  We predict the probability of field induced nucleation (FIN) of conductive
filaments across the nano-thin dielectric layers in memory and switching
devices. The novelty of our analysis is that it deals with a dielectric layer
of thickness below the critical nucleation length. We show how the latter
constraint can make FIN a truly threshold phenomenon possible only for voltage
(not the field) exceeding a certain critical value that does not depend on the
dielectric thickness. Our analysis predicts the possibility of threshold
switching without memory under certain thickness dependent voltages. In
parallel, the thermal runaway mechanism of electronic switching is described
analytically leading to results consistent with the earlier published numerical
modeling. Our predictions offer the possibility of experimental verifications
deciding between FIN and thermal runaway switching.

Mesoscale and Nanoscale Physics