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Groove profiles are computed under isotropic conditions for the intersection of a periodic array of grain boundaries with an external surface, assuming that grain boundary flux I is directed to (I≳0) or away from (I<0) the surface. When I=0, the surface assumes an equilibrium (time-independent) profile. For I≠0, in a range bounded by upper and lower limits that depend on geometry and material parameters, a global steady-state develops in which the entire surface advances (I≳0) or recedes (I<0) from its original position at constant velocity. Beyond these limits, the surface near the groove roots becomes diffusively detached from the remaining surface. A rapidly growing ridge (I≳0) or slit (I<0) then develops along each grain boundary, whose tip ultimately translates at constant velocity in a local steady state, leaving the remaining surface behind. These velocity regimes govern the ultimate stability of polycrystalline materials subjected to large electric (electromigration) or stress (creep) fields, especially in thin films where grain size approximates film thickness.

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The effect of surface and grain-boundary diffusion on interconnect reliability is addressed by extending the theory of thermal grooving to arbitrary grain-boundary flux. For a periodic array of grain boundaries, three regimes are identified: (1) equilibrium, (2) global steady state, and (3) local steady state. These regimes govern the stability of polycrystalline materials subjected to large electric (electromigration) or mechanical (stress voiding) fields, especially in thin films where grain size approximates film thickness.