DIFFUSIVE VOID BIFURCATION IN STRESSED SOLID

Interconnects are susceptible to solid diffusion under residual stress, electric current, and elevated temperature. As atoms diffuse, voids nucleate, drift, and enlarge. At some point, the voids of rounded shape can collapse to narrow slits and sever the interconnects. The fatal slits are often found to be transgranular, i.e., each slit cuts across a single grain. They have raised many concerns, but the underlying mechanism has remained unclear. It is proposed that a void changes shape due to surface diffusion under the combined action of surface energy, elastic energy, and electric current. The void will be rounded if surface energy prevails, but will collapse to a slit if the elastic energy or the electric current prevails. A cylindrical void in an infinite crystal under biaxial stresses, but under no electric current, is analyzed. Four things are done, as follows: (1) A suitable thermodynamic potential is minimized and maximized to select, among a family of ellipses, equilibrium void shapes. The bifurcation diagram consists of a subcritical pitchfork and two Griffith cracks. (2) A void under biased stresses is analyzed to illustrate the effect of imperfections. (3) Exact initial bifurcation modes are determined. The critical loads for the successive modes are closely separated, indicating that the shape evolution will be sensitive to initial imperfections. (4) A variational principle for shape evolution under stress, current and surface energy is identified. Stress-induced evolution time is estimated by using this variational principle.