The Constitutive Model Of Tin Whisker Growth Driven By Stress And Its Numerical Simulation

Along with the development of the electronic information industry, electronic products developed rapidly in the commercial, industrial, military and other related fields. With the trend of miniaturization of the electronic products, the spacing between the components and the components are smaller and smaller. Due to the harm of lead to the human body and the enviroment, many countries have formulated relevant laws banned/limited lead in electronic industry. Therefore, the use of lead-free solder mandatory promotion, will introduce the reliability problems due to tin whisker growth. When the leadframes are used to connect the chip and the package board, a lead free solder is required to be plated on its surface, so that to improve the wettability in welding. At room temperature condition, the tin whisker can be observed in hundreds of micron, and their length is enough to make the adjacent leadframes short. Therefore, it is meaningful to prevent/inhibit the growth of tin whiskers effectively and to improve the reliability of electronic products by researching the tin whisker growth mechanism and describing the effects of various factors on tin whisker growth quantitatively. For stress generation and stress relaxation due to tin whisker growth, some mathematical models are established to study the tin whisker growth behavior in the thesis.The formation of intermetallic compound gives rise to the internal stress in the tin layer. This is characterized with the expansion of inclusion in a plate. Firstly, we determine the eigenstrain of the inclusion. And then the image method is used to obtain the series solution of the stress field in the tin layer. Finally, using the Mises yield criterion, the critical condition of the formation of tin whisker is given by the Mises stress distribution characteristics. The nuclear point of tin whisker is determined and the influence of various parameters is studied.Considering the protective effect of the tin oxide film and the relative thickness between the copper substrate and tin layer, the geometric relation among the oxide film, tin layer and copper substrate is characterized as a finite thickness plate bonded between two infinite elastic bodies. And the formation of intermetallic compounds is considered as the expansion of a spherical inclusion. According to the stress equilibrium and its boundary conditions, the Galerkin vector of center dilatation is given. Applying the Galerkin vector, the stress field in the tin layer is determited. A tin whisker growth model is established based on the grain boundary diffusion mechanism. Using the stress field, the tin whisker growth rate is calculated. And the effects of geometrical parameters on tin whisker growth rate are discussed.Considering the creep phenomenon caused by the atomic diffusion and the local volume expansion due to the formation of the intermetallic compounds, an elasto-plastic creep constitutive model is given to describe the behavior of stress relaxation. Base on ABAQUS, a UMAT subroutine to solve the elasto-plastic creep model is developed by means of the return-mapping algorithm. The model is verified in element level by the finite element simulation, and the results are compared to that calculated by the elastic plastic model in ABAQUS. The results show that the elasto-plastic creep model can well discribe the behavior of stress relaxation. In addition, finite element model is established, and the stress evolution is calculated by the UMAT subroutine. The tin whikser growth rate is estimated, and the effect of grain size on the stress and tin whisker growth rate is discussed.A new variable – vacancy concentration is introduced to describe the atomic diffusion. From the thermodynamics, the potential of the atomic diffusion under stress is given, and the diffusion constitutive equation is obtained. The behavior of stress relaxation due to the atomic diffusion is described by introducing the concentration to the stress constitutive equation. According to the stress equilibrium equations, geometric equations, constitutive equation, diffusion equation, initial condition and boundary conditions, the equivalent integral weak forms of the differential equation are established, and the variational principle is used to derive the finite element equations. Using the developed finite element program, the displacement field and the concentration field are solved numerically, and the tin whisker length is calculated by the vacancy concentration calculation. The effects of various parameters on tin whisker growth rate are studied.