Characterization of the viscoelastic properties of ... - Semantic Scholar
Microelectronics Reliability 52 (2012) 1711–1718
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Characterization of the viscoelastic properties of an epoxy molding compound during cure M. Sadeghinia ⇑, K.M.B. Jansen, L.J. Ernst Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
a r t i c l e
i n f o
Article history: Received 8 November 2011 Received in revised form 20 March 2012 Accepted 21 March 2012 Available online 18 April 2012
a b s t r a c t In the electronics industry epoxy molding compounds, underfills and adhesives are used for the packaging of electronic components. These materials are applied in liquid form, cured at elevated temperatures and then cooled down to room temperature. During these processing steps residual stresses are built up resulting from both cure and thermal shrinkage. These residual stresses add up to the stresses generated during thermal cycling and mechanical loading and may eventually lead to product failure. The viscoelastic properties of the encapsulation material depend highly on temperature and degree of cure. This paper investigates the increase of elastic modulus and the changes in the viscoelastic behavior of an epoxy molding compound, during the curing process. This is done using the shear setup of a Dynamic Mechanical Analyzer DMA-Q800. The cure dependent viscoelastic behavior is determined during heating scans of an intermittent cure experiment. In such an experiment the material is partially cured and then followed by a heating scan at 2 °C/min. During this heating scan continuous frequency sweeps are performed and the shear modulus is extracted. The Time–Temperature superposition principle is applied and the viscoelastic shear mastercurve is extracted. Analyzing the shear modulus, the cure dependent viscoelastic material behavior was modeled using the cure dependent glass transition temperature as a reference and a cure dependent rubbery modulus. It is shown that partial curing would increase the glass transition temperature and rubbery shear modulus. It also shifts the viscoelastic mastercurve to the higher time domain. Taking Tg as the reference temperature for different heating scans, the mastercurves collapse to one graph. In addition, using a Differential Scanning Calorimeter (DSC), the growth of the glass transition temperature, T DSC g , with respect to the conversion level is obtained. These values are coupled to the values of glass , for calculating the conversion level at each step of curing transition temperature in DMA apparatus, T DMA g process in shear mode test. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Epoxy molding compounds (EMCs) are widely used for encapsulating semi-conductor devices. Curing of these materials during the production process will induce residual stresses in the products. In addition due to the mismatch in the coefficient of thermal expansion, the stresses will increase during the cooling down from molding to ambient temperature. These residual stresses will reduce the reliability of the devices and may lead to failure of the product. Therefore, nowadays investigating the thermo-mechanical (and viscoelastic) properties of the molding compounds has become an important issue in electronic packaging. The viscoelastic properties of the encapsulation material depend highly on temperature, degree of cure and moisture. Several studies have been done on characterizing the effect of curing and filler concentration on ⇑ Corresponding author. Tel.: +31 152785707; fax: +31 152782150. E-mail address: [email protected] (M. Sadeghinia). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.03.025
the thermo-mechanical (and viscoelastic) properties of the packaging materials. For example, Yang et al. [1,2] focused on the rubbery modulus of a series of filled epoxy resin and investigated the effect of the filler concentration and curing process on the changes of the rubbery modulus. His results revealed that the growth of rubbery modulus is dependent on the conversion. Jansen et al. [3,4] showed that the glass transition temperature of the fully cured materials is dependent to the curing level and the rubbery CTE decreased with increasing cure. Furthermore, they [5] extracted a full cure dependent viscoelastic model for the shear modulus of a commercial molding compound by monitoring the changes in the viscoelastic properties of the compounds during cure. A cure-dependent viscoelastic model was also proposed [6–9] to describe the evolution of the viscoelastic behavior of an underfill resin in a flip chip package during isothermal and non-isothermal cure. Curing of the molding compounds is always accompanied with the chemical shrinkage which can cause warpage in microelectronic packages. FE modeling of map-molding process [10,11]
M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
was carried out for a map mold encapsulated with the epoxy system and the warpage caused by the curing process and the subsequent cooling down stage was investigated. Moreover, Hu et al. [12] developed a FEA evaluation method for the chemical cure shrinkage based on the measurement of the warpage of biomaterial model and revealed that FEA simulations with chemical cure shrinkage show fair agreement with experimental measurements of package warpage. The effects of moisture on the mechanical properties and glass transition temperature of the epoxy molding compounds were also studied by Lu et al. [13] and Walter et al. [14]. Their experimental results revealed that the absorbed water continuously decreases the mechanical strength of the epoxy molding compound. They also showed that the glass-transition temperature decreases at an early stage. In the present research, the changes in viscoelastic properties of an epoxy molding compound during an intermittent cure experiment are monitored using a Dynamic Mechanical Analyzer (DMA) Apparatus. In such an experiment the material is partially cured for a short period of time at a temperature with low curing rate. The isothermal curing process is then interrupted by a quick temperature drop and afterwards followed by a constant heating ramp. The sequence of partially curing, cooling and heating is then repeated and the viscoelastic data is recorded during each heating step. Independent values of the glassy and rubbery shear modulus were obtained by combining the glassy and rubbery elongation (tensile) and bulk moduli. These latter two values are measured separately by using a DMA (tensile mode) and a GNOMIX high pressure dilatometer-apparatus, respectively. The content of this paper concerned with the first part of our research work. In the next step, these data will be used as an input in our FEM Abaqus model for establishing the critical interfacial fracture properties of EMC-Cu interfaces, which will be reported in the near future.
2. Experimental Since commercial materials often have complicated mixtures of components with unknown chemistry, we chose to use a model epoxy system consisting of similar components as used in commercial molding compounds. The system consists of epoxy Novolac (EPN 1180, Huntsman Advanced Materials, equivalent weight 175– 182 g/eq) as a matrix material, Bisphenol-A (equivalent weight 114 g/eq) as hardener and fused silica spheres (FB-940, ex Denka, median diameter 15 lm, density 2.20 g/cm3) as filler. Triphenylphosphine (TPP, 0.5 g/100 g epoxy) is used as a catalyst. The epoxy Novolac and Bisphenol-A were mixed in a stoichiometric ratio. The material has a filler percentage of 64.5 wt.% (50 vol.%).
The glass transition temperature, Tg, indicates the transition from the glassy (solid) state to the liquid or rubbery state. For molding compounds this glass transition is not a single temperature but covers a range of about 20–50 °C. This is because the glass transition is a kinetic process which depends on both the measurement method and the data evaluation procedure. The Tg values can be obtained from DSC data as the changes in the slope of the heat flow vs. temperature curves. The glass transition temperature during cure vs. conversion was determined by analyzing the heat flow curves of uncured and partly cured samples. Firstly, samples of approximately 5–10 mg were partially cured by performing an isothermal cure for 45, 110, 320 and 1200 min at 120 °C. Then the glass transition temperature of these partially cured samples was obtained by scanning from 30 to 200 °C at a rate of 10 °C/min, Fig. 1a. The sample’s conversion was determined by measuring the heat released during the scan and applying this value to Eq. (1). The measured glass transition temperature as a function of the conversion is shown in Fig. 1b. The glass transition temperature of a thermosetting polymer depends on the crosslink density, the number of free chainends and the rigidity of the polymeric segments. It was shown that the glass transition temperature in crosslinked system increases linearly with the concentration of the crosslinks which restricts the free volume and free chain-ends [16]. Fig. 1b shows that the Tg of partly cured sample increases by the conversion level.
1.5
Heat Flow [J/(g ×s)]
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Tg increase and heat flow reduction for partially cured sample
1
0 -0.5 -1 -30
20
70
ð1Þ
where Htot is the reaction heat released by curing a freshly mixed sample and Hrest is the released heat of partly cured sample. These two values can be obtained from the heat flow vs. time curves of uncured and partly cured samples respectively.
120
170
220
270
320
Temperature [°C] Fig. 1a. DSC heating scan of uncured and 61% cured sample (cured at 120 °C for 110 min), Partial curing increased the Tg for almost 50 °C, However the released heat (area below the peak point) decreased from 63 to 24.5 J/g.
120 100
H a ¼ 1 rest ; Htot
partly cured
0.5
Measured
2.1. Degree of conversion vs. glass transition temperature
DiBenedetto
80
Tg [°C]
A differential scanning calorimetry, TA-instruments DSC2920, was used to obtain the relation between the degree of chemical conversion and the glass transition temperature. The conversion of a partly cured sample, a, is measured by determining the remaining heat of reaction which is released upon further curing of the specimen [15].
uncured
60 Tg0 [°C]= 15.5 Tg1 [°C]= 111.2 λ =0.652
40 20 0 0
0.2
0.4
0.6
0.8
1
Conversion Level [α] Fig. 1b. Tg of partly cured samples along with fitting parameters to the Eq. (2), full lines: fits to Eq. (2), symbols: extracted from the heat scan of partially cured samples.
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b1 and b2 are the fitting parameters. The parameter C1 determines the steepness of slope change during the transition region. Tgp is the pressure dependent glass transition temperature:
0.025
10 20 30 40 50 60 70 80 90 100
3
d(Volume) [cm /g]
0.02
0.015
T gp ¼ T gpv t þ s0 P
ð5Þ
where T pgv t is the fully cured Tg at atmospheric pressure, s0 is a fitting parameter and P is the hydrostatic pressure. Using non-linear curve fitting of Matlab, the parameters of Eqs. (3)–(5) were determined and summarized in Table 1. The volumetric CTE at atmospheric pressure, P = 0, can be calculated by differentiating the volume changes with respect to temperature, resulting in:
Glass transition line
0.01
0.005
1 CTEv ðT; 0Þ ¼ k1 þ k2 ð1 þ tan h½C 1 ðT T gpv t ÞÞ 2 0 40
60
80
100
120
140
160
180
200
220
T [°C] Fig. 2. Volume changes in different temperature and pressure from PVT measurement, symbols: experimental data, full lines: fit to Eq. (3), the legends refer to the applied pressure.
In this paper the empirical model of DiBenedetto is applied for relating the glass transition temperature to the degree of conversion [15].
T g ðaÞ ¼ T g0 þ
ðT g1 T g0 Þka 1 ð1 kÞa
ð2Þ
where a denotes the degree of cure, k is a fitting parameter. Tg0 and Tg1 are the glass transition temperatures of uncured and fully cured polymers, respectively. The parameters obtained from this fit are summarized in Fig. 1b. The Tg value at 29% conversion is slightly higher than the DiBenedetto fit. However since the determination of a Tg value is typically with 2–5 °C accuracy, the deviation is not considered to be significant.Note that the DiBenedetto equation reduces to the equation proposed by Pascault and Williams if the fit parameter k is set to the DC p1 DC p0 ratio, used in their publication [15].
ð6Þ
In which k1 and (k1 + k2) represent the volumetric thermal expansion at low and high temperature respectively. The compressibility b (T) is calculated using the following definition:
bðTÞ ¼
1
t0
@t @P
ð7Þ T
where t is the specific volume. Since viscoelastic effects in the compressibility were shown to be small, the volumetric response is assumed to be elastic, but temperature dependent [18–20]. The bulk modulus is calculated as the reciprocal of the bulk compressibility i.e. Eq. (8).
K¼
1 bðTÞ
ð8Þ
Using the Tait equation, the following equation is derived for the bulk modulus.
KðTÞ ¼
k 1 s0 þ
1 k s 2 2 0
1 n h io C 1 þ tan h C 1 ðT T pgv t Þ þ b1 expðb 2 TÞ
ð9Þ
Fig. 3 shows the calculated bulk modulus of the fully cured material. It ranges from 15.2 GPa at 50 °C to 4.6 GPa at 200 °C.
2.2. Compressibility and bulk modulus
2.3. Elongation (tensile) modulus
The compressibility of the material was measured using a high pressure dilatometer-PVT apparatus. The pressure and temperature were stepwise increased and the corresponding volume changes were recorded. Typical temperature and pressure ranges were 40–200 °C (in steps of 10 °C) and 10–100 MPa (in steps of 10 MPa). The volume changes of the fully cured molding compound are shown in Fig. 2. The volume changes were fitted to a modified form of the Tait equation [17].
The viscoelastic elongation properties of the fully cured material as a function of the excitation frequency and temperature is studied by a Dynamic Mechanical Analyzer, TA instrument Q800. A sinusoidal displacement (strain e) is applied to a sample and the resulting force (stress r) is measured [21]. The sample had the dimension of 22.6 4.9 0.5 mm. The experiment covered the frequency and temperature range of 0.32–32 Hz and 20– 200 °C respectively. For a perfectly elastic material, the resulting stress and the strain will be perfectly in phase. For a purely viscous material, there will be a 90° phase lag of stress with respect to strain. Viscoelastic materials have the characteristics in between where some phase lag will occur during DMA tests.
tðT; PÞ ¼ t00 ðTÞ 1 C ln 1 þ
P b1 expðb2 TÞ
ð3Þ
With C = 0.0894 and t00 (T) as:
00
t
lnðcos h C 1 ðT T gp Þ Þ 1 ðTÞ ¼ t0 1 þ k1 ðT T gp Þ þ k2 ðT T gp Þ þ 2 C1 ð4Þ
where t0, T and P are the initial volume, temperature and hydrostatic pressure respectively.
e ¼ e0 sinðxtÞ
ð10Þ
r ¼ r0 sinðxt þ dÞ
ð11Þ
In which x is the applied frequency and d the measured phase lag. By expanding Eq. (11), the stress can be considered to consist of two components:
Table 1 T pgv t and fitting parameters of Eqs. (3)–(5). Properties t0 (cm3/gm)
k1 (1/°C)
k2 (1/°C)
C1 (1/°C)
b1 (MPa)
b2 (1/°C)
T gpv t (°C)
s0 (°C/MPa)
0.609
7.9E5
1.88E4
0.033
5633.8
9.1 E3
98
0.445
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2.4. Shear modulus during cure
Fig. 3. Bulk modulus of the fully cured material in different temperature.
r ¼ r0 sinðxtÞ cos d þ r0 cosðxtÞ sin d
ð12Þ
The relation between the applied strain and the measured stress can be defined by two parameters: E0 and E00 where:
r0 r0 cos d and E00 ¼ sin d e0 e0
E0 ¼
ð13Þ
E00 ¼ tan d E0
ð14Þ
Complex modulus E can be used to express the moduli E as follows:
E ¼ E0 þ iE
00
ð15Þ
0
E is called the storage modulus, since it is proportional to the stored energy in the test sample and representing the elastic portion. E00 on the other hand is called the loss modulus since it is proportional to the dissipated energy. Similarly the shear storage and loss moduli, G0 and G00 , are defined. Fig. 4 shows that the Eg (elongation glassy modulus) and Er (elongation rubbery modulus) are independent of the frequency and have the values of 7200 MPa and 102 MPa respectively. Note that this storage modulus drops by the factor 70 during the glass transition, where as the bulk modulus only drops by a factor of 3.
2.4.1. Test setup The mechanical properties of the material during the curing process were measured with a specially made shear set up. The setup consists of 3 mm diameter circular surfaces between which the uncured sample is positioned. The samples were gently preheated until they became soft and sticky. Care was taken to avoid preliminary reaction. The size of the shear surfaces were chosen such that the test was performed in a Dynamic Mechanical Analyzer DMA Q800-TA Instrument. The experiment covers the frequency and temperature range of 0.32–60 Hz and 20–160 °C. Fig. 5 shows a schematic diagram of the shear tool. The cure dependent viscoelastic behavior was determined during heating scans of an intermittent cure experiment. As Fig. 6 shows, in such an experiment the isothermal curing process is interrupted by a quick temperature drop, followed by a heating scan at 2 °C/min. The isocure heating is done at a temperature where the reaction is still slow. After a short isothermal period the sequence of cooling and reheating is repeated and viscoelastic data is recorded. The reheating scan from below to above T DMA g (after each isocuring part) is used to determine the glassy and rubbery modulus values as well as the glass transition temperature for is a measure for the actual cure state each heating ramp. This T DMA g after each period of isocuring. During this heating scan continuous frequency sweeps were performed (0.32–60 Hz, 10 lm amplitude). 2.4.2. Deriving the modulus Deriving the mechanical properties of the curing material through the usage of the shear test set up is not simple, since cured molding compounds are about as stiff as the mechanical frame of most tensile testers which complicates the exact determination of modulus values for the molding compounds. As a result, the apparent measured storage modulus may deviate from the real one. We therefore correct the storage modulus by assuming that the measured deformation consists of the sample plus the frame deformation (Fig. 7 and Eq. (16)).
dxa ¼ dxm þ dxf
ð16Þ
The stiffness was derived by dividing Eq. (16) through the force F (1/S = dx/F).
Eg=7.2 GPa
Er=0.1 GPa
Fig. 4. Elongation storage modulus (E0 ) vs. temperature in different frequencies, measured by the DMA experiment.
M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
Gap for sample
1715
Fixed parts
Moving shaft
Fig. 7. Schematic diagram of the frame and sample stiffness. Fig. 5. Schematic diagram of the shear clamps.
1 1 1 ¼ þ S a Sm Sf
ð17Þ
where Sa, Sm, Sf are the apparent, sample and frame stiffnesses respectively. Eq. (17) can be rearranged for extracting the sample stiffness:
Sm ¼
Sa 1 Sa Sf
ð18Þ
The yet unknown frame stiffness, Sf, is obtained by comparing the measured glassy and rubbery stiffness with separately determined glassy and rubbery shear modulus values. The latter is done by measuring the elongation and the bulk modulus. In glassy and rubbery region the material is elastic and therefore the following relation exists between bulk (K), shear (G) and elongation modulus (E) [5].
G¼
3KE 9K E
ð19Þ
Furthermore, the relation between the measured sample’s shear stiffness and the shear storage modulus is:
Gm ¼
Sm bgeo
ð20Þ
where Gm and Sm are the measured sample’s shear storage modulus and the sample’s shear stiffness respectively. bgeo is a geometry factor determined by the shear surface and gap thickness.
1th warming up ramp, Stiffness data
Temperature ramp
Applying the glassy and rubbery bulk and elongation modulus for the fully cured material (Figs. 3 and 4) to the Eq. (19), the glassy and rubbery shear modulus were calculated for the fully cured material (Table 2). Deriving the sample’s stiffness in different heating scans from the apparent one consists of three steps. 1. For the fully cured material, i.e. the last heating scan, the rubbery stiffness of the material is low compared to the frame stiffness. Therefore, the frame stiffness correction (Sf) is small and the bgeo is calculated assuming Sm = Sa via Eq. (20) and Table 2. 2. Using the derived bgeo, Sf will be calculated through using Table 2, Eqs. (18) and (20), for the fully cured material i.e. the last heating scan. 3. Finally the full range of Sm is calculated applying the calculated values of Sa and Sf in Eq. (18). If the frame stiffness is not corrected, the apparent measured storage modulus will be almost half of the true value in the glassy region. However its effect is small in the rubbery state. Therefore, if the uncorrected values are used to calculate the glassy bulk modulus or Poisson ratio, significant errors may occur. 2.4.3. Construction of time-cure mastercurve For each heating scan a mastercurve, related shift factor and glass transition temperature can be derived via the Time–Temperature Superposing principle (TTS). The frequency continuously cycles between 0.32 and 60 Hz and the temperature increases at 2 °C/
Glassy state
th
7 warming up ramp, stiffness data
Rubbery state
Fig. 6. Stiffness and temperature profile of the sample during the intermittent cure test. The stiffness data is shown for different frequencies ranging from 0.32 to 60 Hz. The stiffness curves increase if the temperature drops and decrease during a heating ramp. Each next heating curve is at a higher conversion level.
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Table 2 Elastic moduli at 50 °C (glassy values) and 150 °C (rubbery), fully cured material. Glassy state 50 °C
Rubbery state 150 °C
E (MPa) G (MPa) K (GPa)
7200 2520 15.2
102 37.7 4.9
Table 3 T DMA and conversion level for all heating scans. g Heating ramp (°C) T DMA g
Conversion (a)
1
2
3
4
5
6
7
96
107
113
118
124
127
132
0.71
0.81
0.86
0.9
0.94
0.96
1
Shear Storage Modulus [Mpa]
Property
3
10
2
10
1
10
0
Gðt; T; aÞ Gr ðaÞ Gn ðt; TÞ ¼ Gg Gr ðaÞ
ð21Þ
here Gn denotes the normalized shear curve, Gg and Gr are the glassy and rubbery shear modulus respectively. Without further need for adjustments all relaxation curves collapse to a single mastercurve, Fig. 11. This temperature- conversion mastercurve is therefore sufficient to describe all cure dependent viscoelastic behavior. A Prony series could be fitted to the normalized mastercurves for evaluating them in a finite element program. For each of the intermittent shear mastercurves in Fig. 10, there is a corresponding temperature-shift factor, Fig. 12. It can be seen that the shift factor curves shifted to the right side with increasing
-2
0
10
2
4
10 10 Frequency [rad/s]
10
6
10
Fig. 8. Shear storage modulus mastercurve as a function of frequency for 81% cured material (2th heating scan), data extracted by analyzing the DMA measurement, Tref = 110 °C.
Shear Modulus [MPa]
10
3
0.71
10
2
0.81 0.86 0.9 0.94 0.96 1
10
1
0
10 -15 10
10
-10
10
-5
10
0
10
5
10
10
Time [second] Fig. 9. Shear relaxation mastercurve for different heating scan, Tref = 110 °C.
10
Shear Modulus [MPa]
min such that each frequency scan takes about 1 min. The next step of the analysis process consists of deriving the conversion level at each heating scan. This could be done by applying the T DMA g values of different heating scans (Table 3) to the DiBenedetto modDMA el, Fig. 1b. In order to relate this T g to the conversion level, care . In this should be taken about the exact definition of this T DMA g paper, the maximum in tan d is taken as the criterion for the mechanical glass transition. Fig. 1b, Tables 1 and 3 shows that there is a difference between the Tg values for the fully cured samples in different test methods: 111.2 °C for DSC, 98 °C for PVT and 132 °C for DMA. Such differences are because the glass transition is a kinetic process which takes place in a certain temperature and time range. It therefore depends on both the measurement method and the data evaluation procedure. Therefore, the T DMA turned out g to be about 21 °C higher than the T DSC used to establish the relation g with the conversion. After compensating the difference, the determination of the conversion is done using Fig. 1b. Fig. 8 shows the shear storage modulus vs. frequency for an 81% cured filled material (second heating ramp). The individual lines correspond to the modulus vs. frequency curves at a single temperature. Applying the TTS principle, these curves can be shifted along the frequency axis to form a single mastercurve. The mastercurve in the frequency domain can be converted to relaxation modulus in the time domain using an appropriate formula [22–24]. Using the same procedure, different mastercurves are made for the all heating scans, considering 110 °C as the reference temperature. These curves show the typical development of the relaxation modulus with cure (Fig. 9). Fig. 9 shows that in different heating steps the glassy plateaus are identical. However the rubbery plateaus move upwards as cure proceeds. In addition, the curves shift to the right side, i.e. longer time scales, during cure which can be attributed to the increase of Tg. Therefore we decide to use the Tg as the reference temperature. Fig. 10 shows that now the mastercurves almost coincide. As a next step of data analysis we subtract the rubbery modulus and normalized the mastercurves as Eq. (21):
10 -4 10
3
0.71
10
2
0.81 0.86 0.9 0.94 0.96 1
10
1
0
10 -10 10
10
-5
10
0
10
5
Time [second] Fig. 10. Shear relaxation mastercurves for different heating scans with Tref = T DMA . g
the conversion level. Furthermore, close to the glass transition temperature of each of these curves there is a marked change in
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4 2
10
0
0 10
10
10
10
0.71 0.81 0.86 0.9 0.94 0.96 1
-1
-2
-2
Log a T
Normalized Shear Modulus (Gn) [MPa]
10
0.71 0.81 0.86 0.9 0.94 0.96 1
-4 -6
-3
-8 -10
-4
-12 -5
10 -10 10
10
-5
10
-14 -100
0
-50
0
Time [second] Fig. 11. Normalized shear modulus mastercurve with Tref = T DMA , all relaxation g curves collapse to a single mastercurve.
Fig. 13. Shift factor related to the shear mastercurves in different heating scans vs. T Tg, Tref = T DMA . g
4
2 0.71 0.81 0.86 0.9 0.94 0.96 1
2 0 -2
0 -2
shift factor WLF fit Arrhenius fit
-4
-4
Log a T
Log a T
50
T-T g [°C]
-6
-6
-8
-8
-10
-10
-12
C1= 19.5 C2=107.4 TgDMA [°C]= 132 H [kJ/mol]= 187 T0 [°K]= 289.5 Tc-Tg [°C]= -34
-12
-14 40
60
80
100
120
140
-14 40
T [°C]
log aWLF ¼ T
C 1 ðT T ref Þ ; C 2 þ T T ref
T < Tc
T > Tc
100
120
140
Fig. 14. Details of Arrhenius and WLF fit to the fully cured shift factor curve, Tref = T DMA . g
100
Experiment
α g= 0.45 αf = 1
Gr f = 33.2MPa
Martin & Adolf
Gr [MPa]
slope, which is attributed to a change in relaxation mechanism. Below the switching temperature, Tc, the shift factor follows the Arrhenius behavior (activation energy driven), whereas above this temperature it follows the WLF behavior [25] (free volume mechanism). The first linear parts in Fig. 12 correspond to the shift factors in the glassy state of each heating scan. Since the modulus variation in this region is not much (Fig. 8), care should be taken for finding the right shift factor data in this region. If the shift factors were plotted vs. T Tg, the glass transition regions of all curves collapse onto a single shift factor curve, Fig. 13.
H 1 1 ; 2:30R T T 0
80
T [°C]
Fig. 12. Shift factor related to the shear modulus for different heating scans, Tref = T DMA . g
log aArrh ¼ T
60
10
ð22Þ
ð23Þ
For fully cured sample, last heating scan, the Arrhenius and WLF models fitted to the shift factor’s curve and the corresponding parameters are summarized in Fig. 14.
1 0.6
0.7
0.8
0.9
1
Conversion level [α] Fig. 15. Cure dependency of rubbery shear plateau. Full lines are according to the Martin & Adolf theory, Eq. (24).
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M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
2.4.4. Cure dependency of elastic parts Figs. 6 and 9 clearly shows that the dependency of the glassy modulus on cure is small (within experimental error) and will be neglected here. However the rubbery elastic modulus increases from zero to about 33.2 MPa, starting at the point of gelation. This increase is modeled by Martin & Adolf scaling law [26], Eq. (24). Fig. 15 shows that there is good agreement between the experimental data and the model.
Gr ðaÞ ¼
Gfr
a2 a2g a2f a2g
!8=3 ð24Þ
here af denotes the final conversion (usually 1.0), ag is the gelpoint and Gfr is the rubbery modulus at a = af. Below the gelation point i.e. for a < ag, the rubbery shear modulus vanishes.
3. Conclusions In this paper the mechanical properties of an epoxy molding compound are investigated. The elongation storage and bulk modulus for the fully cured material are measured using a DMA-tensile set up and a PVT apparatus. The glassy and rubbery elongation moduli are almost independent of frequency and have the value of 7 and 0.1 GPa respectively. The room temperature bulk modulus is about 15 GPa and decreases to 4.7 GPa in the rubbery region. Furthermore, the changes in the shear modulus of the EMC are investigated during an intermittent cure test with a DMA apparatus. The Time–Temperature superposition principle was applied to all heating steps, the mastercurves and the related shift factors are extracted. Using these mastercurves, the T DMA in all heating g scans are measured and the conversion level is calculated. It is shown that partial curing increases the glass transition temperature at each heating scan. This phenomena shifts the mastercurves to the longer time domain. In addition partial curing increased the rubbery modulus. However the glassy shear modulus turns out to be almost independent of the conversion level. Considering the T DMA as the reference temperature, the mastercurves and shift facg tors (for temperatures above Tc) collapse to a single curve. The normalized form of the mastercurves which is suitable as the input for the finite element programs is extracted from this curve. Finally, the growth of the rubbery modulus in different conversion level is measured and fitted to the model. The governed techniques and procedures for material characterization during cure cannot only be used for molding compounds but are also well suited to characterize epoxy adhesives and other thermoset materials.
Acknowledgment We acknowledge the European Commission for funding of this work in FP7 under Project NanoInterface (NMP3-SL-2008-214371).
References [1] Yang DG. Cure-dependent viscoelastic behaviour of electronic packaging polymers. PhD thesis, Delft University of Technology, Delft; 2007. [2] Yang DG, Jansen KMB, Ernst LJ, Zhang GQ, Bressers HJL, Janssen JHJ. Effect of filler concentration of rubbery shear and bulk modulus of moulding compounds. J Microelectron Reliab 2007;47:233–9. [3] Jansen KMB, Wang L, van’t Hof C, Ernst LJ, Bressers HJL, Zhang GQ. In: IEEE 5th EuroSime conference, Brussels; May 2004. p. 581–5. [4] Jansen KMB, Wang L, Yang DG, van’t Hof C, Ernst LJ, Bressers HJL, et al. In: IEEE 54th ECTC conference, Las Vegas; June 2004. p. 890–4. [5] Jansen KMB, Qian C, Ernst LJ, Bohm C, Kessler A, Preu H, et al. Modelling and characterization of moulding compound properties during cure. J Microelectron Reliab 2009;49:872–6. [6] Yang DG, Ernst LJ, van’t Hof C, Kiasat MS, Bisschop J, Janssen J, et al. Vertical die crack stresses of flip chip induced in major package assembly processes. J Microelectron Reliab 2000;40:1533–8. [7] Ernst LJ et al. Time- and temperature dependent thermo-mechanical modeling of a packaging molding compound and its effect on packaging process stresses. J Electron Pack 2003;125:539–48. [8] van Driel WD, Janssen JHJ, Zhang GQ, Yang DG, Ernst LJ. Packaging induced die stresses – effect of chip anisotropy and time-dependent behaviour of moulding compound. J Electron Pack 2003;125:520–5. [9] Ernst LJ, van’t Hof C, Yang DG, Kiasat MS, Zhang GQ, Bressers HJL, et al. Mechanical modeling and characterization of the curing process of underfill materials. J Electron Pack 2002;124:97–105. [10] Yang DG, Jansen KMB, Ernst LJ, Zhang GQ, van Driel WD, Bressers HJL, et al. Numerical modelling of warpage induced in QFN array modelling process. J Microelectron Reliab 2007;47:310–8. [11] de Vreugd J, Jansen KMB, Ernst LJ, Bohm C. Prediction of cure induced warpage of micro-electronic products. J Microelectron Reliab 2010;50: 910–6. [12] Hu G, Luan JE, Chew S. Characterization of chemical cure shrinkage of epoxy molding compound with application to warpage analysis. J Electron Pack 2009;131:1–6. [13] Lu MG, Shim MJ, Kim SW. Effects of moisture on properties of epoxy molding compounds. J Appl Polym Sci 2001;81:2253–9. [14] Walter H, Dermitzaki E, Wunderle B, Michel B. In: IEEE 3rd ESTC conference, Berlin; September 2010. p. 1–5. [15] Cheng SZD. Handbook of thermal analysis and calorimetry, vol. 3: application to polymers and plastics. Amsterdam: Elsevier Science; 2002. [16] Fox TG, Loshaek S. Influence of molecular weight and degree of crosslinking on the specific volume and glass temperature of polymers. J Polym Sci 1955;15:371–90. [17] Simha R, Wilson PS, Olabisi O. Pressure–volume–temperature properties of amorphous polymers – empirical and theoretical predictions. Kolloid-Z und Z fur Polym 1973;251(6):402–8. [18] Saraswat MK, Jansen KMB, Patel MD. In: IEEE 9th EuroSime conference, Freiburg im Breisgau; April 2008. p. 463–6. [19] Boehme B, Jansen KMB, Rzepka S, Wolter KJ. In: IEEE 10th EuroSime conference, Delft; April 2009. p. 289–96. [20] Jansen KMB, Patel M, Saraswat MK, Ernst LJ. In: 24th annual meeting of the Polymer Processing Society-PPS conference, Salerno; June 2008. p. 467–8. [21] Ward IM, Sweeney J. An introduction to the mechanical properties of solid polymers. 2nd ed. Chichester, West Sussex: John Wiley & Sons; 2004. [22] Park SW, Schapery RA. Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series. Int J Solids Struct 1999;36:1653–75. [23] Schapery RA, Park SW. Methods of interconversion between linear viscoelastic material functions. Part II-an approximate analytical method. Int J Solids Struct 1999;36:1677–99. [24] He Y. Thermomechanical and viscoelastic behavior of a no-flow underfill material for flip-chip applications. Thermochim Acta 2005;439: 127–34. [25] Williams ML, Landel RF, Ferry JD. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 1955;77:3701–7. [26] Adolf DB, Martin JE. Calculation of stresses in crosslinking polymers. J Compos Mater 1996;30:13–34.
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Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Characterization of the viscoelastic properties of an epoxy molding compound during cure M. Sadeghinia ⇑, K.M.B. Jansen, L.J. Ernst Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
a r t i c l e
i n f o
Article history: Received 8 November 2011 Received in revised form 20 March 2012 Accepted 21 March 2012 Available online 18 April 2012
a b s t r a c t In the electronics industry epoxy molding compounds, underfills and adhesives are used for the packaging of electronic components. These materials are applied in liquid form, cured at elevated temperatures and then cooled down to room temperature. During these processing steps residual stresses are built up resulting from both cure and thermal shrinkage. These residual stresses add up to the stresses generated during thermal cycling and mechanical loading and may eventually lead to product failure. The viscoelastic properties of the encapsulation material depend highly on temperature and degree of cure. This paper investigates the increase of elastic modulus and the changes in the viscoelastic behavior of an epoxy molding compound, during the curing process. This is done using the shear setup of a Dynamic Mechanical Analyzer DMA-Q800. The cure dependent viscoelastic behavior is determined during heating scans of an intermittent cure experiment. In such an experiment the material is partially cured and then followed by a heating scan at 2 °C/min. During this heating scan continuous frequency sweeps are performed and the shear modulus is extracted. The Time–Temperature superposition principle is applied and the viscoelastic shear mastercurve is extracted. Analyzing the shear modulus, the cure dependent viscoelastic material behavior was modeled using the cure dependent glass transition temperature as a reference and a cure dependent rubbery modulus. It is shown that partial curing would increase the glass transition temperature and rubbery shear modulus. It also shifts the viscoelastic mastercurve to the higher time domain. Taking Tg as the reference temperature for different heating scans, the mastercurves collapse to one graph. In addition, using a Differential Scanning Calorimeter (DSC), the growth of the glass transition temperature, T DSC g , with respect to the conversion level is obtained. These values are coupled to the values of glass , for calculating the conversion level at each step of curing transition temperature in DMA apparatus, T DMA g process in shear mode test. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Epoxy molding compounds (EMCs) are widely used for encapsulating semi-conductor devices. Curing of these materials during the production process will induce residual stresses in the products. In addition due to the mismatch in the coefficient of thermal expansion, the stresses will increase during the cooling down from molding to ambient temperature. These residual stresses will reduce the reliability of the devices and may lead to failure of the product. Therefore, nowadays investigating the thermo-mechanical (and viscoelastic) properties of the molding compounds has become an important issue in electronic packaging. The viscoelastic properties of the encapsulation material depend highly on temperature, degree of cure and moisture. Several studies have been done on characterizing the effect of curing and filler concentration on ⇑ Corresponding author. Tel.: +31 152785707; fax: +31 152782150. E-mail address: [email protected] (M. Sadeghinia). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.03.025
the thermo-mechanical (and viscoelastic) properties of the packaging materials. For example, Yang et al. [1,2] focused on the rubbery modulus of a series of filled epoxy resin and investigated the effect of the filler concentration and curing process on the changes of the rubbery modulus. His results revealed that the growth of rubbery modulus is dependent on the conversion. Jansen et al. [3,4] showed that the glass transition temperature of the fully cured materials is dependent to the curing level and the rubbery CTE decreased with increasing cure. Furthermore, they [5] extracted a full cure dependent viscoelastic model for the shear modulus of a commercial molding compound by monitoring the changes in the viscoelastic properties of the compounds during cure. A cure-dependent viscoelastic model was also proposed [6–9] to describe the evolution of the viscoelastic behavior of an underfill resin in a flip chip package during isothermal and non-isothermal cure. Curing of the molding compounds is always accompanied with the chemical shrinkage which can cause warpage in microelectronic packages. FE modeling of map-molding process [10,11]
M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
was carried out for a map mold encapsulated with the epoxy system and the warpage caused by the curing process and the subsequent cooling down stage was investigated. Moreover, Hu et al. [12] developed a FEA evaluation method for the chemical cure shrinkage based on the measurement of the warpage of biomaterial model and revealed that FEA simulations with chemical cure shrinkage show fair agreement with experimental measurements of package warpage. The effects of moisture on the mechanical properties and glass transition temperature of the epoxy molding compounds were also studied by Lu et al. [13] and Walter et al. [14]. Their experimental results revealed that the absorbed water continuously decreases the mechanical strength of the epoxy molding compound. They also showed that the glass-transition temperature decreases at an early stage. In the present research, the changes in viscoelastic properties of an epoxy molding compound during an intermittent cure experiment are monitored using a Dynamic Mechanical Analyzer (DMA) Apparatus. In such an experiment the material is partially cured for a short period of time at a temperature with low curing rate. The isothermal curing process is then interrupted by a quick temperature drop and afterwards followed by a constant heating ramp. The sequence of partially curing, cooling and heating is then repeated and the viscoelastic data is recorded during each heating step. Independent values of the glassy and rubbery shear modulus were obtained by combining the glassy and rubbery elongation (tensile) and bulk moduli. These latter two values are measured separately by using a DMA (tensile mode) and a GNOMIX high pressure dilatometer-apparatus, respectively. The content of this paper concerned with the first part of our research work. In the next step, these data will be used as an input in our FEM Abaqus model for establishing the critical interfacial fracture properties of EMC-Cu interfaces, which will be reported in the near future.
2. Experimental Since commercial materials often have complicated mixtures of components with unknown chemistry, we chose to use a model epoxy system consisting of similar components as used in commercial molding compounds. The system consists of epoxy Novolac (EPN 1180, Huntsman Advanced Materials, equivalent weight 175– 182 g/eq) as a matrix material, Bisphenol-A (equivalent weight 114 g/eq) as hardener and fused silica spheres (FB-940, ex Denka, median diameter 15 lm, density 2.20 g/cm3) as filler. Triphenylphosphine (TPP, 0.5 g/100 g epoxy) is used as a catalyst. The epoxy Novolac and Bisphenol-A were mixed in a stoichiometric ratio. The material has a filler percentage of 64.5 wt.% (50 vol.%).
The glass transition temperature, Tg, indicates the transition from the glassy (solid) state to the liquid or rubbery state. For molding compounds this glass transition is not a single temperature but covers a range of about 20–50 °C. This is because the glass transition is a kinetic process which depends on both the measurement method and the data evaluation procedure. The Tg values can be obtained from DSC data as the changes in the slope of the heat flow vs. temperature curves. The glass transition temperature during cure vs. conversion was determined by analyzing the heat flow curves of uncured and partly cured samples. Firstly, samples of approximately 5–10 mg were partially cured by performing an isothermal cure for 45, 110, 320 and 1200 min at 120 °C. Then the glass transition temperature of these partially cured samples was obtained by scanning from 30 to 200 °C at a rate of 10 °C/min, Fig. 1a. The sample’s conversion was determined by measuring the heat released during the scan and applying this value to Eq. (1). The measured glass transition temperature as a function of the conversion is shown in Fig. 1b. The glass transition temperature of a thermosetting polymer depends on the crosslink density, the number of free chainends and the rigidity of the polymeric segments. It was shown that the glass transition temperature in crosslinked system increases linearly with the concentration of the crosslinks which restricts the free volume and free chain-ends [16]. Fig. 1b shows that the Tg of partly cured sample increases by the conversion level.
1.5
Heat Flow [J/(g ×s)]
1712
Tg increase and heat flow reduction for partially cured sample
1
0 -0.5 -1 -30
20
70
ð1Þ
where Htot is the reaction heat released by curing a freshly mixed sample and Hrest is the released heat of partly cured sample. These two values can be obtained from the heat flow vs. time curves of uncured and partly cured samples respectively.
120
170
220
270
320
Temperature [°C] Fig. 1a. DSC heating scan of uncured and 61% cured sample (cured at 120 °C for 110 min), Partial curing increased the Tg for almost 50 °C, However the released heat (area below the peak point) decreased from 63 to 24.5 J/g.
120 100
H a ¼ 1 rest ; Htot
partly cured
0.5
Measured
2.1. Degree of conversion vs. glass transition temperature
DiBenedetto
80
Tg [°C]
A differential scanning calorimetry, TA-instruments DSC2920, was used to obtain the relation between the degree of chemical conversion and the glass transition temperature. The conversion of a partly cured sample, a, is measured by determining the remaining heat of reaction which is released upon further curing of the specimen [15].
uncured
60 Tg0 [°C]= 15.5 Tg1 [°C]= 111.2 λ =0.652
40 20 0 0
0.2
0.4
0.6
0.8
1
Conversion Level [α] Fig. 1b. Tg of partly cured samples along with fitting parameters to the Eq. (2), full lines: fits to Eq. (2), symbols: extracted from the heat scan of partially cured samples.
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b1 and b2 are the fitting parameters. The parameter C1 determines the steepness of slope change during the transition region. Tgp is the pressure dependent glass transition temperature:
0.025
10 20 30 40 50 60 70 80 90 100
3
d(Volume) [cm /g]
0.02
0.015
T gp ¼ T gpv t þ s0 P
ð5Þ
where T pgv t is the fully cured Tg at atmospheric pressure, s0 is a fitting parameter and P is the hydrostatic pressure. Using non-linear curve fitting of Matlab, the parameters of Eqs. (3)–(5) were determined and summarized in Table 1. The volumetric CTE at atmospheric pressure, P = 0, can be calculated by differentiating the volume changes with respect to temperature, resulting in:
Glass transition line
0.01
0.005
1 CTEv ðT; 0Þ ¼ k1 þ k2 ð1 þ tan h½C 1 ðT T gpv t ÞÞ 2 0 40
60
80
100
120
140
160
180
200
220
T [°C] Fig. 2. Volume changes in different temperature and pressure from PVT measurement, symbols: experimental data, full lines: fit to Eq. (3), the legends refer to the applied pressure.
In this paper the empirical model of DiBenedetto is applied for relating the glass transition temperature to the degree of conversion [15].
T g ðaÞ ¼ T g0 þ
ðT g1 T g0 Þka 1 ð1 kÞa
ð2Þ
where a denotes the degree of cure, k is a fitting parameter. Tg0 and Tg1 are the glass transition temperatures of uncured and fully cured polymers, respectively. The parameters obtained from this fit are summarized in Fig. 1b. The Tg value at 29% conversion is slightly higher than the DiBenedetto fit. However since the determination of a Tg value is typically with 2–5 °C accuracy, the deviation is not considered to be significant.Note that the DiBenedetto equation reduces to the equation proposed by Pascault and Williams if the fit parameter k is set to the DC p1 DC p0 ratio, used in their publication [15].
ð6Þ
In which k1 and (k1 + k2) represent the volumetric thermal expansion at low and high temperature respectively. The compressibility b (T) is calculated using the following definition:
bðTÞ ¼
1
t0
@t @P
ð7Þ T
where t is the specific volume. Since viscoelastic effects in the compressibility were shown to be small, the volumetric response is assumed to be elastic, but temperature dependent [18–20]. The bulk modulus is calculated as the reciprocal of the bulk compressibility i.e. Eq. (8).
K¼
1 bðTÞ
ð8Þ
Using the Tait equation, the following equation is derived for the bulk modulus.
KðTÞ ¼
k 1 s0 þ
1 k s 2 2 0
1 n h io C 1 þ tan h C 1 ðT T pgv t Þ þ b1 expðb 2 TÞ
ð9Þ
Fig. 3 shows the calculated bulk modulus of the fully cured material. It ranges from 15.2 GPa at 50 °C to 4.6 GPa at 200 °C.
2.2. Compressibility and bulk modulus
2.3. Elongation (tensile) modulus
The compressibility of the material was measured using a high pressure dilatometer-PVT apparatus. The pressure and temperature were stepwise increased and the corresponding volume changes were recorded. Typical temperature and pressure ranges were 40–200 °C (in steps of 10 °C) and 10–100 MPa (in steps of 10 MPa). The volume changes of the fully cured molding compound are shown in Fig. 2. The volume changes were fitted to a modified form of the Tait equation [17].
The viscoelastic elongation properties of the fully cured material as a function of the excitation frequency and temperature is studied by a Dynamic Mechanical Analyzer, TA instrument Q800. A sinusoidal displacement (strain e) is applied to a sample and the resulting force (stress r) is measured [21]. The sample had the dimension of 22.6 4.9 0.5 mm. The experiment covered the frequency and temperature range of 0.32–32 Hz and 20– 200 °C respectively. For a perfectly elastic material, the resulting stress and the strain will be perfectly in phase. For a purely viscous material, there will be a 90° phase lag of stress with respect to strain. Viscoelastic materials have the characteristics in between where some phase lag will occur during DMA tests.
tðT; PÞ ¼ t00 ðTÞ 1 C ln 1 þ
P b1 expðb2 TÞ
ð3Þ
With C = 0.0894 and t00 (T) as:
00
t
lnðcos h C 1 ðT T gp Þ Þ 1 ðTÞ ¼ t0 1 þ k1 ðT T gp Þ þ k2 ðT T gp Þ þ 2 C1 ð4Þ
where t0, T and P are the initial volume, temperature and hydrostatic pressure respectively.
e ¼ e0 sinðxtÞ
ð10Þ
r ¼ r0 sinðxt þ dÞ
ð11Þ
In which x is the applied frequency and d the measured phase lag. By expanding Eq. (11), the stress can be considered to consist of two components:
Table 1 T pgv t and fitting parameters of Eqs. (3)–(5). Properties t0 (cm3/gm)
k1 (1/°C)
k2 (1/°C)
C1 (1/°C)
b1 (MPa)
b2 (1/°C)
T gpv t (°C)
s0 (°C/MPa)
0.609
7.9E5
1.88E4
0.033
5633.8
9.1 E3
98
0.445
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2.4. Shear modulus during cure
Fig. 3. Bulk modulus of the fully cured material in different temperature.
r ¼ r0 sinðxtÞ cos d þ r0 cosðxtÞ sin d
ð12Þ
The relation between the applied strain and the measured stress can be defined by two parameters: E0 and E00 where:
r0 r0 cos d and E00 ¼ sin d e0 e0
E0 ¼
ð13Þ
E00 ¼ tan d E0
ð14Þ
Complex modulus E can be used to express the moduli E as follows:
E ¼ E0 þ iE
00
ð15Þ
0
E is called the storage modulus, since it is proportional to the stored energy in the test sample and representing the elastic portion. E00 on the other hand is called the loss modulus since it is proportional to the dissipated energy. Similarly the shear storage and loss moduli, G0 and G00 , are defined. Fig. 4 shows that the Eg (elongation glassy modulus) and Er (elongation rubbery modulus) are independent of the frequency and have the values of 7200 MPa and 102 MPa respectively. Note that this storage modulus drops by the factor 70 during the glass transition, where as the bulk modulus only drops by a factor of 3.
2.4.1. Test setup The mechanical properties of the material during the curing process were measured with a specially made shear set up. The setup consists of 3 mm diameter circular surfaces between which the uncured sample is positioned. The samples were gently preheated until they became soft and sticky. Care was taken to avoid preliminary reaction. The size of the shear surfaces were chosen such that the test was performed in a Dynamic Mechanical Analyzer DMA Q800-TA Instrument. The experiment covers the frequency and temperature range of 0.32–60 Hz and 20–160 °C. Fig. 5 shows a schematic diagram of the shear tool. The cure dependent viscoelastic behavior was determined during heating scans of an intermittent cure experiment. As Fig. 6 shows, in such an experiment the isothermal curing process is interrupted by a quick temperature drop, followed by a heating scan at 2 °C/min. The isocure heating is done at a temperature where the reaction is still slow. After a short isothermal period the sequence of cooling and reheating is repeated and viscoelastic data is recorded. The reheating scan from below to above T DMA g (after each isocuring part) is used to determine the glassy and rubbery modulus values as well as the glass transition temperature for is a measure for the actual cure state each heating ramp. This T DMA g after each period of isocuring. During this heating scan continuous frequency sweeps were performed (0.32–60 Hz, 10 lm amplitude). 2.4.2. Deriving the modulus Deriving the mechanical properties of the curing material through the usage of the shear test set up is not simple, since cured molding compounds are about as stiff as the mechanical frame of most tensile testers which complicates the exact determination of modulus values for the molding compounds. As a result, the apparent measured storage modulus may deviate from the real one. We therefore correct the storage modulus by assuming that the measured deformation consists of the sample plus the frame deformation (Fig. 7 and Eq. (16)).
dxa ¼ dxm þ dxf
ð16Þ
The stiffness was derived by dividing Eq. (16) through the force F (1/S = dx/F).
Eg=7.2 GPa
Er=0.1 GPa
Fig. 4. Elongation storage modulus (E0 ) vs. temperature in different frequencies, measured by the DMA experiment.
M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
Gap for sample
1715
Fixed parts
Moving shaft
Fig. 7. Schematic diagram of the frame and sample stiffness. Fig. 5. Schematic diagram of the shear clamps.
1 1 1 ¼ þ S a Sm Sf
ð17Þ
where Sa, Sm, Sf are the apparent, sample and frame stiffnesses respectively. Eq. (17) can be rearranged for extracting the sample stiffness:
Sm ¼
Sa 1 Sa Sf
ð18Þ
The yet unknown frame stiffness, Sf, is obtained by comparing the measured glassy and rubbery stiffness with separately determined glassy and rubbery shear modulus values. The latter is done by measuring the elongation and the bulk modulus. In glassy and rubbery region the material is elastic and therefore the following relation exists between bulk (K), shear (G) and elongation modulus (E) [5].
G¼
3KE 9K E
ð19Þ
Furthermore, the relation between the measured sample’s shear stiffness and the shear storage modulus is:
Gm ¼
Sm bgeo
ð20Þ
where Gm and Sm are the measured sample’s shear storage modulus and the sample’s shear stiffness respectively. bgeo is a geometry factor determined by the shear surface and gap thickness.
1th warming up ramp, Stiffness data
Temperature ramp
Applying the glassy and rubbery bulk and elongation modulus for the fully cured material (Figs. 3 and 4) to the Eq. (19), the glassy and rubbery shear modulus were calculated for the fully cured material (Table 2). Deriving the sample’s stiffness in different heating scans from the apparent one consists of three steps. 1. For the fully cured material, i.e. the last heating scan, the rubbery stiffness of the material is low compared to the frame stiffness. Therefore, the frame stiffness correction (Sf) is small and the bgeo is calculated assuming Sm = Sa via Eq. (20) and Table 2. 2. Using the derived bgeo, Sf will be calculated through using Table 2, Eqs. (18) and (20), for the fully cured material i.e. the last heating scan. 3. Finally the full range of Sm is calculated applying the calculated values of Sa and Sf in Eq. (18). If the frame stiffness is not corrected, the apparent measured storage modulus will be almost half of the true value in the glassy region. However its effect is small in the rubbery state. Therefore, if the uncorrected values are used to calculate the glassy bulk modulus or Poisson ratio, significant errors may occur. 2.4.3. Construction of time-cure mastercurve For each heating scan a mastercurve, related shift factor and glass transition temperature can be derived via the Time–Temperature Superposing principle (TTS). The frequency continuously cycles between 0.32 and 60 Hz and the temperature increases at 2 °C/
Glassy state
th
7 warming up ramp, stiffness data
Rubbery state
Fig. 6. Stiffness and temperature profile of the sample during the intermittent cure test. The stiffness data is shown for different frequencies ranging from 0.32 to 60 Hz. The stiffness curves increase if the temperature drops and decrease during a heating ramp. Each next heating curve is at a higher conversion level.
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Table 2 Elastic moduli at 50 °C (glassy values) and 150 °C (rubbery), fully cured material. Glassy state 50 °C
Rubbery state 150 °C
E (MPa) G (MPa) K (GPa)
7200 2520 15.2
102 37.7 4.9
Table 3 T DMA and conversion level for all heating scans. g Heating ramp (°C) T DMA g
Conversion (a)
1
2
3
4
5
6
7
96
107
113
118
124
127
132
0.71
0.81
0.86
0.9
0.94
0.96
1
Shear Storage Modulus [Mpa]
Property
3
10
2
10
1
10
0
Gðt; T; aÞ Gr ðaÞ Gn ðt; TÞ ¼ Gg Gr ðaÞ
ð21Þ
here Gn denotes the normalized shear curve, Gg and Gr are the glassy and rubbery shear modulus respectively. Without further need for adjustments all relaxation curves collapse to a single mastercurve, Fig. 11. This temperature- conversion mastercurve is therefore sufficient to describe all cure dependent viscoelastic behavior. A Prony series could be fitted to the normalized mastercurves for evaluating them in a finite element program. For each of the intermittent shear mastercurves in Fig. 10, there is a corresponding temperature-shift factor, Fig. 12. It can be seen that the shift factor curves shifted to the right side with increasing
-2
0
10
2
4
10 10 Frequency [rad/s]
10
6
10
Fig. 8. Shear storage modulus mastercurve as a function of frequency for 81% cured material (2th heating scan), data extracted by analyzing the DMA measurement, Tref = 110 °C.
Shear Modulus [MPa]
10
3
0.71
10
2
0.81 0.86 0.9 0.94 0.96 1
10
1
0
10 -15 10
10
-10
10
-5
10
0
10
5
10
10
Time [second] Fig. 9. Shear relaxation mastercurve for different heating scan, Tref = 110 °C.
10
Shear Modulus [MPa]
min such that each frequency scan takes about 1 min. The next step of the analysis process consists of deriving the conversion level at each heating scan. This could be done by applying the T DMA g values of different heating scans (Table 3) to the DiBenedetto modDMA el, Fig. 1b. In order to relate this T g to the conversion level, care . In this should be taken about the exact definition of this T DMA g paper, the maximum in tan d is taken as the criterion for the mechanical glass transition. Fig. 1b, Tables 1 and 3 shows that there is a difference between the Tg values for the fully cured samples in different test methods: 111.2 °C for DSC, 98 °C for PVT and 132 °C for DMA. Such differences are because the glass transition is a kinetic process which takes place in a certain temperature and time range. It therefore depends on both the measurement method and the data evaluation procedure. Therefore, the T DMA turned out g to be about 21 °C higher than the T DSC used to establish the relation g with the conversion. After compensating the difference, the determination of the conversion is done using Fig. 1b. Fig. 8 shows the shear storage modulus vs. frequency for an 81% cured filled material (second heating ramp). The individual lines correspond to the modulus vs. frequency curves at a single temperature. Applying the TTS principle, these curves can be shifted along the frequency axis to form a single mastercurve. The mastercurve in the frequency domain can be converted to relaxation modulus in the time domain using an appropriate formula [22–24]. Using the same procedure, different mastercurves are made for the all heating scans, considering 110 °C as the reference temperature. These curves show the typical development of the relaxation modulus with cure (Fig. 9). Fig. 9 shows that in different heating steps the glassy plateaus are identical. However the rubbery plateaus move upwards as cure proceeds. In addition, the curves shift to the right side, i.e. longer time scales, during cure which can be attributed to the increase of Tg. Therefore we decide to use the Tg as the reference temperature. Fig. 10 shows that now the mastercurves almost coincide. As a next step of data analysis we subtract the rubbery modulus and normalized the mastercurves as Eq. (21):
10 -4 10
3
0.71
10
2
0.81 0.86 0.9 0.94 0.96 1
10
1
0
10 -10 10
10
-5
10
0
10
5
Time [second] Fig. 10. Shear relaxation mastercurves for different heating scans with Tref = T DMA . g
the conversion level. Furthermore, close to the glass transition temperature of each of these curves there is a marked change in
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M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718 1
4 2
10
0
0 10
10
10
10
0.71 0.81 0.86 0.9 0.94 0.96 1
-1
-2
-2
Log a T
Normalized Shear Modulus (Gn) [MPa]
10
0.71 0.81 0.86 0.9 0.94 0.96 1
-4 -6
-3
-8 -10
-4
-12 -5
10 -10 10
10
-5
10
-14 -100
0
-50
0
Time [second] Fig. 11. Normalized shear modulus mastercurve with Tref = T DMA , all relaxation g curves collapse to a single mastercurve.
Fig. 13. Shift factor related to the shear mastercurves in different heating scans vs. T Tg, Tref = T DMA . g
4
2 0.71 0.81 0.86 0.9 0.94 0.96 1
2 0 -2
0 -2
shift factor WLF fit Arrhenius fit
-4
-4
Log a T
Log a T
50
T-T g [°C]
-6
-6
-8
-8
-10
-10
-12
C1= 19.5 C2=107.4 TgDMA [°C]= 132 H [kJ/mol]= 187 T0 [°K]= 289.5 Tc-Tg [°C]= -34
-12
-14 40
60
80
100
120
140
-14 40
T [°C]
log aWLF ¼ T
C 1 ðT T ref Þ ; C 2 þ T T ref
T < Tc
T > Tc
100
120
140
Fig. 14. Details of Arrhenius and WLF fit to the fully cured shift factor curve, Tref = T DMA . g
100
Experiment
α g= 0.45 αf = 1
Gr f = 33.2MPa
Martin & Adolf
Gr [MPa]
slope, which is attributed to a change in relaxation mechanism. Below the switching temperature, Tc, the shift factor follows the Arrhenius behavior (activation energy driven), whereas above this temperature it follows the WLF behavior [25] (free volume mechanism). The first linear parts in Fig. 12 correspond to the shift factors in the glassy state of each heating scan. Since the modulus variation in this region is not much (Fig. 8), care should be taken for finding the right shift factor data in this region. If the shift factors were plotted vs. T Tg, the glass transition regions of all curves collapse onto a single shift factor curve, Fig. 13.
H 1 1 ; 2:30R T T 0
80
T [°C]
Fig. 12. Shift factor related to the shear modulus for different heating scans, Tref = T DMA . g
log aArrh ¼ T
60
10
ð22Þ
ð23Þ
For fully cured sample, last heating scan, the Arrhenius and WLF models fitted to the shift factor’s curve and the corresponding parameters are summarized in Fig. 14.
1 0.6
0.7
0.8
0.9
1
Conversion level [α] Fig. 15. Cure dependency of rubbery shear plateau. Full lines are according to the Martin & Adolf theory, Eq. (24).
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M. Sadeghinia et al. / Microelectronics Reliability 52 (2012) 1711–1718
2.4.4. Cure dependency of elastic parts Figs. 6 and 9 clearly shows that the dependency of the glassy modulus on cure is small (within experimental error) and will be neglected here. However the rubbery elastic modulus increases from zero to about 33.2 MPa, starting at the point of gelation. This increase is modeled by Martin & Adolf scaling law [26], Eq. (24). Fig. 15 shows that there is good agreement between the experimental data and the model.
Gr ðaÞ ¼
Gfr
a2 a2g a2f a2g
!8=3 ð24Þ
here af denotes the final conversion (usually 1.0), ag is the gelpoint and Gfr is the rubbery modulus at a = af. Below the gelation point i.e. for a < ag, the rubbery shear modulus vanishes.
3. Conclusions In this paper the mechanical properties of an epoxy molding compound are investigated. The elongation storage and bulk modulus for the fully cured material are measured using a DMA-tensile set up and a PVT apparatus. The glassy and rubbery elongation moduli are almost independent of frequency and have the value of 7 and 0.1 GPa respectively. The room temperature bulk modulus is about 15 GPa and decreases to 4.7 GPa in the rubbery region. Furthermore, the changes in the shear modulus of the EMC are investigated during an intermittent cure test with a DMA apparatus. The Time–Temperature superposition principle was applied to all heating steps, the mastercurves and the related shift factors are extracted. Using these mastercurves, the T DMA in all heating g scans are measured and the conversion level is calculated. It is shown that partial curing increases the glass transition temperature at each heating scan. This phenomena shifts the mastercurves to the longer time domain. In addition partial curing increased the rubbery modulus. However the glassy shear modulus turns out to be almost independent of the conversion level. Considering the T DMA as the reference temperature, the mastercurves and shift facg tors (for temperatures above Tc) collapse to a single curve. The normalized form of the mastercurves which is suitable as the input for the finite element programs is extracted from this curve. Finally, the growth of the rubbery modulus in different conversion level is measured and fitted to the model. The governed techniques and procedures for material characterization during cure cannot only be used for molding compounds but are also well suited to characterize epoxy adhesives and other thermoset materials.
Acknowledgment We acknowledge the European Commission for funding of this work in FP7 under Project NanoInterface (NMP3-SL-2008-214371).
References [1] Yang DG. Cure-dependent viscoelastic behaviour of electronic packaging polymers. PhD thesis, Delft University of Technology, Delft; 2007. [2] Yang DG, Jansen KMB, Ernst LJ, Zhang GQ, Bressers HJL, Janssen JHJ. Effect of filler concentration of rubbery shear and bulk modulus of moulding compounds. J Microelectron Reliab 2007;47:233–9. [3] Jansen KMB, Wang L, van’t Hof C, Ernst LJ, Bressers HJL, Zhang GQ. In: IEEE 5th EuroSime conference, Brussels; May 2004. p. 581–5. [4] Jansen KMB, Wang L, Yang DG, van’t Hof C, Ernst LJ, Bressers HJL, et al. In: IEEE 54th ECTC conference, Las Vegas; June 2004. p. 890–4. [5] Jansen KMB, Qian C, Ernst LJ, Bohm C, Kessler A, Preu H, et al. Modelling and characterization of moulding compound properties during cure. J Microelectron Reliab 2009;49:872–6. [6] Yang DG, Ernst LJ, van’t Hof C, Kiasat MS, Bisschop J, Janssen J, et al. Vertical die crack stresses of flip chip induced in major package assembly processes. J Microelectron Reliab 2000;40:1533–8. [7] Ernst LJ et al. Time- and temperature dependent thermo-mechanical modeling of a packaging molding compound and its effect on packaging process stresses. J Electron Pack 2003;125:539–48. [8] van Driel WD, Janssen JHJ, Zhang GQ, Yang DG, Ernst LJ. Packaging induced die stresses – effect of chip anisotropy and time-dependent behaviour of moulding compound. J Electron Pack 2003;125:520–5. [9] Ernst LJ, van’t Hof C, Yang DG, Kiasat MS, Zhang GQ, Bressers HJL, et al. Mechanical modeling and characterization of the curing process of underfill materials. J Electron Pack 2002;124:97–105. [10] Yang DG, Jansen KMB, Ernst LJ, Zhang GQ, van Driel WD, Bressers HJL, et al. Numerical modelling of warpage induced in QFN array modelling process. J Microelectron Reliab 2007;47:310–8. [11] de Vreugd J, Jansen KMB, Ernst LJ, Bohm C. Prediction of cure induced warpage of micro-electronic products. J Microelectron Reliab 2010;50: 910–6. [12] Hu G, Luan JE, Chew S. Characterization of chemical cure shrinkage of epoxy molding compound with application to warpage analysis. J Electron Pack 2009;131:1–6. [13] Lu MG, Shim MJ, Kim SW. Effects of moisture on properties of epoxy molding compounds. J Appl Polym Sci 2001;81:2253–9. [14] Walter H, Dermitzaki E, Wunderle B, Michel B. In: IEEE 3rd ESTC conference, Berlin; September 2010. p. 1–5. [15] Cheng SZD. Handbook of thermal analysis and calorimetry, vol. 3: application to polymers and plastics. Amsterdam: Elsevier Science; 2002. [16] Fox TG, Loshaek S. Influence of molecular weight and degree of crosslinking on the specific volume and glass temperature of polymers. J Polym Sci 1955;15:371–90. [17] Simha R, Wilson PS, Olabisi O. Pressure–volume–temperature properties of amorphous polymers – empirical and theoretical predictions. Kolloid-Z und Z fur Polym 1973;251(6):402–8. [18] Saraswat MK, Jansen KMB, Patel MD. In: IEEE 9th EuroSime conference, Freiburg im Breisgau; April 2008. p. 463–6. [19] Boehme B, Jansen KMB, Rzepka S, Wolter KJ. In: IEEE 10th EuroSime conference, Delft; April 2009. p. 289–96. [20] Jansen KMB, Patel M, Saraswat MK, Ernst LJ. In: 24th annual meeting of the Polymer Processing Society-PPS conference, Salerno; June 2008. p. 467–8. [21] Ward IM, Sweeney J. An introduction to the mechanical properties of solid polymers. 2nd ed. Chichester, West Sussex: John Wiley & Sons; 2004. [22] Park SW, Schapery RA. Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series. Int J Solids Struct 1999;36:1653–75. [23] Schapery RA, Park SW. Methods of interconversion between linear viscoelastic material functions. Part II-an approximate analytical method. Int J Solids Struct 1999;36:1677–99. [24] He Y. Thermomechanical and viscoelastic behavior of a no-flow underfill material for flip-chip applications. Thermochim Acta 2005;439: 127–34. [25] Williams ML, Landel RF, Ferry JD. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 1955;77:3701–7. [26] Adolf DB, Martin JE. Calculation of stresses in crosslinking polymers. J Compos Mater 1996;30:13–34.
