# Heat transfer and SET voltage in filamentary RRAM devices

## TL;DR

This paper investigates heat transfer mechanisms in filamentary RRAM devices using COMSOL simulations and analytical models, revealing improved approximations and proposing a universal expression for SET voltage related to material properties.

## Contribution

The study introduces refined analytical models for heat transfer in filamentary RRAM, compares them with detailed simulations, and proposes a universal SET voltage expression based on Lorenz number considerations.

## Key findings

- Parallel heat transfer mechanisms improve temperature estimation.
- Electrode proximity significantly affects heat transport modeling.
- Low Lorenz number materials may enable lower SET voltages.

## Abstract

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.