Modelling Methodology for Linear Elastic Compound Modelling Versus Visco-Elastic Compound Modelling R.B.R van Silfhout 1), J.G.J Beijer 1), Kouchi Zhang 1), W.D. van Driel 2) 1) Philips Applied Technologies, P.O. Box 218, 56 MD, Eindhoven, The Netherlands richard.van.silfhout@philips.com 2) IMO Back-end Innovation, Philips Semiconductors, P.O. Box 38, 6534 AE, Nijmegen, The Netherlands Abstract Finite Element (FE) simulations take an important place in predicting the thermo-mechanical plastic-package behaviour. Several studies in both industry and research cover this topic since the mechanical impact of the Epoxy Moulding Compound (EMC) behaviour is of major impact on package reliability and the understanding of the material behaviour is limited. In the history of package modelling, large differences in thermo-mechanical stresses are found between (temperature dependent) elastic calculations and time dependent calculations, such as visco-elastic calculations. Visco-elastic compound behaviour is often recommended to take into account to predict stresses reliably, but takes significant effort and time for material characterisation. In this paper the origin of stress differences will be analysed for different EMC material models in different realistic process conditions. By understanding the impact of realistic compound behaviour during real process conditions, an effective modelling approach is proposed which takes less material characterisation and less calculation time. The modelling method is applied on a package simulation analysing 3 different compounds and is verified by visco-elastic simulations. 1. Introduction The EMC behaviour is a dominant factor in package reliability and therefore takes an important position in stress simulations. This section discusses the packaging process conditions in combination with available material models used for EMCs. Figure 1 represents the typical packaging and testing process conditions showing die attach, moulding, and PMC (Post Mould Cure) to assemble the package. After package assembly, process take place for ink marking, solder testing, and temperature cycling. During these processes, the compound stiffness and Coefficient of Thermal [ C] Complete Process Pattern 24 2 29 sec 3 times 1 17 15 11 8 3 min 1 hour 2 2 min min 9 sec 9 sec 1 sec 1 sec 6 sec 1 sec 1 hour 5 hours 1 1 hour hour 3 min 3 min 1 hour 3 3 min min 3 sec 3 sec 3 sec 3 sec 15 min +15 C 3 min 3 3 min min I) Glue the Die II) Wire III) Molding IV) PMC V) Ink Mark Bond 3 3 min min Time VI) Solder VI) TMCL Test -65 C 15 min Figure 1: Typical process temperatures and times for assembly and testing.
Expansion (CTE) are dominant factors determining the mechanical behaviour of the package. Figure 2 shows the stiffness as a function of temperature for three different EMCs obtained from a 1Hz measurement and the 1Hz curves from a visco-elastic material model. The different stiffness below and above glass transition temperature (Tg) explains a bit of the relevance of EMC behaviour. E[MPa ] 2 15 1 5 E(T) of compounds 2 15 1 5 E(T) 1Hz (master)curves from visco-elastic fit assembled from different batches. The CTEs of these matererials are also measured for their temperature dependency, but will not be discussed in much detail because no special care has to be taken in FE modelling simulations to correctly model this behaviour. The viscoelastic material model from Figure 2 for is applied to relate the EMC behaviour to different process conditions. Figure 3 shows the stiffness as function of temperature for two different step times: heating/cooling in 1 seconds and in 1 hour. These timescales correspond to Figure 1 and are taken to show that the differences in material behviour are small. Besides, the two measuring frequencies are given withwhich the corresponding material behaviour could be measured. 2 1 2 Temp [ C] 1 2 Temp [ C] 15 Figure 2: Compound stiffness for a) 1Hz measurement and b) 1Hz derived from full-frequency sweep measurement. The EMC behaviour is strongly depending on process conditions such as temperature, time, humidity, etc. In several studies temperature and time effects are measured by measuring stiffness in a full frequency sweep at different temperatures. From the measured data, viscoelastic material models are derived and prove to predict package behaviour reliably during processing [1]. Present studies focus on the effect of curing conditions (PMC) on the eventual EMC behaviour [2, 3, 4] and the effect of humidity on package failures [5]. Both the academic and industrial community is involved to understand and optimise the package assembly to control issues such as package stresses and warpage [6, 7, 8]. The EMC material behaviour is investigated by FE studies and can show different results when different material models are applied [9, 1]. In the next section we will combine process conditions and material behaviour to understand the EMC material models to be applied and to support a different FE modelling methodology. 2. Moulding Compound Behaviour EMCs are measured and simulated for their mechanical behaviour in various ways as described in the previous section. To understand the behaviour of EMCs and estimate dominant parameters, we will use from Figure 2. By understanding the EMC behaviour during assembly processes, the unfoundedness of linear elastic modelling will be explained and a correct elastic approach will be proposed. Figure 2 shows stiffness (E) as a fuction of temperature for three different compounds. As mentioned before, the data is obtained from different measurements and show a good agreement except for the difference in Tg for. This difference can be explained by measuring on different compound samples being 1 5 1 1 2 [ C] 1 sec 1 hr.1hz measurement 1e-4Hz measurement Figure 3: Stiffness for different process cool/heat times and corresponding measuring frequencies. From the Figure it can be seen that the Tg is about 15 C for a 1-sec step time (i.e. after moulding) and about 13 C for a 1-hour step time (i.e. PMC). In a visco-elastic material model, this difference in Tg of about 2 C will be taken into account automatically. In the following section we will however analyse the effect of Tg on package stresses. Furthermore the stiffness below Tg (E1) is of similar order for the 2 process step times as well as the rubbery modulus (E2 above Tg). With a 1 seconds temperature step time the corresponding measuring frequency would be.1hz. This is about 1e-4Hz for 1hr temperature step time. A regularly applied measuring frequency is 1Hz (i.e. applied by suppliers for material data on data sheets). These material effects can also be depicted as time dependency at different steady temperatures. Figure 4 and Figure 5 show the stiffness as a function of time for for different temperatures. Figure 5 is in fact a magnification of Figure 4 on a time scale till 3 seconds. The background for the time and temperature scales can be found in the process conditions given in Figure 1.
2 15 1 5 1 2 3 4 5 6 Time [s] -4 C C 11 C 1 C 2 C Figure 4: Time effect till 1 week (~6 s) at different temperatures for (from visco-elastic material model). 2 15 1 5 5 1 15 2 3 Time [s] -4 C C 11 C 1 C 2 C Figure 5: Zoom in from Figure 4 for first 3 seconds. Considering the small stiffness change at temperatures from room temperature till -4 C, hardly any stress relaxation will take place on these time scales. At higher temperatures about 1 C it can be seen that the EMC stiffness will relax to its rubbery modulus within a time scale of about 3 seconds and. For example during solder testing at 2 C stresses in the package will relax rapidly to a stress situation for the compound having its rubber modulus. We emphasise that package stresses will not relax towards zero, but to the equilibrium for a LF, die attach, die and compound with rubbery modulus. Calculating with the rubbery modulus might therefore approximate package stress behaviour at high temperatures. By applying this material model in a simple uni-axial test, we will analyse the effects of Linear Elastic (LE) modelling and Linear Visco-Elastic (LVE) modelling. Figure 6: Simple model for testing material models. Figure 6 shows the simple FE model with the boundary conditions. In this simulation we cool down the model from 1 C to C. Again the CTE is also temperature dependent, but no details are provided in this paper. Figure 7 compares the stress results from a LE simulation with a material model like in Figure 2a and a LVE model such as described above. 8 7 6 5 4 3 2 1 LVE 5 1 1 15 1 LE Figure 7: with LE and LVE cool down. Large differences in stress history are found. The LVE calculation builds up the stress reliably: The stress gradient increases with increasing stiffness below Tg. The LE calculation builds up stress rapidly around Tg. This is not expected from the material behaviour and is caused by the linear relation between strain and stress, which multiplies total elastic strain ε el with the stiffness E at that specific temperature (see Equation 1). This explains the rapid stress increase around Tg because the total elastic strain, which is built up above Tg, is multiplied by the high stiffness just below Tg (see Figure 2). el el 1 σ = ε Ei This is common knowledge, but when an elastic FE model is developed in commercial software with temperature dependent material data, the LE methodology still is applied for the stiffness. For a temperature dependent CTE however, the thermal strains are calculated incrementally by multiplying incremental dt with CTE i in that temperature range. It is remarked that different definitions may be used in different software vendors for a temperature dependent CTE [11, 12]. The developer of the model should consider whether this is the requested numerical approach or if an incremental elastic approach should be followed. For simulations such as cooling of compounds, we would propose an incremental linear elastic (ILE) approach according to Equation 2. el el 2 σ = (ε E ) i i When a temperature change is applied to the compound, this approach takes stress history into account by accumulating the incremental stresses. By understanding these basics, it can be understood that temperature dependent elastic simulations cause different stresses compared to visco-elastic simulations. In the following of this section we compare the LVE, LE, and ILE approach with the simple model for both cool down loadings
(1 C to C) and heating ( C to 1 C). Because time scale is important for the LVE simulation, 18 second is applied to cool down or heating. The following Figures show the temperature loading and stress results as a function of increments. Figure 8, Figure 9, and Figure 1 show the results for cooling and Figure 11Figure 12, and Figure 13 show the results for heating. For the cooling of LVE and LE model (Figure 8 and Figure 9) the results are the same as shown above in Figure 7 but are in another layout. 8 7 6 5 4 3 2-3 1-1 5 1 15 2 3 35 4 5-2 1 15 1 1 stress is predicted unreliably and is discussed above. By applying the ILE approach (Figure 1), the stress is calculated in a similar way as in LVE. is somewhat higher in LE simulation (3MPa) compared to LVE simulation (24MPa). This is explained by the position of Tg. ILE has a fixed Tg belonging to the 1Hz measurement and is at a higher temperature compared to the LVE simulation, which adapts the Tg automatically. Figure 14 shows the higher Tg for ILE compared to LVE corresponding to 18 second cool down time. 8 7 6 5 4 3 2-3 1-1 5 1 15 2 3 35 4 5-2 1 15 1 1 Figure 8: LVE results during cool down. 8 1 7 6 15 5 4 1 3 2 1 1-1 5 1 15 2 3 35 45-2 -3 Figure 9: LE results during cool down. 8 1 7 6 15 5 4 1 3 1 2 1-1 5 1 15 2 3 35 45-2 -3 [ C] Figure 11: LVE results during heating. 8 1 7 6 15 5 4 1 3 2 1 1-1 5 1 15 2 3 35 4 5-2 -3 Figure 12: LE results during heating. 8 1 7 6 15 5 1 4 3 1 2 1-1 5 1 15 2 3 35 4 5-2 -3 [ C] Figure 1: ILE results during cool down. results are comparable for LVE and ILE approaches. With the visco-elastic simulations (Figure 8), stress will build up during the cool down due to increasing stiffness. With LE calculations (Figure 9) Figure 13: ILE results during heating. During heating of a compound, the stiffness will decrease above Tg. In Figure 11 the LVE simulation takes the decreasing stiffness into account by lowering the stress above Tg even though the thermal strain is
increasing. With the LE simulation (Figure 12) results are similar to the LVE results. This can be explained by the effect of stress history is fading out with decreasing stiffness and results will converge to the stress belonging to rubbery stiffness. By applying ILE (Figure 13) the incremental stress is accumulated and shows a higher stress compared to the LVE simulation. 2 As an example the effect of downset will be analysed. Figure 15 illustrates the downset, which determines the position of the die in the package. This can be an important optimisation parameter in determining the thermo-mechanical stress balance of the package. Die LF Glue EMC 15 1 18sec for LVE calculation downset 5 1Hz for ILE calculation 1 1 2 [ C] Figure 15: 3D model with boundary conditions and. Table 2: Material models. Figure 14: Different Tgs for ILE and LVE calculations. It is concluded that incremental linear elastic calculations (ILE) give similar results compared to viscoelastic calculations (LVE) for compounds cooling down and linear elastic calculations (LE) give similar results for heating up compounds. By understanding and applying the correct stress strain relation the requested package processes can be simulated qualitatively reliably by using temperature dependent material data. 3. FE Package Modelling Using ILE Methodology. A 3D parametric FE model is developed to study effects of the three compounds from Figure 2. Figure 15 shows the model, which contains the Lead Frame (LF), glue, die, and EMC. Table 1 shows the nominal geometry of the model and Table 2 briefly summarises the applied material models. This section discusses the resulting compound stresses from ILE calculations and will be verified by the LVE calculations. The ILE approach is chosen because the compound is activated at 1 C after PMC and will be cooled down so an incremental approach should be followed. A subroutine was developed to incorporate the ILE calculations numerically. Table 1: Geometrical properties. Parameters Dimension [mm] Die size 4 x 3 x.28 Glue thickness 15e-3 LF size 5 x 4 x. Package size 8 x 5 x 1.55 Downset till. Item Material Material model Lead Frame Cu Elastic-plastic Die attach Glue dependent ILE Die Silicon LE Compound 3 EMCs As described in paper. Figure 16 shows the process loadings. During die attach and wire bonding processes, the compound elements are not activated. At PMC temperature (1 C) the compound elements are activated in a stress free state. In this way the stress history is correctly taken into account. For the resulting stresses we will focus on the compound stresses at the critical process step at -4 C. Maximum stresses occur at lower temperatures because the biggest temperature difference exists here (1 C to -4 C). Figure 16: Process loading for the 3D model.
Figure 17a shows the resulting stresses of the implemented incremental linear elastic approach. To verify the results, Figure 17b shows the visco-elastic simulation results. The stress values in the top centre of the compound are shown at -4 C. The effect of downset can be seen as well as the effect of the EMCs in one graph. By comparing the 2 graphs, the difference between LVE and LE results can be analysed. Linear Incremental Elastic Linear Visco Eelastic Different simulations are performed with various material properties and the maximum variations in compound stress are plotted in Figure 18. 1 Effects Tg, E1, and CTE1 on compound stress 1% is stress 9 6 45 3 15 5 1 15 2 downset [um] ` 9 6 45 3 15 5 1 15 2 downset [um] Figure 17: Comparison of a) ILE simulations and b) LVE simulations for 3 different compounds. The results show that the compound stresses predicted by ILE calculations are in good agreement with LVE calculations. The ranking of EMCs causing high stresses match and also the effect of downset is predicted similarly. The different Tgs can explain the differences in stress levels between ILE and LVE. By using knowledge on existing compound simulations, measurements, and processes 1 (better) measuring frequency can be chosen to have a more reliable Tg in order to predict stress levels more reliably and obtain smaller differences between ILE and LVE calculations. As a last step in this study we show the eventual effect of varying Tg against variations in stiffness (E) and CTE. To determine realistic variations that can occur in real EMC behaviour, the following issues are considered: Statistical variation of mechanical behaviour, Measuring accuracy, Various process conditions. Table 3: Variation on material properties. B C dtg [ C] 4 3 3 de1 [MPa] 2 35 35 dcte1 [ppm/ C] 2 (CTE1 = 1ppm) 5 (CTE1 = 15ppm) 5 (CTE1 = 2ppm) Table 3 shows the summary of variations as a result of the above considerations. Tg levels are varied in a wider range than might occur in reality (see Figure 3 for dtg in reality for ). In case of varying E and CTE, only values below Tg are varied. For CTE, also the absolute levels are given in the table to correlate the variations. Max. Variation in compound stress [%] 8 6 4 2 dtg de dcte Figure 18: Sensitivity study of compound parameters. When we consider dtg being the (time-) effect that can be modelled with a visco-elastic model, it can be concluded that variations in CTE are more dominant for predicting package stresses. Especially for compounds with low CTEs (~8e-6 ppm/ C) the accuracy of measuring and the sensitivity of compound manufacturing are determining the outcome of package stresses rather than the visco-elasticity. It is emphasised that this only holds for cooling and heating processes, no long relaxation times at high temperatures are considered. 4. Discussion In this paper an alternative linear elastic modelling methodology for epoxy moulding compounds is presented as well as the backgrounds for application of the methodology. The methodology requires less material characterisation but rather combines experience of material behaviour, measuring techniques, and process conditions. A first approach is presented to apply the ILE methodology in package simulations. The method makes sensitivity studies with FE easier to perform compared to using visco-elastic models. As a result the mechanical backgrounds for package behaviour are better understood. By combining compound material knowledge with process knowledge the following is concluded: Incremental linear elastic simulations are feasible for simulating typical package assembly processes and testing processes. The spread in CTE level is a dominant factor in package behaviour, especially for new low stress compounds. Acknowledgments We sincerely appreciate the support from Ruud Voncken and Peter Timmermans in the field of numerical modelling and from Will de Haas and Hedzer de Boer for their initiatives in measurements and cooperation.
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