Characterization of interfacial mechanical properties using wedge indentation method 5

Chapter 4 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 P

Chapter 4 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) h p (nm) P (mN) h p (nm) P (mN) h p (nm)

Interfacial crack* 15.0 334.0 2.6 242.0 10.0 288.0 Interfacial crack

kinks to film

surface

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

circular-like shaped delamination (Fig.4.6(c)) Table 4.1 shows the indentation load (P) and plastic depth (h p) 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, h p is greater

Chapter 4 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)

Chapter 4

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 indentation-fracture 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

P-h curves for 500 nm BD film TP-he indentations are made witP-h increasing maximum indentation load, P max from 7 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 7 mN to 10 mN [2]

i

c

t

t

h

c

t

i

l

t

s

Fig 4.8: F

indentation

central crack

the 500 nm

the central c

The

have some s

chemical st

tetrahedral s

is a dense P

low-k film w

this work, i

significant p

FESEM pla

loads of (a

k; and (c) 1

BD film w

crack has re

indentation

similarities

tructures B

silica netwo

PECVD dep

with the por

it is found

pop-in even

ane-view im a) 7 mN: on

0 mN: com with a maxim eached to th

n-fracture c but also som Both of the ork structure posited low-res created b that simila

nt on the

P-mages of nly plastic d mplete spall o mum load o

e interface

correlations

me differen

e films are

e terminated

-k film, wh

by removal

ar to the ob

h curve, wh

500 nm B deformation off (d) FIB

of 9 mN sho [2]

for the MS nces; this mi

e hybrid m

d by organic hile the MSQ

of porogen bservations hen indentat

BD film w n; (b) 8.5 m

B cross-secti owing no in

SQ/Si and ight be relat materials co

c (-CH3) en

Q film is a

ns added to

on the MS tion depth i

C

with the m mN: film cor ional view i nterfacial cr

the BD/Si ted to their onsist of in nds, but the porous spin the matrix

SQ film, th

is about 50%

Chapter 4

maximum rner and image of rack, but

systems intrinsic norganic

BD film n-coated [3-5] In here is a

% of the

Chapter 4

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

Chapter 4

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 3 to 9 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 – 9

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

Chapter 4 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 co-workers 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:

Chapter 4

' 0

c

V

E

V

The effective film elastic modulus, E ’ f in Eq (4.1) is given by:

'

f

f

f

E

E

ν

=

or

'

2

f

f

f

E

E

ν

=

In Eqs (4.1) and (4.2), E f is the film modulus, V 0 is the plastic indentation volume, V c

is the volume of thin film above the interfacial crack, and ν f 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 (V 0 /V c)

Eq.(4.1) can be easily converted back to the formula derived by Marshall and

co-workers [9,18], by taking V 0 as the deformation volume by a conical shaped

indenter and interfacial crack area, A c 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 V 0

as the deformation volume by a wedge shaped indenter and A c as rectangular shape (Appendix B) It should be noticed that the two types of indenter tips (conical and

Chapter 4 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 fine-line 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

Chapter 4

Fig 4.9: Configuration of cracks during the steady state propagation of interfacial

crack [19] Solid-line shows the elliptical-shape delamination Normal T n and shear traction T s 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

' '

c

and