A new method for estimating the conductive filament temperature in OxRAM devices based on escape rate theory

Because of the atomic nature of the system under study, an estimation of the temperature of the conductive filament (CF) in OxRAM devices as a function of the applied bias can only be obtained by means of indirect methods, usually electrothermal simulations. In this paper, a heuristic approach that combines time-dependent dielectric breakdown (TDDB) statistics for the electroformed device with field and temperature-assisted ionic transport within the framework of escape rate theory is presented. Extended expressions for the time-to-failure acceleration law (E-model) and for the Kramers' rate compatible both with the standard models at moderate/high biases and with the principle of detailed balance at equilibrium are proposed. An approximate expression for the CF temperature is reported. For the investigated stress voltage range (0.30 V-0.65 V), the estimated CF temperature at the SET condition is found to be in the range 350 K-600 K.