edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 3 30 motion. Figure 3 shows the temperature time history used in the analysis, thus taking the loading situation effectively one thermal cycle of the temperature range from 25-500°C. The material properties used in this model are shown in Table 2. Two material model cases were used to describe the material behavior of the structure: One is 96% Al2O3 modeled as linear, elastic, isotropic, and assumed the Young’s modulus (E) and thermal expansion coefficient (CTE) are constant during thermal loading, and the other is gold modeled as nonlinear, elastic-plastic, isotropic, and temperature dependent. To obtain accurate simulation, temperature-dependent material properties for gold wire are obtained from the stress-strain curves from Lemaire et al.[8] T is the absolute Kelvin temperature. The distribution of the shear and normal plastic strains of wire bonds at a temperature of 500°C are shown in Fig. 4a and b, respectively. It is observed that the normal plastic strain occurred at the wire bonds and the extreme plastic shear strain values are located at the corners of the bond pad. This can clearly be seen in Fig. 5, which shows the distributions from left to right in the bond pad. Finite-element analysis results indicate that the failure would start from the corner at the interface between wire/bond-pad and bond-pad/substrate. The normal and shear plastic strain at the interface might be significantly reduced by shrinking the pad size. STRUCTURAL RELIABILITY METHOD To evaluate the reliability of wire bonds with the method presented below, it is necessary to characterize the constitutive behavior laws of different materials with the uncertainties on the different coefficients, and to define the failure function depending on the failure mode. All relevant uncertainties influencing the probability of failure are then introduced in the vector X of basic random variables. The statistical parameters and probability distribution of these variables are listed in Table 3. The limit state function, regarding the thermomechanical failure of the wire bonds, is written by considering the system fails when the maximum equivalent von Mises stress reaches a yield stress value: G(X) = Syield — Svmis (Eq 2) Syield and Svmis are respectively the yield stress and the equivalent maximum von Mises stress. This stress can either be implicit (e.g., the outcome of a numerical FEM code), or explicit (e.g., an approximate equation obtained using the response surface method). The failure probability is then calculated by: (Eq 3) where Pf is the failure probability, fx(x) is the joint den- sity function of the random variables X and Pr is the Fig. 4 Plastic strain distribution in wire bond at temperature 500°C; (a) normal strain; (b) shear strain. Fig. 3 Thermal time history. (a) Table 2 Material properties for the adherent layers Substrate Elastic modulus, GPa Poisson’s ratio CTE, ppm/°C Density, gm/cm3 Al2O3 300 0.21 7.1 3.9 Gold wires 97 (1-T/2032) 0.42 14.2 19.32 (b)
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