Study On The Mechanism Of Electromigration Induced Damage Evolution And Failure In The Microelectronic Packaging Interconnect Structures

Electromigration is the transport of material by the gradual movement of ions in the conductor due to the momentum transfer between conduction electrons and diffusing metal atoms under high current density.Electromigration mainly occurs in the interconnects of microelectronic packaging under high current density.As atoms are diffusing,voids will nucleate at the cathode side and cause failure until it collapses to crack.The trend of miniaturization and integration of the microelectronic devices leads to a significant increase of working current density which brings the electromigration damage.Consequently,electromigration has become a serious reliability issue for the next-generation microelectronic packaging technology.In this thesis,several mechanics models are developed to describe the electromigration-induced damage evolution and failure,which will help to the microelectronic packaging reliability study under high current density.Firstly,Electromigration-induced pancake shape void propagation is studied and a two-order nonlinear ordinary differential equation is obtained which is governed by the surface diffusion process.The finger shape void propagation velocity is obtained and the relationship between the velocity and the void width is established.It shows that the void velocity is very sensitive to the void width with an inverse proportional relationship.The theoretical result is compared with th experiment which shows good coincide.Furthermore,the electromigration induced void shape evolution is further studied based on mass diffusion theory.The analysis is conducted to three typical experimentally observed void shapes:circular,ellipse and cardioid.The electric current distribution along the void surface in the infinite domain is solved using conformal mapping method and Cauchy integral.The void evolution normal velocity is obtained based on mass conversation and the void shape evolution trend is obtained.The mechanisms of the void migration,void collapse to crack and void concavity are clarified.It shows that the circular void will migrate in the conducter when its radius is small.When the void radius grows to a critical value,the void will collapse to fingershape or concave shape.In particular,the analysis to the single void is extended to the multi voids shape evolution.The electric current field containing two circular voids on the plate is solved analytically and the electromigration induced multi voids shape evolution is clarified.It shows when multi-voids are taken into account,due to the asymmetry of the current distribution around the voids surface,the steady shape of the initial circular void will be broken and bifurcation could occur.Two intrinsic models are established to predict how the void collapses to crack,coalesces with each other or splits into smaller voids.In addition,a statistic model is proposed to predict the stochastic characteristic of the cotton type voids growth under high current density and an analytical solution of the cotton type voids volume growth over time is obtained which could match the experiment result well.Even more important,a physically based model to predict the mean time to electromigration induced failure?MTTF?is developed,the traditional Black's equation is improved with clear physical meaning.The electromigration induced voids initiation,growth and joule heating effect are all taken into account.Base on diffusion-stress model,the voids initiation issue is solved.On the other hand,by considering the grainboudnary diffuision,the voids growth over time is obtain.What's more,a coupled thermal-electric FEM model is developed which could well describe the temperature corwding effect in the solder joints.The variation regulation of electric current exponent,typically with j^-n form which is the key parameter in the MTTF prediction is clarified.At last,the computational mechanics is studied to further solve the multi-physics coupled issues.A new error control finite element formulation is developed and implemented based on the variational multiscale method,the inclusion theory and the Zienkiewicz-Zhu error estimator.The Eshelby tensor for an arbitrary polygon inclusion in the finite domaini is used in the fine scale feedback procedure to take into account the interactions among different scales and elements.The upgraded multiscale method is compared with the traditional FEM and the traditional multiscale method proposed by Li et al.It shows that the proposed method is with higher accuracy no matter using triangle element or quadrilateral element in a self-adaptive and a self-adjusting manner.What's more,the developed numerical method is less sensitive to the element shape as the polygon incluisoin Eshebly tensor in the finite domain is used.