Department of PhysicsUmeå University December 19, 2021

Warpage Prediction of Electronic Underfill ComponentsDuring Curing

David Lindblomdali0122@student.umu.se

Master thesis, M.Sc. Engineering Physics at Umeå university

Warpage Prediction of Electronic Underfill Components During CuringDavid Lindblom, dali0122@student.umu.se

Supervisors: Sibin Saseendran Research Institutes of SwedenDaniel Berlund Research Institutes of SwedenClayton Forssén Department of Physics

Examiner: Krister Wiklund Department of Physics

Copyright © 2021. All Rights Reserved.

Master of Science thesis in Engineering Physics, 30 ECTSDepartment of PhysicsUmeå UniversitySE-901 87 Umeå, Sweden

Abstract

To ensure the shelf life of a semiconductor, the integrated circuits are usually em-bedded in an epoxy molding compound (EMC) to shield it from stress and corrosion.The EMC is a viscoelastic material and is categorized as a thermoset. Working withviscoelastic material appose a challenge due to the cure-induced warpage. Warpageis a deformation that reduces stress resistance and can also make for assembly issues.Being able to predict the warpage accurately is an essential part of the electronicsindustry. To simulate the warpage, the finite element method is usually used. TheResearch Institutes of Sweden (RISE) in Piteå, which focuses on composites, havecreated a solver and corresponding material definition for simulating the curingprocess of a viscoelastic material. In this thesis, the solver created by RISE wasinvestigated to see how well it could predict the warpage during the curing of anEMC. The investigation consisted of reproducing the simulating conducted by Lin etal. in the article "Modeling and Characterization of Cure-Dependent Viscoelasticityof Molded Underfill in Ultrathin Packages" where the curing of an ultrahtin flip-shipChip-Scale Package (fcCSP) was simulated. The result will be reproduce using thesimulating program LS-Dyna and both the RISE material definition and an build-inmaterial definition will be simulated to see the difference. From the investigation,we could conclude that although the result from the article was unobtainable, theRISE model could predict the warpage more accurately which shows the importanceof the cure shift factor. The investigation also found that the RISE model has someimplementation errors for the stress-strain calculations in the RISE model. In con-clusion, the RISE model was able to predict the warpage in a desired way, but morestudies need to be created to ensure the model’s accuracy for the correct warpagemagnitude.

Acknowledgement

I want to thank the department at RISE Piteå for letting me do my master thesis attheir department and for the help I have received with license problems. I want to givea special thanks to Sibin Saseendran for the help received during the work, especiallywith problems correponding to the simulation. Without the help from Sibin it wouldhave been a lot harder to produce a master thesis from home.

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 42.1 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Curing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Shift factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Implementation of the stress calculation . . . . . . . . . . . . . . . . . . . 9

3 Method 123.1 Model dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Model differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Boundary, initial and load conditions . . . . . . . . . . . . . . . . . . . . . 15

4 Result & discussion 174.1 Cure kinetics verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2 Warpage prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3 RISE vs LS-Dyna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.4 Secondary scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

List of Figures

1 Flip-chip chip-scale package (fcCSP)[2]. . . . . . . . . . . . . . . . . . . . 12 Schematic cross section of an ultrathin fcCSP with exposed die and molded

underfill[10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Curing process of thermoset from monomer(1) to fully cured cross-linked

networks(4)[3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Schematic of the shift in response time of the relaxation modulus depen-

dent on cure and or temperature shift factor. . . . . . . . . . . . . . . . . 85 A quarter FE model of fcCSP with die size of 10× 10 mm2. . . . . . . . . 126 Temperature profile of the in-mold and post-mold cure process. . . . . . . 167 The glass transition temperature as a function of the degree of cure. . . . 178 The cure shift factor as a function of the glass transition temperature

compared using a simulated model and the calculated values. . . . . . . . 189 The cure and temperature development depicted against time to see how

the degree of cure of cure for the MUF depends on the temperature. . . . 1910 Warpage prediction measured in center of die for an fcCSP using two

different viscoelastic FE models. To the left the fcCSP is simulated witha die size of 8× 8 mm2 and to the right with a die size of 10× 10 mm2. . 20

11 Warpage prediction measured in center of die for an fcCSP using twodifferent viscoelastic FE models with a die size of 12× 12 mm2. . . . . . . 21

12 Warpage profile for a fcCSP with die size of 10 × 10 mm2 for the article[10] and the two simulated models. The left y-axis shows the predictedwarpage for the RISE and LS-Dyna model while the right y-axis showsthe warpage value for the article published by Lin et al.. . . . . . . . . . 22

13 Warpage profile prediction for a die size of 10× 10 mm2, for the LS-Dynamodel, and RISE model with and without cure shift factor. . . . . . . . . 23

14 Warpage depiction of the full fcCSP at 250C with die size of 10×10 mm2

simulated using: a) RISE model b) LS-Dyna model. . . . . . . . . . . . . 2415 Displacement in the x-direction (to the left) and y-direction (to the right)

for the LS-Dyna model and the RISE model without cure shift factor. . . 2516 Warpage prediction using the RISE Model with different CTE values. . . 27

List of Tables

1 Material properties of fcCSP components. . . . . . . . . . . . . . . . . . . 132 Generalized Prony series constants. . . . . . . . . . . . . . . . . . . . . . . 133 Reduced Prony series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Estimated cure kinetics parameters for the Kamal equation. . . . . . . . . 145 Degree of cure and their corresponding glass transition temperature . . . 156 Warpage predicted[µm] in middle of fcCSP for the different models and

die sizes at the lowest and highest temperature. . . . . . . . . . . . . . . 20

1 Introduction

One of the key components for the electrical industry are the semiconductor.To ensure asemiconductor can be relied on for years and years, the chips must be protected from theelements and stress. Integrated circuit packaging or IC packaging refers to the last stagein the production process of a semiconductor. During this procedure, the semiconductorare covered in a outer shell of that protects the IC from potential threats[1].

1.1 Background

There are many different types of IC packages, but on the basic level, the IC packagescan be divided into two types: the lead-frame type and the substrate type. In this thesis,the IC package investigated are the flip-chip chip-scale package (fcCSP) seen in Fig. 1[1].The protective outer shell of the fcCSP are made of composites. The composites that

Figure 1: Flip-chip chip-scale package (fcCSP)[2].

are commonly used in industrial applications are thermosets and thermoplastics, and inthe case of IC packages usually epoxy or epoxy blends are used[1]. Epoxy belongs to thecomposite subgroup thermosets. Thermosets offers enhanced mechanical and chemicalproperties over thermoplastics. There are many methods to manufacture modern ther-mosets, such as resin transfer molding (RTM) and prepreg lay-ups. The RTM processintroduces dry fibers by injecting them into a sealed mold. The polymer is injected intothe mold by pressure, making the resin merge with the fiber network sufficiently. Themold is then left at an elevated temperature so the thermoset can be cured. Duringcuring, the monomers are polymerized with cross-linked networks. Sometimes a post-cure is necessary where the material is removed from the mold and placed in an oven tocomplete the curing of the material[3].

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The curing process will introduce residual stress, which in turn will distort fully curedstructures. The distortion is classified as warpage. The residual stresses are mainlybuilt up due to thermal expansion. The mechanism of the warpage is essentially thesame as how a bimetallic strip would warp under different temperatures. Although thethermal expansion (CTE) is the primary cause of warpage, other properties such asshrinkage have a secondary role. Warpage has been recognized as a significant issue forpackage reliability. Not only does the warpage reduce the lifespan of the component,but it can also change the dimensions of the package to such a degree that it becomesan assembly issue[4]. The residual stress that occurs during curing is mainly influencedby two parts, the thermal and chemical shrinkage. Thermal shrinkage is introduceddue to the temperature change during curing. In contrast, chemical shrinkage is avolumetric shrinkage that occurs during the curing reactions when crosslinking reactionsincreases chain length[3]. Due to the necessity of understanding the material propertiesand behavior during manufacture, much research has been performed to get a greaterunderstanding of the behavior of the material during curing[4, 5, 6]. This research hasdeveloped many ways to determine the stress and warpage. One possible approach isan analysis of stress in multilayered structures. However, the more traditional way toanalyze the IC package’s mechanical behavior is to use finite element (FE) simulations[3].

In this thesis, the software LS-Dyna is used for the simulations. LS-Dyna is an FEprogram capable of simulating real-world problems. LS-Dyna is one of the most robustFE software available and can be used in many different scenarios, such as Automotivecrashes, explosions failure analyses, and incompressible CFD, to name a few[7, 8]. LS-Dyna uses a single executable file and is solely command line driven[7]. Not only doesLS-Dyna provide several inbuilt material definitions for a variety of applications, butLS-Dyna also allows for user defined material definition.

At RISE in Piteå, Saseendran et al.[9] have created a FE model to simulate the vis-coelastic properties. The model made by Saseendran et al. calculates the stress andstrain for a viscoelastic material where the cure and temperature shift factors are con-sidered[9]. The model is implemented into LS-Dyna using the user defined material andcreates an executable to accommodate the material model. In this thesis, the inbuilt ma-terial definition "MAT_ADHESIVE_CURING_VISCOELASTIC" (Dyna model) willbe compared to the user defined created by Saseendran et al. model (RISE model).The reason for the inclusion of the LS-Dyna model is to show the comparison betweena model containing the cure shift factor and one without this correction.

2

The models were compared using the experimental data provided by Lin et al.[10] in theirarticle "Modeling and Characterization of Cure-Dependent Viscoelasticity of MoldedUnderfill in Ultrathin Packages". In the article, Lin et al. are simulating the warpage ofan ultrathin fcCSP and the schematic can be seen in Fig. 2

Figure 2: Schematic cross section of an ultrathin fcCSP with exposed die and molded underfill[10].

As shown by the schematic in Fig. 2 the fcCSP consists of a silicon die, the moldedunderfill (MUF), which is a type of epoxy molding compound, substrate, and controlledcollapse chip connection (C4).

To simulate the warpage in the IC package Lin et al. use the viscoelastic approach todescribe the MUF. Using this article as a bench mark test the RISE and LS-Dyna modelcan be compared to an already established model.

1.2 Aim

This thesis aims to study the accuracy of predicting warpage formation during curingfor the RISE model. The investigation consists of a main and secondary investigation.The main investigation attempts to reproduce the result from Lin et al.[10] by usingthe experimental data provided. The experimental data will be simulated using boththe RISE and LS-Dyna model. The secondary investigation consider the influence ofthermal expansion has on the warpage for the RISE model.

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2 Theory

To achieve the aim we first need to look at the necessary theory needed to be able toaccurately simulate the viscoelastic effect of the MUF material.

2.1 Viscoelasticity

A viscoelastic(VE) material displays both elastic and viscous characteristics. When itgoes through deformation, the material will exhibit time-dependent strain. The VEmaterial will usually show elastic properties due to the bond stretching along crystallo-graphic planes in an arranged solid. The viscous characteristics result from the diffusionof atoms or molecules inside the amorphous(non-crystalline solid) material. When de-scribing the manufacturing process of a composite material where the matrix is usuallythe amorphous or semi-crystalline phase, the VE effects are more suitable. The VEmaterials can be sub-categorised into either thermo-rheologically (TR) simple or com-plex materials depending on the chemical constituents of the material. TR materialsis defined as a material that follows the principle of Time-Temperature superposition(TTS). Most of the resins used in the composites industry have low to medium molecularweight, so they can be viewed as TR simple materials; hence, only TR simple will beconsidered[3].

The stress-strain relationship of a simple VE material in one dimension can be describedby

σ(t) =

∫ t

−∞Erel(t− t′)

dε

dt′dt′, (1)

where σ is the stress, ε the strain and Erel the relaxation modulus[3]. The relaxationmodulus are a characteristic of VE materials which describes the stress relaxation ofmaterials with respect to time. Erel can be described in terms of free volume of relaxationtime[11]. The relaxation modulus is usually described by a Prony series

Erel = E0

[ω∞ +

N∑i=1

ωi exp

[− t

τi

]], (2)

where E0 is the glassy modulus, N the number of Prony elements, τi the relaxationtime, ωi the weighting factor for element i and ω∞ weighting factor corresponding to therubbery modulus. ω∞ is determined in such a way that ω∞+

∑ωi = 1. The relaxation

times τi, weighting factors ωi and the glassy modulus is determined experimentally. Oneway to experimentally determine the constants is by using dynamic mechanical analysis(DMA)[3].

The stress-strain behavior in Eq. 1 assumes that all material data is obtained at aconstant temperature. To account for temperature fluctuations, Eq. 1 needs to bemodified and written in terms of reduced time ψ. The stress-strain relationship for thelinear VE is then described by

4

σ(t) =

∫ ψ

−∞Erel(ψ − ψ′)

dε

dψ′dψ′, (3)

where the reduced time is defined as

ψ =

∫ t

−∞

dt′

αT (T ). (4)

αT (T ) is known as the time-temperature shift factor[3].

2.2 Curing

To accurately describe the relaxation modulus the curing needs to be taken into account.In the beginning, the resin, which is in its liquid phase, consists of very short monomerchains see Fig. 3 a). If the temperature of the fluid increases or specific agents is in-troduced, the monomers will start to bind to the adjacent monomers. The monomersbind to each other by sharing hydrogen bonds, which is called protonation. Once themolecules are protonating, they increase in length to become long chains with somefree-body motion, just enough to move past each other. This movement is minimal incomparison with the degree of freedom in the unreacted state. As the curing continues,the chains grow longer and longer up to a point where the protonating process startsto slow down. As the protonating process slows down, a new phenomenon called nucle-ophilic attack starts to take over. The long chains now begin binding to the adjacentchains using one of two different processes, either by van Der Waal forces or by forma-tions of complexes that are cured further. During this part of the curing process, thechains become interlinked and start to form three-dimensional networks. The networkscontinue to grow until the energy becomes insufficient to make the network grow, andthe process begins to slow down. At this point, the material is considered fully cured[3].A depiction of the curing process can be seen in Fig. 3

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Figure 3: Curing process of thermoset from monomer(1) to fully cured cross-linked networks(4)[3].

On a more macroscopic scale, the fluid becomes more viscous as the chains increases inlength. When nucleophilic attack takes over, a very sharp rise in the viscosity of theresin can be observed. This irreversible transformation is known as the gel point. Thegelation usually occurs at conversion between 55%−80%, which corresponds to a degreeof cure α[12]. At the gel point, the material is very rubbery Fig. 3 between c)-d). As thecuring proceeds, the material goes from its rubbery state into a solid glass-like materialFig. 3 d), and this process is called vitrification. Vitrification occurs when the glasstransition of the resin is coincidental with the cure temperature and is reversible. Oncethe curing rate starts to slow down, the material vitrifies into its final solid form. Todescribe the cure kinetics that takes place, the Kamal autocatalytic model is a commonapproach to use.The Kamal autocatalytic model is described as

da

dt= (K1 +K2a

m) · (1− a)n , (5)

where α is the degree of cure, m and n are reaction orders, and K1 and K2 are reac-tion rate constants. The reaction rate constants have an Arrhenius-type temperaturedependence

Ki = Ai exp

(−∆EiRT

), i = 1, 2, (6)

where Ai is a constant, Ei the activation energy of the material, and R the ideal gasconstant[3].

6

To fully understand the curing process, it is essential to know how the temperature andcure are associated. The glass transition temperature Tg defines the temperature abovewhich the resin returns from its glassy state to the rubbery state. The Tg is dependenton the cure temperature but also on the cross-link density and chain stiffness. Materialscured at a higher temperature will have a higher Tg than materials cured at a lowertemperature. Although Tg is dependent on the cure temperature, every resin has anabsolute Tg that can not be increased as the curing temperature rises, which is calledthe ultimate Tg. The relationship between Tg and the degree of cure is formulated usingthe DiBenedetto equation

Tg − Tg0Tg∞ − Tg0

=λα

1− (1− λ)α, (7)

where Tg0 is the glass transition temperature of the uncured resin, Tg∞ the glass tran-sition temperature for fully cured resin and λ is a fitting parameter[3, 4, 6].

2.3 Shift factors

As mentioned earlier, thermosets are categorised as thermo-rheologically polymers. Thetime-temperature superposition is applied to make correlations between temperatureand time. TTS implies that temperature and time are generally equivalent in affectingthe relaxation modulus of the polymer. The TTS is implemented as a horizontal shiftfactor, and the resulting curve of the different times and temperatures is called themaster curve.

Since the temperature dependence of the response time of the relaxation modulus can bedetermined by the temperature shift factor αT many different models have been producedto generalize the shift factor based on the free volume, such as Williams-Landel-Ferry(WLF), Doolittle, Goldstein [3], and Vogel[4]. The most noteworthy of these is the WLFequation, which has found a lot of success in accurately model polymers above their glasstransition temperature Tg. The WLF is described as follows

log(αT ) =−c1(T − Tref )

c2 + T − Tref, (8)

where Tref is the reference temperature, c1 and c2 are fitting parameters[3, 10].

The relaxation modulus is not just dependent on temperature. In previous studies[3, 4,5, 6] it was observed that the relaxation modulus chages with degree of cure also. Asthe degree of cure increased, so did the relaxation modulus. Therefore the concept ofcure shift factor is applied. The cure shift factor αc is usually based on experimentaldata, and there is no commonly used model like the WLF for αT . The αc implementedin this thesis are as follows

αc = exp

[−∆E

R(

1

Tg(α)− 1

Tg∞

], (9)

7

where ∆E is the activation energy of the material and Tg(α) the glass transition tem-perature at different values of degree of cure[10].

As mentioned earlier, αT moves the response of the relaxation modulus horizontallywith respect to time, and the αc has the same effect. The response time increases as thetemperature decreases or as the degree of cure increases, in Fig. 4 a schematic of therelaxation modulus dependence on the shift factors.

Figure 4: Schematic of the shift in response time of the relaxation modulus dependent on cureand or temperature shift factor.

As seen in Fig. 4 it takes time for a VE material to transition from the the glassy to therubbery. But depending on the temperature and curing the transition time can becomemuch shorter as mentioned earlier. The relaxation modulus has an direct impact onthe stress and strain. The warpage that occurs during curing is due to the in-buildstress, and when it relaxes, this will cause the effect of warpage. What we expect for thewarpage is that when the stress changes in Fig. 4 the warpage will change. The faster therelaxation of the stresses, the more distortion, i.e., warpage, will occur. Since the shiftfactors shift the response time, they are essential factors to consider when describing thewarpage of viscoelastic materials.

To account for the cure shift factor the response time in Eq. 4 needs to be modified as

8

follows

ψ =

∫ t

−∞

dt′

αTC. (10)

where the αTC is the product of the temperature and cure shift factors,

αTC = αc · αT , (11)

making the total shift in the logarithmic scale the sum of the two shift factors

log(αTC) = log(αc) + log(αT ).

The product definition in Eq. 11 is the key stone in the RISE model, other models donot use the same definition where the shift factors are defined as a product[3].

2.4 Implementation of the stress calculation

The viscoelastic model created by RISE is based on the two following assumptions:

1) The degree of cure and temperature changes may have an equal time scale as theprocessing time and the time derivatives of the material functions for the modelcannot be neglected.

2) Viscoplasticity is excluded, and the material is linear viscoelastic.

To keep the following section easier to go through, only one dimension is described. Butkeep in mind that the following calculations are applied in all directions. For a morerigorous derivation, the reader can find the details given in the paper by Saseendran etal.[13]. Free thermal expansion or curing shrinkage are not explicitly included in theexpressions. This results in the strain expression

ε = εapplied − εfreethermal − εfreecuring. (12)

The strain in Eq. 12 is only valid for small strains, which are assumed in this thesis.We will now briefly discuss the main steps and assumptions before looking at how theequations are implemented. For a nonlinear viscoelastic material, using assumption 1)the first Helmholtz free energy function expansion is written in terms of the appliedstrain

F = φ0(α, T )ε2

2−∑i,n

A0ih1(α, T )ε(t)ξi +

1

2

∑i

B0inh2(α, T )ξi, ξn, (13)

where ξi is the internal state variables and i and n goes from 1, ..., I where I is thenumber of Prony terms, A0

i and B0in are constants,h1 is the weight factor in front of the

convolution integrals and h2 describes how the strain changes during the whole history

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affects the current instance. In Eq. 13 the parameters are dependent on the degree ofcure and temperature. Using Eq. 13 the stress-strain can be described as

σ = Ω0(α, T )ε− h1(α, T )∑i

A0i ξi. (14)

Assuming that the rate of the internal state variables are linear with respect to conju-gated thermodynamic forces and using assumption 2) the reduced time in Eq. 10 areintroduced and Sessandran et al. obtain the following stress-strain relationship

σ = Er(α, T ) + h1(α, T )

∫ ψ

0(ψ − ψ′)d(h2(α, T )ε)

dψdψ′, (15)

where ∆C are described as follows

∆C =∑i

Ciexp(− t

τi). (16)

In the prony series in Eq. 16, Ci are constants and τi are constant relaxation time. Inthe stress-strain relation described in Eq. 15 the Er corresponds to the rubery modulus.In the prony series in Eq.16, Ci are constants and τi are constant relaxation time.Saseendran et al.[9] assumes that during a small interval δtk+1 the viscoelastic parametercan be approximated as linear functions of time τ ∈ [tk, tk+1]. This gives us the followingrelations,

α = αk + dk+1α (τ − tk) where dk+1

α =αk+1 − αk

tk+1 − tk, (17)

h2(τ) = h2(tk − 0) + dk+1h2 (τ − tk)H(τ − tk), where dk+1

h2 =hk+1

2 − hk2tk+1 − tk

, (18)

ε(τ) = ε(tk − 0) + dk+1ε (τ − tk)H(τ − tk), where dk+1

ε =εk+1 − εk

tk+1 − tk. (19)

In Eq.18 and 19, H is the Heaviside step function. Using the linear approximations Eq.17, 18 and 19 leads to a calculation scheme that converges much faster than commonschemes where values of parameters in the starting point of the increment are used[9].Any function with fk−1 = f(tk−1), fk = f(tk) and fk+1 = f(tk+1).

Sesanndran et al.[9] implements the RISE model using the Euler forward method, whichis a first-order numerical method. The stress-strain relationship are implemented asfollows,

∆σk+1 = ∆Ck+1 ·∆εk+1 + ∆σkR. (20)

10

Here ∆σkR is the viscoelastic contribution which are dependent on the strain in timeinstant tk and before and is calculated as

∆σkR =∆Ek+1r · εk + hk+1

1 · hk+12 · εk ·

∑i

Ci ·∆Ik+1i

+ ∆hk+11

∑i

CiSki − hk+1k

∑i

CiSki

[1− exp

(−∆ψk+1

τi

)],

(21)

and ∆Ck+1 is expressed as follows

∆Ck+1 = Ek+1r + hk+1

1

∑i

Ci[hk2 ·∆Ik+1

i + 2∆hk+12 · Nk+1

i

]. (22)

As mentioned earlier we will only consider viscoelastic materials that are thermorheo-logically simple. For thermorheologically simple Er is assumed to be constant and theweight factors h1 = h2 = 1. For thermorheologically simple materials Eq. 21 and Eq.22 can be rewritten.

∆σkR = −∑i

CiSki

[1− exp

(−∆ψk+1

τi

)], (23)

and ∆Ck+1 as∆Ck+1 = Ek+1

r +∑i

Ci∆Ik+1i (24)

Ik+1i is obtained using the following equation

Ik+1i =

1

dkα + 1/τi

(dkα +

1− exp(−∆ψkτ1

∆tk · αk+1

), (25)

and Ski is calculated using

Ski = Sk−1i exp

(−∆ψk

τi

)+ ∆Iki ·∆ε

k. (26)

The reduced time in Eq. 10 is calculated using the following equation

∆ψk+1 =∆tk+1

∆αk+1ln

(1 +

∆αk+1

αk

). (27)

Assuming that in a small time interval tk to tk+1 the change of the VE parameters canbe approximated as linear so we can use the following linear function in the intervalτ ∈ [tk, tk+1].

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3 Method

The FE model of an ultrathin (fcCSP) was modeled as described by Lin et al. in LS-Prepost, which is the modeling tool for LS-Dyna.The FE model can be seen in Fig.5.

3.1 Model dimensions

The dimension of the fcCSP are 16(x)×16(y)×0.68(z) mm3, where the die measured at10(x)×10(y)×0.3(z) mm3. The height of the C4 layer connecting the die to the substrateare measured at 0.06(z) mm. The C4 layer was simulated as MUF since the layer is acombination of both C4 jonits and MUF, and only 9% of the layer’s volume consists ofC4 joints. This assumption makes the FE model consist of three components, substrate,silicon die, and MUF. Due to the symmetry of the package, only a quarter needs to besimulated for the analysis.

Figure 5: A quarter FE model of fcCSP with die size of 10× 10 mm2.

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3.2 Modeling

The model was meshed with eight-node solid element.The silicon die and substrate wereassumed to be elastic isotropic due to no information from the authors[10]. The MUFwas modeled as viscoelastic using the RISE definition or the LS-Dyna"MAT_ADHESIVE_CURING_VISCOELASTIC" material definition. The materialproperties for the different components can be found in Tab. 1. Furthermore, the

Table 1: Material properties of fcCSP components.

Material E[GPa] ν CTE [ppm/K]Die 169.54 0.278 3.5Substrate 18.62 0.42 16

20@25C35@100C

MUF Tab.2 0.26 87@150C100@250C

densities of the materials needed to be taken into account. Lin et al.[10] did not providethese, but we know that the die is silicon from which has a density of 2330 kg/m3[14], thePCB has a density of 1850 kg/m3[15]. Finding the density of the MUF was a challenge,but since the MUF is a type of epoxy resin with a density span of 1100− 1400 kg/m3 sofor simplicity, the MUF was assumed to have a density of 1250 kg/m3[16]. The Pronyseries representing the relaxation modulus of the MUF can be seen in Tab. 2, whichneeded to be recalculated due to the subroutine created by RISE only being able tohandle seven Prony terms. The Prony terms were redueced by adding the weight inTab. 2 in an appropriate way.

Table 2: Generalized Prony series constants.

E0 = 15GPai ωi τi[s] i ωi τi[s]1 6.54e-11 1e-1 8 5.94e-2 1e172 3.32e-2 1e4 9 2.14e-2 1e193 7.15e-2 1e7 10 2.28e-3 1e204 1.45e-1 1e9 11 8.46e-3 1e215 2.96e-1 1e11 12 6.77e-7 1e226 2.15e-1 1e13 13 5.93e-3 1e237 1.16e-1 1e15 14 1.20e-2 1e26

13

The Prony terms from Tab. 2 where added as follows 1 + 2, 3 + 4,7 + 8,9 + 10 + 11and 12 + 13 + 14. The reason for adding the terms as described is the magnitude ofthe weights corresponding to each term. The terms with larger magnitudes is left alonewhich is the easiest way to still have a good estimation of the relaxation modulus. Thereduced Prony series implemented in the models can be seen in Tab. 3. The reason fornot using Tab. 2 for the LS-Dyna model is so the models are implemented in the sameway for more accurate comparisons.

Table 3: Reduced Prony series.

E0 = 15GPai ωi τi[s]1 3.32e-2 1e42 2.165e-1 1e93 2.96e-1 1e114 2.15e-1 1e135 1.754e-1 1e176 3.21e-2 1e217 1.79e-2 1e22

The Kamal cure kinetics in Eq. 5 and Eq. 6 was implemented with both models usingthe experimental data from Tab. 4. The temperature shift factor implemented usingthe WLF definition in Eq. 8 where Tref = 298[K], c1 = 220 and c2 = 1731[K].

Table 4: Estimated cure kinetics parameters for the Kamal equation.

A1[1/s] A2[1/s] ∆E1/R [K] ∆E2/R[K] m n1.0147e2 1.9051e6 6.5571e3 8.0093e3 3.0746e-1 1.0089

3.3 Model differences

Although most of the parameters in the simulation of the viscoelastic material are thesame for the RISE and LS-Dyna models, some key implementations are different.

One of the significant differences is in how the relaxation modulus is defined and used.In the LS-Dyna model, the relaxation modulus is calculated using bulk and shear. Incontrast, the RISE model looks at different states of the material, i.e., the rubbery andglassy states. Another difference regarding the relaxation modulus is how the experi-mental data in Tab.3 are used. For LS-Dyna, the experimental data for the relaxationmodulus in Tab. 3 are assumed to correspond to a fully cured material. On the otherhand, the RISE model uses the weights in Tab.3 and Eq.2 to calculate the differentvalues of the relaxation modulus for the glassy and rubbery states. The CTE is alsoimplemented differently in the models. For the LS-Dyna model, the CTE as a functionof temperature in Tab.1 can be used. In the case of the RISE model, only one value per

14

state is used. The minimum value of 20 ppm is selected for the glassy state, and themaximum value of 100 ppm for the rubbery state. Chemical shrinkage is implementedin the same way where the 15 ·10−4 and 22 ·10−4 are selected for the glassy and rubberystates, respectively. For the LS-Dyna model chemical shrinkage is assigned to the DoC,15 · 10−4 at the initial degree of cure of α = 0.7 and 22 · 10−4 when the material is fullycured α = 1.

However, the most significant difference between the two models is the inclusion of thecure shift factor Eq. 9, Eq. 11 and the DiBenedetto equation, Eq. 7. The inclusion ofthe DiBenedetto equation makes it possible for the RISE model to consider the rubberyand glassy states since they are connected to the glass transition temperature Tg. Theconstants in Eq. 7 was estimated by Lin et al. to be Tg0 = 308 K, Tg∞ = 393 K andλ = 0.2294. In Tab. 9 experimental values obtained by Lin et al. are shown. Thesevalues are correlating the degree of cure to the glass transition temperature which isused in Eq.9.

It is important to understand that the RISE model is only different from the LS-Dynamodel in implementing the stress-strain calculations described above. So how the modelshandle the temperature difference are the same. The same can be said for the spatialcalculation, where the nodes’ placement is calculated using LS-Dyna.

Table 5: Degree of cure and their corresponding glass transition temperature

α 0.73 0.80 0.90 0.92 1.0Tg[K] 342.02 351.20 360.20 370.20 393.00

3.4 Boundary, initial and load conditions

To avoid movement in z-direction during the simulation, a constraint was put on thebottom node in the model’s center. Since only a quarter of the model was createdsymmetric boundary conditions were applied to simulate the whole package using justa quarter. To create a symmetric boundary condition, constraints on the degrees offreedom are applied. For example, applying symmetric boundary conditions along they-axis means to constrain the motion of the nodes in the x-direction and the rotationalmotion in both x and z. In Fig. 5 the placement of the symmetric boundary conditionsare shown. The MUF was assumed to have an initial degree of cure α = 0.7.

The loading conditions used by Lin et al. were composed of two parts, an initial strain toaccount for the effective chemical shrinkage and the temperature profile imposed in thesubsequent in-molding and post-mold cure(PMC) process. The initial strain value usedwas 0.067%. The curing process was simulated over 18330 seconds with the followingtemperature profile: initial temperature set at 433 K and staid at 433 K for 50 s, followedby cooling down from 433 K to 298 K over 30 min. The model was then heated againfrom 298K to 488 K in 300 s. The temperature was then set at 488 K for four hours to

15

account for the PMC process. The package was then cooled down from 488 K to 298 Kfor 30 min. The model was finally heated again from 298 K to 523 K in 480 s, see Fig.6.

0 0.5 1 1.5 2

Time [s] 104

0

50

100

150

200

250

Tem

pera

ture

[°C

]

Figure 6: Temperature profile of the in-mold and post-mold cure process.

For the secondary scope only the RISE model where simulated. The investigation con-sisted of simulating the effect of the CTE and chemical shrinkage of the model. To seethe effect CTE has on the model the model was simulated by increasing and decreasingthe values of the CTE by two and four, i.e the CTE values where multiplied with twoand four or divided by the same amount to make four different simulations.

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4 Result & discussion

4.1 Cure kinetics verification

To verify the viscoelastic material definition created By RISE [9], the cure kinetics wascompared with the values obtained by Lin et al. [10]. First, we compare the tabulatedvalues from Tab. 5 with the simulated values from the RISE model. Fig. 7 shows thesimulated values are a perfect fit for all the tabulated values except for the α = 0.92.Still, overall the RISE model was able to simulate the relationship between the glasstransition temperature Tg and the degree of cure (DoC) exceptionally well. We can also

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Degree of cure

60

70

80

90

100

110

120

Gla

ss tra

nsitio

n tem

pera

ture

[°C

]

Simulated values

Experimental data

Figure 7: The glass transition temperature as a function of the degree of cure.

analyze how the cure shift factor as a function of Tg is calculated in the RISE model andcompare it with the calculated values using Eq. 9. In Fig. 8 we can see the Log10(αc)as a function of Tg.

17

60 70 80 90 100 110 120

Glass transition temperature [°C]

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Tim

e-c

ure

sh

ift

facto

r, L

og

10(a

c)

Simulated values

Vogel Model Fit

Figure 8: The cure shift factor as a function of the glass transition temperature compared usinga simulated model and the calculated values.

Comparing the experimental values with the simulated model, we can see that the sim-ulated values are slightly higher than the calculated values based on the Vogel model inEq. 9. We can see that although the RISE model has a bit higher values than expected.

The last thing we use to verify the cure kinetics of the RISE model is the degree of cureas a function of time. In Fig 9 we can see the cure development as a function of timefor both the RISE model in comparison with data from the article by Lin et al.[10]. InFig. 9 we also show the temperature profile as a function of time.

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0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time [s]

0

50

100

150

200

250

Tem

pera

ture

[°C

]

0.7

0.75

0.8

0.85

0.9

0.95

1

Degre

e o

f cure

Temperature

RISE model

Lin et al.

Figure 9: The cure and temperature development depicted against time to see how the degreeof cure of cure for the MUF depends on the temperature.

The degree of cure profile for the RISE model and the article, shows that the onlydifference is where the cure profile stagnates during the temperature decrees. The valuefrom the article stagnates at α = 0.9 while the RISE model stagnates at a value ofα = 0.97. The cure profile has the same trajectory and the time at which the profilesstagnate and becomes fully cured are at the same time points for the two comparedprofiles.

What we can conclude from Fig. 7, 8 and 9 are that there is some slight difference inthe cure kinetics between the RISE model and the article. But overall, we can withconfidence say that the RISE model has the desired cure kinetics.

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4.2 Warpage prediction

The predicted warpage, shown in Fig. 10 includes the result of simulating with a die sizeof 8× 8 mm2(to the left) and 10× 10 mm2 (to the right). The warpage is determined bycalculating the displacement in the z-direction and comparing it to the relaxed state. We

0 0.5 1 1.5 2

Time[s] 104

-3

-2

-1

0

1

2

Warp

age[

m]

RISE model

Ls-dyna model

0 0.5 1 1.5 2

Time[s] 104

-3

-2

-1

0

1

2

Warp

age[

m]

RISE model

Ls-dyna model

Figure 10: Warpage prediction measured in center of die for an fcCSP using two different vis-coelastic FE models. To the left the fcCSP is simulated with a die size of 8× 8 mm2 and to theright with a die size of 10× 10 mm2.

can see that RISE and Ls-Dyna predict the warpage differently. The magnitude of thewarpage is the same, but how the warpage change with time is different. The residualstress will decrease in a VE material if the external factors that can affect the residualstress are kept constant. If we consider Fig. 10 and remember that the temperatureis kept constant during the main part of the simulation, we can see that the warpageis increasing, which is a direct consequence of the residual stress decreasing. Let uscompare the result obtained in this thesis with the article by Lin et al. The warpagepredicted in the article was about 100 times larger than the expected warpage in thisreport, Tab. 6, even though all the experimental data provided by Lin et al was used inthis thesis. However, since both the RISE and Ls-Dyna models gave the same magnitude

Table 6: Warpage predicted[µm] in middle of fcCSP for the different models and die sizes at thelowest and highest temperature.

Model/Die size 8 10 12Lin et al.[10] -39 -72 -118RISE -2.4 -2.5 -0.53LS-Dyna -0.13 -0.13 -0.53

(a) At 25 C.

Model/Die size 8 10 12Lin et al.[10] 11 22 34RISE 0.24 0.13 1.2LS-Dyna 1.6 1.6 1.2

(b) At 250 C.

difference, we conclud that the article did not include all the necessary information forthe die and substrate to reproduce their result. We know that the viscoelastic materialfor the RISE model is calculated accurately due to the result in Fig. 8 and Fig. 9, so

20

this is not the issue.

We can further strengthen this argument by considering the predicted warpage for themodels with a die size of 12× 12 mm2, see Fig.11.

0 0.5 1 1.5 2

Time[s] 104

-1

-0.5

0

0.5

1

1.5

Warp

age[

m]

RISE model

Ls-dyna model

Figure 11: Warpage prediction measured in center of die for an fcCSP using two different vis-coelastic FE models with a die size of 12× 12 mm2.

21

Fig.11shows that both models predicts the same warpage. One possible reason is thatthe die size is to big. Since the die is 12 × 12 mm2 and the whole fcCSP has a bodysize of 16 × 16 mm2, the viscoelastic material MUF has too little of an influence, butthe warpage is still in the same magnitude as the rest of the different die sizes, which isnot the case for the article where the warpage is increasing in magnitude with the diesize. But although the magnitude of the warpage can not be compared with the articlewe can consider the warpage profile in Fig 12.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time [s] 104

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Warp

age [

m]

-80

-60

-40

-20

0

20

40

60

Warp

age [

m]

Ls-Dyna

RISE

Lin et al.

Figure 12: Warpage profile for a fcCSP with die size of 10× 10 mm2 for the article [10] and thetwo simulated models. The left y-axis shows the predicted warpage for the RISE and LS-Dynamodel while the right y-axis shows the warpage value for the article published by Lin et al..

Comparing the warpage profile for two different models with the result obtained from Linet al., the profiles for a die size of 10×10 are shown in Fig. 12. As is shown in Tab. 6 theresult for the article by Lin et al. is larger with a factor of about 10. The most significantdifference between all models is during the PMC process when the temperature is at aconstant temperature of 120C. The warpage of LS-Dyna only change slightly duringthis process, while the warpage for the RISE model changes drastically during the PMCprocess. The RISE model have the same change pattern as the article which is shown inFig. 12. The relaxation modulus keeps changing with respect to time and temperature

22

for a viscoelastic material due to the shift factors introduced in the method. This, inturn, will affect the stress state of the material, which consequently affects the warpage,and since the LS-Dyna model omits the αc, the warpage will not have the same behavior.

4.3 RISE vs LS-Dyna

Even if the warpage from the article could not be obtained, we can continue to investigatethe simulated models and compare them. For the model comparison, I will only includesimulations for the die size of 10× 10 mm2. To compare the models one simulation forthe RISE model was created where the αc = 0 to create a model which is more like theLS-Dyna model. In Fig. 13 we can see the simulations of the LS-Dyna model and theRISE model with both the αc included and not included.

0 0.5 1 1.5 2

Time [s] 104

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Warp

age [

m]

Ls-Dyna

RISE with cure shift

RISE without cure shift

Figure 13: Warpage profile prediction for a die size of 10× 10 mm2, for the LS-Dyna model, andRISE model with and without cure shift factor.

We start by comparing the result for the RISE model with and without αc. The inclusionof αc reduces the stress relaxation time compared to the models where αc is not included.The reduced relaxation time is to be expected since the shift factors is the reason for thetime shift of the stress curve in Fig.4. If we instead look at the result from LS-dyna incomparison with the RISE model without αc we can see that during the PMC process,

23

the warpage profile is relatively similar, which is expected since the stress relaxation forthese two models should have similar relax time and distortion.

(a)

(b)

Figure 14: Warpage depiction of the full fcCSP at 250C with die size of 10× 10 mm2 simulatedusing: a) RISE model b) LS-Dyna model.

24

Instead of studying the warpage profile for one node, we can consider the warpageprediction of the whole fcCSP at the end of the simulation.Fig. 14 shows the predictedwarpage for the fcCSP with a die size of 10 × 10 mm2, at 250 C, and it shows thatthe models have a notable difference between the two models.For the RISE model, weget a lot of bending at the edges of the fcCSP. We still have warpage for the LS-Dynamodel, but it is significantly smaller than the RISE model. The LS-Dyna model has thesymmetric warpage prediction which we want to obtain while the RISE model does notobtain it. The symmetric prediction by the LS-Dyna model is what we expect since thefcCSP is a symmetric product.

To investigate the problem with the symmetry, we can look at the x- and y-displacementwith respect to time during the simulation. To make a fair comparison, shown in Fig. 15the displacement for the RISE model without αc and compare it to the LS-Dyna model.15.

Figure 15: Displacement in the x-direction (to the left) and y-direction (to the right) for theLS-Dyna model and the RISE model without cure shift factor.

The x-displacement for the different models is a perfect fit, the only difference is thatthe LS-Dyna model overshoots at the beginning of the PMC process and then goes downwith time. The y-displacement is another story.

25

The RISE model has a significantly lower value during the PMC process, which couldbe the reason for the unsymmetrical warpage. From Fig. 15 we can conclude thatproblem are in the y-direction. Since the implementation of the stress in each directionis independent of each other for the RISE model as mentioned in section 2.4, we canwith good certainty conclude that there exist an implementation error in the y-direction.Discussions with the author of the code was conducted and the possibility for error duringthe implementation is possible, strengthening the argument. This argument is furtherstrengthened by considering that the RISE model only calculates the stress differentlythan the LS-Dyna model i.e, the node displacement is calculated in the same way.

26

4.4 Secondary scope

In the secondary scope, we investigated how the CTE influences the warpage predictionof the RISE model. The RISE model was simulated with both two and four timeshigher and lower CTE values.Fig. 16 shows the resulting warpage for the simulationswith different CTE values. As we can see the warpage becomes more prominent with

Figure 16: Warpage prediction using the RISE Model with different CTE values.

higher values of CTE. Also the magnitude of the warpage is significantly large betweenthe original values and the four times higher and four times lower values. As also canbe seen is that the simulations with lower values of CTE have lesser warpage than theoriginal. A simulation was also done where the CTE of the MUF was set to almost zero1e-10. The warpage predicted was the same as in Fig. 11, which further strengthens theargument that the lack of VE effect on the warpage is due to the die and substrate.

27

4.5 Conclusions

Fig.10 and 11 shows the warpage profile for the RISE and LS-Dyna for the different diesizes. The warpage profile with die size 8× 8 and 10× 10 are similar to each other. Butfor the die size of 12 × 12, the warpage is different compared to the previous warpagesin Fig. 10. What can be noted, though in Fig. 11 is that the warpage for die size12 × 12 are the same for both the models. The conclusion was drawn that when thedie size becomes too big, the viscoelastic MUF has little effect on the warpage. Thewarpage in Fig.11 was a part of the conclusion of the magnitude difference between thearticle and the two simulated models are due to information about the article simulationwas left out. If we compare the warpage profile in Fig.11 we can see that the predictedprofile for the RISE model follows the same trajectory as the result from Lin et al.[10].Although the magnitude of the warpage was unobtainable in this thesis, the RISE modelis getting the desired decrease of the warpage when including the cure shift factor duringthe PMC process. The desired decrees were not obtainable using the LS-Dyna model,indicating that the cure shift factor is necessary to simulate the warpage of viscoelasticmaterials accurately. Looking at the warpage at the end of the simulation, the RISEmodel did not produce symmetric warpage prediction for the whole fcCSP in Fig.14. Incontrast, the LS-Dyna model produced symmetric warpage prediction. An investigationinto the RISE model where conducted, and we could see in Fig.15 that the stress andstrain in the y-direction could be wrongly implemented. Since both models are using theLS-Dyna method for calculating the nodal displacement and the models are simulatedusing the same mesh, the miss implementation in the y-direction is further strengthenas the cause. For the second scope in this thesis, Fig.16 shows that the RISE modelhas a high response on the CTE values. In conclusion, the RISE model still needs somework, particularly in investigating the unsymmetric behavior, but the RISE model isproducing the aspired warpage profile prediction.

In further projects, I would recommend starting by investigating the implementationof the stress-strain calculations for the y-direction. I would then recommend the RISEdepartment in Piteå to make a simulation based on their investigation so that all stepsin the simulation are well known and no information is lost.

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