Characterization of interfacial mechanical properties using wedge indentation method 8

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 time-dependent fractu

Chapter 5 The interfacial adhesion energy for the same 500 nm thickness BD film

obtained by using the interfacial energy-strength contour (Γ 0=5.58-8.49 J/m2) is slightly higher than the interfacial toughness determined in Section 4.4.3 using the

Chapter 5 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, pop-

in 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, P c 90 /(σyfΔ0 ) and P c 120 /(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 (P c 90 /(σyfΔ0 )=6.78µm and P c 120 /(σyfΔ0 ) =11.31µm) in the interfacial energy – strength contour, it can be found that the interfacial energy, Γ 0

is 2.61J/m2 and interfacial strength, σ strength, 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 Γ 0 = 2.13J/m2 and σ strength = 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 Γ 0 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

Chapter 5 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 4 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 Γ 08.49 J/m2 and σ strength =0.71-0.78 GPa, for the BD/Si system; and Γ 0=2.13-2.61 J/m2

=5.58-and σ strength=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/m 2 for the BD/Si system and Γ0,m=2.37 J/m 2 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

Chapter 5 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 (P c 90 and P c 120), 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

Chapter 5

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)

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 time-dependent fracture properties in terms of a strain energy released rate – crack velocity

Chapter 6

(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 deposited thin film sample for a complete time-dependent properties characterization Cook and Liniger [4] developed an experimental methods using Vickers indentation to

as-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 cross-sectional 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 1 of this thesis, a simple analysis and a straight forward experimental methodology to characterize interfacial properties by wedge indentation

Chapter 6

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 low-

k/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 time-dependent 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

Chapter 6

This section presents two indentation tests (load-holding test and

varying-loading-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

varying-loading-rate tests that are conducted at ambient environment

Chapter 6

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

against holding time, i.e the h-t curves, in general, it follows a consistent S-shaped curve for Pmax =5mN, 6mN and 7mN (Fig.6.1(b)), which can be further divided into three main stages and each of the stages can be related to a fracture process The

details about the h-t curve for BD/Si system are discussed in Section 6.3

On the other hand, the MSQ/Si system has different penetration-time

characteristics in the load-holding tests Fig.6.2 depicts the h-t curves for various Pmax

values (1.4 - 7 mN), and it is obviously resembling a simple creep-like curves consisted of two stages: primary and secondary stages The primary stage shows that

the penetration depth increases in such a way that the penetration rate (dh/dt) decreases

with the holding time; whereas in the secondary stage, the penetration depth increases

with time in an approximately constant displacement rate, dh/dt However, as

confirmed by FESEM and FIB images of the wedge impressions, the increases of penetration depth in the holding segment are less than ~20nm and are restricted to the deformation of the film

Chapter 6

Fig 6.2: The load-holding test results for the MSQ/Si system at ambient environment,

showing the penetration depth - holding time (h-t) curves for different maximum loads, Pmax that assemble simple creep-like curves [9]

As discussed in Section 4.1.1, in a fast loading-unloading test on the MSQ/Si system, film crack initiation occurred at the pop-in load (2mN) and interfacial crack propagation occurred as the indentation load was increased from 3mN to 9mN In contrast to the load-holding test results of BD/Si system, holding at a specific load

below the pop-in load (Pmax = 1.4mN) for more than 20,000s does not lead to the

initiation of film or interfacial crack in the MSQ/Si system Furthermore, when Pmax is holding between 3mN and 7mN, the interfacial crack does not propagate and kink to the film surface; thus, the complete film delamination does not occur in the MSQ/Si system during load-holding tests

Chapter 6

Fig 6.3: The load-holding test results for the BD/Si systems with two different film thickness (300 nm and 500 nm BD films) at ambient environment with indentation load of 5mN The penetration depth is normalized by film thickness [9]

Furthermore, in order to verify whether or not the different time-dependent deformation behaviors in BD and MSQ films are related to the film thickness, the load-holding tests are also conducted on a 300 nm thick BD film Fig.6.3 shows that the two BD films (300 nm and 500 nm thickness) have a similar time-dependent crack

growth behavior, i.e three-stages on the h-t curve and a complete film spall-off from

the substrate after a long holding time (Section 6.3) Therefore, the difference in film thickness may be eliminated from the possible causes of the discrepancy between the BD/Si and the MSQ/Si systems in their load-holding tests results

Chapter 6

Fig 6.4: The varying-loading-rates test results for the MSQ/Si system at ambient

environment, showing the load-penetration (P-h) curves for different loading rates, dP/dt [9]

The second wedge indentation test, i.e varying-loading-rates test, at ambient

environment for the two low-k/Si systems indicates that: (a) for the MSQ/Si system, as the loading rates (dP/dt) decrease, the pop-in loads remain at a constant value (2mN) and the characteristics of the indentation P-h curves do not change much (Fig.6.4); and (b) for BD/Si system, as the loading rates decrease from 242.15µN/s to 5.43µN/s, the P-h curves are similar before the onset of fracture, but the fracture-onset load, Ponset,

decreases from Pcritical at 7.5mN to a threshold load, Pthreshold at 3.14mN (Fig.6.5(a)) Further analysis of the test data for the BD/Si system is presented in Section 6.2 These results show that the crack growth in BD/Si system is dependent on time, whereas the crack growth in MSQ/Si system is not Based on the results from the load-holding tests and the varying-loading-rates tests, it can be concluded that the BD/Si system is susceptible to time-dependent crack growth both within the film and at the interface

Chapter 6

Fig 6.5: The varying-loading-rates test results for the BD/Si system: (a)

load-penetration (P-h) curves for different loading rates, dP/dt, and (b) the plot of onset load, Ponset against loading rate, dP/dt [9]

fracture-Chapter 6 organic-inorganic materials with siloxane network structure that are terminated by methyl group (–CH3), but the two low-k films behave different significantly in the

load-holding and varying-loading-rates tests Recent research works have shown that,

in molecular-level tailoring of silica-based dielectric films, such as MSQ film, molecular bridgings might be formed across the fracture surfaces, and this could improve the interfacial toughness to more than 20J/m2 [8,10,11] Due to the formation

of molecular bridgings behind the crack tip, a greater driving force may be required to stretch and break these molecular bridgings The polymeric molecular bridgings in the pores inside the MSQ film must be relatively unaffected by environments as compared

to the siloxane bonds, so that the crack growth is independent of the time for MSQ/Si system, but this is not for the case of BD/Si system As the occurrence of time-dependent fracture phenomenon at ambient environment are confirmed in the BD/Si system, load-holding and varying-loading-rates tests are further performed at watered and inert environments In Sections 6.2 – 6.3, a qualitative analysis for two wedge indentation tests and the fracture mechanism under the three test environments will be discussed

Chapter 6

Based on the experimental observations of the load-holding and loading-rates tests on BD/Si system, the time-dependent fracture behaviors are described by the following parameters and relationships: (a) the threshold load

varying-(Pthreshold), (b) the relationship between the fracture-onset load and the loading rate

(Ponset - dP/dt), and (c) the relationship between the time-to-failure and the maximum load (tf - Pmax) During the load-holding test at the ambient environment, it is found

that holding at Pmax = 3mN for 20,000s does not lead to any crack formation in the

film; this suggests that there is a threshold load, Pthreshold for time-dependent fracture to

initiate When a very slow loading rate (~5µN/s) is applied in the rates test, Ponset is found to be a constant equals to Pthreshold; the value of Pthreshold for both ambient and inert (sample surface covered by Si oil) environments are therefore

varying-loading-determined to be 3.14mN, while the value of Pthreshold for watered environment (sample surface covered by water) is 2.82mN On the other hand, when a very fast loading rate

(~200µN/s) is applied, Ponset is found to be a constant equals to Pcritical Due to the

decrease of loading rate from 200µN/s to 5µN/s, Ponset decreases from Pcritical to

Pthreshold by 58% for ambient and inert environments, and by 62% for watered

environment For the loading rate in between 5µN/s and 200µN/s, linear relationships between Ponset and the loading rate, dP/dt, can be found in all the test environments

(Fig.6.5(b)), as given by

dP

Chapter 6

where C is the slope of the linear relation For ambient and inert environments the

linear functions are similar, but for the same loading rate, the time-dependent fracture

occurs at much lower Ponset in watered environment The time-to-failure, based on the

duration of time needed for indentation load to reach the Ponset, is related to the slope,

test, Pmax is equivalent to Ponset Following these definitions, the relationship between tf

and Pmax can be determined for all the test environments As can be seen in Fig.6.6, tf

decreases with the increasing of Pmax in an approximately exponential relation At a lower Pmax, the values of tf for ambient and inert conditions are different, but they

converge to the same minimum value of time-to-failure (tmin), as Pmax is increased to

Pcritical For ambient environment, tf increases when Pmax < 4.5 mN, whereas for inert

environment, tf increases only when Pmax < 5.5 mN; this indicates that a higher indentation load is needed at the inert environment On the other hand, when the load-holding test is conducted on the water-covered BD film surface (watered

Chapter 6

environment), the value of tf is at least an order of magnitude shorter than that for ambient and inert environments; this indicates that the time-dependent crack growth

can be significantly enhanced by water molecules For example, at Pmax = 3.5mN, the

tf for inert environment and ambient environment are 2752 ± 1023s and 3088 ± 602s,

respectively; whereas the tf for watered environment is only 187 ± 67s

Fig 6.6: The relationship between the time-to-failure, tf and the maximum load, Pmax

for the BD/Si system at ambient, inert and watered environments [9]

The crack lengths measured from FESEM plan-view images are approximately

the same at different fracture-onset-load, Ponset during the load-holding tests; hence,