ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Advancement of a fine slit along a planar grain boundary in an electric field E0, applied parallel to the slit, is investigated by considering electromigration along both the grain boundary and the slit surface. Electrically induced flux in the grain boundary Igb (+ toward the slit tip) and both electrically and curvature-induced fluxes on the slit surfaces are considered assuming 2Is〉Igb, where Is is the flux (+ away from the slit tip) on each of the parallel slit surfaces far removed from the tip. Steady-state solutions of the transport equations are classified according to the value of a parameter β=tan−1 (2Is/Igb) which, under reasonable assumptions, depends on material parameters only. For 5π/4≥β≥β2, unique steady-state solutions exist; for β2〉β〉β1, multiple steady-state solutions occur; below β1≥π/4, no steady-state solution is possible. Since β1〈π/2, Igb〉0 (flux exiting the grain boundary into the slit) for all cases in which no steady-state solution is possible. In the case of multiple solutions, those corresponding to smallest width (and hence largest velocity) are determined. For all steady-state solutions, slit width and tip velocity scale as E−1/20 and E3/20, respectively. Results also apply to the propagation of a slit within a grain or along a passivation layer. Generally, tip velocities can approach 1 nm/s (3.6 μm/h), thereby representing a likely failure mechanism in fine-line (near bamboo structure) interconnects. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.363792
