We present a theory of second phase conductive filaments in phase transformable systems; applications include threshold switches, phase change memory, and shunting in thin film structures. We show that the average filament parameters can be described thermodynamically. In agreement with the published data, the predicted filament current voltage characteristics exhibit negative differential resistance vanishing at high currents where the current density becomes a bulk material property. Our description is extendible to filament transients and allows for efficient numerical simulation.
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