Heat Transfer and SET Voltage in Filamentary RRAM Devices
We study the heat transport in filamentary RRAM nano-sized devices by comparing the accurate results of COMSOL modeling with simplified analytical models for two complementary mechanisms: one neglecting the radial heat transfer from the filament to the insulating host, while the other describing the radial transport through the dielectric in the absence of the filament heat transfer. For the former, we find that the earlier assumed simplification of the electrodes being ideal heat conductors is insufficient; a more adequate approximation is derived where the heat transport is determined by the adjacent proximities of the filament tips in the electrodes. We find that both complementary mechanisms overestimate the maximum temperature yet offering acceptable results. However, the two in parallel provide a better analytical approximation. In addition, we show that the Wiedemann-Franz-Lorenz law helps the analysis when the Lorenz parameter is chosen from the actual data. We present an approximate expression for the SET voltage possessing a high degree of universality and predicting that filament materials with low Lorenz numbers can be good candidates for the future low set voltage devices.