Research Of Electromigration Simulation Algorithm With Considering Multiple Migration Mechanisms And Sensitivity Analysis

With the successful application in micro-electronic packages of Flip-chip wafer-level technology, the electromigration (EM) reliability of solder bump interconnects became the urgent focus. The EM of solder bump involved in multi-physics problem, due to lacking of the effective simulation methods, it is still difficult to make the failure mechanism of EM and EM voids evolution clear by only relying on experimental analysis.With consideration of the limitations of conventional atomic flux divergence (AFD) method, a new EM algorithm for void formation and growth of the chip interconnect structure is presented in this paper. The impacts of size and shape of the interconnection structure, EM parameters and material parameters on EM are also researched.First of all, according to the basic EM theory, the influencing factors of EM are summarized, and the existed problems of the conventional AFD method are discussed. With general considering a variety of EM driving mechanisms (electron wind force (EWF), stress gradient induced driving force (SGIDF), temperature gradient induced driving force (TGIDF) and atomic density gradient induced driving force (ADGIDF)), the atomic density redistribution Equation is derived from the Galerkin method, and the corresponding effective numerical algorithm is further studied. Comparison of the results from the atomic density redistribution algorithm with analytical solutions shows the algorithm in this paper is reliable and stable.Secondly, a new 3D numerical simulation method for electromigration induced void incubation and growth in metal interconnects and the solder bump is presented, based on the commercial software ANSYS Multi-physics and self-developed FORTRAN codes. Comparison between our numerical simulation results and the measured results obtained by previous studies has shown very good agreement. Results show that the atomic density will be retarded by considering the atomic density gradient item in the time-dependent EM evolution equation. It is also found that EM depends on the atomic density gradient and the stress gradient of the structure greatly. And at a lower temperature, the temperature gradient item in the time-dependent EM evolution equation can almost be negligible. The Time to Failure (TTF) of the lead-free solder bump is nearly 1.5～2 times of the lead solder bump.Furthermore, a full factorial design of experiment was employed on the CSP structure to study the effect of back end design rules on current crowding which was demonstrated by using 3D modeling based on FEA. It's shown that: the UBM geometry has a significant impact on the solder bump void growth and TTF. The 75°UBM rim angle arrives the longest the solder bump TTF, the 0°UBM and the 90°UBM rim angle is the poor structure to endure the electromigration failure; the thicker of UBM, the longer of the EM life for it; With the diameter of UBM increase, the longer of the EM life; Longer pitch of the CSP, shorter EM life for it; As the height of the ball increase, the EM life decrease; As the trace width increase, the EM life also increase; the cylinder gets the longest TTF life following by the cube and the single ball. Therefore, the cylinder bump is the best structure of Anti-EM.Finally, EM sensitivity analysis is implemented on CSP structure. The EM sensitivity analysis equation and the corresponding numerical algorithm is proposed. The involved EM sensitivity design variables can be the activation energy and the initial self-diffusion coefficient and mechanical properties of the material parameters (elastic modulus, Poisson's ratio, etc.). The results show that the EM of solder bump is very sensitive to the activation energy, followed by the initial self-diffusion coefficient. The mechanical properties of materials parameters have the minimum impact on EM.