Testing and Modeling of Solders Using New Test Device, Part 2: Calibration and Validation

Contributed by the Electronic and Photonic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received May 2003; final revision, January 2004. Associate Editor: W. King. The compendium paper (Part 1: Models and Testing) presents details of the thermomechanical-digital image correction (TM-DIC) for testing of solders, test plan under variable temperature and strain rates for 63/37 Sn/Pb solder, and typical test results. This paper (Part 2: Calibration and Validation) presents determination of DSC parameters based on the test results, dependence of parameters on temperature and strain rates, and typical validation with respect to test data and predictions from finite element method with the DSC model for chip-substrate problem. The DSC parameters (Table 1, Part 1) were determined by following the procedures presented in various publications 12345. It was found that some of the parameters were not significantly influenced by temperature and strain rates. Typical results for those influenced to a significant extent are discussed below. Figure 1 shows variation of shear modulus, G, with temperature T for 63/37 Sn/Pb 7solder for different shear strain rates γ˙. The shear modulus increases with increase in γ˙ and decreases as T increases. Shi et al. 6 have reported effect of T and γ˙ on the Young’s modulus, E, from uniaxial tensile tests for bulk 63/37 Sn/Pb solders. Based on the shear tests and shear modulus, G, Fig. 1, in this study, E was computed by using G=E/21+ν. Figure 2 shows results of Shi et al. and those from the tests herein. The E values computed from the shear tests are lower than from the uniaxial tensile tests 6; this may be due to experimental factors such as different sample and test procedures. Figure 3 shows variation of the ultimate (peak) shear stress, which decreases with increasing T and increases with increasing γ˙. Figure 4 shows variation of the hardening parameter a1 and η1 (Eq. (2b), Part 1), with γ˙ and T. The parameter a1 is the reference value at high plastic strain trajectory ξ=1 and η1 characterizes the rate of hardening. Figures 5(a) and b shows disturbance (softening or damage) parameters A and Z (Eq. (3a), Part 1) with γ˙ and T;A is the reference value of D for large values of ξDξD=1 and Z denotes the rate of disturbance. The bonding stress 3R (Eq. (2a), Part 1), is computed by using the following equation: (1)R=τult3γwhere τult is the ultimate stress and γ is the slope of the ultimate envelope in J2D−J1 space, Fig. 6(a), for the given T and γ˙. Figure 6(b) shows the variation of R with T and γ˙.The phase parameter, n, (Eq. (2a), Part 1), is evaluated by using the following equation: (2)n=21−τ23R s˙1γτ=τywhere τy is the initial yield strength corresponding to the plastic strain=0.05%, which varies with T and γ˙. Figure 7 shows the variation of n with T and γ˙.The other parameters in the DSC model were found to be not affected significantly by T and γ˙. Their constant values were adopted, e.g., β≈0 and ν≈0.40.The parameters p in Figs. 1 to 7, can be expressed as function of T and γ˙, as (3)pT,γ˙=fT,γ˙Also, the specific values of parameters for given T and γ˙ can be used for validation of stress-strain data. In finite element computations, the values of the parameters are adopted based on computed temperatures and strain rates by using interpolation according to the foregoing variations. The DSC model was introduced in the nonlinear finite element code DSC-SST2D 7. It was used to predict typical stress-strain data and for a boundary value problem involving a thin small outline package (TSOP). The solder joint, Fig. 3 (Part 1), was idealized (plane stress) as one six-noded isoparametric finite element, Fig. 8(a), subjected to the displacement at the top nodes according to the applied values in a test. Figure 8(b) to d shows typical comparison for strain rate, γ˙=2.78×10−21/s and T=−20°C;γ˙=2.78×10−31/s and T=25°C, and γ˙=2.78×10−61/s and T=125°C, respectively. The results also show the predictions for the RI response using plasticity (HISS) model without disturbance. The observed predictions (FEM-observed) include effect of microcracking and resulting softening and disturbance. It can be seen that the DSC model (FEM-observed) predictions compare very well with the observed test data. Figure 9 shows the finite element (plane stress idealization) mesh for one lead in the TSOP package, 40 leads, 0.5 mm pitch attached to a multifunctional board by 60/40 Sn/Pb solder. This analysis is performed to validate the DSC model. Barker et al. 8, has reported laboratory tests on the TSOP package. The thermal loading involved 800 cycles with temperature variation from 273 K to 398 K during each cycle (N). The material properties for 60/40 Sn/Pb solder were adopted based on previous data from Desai et al. 1. Other materials were assumed to be linearly elastic. Figure 10 shows the computed growth of disturbance, D, after typical N=100, 250, 400 and 600 cycles. The darkest zone has experience the critical disturbance of over 0.85 1; it can be seen that such zones grow from the heel to the toe.Figure 11 shows the growth of the disturbance with number of cycles for 23 elements along A-B in Fig. 9. About 16 elements have reached the critical disturbance Dc=0.85 after about 400 cycles. After 500 cycles, about 18 elements and after 600 cycles about 20 elements have reached Dc=0.85. Hence, joint failure can be considered to occur after 500 cycles. These results compare well with those reported by Barker et al. 8, Fig. 10b.From the above comparisons and those presented for other measurements 9, the DSC model can provide highly satisfactory prediction of the thermomechanical and failure responses of electronic packaging systems. The new testing device provides comprehensive test data for the influence of strain rate and temperature for thermomechanical response of joining (solder) material. The DSC model can provide a unified approach toward modeling the behavior including elastic, plastic and creep strains, and microcracking leading to fracture, softening and failure. The test data is used to calibrate for the DSC parameters. Then the model is validated with respect to stress-strain tests and a typical boundary value problem. The new test device can provide an improved means for testing of materials and joint in electronic packaging. The DSC modelcan provide a general and unified framework for modeling the thermo-mechanical behavior of materials, including solders in electronic packaging.The research results presented were supported by the Grant No. 9812696, Material Processing and Manufacturing Division of the National Science Foundation, Washington, DC. The project involved industrial collaboration with Boeing Electronics (Dr. M. Rassaian), Raytheon (Mr. W. Zwick), Sandia (Drs. D. Frear and P. Vianco), AT&T (Dr. E. Suhir), and participation of co-investigator (Dr. J.L. Prince), at The University of Arizona. The assistance of various persons, e.g., Dr. T. Dishongh, Mr. E. Singer, Mr. Alan Townsend and other technicians, and Mr. M. Dube towards the development of the TM-DIC device is acknowledged.