In service, an interconnect line carries an intense electric current. The conduction electrons impact metal atoms, and motivate the atoms to diffuse in the direction of electron flow. The process, known as electromigration, has been the most menacing and persistent threat to interconnect reliability.
Early aluminum lines had the width much larger than the thickness. They behaved like blanket films. When narrow aluminum lines were introduced, in early 1980s, with the width comparable to the thickness, voids were observed in such narrow interconnects on wafers held in ovens, or even on wafers left on shelves at room temperature. The voids may sever the interconnects.
A polycrystal, held at temperature for some time t, the average grain diameter grows. A grain grows at the expense of its neighbors: small grains disappear and big ones get bigger. Total number of atoms is conserved.
Hull and Rimmer (1959) studied grain boundary cavitation. Small voids were observed at grain boundaries, particularly those transverse to the applied tensile stress. Fracture results from the growth and coalescence of these voids.
I am a freshman in micromechanics area. Many books and papers always say the linear elastic equilibrium equation(Someone also called Navier type function) could be solved with Green Function and Fourier Transformation, but without details. May be the writers think anyone should know these two popular methods in solving the PDE. I have search many books(both mathmatic and mechanics), However, there are little information about solving the navier type function with those two methods.
Rayleigh (1878) examined a common experience: a thin jet of liquid is unstable and breaks into droplets. When a jet is thin enough, the effect of gravity is negligible compared to surface energy. The jet changes its shape to reduce the total surface energy. Liquid flow sets the time.
A polished polycrystal has a flat surface. At room temperature, the surface remains flat for a long time. At an elevated temperature atoms move. The surface grows grooves along triple junctions, where the surface meet grain boundaries. The grooves reveal the grain boundaries in the microscope. Atoms may move in many ways. They may diffuse in the lattice, diffuse on the surface, or evaporate into the vapor phase. Here we will only consider surface diffusion. Atoms diffuse on the surface away from the triple junction, making a dent along the junction, and piling two bumps nearby.
Some phenomena due to surface diffusion:
Diffusion and creep involve the same atomic process: atoms must change neighbors, aided by thermal energy. We explore their relation in this lecture.
I have taught this course four times before, but have never devoted lectures on basic thermodynamics. It is a subject I’m not good at, but I have used it often in research, in a loose way. One can ride a bicycle without knowing Newton’s laws, even though bicycle-riding is governed by Newton’s law. If thermodynamics gives me so much trouble, perhaps it also gives my students a lot of trouble. I have taken lectures from many teachers on the subject. None have really made me feel comfortable with it. Now I’m trying to teach you. I hope that I can help you become comfortable with the subject. Maybe you already are. Maybe you never will. I have no evidence that I can be more effective than these other teachers, but I have the enthusiasm of an amateur.
