Dimensional quantization effects in the thermodynamic of conductive filaments

We consider the physical effects of dimensional quantization in conductive filaments that underlie operations of some modern electronic devices. We show that, as a result of quantization, a sufficiently constricted filament acquires a positive charge. Several applications of this finding include describing the local host material polarization, the stability limit of filament constrictions, equilibrium filament radius, effects of polarity in device switching, and quantization of conductance.