Thermal assistance has been shown to significantly reduce the required operation power for spin torque transfer magnetic random access memory (STT-MRAM). Proposed heating methods include modified material stack compositions that result in increased self-heating or external heat sources. In this work we analyze the self-heating process of a standard perpendicular magnetic anisotropy STT-MRAM device through numerical simulations in order to understand the relative contributions of Joule, thermoelectric Peltier and Thomson, and tunneling junction heating. A 2D rotationally symmetric numerical model is used to solve the coupled electro-thermal equations including thermoelectric effects and heat absorbed or released at the tunneling junction. We compare self-heating for different common passivation materials, positive and negative electrical current polarity, and different device thermal anchoring and boundaries resistance configurations. The variations considered are found to result in significant differences in maximum temperatures reached. Average increases of 3 K, 10 K, and 100 K for different passivation materials, positive and negative polarity, and different thermal anchoring configurations, respectively, are observed. The highest temperatures, up to 424 K, are obtained for silicon dioxide as the passivation material, positive polarity, and low thermal anchoring with thermal boundary resistance configurations. Interestingly it is also found that due to the tunneling heat, Peltier effect, device geometry, and numerous interfacial layers around the magnetic tunnel junction (MTJ), most of the heat is dissipated on the lower potential side of the magnetic junction. This asymmetry in heating, which has also been observed experimentally, is important as thermally assisted switching requires heating of the free layer specifically and this will be significantly different for the two polarity operations, set and reset.
Mathematical Modelling of the Self-Heating Process in Compost Piles
