Kinetic Characterisation of Molding Compounds
K.M.B. Jansen1, C. Qian1, L.J. Ernst1, C. Bohm2, A. Kessler2, H. Preu2, M. Stecher2 1Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
2Infineon Technologies AG (AIM AP), 81726 Munich, Germany
k.m.b.jansen@tudelft.nl
Abstract
During the packaging of electronic components stresses are generated due to curing effects and the difference in thermal shrinkage between molding compound and die. For a reliable simulation of the stresses generated in a package during cure and subsequent cooling it is essential to have accurate data for the thermal and mechanical properties of the molding compound, die, solder and substrate materials. Of these materials the molding compound is by far the most difficult one to model since these properties vary widely and are time, conversion and temperature dependent.
The present paper consists of an extensive study on serveral commercial molding compounds of which the kinetic parameters we obtained by analysing both isothermal and non-isothermal Differential Scanning Calorimetry (DSC) data.
For the modelling of the kinetics data it turned out to be necessary to take the diffusion limitation effect (incomplete cure at lower temperatures) into account. The glass transition versus conversion could be modelled satisfactory using the well known DiBenedetto equation.
1. Introduction
Experiments with different loading conditions showed that time and temperature dependent effects have significant impact on the type and extent of observed failure modes like cracks, interconnect reliability etc. Especially the molding compound is responsible for high stress and strain levels on the chip and interconnects. Depending on the selected material set, these results vary greatly. Reliable material data is thus essential for obtaining accurate stress predictions.
Material selection for future products and transfer of results from accelerated testing to product assembly and application conditions is only possible by understanding and optimizing relevant material properties. To be able to consider these in simulation, detailed thermal-mechanical properties of the molding compounds are crucial.
For a full characterisation of the molding compound properties it is required to know the
• Conversion as a function of time and temperature (the so-called cure kinetics)
• Shear modulus as a function of time, temperature and conversion
• Bulk modulus as a function of time, temperature and conversion
• Coefficient of thermal expansion as a function of temperature and conversion
• Cure shrinkage as a function of conversion
In a joint project between TU Delft and Infineon Technologies we therefore aim to fully characterise a set of six commercially available molding compounds. This is a rather involved task since most of the standard measurement techniques cannot be used for materials which react during characterisation. In the past we therefore developped experimental methods to characterise the change in mechanical properties during cure [1,2]. The material used was a model epoxy novolac resin with relatively simple chemistry. In the present project we will use these techniques on commerial molding compounds, which are known to have a complex chemistry and consists not only of the resin, hardener and filler but also of accelerator, flame retarder, mold-release agent, tackifyers and colorant.
The present paper is the first in a series of papers and will focus on the kinetics part only. The other topics will be published in subsequent papers.
The modelling of the conversion as a function of time and temperature is usually referred to a the cure kinetics. Reliable cure kinetics models are important for two reasons. First of all, they are needed to predict cure shrinkage and stress development during the actual molding process and are thus indispensible if curing is to be taken into account in process simulations and optimisations. This requires a good description for the kinetics at a higher temperature range (molding and post curing are usually done at 175-200 °C). The second reason for accurate kinetic modelling is that most characterisation experiments are performed at lower temperatures where the reaction is slower such that there is enough time to do the measurements. Therefore, the kinetic modelling should be accurate at the lower temperature region as well.
2. Kinetic model
n m T T k dt dα = ( )α (1−α) , Eq.1 where m and n are constants of order unity. The above model is therefore able to capture the common nth order
kinetics (if m=0) as well as autocatalytic reactions (n=0).
kT is the temperature dependent rate constant with units
[1/s]. In literature it is often assumed that the reaction rate follows an Arrhenius temperature dependency
⎥⎦ ⎤ ⎢⎣ ⎡− = RT E k T kT 0 0exp ) ( . Eq.2
Here R denotes the gas constant (8.314 J/mol/K), E0 is the
activation energy and T is the absolute temperature (in degrees Kelvin). Note that in principle also other alternatives for kT(T) are possible.
The parameter needed in all subsequent modelling is, however, not the reaction rate but the degree of cure α. In order to find this we must rewrite and integrate Eq.1
c t T n m k T dt t d ( ) ~ ) 1 ( 0 0 ≡ = −
∫
∫
α α α α , Eq.3 The left hand side is a function of α only whereas the right hand side can be interpreted as the dimensionless cure timet~
c. Therefore the above equation can be rewritten asc
t F(α)=~
and the desired conversion is obtained by inversion
) ~ ( ) , ( 1 c c F t t T = −
α
. Eq.4 3. Diffusion limitationThe above kinetic model is not yet complete since it does not account for the fact that at relatively low temperatures the reaction stops at a certain maximum conversion level. A molding compound stored for one week at room temperature for example will react not further than about 10 to 20% conversion whereas the equations above predict 100% conversion after an infinitely long time. For higher temperatures these maximum conversion levels are higher (e.g. about 90% for 90 C). The reason for this phenomena is that during isothermal cure the glass transition temperature rises to a value above the cure temperature. That means that the material vitrifies into a glassy state which hinders the diffusion of the molecular segments. Therefore reactive sites will have more and more difficulty to meet until, eventually, the reaction stops completely. A simple way to incorporate this so-called diffusion limitation effect is by modifying Eq.1 such that the maximum conversion level is incorporated explicitly:
n m T k dt d ) (αmax α α α = − .
In that way the condition of zero reaction rate at the maximum conversion is automatically satisfied. For
convenience this can be written in the form of Eq.1 by normalising with respect to αmax:
n m T k dt d ) ˆ 1 ( ˆ ' ˆ α α α = − , max ˆ α α α= . Eq.5
The temperature dependency of αmax decreases inversely
with decreasing (absolute) temperature [4]
T a a Tc 0 1 max( )= − α , 0≤αmax ≤1 Eq.6
where Tg1 denotes the final (fully converted) glass
transition temperature and T is the applied cure temperature in degrees Kelvin. Notice that his maximum conversion αmax is bounded between 0 and unity. Direct
estimates of a0 and a1 can be obtained by assuming that
the limits for αmax (conversion levels of 0 and 1) occur at
the lowest and highest glass transition temperatures (Tg0
and Tg1, respectively). In this study, however, we will
treat a0 and a1 as fit parameters.
The diffusion limitation can only be observed from the isothermal cure experiments since in the non-isothermal heat rate tests the temperature will always increase until curing is complete. An example of the diffusion limitation effect can be seen in Figure 1 for the 90 C cure experiments. This experiment clearly show that the conversion level does not increase beyond 90%, even for prolonged curing times of 10 hours.
4. Experimental
The molding compounds considered here are commercially availble and are refered to a materials A, C, E, F, G and H. They all have an ash content (filler concentration) in the range of 87 to 90%. The reaction kinetics of these compounds were analysed with a TA-Instruments DSC 2980 Differential Scanning Calorimeter. This device accurately measures the heat released during reaction, H, per unit of time. The total reaction heat is obtained by integrating the recorded heat flow dH/dt over the time needed to complete the reaction. The fact that each time when an epoxy group reacts a fixed amount of heat is released, means that the reaction rate and heat flow must be proportional. Therefore the experimentally obtained reaction rate becomes
dt dH H dt d tot 1 =
α
. Eq.7 The experimental conversion level then simply follows by integration of the above expression.Two sorts of experiments were performed to determine the kinetic parameters. Firstly uncured samples were subjected to a series of different heating rate tests (1, 2, 5, 10 and 15 °C/min) and the released reaction heat was recorded as a function of temperature. Secondly a series of isothermal cure experiments was performed. In these experiments the molding compound samples were cured at a specific temperature and for a specific time, after which the conversion level is obtained from a second DSC scan (10 °C/min) as α=1-Hres/Htot, where Hres is the
these isothemal cure experiments are close to those expected in the characterisation tests and the isothermal expriments are therefore important to include in the kinetic modelling. This second set of experiments also provides the relation between conversion level and glass transition temperature.
5. Isothermal cure experiments
Samples of about 10 mg were cured at temperatures of 90 to 120 C for 10 to 300 minutes (and more if needed). Curing for shorter times resulted in an undesirable large contribution of the reaction progress during the heating period. That means that for this type of experiments it is not useful to apply curing temperatures above Tg
(typically 120 C for these materials). A typical plot of the data obtained with isothermal cure experiments is shown in Figure 1. This shows for example that it takes about 80 minutes for the reaction to complete at 120 C and 240 minutes at 110 C.
An important reason to perform isothermal cure experiments is that together with the conversion level also a glass transition temperature can be extracted for each of the experiments. If both the Tg and the conversion are
collected in a single plot we obtain for compound G a plot as shown in Figure 2. The full line is the curve according to the so-called DiBenedetto equation
α
λ
λα
α
) 1 ( 1 ) ( ) ( 0 −1 −0 − + = g g g g T T T T , Eq.8where Tg0 and Tg1 denote the glass transition temperature
at α = 0 and 1, respectively and λ is a shape parameter with a value between 0.2 and 0.6. Since the glass transition temperature can usually be determined with more accuracy than the heat of reaction, from now on the reported conversion levels from isothermal cure experiments will be determined from in Eq.8 instead of using the measured residual heat.
Isothermal cure experiments as described above were performed for all molding compounds under study. This resulted in plots similar to Figures 1 and 2. The corresponding DiBenedetto parameters are listed in Table 1. Please note that these parameters for the glass transition temperature only apply for Tg’s determined
from DSC experiments at 10 C/min heating. Glass transition temperatures determined from DMA experiments are typically 10-15 C higher and depend on the heating rate as well.
In order to investigate the diffusion limitation effect additional isothermal experiments were performed at room temperature and at 70 C. An example of a plot of the thus determined maximum conversion levels versus the reciprocal temperature is shown in Figure 3. The full line is the fit according to the Gonzalez equation (Eq.6). The corresponding parameters a0 and a1 are also included
in Table 1. Compound G 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 250 300 time [min] conv er si on [ -] 90C 100C 110C 120C
Fig.1: Isothermal cure experiments of compound G. Full lines are predictions (see text).
Compound G 0 20 40 60 80 100 120 140 0.00 0.20 0.40 0.60 0.80 1.00 conversion T g [C ]
Fig.2: Glass transition versus conversion obtained from isothermal cure experiments. Full line: DiBenedetto fit.
Compound G 0.0 0.2 0.4 0.6 0.8 1.0 0.002 0.0025 0.003 0.0035 reciprocal temperature [1/K] m ax im u m c onv er si on [-]
Fig.3: Measured maximum conversion levels (symbols) and fit to Equation 6 (full line)
A C E F G H Tg0[°C] 29.7 20.6 32.4 17.8 23.7 17.8 Tg1[°C] 136.6 114.4 124.6 103.9 132.8 81.9 λ [-] 0.51 0.251 0.357 0.566 0.559 0.608 a0 [-] 4.446 4.469 4.130 4.408 4.226 4.876 a1 [K] 1289 1293 1181 1231 1204 1382
5. Heat rate tests
The DSC tests at different heating rates were used to obtain first estimates of the parameters in the (modified) Kamal-Sourour equation (Eqs.1 and 5). A typical result is shown in Figure 4 (full lines).
Compound G 0.E+0 2.E-3 4.E-3 6.E-3 8.E-3 1.E-2 40 90 140 190 240 temperature [C] h ea t f lo w r at e [ 1/s ] 1Cpmin2Cpmin 5Cpmin 10Cpmin 15Cpmin
Fig.4: DSC results of heat rate tests (full lines) and final model predictions (dashed lines).
This shows a collection of heat flow curves with increasingly larger peaks and a maximum which shifts to higher temperatures with increasing heating rate. Notice that when these peaks are integrated with respect to time the total heat of reaction turns out to be approximately independent of the heating rate. For the molding compounds in this study these total heat of reaction varies between 12 and 30 J/g. The procedure for evaluating the kinetic constants is as follows:
o First determine the total heat of reaction Htot and the
initial glass transition temperature Tg0 from the
constant heat rate tests on uncured samples. These data are never exactly equal since part of the heat may remain unrecorded because of the error of DSC machine and Htot also depends on the choice of the
baseline.;
o Then calculate the activation energy Ea and the front
factor k0 from the slope of the reciprocal of the peak
temperature versus the logarithm of the applied heating rate (Kissinger method [5,6]);
o Next divide the experimental reaction rate (Eq.7) by kT
using E0 and k0. In a plot of the thus obtained
normalized reaction rate versus conversion all heat rate date then should overlap (Figure 5). The constants
m and n are then obtained by fitting to the remaining
part of Eq.5.
o From the isothermal experiments we first determine the DiBenedetto parameters and the diffusion limitation constants a0 and a1 (see section 5);
We then have a complete set of kinetic parameters which can be used to predict conversion levels at any desired temperature and curing time. As a check for internal consistency we therefore used the thus determined parameter set to make predictions for the isothermal cure data. For some materials (like compound F) this turned
out to work quite well, but for others there appeared to be a systematic under prediction of the conversion levels at lower curing times. There can be many reasons for this and below we will discuss this in more detail and propose a way to explain the difference.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6x 10 6 X/Xmax [-] k0 *f (X ) 1.0 2.0 5.0 10.0 15.0
Fig.5: Normalized reaction rate plot (symbols) to determine constants m and n; Full line: fit.
The first explanation for the apparent inability to predict both heat rate and isothermal data with the same model is that the reaction kinetics is more complex than can be described with the present model. In literature a more general version of Eq.2 is proposed which contains the additional term k1 exp(-E1/RT)[1-α]p (Prime, [5]).
Alternatively, the experimental data can be tried to model using the so-called “model free kinetics” method [7]. In this method the activation energy is not a constant but is allowed to vary with conversion. Both methods are reported to be capable of reproducing experimental data in a satisfactory way. The problem is, however, that it is then necessary to introduce (many) extra fit parameters at the cost of a loss of simplicity relative to the original kinetic model. Moreover, the problem may not even be the lack of fit parameters since good fits for the heat rate data can be obtained with the present model for several, distinct, sets of parameters (k0, E0, m, n). A small change
in the activation energy is for example compensated by a change in k0 [7,8]. Furthermore also simultaneous
changes in m and n (and k0) are possible which hardly
affect the predictions for the peaks in the heat rate experiments but have a rather large effect on the isothermal predictions. It should therefore be possible to optimise the kinetic parameter set for the present model such that it fits both sets of experiments. The predictions then will no longer result in perfect agreement with the experimental data but this can be justified by considering the fact that for the present materials there is always some uncertainty in the experimental data itself.
suggests that there can be a difference in activation energy below and above Tg. This was tested by shifting
the isothermal cure curves along the log(t) axis until they overlapped (notice that this in fact uses the dimensionless cure time concept as mentioned in section 2). The temperature dependency of the shift factors, however, revealed that the change in activation energy was small.
The last explanation for the discrepancy between heat rate and isothermal data is an initial conversion level which appears to be present for the isothermal data but not for the heat rate test data. This effect can be seen by focusing on the initial part of the measured isothermal data (Figure 1). It appears then that extrapolation to zero curing time does not result in a zero conversion level but in an apparent initial cure of about 5-15%. Such initial conversion levels may have resulted for several reasons. First of all, some cure during storage and sample preparation may have occurred. The second reason is the conversion during heating up. In order to minimize the cure during heating, a heat ramp of 20 °C/min was programmed. Even with this fast heating rate, it takes about 4 or 5 minutes to reach the required isothermal temperature. In practice, it takes even longer since the DSC software slows down the heating rate when approaching the desired temperature. The effect of initial conversion can be taken into account by modifying the lower integration limit to a non-zero value α0 in equation
3. It then turned out that with initial cure levels of 0.007, 0.15, 0.095, 0.00, 0.05 and 0.03 for compounds A, C, E, F, G and H respectively a good agreement between measured isothermal conversions and predictions from the heat rate tests could be obtained. An example is shown for material G in Figure 1 (dashed lines are predictions, symbols with full lines are measured data). The predictions for the heat rate test are shown in Figure 4 as the dashed lines.
The recommended kinetic parameter sets for all materials evaluated in this study are listed in Table 2.
A C E F G H k0 [106 s-1] 3.10 7.98 11.1 1.63 12.9 8.53 E0 [kJ/mol] 66.1 71.3 72.7 64.7 70.2 71.3 m [-] 0.71 0.272 0.168 0.344 0.671 0.313 n [-] 1.60 1.13 1.07 0.98 1.35 1.23 Htot [J/g] 21.7 13.85 21.73 12.18 30.1 15.5
Table 2: Kinetic parameters for Equations 2 and 5
6. Conclusions
The kinetic parameters for six commercial molding compounds were carefully evaluated from a set of heat rate tests and isothermal cure tests. In particular care was taken to also have reliable predictions in the lower temperature region. For that purpose the kinetic model was modified to include the diffusion limitation effect
(maximum cure levels at temperatures below the glass transition). These maximum cure levels were seen to be proportional to the reciprocal of the absolute cure temperature. The conversion dependency of the glass transition temperature was modelled using the well known DiBenedetto equation.
Acknowledgments
We kindly acknowledge the material suppliers Hitachi, Shin-Etsu and Sumitomo for supplying the molding compounds used in this study.
References
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