Keywords: IGBT, power module, reliability, FORM, bump, Sn-Ag solder.

The weak point for the standard power insulated gate bipolar transistor (IGBT) modules in term of reliability is the thermal fatigue in solder joints as a result of the thermal stress induced by constitutive materials with different coefficients of thermal expansion. The main approches to evaluate predictive fatigue life are based on the constitutive equations of alloys describing their behavior and relationships between inelastic strain dissipation during thermal cycling and the number of cycles before failure. The fatigue life of solder joints strongly depends on geometric shape, solder behavior and applied load. The aims of this paper is to estimate the probability of the failure of the power module with the structural reliability methods. Thus the materials variables are considered as random variables and the failure mode is modelled with the limit state function. The sensitivities of the mean and the standard deviation for each random variable has been evaluated.

The probabilistic structural approach consist in methods to determine the probability of failure of a given system. Probabilistic analysis is then an extension of the deterministic analysis where the input parameters are not considered as fixed value in a mechanical model but as random variables [1]. All relevant uncertainties influencing the probability of failure are then introduced in the vector of basic random variables. In addition, the failure of the system is modeled by a functional relation called limit state function and defined to take a null or negative value in the failure domain. It's then possible to define the probability of failure for the system as:

Approximation methods can be established to compute the multi-dimensional integrate in Equation (4) by substituting the limit state function by a linear or second order hyperplane in the standardized Gaussian space called respectively first order and second order reliability methods (FORM and SORM) [2,3]. Gradient and step size with Armijo rules are computed with a parallelized algorithm to solve the under constrained optimization problem with the iHLRF algorithm [4].

The package modeled in this study is a new power module where the IGBT connections are derived from the flip-chip technologies. To evaluate the reliability of this package with the method listed above, it is necessary to caracterize the constitutive behavior laws. This constitutive model is the mathematical representation of the materials response to one or several variables. The law called power law, Equation (5), can describe the mechanical behaviour of the alloy in low or medium stress [5]:

The model proposed to evaluate the predictive fatigue life of the solder joints is based on the creep strain model of Kanchanomai [6]:

where is the equivalent creep strain during one cycle. We assume that the power module fall in the failure domain when the output predicted fatigue life of the mechanical model does not exceed a given number of cycles. This present study is focused on material behavior considering the Young modulus and behavior law coefficients. Indeed, the resolution of non-linear mechanical problem with a finite element solver by integration of the constitutive solder law. The non-linear mechanical reliability is difficult to obtain due to the finite element integration approximation and the error with respect to the gradient evaluation. A good choice for step of the DDM method must be made and an error control is implemented to make the step size more appropriate. The reliability analysis shows the importance of the value of the power law coefficient and the variability of the Sn-Ag CTE. It is shown that the material behavior is not sufficiently understood and another study must be made to consider the geometric uncertainties such as volume of solder and distance between silicium chip and copper insert.

1

M. Lemaire, "Fiabilité des structures" Hermes, Collection Génie civil, 2005.

2

A.M. Hasofer, N.C. Lind., "Exact and invariant second-moment code format." J. Eng. Mech., 100(1), pp 111-21, 1974.

3

R.Rackwitz, B. Fiessler, "Structural reliability under combined load sequences." Comput. Struct., 9, pp 489-94, 1978. doi:10.1016/0045-7949(78)90046-9

4

P-L Liu, A. Der Kuireghian, "Optimization algorithms for structural reliability", Struct Safety;9(3):pp 489-94, 1991. doi:10.1016/0167-4730(91)90041-7

5

S.Wiese, F. Feustel, E. Meusel, "Characterisation of constitutive behaviour of SnAg, SnAgCu and SnPb solder in flip chip joints", Sensors and Actuators, pp 188-193, 2002. doi:10.1016/S0924-4247(01)00880-9

6

C. Kanchanomai, S. Yamamota, Y. Miyahita, Y. Mutoy, A. J. McEvily, "Low cycle Fatigue Test for Solders Using Non-contact Digital Image Measurement System", International Journal of Fatigue, 24, 2002. doi:10.1016/S0142-1123(01)00052-4

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