This study presents an integrated approach for the simulation of hygro-thermo-vapor-deformation analysis of electronic packages by using peridynamics. This theory is suitable for such analysis because of its mathematical structure. Its governing equation is an integro-differential equation and it is valid regardless of the existence of material and geometric discontinuities in the structure. It permits the specification of distinct properties of interfaces between dissimilar materials in the direct modeling of thermal and moisture diffusion, and deformation. Therefore, it enables progressive damage analysis in materials or layered material systems such as the electronic packages. It describes the validation procedure by considering a particular package for each thermomechanical, hygromechanical deformation as well as vapor pressure predictions. Also, it presents results concerning failure sites and mechanisms due to hygro-thermovapor-deformation. Introduction During packaging, transportation and storage, IC packages may absorb moisture leading to differential swelling between the polymeric and nonpolymeric materials, and among the polymeric materials. This differential swelling exacerbates the thermal deformation during the solder reflow process. In order to minimize the mismatch in swelling of the dissimilar materials of the IC packages during the solder reflow process, the packages are subjected to moisture conditioning (baking) for a period of time prior to this process. The estimate of baking period necessary to minimize the differential swelling and prevent possible cracking during the solder reflow process was investigated by Tay and Lin [1]. Although the baking process is essential in reducing the thermo-mechanical deformation during the solder reflow, it influences the moisture concentration distribution, and induces significant hygro-mechanical deformation. Also, the distribution of moisture concentration dictates the vapor pressure in micro voids while reducing the interfacial adhesion strength. The decrease in adhesion strength is caused by moisture absorption. Furthermore, the package cracking is not controlled by the absolute moisture content but its concentration at the critical interface, Kitano et al. [2]. An extensive discussion of moisture induced failure mechanisms in IC packages can be found in a study by Tee and Ng [3]. Coupled with the vapor pressure in micro voids, hygromechanical and thermo-mechanical deformation may cause interfacial delamination, and subsequent cracking at the padencapsulant interface, die-attach layer, and the die-encapsulant interface. Delamination and/or cracking at the die-attach layer is one of the primary failure mechanisms in plastic IC packages and often lowers the threshold for other mechanical, and electrical failures, Suhir [4] and Wong et al. [5]. The vapor pressure, dictated by the moisture concentration after baking, saturates much faster than the moisture diffusion, and that a near uniform vapor pressure is reached in the package, Tee and Ng [3]. The vapor pressure introduces an additional strain of the same order as that of the hygromechanical strains to the package. The hygro-mechanical stresses induced through moisture conditioning (baking) are significant compared to the thermo-mechanical stresses induced during the solder flow. Combination of these stresses can be detrimental to the reliability of the IC packages. Therefore, the determination of the moisture concentration and temperature distributions is essential in order to determine the vapor pressure in micro voids, hygro-mechanical and thermo-mechanical stresses. There exists no known technique for the measurement of moisture distribution inside the package. Therefore, the predictive methods become unavoidable for investigating the effect of moisture conditioning. Traditionally, moisture diffusion analysis is performed by using thermal-moisture analogy. Since the moisture concentration is not continuous along interfaces, a new parameter called “wetness” is introduced to render it continuous. Wetness is the ratio of the moisture concentration to its value at the saturated state, and it is continuous along interfaces. Although this approach is commonly accepted, it is not always valid because the saturated moisture concentration is not constant during the reflow process. A direct concentration approach (DCA) (Fan et al. [6]) should be employed to address this issue by imposing continuity condition along the interface between dissimilar materials. A new continuum mechanics theory referred to as peridynamics (Silling [7]), removes this requirement because it is not necessary to impose continuity conditions. This feature of peridynamics emerges because the governing equations are based on integro-differential equations rather than partial differential equations of classical theory. Furthermore, peridynamics is also very suitable for failure prediction which allows cracks to initiate and grow naturally in the structure without resorting to any external crack growth law. This study presents an integrated hygro-thermo-vapordeformation analysis using peridynamics to predict failure in electronic packages. Peridynamic (PD) Theory The peridynamic theory is a nonlocal continuum theory, and its continuum mechanics formulation was introduced by Silling [7] to overcome the difficulties arising due to the existence of discontinuities in the structure. The theory depends on integration rather than the spatial differentiation of PDEs as in classical continuum mechanics. Hence, it can be easily applicable to problems with discontinuities. As opposed to classical continuum mechanics, a material point inside the body can interact with other material points within its domain of influence called horizon, as shown in Fig. 1. The interaction (bond) between two material points x and x are expressed by using a response function, f . Although PD formulation is originally given for mechanical field, it is applicable in other fields as well. The detailed derivation and capability of PD theory is given in the book by Madenci and Oterkus [8]. Fig. 1. Interaction of a material point with its neighboring points. Basics According to the PD theory, the field is analyzed by considering the interaction of a PD material point, x , with the other, possibly infinitely many, material points in the body. Therefore, an infinite number of interactions may exist between the material point at location x and other material points. Hence, the PD state may contain particular information on an infinite number of interactions. However, the influence of the material points interacting with x is assumed to vanish beyond a local region (horizon), denoted by shown in Fig. 1. The range of material point, x is defined by referred to as the “horizon”. Also, the material points within a distance of x is called the family of x , . The interaction of material points is prescribed through the response function which contains all of the constitutive information associated with the material. The response function also includes a length parameter (horizon), . The locality of interactions depends on the horizon, and the interactions become more local with a decreasing horizon. Hygrothermomechanics with vapor pressure For known temperature and moisture concentration, the equation of motion of a material point can be expressed as , , , t dV t x x u x f u u x x b x (1) where the response function is defined as , avg avg c s T C p x u x u f u u x x x u x u (2) in which c is the bond constant and can be expressed in terms Young’s modulus, E 3 9 E c h for 2D, 4 12E c for 3D (3) with h denoting the thickness. The parameter s represents the stretch between material points and given by s x u x u x x x x (4) where u and u are the displacements of material points, x and x . Thermal related parameter is the coefficient of thermal expansion and avg T is defined as
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