On the Thermal Models for Resistive Random Access Memory Circuit Simulation

Abstract

Resistive Random Access Memories (RRAMs) are based on resistive switching (RS) operation and exhibit a set of technological features that make them ideal candidates for applications related to non-volatile memories, neuromorphic computing and hardware cryptography. For the full industrial development of these devices different simulation tools and compact models are needed in order to allow computer-aided design, both at the device and circuit levels. Most of the different RRAM models presented so far in the literature deal with temperature effects since the physical mechanisms behind RS are thermally activated; therefore, an exhaustive description of these effects is essential. As far as we know, no revision papers on thermal models have been published yet; and that is why we deal with this issue here. Using the heat equation as the starting point, we describe the details of its numerical solution for a conventional RRAM structure and, later on, present models of different complexity to integrate thermal effects in complete compact models that account for the kinetics of the chemical reactions behind resistive switching and the current calculation. In particular, we have accounted for different conductive filament geometries, operation regimes, filament lateral heat losses, the use of several temperatures to characterize each conductive filament, among other issues. A 3D numerical solution of the heat equation within a complete RRAM simulator was also taken into account. A general memristor model is also formulated accounting for temperature as one of the state variables to describe electron device operation. In addition, to widen the view from different perspectives, we deal with a thermal model contextualized within the quantum point contact formalism. In this manner, the temperature can be accounted for the description of quantum effects in the RRAM charge transport mechanisms. Finally, the thermometry of conducting filaments and the corresponding models considering different dielectric materials are tackled in depth.

Dynamic Behaviors and Training Effects in TiN/Ti/HfOx/TiN-Nanolayered Memristors with Controllable Quantized Conductance States: Implications for Quantum and Neuromorphic Computing Devices

“…This indicates the high modulability of a very narrow filament even with a very low current, which points to the criticality of the current density and the local temperature enhancement based on heat transfer around the constriction (i.e., the narrowest point) of the filament during the reset procedure. 21,54 On the other hand, there are other previous studies on conductance quantization of memristors that also demonstrate state switching upon short pulsed voltage stimuli, but with much lower precision of the quantized conductance values. 14 As analytical differentiation of the I−V m characteristics (Figure 5) is employed in our experiment during device selection and measurements, the precision and signal-to-noise ratios of the quantized conductance are significantly improved in our experiment compared to previous reports, and thereby brings the study of memristors closer to practical application in neuromorphic computing.…”

“…The pulse width and amplitude are chosen from among multiple tests to achieve the optimal result, that is, to stimulate switching to the next conductance state with a minimal average number of pulses. The pulse value −0.35 V, which is very close to the onset voltage of the reset process observed in dc voltage sweeps with a fair set (Figure d), is speculated to be a favorable value for our device to activate recombination between oxygen ions and vacancies through oxygen migration by providing a proper electric field and a local temperature enhancement due to Joule heating. , After each pulse, the current is read at −0.01 V for 5 s, from which the conductance of the point contact is computed and then presented in units of G 0 . It can be seen that the conductance decreases stepwise from 9 G 0 to 0.5 G 0 in steps of 0.5 G 0 with great precision, with an average standard deviation of only ∼0.014 G 0 for the quantized plateaus.…”

Exploiting Non-idealities of Resistive Switching Memories for Efficient Machine Learning

“…Thus, even with the best control circuit, it appears to be impossible to program a resistance state under an arbitrary precision threshold, usually between 1-5% of the resistance range (Adam et al, 2018;Xia and Yang, 2019;Xi et al, 2021). This writing variability is most likely attributable to the local environment [room temperature (Abunahla et al, 2016;Bunnam et al, 2020;Roldán et al, 2021), humidity (Messerschmitt et al, 2015;Valov and Tsuruoka, 2018)] and the internal state of the RSM at the atomic scale. In valence change memories, for example, the conductive filament may break abruptly and result in a state that is more resistive than expected (Gao et al, 2009;González-Cordero et al, 2017;Wiefels et al, 2020).…”

GERARD: GEneral RApid Resolution of Digital Mazes Using a Memristor Emulator

“…Another approach is using charge and flux, as proposed in [33]. Following this approach, some models have also been proposed [34][35][36][37], and many more models can be found in the literature; for reviews, see [38][39][40] .…”