Manchester Applied Mathematics and Numerical Analysis Seminars Winter 1998

October 14, 1998, 4.00 pm

Lecture Theatre D13 Material Science

How can continuum theory help to improve the reliability of microelectronics structures and materials?

Dr. Wolfgang Müller, Mech. & Chem. Engineering, Herriot-Watt

After a short introduction to microelectronics structures and materials and the reliability problems encountered therein, a model will be presented in the first half of this talk, which is capable to simulate the coarsening process observed during thermo-mechanical treatment of binary tin-lead solders. Fourier transforms and spectral theory are used for the numerical treatment of the thermo-elastic as well as of the diffusion problem encountered during phase separation in these alloys. More specifically, the analysis will be based exclusively on continuum theory and, in a first step, relies on the numerical computation of the local stresses and strains in a representative volume element. Second, this information is used in an extended diffusion equation to predict the local concentrations of the constituents of the solder. Besides the classical driving forces for phase separation, as introduced by Fick and Cahn-Hilliard, this equation contains an additional term which links the mechanical to the thermodynamical problem. It connects internal and external stresses, strains, temperature, as well as concentrations and allows for a comprehensive study of the coarsening and aging process. The second half of the talk is dedicated to non-linear finite element analyses which are used to study the thermo-mechanical behavior of complete micro-electronics structures. In here the emphasis is on life-time-prediction of solder balls through calculation of accumulated creep energy densities during thermal cycling as well as the determination of crack growth driving forces along bimaterial interfaces in such structures which will be basedx on J-Integral theory.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).