The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

摘要

The first order unified linear instability analysis (ULISA) of the governing equation for evolutions of surfaces and interfaces under the capillary, electromigration, and elastostatic forces including the thermomigration (Soret effect) is developed very recently by the author. In the present application of the theory, the concurrent effects of uniaxial applied stresses and the electrostatic field on the sidewall morphological evolution of a single crystal thin metallic film are explored by dynamic computer simulations by taking the surface drift diffusion anisotropy fully into account. These computer experiments, which are supported by ULISA, clearly show that only the applied elastic compressive stresses are primary agents responsible for the morphological instability of the surface undulations through the elastic dipole tensor interactions but not the uniaxial tension loading in thin solid films. It is also demonstrated that these morphological instabilities manifested themselves as formations of the surface cracks and thus one may fully control the roughness. To do that, one needs to select crystal orientations properly with respect to the applied field so that a counteraction of the applied electrostatic fields (healing effect) is created above well defined threshold levels of electromigration. On the contrary to the healing effects, the improper selection of crystal orientations may drastically enhance the instability and eventually may cause catastrophic interconnect failure. At large normalized surface undulation amplitudes (a ≥ 0.20), the drastic reductions in the decay rate constants (i.e., the strain relaxation rate) are detected in the nonlinear uniaxial tension regime compared to the ULISA theory regardless of the intensity of the normalized stress by analyzing the data obtained from the computer simulations. This situation is contrary to the results deduced from the low to moderate normalized amplitude (a≤0.10) measurements, where one finds that the decay rate constant closely obeys the prediction of the ULISA theory even for very high stress intensities.