Thank you Brian and all of you for drawing my attention to the mix up in paper numbers. You are correct there was a mix up with the paper numbers, my apologies to the authors and organizations concerned. I will try and get the posted version corrected. I wanted readers to go back to the IEDM 2013 Proceedings so that all the many authors of each paper would get the equal exposure and credit they deserve so I decided to use just the paper numbers as references. My memory coverage was divided into three parts, PCM, Hafnia and 3D and matrix isolation/devices is next. Paper 22.3 is a phase change paper.
Paper 22.3 uses in a sense a combination of a Percolation Network of resistors with site differentiation between "empty" (vacancies) and filled (ions) sites (I am assuming site percolation and not bond percolation). The Monte Carlo technique statistically assigns oxidation numbers as the coordination sphere of each filled site is modified during the flow of vacancies, electrons, holes and intersticial ions. This approach is interesting and somewhat better in demonstrating the underlying physics but still there are two questions: (1) Valency changes, do not necessarily means that a metal/insulator transition can occur in HFOx (and for that matter also in Ta2O3-x). And, (2) It is possible that filaments can still be created in the bulk HfOx, but the "connect/disconnect" region is really provided at the Ti or TiN(partially oxidized) in which such a phase transition is more possible due to the Mott Transition of TiOx within the oxidation number change in the 2d(1) = d(0) + d(2) disproportionation. Furthermore, as you explain, the fixed location of the filaments in the model, may be non-realistic from bit to bit. The quantum aspect searched by these papers will continue to elude the models if statistics and percolation are the only theories really used. A fundamental explanation of the Metal/insulator transition in these materials, and most importantly, control of such a transition is afforded by the CeRAM concept which is on its way soon.