Space Charge Limited Current with Self-heating in Pr$_{0.7}$Ca$_{0.3}$MnO$_3$ based RRAM

Space Charge Limited Current (SCLC) based conduction has been identified for PCMO-based RRAM devices based on the observation that $I \propto V^{\alpha}$ where $\alpha \approx 2$. A critical feature of the IV characteristics is a sharp rise in current ($\alpha \gg 2$) which has been widely attributed to trap-filled limit (TFL) followed by an apparent trap-free SCLC conduction. In this paper, we show by TCAD analysis that trap-filled limit (TFL) is insufficient to explain the sharp current rise ($\alpha \gg 2$). As an alternative, we propose a shallow trap SCLC model with selfheating effect based thermal runaway to explain the sharp current rise followed by a series resistance dominated regime. Experimental results over a range of 25{\deg}C-125{\deg}C demonstrate all 4 regimes (i) Ohmic ($\alpha = 1$), (ii) shallow trap SCLC ($\alpha \approx 2$), (iii) current shoot up ($\alpha \gg 2$) and (iv) series resistance ($\alpha = 1$). Further, TCAD simulations with thermal modeling are able to match the experimental IV characteristics in all the regimes. Thus, a current conduction mechanism in PCMO-based RRAM supported by detailed TCAD model is presented. Such a model is essential for further quantitative understanding and design for PCMO-based RRAM.