Abstract
Solid state memory and switching devices aimed at replacing the flash memory technology operate by switching from the high to low resistance when conductive filaments are created in response to the electric pulse. The filaments are identified with either structurally different protrusions or purely electronic conductive pathways. The former can appear via the field induced nucleation (FIN), while the latter do not require phase transformations and are attributed to certain types of temperature and bias dependent conductivity. The existing understanding of those processes ignores features related to extremely small linear sizes of nano-structures. Such are, for example, the device sizes smaller than critical nucleation radii, and/or the electron energy relaxation lengths exceeding the structure dimensions. This paper develops a theory of switching under nano-size conditions. We show how the structure thinness can make FIN a truly threshold phenomenon possible only for voltage (not the field) exceeding a certain critical value. We predict the possibility of threshold switching without memory for certain thickness dependent voltages. The thermal runaway mechanism of electronic switching is described analytically leading to results consistent with the published numerical modeling. Our predictions offer possible experimental verifications deciding between FIN and thermal runaway switching.