Interface Characterization and Failure Modeling for Semiconductor Application

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i

Interface Characterization and Failure Modeling for Semiconductor Application

Proefschrift

Ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben voorzitter van het College voor Promoties,

in het openbaar te verdedigen op vrijdag, 30. november 2012 om 12:30 uur

door AN XIAO

Werktuigbouwkundig Ingenieur Geboren TianJin China

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Dit proefschrift is goedgekeurd door de promotor: Prof. Dr. Ir. L. J. Ernst

Copromotor: Dr. Ir. K. M. B. Jansen, Technische Universiteit Delft

Samenstelling Promotiecomissie:

Rector Magnificus voorzitter

Prof. Dr. Ir. L J. Ernst Technische Universiteit Delft, promotor Dr. Ir. K. M. B. Jansen Technische Universiteit Delft, copromotor Prof. Dr. Ir. G.Q. Zhang Technische Universiteit Delft

Prof. Dr. A. Dasgupta University of Maryland

Prof. Dr. Ing. B. Wunderle Technische Universiteit Chemnitz

Prof. Dr. D. G. Yang Guilin University of Electronic Technology H. Pape (Dipl. Phys.) Infineon Technologies AG

Reserve:

Prof. Dr. ir. F. van Keulen Technische Universiteit Delft

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.

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iii

Samenvatting

Door het feit dat micro elektronica is opgebouwd uit verschillende materialen met sterk verschillende thermo-mechanische eigenschappen, is de interface tussen twee naburige materialen in het algemeen de plaats waar delaminatie gerelateerd falen zeer waarschijnlijk zal optreden. Falen van deze interfaces leidt tot verminderde betrouwbaarheid en prestaties van micro-elektronische componenten. Daarom is adequate kennis van delaminatie voorspelling gewenst. Teneinde in staat te zijn om delaminatie groei te voorspellen dient de incrementele energie die vrijkomt bij een incrementele groei van de delaminatie, de “Energy Release Rate“ G, eerst te worden berekend. De waarde kan worden vergeleken met de “Critical Energy Release Rate”, of wel the zogenoemde interface taaiheid Gc. Deze interface taaiheid kan

worden verkregen door middel van een gecombineerde experimentele en numerieke aanpak. De metingen zijn gecompliceerd omdat de “critical energy release rate” temperatuur, vochtigheid en spanningstoestand (mode mix) afhankelijk is. Bovendien is de voorspelling van delaminatie sterk afhankelijk van de nauwkeurigheid van het materiaal model dat wordt gebruikt in de simulaties. In het bijzonder is een nauwkeurig materiaalmodel nodig voor de berekening van de spanningen en vervormingen als gevolg van het afkoelen vanaf de “molding”- temperatuur en te gevolge vocht opname. Het succes van het analyseren en voorspellen van interface delaminatie problemen in micro-elektronische componenten is sterk afhankelijk van de nauwkeurigheid van de bepaalde “critical energy release rate”.

Het doel van dit onderzoek is om een testmethode te bouwen voor het bepalen van de delaminatie sterkte van interfaces tussen “epoxy molding compound” (EMC) en “copper lead frame”. Uit diverse test mogelijkheden, is de zogenaamde “Mixed Mode Bending” setup gekozen als basis voor de methode ontwikkeling. Gerealiseerd dient te worden dat voor een interface delaminatie, als gevolg van het verschil in thermo-mechanische eigenschappen van de naburige materialen en ook vanwege de aanwezige restspanningstoestand de scheur altijd groeit onder “mixed mode” condities. De proefstukken worden gesneden uit elektronische componenten die zijn vervaardigd met het reguliere productieproces. Als gevolg hiervan zijn de proefstukafmetingen relatief klein en daarom is een speciale proefopstelling van klein formaat gerealiseerd. De testopstelling voorziet in de mogelijkheid om twee afzonderlijke belastingen (Mode I en Mode II) op een enkel proefstuk aan te brengen. De proefopstelling

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is flexibel en aanpasbaar voor het meten aan proefstukjes met verschillende afmetingen. Voor metingen onder verschillende temperatuur en vochtigheids condities is een speciale klimaatkamer ontworpen. De "momentane scheurlengte" is nodig voor de interpretatie van de resultaten door FEM-breukmechanica simulaties. Daarom wordt tijdens het testen de momentane scheurlengte geregistreerd met behulp van een CCD-camera. Teneinde de interface breuktaaiheid nauwkeurig te kunnen vaststellen, worden eerst de visco-elastisch materiaal eigenschappen van de toegepaste “molding compound” vastgesteld en vervolgens toegepast in de FEM simulaties. Een speciale belastingprocedure wordt gebruikt om het breukgedrag te onderzoeken in het visco-elastische overgangs (temperatuurs) gebied van de EMC. De kritische breukeigenschappen worden verkregen door het interpreteren van de experimentele resultaten door middel van geschikte eindige elementen modellering. De (stress)-mode mixity is gedefinieerd als de verhouding tussen mode I (trek-) en mode II (afschuif-) belasting op de interface nabij de scheurtip. In de huidige studie wordt de mode mixity op alternatieve wijze verkregen, gebruik makend van de scheur openingsverplaatsingen in de nabijheid van de scheurtip. Het eindige elementen (FEM) model gebruikt om het visco-elastisch materiaal gedrag te simuleren zal worden besproken. De delaminatie taaiheid (critical energy release rate) als functie van de mode mixity bij verschillende temperaturen zal worden gegeven in de resultaten sectie.

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1

Summary

Due to the fact that microelectronics is made up from various materials with highly dissimilar thermo-mechanical properties, generally the interface between two adjacent materials is the place where delamination related failure most likely would occur. Failure of these interfaces results in decreased reliability and loss of performance of microelectronic components. Therefore, adequate knowledge of delamination prediction is desirable. To be able to predict delamination growth the incremental energy being released when a crack propagates over an incremental crack area growth, the “Energy Release Rate’’ G, should be firstly calculated. The value can be compared with the “Critical Energy Release Rate” or so-called interface toughness Gc. This interface toughness can be obtained through combined

experimental and numerical approaches. The measurements are complicated due to the fact that the critical energy release Rate is temperature, moisture and stress state (mode mixity) dependent. Moreover, the prediction of delamination depends very much on the accuracy of the material model used in the simulations. In particular an accurate material model is necessary to calculate the stresses and strains due to cooling down from the molding temperature and due to moisture absorption. The success of analyzing and predicting the interfacial delamination problems in microelectronic components strongly depends on the accuracy of the established critical interfacial energy release rate.

The goal of this research is to build a test method for establishing the delamination strength of interfaces between epoxy molding compound (EMC) and copper lead frame. Among various test method possibilities, the so-called mixed mode bending (MMB) test method was selected as a base of the method development. It should be realized that for an interface delamination, due to the mismatch in thermal-mechanical properties of the materials adjacent to the interface and also because of the residual stress state the crack will always propagate under mixed mode conditions. The test samples are cut from electronic components being fabricated with the regular production process. Consequently, the specimen dimensions are relatively small and therefore, a dedicated small-size test set-up was realized. The test setup allows the possibility to transfer two separate loadings (mode I and mode II) on a single specimen. The test setup is flexible and adjustable for measuring specimens with various dimensions. For measurements under various temperatures and moisture conditions, a special climate chamber is designed. The “current crack length” is required for the interpretation of measurement

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results through FEM-fracture mechanics simulations. Therefore, during testing the “current crack length” is captured using a CCD camera. In order to be able to establish the interface fracture toughness accurately, the viscoelastic material properties of the applied molding compound are first established and subsequently considered in the FEM simulations. A special loading procedure is used to investigate the fracture properties in the viscoelastic transition (temperature) region of the EMC. The critical fracture properties are obtained by interpreting the experimental results through dedicated finite element modeling. The (stress) mode mixity is defined as a ratio of mode I (tensile-) to mode II (shear-) loading on the interface near the crack tip. In the present study the mode mixity is obtained through an alternative manner, using the crack opening displacements ahead of the crack tip. The FEM model used to simulate the viscoelastic material behavior will be discussed. The delamination toughness (critical energy release rate) as a function of mode mixity at different temperatures will be given in the result section

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Chapter 1

1. _Introduction

Microelectronic devices have pervaded our lives for the past several decades, with massive penetration into health, mobility, security, communication, education, entertainment, etc. Nowadays, the ongoing challenges for such microelectronic devices are IC miniaturization, increasing functionality, low cost and short time to market. To master these challenges, the trends of microelectronic devices are to integrate more systems on chip (SoC) and more systems in package (SiP). These integrations give high design complexity and risks to the manufacturers, caused by more interfaces, new materials, more cost and time consuming development.

It was found that approximately 65% of all failures can be attributed to thermo-mechanical related effects during manufacturing and processes. In most cases, these thermo-mechanical reliability problems originate from the design phase of product and process. Examples of these failures are cracks, voids, delamination, wire fatigue, and many more. Thermal-mechanical reliability is becoming one of the major bottlenecks for both current and future microelectronic technologies [13].

To understand interfacial delamination related failure in IC packages, that is caused by thermal-mechanical loading, the extension of fracture mechanics application from cracking in homogenous material to bi-material interface delamination problems has become of great interest. The bi-material interface delamination theory is widely used experimentally and numerically. It enables the prediction of interfacial delamination related failures of IC packages in qualification tests to enable a designer to design more reliable IC packages. On the other hand, the experimental methodologies are still

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CHAPTER 1

underdeveloped due to lack in quality and poor reproducibility. More reliable test methods with quantitatively and qualitatively reproducible results are needed.

In this study, a mixed mode bending method for delamination prediction is developed. An interfacial characterization methodology is established. It is capable of testing a sample at different temperature and moisture conditions as well as at different loading mixities. The interfaces between epoxy molding compound (EMC) and copper (-oxide) lead frame, are used as case study to investigate the feasibility of the experimental setup and for verifying the characterization procedure.

1.1 Background and Motivation

Nowadays, one of the ongoing challenges for microelectronic devices is IC integration. As a result, more and more thin films of dissimilar materials are coated in most microelectronic assemblies in order to achieve specialized functional requirements. This integration gives high design complexity and risks to the manufacturers, caused by more interfaces, and new materials. Generally, due to the mismatch in thermo-mechanical properties, such as Young’s modules, coefficients of thermal expansion, hygro-swelling, and vapor pressure induced expansion, the interface between two different materials is a weak link as a consequence of imperfect adhesion and stress concentrations. Furthermore, the residual stresses from the production processes and the changing thermal and moisture conditions are often acting as crack driving factors for interface delamination. Failure of interfaces induces decreased reliability and performance of microelectronic packages. Therefore, the qualification of the driving mechanisms of delamination related problems are desirable.

A typical example of a lead frame based package is shown in figure 1. It consists of a silicon die attached onto a lead frame. Gold wires connect the chip to the lead frame. EMC is used to encapsulate the die and the lead frame. Figure 2 indicates typical interfacial delamination problems in lead frame based packages.

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INTRODUCTION

7 Figure 1 Cross section of lead frame based package

Figure2. Picture of delamination

In order to explore the risk of interface damage, FE simulations of the fabrication steps as well as the testing conditions are generally performed during the design stage. In order to be able to access the risk for interface fracture, the critical fracture properties of the interfaces being applied should be available and this include their dependency on the occurring combinations of temperature and moisture preconditioning. As a consequence, there is an urgent need to establish these critical interface fracture parameters. For brittle interfaces such as between epoxy molding compound (EMC) and metal (-oxide) substrates, the critical energy release rate (or delamination toughness, Gc) can be considered as the

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CHAPTER 1

moisture content of the materials involved and on the so-called mode mixity of the stress state near the crack tip.

Until now, much attention has been paid to interface characterization for various material interfaces that are used in microelectronic applications. However, it is commonly necessary to fabricate special test specimens for establishing the critical fracture properties. Usually, those specially made specimens do not have the identical surface conditions as real product interfaces. As a consequence, there always remained an uncertainty on the applicability of the critical fracture properties thus obtained. Moreover, during the sample production processes, residual stress is generated in the sample. In many literatures the residual stress is not well established or is even omitted when interpreting the interface fracture measurement results by means of FEM simulation. However, it turns out that the crack tip singularity is seriously influenced by the contribution due to residual stress. The residual stress level in the specially made specimens may not be the same as in the real product. Therefore, in the present study, the test specimens are created from the real production line packages, such that they really are made with identical fabrication processes and materials, and the residual stress from the fabrication process is well considered and predicted throughout experimental measurements and FE analysis as well.

Generally, a fracture experiment should start with an “infinitely sharp” initial crack to provide a stress singularity at the onset of delamination. Only then, the fracture toughness and mode mixity can be adequately approximated through FEM-fracture mechanics simulations. Testing the sample without a real “infinitely sharp” initial crack would result into unreliable simulation results and thus cannot provide an accurate prediction of the critical energy release rate. In previous work, a thin small weak layer was commonly stuck or inserted on the interface (e.g. gold or Teflon) to initiate an “infinitely sharp” delamination at the sample fabrication. Sometimes a fatigue loading was applied to try to initiate a delamination. It appears that with this procedure an “infinitely sharp” initial crack generally is not obtained. In this study, a new method to initiate an “infinitely sharp” initial crack is discussed. Since test samples are obtained from real production line packages, the traditional method where a small weak layer on the interface is added for crack initiation is not even possible. The newly developed method can well be used for initiation of an “infinitely sharp” initial crack in test samples obtained from real production line packages.

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INTRODUCTION

9 A non-trivial problem in interface delamination testing and the interpretation of fracture properties via FEM-simulation is the choice of the relative sample width. Some researchers used a relatively wide sample, as it was thought that then the FE model could be reduced to a 2D model with plane strain assumption. However, this assumption appears to be erroneous for Cu-EMC interfaces because of the high level of residual stresses in the lateral direction. Instead, the sample should be chosen quite narrow, such that a 2D model with plane stress assumption can be used for a good approximation of reality. As the present study deals with establishing the delamination toughness of an EMC - Cu lead frame interface that is directly manufactured from production line packaging, the specimen dimensions are relatively small and therefore a dedicated small-size test set-up was designed and fabricated.

Characteristic for the procedure of establishing the fracture toughness from fracture test results is that adequate FE simulations of the fracture test are required. Therefore, in the present research a dedicated non-linear FEM model was used. Details of this model will be presented. The temperature dependent data for the established critical energy release rate of the EMC - Cu lead frame combination being considered will be given.

1.2 Project Objective and Description

PHD project entitled:

“Interface Characterization and Failure Modeling for Semiconductor Applications”

The overall objective is to develop a common framework of experimental and modeling methodologies for predicting the interface reliability for lead frame based packages. This report describes the efforts in developing a methodology to characterize the interfacial fracture toughness as a function of mode mixity, temperature and moisture combining experimental tests and finite element analysis, as well as the consideration of the material model. The major contribution is to characterize the interfacial fracture energy so that they can be used in modeling for predicting the interfacial delamination of micro-electronic packages.

It is expected that the methodology being developed is generic enough to be extended to other bi-material interfaces. All relevant aspects should also be considered, such as sample preparation, temperature and moisture.

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CHAPTER 1

The major efforts are put in the design of a test setup and in measuring the fracture energy of critical interfaces namely: EMC attached on copper lead frame with several surface treatments. The critical energy release rate is calculated using finite element models containing a crack tip, based on numerical

J-integral and global energy approaches. These methods measure the energy changing associated with

crack growth.

1.3 Overview of the Report

The topics covered in this report are organized in nine chapters. In chapter 2, a literature review shall be given leading to an analysis of the problem that is mentioned in this chapter.

Chapter 3 provides a detailed description about design of the test setup and experimental procedure. The design purpose, concept and approach shall be given. A comparison of the new design with the old setup will be described. The design of the temperature and moisture oven is also discussed. The interface characterization procedure is given.

Chapter 4 gives a detailed description about test sample preparation and fabrication. In the first section, procedure of the sample production process will be given. In the second section, the comparison of the wide sample and narrow sample will be discussed. The method to create a sharp initial crack is discussed. The reason to use industrial fabricated samples shall be clarified.

In chapter 5, the basic EMC viscoelastic material model characterization procedure is described. Warpage results from both experimental measurement and FE calculation shall be given. A possible source of changing interface toughness is aging due to storage time of the sample. A necessary procedure of Reconditioning of the physical Aging effect will be discussed. The effect of residual stresses on fracture experiment is also discussed.

Chapter 6 describes the experimental results. The tests are performed on two benches of EMC and copper lead frame interfaces. The copper substrates had various surface treatments. The complete sample list shall be given in this chapter. Tests are executed at different loading mixity, temperature, and moisture conditions using the MMB setup. In order to verify the viscoelastic property and the influence of residual stresses, a benchmark study is done.

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INTRODUCTION

11 Chapter 7 presents the simulation method that was used to calculated fracture toughness at room temperature and in the glass transition temperature region. Representative results are shown in this chapter. The simulation results were captured based on the implantation of the experimental data to finite element simulation. To validate simulation and mode mixity calculation methods, some validation models were also performed.

In chapter 8, the effect of delaminated surfaces is further studied in order to get better understanding of the established fracture toughness. After the delamination experiments, some of the delaminated samples were subjected to various surface analysis (SEM, FIB, EDX). Depending on the loading mode mixture and the environmental conditions, two types of failure patterns are found.

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Chapter 2

2. _{Basic Theory of Fracture}

In this chapter, a brief literature study shall be given. The classical theory of linear elastic fracture mechanics (LEFM) in interface crack problems will be discussed. Based on the theory, the definition of (critical) energy release rate, stress intensity factors and mode mixity will be described for homogenous material crack and interface crack problems, respectively. The time dependent effect on interface fracture will also be discussed. The principle of some typical fracture test methods will be explained. The most commonly used numerical approach for prediction of crack growth will be discussed.

2.1 Introduction

Fracture mechanics was invented last century by A. A. Griffith to explain the failure of brittle materials [1]. This theory deals with the quantitative description of the mechanical state of a deformable body with a crack and the prediction of crack propagation. Conventional fracture mechanics was used to analytically calculate the driving force on a crack and to experimentally characterize materials’ fracture resistance in homogenous media. In modern material science, fracture mechanics is an important tool to describe fracture behavior of materials and composites. For homogenous materials, the use of fracture mechanics for describing and solving crack problems is almost mature. However, in nowadays engineering problems, fracture covers a broad range in which there are more interface crack problems beside homogenous crack problems. Microelectronic packages are typical examples that are made of composite materials. Due to the mismatch in thermo-mechanical properties, such as Young’s modules and Poisson’s ratio, the coefficients of thermal expansion, the hygro-swelling, and vapor pressure induced expansion [2], the interface between two dissimilar materials is where fracture most likely will

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CHAPTER 2

occur. Conventional fracture mechanics for homogenous cracks is not sufficient for analyzing such kind of failures.

Recently, the extension of linear elastic fracture mechanics in homogenous material to bi-material interface crack problems has become of interests. Many researchers have made important contributions on bi-material interface fracture mechanics. However, the analytical solutions are limited to very simplified cases and cannot directly be applied to real engineering applications. Generally speaking, there are two approaches in fracture analysis: the stress intensity approach and the energy approach. The stress intensity approach regards the crack growth when the stress intensity factor exceeds a critical material specific fracture resistance. Comparing to the stress intensity approach, the energy approach is more attractive [3, 4]. It turns out that the crack propagates as a result of the so-called energy release rate exceeding its critical value. The critical value can be obtained experimentally. However, its measurement is complicated due to the fact that the critical energy release rate is not only temperature and moisture dependent but also stress state (mode mixity or mode angle) dependent.

At present, research on interface delamination analysis is based on linear elastic or elastic plastic material for the sake of simplicity. However, the assumption of elastic or plastic behavior is not applicable for most of the polymer materials which have strong time and temperature dependent viscoelastic properties. Study of interface cracking for viscoelastic materials has been done in [5, 6]. However, most of the present research on viscoelastic material interface delamination only allows for a limited description of some simple observations in viscoelastic behavior.

2.2 Linear Elastic Interface Fracture Mechanics

Conventional fracture problems usually refer to cracks embedded in homogenous media. The crack problems in homogenous material have been investigated in the last century and the methodologies for describing and solving for such crack problems are almost mature. However, in practical engineering problems, fracture covers a substantially broader range in which there are many bi-material interface problems besides homogenous crack problems. Composite components such as electronic packages are typically examples where bi-material interface delamination usually happens due to mismatch in thermal and thermal mechanical material properties.

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BASIC THEORY OF FRACTURE

15 It is generally agreed that an interfacial crack will propagate when the load at the crack tip exceeds critical strength values. The success of predicting delamination in IC packaging strongly depends on accurate characterization of the critical interface strength. In general, as mentioned before, for dissimilar materials, due to material mismatch, the interface cracks propagate under a mixed mode combined condition. This means that mode I, mode II and even mode III (3D case) may co-exist together. The crack propagation under pure mode I (opening mode) and pure mode II (sliding mode) have been extensively studied in many literatures. However, more and more attention must be paid to mixed mode loading because it is the most realistic situation. Usually, for composite structures, crack propagates under mixed mode I and mode II combined conditions [12, 13]. Thus two fracture parameters, namely the fracture toughness and mode mixity are needed to effectively characterize the propagation of interfacial cracks. The contribution of mode III (tearing mode) is often neglected because the effect on fracture is rather small in comparison with mode I and II. In this report, some basic theory of linear elastic interface fracture mechanics for interfaces is given. Some more details are described in [14-16].

Figure 2-1 Three fracture failure modes

2.2.1 Energy Release Rate

Linear elastic interface fracture mechanics is the extension of linear elastic fracture mechanics for homogenous material to bi-material interface crack problems. This theory describes if and how a crack will grow under given loading conditions when assuming an initial crack with given length and location. It assumes the existence of some detectable cracks and predicts the probability of crack propagation during processing and operational cycles. It applies when the nonlinear deformation of the material is confined to a small region near the crack tip compared to the size of the crack. For brittle materials, it accurately establishes the criteria for the failure analysis. In this theory, it first assumes that the material is isotropic and linear elastic. Based on the assumption, the stresses and/or the energy near the crack tip

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CHAPTER 2

are calculated. In linear elastic fracture mechanics, to predict interface delamination, fracture quantities are needed for comparison to the critical data such as fracture toughness. In general, stress intensity factors (SIF) and/or energy release rate are used to define the loading state at the crack tip. For linear and homogeneous material, both the stress intensity factors and energy release rate can be used. A criterion for crack growth can be obtained by regarding the energy balance of the material (2.1).

e i a d k

dU dU dU dU dU

=

+

_(2.1)

dUe is the change of external mechanical energy that is supplied to the system, dUi is the change in

elastic energy that is stored in the material, dUa is the change in energy dissipated by crack growth, dUd

is the change in energy dissipation caused by other mechanisms (e.g. heating, plastic deformation), and

dUk is the change in kinetic energy. It is assumed that dUd is zero, implying that the crack growth is the

only cause of energy dissipation. dUk is zero means that the crack growth is that slow that the kinetic

energy change is negligible. The remaining energy balance is known as the Griffith’s energy balance (1921), which regards energy per unit of newly created fracture surface, or when the material width is taken to be constant, per unit of crack length a:

e i a

dU

da

−

da

=

da

(2.2) Dividing the left hand of equation by the material width B, it gives the energy release rate (2.3).

1 dU

_e

dU

_i

d U

p

G

B da

da

=

−

≡

_(2.3)

So the energy release rate is the absolute change in potential energy per unit of crack area. This energy release rate is than compared to the so-called critical energy release rate Gc. The initial crack will

propagate if the energy release rate is larger or equals its critical value:

c

G G

≥

(2.4)

2.2.2 Mode Mixity

The critical energy release rate Gc is generally considered as a material property of the material under

consideration. However, its value is not really unique: It depends on the kind of stress state in front of the crack tip: how much shear there is compared to the tensile stress. Generally, a so-called mode mixity Ψ is used as a measure for this. A possible definition for this mode mixity is:

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BASIC THEORY OF FRACTURE

17 1 0 0

lim tan

xy r yy _y

σ

− → =



_

_







Ψ =



_



_



_

_







_(2.5)

Figure 2-2 Crack tip coordinate and stresses

For an isotropic homogeneous material, a mode angle of 0° describes pure mode I loading, and mode angles of -90° or 90° describes pure mode II loading. In general, interface strength is higher under mode II loading than under mode I loading, shown in figure.2-3.

Figure 2-3 Interface Strength as function of mode angle

So, the fracture condition can thus be written as:

( )

c

( )

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CHAPTER 2

An additional problem is that the critical energy release rate appears to depend on Temperature (T) and on the moisture concentration (M) of the material. So condition (2.6) is extended as follows:

( , , )

cr

( , , )

G

Ψ

T M

≥

G

Ψ

T M

(2.7)

Electronic packages generally are made up from various materials. Just the interfaces between these materials appear to be quite sensitive for fracture initiation and/or fracture propagation. Generally we speak here about “delamination”.

For a bi-material interface the fracture criterion (2.6) again appears to be well applicable. However the calculation of the mode mixity needs some more attention. Before this can be discussed, we need some more basic theory of linear fracture mechanics for interfaces. Some more details are described in [14, 15, and 16].

Consider a semi-infinite traction-free crack at the interface between two homogeneous, isotropic and linear elastic materials, with material 1 above the interface and material 2 below as shown in Figure 2-4.

θ x r y Material 1 Material 2 Material 1: µ1 = Shear Modulus E1 = Young’s modulus ν1 = Poisson’s ratio Material 2: µ2 = Shear Modulus E2 = Young’s modulus ν2 = Poisson’s ratio

Figure 2-4 A crack along a bi-material interface and basic material properties

The stress solution in the neighborhood of the crack tip typically has the following form [4] [12]:

Re

( , )

2

i ij

K

r f

ij

r

ε

σ

θ ε

π





=

_

⋅

_





, (2.8)

where _f_ij_{( , )}θ ε is a complex function.

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BASIC THEORY OF FRACTURE

19

I II

K K i K

=

+ ⋅

(2.9)

Here KI and KII represent intensities of mode I (= traction) and mode II (= shear) stress states,

respectively.

The coordinates x,y,z are now replaced by numbers 1,2,3, respectively. Here ε represents the so-called oscillatory index with:

1 _ln

1

2

1

D_D

β

ε

π

β



−



=

_

_

+





(2.10)

Here αD and βD represent Dundur’s parameters:

1 2 2 1 1 2 2 1

(

1)

(

1)

(

1)

(

1)

D

µ κ

β

µ κ

− −

−

=

+ +

+

_(2.11)

With:

κ

_i

= −

(3

ν

_i

) /(1

+

ν

_i

)

for plane strain

and

κ

_i

= −

3 4

ν

_i for plane stress. (2.12)

On the interface (θ = 0) the solution has a more simple form:

Stress state: 1 2 22

i

12

K

(2 )

r r

iε

σ

π

−

+

= ⋅

(2.13) Crack tip opening displacements:

2 1 *

4 (1 2 )cosh( ) 2

i

K

r

i

r

E

i

ε

δ

ε

πε

π

+

=

⋅

+

(2.14)

The bi-material modulus (E*) and the complex exponent riε_{are defined by:}

1 2 * 1 2

1 (1

) (1

)

2

2 E

ν

µ



−



=

_

+

_





(2.15) cos( ln ) sin( ln ) i rε ₌

_ε

_⋅ r _{+ ⋅}i

_ε

_⋅ r (2.16)

According to this basic solution the stresses along the interface as well as the crack tip opening displacements (COD’s) are oscillatory. It is even so that at some places along the crack surface δ1 is

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CHAPTER 2

negative, which is physically unrealistic. There is also an exact solution available with δ1≥0, the

“Comninou solution” [52] which generally is not used in linear fracture mechanics.

Figure 2-5. Schematic of the stress field close to the crack tip at θ=0

For various crack configurations various analytic solutions are found from literature. In the general case the (magnitude of the complex) stress intensity can be written as:

( ) i

K ₌ stress _⋅

_π

L L_⋅ −ε

(2.17)

Here L represents a characteristic length of the oscillation. In accordance with our previous definition (2.3) the mode mixity can (again) be defined as:

1 12 0 ₂₂ 0

tan

lim

r θ

σ

ψ

σ

− → =



_

_



=

_

_

_

_













(2.18)

It should be noted that βD ≠0 the stress components very close to the crack tip are oscillatory. Further,

both stress components σ12 and σ22 are singular. As a consequence the mode mixity according to (2.18) cannot well be obtained by FEM analysis. Therefore often an alternative mode mixity definition is used. There are various alternative mode mix definitions possible that can well be established through FEM simulation. Some of these are suggested by A. Tay in [14, 15].

A possible choice of alternative mode mixity definition is obtained by using the interface stresses (traction and shear) at a chosen distance from the crack tip (this distance is called characteristic length) (_Lˆ): 1 12 ˆ 22 0, ˆ tan r L θ

σ

ψ

σ

− = =   = _ _   or equivalently: 1

Im(

ˆ

)

ˆ tan

_ˆ

Re(

)

i i

KL

ε ε

ψ

₌

−













(2.19) Material 1 Material 2

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BASIC THEORY OF FRACTURE

21 Here the choice of ˆL is somewhat arbitrary.

Alternatively the phase angle ϕ is often used to define a mode mixity:

1

tan

II I

K

ϕ

₌

− (2.20)

The choice of the arbitrary length

ˆL

in the definition of mode mixity may results into transformation of Ψ from one location to another. Let Ψ1 be associated with reference length L1 and Ψ2 be associated with L2, the transformation formula is shown as follows:

2 1

ln(

L L

ˆˆ

2 1

)

ψ

=

ψ

+

ε

_(2.21)

Alternatively, Yuuki and Cho [23-24] proposed a crack surface displacement extrapolation method (CSDEM) to calculate a mode mixity.

1 0

2 lim tan

ln

2

x y r y x

u

_r

u

a

δ

εδ

ψ

ε

δ

εδ

− →





+



_

_



=





_

₋



_

−

_

_



















(2.22)

Where δux and δuy are the components of the crack surface opening displacement, parallel and

perpendicular to the crack tip, respectively (see Figure 2-6). ε is the oscillatory index, r is the distance

from the crack tip. 2a is an arbitrary length and here it is equal to the initial crack length.

Figure 2-6. Schematic of Crack Opening Displacements

In FEM approximations the limit for r0 in expression (2.22) is obtained using fit functions for the differential nodal point displacements n

x

u

δ

and

δ

un_y (n is the node number). Depending on the fit function used, different mode mixity values are obtained. In our present work and in accordance with [52] a linear fit function is used.

Material 2 Material 1

δux δuy

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CHAPTER 2 2.3 Fracture Test Methods

Fracture mechanics has found extensive applications in delamination analysis. One of the most important parameters in the application of fracture mechanics is the strain energy release rate. In order to determine the critical strain energy release rate, fracture experiments must be performed. Figures 2-7 and figure 2-8 list the most popular tests for measuring fracture toughness.

Figure 2-7. Different test methods for interface strength measurement: (a) Double cantilever beam(DCB), (b) Three point bending (TPB), (c) Single leg bending(SLB), (d) Four point bending(FPB), (e) Asymmetric double cantilever beam (ADCB), (f) Button shear(BS), (g) Wedge test.

(e) (d)

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BASIC THEORY OF FRACTURE

23 Figure 2-8. Mixed mode bending test method

It is generally agreed that an interfacial crack will propagate when the loading at the crack tip exceeds critical energy release rate values. The success of predicting delamination in IC packaging strongly depends on accurate characterization of the critical interface strength. Due to elastic mismatch, bi-material interface cracks are always mixed mode cracks with both mode I and mode II (shear mode) components. The crack propagation under mixed mode conditions has been extensively studied in many literatures [25-27]. Experimental determinations of mixed mode toughness have been performed for crack propagation in the interface between various material combinations. In all these systems, the interface toughness is not a single material parameter; it is a function of the mode mixity acting on the interface, the climate temperature of the measurement system, the humidity content of the material combinations.

The test methods listed in figure 2-7 give advantage that they can provide fast estimates of the level of interfacial toughness and the influences by temperature and moisture. However, these estimates may not be quantitatively realistic due to the fact that the initial stress situation in the sample is not accounted for interfacial fracture toughness also depends on the mode mixity at the crack tip for an interface crack. Using the shown test methods to determine the influence of mode mixity on the interfacial fracture toughness, combining normal and shear stresses on the delamination plane, different thickness ratios of material layers should be generated. However, it is highly impractical as it requires the development of different types of samples for each mode mixity. Also, even when changing the thickness ratio, none of the shown test methods can cover the full range of mode mixity. Moreover, to determine pure mode I, pure mode II, and mixed mode critical values (Gc, and Gc(ψ), respectively), different types of samples need

to be subjected to different loading configurations, these configurations can involve different test variables and analysis procedures that can influence test results in ways that are difficult to predict.

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CHAPTER 2

Therefore, more and more attention must be paid to mixed mode loading because it is the most realistic situation.

Instead of using Gc as the fracture toughness parameter in homogenous crack problems, one now has Gc

(

ψ

,

T C

_,

) where the interface toughness is a function of the mode mixity, climate temperature, and the moisture content. During the test, the applied load and corresponding displacement are measured and correlated to the length of delamination. From the correlated data, the fracture toughness can be obtained using some beam theory principles or simple expressions. However, these simple mathematical expressions are usually not accurate because they do not take initial stress into account. There are a few papers [48, 49, 50] which try to include the effect of residual stresses. However, more precise finite element models (FEM) should be used to refine the analytical evaluation of the test configurations. In the following sections, four often used test methods namely, double cantilever beam (DCB), three point bending (TPB), four point bending (FPB), and mixed mode bending (MMB) will be described. All formulas given are only for one material samples.

2.3.1 Double Cantilever Beam

The double cantilever beam test has been used extensively for measuring mode I fracture toughness. In the standard mode I double cantilever beam (DCB) test the crack is centrally located, as shown in figure 2-9. Assuming there are no residual stresses, the toughness may be found from the load and deflection data by compliance calibration by using the following equation [28].

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BASIC THEORY OF FRACTURE

25 2

2 P C

G

b a

∂

=

∂

(2.23)

Here, b is the specimen’s width, C is its compliance, and a is the crack length.

2.3.2 Three Point Bending

Extensive studies have been carried out on analysis, modeling and design of three point bending (TPB) specimens. A typical TPB specimen is essentially a beam with a mid plane initial crack of a desired length

a at one end of the beam as shown in figure 2-10. According to beam theory, the mode II energy release

rate as a function of the applied load and the compliance for the TPB test can be respectively determined as [29] 2 2 2 3

9

16

II

P a

G

b Eh

=

(2.24)

Where P stands for concentrated load, a is crack length, b is the width of the beam, h is the half height of the beam, and E is the Young’s modulus of isotropic material.

Figure 2-10 Three point bending test [29]

One of the inconveniencies of this test is that it is only possible to obtain steady interface crack growth in a relatively small length range and likely to be affected by the central roller [31]. Another inconveniency of the TPB test is the relative friction and shear force between both beams of the specimen when the load is applied to the specimen. Research effort has been spent on the analysis of the three point bending

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CHAPTER 2

specimen, one of the most widely used test configurations for evaluating mode II delamination fracture toughness. Carlsson [31] has compiled a comprehensive review of fracture mechanics approaches to characterize mode II interlaminar fracture of composites. The review focuses on the analytical solutions include shear deformation beam theory.

2.3.3 Four Point Bending

A large number of methods exist to measure the interfacial fracture energy G and four point bending (FPB) test is one of the most popular method in industrial and academic research. In principle, one test gives only one mode mixity. Cao and Evans [33] used four point bending specimens to obtain a wide range of mixed mode deformation by repeating the test with different geometrical properties. A typical four point bending specimen is shown in figure 2-11 and the energy release rate of interfacial crack without considering initial stresses is given by

2 2 2 3

21(1

)

4 M

G

Eb h

υ

−

=

_(2.25)

Where the bending moment

M Pl

=

/ 2

, with P is bending the load and l is the spacing between the inner and outer loading lines. b is the beam width, h is the half thickness, E and v are elastic modulus and poisson’s ratio of the bulk substrate, respectively.

Figure 2-11. Four point bending test

When the crack tip is sufficiently far away from the vertical pre-crack (a >2h), the strain energy release rate becomes independent of the crack length. The disadvantage of this test is that the crack growth is not symmetrical.

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BASIC THEORY OF FRACTURE

27

2.3.4 Mixed Mode Bending

The more commonly used test is the so called mixed mode bending (MMB) test. It simply combines the DCB and TPB tests. The test was initially proposed by Reeder and Crew [34]. The test allows the determination of the interlaminar facture toughness with a mixed mode I/II ratio range from almost pure mode I to pure mode II. Since the first design showed the error in G when calculated using linear theory [35-36] and it would be inconvenient to use a nonlinear analysis to analyze MMB data, the MMB apparatus was therefore redesigned (figure 2-12) to minimize the nonlinearity so that a linear analysis could be used.

Figure 2-12. Mixed mode bending setup [29]

In the redesign, different mixed mode ratios can be achieved with the variation of the loading point on the lever (varying distance c or d). During the test, loads are applied to the specimen through hinges bonded to the specimen beams at the delamination end. The rollers at the non-delaminated area reduce the friction force. The bottom hinge is fixed to the base of the rig while the other extreme of the specimen is supported by a roller. When a downward load is applied on the lever arm, a downward force is applied to the central part of the specimen and meanwhile the upper hinge is pulled up. To ensure that the load applied on the lever arm remains vertical, a saddle and yolk arrangement is used in combination with rollers to reduce friction loads.

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CHAPTER 2

Figure 2-13 Mixed mode bending test as superposition of DCB and TPB tests

As shown in figure 2-13, the MMB test can be seen as the superposition of the mode I DCB test and Mode II TPB test. According to this superposition the different loads can be expressed as function of the applied load P and test configuration as

1

c

P P

d

=

(2.26) 2

(

c d

₂

1)

P P

L

+

=

−

(2.27) 3

(

c d

)

P P

d

+

=

(2.28) 4

c d

₂

P P

L

+

=

(2.29) 5

P c d c d

₂

(

₂

)

P

d

L

−

+

=

+

(2.30) 6

₂

P c d c d

(

₂

)

P

d

L

+

=

−

(2.31)

According to beam theory, the mode I and mode II energy release rate as functions of the applied load for MMB test can be respectively determined as [29]:

2 2 2 2 3

3 ₍

₁

₎

2

I

P a c d

c

G

b Eh

L

d

+

=

− +

(2.32)

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BASIC THEORY OF FRACTURE

29 2 2 2 2 3

9 ₍

₁

₎

4

2

II

P a c d

c

G

b Eh

L

d

+

=

− −

(2.33)

2.4 Numerical Methods for Interface Fracture

Numerically, there are several methods available for calculation of the energy release rate and stress intensity factors (e.g. J-integral, virtual crack closure, cohesive zone, area release energy, etc). It is very important to note that there is no standard method available to predict initiation and propagation of interfacial delamination. In this study, the J-integral method is used for calculations at room temperature. Since this method is not suitable for dealing with viscoelastic materials calculations the global energy approach is used to calculate Gc when test temperature is in and above glass transition

temperature of EMC being considered.

2.4.1 J Integral Method

This method was first introduced by Cherepanov [37] and Rice [38]. It is widely used in path-independent quasi-static fracture analysis to characterize the energy release rate associated with crack growth. For the two dimensional problems, the J-integral equation is written as:

(

i

)

i

u

J

Wdy T

ds

x

Γ

∂

=

−

∂

∫

(2.34) 0 ij ij

W

=

∫

ε

σ

d

ε

(2.35)

Where W is the strain energy density per unit volume, ds is an infinitesimal element of the contour arc length, Γ denotes any contour path surrounding the crack tip, here T denotes traction vectors and u denotes displacement vectors along Γ curve, W can be further written in equation (2.35), with σij and εij

denoting the stress and strain tensors, respectively. According to the definition, J-integral is the decrease of strain energy in the field per unit crack growth. The J-value implies that it is the work available in the material to propagate a crack. For a uniform linear elastic material, J-value is equal to the energy release rate G, i.e. J = G.

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CHAPTER 2

Figure 2-14 The path contour of a two-dimensional crack in an elastic-plastic material [39].

In finite element analysis, the J-integral method is used to evaluate the energy release rate corresponding to a crack formation for linear elastic or elastic plastic materials. Through a path-independent contour integral, the available energy to delaminate the given interface can be calculated. The advantages of this method are following:

a) The J-integral method is easy to use. Most of the commercially available finite element packages have the option to compute the value.

b) The J-integral method provides relative short calculation times compared to other methods. Disadvantages are:

a) In fracture mechanics calculation, the crack location has to be fixed in the model. In other words, the exact location of the delamination needs to be known a priori. If the crack is propagating then J value equals to the critical energy release rate.

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BASIC THEORY OF FRACTURE

31

2.4.2 Global Energy Approach

It appeared that in many standard FEM packages the calculation of the energy release rate through the implemented J-integral gave erroneous results in the case of viscoelastic material behavior. As it was found that this also holds for Abaqus (see section 7.3.2) the following approximation of expression (2.3) was used to calculate the energy release rate. This method will be referred to as the global energy approach.

1 U

p

G

b

a

∆

≈

∆

(2.36)

Here ΔUp represents the calculated change in potential energy because of the small but finite crack

extension Δa. The small but finite crack extension Δa cannot be arbitrarily chosen. Its value should be chosen between certain upper and lower bounds as will be discussed in section 7.3.2.

2.5 Time Dependent Effects

In this research, the interface being considered is between polymer (epoxy molding compound) and metal (copper) interface. It is well known that polymer exhibits viscoelastic behavior which causes its Young’s modulus to be not only temperature dependent but also time dependent. For microelectronic applications, it is quite easy for polymers to experience considerable viscoelasticity since the glass transition temperature of polymers is usually below the solder reflow temperature. These properties can lead to viscoelastic crack growth. In the analysis of plastic encapsulated IC packages, the viscoelastic property of materials such as epoxy molding compound has usually been neglected and the epoxy molding compound is often modeled as an elastic material. The prediction of the interface delamination between molding compound and copper during for example solder reflow can be true only if the complex time and temperature dependent viscoelastic properties of molding compound are taken into account.

Some work has been done in understanding the effect of viscoelastic behavior of molding compound on delamination analysis in plastic IC package. Xiong and Tay [40] reported that there is not negligible discrepancy between the temperature elastic model and the viscoelastic model based on J integral analysis. Liu and Shi [41] also found that the visco-elasticity of molding compound has a significant effect on the energy release rate.

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CHAPTER 2

The problems of time dependent interface crack growth have recently been the focus of research due to the widespread use of polymers in composite materials and adhesive bonds. Mueller and Knauss [42] extended Griffith’s energy concept of intrinsic material surface energy to linearly viscoelastic materials. They derived a differential equation to study the growth of a finite crack in an infinite plate loaded by remote tension. Williams and Marshall [43] put forth the idea that fracture mechanics for viscoelastic materials could be treated with an approach that is similar to traditional fracture mechanics by simply replacing the time independent values of modulus and flow stresses with equivalent viscoelastic relaxation modulus and flow stresses. Schapery [44-45] demonstrated that indeed viscoelastic crack growth could be described with the replacement of the elastic modulus with a viscoelastic modulus. He further indicated how to determine the appropriate time at which this viscoelastic modulus should be evaluated using linear visco-elasticity. Later, the analytical approaches introduced by Schapery [46] allow for prediction of crack growth in nonlinear viscoelastic media with finite deformation behavior. The work of Schapery has further been extended by Srinivas and Ravichandran [47]. In their work, they developed a simple analytical model for studying a crack growth along the interface of a thin viscoelastic film bonded to an elastic substrate. They used a single Maxwell model to construct the time dependent crack growth. They demonstrated that by discrediting the strain energy function, the energy release rate was obtained during small time steps using the Griffith’s energy balance approach showed good agreement with the finite element results.

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Chapter 3

3. _{Measurement Setup and Experiment Procedure}

This chapter provides a detailed description about design of the test setup and experimental procedure. The design purpose, concept and approach shall be given. A comparison of the new design with the old setup will be described. The design of the temperature and moisture oven is also discussed. The interface characterization procedure is given.

3.1 Introduction

Measuring interfacial adhesion strength requires loading a sample consisting of at least two material layers. To determine the interfacial strength, various test methods (see figures 2-7 and 2-8) have been used. Such as the double cantilever beam (DCB) test, three point bending (TPB) test, and four point bending (FPB) test, etc. Note that generally, the interfacial delamination fracture energy is dependent on temperature and moisture changes. More importantly, mode mixity plays an important role when calculating the fracture toughness. Using the shown test methods to determine the influence of mode mixity on the interfacial fracture toughness, combining normal and shear stresses on the delamination plane, different thickness ratio of material layers has to be generated. However, it is highly impractical as it requires the development of different types of samples for each mode mixity.

In this research, a mixed mode bending test method is proposed. A dedicated small-size test set-up was designed and fabricated. It allows for transferring two separated loadings (mode I and mode II) on a single specimen by using a lever system. The setup is flexible and adjustable for measuring specimens with various dimensions. The test specimen is first inserted in the load transfer setup. Then, the setup is

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CHAPTER 3

clamped in a sensitive tensile tester. For measurements under various temperatures and moisture conditions, a special climate chamber is designed.

During the sample production processes, residual stress is generated in the sample. In many literatures the residual stress is not well established or is even omitted when interpreting the interface fracture measurement results by means of FEM simulation. However, it turns out that the crack tip singularity is seriously influenced by the contribution due to residual stress. It is important to note that for large scale samples, they often cannot be used for interface fracture testing by the fact that various arbitrary cracks are often present beforehand due to high residual stresses. In this chapter, the choice of the sample width for delamination testing will be discussed.

3.2 Preliminary Approach

The mixed mode bending test method, which is used in this research, was first introduced by Reeder and Crews [34]. This method has been widely used to measure the interfacial strength experimentally [27][29]. It provides the steady crack growth over the full range of mode mixities. In their published paper, it had also been proved that the MMB test was rather simple and was believed to offer several advantages over most current mixed mode test methods.

Figure 3-1 (a) Mixed mode bending setup [Reeder and Crews 1990] initial configuration. (b) Loading configuration

The original idea (figure 3-1) was to attach a sample at points A and B. Points C and D represent supports, which only support the sample in the vertical direction. Point C was located in the middle of the sample. By changing the loading position L of the force acting on the loading beam, the mode mixity can be

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MEASUREMENT SETUP AND EXPERIMENT PROCEDURE

35 controlled. The relation between L and mode mixity without residual stresses is schematically shown in figure 3-2. When the loading distance L equals half of the sample length, the force at the point A will be zero. The test is equal to a mode II TPB test. When L equals to zero there will be no force acting at point C, mode I DCB loading occurs.

Figure 3-2. Schematic relation between mode mixity and loading distance without residual stresses

In the original and redesign (figure2-12) of Reeder and Crews, the force acting on the samples resulting from the weight of the upper loading beam was assumed to be negligible. This setup was designed and used mostly for testing large plates or layered samples with applications in aerospace engineering. However, samples that are used for testing microelectronic packaging materials are quite tiny. As a consequence, the stiffness of these samples is quite low and the forces to be measured will also be small. Initially, when placing the test sample in the setup, they may already delaminate due to the weight of the loading beam. For smaller test samples, the weight of the loading beam is not negligible.

For this reason, in 2005 Thijsse [54] re-designed the MMB test setup. A schematic drawing is shown in figure 3-3. In this design, a sort of compensation for the weight was added on the loading beam to ensure that no initial load was present on the sample at the beginning of the test. This has been achieved by mounting the MMB setup upside down, extending the loading beam beyond the loading point, and adding a horizontally adjustable counterweight (Figure 3-3). The loading position can be adjusted by horizontally moving the supports (figure 3-4). By doing this, different mode mixities can be controlled.

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CHAPTER 3

Figure 3-3 (a) Mixed mode bending setup with weight compensation (Thijsse 2005) (b) Loading position

Figure 3-4 (a) mixed mode bending setup (Thijsse 2005) with adjusted position of the loading point. (b) A change of loading position L.

In the design of Thijsse, it was found that friction in the setup very much influenced the test results. Especially in the TPB test, there was an unexpectedly a large amount of friction present during crack growth. It has been proved that the amount of friction is not only caused by the setup but also caused by the contact between two large surfaces. Moreover, this test setup is difficult to be operated. Change of the loading position means that all the supports and hinges need to be re-installed and the loading distance L has to be measured very accurately. Furthermore, using this setup, it is hard to test a sample under different temperature and moisture combined conditions.

50 mm

Interface Characterization and Failure Modeling for Semiconductor Application