstrength = 0.24GPa in a similar way using the pop-in loads (2mN and 3.25mN). The interfacial energy for MSQ/Si system determined using the experimental method are 1.89±0.28 J/m2 and 1.92±0.08 J/m2 for 90° and 120° wedge indentation, respectively (Section 4.4.2). The BD/Si and the MSQ/Si systems’ interfacial energies determined with the forward-reverse calculation scheme in this section are also slightly higher than the results obtained with the experimental method (Section 4.4). Nevertheless, the two independent methods (experimental method and forward-reverse method) have confirmed the validity of each other. One possible reason that the values of Γ0 determined from the contour-plots are higher than those determined from the experimental method is the discrepancy between the stress-strain condition reproduced by a FEM simulation and the actual 132 Chapter condition in an experiment. In the simulation, a 2D plane-strain condition is assumed since the wedge is infinitely long. In the experiments, however, the wedge indenter length (approximately μm) may not be long enough to achieve a complete plane strain condition, especially at the two ends of the wedge tips. The film cracking at the ends of the wedge tip may alter the strain conditions and introduce some errors in the calculations. Therefore, if a longer wedge tip is used, the disagreement between experiment and simulation in the stress-strain conditions may be reduced and the interfacial adhesion results could be more accurate. The interfacial energy and strength values determined from the contour-plots are within a certain range for both the BD/Si and the MSQ/Si systems (i.e. Γ0=5.588.49 J/m2 and σstrength=0.71-0.78 GPa, for the BD/Si system; and Γ0=2.13-2.61 J/m2 and σstrength=0.24-0.29 GPa, for the MSQ/Si system). It is intriguing that if one takes the middle values of these ranges as the interfacial energy (i.e., Γ0,m=7.04 J/m2 for the BD/Si system and Γ0,m=2.37 J/m2 for the MSQ/Si system), then the values of interfacial energy are approximately 25% to 30% higher than the values determined by the analysis and experimental methodology in Section 4.4. These results suggest that a constant may be needed for the equation for indentation induced stress (Eq.(4.1)) to accommodate for the plastic energy dissipation at the side walls of corner cracks (shown by bulge-out in Fig.4.9) but this potentially important improvement to the previous analysis still requires further study. Despite the potential errors discussed above, the interfacial adhesion properties determined in this work are quite similar to the previously obtained experimental 133 Chapter values. The forward-reverse analysis proposed in this work is useful for the determination of the interfacial mechanical properties. 5.3 Conclusions From the comparison of the simulation and experimentally obtained P-h curves before the onset of delamination, the yield strength and the strain hardening exponential values of the BD and MSQ film have been estimated from the FEM simulations and the wedge indentation experiments. The elastic-plastic properties of these two low-k films are then implemented to the FEM simulations of the wedge indentation induced delamination, whereby the interfacial energy-strength contours are developed. Using these contour plots and the experimentally-determined critical indentation loads for delamination (Pc90 and Pc120), the interfacial energy and the interfacial strength of BD/Si and MSQ/Si system are successfully determined. In conclusion, this study has provided a numerical solution to the wedge indentation induced delamination problem and the results are comparable to what were obtained in the previous experimental works (Section 4.4). Although the numerical results are not 100% matched with the experimental results, these two independent results still provide sufficient supports for each others. The new forward-reverse analysis scheme is capable to measure interfacial energy and interfacial strength of the low-k thin films. 134 Chapter References: 1. L. Chen, K.B. Yeap, K.Y. Zeng and G.R. Liu, Phil. Mag., 89, p.1395-1413, (2009). 2. K.L. Johnson, J. Mech. Phys. Solids, 18, p.115-126, (1970). 3. V. Tvergaard and J.W. Hutchinson, Phil. Mag. A, 70, p.641-656, (1994). 4. V. Tvergaard and J.W. Hutchinson, Int. J. Solid. Struct., 33, p.3297-3308, (1996). 135 Chapter 6: Wedge Indentation Studies of Low-k Films at Inert, Water and Ambient Environments As discussed earlier (Section 1.2), the introduction of low-k films are essential to reduce the RC delay in a microelectronic device. One of the promising low-k candidates is hybrid organic-inorganic glass materials, such as BD and MSQ films. Similar to other silica-based materials, these hybrid low-k materials are also susceptible to time-dependent fracture (also known as stress corrosion cracking, slow crack growth or subcritical crack growth). During the fabrication processes, such as chemical-mechanical-polishing (CMP) and chemical etching, the low-k dielectrics are subjected to different levels of mechanical stresses and contacted with various reactive species. After the fabrication processes are completed, microelectronic devices are usually sealed; in addition, there are various device operating conditions and the devices may be subjected to temperature-change induced thermal stresses and possible mechanical stresses. Therefore it is important to study crack growth phenomena in different environments such as inert, water and ambient conditions. In general, the experimental techniques to characterize the time-dependent fracture properties of thin films include bending tests [1-3] and indentation tests [4]. Four-point bending [1,5] and double-cantilever-cleavage techniques [2,3] have been widely used to characterize the time-dependent crack growth in various low-k systems. However, the bending techniques are accompanied by a complicated sample preparation procedure and a long preparation time. In order to characterize the timedependent fracture properties in terms of a strain energy released rate – crack velocity 136 Chapter (G-v) relation, which consists of reaction-controlled regime, diffusion-controlled regime and spontaneous fracture regime [5], one must obtain at least 10 – 20 data points, and each data point requires about 30 sets of tests. Therefore, tremendous amount of bending samples are needed to fully-characterize the time-dependent fracture properties of a certain low-k system, which may be subjected to a wide range of environmental conditions. On the other hand, indentation technique requires only a small piece of asdeposited thin film sample for a complete time-dependent properties characterization. Cook and Liniger [4] developed an experimental methods using Vickers indentation to characterize these properties of the low-k thin film. They have measured the film cracks extension with time from the impression corners, but the possibility of interfacial cracks formation were not discussed [4]. In Section 4.1.1, the crosssectional images of Berkovich indentation impressions on MSQ/Si sample (Fig.4.6(a)), which are obtained from focused-ion-beam (FIB) cutting of the impressions, have shown that the interfacial crack may form during the indentations with Berkovich tips. Therefore, it can be anticipated that the Vickers indentation on low-k thin film may also result in the interfacial cracks. When the sample is exposed to water-contained environment, not only the film cracks could propagate, the interfacial cracks might also propagate. In the Chapter of this thesis, a simple analysis and a straight forward experimental methodology to characterize interfacial properties by wedge indentation technique are developed and applied to low-k/Si systems to determine the interfacial toughness. The wedge indentation imposes a plane-strain condition and has a great 137 Chapter interfacial crack driving force to induce the interfacial delamination on the low-k/Si systems. In addition, the interfacial toughness of the MSQ/Si and the BD/Si systems measured using the wedge indentation technique are confirmed to be accurate and repeatable [6,7]. On the other hand, the time-dependent fracture behaviors for the lowk/Si systems are also found during the wedge indentation experiments. This behavior is therefore studied in details in this chapter. Instead of using normal indentation procedures, the low-k/Si systems are indented with the wedge indenter tip and hold at the maximum load for a period of time, allowing the time-dependent fracture to occur. The resulting indentation data (load, loading rate, penetration depth and holding time) are analyzed in Section 6.1 and 6.2 to determine (i) the minimum load before the timedependent fracture starts (defined as threshold load); (ii) the changes of the onset of time-dependent fracture when different loading rates are applied; and (iii) the total time needed from film cracking to interfacial delamination (defined as time-to-failure). The results from these experiments depend on the degree of water exposure of a sample. In order to vary the water exposure levels, three different test environments are used (ambient, watered and inert environments). The influence of the test environments on the cracks initiation and propagation are studied by comparing the penetration depth – holding time (h-t) curves obtained from different test environments; this is because when the indentation load is fixed for a period of time, massive penetration of the indenter can be related to various fracture events at film and interface (Section 6.3). The feasible water diffusion paths and fracture mechanisms for BD/Si system, when it is subjected to wedge indentations at the three test environments, are also discussed. 138 Chapter 6.1 Time-Dependent Fracture during Wedge Indentation Tests This section presents two indentation tests (load-holding test and varyingloading-rates test) developed to study the time-dependent fracture behavior of low-k/Si systems. In the load-holding test, a maximum load, Pmax is maintained in the holding segment, and changes of penetration depth with the holding time are recorded; whereas in the varying-loading-rates test, different loading rates, dP/dt, are applied, and the corresponding fracture-onset loads, Ponset, are determined. In Section 4.1.2, it is found that there are significant differences in the fracture resistance for BD/Si and MSQ/Si systems. In the MSQ/Si system, there is an extra plastic energy dissipation mechanism possibly due to the stretching of molecular bridgings behind the crack tip, but this mechanism is unavailable in the plasma enhanced chemical vapor deposited BD/Si system. The molecular bridgings were also anticipated to provide a stronger resistant toward time-dependent crack growth [8], therefore it would be interesting to first compare the two low-k systems based on the load-holding tests and the varyingloading-rate tests that are conducted at ambient environment. 139 Chapter Fig. 6.1: The load-holding test results for the BD/Si system at ambient environment: (a) load-penetration depth (P-h) curves for different maximum loads at holding, Pmax; (b) penetration depth-holding time (h-t) curves for different Pmax, showing the consistent S-shaped curves, consisting of three stages [9]. In the load-holding and the varying-loading-rates tests, the film cracking and the interfacial delamination that occur below the critical load, Pcritical (i.e. the indentation load associated with the onset of fracture in a fast loading-unloading condition) are defined as the time-dependent fracture. For the BD/Si system, during the fast loading condition, when the indentation load reaches to Pcritical = 7.5mN, there is a pronounced pop-in at the indentation P-h curve, i.e., a sudden displacement of the 140 Chapter On the other hand, for ambient and inert tests, the slopes of the curves and times for each stage are similar (different by less than 10%), except for the slope and time at stage 2B (S2B and t2B). It is noticed that S2B of the ambient test is about 40% higher than that of the inert test, and t2B of the ambient test is about 30% shorter than that of the inert test. In the ambient environment, because the water molecules in air are further apart from each others as compared to those in the liquid-form, the possibility for the diffusion of water molecules into the film is therefore much less. However, it is possible for small amount of water molecules to move into the film crack and assist the film crack propagation in the stage 2B. Since the t2C and S2C in ambient test are similar with those in the inert tests, it may be expected that the interfacial crack growth rates for ambient and inert tests should be similar. This may be due to the following reason: for an ambient test, there is only a small amount of water molecules moving into the film crack and it may be fully consumed during film crack propagation stage, and therefore little has been left to enhance the interfacial crack growth. Furthermore, it is noticed that the standard deviations of t2C for the ambient and inert tests are particularly large compared to that of the watered test, suggesting that defects dependency is greater when there is less amount of water to assist interfacial crack growth. This also suggests that the time-dependent crack propagation without reactive species may have greater dependence on the crack tip structure, and therefore leading to greater deviations of the results (Section 6.4). 154 Chapter 6.4 Crack Growth at Inert Environment There are several mechanisms proposed to explain the time-dependent fracture (also known as stress corrosion cracking, slow crack growth or subcritical fracture), but the theories proposed by Michalske and Freiman [16], and Cook and Liniger [17,18] are commonly used to explain the behaviors in low-k materials (Section 2.4.2). The stress corrosion mechanism in silica was usually believed to be in a three-reaction sequence [16]: (a) water molecules were adsorbed to strained siloxane bonds, (b) a concerted reaction occurred and led to the siloxane bonds ruptured, and (c) silanol groups form at fracture surface. During rapid or spontaneous fracture, the activation barrier for siloxane bond rupturing is mainly overcome by strain energy. Michalske and Freiman [16] proposed that when water was presented, this energy barrier was reduced by the chemical reactions between siloxane bond and water molecule, hence the growth rate was enhanced. On the other hand, Cook and Liniger [17,18] proposed that, in reactive environments, (a) surface energy reduced, and (b) when strain energy release rate was greater than the reduced surface energy, fracture was thermally activated. These two theories considered that the activation energy was needed to rupture one atomic bonding under reactive environment, but the effects of the neighboring atoms and lattice-structure within the cohesive width - the width of cohesive region located at transition between broken and highly strained crack tip bonds - were not taken into account. In this study, the BD/Si system is found to be susceptible to time-dependent fracture at inert environment (i.e. sample surface is covered with silicone oil). This anomalous behavior is possibly due to the effects of silica network terminal group 155 Chapter (methyl -CH3) in the BD film structure. In their earlier study, Wiederhorn et al. described that the time-dependent fracture could occur in vacuum for glasses with high content of network modifiers, whereas rapid or spontaneous fracture was observed for pure silica glass [19]. This observation has led to the discussion about the dependence of fracture on molecular structure at the crack tip. Wiederhorn et al. also argued that the inhibition of siloxane bond’s transverse vibration and bending possibly by the network modifier, and the relatively more open structure might cause a narrower cohesive width in the glasses with high content of network modifier [19]. A similar effect as the network modifier may have occurred in the BD film structure, in which the -CH3 terminal groups are added to break the siloxane backbone. Lin et al. [20] showed that adding the -CH3 terminal group would (a) reduce the film density, leading to a more open structure; and (b) reduce the Si-O-Si bond angle to less than 144◦, inhibiting the bond vibration and bending. The narrowing of cohesive width due to the -CH3 terminal groups is therefore a possible reason for the occurrence of timedependent fracture at inert environment. Further study is required to understand the effects of the terminal groups on the fracture of the low-k film. 6.5 Conclusions In this work, wedge indentation experiments have been conducted to characterize the time-dependent fracture properties of BD/Si and MSQ/Si systems. It is found that, for BD/Si system, the relationship between the time-to-failure and the maximum indentation load follows an exponential function in all three test environments (ambient, inert and water). However, when water is supplied to the 156 Chapter surface of the BD/Si system during wedge indentation test, the crack growth rate is greatly enhanced, as shown by shortening of the time-to-failure by an order of magnitude. In addition, the resistance of the low-k/Si systems toward time-dependent fracture is found to be highly dependent on their chemical structures. The MSQ film, which has an extra plastic energy dissipation mechanism possibly due to formation of molecular bridging across the fracture surface, is found to be impervious to timedependent fracture. On the contrary, the BD film shows obvious time-dependent fracture behaviors, such as the decrease of the indentation load at onset of fracture due to slow loading rate. Most importantly the time-dependent crack growth still persists in the BD/Si system, when the sample surface is covered with a layer of silicone oil, rendering an inert test environment. A possible explanation for this anomalous phenomena is that the –CH3 group in BD/Si system has disrupted the siloxane network and caused a narrow cohesive width, which may lead to time-dependent crack growth under inert environment. 157 Chapter References: 1. J.J. Vlassak, Y. Lin and T.Y. Tsui, Mater. Sci. Eng. A, 391, p.159-174, (2005). 2. E.P. Guyer and R.H. Dauskardt, Nat. Mater., 3, p.53-57, (2004). 3. E.P. Guyer, M. Patz and R.H. Dauskardt, J. Mater. Res., 21, p.882-894, (2006). 4. R.F. Cook and E.G. Liniger, J. Electrochem. Soc., 146, p.4439-4448, (1999). 5. M.W. Lane, J.M. Snodgrass and R.H. Dauskardt, Microelectron. Reliab., 41, p.1615-1624, (2001). 6. K.B. Yeap, K.Y. Zeng and D.Z. Chi, Acta Mater., 56, p.977-984, (2008). 7. K.B. Yeap, K.Y. Zeng, H.Y. Jiang, L. Shen and D.Z. Chi, J. Appl. Phys., 101, 123531, (2007). 8. D.A. Maidenberg, W. Volksen, R.D. Miller and R.H. Dauskardt, Nat. Mater., 3, p.464-469, (2004). 9. K.B. Yeap, K. Zeng and D. Chi, Mater. Sci. Eng., A, 518, p.132-138, (2009). 10. D.D. Gandhi, M. Lane, Y. Zhou, A.P. Singh, S. Nayak, U. Tisch, M. Eizenberg and G. Ramanath, Nature, 447, p.299-302, (2007). 11. G. Dubois, W. Volksen, T. Magbitang, R.D. Miller, D.M. Gage and R.H. Dauskardt, Adv. Mater., 19, p.3989-3994, (2007). 12. W.Z. Li and T. Siegmund, Acta Mater., 52, p.2989-2999, (2004). 13. Y.W. Zhang, K.Y. Zeng and R. Thampurun, Mater. Sci. Eng. A, 319, p.893897, (2000). 14. E.P. Guyer, J. Gantz and R.H. Dauskardt, J. Mater. Res., 22, p.710-718, (2007). 15. Y.B. Lin, T.Y. Tsui and J.J. Vlassak, Acta Mater., 55, p.2455-2464, (2007). 16. T.A. Michalske and S.W. Freiman, Nature, 295, p.511-512, (1982). 158 Chapter 17. R.F. Cook, Mater. Sci. Eng., A, 260, p.29-40, (1999). 18. R.F. Cook and E.G. Liniger, J. Am. Ceram. Soc., 76, p.1096-1105, (1993). 19. S.M. Wiederhorn, H. Johnson, A.M. Diness and A.H. Heuer, J. Am. Ceram. Soc., 57, p.336-341, (1974). 20. Y. Lin, Y. Xiang, T.Y. Tsui and J.J. Vlassak, Acta Mater., 56, p.4932-4943, (2008). 159 Chapter 7: Wedge Indentations on Hard-Film-Soft-Substrate System This Chapter presents the further development of the wedge indentation method (Section 4.1) to a hard-film-soft-substrate system – a 150nm thick ruthenium dioxide (RuO2) film on a silicon substrate – to determine the interfacial toughness. The RuO2/Si samples are prepared by another PhD student* using DC reactive magnetron sputtering technique. The chemical composition and crystal structure of the RuO2 are also characterized by others and are reported elsewhere [1]. The transition metal oxide, RuO2, has many attractive properties (e.g. low resistivity, high chemical and thermodynamic stability, excellent corrosion resistance and diffusion barrier properties), making it particularly suitable as: (a) the contacts of integrated-circuits with the ferroelectric storage capacitors and the high density dynamic-random-access memory (DRAM); and (b) the electrodes in the thin film microsupercapacitors and the microbatteries for the microelectronic mechanical system (MEMS) [2-4]. The material structure and electrical properties of RuO2 film have been well studied [5-9], but the mechanical and fracture behavior of the film are not fully understood yet [10,11]. During the charge-discharge cycles of a micro-battery, the electrodes (e.g. RuO2 film) may undergo significant volume expansion and contraction due to the formations of new phases in the reaction with lithium, causing the film residual stress build-up and ultimately the interfacial and film cracking. In order to ensure reliable device operation, it is important to understand and improve the mechanical and fracture properties of these thin films. Section 7.1 presents the correlation study on the RuO2/Si system to determine the relation between indentation P-h curve and fracture processes. * Courtesy of Ms. Zhu Jing, PhD student of Associate Prof. Dr. Zeng Kaiyang. 160 Chapter Section 7.2 presents the calculations of the interfacial toughness of the RuO2/Si system, using the wedge indentation method. 7.1 Correlation Study on RuO2/Si System The indentation-fracture correlation study is a crucial step before the interfacial toughness measurement, because it can help to recognize the fracture-related characteristics in a P-h curve and eliminate certain potential errors in the experiment. This section discusses the correlation studies on the wedge indentations on the RuO2/Si system in comparison to the studies of the low-k/Si systems. There are notable similarities in the indentation-fracture correlations of the RuO2/Si and the lowk/Si systems. First, for both systems, the interfacial delamination can be induced without indenter penetration into the Si substrate (Figs.7.1 and 7.2), reducing the strain energy calculation error due to the plastic deformation of the substrate. In addition, pop-ins can be seen in the P-h curves (at penetration depth about 50% of the film thickness) for 90° and 120° wedge indentation tests on both systems (Fig.7.3). On the other hand, conical indentations on the RuO2/Si system show smooth P-h curves (Fig.7.3), similar to that of the Berkovich indentations on the low-k/Si systems (Fig.4.1); this similarity is within expectation, since both conical and Berkovich indenters belong to the axisymmetric indenter type. 161 Chapter C Fig. 7.1: Cross-sectio F C onal images of 90° wedge inddentations oon the RuO O2 film ( (thickness, t = 150 nm m): (a) Interrfacial crack k is found at the pop--in load. (b)) As the i indentation load increaases, minorr film crack ks can be foound at thee end of thee wedge i indentation impression. [1]. Fig. 7.2: (aa) Cross-seectional imaage of 120 F 0° wedge inndentation on the Ru uO2 film ( (thickness, t = 150 nm)), showing the formatiion of interffacial crackk at the pop--in load. ( Plane-vview image of 120° wedge (b) w indeentation on the RuO2 film, show wing no o observable f film crack. [1] 162 Chapter Fig. 7.3: Load versus penetration depth (P-h) curves for the RuO2/Si system: (a) the 90° wedge indentation, (b) the 120° wedge indentation, and (c) the conical indentation [1]. However, there are some important differences between indentation characteristics of the RuO2/Si and the low-k/Si systems. The pop-ins on the P-h curves of low-k/Si systems are attributed to the film central crack, whereas those of RuO2/Si system are related to the interfacial crack. When the indentation load is higher than the pop-in load, the interfacial crack in the RuO2/Si system does not propagate much, but some extension of the film buckling can be easily spotted (Fig.7.1). Unlike the lowk/Si system, during the interfacial crack propagation in the RuO2/Si system, no film crack can be observed on 120° wedge indentation impressions (Fig.7.2), and only minor film cracks can be seen in the two ends of the 90° wedge indentation impression 163 Chapter as the indentation load increases (Fig.7.1). This observation may indicate that the RuO2 film toughness is higher than the RuO2/Si interfacial toughness. 7.2 Interfacial Toughness of RuO2/Si System The interfacial toughness of RuO2/Si system is measured here following the simple analytical methodology presented in Section 4.2. The key parameters in the calculations are summarized in Tables 7.1 – 7.3. The indentation induced stresses of 90° and 120° wedge indentations and conical indentation can be calculated by multiplying the film effective modulus with the volumetric strains, V0/Vc (Eqs. (4.1) – (4.4)). For the conical indentation, the indentation volume, V0 and the interfacial crack volume, Vc are given as V0 = π h3p tan φ , (7.1) and Vc = π a '2 t , (7.2) where hp is the plastic depth, t is the film thickness (150nm), and 2φ is the inclination angle of the conical indenter (90°). The crack radius of the circular-shaped delamination induced by the conical indentation, a’, is determined from the FIB crosssectioning along the radial direction and through the center of the conical indentation 164 Chapter C i impression (Fig.7.4). The T elastic modulus m of the t RuO2 fiilm is determ mined by th he S2–P a analysis (seee details inn Section 4.4.1). Based d on the range of penetration dep pth with c constant values of the ratio P/S2 (9.93nm to o 22.52nm),, the elasticc modulus of o RuO2 f film is founnd to be 2332.74 ± 22.03GPa. Th he elastic modulus m repported for the t bulk R is 2600.30GPa [122]. The valuue is slightly RuO y higher thaan what we found in th his study p possibly duee to the effeects of the softer substrrate. Fig. 7.4: Cross-section F C nal image of the nical indenntation (Pmaax = 6mN) on the R 2/Si system, show RuO wing the cirrcular-shapeed delaminaation and thhe crack raadius, a’ [ [1]. As shown s in Taables 7.1 – 7.3, the ind dentations induced i streesses calcullated for t 90° and 120° wedgge indentatioon and the conical the c indeentation aree much smaller than t respectiive critical buckling stresses; the s hen nce, the intterfacial touughness, Γi can be c calculated u using Eq.(4.5). Γi for 900° and 120°° wedge inddentation aree 0.046±0.003J/m2 a and 0.050±0.004J/m m2, respecttively, whereas Γi for conical indentaation is 0.051±0.00 03J/m2. Thee average values v of Γi determineed from thee three ind dentation t tests are diffferent by abbout 10% only. o The co onsistency in i the Γi meeasurements shown 165 Chapter here suggests that the application of our analysis and experiment methodology (Section 4.2) on the RuO2/Si system should be valid. Table 7.1: Calculations of the interfacial toughness of the RuO2/Si system (90° wedge indentation). Notes: (a) The average value of the long axis length, 2b’ is 5.0μm. (b) The critical buckling stress for the straight-sided buckle is applied. [1] 90° wedge indentation No. Short axis crack length, 2a’ (μm) Indentation plastic depth, hp (nm) Indentation induced stress, ߪ0 (MPa) Critical buckling stress, ߪc (MPa) Interfacial toughness, Γi (J/m2) 1.44 26.0 401.10 8862.58 0.049 1.31 24.4 388.24 10708.84 0.046 1.45 25.4 380.10 8740.76 0.044 1.30 24.6 397.72 10874.23 0.048 1.53 26.0 377.51 7850.59 0.043 Table 7.2: Calculations of the interfacial toughness of the RuO2/Si system (120° wedge indentation). Notes: (a) The average value of the long axis length, 2b’ is 6.6μm. (b) The critical buckling stress for the straight-sided buckle is applied. [1] 120° wedge indentation No. Short axis crack length, 2a’ (μm) Indentation plastic depth, hp (nm) Indentation induced stress, ߪ0 (MPa) Critical buckling stress, ߪc (MPa) Interfacial toughness Γi (J/m2) 1.27 21.6 427.01 11394.04 0.056 1.37 21.6 395.83 9791.38 0.053 1.13 19.4 387.09 14392.24 0.045 1.18 20.1 397.90 13198.40 0.048 1.16 19.9 396.82 13657.44 0.048 166 Chapter Table 7.3: Calculations of the interfacial toughness of the RuO2/Si system (conical indentation). Note: The critical buckling stress for the circular buckle is applied. [1] Conical indentation No. Interfacial crack diameter, 2a’ (μm) Indentation plastic depth, hp (nm) Indentation induced stress, ߪ0 (MPa) Critical buckling stress, ߪc (MPa) Interfacial toughness, Γi (J/m2) 2.29 99.9 317.81 3950.18 0.049 2.27 99.2 317.21 4027.26 0.049 2.26 98.5 313.60 4066.64 0.048 2.15 97.5 336.14 4494.43 0.055 2.17 96.9 323.30 4403.63 0.051 As shown in Fig.7.5, when a high indentation load is applied (Pmax = 40mN), the lateral stress induced by the 90° wedge indentation can cause the Si substrate cracking in the direction normal to the film surface [13]. Strain energy released due to the substrate cracking can affect the accuracy of the interfacial toughness measurement. However, the substrate cracking can only occur after the indentation penetration is deep into the substrate. Therefore, in the interfacial toughness calculations for the 90° and 120° wedge indentations (Tables 7.1 – 7.2), all the key parameters (e.g. crack length and plastic depth) have been taken at the moment when pop-ins appears in the P-h curves (Pmax = 6mN for 90° wedge indentation; Pmax = 10mN for 120° wedge indentation). At the pop-in load, the penetration depth is about 50% of the RuO2 film thickness, so the plastic deformation in the substrate should be small, if not confined within the film. Furthermore, FIB cross-sectional images of the 167 Chapter wedge indentation impression at the pop-in load are showing no observable crack within the Si substrate (Fig.7.1(a)). Fig. 7.5: Cross-sectional image of the 90° wedge indentation on the RuO2 film at Pmax = 40mN, showing the interfacial and substrate cracks as the indenter penetrates deeply into the substrate [1]. 7.3 Conclusions This study has shown the potential application of the wedge indentation experiment and analysis developed in the Section 4.2 to determine the interfacial toughness of a hard-film-soft-substrate structure, such as the RuO2/Si. In the correlation study, pop-ins have been observed on the P-h curves of the wedge indentations with 90° and 120° inclination angles, when the RuO2/Si interface begin to fracture. For 90° wedge indentation, minor film cracking can be observed at the two ends of the wedge impression, as the indentation is increased to higher than the pop-in 168 Chapter load, whereas for 120° wedge indentation, there is no film cracking until complete delamination occurs. By measuring the volumetric strain induced by the indentation, consistent results of the interfacial toughness of RuO2/Si system has been acquired for the 90° and 120° wedge indentations and the conical indentation. As far as our literature review on the RuO2 film, this study has measured the value of interfacial toughness of RuO2/Si system for the first time. The interface between RuO2 and Si is found to be very weak (only about 0.05 J/m2). Further study to enhance the interfacial toughness is required. To improve the interfacial toughness, an adhesion promoter layer could be deposited below the RuO2 film or a substrate material that would allow a better RuO2 film adhesion could be selected. 169 [...]... (nm) Indentation induced stress, 0 (MPa) Critical buckling stress, c (MPa) Interfacial toughness, Γi (J/m2) 1 1.44 26.0 401.10 88 62. 58 0.049 2 1.31 24.4 388 .24 107 08. 84 0.046 3 1.45 25.4 380 .10 87 40.76 0.044 4 1.30 24.6 397.72 1 087 4.23 0.0 48 5 1.53 26.0 377.51 785 0.59 0.043 Table 7.2: Calculations of the interfacial toughness of the RuO2/Si system (120° wedge indentation) Notes: (a) The average value of. .. ε = 0 .8 The errors are standard deviations of the data Experiment Parameters Test Environments Ambient Inert Watered Time-to-Failure, tf (s) 315.52 ± 68. 69 329.00 ± 61.90 38. 24 ± 8. 43 Time of Stage 1, t1 (s) 137.74 ± 10.61 140.57 ± 14.27 12.01 ± 2.69 8. 88 ± 0.99 6. 18 ± 0.94 30.60 ± 13.93 t2A 54.21 ± 12.54 52.50 ± 6. 78 12.59 ± 2.17 t2B 40.26 ± 13.53 53. 18 ± 18. 59 6.15 ± 1 .87 t2C 84 .15 ± 65.05 78. 01 ±... 18. 59 6.15 ± 1 .87 t2C 84 .15 ± 65.05 78. 01 ± 72.34 8. 48 ± 4.22 S2A 6.57 ± 1 .82 7.93 ± 1.22 41.16 ± 9.35 S2B 42.41 ± 15. 48 28. 65 ± 10.56 165 .89 ± 58. 82 S2C 2.76 ± 1.73 3.04 ± 1.09 44.34 ± 22.04 Slope of Stage 1, S1 (×10-5µm/s) Time of Stage 2, t2 (s) Slope of Stage 2, S2 (×10-4µm/s) The influences of test environments on the fracture processes during wedge indentation are studied by comparing the h–t curves... buckle is applied [1] 120° wedge indentation No Short axis crack length, 2a’ (μm) Indentation plastic depth, hp (nm) Indentation induced stress, 0 (MPa) Critical buckling stress, c (MPa) Interfacial toughness Γi (J/m2) 1 1.27 21.6 427.01 11394.04 0.056 2 1.37 21.6 395 .83 9791. 38 0.053 3 1.13 19.4 387 .09 14392.24 0.045 4 1. 18 20.1 397.90 131 98. 40 0.0 48 5 1.16 19.9 396 .82 13657.44 0.0 48 166 ... application of our analysis and experiment methodology (Section 4.2) on the RuO2/Si system should be valid Table 7.1: Calculations of the interfacial toughness of the RuO2/Si system (90° wedge indentation) Notes: (a) The average value of the long axis length, 2b’ is 5.0μm (b) The critical buckling stress for the straight-sided buckle is applied [1] 90° wedge indentation No Short axis crack length, 2a’ (μm) Indentation. .. p.4932-4943, (20 08) 159 Chapter 7: Wedge Indentations on Hard-Film-Soft-Substrate System This Chapter presents the further development of the wedge indentation method (Section 4.1) to a hard-film-soft-substrate system – a 150nm thick ruthenium dioxide (RuO2) film on a silicon substrate – to determine the interfacial toughness The RuO2/Si samples are prepared by another PhD student* using DC reactive... fracture processes * Courtesy of Ms Zhu Jing, PhD student of Associate Prof Dr Zeng Kaiyang 160 Chapter 7 Section 7.2 presents the calculations of the interfacial toughness of the RuO2/Si system, using the wedge indentation method 7.1 Correlation Study on RuO2/Si System The indentation- fracture correlation study is a crucial step before the interfacial toughness measurement, because it can help to... characterized in terms of the (G - v) relation [1-5], to determine the G - v relation from the wedge indentation, more works are therefore needed to determine the dependence of G on Ponset for wedge indentations Fig 6.7: The invert time-to-failure, 1/tf vs the fracture-onset-load, Ponset [9] 150 Chapter 6 6.3 Influences of Test Environments on Fracture Processes Fig 6 .8: At stage 2C of the penetration... the interfacial crack propagation in the RuO2/Si system, no film crack can be observed on 120° wedge indentation impressions (Fig.7.2), and only minor film cracks can be seen in the two ends of the 90° wedge indentation impression 163 Chapter 7 as the indentation load increases (Fig.7.1) This observation may indicate that the RuO2 film toughness is higher than the RuO2/Si interfacial toughness 7.2 Interfacial. .. RuO2/Si interfacial toughness 7.2 Interfacial Toughness of RuO2/Si System The interfacial toughness of RuO2/Si system is measured here following the simple analytical methodology presented in Section 4.2 The key parameters in the calculations are summarized in Tables 7.1 – 7.3 The indentation induced stresses of 90° and 120° wedge indentations and conical indentation can be calculated by multiplying the film . determined using the experimental method are 1 .89 ±0. 28 J/m 2 and 1.92±0. 08 J/m 2 for 90° and 120° wedge indentation, respectively (Section 4.4.2). The BD/Si and the MSQ/Si systems’ interfacial. experimental methodology to characterize interfacial properties by wedge indentation technique are developed and applied to low-k/Si systems to determine the interfacial toughness. The wedge indentation. determination of the interfacial mechanical properties. 5.3 Conclusions From the comparison of the simulation and experimentally obtained P-h curves before the onset of delamination,