  Pr$_{0.7}$Ca$_{0.3}$MnO$_3$ (PCMO) based RRAM shows promising memory
properties like non-volatility, low variability, multiple resistance states and
scalability. From a modeling perspective, the charge carrier DC current
modeling of PCMO RRAM by drift diffusion (DD) in the presence of fixed oxygen
ion vacancy traps and self-heating (SH) in Technology Computer Aided Design
(TCAD) (but without oxygen ionic transport) was able to explain the
experimentally observed space charge limited conduction (SCLC) characteristics,
prior to resistive switching. Further, transient analysis using DD+SH model was
able to reproduce the experimentally observed fast current increase at ~100 ns
timescale, prior to resistive switching. However, a complete quantitative
transient current transport plus resistive switching model requires the
inclusion of ionic transport. We propose a Reaction-Drift (RD) model for oxygen
ion vacancy related trap density variation, which is combined with the DD+SH
model. Earlier we have shown that the Set transient consists of 3 stages and
Reset transient consists of 4 stages experimentally. In this work, the DD+SH+RD
model is able to reproduce the entire transient behavior over 10 ns - 1 s range
in timescale for both the Set and Reset operations for different applied biases
and ambient temperatures. Remarkably, a universal Reset experimental behavior,
log(I) is proportional to (m X log(t)) where m~-1/10 is reproduced in
simulations. This model is the first model for PCMO RRAMs to significantly
reproduce transient Set/Reset behavior. This model establishes the presence of
self-heating and ionic-drift limited resistive switching as primary physical
phenomena in these RRAMs.
