Non-Linear Viscoelastic Modeling of Epoxy Based Molding Compound for Large Deformations Encountered in Power Modules

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1 2017 IEEE 67th Electronic Components and Technology Conference Non-Linear Viscoelastic Modeling of Epoxy Based Molding Compound for Large Deformations Encountered in Power Modules Przemyslaw Gromala, Alexandru Prisacaru, Mateus Jeronimo Automotive Electronics Robert Bosch GmbH Reutlingen, Germany Hyun-Seop Lee, Yong Sun and Bongtae Han Mechanical Engineering Department University of Maryland College Park, MD 20742, USA Abstract Two experimental techniques (dynamic mechanical analyzer and fiber Bragg grating sensor) are used to characterize the viscoelastic properties of epoxy molding compounds. The creep and stress relaxation tests over a wide temperature range are conducted, and they are used to determine (1) the linear viscoelastic properties based on the thermo-rheological simplicity (master curve, Prony series and shift factor) and (2) the non-linear viscoelastic properties of one of Parallel Rheological Framework model (PRF) known as Bergstrom-Boyce (B-B) Model. The models are implemented for the EMC-based power module. The results obtained from the linear viscoelastic analysis and the non-linear viscoelastic analysis are compared, and the technical discussions including the limitation of the B-B model are followed. Keywords- Material characterization and modeling, epoxy based polemers, linear and non-linear viscoelasticity, optimization, Fiber Bragg Grating. I. INTRODUCTION Numerical simulation is one of the critical tools that actively support product development at every design phase, starting from the circuit design of the front and -back end of line (FEOL and BEOL), through the IC package, finishing with the analysis of an ECU. Virtual development of electronic systems can be done only through a quantitative FEM simulation. Such a high level of accuracy of numerical analysis is possible through utilizing a simulation driven design, which considers four stages: - Virtual design of experiment by means of simulation, an optimized bill of materials can be defined, and geometries or layouts can be suggested before the first sample is manufactured. - Material characterization this is one of the most important stages in the simulation driven design. Especially in power electronics, most of the materials works in a strain range where non-linear effects cannot be neglected. This requires very detailed understanding about material behaviors including aging mechanism. - Physics of failure (PoF) simulation after material characterization is conducted, simulation can provide quantitative results. This is achieved by multi-domain and multi-scale simulations. Necessary is to consider manufacturing and assembly steps, including accurate description of the load and boundary conditions. Finally, in the PoF simulation, a proper failure criterion must be considered. - Veryfication this is the last stage which is used to confirm that numerical prediction is able to virtually model the physical world. Different measurements techniques are used such as warpage measurements, moire interferometry, and thermal impedance measurements. In novel power electronic modules for hybrid and electric vehicles, integrated circuitry is encapsulated using epoxybased molding compounds (EMCs). EMCs are known to exhibit strong viscoelastic behavior. The viscoelastic behavior of semiconductor packages containing EMCs has been analyzed by a linear viscoelastic modeling, in which the relaxation modulus (or reduced modulus) is independent of strain. This assumption is valid only when the total strain is small. In power modules, encapsulated by EMC subjected to transient operations, extreme strain rates and large strain magnitudes have been realized. In these deformation regimes, the relaxation modulus is no longer independent of strain (i.e., the relaxation modulus is a function of not only temperature but also strain magnitude), and non-linear viscoelastic approaches have to be employed to accurately predict the deformation behavior. II. LINEAR VISCOELASTICITY A. Master Curves and Shift Factors Fiber Bragg Grating FBG sensors have been used effectively to characterize mechanical properties of polymers. The linear viscoelastic property of the EMC was characterized using the FBG sensor. The EMC was cured into a cylindrical shape under the required pressure while a FBG was embedded in the center of the EMC [1]. The cured EMC was subjected to constant compressive uniaxial and hydrostatic loadings at various temperatures. Test setups used are schematically shown in Fig. 1(a) and for compressive and hydrostatic testing, respectively [1]. The constant uniaxial loading was achieved by a plunger connected to a piston operated by compressed air (Fig. 1(a)), while the constant hydrostatic pressure was achieved by compressed He gas (Fig. 1). The temperature control was achieved by mounting the test chambers on a high precision hot/cold plate /17 $ IEEE DOI /ECTC

2 (a) Fig. 1 Schematic description of experimental setup for (a) uniaxial test and hydrostatic test The embedded FBG deformed together with the specimen. The Bragg wavelength (BW) changes were documented as a function of time while the loading was maintained. The BW changes under two loading conditions are shown in Fig. 2. The BW changes were converted into the corresponding strains, and time dependent Young s modulus and bulk modulus at each temperature were obtained from the measured strains and applied loading conditions [2]. The initial strain ranged from 50 to 200 με, and the maximum stain at the end of the tests was approximately 350 με. Based on the thermo-rheological simplicity, the master curves of Young s modulus and bulk modulus as well as the shifting factors were obtained. Then, the master curve of the shear modulus was calculated from the two properties based on the relationship among the linear elastic properties. The results are shown in Fig. 3(a) and for the master curves and the shift factors, respectively. Master curves are normalized by the maximum value of the Young s modulus. (a) (a) Experiment data Fitted Shift factors T ( C) Fig. 3 (a) The master curves and shift factors obtained from the test [1] Fig. 2 Raw data of (a) the compressive uniaxial creep test and the hydrostatic creep test [2] B. Validation of Linear Viscoelasticity Thermo-rheological simplicity: The time-temperature superposition process is based on the thermo-rheological simplicity (TRS). The assumption states that the shapes of the 835

3 master curve are the same in the log time scale at different temperatures. An extra long-term creep test was conducted to verify the validity of the assumption. The long-term test was conducted at 125 ºC for roughly 4 hours. The temperature was chosen to obtain the strong viscoelastic behavior. The time dependent Young s modulus obtained from the long-term creep test is plotted in the logtime scale and is compared with the master curve in Fig. 4. Both curves are normalized by the initial value of the Young s modulus in the master curve. It is evident that the long term creep data overlaps with the master curve very well, which confirms that the TRS assumption is valid for the EMC material tested in the study. the predicted values indicating the validity of Boltzmann superposition principle for the material. Fig. 5 Validation of the Boltzmann superposition principle Fig. 4 Comparison of the long-term test result with the master curve to verify the TRS assumption Boltzmann superposition principle: The Boltzmann superposition principle (BSP) states that in the linear viscoelastic regime the strain response to successive stress are additive. It is the key to develop the linear viscoelastic constitutive law. In order to verify this assumption, a supplementary experiment was conducted at 130 ºC with a two-step loading. An initial loading was applied at t = 0 and an additional pressure was applied at t = 100 s. The BW change measured during the whole process was documented. Based on the BSP, the strain change due to the step loading can be calculated from the equation: ε() t = J() t σ + J( t τ) Δ σ (1) where ε () t is the strain change as a function of time; J() t is the time-dependent compliance which can be determined from the time-dependent Young s modulus; and σ and Δ σ are the applied stress. The BW change under the same loading can be calculated from the strain. The measured BW changes are compared with the predicted values in Fig. 5. In Fig. 5, the values of applied loading are normalized by the final loading level. The measured values match extremely well to Strain-independent Reduced Modulus: In the domain of linear viscoelastic behavior, the time-dependent (or reduced) modulus should be independent of the applied stress (or strain) level. Three independent tests were conducted to verify the validity. The specimen of each test was subjected to a different stress levels at the temperature in the middle of the glass transition range. The BW changes are shown in Fig. 6(a). The Young s modulus was calculated from the BW, and the values normalized by the initial modulus of the master curve are shown in Fig. 6. The reduced Young s modulus is independent of the applied stress, confirming that the linear viscoelastic assumption is valid for the material. It is to be noted that the maximum strain level applied during this test was smaller than 400 με. (a) 836

4 1.0 Normalized Stress C, 300 με/s 100 C, 300 με/s 125 C, 300 με/s Normalized Strain Fig. 6 Time dependent behavior of EMC during the creep test at different stress level: (a) BW and Young s modulus III. NON-LINEAR VISCOELASTIC CHARACTERIZATION Non-linear behavior of epoxy based thermoset under uniaxial tensile loading condition was investigated using Zwick Roel Z100 machine. A dog bone sample (2) with a standard geometry was mounted in the hydraulic clamps (1), as shown on Fig. 7. The displacement was recorded using an extensometer (3). Fig. 8 Results of the uniaxial investigation Relaxation behavior was investigated until failure with relaxation segments occurred. Test procedure started with loading the sample with a strain rate of 300 με/sec. After reaching 10% of the ultimate strain which was determined from the uniaxial testing, stress relaxation behavior was recorded for 120 min while the specimen was kept under the constant strain. After the 1 st relaxation segment, the specimen was unloaded to 0 N and was held for 120 min. This procedure provided more information about the non-linear material response. Next, the procedure of loading and relaxation was repeated two more times. The relaxation segments were at 45% and 90% of the ultimate strain. At the end of the 3 rd relaxation segment, material was loaded until failure occurred. Fig. 8 depicts the results obtained at 25 C. It is clearly seen that relaxation was very small (or virtually no relaxation) as long as material was within the small strain regime. When the strain range was increased to be in the nonlinear regime, the amount of relaxation became significant nd Segment 3rd Segment Fig. 7 Experimental setup for uniaxial test until failure and relaxation experiment Mechanical response of a fully cured epoxy based molding compound was investigated over a temperature range between -40 and 175 C. Time dependency was obtained by using two different strain rates 40 με/sec and 300 με/sec. For the purpose of material modeling, a minimum of 5 samples per temperature and strain rate were tested. Representative uniaxial testing results at different temperatures are shown in Fig. 8. Strong non-linearity at high strains is evident. Normalized stress st Segment Normalized Strain Fig. 9 Results of relaxtion investigation 837

5 With the current version of ANSYS, the non-linear behavior can be captured only by using Bergstrom-Boyce (BB) model. The theoretical basis of the model is the micromechanical model proposed by Bergström et al. [3], which was originally developed for the non-linear time-depended behavior of elastomers. This complex material behavior is represented by two interacting networks (Fig. 9). Network A is a hyperelastic spring element (eight chain hyperelastic model), which represents the equilibrium response of an elastomer. Network B is composed of an elastic spring and a non-linear time dependent element. This element accounts for the network s strain relief with time, which represents timedependent deviation from the equilibrium. The time dependent flow is captured by using a reptation based energy activation that actually describes a snake like movement of polymer chains. Fig. 10 Bergtrom-Boyce model representation The optimization procedure starts with the definition of the BB constants (Fig. 11 a). In the next step the geometries, materials, boundary and loading conditions are defined (Fig 11 b). The results of simulations are saved as an ASCI file (Fig. 11 c). In this particular study, three test results were investigated: - Uniaxial test until failure with load rate 300 με/sec; - Uniaxial test until failure with load rate 40 με/sec; - Uniaxial test until failure 300 με/sec with relaxation segments (120 min) during loading and unloading. At the end of each simulation, the result is compared with the results obtained from the tests (Fig. 11 d). Accuracy of the material parameters is confirmed by calculating a root mean square error between the simulations and the test results (Fig 11 e). Post-processing is conducted at the end of each simulation leg. The optimization procedure described in Fig. 11 is divided in three major steps: (1) sensitivity analysis, (2) global search optimization, and (3) local search optimization. The goal of the sensitivity analysis is to identify the parameters that have the most significant effect on the response. This allows to reduce the number of parameters to be considered and thus to accelerate the optimization procedure. The dependency between inputs and outputs is determined using the Advanced Latin Hypercube Sampling (ALHS) method. Generated samples are solved by ANSYS and corresponding output vectors are generated. In the next run, an evolutionary algorithm is used to optimize the material constants. This typically takes about 200 simulation runs. Final optimization is done using local search optimization method. A. Optimization procedure In this study, an optimum set of material constants are obtained using a commercially available code: OptiSlang. In ANSYS, a total of nine material constants are required to define the BB model at elevated temperatures. The parameters used during optimization are listed in Table I. TABLE I. B-B MATERIAL CONSTANTS USED FOR OPTIMIZATION Constant Property Optimization status μ A Initial shear modulus network A Yes Limiting chain stretch of Yes network A μ B Initial shear modulus network B Yes Limiting chain stretch of network B Yes Effective creep rate Yes C Strain dependency No M Stress dependency Yes ε Additional material constant No 1/K Reciprocal of bulk modulus Yes Fig. 11 Optimization procedure Fig. 12 depicts the optimized material constants obtained at 75 C from the uniaxial test with a strain rate of 40 με/sec. Grey curves correspond to single simulation results obtained during optimization procedure. The red curve represents the experimental results, and the green line does the results of the optimum solution. 838

6 Fig. 12 Results of optimization Fig. 13 depicts the results of the optimized material model for uniaxial tensile test with the relaxation segments. The results clearly indicate that the temperature change from 25 to 75 C does not affect the non-linear behavior significantly, but, the non-linear effects are so significant at 100 C that any further quantitative prediction of the stress state using the LVE material model is no longer possible. As mentioned earlier, the strain magnitudes inside power electronics will be in the non-linear regime, and the NLVE model should be used to predict the stress state quantitatively. behavior under hydrostatic loadings. As seen from Fig. 2b, however, the EMC shows signiant time-dependent deformations under hydrostatic loadings. Hydrostatic creep test results obtained at 130 C are compared with the predictions of the LVE and BB models in Fig. 15, where the results are normalized by their initial strain value. The LVE model predicts the creep behavior reasonably well. As expected, however, the BB model cannot produce the time-dependent behavior under the hydrostatic loading. The EMC is subjected to large hydrostatic stresses after molding process, and the effect of hydrostatic stresses should be carefully investigated if the BB model is to be used in the analysis. V. CONCLUSSIONS The time-dependent behavior of EMC was studied. Two separate tests were conducted to determine (1) a complete set of elastic constants of the LVE model based on the thermorheological simplicity, and (2) the material constants of one of NLVE models called the BB model through optimization. The models were implemented in ANSYS to illustrate their performance under different loading conditions. The results indicated that the two approaches have distinct advantages and limitations. Further investigations are warranted to develop a model to cope with the limitations. [4-6] C, 300 με/s 75 C, 300 με/s 100 C, 300 με/s 2.0 Normalized Stress Normalized Stress Normalzied Strain LVE model BB model Experimental data strain Fig. 13 Modeling results of relxation test Fig. 14 Experimental result of a uniaxial tensile test is compared with the LVE and BB models IV. DISCUSSION It has been shown that the molding compound has strong non-linearity at high strain levels. The result of the uniaxial tensile test with a constant strain rate at 125 C is compared with the predictions of the LVE and BB models in Fig. 14, where the stress values are normalized by the experimental data at 1% strain. The non-linear behavior after 0.4% is evident. The LVE model predicts the behavior correctly only when the strain is below 0.4%, while the BB model predicts the behavior correctly over the entire strain range. It is important to recall that the BB model was originally developed for hyperelastic materials as such the model did not account for the reduced bulk modulus, i.e., the time-dependent 839

7 -1.0 Normalized Strain LVE model BB model Experimental Result time (s) Fig. 15 Hydrostatic creep test results compared with LVE and BB model REFERENCES [1] Y. Sun, H.-S. Lee, and B. Han, "Measurement of Elastic Properties of Epoxy Molding Compound by Single Cylindrical Configuration with Embedded Fiber Bragg Grating Sensor," Experimental Mechanics, pp. 1-12, [2] Y. Sun, H.-S. Lee, and B. Han, "Measurement of the Comprehensive Viscoelastic Properties of Advanced EMC Using FBG Sensor," in Electronic Components and Technology Conference (ECTC), 2016 IEEE 66th, 2016, pp [3] J. Bergström and M. Boyce, "Constitutive modeling of the large strain time-dependent behavior of elastomers," Journal of the Mechanics and Physics of Solids, vol. 46, pp , [4] J. S. Bergström, "Large strain time-dependent behavior of elastomeric materials," Massachusetts Institute of Technology, [5] [6] P. Gromala, B. Muthuraman, B. Öztürk, K. Jansen, and L. Ernst, "Material characterization and nonlinear viscoelastic modelling of epoxy based thermosets for automotive application," in Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), th International Conference on, 2015, pp