Characterization of interfacial mechanical properties using wedge indentation method 5

Chapter Table 4.1: Indentation load and plastic depth that are associated with the crack profiles induced by the wedge and the Berkovich indentations on the MSQ/Si system [1]. Crack Profiles Berkovich indentation 90° Wedge indentation 120° Wedge indentation P (mN) hp (nm) P (mN) hp (nm) P (mN) hp (nm) Central crack 15.0 334.0 2.0 200.0 6.0 240.0 Corner crack 15.0 334.0 2.6 242.0 8.0 280.0 Interfacial crack* 15.0 334.0 2.6 242.0 10.0 288.0 Interfacial crack kinks to film surface 30.0 431.0† 9.0 355.0 15.0 358.0 Further analysis on cross-sectional view and plane view images of the Berkovich indentation impressions (Fig.4.6) shows that the fracture processes induced by the wedge and the Berkovich indentations are dissimilar in several aspects: (a) the Berkovich indentation does not lead to any pop-in event (Figs.4.1(c) and 4.6(b)), when a central crack forms; (b) the corner cracks propagations are found along the radial direction of the Berkovich indentation impression and are originated from the impression corners (Fig.4.6(b)); and (c) the Berkovich indentation induces a circularlike shaped delamination (Fig.4.6(c)). Table 4.1 shows the indentation load (P) and plastic depth (hp) that are associated with the crack profiles induced by the Berkovich and the wedge indentations. As can be seen, the Berkovich indentation on the MSQ film (400nm thick) at indentation load 30mN has an indentation plastic depth greater than the film thickness, resulting in the plastic deformation of the Si substrate. The * The interfacial crack was observed from the FIB sectioning perpendicular and at the middle of the indent. † MSQ film thickness is 400nm. The Berkovich indentation plastic depth, hp is greater than film thickness, when indentation load is 30mN. 73 Chapter substrate plastic deformation during the interfacial delamination will affect the strain energy release rate; thus the analysis methodology developed to determine interfacial toughness (Section 4.2) may give less accurate results for the Berkovich indentation. The crack profiles for 90° and 120° wedge indentations on the MSQ/Si system are found to be similar, with minor differences in the indentation load and the plastic depth that are associated to the cracks (Table 4.1). Comparing the FIB cross-sectional images at the center of the indentation impression, it is found that: (a) for the 120° wedge indentation, the corner crack (8mN) appears prior to the interfacial crack (10mN) (Fig.4.3(a)); and (b) for the 90° wedge indentation, both the corner crack and the interfacial crack are observed to initiate simultaneously at ~3mN (Fig.4.2(b)). Before the complete spall-off of the film from substrate, the interfacial crack length for the 120° wedge indentation (2a’ ≈ 3.92µm*) is found to be greater than that for the 90° wedge indentation (2a’ ≈ 3.01µm). Nevertheless, for both 90° and 120° wedge indentations, it is reasonable to make the assumption that the Si substrate does not undergo any plastic deformation, because the indentation plastic depths are generally less than the film thickness even when the interfacial crack kinks to the film surface (Table 4.1). Comparing to the Berkovich indentation, the wedge indentations have greater interfacial crack driving force; therefore, it can confine the indentation plastic zone within the film. In conclusion, the wedge tips have been identified as the most suitable indenter geometry to characterize the interfacial toughness of thin film systems with brittle interface. * 2a’ is the short-axis crack length of the elliptical shaped delamination, as shown in Fig.4.4(d). 74 Chapter 4.1.2 The Correlation Studies on the BD/Si System A correlation study similar to that on the MSQ/Si system is conducted on the BD/Si system to confirm the crack configuration and to compare the indentationfracture correlations for the BD/Si and the MSQ/Si systems. It is important to note that the intrinsic chemical structure of BD/Si and MSQ/Si are different, and this might be reflected by the indentation-fracture correlation. Fig. 4.7 shows the nanoindentation Ph curves for 500 nm BD film. The indentations are made with increasing maximum indentation load, Pmax from to 10 mN using a 90° wedge tip. The P-h curves for BD films with other thickness will not be presented, as the discussions on the correlation are similar. Fig. 4.7: Load-penetration depth (P-h) curves for the 500 nm BD film with the maximum indentation loads varying from mN to 10 mN. [2] 75 Chapter C Fig. 4.8: FESEM F F plaane-view im mages of 500 nm BD B film w with the maximum m i indentation loads of (aa) mN: onnly plastic deformation d n; (b) 8.5 m mN: film corrner and c central crackk; and (c) 10 mN: com mplete spall off. o (d) FIB B cross-sectiional view image i of t 500 nm BD film with the w a maxim mum load of o mN shoowing no innterfacial crrack, but t central crack the c has reeached to the interface. [2] The indentationn-fracture correlations c for the MS SQ/Si and the BD/Si systems h have some similarities s but also som me differen nces; this miight be relatted to their intrinsic c chemical sttructures. Both B of thee films aree hybrid materials m coonsist of in norganic t tetrahedral s silica netwoork structuree terminated d by organicc (-CH3) ennds, but the BD film i a dense PECVD is P depposited low--k film, wh hile the MSQ Q film is a porous spin n-coated l low-k film with w the porres created by b removal of porogenns added to the matrix [3-5]. In t this work, it i is found that similaar to the ob bservations on the MS SQ film, th here is a s significant p pop-in evennt on the P-h curve, wh hen indentattion depth iis about 50% % of the 76 Chapter BD film thickness. The actual critical load for interfacial crack initiation is slightly higher than the pop-in load. The pop-in during wedge indentation on the BD film, however, is much pronounced compared to that on the MSQ film. FESEM plane-view imaging, and FIB sectioning and imaging are performed on the indentation impressions to relate the delamination processes and the characteristics of the P-h curves. Similar to the findings for the MSQ film, before the pop-in event (7 mN), there is no observable crack on the film surface (Fig.4.8(a)), and as the pop-in occurs (8.5 mN), central and corner cracks can be clearly spotted in the film (Fig.4.8(b)); this suggests that the pop-in on the indentation P-h curve is associated with both the central and corner cracks. Further increasing the indentation load to that above the pop-in load (10 mN) will cause a complete delamination (Fig.4.8(c)). In addition, the FIB sectioning at the middle of wedge indentation impression right before the completion of pop-in (9 mN) does not show any interfacial crack, but the central crack has obviously reached the BD/Si interface (Fig.4.8(d)). Therefore, it can be concluded that the interfacial crack has been formed, propagated and kinked to the film surface instantaneously at the critical indentation load slightly above the pop-in load (~10 mN), preventing any observation of the interfacial fracture process by the FIB sectioning and imaging method. This sequence of interfacial crack initiation and propagation processes is significantly different from that observed in the MSQ film. During the wedge indentation on the porous MSQ film, the interfacial crack is initiated at a lower load (3 mN), then propagates slowly with increasing load and finally kinks to the film surface at a much greater load (9 mN). In other words, for the MSQ film, there is a visible crack-propagation process (under FIB sectioning) before the film around the indentation impression spalls off from the surface. However, for the BD film, fracture occurs instantaneously with almost constant indentation load. 77 Chapter These differences between the BD and the MSQ films, in terms of the crack initiation and propagation processes, can be explained by the differences in the chemical bonding and structure of the films due to their different fabrication methods [5,6]. As reported by Maidenberg et al. [5], porogen remnants within the pores of the MSQ film might generate molecular bridgings behind the crack tip, and hence a greater driving force was needed to stretch and break these bridgings to propagate the cracks further. It is therefore possible that due to the energy dissipation provided by stretching of molecular bridgings, further increases of indentation load (from to mN) are required for the film crack and the interfacial crack propagations in the MSQ/Si system. For the BD/Si system, however, both the film and interfacial cracks are initiated and propagated instantaneously at approximately the same load (7.5 – mN for film crack and ~10 mN for interfacial crack), which suggests the lack of energy dissipation mechanisms that can slow down the crack-propagation process. 4.2 Mechanics of Interfacial Adhesion The fracture and failure of thin film/substrate systems can occur in a number of patterns, such as surface crack, channeling, substrate damage, spalling and debonding [7,8]. To characterize the interfacial adhesion properties (e.g. interfacial energy and interfacial strength), the interfacial cracking pattern is of particular interest. The wedge and the conical indentation methods have been used to determine the interfacial toughness of various thin film/substrate systems, including ZnO/Si [9], diamond/titanium alloys [10], W/SiO2 [11] and low-k/SiO2 systems [12]. For the 78 Chapter systems with strong interface, a significant penetration into the substrate is usually needed to cause interfacial delamination, whereas for the systems with brittle interface, interfacial delamination can occur as the indenter tip penetrates within the film. Therefore, the analysis methodology to determine interfacial toughness is different for the system with strong interface [10,13-16] and the system with brittle interface [9,11,17,18] (Section 2.2). For the systems with brittle interfaces, de Boer and Gerberich have followed the analysis originally developed by Marshall and coworkers for conical indentation [9,18], and have developed the analysis for microwedge indentation test on thin metallic lines [11,17]. In this study, i.e. the wedge indentation test on continuous low-k films, the interfacial delamination occurs when indentation depth is less than the film thickness; therefore, the analyses developed for system with brittle interface should be adopted here [9,11,17,18]. However, certain modifications on the analyses are necessary, as the delamination crack shapes observed for these three indentation experiments are generally different: (a) for conical indentation, it is a circular shape; (b) for microwedge indentation on thin metallic lines, it is a rectangular shape; and (c) for wedge indentation on continuous film, the shape of the delamination cracks is closed to an elliptical shape (Fig.4.4(d) and 4.5(d)). The remaining of this section will therefore present the derivation of the new analysis methodology and the crack configuration for the interfacial crack propagation during the wedge indentations on a continuous film. Following the interfacial fracture mechanics analysis developed by Marshall et al. [9,18] and de Boer and Gerberich [11,17], we have generalized the expression for the indentation induced stress in terms of the ratio of the indentation deformation volume to the volume of the materials above the interfacial delamination crack: 79 Chapter σ = E 'f V0 . Vc (4.1) The effective film elastic modulus, E’f in Eq. (4.1) is given by: E 'f = Ef 2(1 −ν f ) (For Conical Indentation) (4.2a) (For Wedge Indentation) (4.2b) or E 'f = Ef (1 −ν 2f ) In Eqs. (4.1) and (4.2), Ef is the film modulus, V0 is the plastic indentation volume, Vc is the volume of thin film above the interfacial crack, and νf is the Poisson’s ratio of the film (assumed the value to be 0.34). Since the wedge indenter only penetrates into the film, the interfacial delamination is therefore caused by the volumetric strain of the thin film (V0/Vc). Eq.(4.1) can be easily converted back to the formula derived by Marshall and co-workers [9,18], by taking V0 as the deformation volume by a conical shaped indenter and interfacial crack area, Ac as circular shape. Likewise, Eq.(4.1) can also be converted back to the formula derived by de Boer and Gerberich [11,17], by taking V0 as the deformation volume by a wedge shaped indenter and Ac as rectangular shape (Appendix B). It should be noticed that the two types of indenter tips (conical and 80 Chapter wedge) create different stress-strain fields during indentation. Microwedge indentation created a plane strain condition, while conical indentation created a plane stress condition. Despite these differences, the functional form of the indentation induced stress in the films is the same for both cases. Even though the MSQ and BD films in our study are not fabricated in a fineline shape, the analysis proposed for microwedge indentation method [11,17] can still be applicable. When a wedge-tip with a very long length is indented on a continuous film, the wedge indentation can induce a plane-strain condition at the central portion of the impression, but at the ends of the wedge-tip’s length, the stress-strain condition is non plane-strain. The extent of the plane strain region is dependent on the film’s thickness and the wedge length, and can be estimated by measuring the curvature of crack front (Section 4.3). When the ratio between wedge length and film’s thickness, l/t ratio is greater than 25, the crack front curvature is found to be extremely straight, i.e. the plane strain region has dominated most part of the crack front. In this case, the calculation scheme proposed for the plane strain condition, as in the analysis of microwedge indentation [11,17], can be used without much error. However, when l/t ratio is less than 25, the shape of delamination will change from rectangular shape to elliptical shape; and consequently, there might be some errors due to the emergence of the non plane-strain regions along the length of wedge indenter. The effects of l/t ratio on the interfacial toughness measurement will be discussed in Section 4.4.3. 81 Chapter Fig. 4.9: Configuration of cracks during the steady state propagation of interfacial crack [19]. Solid-line shows the elliptical-shape delamination. Normal Tn and shear traction Ts are acting on the crack front, while there is no contact or no traction at the corner crack surface. Dashed line shows the displacement of the film above the interfacial crack, δ, due to the indentation induced stress. Bulge-out at the corner crack might happen during the indentation, causing a minor error in the calculation [1]. From the crack patterns observed in the FESEM images (Figs.4.4(d) and 4.5(d)) and the schematic illustration in Fig.4.9, it can be deduced that if we consider the real shape of the interfacial crack, using Eq.(4.1), the contribution of the non plane-strain region can be taken into consideration. In the initial study, we have assumed the shape of the interfacial crack area as an elliptical shape [1]. Hence, the interfacial crack area and the volume of the thin film above the interfacial crack are given as Ac = π a ' b ' , (4.3a) and 82 Chapter Vc = Act , (4.3b) where 2a’ is the short axis length, 2b’ is the long axis length and t is the film thickness (Fig.4.4(d)). In the later study (Section 4.4.3), the Scion image analyzing software is used to accurately measure the interfacial crack area from the plane view image of the delamination crack. As can be seen in Fig. 4.9, there are normal and shear tractions acting at the interfacial crack front, while at the sidewall of the corner crack, there is no contact between the remaining film and the film above the crack. When the film above the interfacial crack (shown schematically by the full line in Fig.4.9) is subjected to indentation induced stress, it will be displaced in the X1 direction (shown by the dashed line in Fig.4.9). When the corner crack angle, θ, is equal to zero, the shape of the interfacial crack area is the same as that in the analysis of de Boer and Gerberich [11,17], which is rectangular shaped, and the crack area is determined by multiplying the interfacial crack length and the wedge tip length. When θ is non-zero, the average strain or volumetric strain for the film above the interfacial crack is given by the volume ratio V0/Vc, with a small error at the sidewall of the corner crack possibly due to the plastic deformation at the corner crack (as shown by the bulge-out in Fig.4.9). A numerical study will be needed to further understand this error and to match the crack shape between experimental and numerical studies [19,20]. By assuming that the material in the plastic zone around the wedge tip is incompressible and the volume displaced is conservative, the indentation volume is given as 83 Chapter V0 = δ tl = lh2p tan φ . (4.4) For simplification, it is assumed that the indentation induced stress is the only stress causing the interfacial delamination. The effects of residual stress are ignored in this analysis. For the case of no buckling, the interfacial toughness Γi can be given as Γi = Gc = (1 −ν 2f )tσ 02 2E f . (4.5) In Eqs.(4.4) and (4.5), δ is the displacement of the film above the interfacial crack in the X1 direction due to the indentation induced stress (Fig.4.9), hp is the indentation plastic depth, l is the length of the wedge tip, t is the thickness of the thin film, and 2φ is the inclination angle of the wedge indenter tip. The indentation plastic depth hp can be determined by linear-fitting the top 30% of the indentation unloading curve and then extrapolating to the depth axis. There are three possible buckling-situations when the interfacial crack propagates under the indentation induced stress. The film above the interfacial crack may show (a) no buckling, (b) single-buckling, or (c) double-buckling [9,11,17,18]. It is dependent on the magnitudes of the indentation induced stress and the critical buckling stress* of the film. If the indentation induced stress reaches the critical buckling stress, the film above the interfacial crack is expected to buckle. Strain energy is released when buckling happens [9,11,17,18]. Thus, to quantify the work of * Critical buckling stress is the critical value of in-plane compressive stress, above which buckling could occurs. 84 Chapter fracture or interfacial adhesion, the strain energy associated with buckling has to be taken into consideration. As reported by Moon et al. [21], Thouless et al. [22] and Hutchinson et al. [23] the critical buckling stress for the straight sided buckles in the plane strain condition is π2 ⎛ E σc = ⎜ f 12 ⎜⎝ −ν f ⎞ ⎛ t ⎞2 ⎟⎟ ⎜ ⎟ . ⎠⎝ a' ⎠ (4.6) For a clamped circular-plate in the plane stress condition, the critical buckling stress is 1.488σc, which is around 50% higher than that for the straight-sided buckles (Eq.(4.6)). For the crack configuration in Fig.4.9, which is approximately elliptical shape, it can be predicted that the critical buckling stress should be somewhat between that of the circular and the straight sided buckles. Section 4.3 presents an appropriate way to estimate the critical buckling stress for the elliptical delamination shapes in the BD/Si systems. Nevertheless, in the initial study, the critical buckling stress has been approximated according to the shape of the crack front. For instance, the critical buckling stress for straight sided buckles will be used if the crack front is parallel to the wedge indentation impression, while for the curved crack front, critical buckling stress for circular buckles will be used. Taking the post-buckling slope to be zero, the Gc is given by de Boer and Gerberich [17] as t (1 −ν 2f ) ⎡ Γi = Gc = 4σ 0σ c − (σ c ) ⎤ , ⎢ ⎣ ⎦⎥ 2E (4.7) f where σc is the critical buckling stress for either straight sided or circular buckles. 85 Chapter Fig. 4.10: Formation of an edge crack on the interface of a thin film/substrate structure and the conventions for interfacial fracture mechanics analysis (Fig.57 of ref. [7]). Fig. 4.11: Conventions for interfacial fracture mechanics analysis (Fig.5 of ref. [7]). The approach given by Hutchinson and Suo [7] is implemented to estimate the phase angle of the steady state crack propagation in the low-k/Si interface. The phase angle ψ is given by tanψ = 12M cos ω + tΔN sin ω , − 12M sin ω + tΔN cos ω (4.8) 86 Chapter parameters (α and β) and the relative height η. In determining these three parameters: α, β and η, the conventions in Fig.4.11 are used. Firstly, the low-k films are extremely compliant as compared to the Si substrate. Therefore, α is close to −1. Subsequently, for a plane strain condition, β = α /4 when ν1 = ν2 = 1/3. Finally, the film thickness (400 nm) is extremely thin as compared to the substrate thickness (1.5 mm); thus, η=0. These values of α, β and η give ω =56° by referring to Fig.4.12. Fig. 4.12: Phase factor, ω(α, β) in Eq. 4.8 (Fig.58 of ref. [7]). Prior to buckling, M = 0; thus, ψ = ω = 56°. de Boer and Gerberich [17] have shown that phase angle would change when buckling occurs. In the case of low-k films, however, due to the constraints at the two ends of the wedge indentation and the small residual tensile stress (about 10 to 20MPa), the extent of buckling should be limited. Hence, the total moment/unit length ∑M is closed to zero. Therefore, it is highly possible that the changes of the phase angle are insignificant. ψ will probably remain at 56° until the crack starts to kink into the film. On the other hand, for thin films with high compressive residual stress, buckling could occur when the superimposed of indentation induced stress and residual stress is greater than the 87 Chapter critical buckling stress. Huang et al. have calculated the phase angle as a function of the delamination crack radius, presuming that buckling occurs during an axisymmetric indentation induced delamination [24]. For the wedge indentation on a continuous film, finite element simulation* will be needed to determine the changes of phase angle angle due to film buckling [25], and the effects of phase angle to the interfacial toughness should be considered in the future FEM simulations. 4.3 Curvature of the Crack Front From the initial research works, it was found that the interfacial crack in thinner film has a straighter front, whereas the crack in thicker film has a curved crack front. For instance, when a 120° wedge indenter tip was indented on 200 nm and 500 nm BD films, the interfacial crack front was found to be parallel to the length axis of the wedge indentation impression on the 200 nm BD film, and a curved interfacial crack front was found for the wedge indentation on the 500 nm BD film (Fig.4.13) [1]. These changes in the delamination crack shape due to the different film thickness have led to the discussion on the dependence of critical buckling stress on the film thickness. It is known that the critical buckling stress for a circular buckle is about 50% higher than that for a straight buckle [9,11,17,18]; therefore, in order to determine the critical buckling stress for different film thickness, the curvature of the delamination crack front has to be measured. After determining the critical buckling stresses for the films with different thickness, one can then verify the delamination mode, i.e. with or without buckling, by comparing the critical buckling stress with the * Courtesy of Mr. Chen Lei, PhD student of Associate Prof. Dr. Zeng Kaiyang 88 [...]... Γi = Gc = 2 (1 −ν 2 )tσ 0 f 2E f (4 .5) In Eqs.(4.4) and (4 .5) , δ is the displacement of the film above the interfacial crack in the X1 direction due to the indentation induced stress (Fig.4.9), hp is the indentation plastic depth, l is the length of the wedge tip, t is the thickness of the thin film, and 2φ is the inclination angle of the wedge indenter tip The indentation plastic depth hp can be determined... or circular buckles 85 Chapter 4 Fig 4.10: Formation of an edge crack on the interface of a thin film/substrate structure and the conventions for interfacial fracture mechanics analysis (Fig .57 of ref [7]) Fig 4.11: Conventions for interfacial fracture mechanics analysis (Fig .5 of ref [7]) The approach given by Hutchinson and Suo [7] is implemented to estimate the phase angle of the steady state crack... substrate thickness (1 .5 mm); thus, η=0 These values of α, β and η give ω =56 ° by referring to Fig.4.12 Fig 4.12: Phase factor, ω(α, β) in Eq 4.8 (Fig .58 of ref [7]) Prior to buckling, M = 0; thus, ψ = ω = 56 ° de Boer and Gerberich [17] have shown that phase angle would change when buckling occurs In the case of low-k films, however, due to the constraints at the two ends of the wedge indentation and the... zone around the wedge tip is incompressible and the volume displaced is conservative, the indentation volume is given as 83 Chapter 4 1 V0 = δ tl = lh2 tan φ p 2 (4.4) For simplification, it is assumed that the indentation induced stress is the only stress causing the interfacial delamination The effects of residual stress are ignored in this analysis For the case of no buckling, the interfacial toughness... calculated the phase angle as a function of the delamination crack radius, presuming that buckling occurs during an axisymmetric indentation induced delamination [24] For the wedge indentation on a continuous film, finite element simulation* will be needed to determine the changes of phase angle angle due to film buckling [ 25] , and the effects of phase angle to the interfacial toughness should be considered... simulations 4.3 Curvature of the Crack Front From the initial research works, it was found that the interfacial crack in thinner film has a straighter front, whereas the crack in thicker film has a curved crack front For instance, when a 120° wedge indenter tip was indented on 200 nm and 50 0 nm BD films, the interfacial crack front was found to be parallel to the length axis of the wedge indentation impression... linear-fitting the top 30% of the indentation unloading curve and then extrapolating to the depth axis There are three possible buckling-situations when the interfacial crack propagates under the indentation induced stress The film above the interfacial crack may show (a) no buckling, (b) single-buckling, or (c) double-buckling [9,11,17,18] It is dependent on the magnitudes of the indentation induced stress... Scion image analyzing software is used to accurately measure the interfacial crack area from the plane view image of the delamination crack As can be seen in Fig 4.9, there are normal and shear tractions acting at the interfacial crack front, while at the sidewall of the corner crack, there is no contact between the remaining film and the film above the crack When the film above the interfacial crack (shown... buckling stress* of the film If the indentation induced stress reaches the critical buckling stress, the film above the interfacial crack is expected to buckle Strain energy is released when buckling happens [9,11,17,18] Thus, to quantify the work of * Critical buckling stress is the critical value of in-plane compressive stress, above which buckling could occurs 84 Chapter 4 fracture or interfacial adhesion,... subjected to indentation induced stress, it will be displaced in the X1 direction (shown by the dashed line in Fig.4.9) When the corner crack angle, θ, is equal to zero, the shape of the interfacial crack area is the same as that in the analysis of de Boer and Gerberich [11,17], which is rectangular shaped, and the crack area is determined by multiplying the interfacial crack length and the wedge tip . the interfacial adhesion properties (e.g. interfacial energy and interfacial strength), the interfacial cracking pattern is of particular interest. The wedge and the conical indentation methods. crack * 15. 0 334.0 2.6 242.0 10.0 288.0 Interfacial crack kinks to film surface 30.0 431.0 † 9.0 355 .0 15. 0 358 .0 Further analysis on cross-sectional view and plane view images of the. 90° Wedge indentation 120° Wedge indentation P (mN) h p (nm) P (mN) h p (nm) P (mN) h p (nm) Central crack 15. 0 334.0 2.0 200.0 6.0 240.0 Corner crack 15. 0 334.0 2.6 242.0 8.0 280.0 Interfacial