S-shaped negative differential resistance modeling in electro-thermal simulation of phase-change memory programming

Electro-thermal modeling has been commonly employed to model the RESET (crystalline-to-amorphous) transition in phase-change memory devices. However, to fully model the SET (amorphous-to-crystalline) transition, it is required to comprehend the S-shaped negative differential resistance (NDR) that precedes the phase transition, as input current is ramped up. Carrier dynamics on nanosecond time scales have been invoked to model the "snapback" phenomenon. To build S-shaped NDR models within commercial electrothermal simulation packages, we consider various resistivity models which may be calibrated to provide a good flt with experimental data. We find that regardless of the model, it is necessary to include a constant offset in the resistivity formula, in order to consistently obtain the observed ON state portion of the l-V curve.