A numerical procedure for simulating thermal oxidation diffusion of

Microelectronics Reliability 55 (2015) 1877–1881

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Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr

A numerical procedure for simulating thermal oxidation diffusion of epoxy molding compounds Zaifu Cui a,b, Miao Cai a, Ruifeng Li a, Ping Zhang a, Xianping Chen a, Daoguo Yang a,⁎ a b

Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin, China Department of Electronic Engineering, Luzhou Vocational & Technical College, Luzhou, China

a r t i c l e

i n f o

Article history: Received 25 May 2015 Received in revised form 24 June 2015 Accepted 25 June 2015 Available online 25 August 2015 Keywords: Epoxy molding compounds Thermal oxidation diffusion Simulation Heat conduction Aging

a b s t r a c t A new numerical procedure is developed for simulating the thermal oxidation diffusion of epoxy molding compounds (EMC). In this approach, the formal similarity of oxidation diffusion equation and the heat conduction equation is utilized to convert the oxidation diffusion issue to heat conduction issue, then a 2D finite element model of EMC is established, and the oxidation diffusion of EMC aged under 150 °C is implemented with the thermal conduction modules of software ANSYS. The concentration distribution of oxidation products and the distribution of elastic modulus are calculated in ANSYS in the oxidized layer after 100 h, 600 h and 1000 h of isothermal aging at 150 °C under atmospheric air. The comparison between the calculated results and the simulated and experimental data obtained from literature is conducted. Moreover, the influence of silica filler in EMC on the oxidation diffusion is analyzed preliminarily. The results indicate that the oxidation diffusion can be effectively simulated, and the fillers in EMC probably affect the oxidation diffusion process. Evidently, the proposed procedure is effective for simulating the issues of thermal oxidation of EMC, while further experimental validations are needed. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Plastic packaging makes up the overwhelming majority in microelectronics packaging. As a main material for plastic packaging, epoxy molding compounds (EMC) are a polymer matrix composite. Due to their low cost, simple processing, light weight, small size, easy transportation and storage, EMC has been increasingly used in microelectronics packaging. With the improvement of people's demand for microelectronics products, low cost plastic products are used more and more in high temperature applications [1]. For example, the microelectronic devices of electronic control unit (ECU) in automotive engine during work have to experience high temperatures [2]. EMC in high temperature will react with oxygen chemically, which makes the electronic devices packaged by EMC have failure phenomena such as cracking and other phenomena. So it is necessary to study thermal aging of EMC. Many researchers found that the thermal aging of EMC is caused by thermal oxidation [1–3]. Few researchers studied thermal oxidation diffusion of EMC, while many researchers focused on thermal oxidation diffusion of other composites. Colin et al. [4] presented a strategy of research built at the laboratory in order to reduce empirism in lifetime prediction of organic matrix composites, which was based on a model ⁎ Corresponding author. E-mail address: [email protected] (D. Yang).

http://dx.doi.org/10.1016/j.microrel.2015.06.112 0026-2714/© 2015 Elsevier Ltd. All rights reserved.

which couples the O2 diffusion and consumption kinetics and gives access to the thickness distribution of all the chemical modifications involved in the aging process. Olivier et al. [5] used finite element software ABAQUS to simulate the stress and strain of CFRP under aging. In this paper, a new numerical approach is developed for simulating thermal oxidation diffusion of EMC. In this approach, due to the formal similarity of oxidation diffusion equation and heat conduction equation, a two-dimensional (2D) finite element model of EMC is established, and by using the thermal conduction modules of ANSYS, the oxidation diffusion of EMC aged under 150 °C is implemented. Furthermore, the influence of fillers on the oxidation diffusion of EMC is analyzed. 2. Theory and modeling 2.1. Equations of oxidation diffusion and heat conduction The variation rate of the oxygen concentration C at any point (x, y, z) and any time t can be written as [6]: 2

2

∂C ∂ C ∂ C ðx; y; z; t Þ ¼ Dx 2 ðx; y; z; t Þ þ Dy 2 ðx; y; z; t Þ ∂t ∂x ∂y 2 ∂ C þ Dz 2 ðx; y; z; t Þ−r ðC ðx; y; z; t ÞÞ ∂z

ð1Þ

where C is O2 concentration in the polymer, Dx, Dy, Dz are the diffusion coefficients of oxygen in the polymer, respectively, in the x, y and z

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Z. Cui et al. / Microelectronics Reliability 55 (2015) 1877–1881

Table 1 Parameters of 977-2 epoxy resin at different temperatures from literature [8]. Temperatures (°C)

120

150

180

Cs (mol/l) D (m2/s) 2β r0

3.3 × 10−3 8 × 10−13 1.13 × 102 1.03 × 10−6

3.3 × 10−3 1.3 × 10−12 3.00 × 102 5.03 × 10−6

3.3 × 10−3 1.8 × 10−12 6.99 × 102 1.99 × 10−5

directions, r(C(x,y,z,t)) is the oxidation rate. If the material is isotropic, then Dx = Dy = Dz = D. The 3D equation of heat conduction in the thermal analysis module of ANSYS is [7]: 2

ρc

2

∂T ∂ T ∂ T ðx; y; z; t Þ ¼ k 2 ðx; y; z; t Þ þ k 2 ðx; y; z; t Þ ∂t ∂x ∂y 2

∂ T þ k 2 ðx; y; z; t Þ þ qðx; y; z; t Þ ∂z

ð2Þ

where ρ is the density of material, c is the specific heat capacity, T is temperature, k is thermal conductivity, q is the heat generation rate. Eq. (2) is a consequence of Fourier's law of conduction, which indicates the relation of the variation rate of the temperature T at any point (x, y, z) and any time t with other parameters such as specific heat capacity c, mass density ρ and heat generation rate q. Eq. (2) is used to determine the change of T over time. Eqs. (1) and (2) are analogous when some of their parameters are set to some values. In Eq. (2), if ρc is set to 1, the left part of Eq. (2) turns to be the variation rate of temperature T at any point (x, y, z) and any time t, which corresponds to the variation rate of the oxygen concentration C at any point (x, y, z) and any time t. In the right part of Eqs. (1) and (2), if the material is assumed to be isotropic, the thermal conductivity k corresponds to the diffusion coefficient of oxygen in the polymer D and the heat generation rate q corresponds to the negative value of the oxidation rate r. For the two equations, the temperature T corresponds to the oxygen concentration C. So the two equations are formally analogous. 2.2. Determination of the parameters In order to solve Eq. (1), D, CS, r(C) should be given. CS is the oxygen concentration at the surface of the sample. r(C) is the local rate of O2 consumption. Then the concentration in reaction products Q at any time ta is [6]: Zt a Q ðx; y; zÞ ¼

r ðC Þdt 0

Fig. 1. Geometry of the model used in the bi-dimensional calculus of oxidation.

ð3Þ

Fig. 2. The meshed 2D model.

According to Colin et al. [9], the local rate of O2 consumption r(C) is determined by:

r ðC Þ ¼ 2r o

βC βC 1− 1 þ βC 2ð1 þ βC Þ

ð4Þ

In Eq. (4), β is a middle value of the mechanistic scheme by Colin [9]:

β¼

k2 k6 2k5 k3 ½PH

ð5Þ

where k2, k3, k5, k6 stand for the different rate constant in the scheme and [PH] stands for the substrate concentration [9]. Due to lack of the related parameters of EMC, the parameters of 9772 epoxy resin were selected. Table 1 shows the parameters of that type of epoxy resin at different temperatures from literature [8]. 2.3. Finite element implantation of oxidation diffusion The model is based on an 18 mm × 9.5 mm × 2 mm sample made of 977-2 epoxy resin. The sample is illustrated in Fig. 1. We consider, in the x-y plane, a corner of dimensions 500 μm × 500 μm to be modeled in ANSYS. This section is discretised along the directions X and Y (total 625 nodes for the 2D mesh) as shown in Fig. 2.

Fig. 3. Oxygen concentration distribution in the sample aging at 150 °C condition.


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Fig. 4. The concentration of oxidation products Q (a) and elastic modulus obtained by calculating in ANSYS (b), in the oxidized layer after 100 h, 600 h and 1000 h of isothermal aging at 150 °C under atmospheric air.

2.4. Boundary conditions To solve Eqs. (1) and (2), the boundary conditions should be given. In Eq. (1), the boundary conditions are: at t = 0, C = CS (oxygen concentration at the sample surface). In Eq. (2), the boundary conditions are: at t = 0, T = T0 (temperature at the sample surface). It is concluded that the boundary conditions of the two equations are formally analogous. In this paper, CS is 3.3 × 10−3 mol/l taken from [6]. In the model, the fixed oxygen concentration (3.3 × 10−3 mol/l) is applied to the edge of the model. Due to the analog of heat diffusion and oxidation diffusion equation, oxygen concentration can be set as a temperature. The oxygen is dissipated from the edge by conduction through the sample at the rate of the diffusion coefficient of oxygen into the polymer.

3. Results and discussions 3.1. Concentration distribution of oxidation As shown in Fig. 3, the oxygen concentration distribution of the sample aged at 150 °C after 1000 h is presented. The maximum oxygen concentration (QMX), appearing at the surface of the sample, is 3.3 × 10−3 mol/l after aging for 1000 h, which is in line with the boundary conditions in the model. The simulation results after aging for 100 h and 600 h are also showed in Fig. 3. The dynamic process of oxygen diffusion is evident in the proposed modeling. Moreover, along the axis x = 0 and y = 0, the oxygen concentration decreases dramatically from the edge to the sample center.

According to previous study [5] and Eq. (3), the concentration of oxidation products Q and elastic modulus E can be calculated based on the post process function of ANSYS, in the oxidized layer after 100 h, 600 h and 1000 h of isothermal aging at 150 °C under atmospheric air. As shown in Fig. 4(a), the concentration of oxidation products Q is mainly distributed within a thin distance range of approximately 100 μm at the surface of the sample, and reduces rapidly in the range. After 100 h, 600 h and 1000 h of isothermal aging, the concentration of oxidation products Q in the model is about 1 mol/l, 6 mol/l and 10 mol/l, respectively. It is highlighted that the concentration of oxidation products Q increases significantly with increasing cumulative time under the 150 °C aging condition. By contrast, the elastic modulus of EMC in the model undergoes a significant rise, with 4600 MPa, 5400 MPa and 5500 MPa, respectively, as shown in Fig. 4(b). The elastic modulus, similar to the shifting trend of concentration of oxidation products Q, increases significantly with increasing cumulative time, with a slow rate, which elucidates that material properties of EMC experience a gradual degradation during aging process. By comparison, the results of isothermal aging simulation and experiments from literature [6] are showed in Fig. 5, After 100 h, 600 h and 1000 h of isothermal aging [6], the concentration of oxidation products Q is approximately 0.8 mol/l, 4.2 mol/l and 5.8 mol/l respectively (Fig. 5(a)), and the elastic modulus is respectively 4400 MPa, 5300 MPa and 5600 MPa (Fig. 5(b)). Evidently, the simulating results from the proposed procedure, in particular the trends of the concentration of oxidation products and material elastic modulus, agree extremely to that in the simulation and experimental data from literature [6]. Therefore, the oxidation diffusion can be effectively simulated. The

Fig. 5. Epoxy resin, prediction of the concentration of oxidation products Q (a) and elastic modulus obtained by ultra-micro indentation (b), in the oxidized layer after 100 h, 600 h and 1000 h of isothermal aging at 150 °C under atmospheric air [6].

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Z. Cui et al. / Microelectronics Reliability 55 (2015) 1877–1881 Table 2 Parameters of a type of EMC at 175 °C. Temperature (°C)

175

Cs (mol/l) D (m2/s) 2β r0

3.3 × 10−3 3.94668 × 10−13 6.111 × 102 1.587 × 10−6

procedure proposed in this study is effective for simulating the issues of thermal oxidation of EMC. 3.2. Influence of fillers in EMC on the oxidation diffusion Generally, EMC mainly consists of epoxy resin, accelerator and filler [3]. Fillers occupy the most weight of EMC. Filler concentration has evident influences on EMC properties [11]. For example, fillers may affect the thermal oxidation diffusion, because they are stable and never react with oxygen under high ambient temperature. Silica is commonly used as fillers occupying the most weight content varying from 60% to 92% [10], in order to achieve excellent properties, such as dielectric property, low coefficient of thermal expansion (CTE), and high coefficient of thermal conductivity. When EMC is aged at high temperature, epoxy resin will react with the oxygen, while the filler won't react with oxygen. And as the oxygen diffuses into the EMC, an oxidized layer appears at the surface of the EMC [12]. In this study, a type of EMC with 88 wt.% silica fillers is selected to analyze the influence of EMC fillers on the oxidation diffusion. According to the report [13], if the diffusion coefficient of oxygen into EMC is D, and the diffusion coefficient of oxygen into epoxy resin is Dr, the volume percent of the filler occupying the EMC is Vf, then: D ¼ Dr ð1−V f Þ:

ð6Þ

Because many studies on isothermal aging of EMC were conducted under 175 °C or higher temperature [1,3,12,14,15], it is assumed that EMC is aged at 175 °C, and the parameters of 2β, r0, and Dr can be calculated according to Lagrange's interpolation. The diffusion coefficient of oxygen into EMC can be calculated based on Eq. (6). When the density of the silica (ρ1) and epoxy resin (ρ2) are provided, Vf can be calculated. If w = 88%, ρ1 = 2.64 × 103 kg/m3, ρ2 = 1.2 × 103 kg/m3, then Vf = 76.92%. The boundary condition is still: t = 0, CS = 3.3 × 10−3 mol/l. Therefore, the parameters are listed in Table 2. Then the proposed numerical procedure is carried out using the same 2D model (see Fig. 2) and the parameters of Table 2. The model is numerically solved in ANSYS, and the oxygen concentration distribution in the EMC after 1000 h of aging at 175 °C is presented, as shown in Fig. 6. The oxygen concentration decreases rapidly from the edge to the model center.

Fig. 6. Oxygen concentration distribution in the EMC after 1000 h aging at 175 °C.

However, as shown in Fig. 7, considering the influence of 88 wt.% silica filler, the thickness of the oxidized layer declines to less than 100 μm, even under a higher ambient temperature. Meantime, after 100 h, 520 h and 1000 h of isothermal aging, the concentrations of oxidation products Q are about 5.0 mol/l, 22.5 mol/l and 42.5 mol/l, respectively; the concentration of oxidation products Q increases a lot. The results indicated that oxygen is probably prevented from diffusing into the EMC while the suitable filler is added into EMC, so that the thermal oxidation phenomenon of EMC can be improved. Further study should be implemented to validate these preliminary results in the future. In addition, the parameters, such as diffusion coefficients of oxygen, density, CS, 2β and r0, are different for different types of EMC. Since there are few studies on the thermal oxidation diffusion of EMC, many parameters such as D, CS, 2β, and r0 can't be found in literature. Experiments should be conducted to acquire the parameters in further study, such as D, CS, 2β, and r0 at certain temperatures for different EMC. The validation experiments should also be conducted, for example, measurement of the distribution of elastic modulus and the thickness of oxidized layer in EMC after certain time under certain temperature for different EMC. 4. Conclusions A new numerical approach is developed for simulating the thermal oxidation diffusion of EMC. By using the formal similarity of oxidation diffusion equation and heat conduction equation, the issues of oxidation diffusion of EMC are converted into thermal diffusion problems. The concentration of oxidation products Q and the elastic modulus increase significantly with the increasing cumulative time, which illustrates that the EMC experiences a gradual degradation process. The comparison between the results from the proposed procedure and the data observed from literature proves that the oxidation diffusion of EMC can be effectively simulated. The proposed procedure is effective for simulating the issues of thermal oxidation of EMC. Moreover, considering the influence of fillers in EMC, the thickness of the oxidized layer becomes thinner and the concentration of oxidation products Q increases dramatically, which implies that the oxygen is probably prevented from diffusing into the EMC while the suitable filler is added into EMC, so that the thermal oxidation phenomenon of EMC can be improved. In the further study, we are of interest to do experimental measurements to validate the proposed simulating approach and to obtain more correct parameters for different types of EMC. Furthermore, more accurate models may be built for the thermal oxidation diffusion. Acknowledgments The work is co-supported by the Natural Science Foundation of China (no. 51366003), the Guangxi Key Laboratory of Manufacturing

Fig. 7. The concentration of oxidation products Q obtained by calculating in ANSYS, in the oxidized layer after 100 h, 520 h and 1000 h of isothermal aging at 175 °C under atmospheric air.


System and Advanced Manufacturing Technology (no. 14-045-15002Z) and the Innovation Project of Guangxi Graduate Education (no. YCBZ2015037). References [1] J. de Vreugd, A. Sánchez Monforte, K.M.B. Jansen, et al., Effect of postcure and thermal aging on molding compound properties, 2009 11th Electronics Packaging Technology Conference 2009, pp. 342–347. [2] J. Li, Packaging needs for high temperatures and harsh environments, http://www. sengenuity.com/news/adv_pack_jli_032007.pdf. [3] J. de Vreugd, The effect of aging on molding compound properties(D.Phil. Thesis) Delft University of Technology, Delft, 2011. [4] X. Colin, J. Verdu, Strategy for studying thermal oxidation of organic matrix composites, Compos. Sci. Technol. (2005) 411–419. [5] L. Olivier, C. Baudet, D. Bertheau, et al., Development of experimental, theoretical and numerical tools for studying thermo-oxidation of CFRP composites, Compos. A: Appl. Sci. Manuf. (2009) 1008–1016. [6] L. Olivier, N.Q. Ho, J.C. Grandidier, et al., Characterization by ultra-micro indentation of an oxidized epoxy polymer: correlation with the predictions of a kinetic model of oxidation, Polym. Degrad. Stab. (2008) 489–497. [7] Wikipedia, Heat equation, http://en.wikipedia.org/wiki/Heat_equation#cite_note-5.

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[8] J. Decelle, N. Huet, V. Bellenger, Oxidation induced shrinkage for thermally aged epoxy networks, Polym. Degrad. Stab. (2003) 239–248. [9] X. Colin, C. Marais, J. Verdu, A new method for predicting the thermal oxidation of thermoset matrices Application to an amine crosslinked epoxy, Polym. Test. (2001) 795–803. [10] H.J. Mei, X.Y. Du, L.X. Li, et al., Optimal packing research of spherical silica fillers used in epoxy molding compound, 2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP) 2009, pp. 623–626. [11] D.G. Yang, K.M.B. Jansen, L.J. Ernst, et al., Effect of filler concentration of rubbery shear and bulk modulus of molding compounds, Microelectron. Reliab. (2007) 233–239. [12] Daoguo Yang, Zaifu Cui, The effect of thermal aging on the mechanical properties of molding compounds and the reliability of electronic packages, 2011 12th International Conference on Electronic Packaging Technology & High Density Packaging 2011, pp. 1030–1033. [13] L. Kumosa, B. Benedikt, D. Armentrout, et al., Moisture absorption properties of unidirectional glass/polymer composites used in composite (non-ceramic) insulators, Compos. Part A (2004) 1049–1063. [14] D.G. Yang, F.F. Wan, Z.Y. Shou, et al., Effect of high temperature aging on reliability of automotive electronics, Microelectron. Reliab. (2011) 1938–1942. [15] D.G. Yang, D.J. Liu, W.D. van Driel, et al., Advanced reliability study on high temperature automotive electronics, 11th International Conference on Electronic Packaging Technology & High Density Packaging 2010, pp. 1246–1249.