Thermal Compact Modeling and Resistive Switching Analysis in Titanium Oxide-Based Memristors.

Resistive switching devices based on the Au/Ti/TiO2/Au stack were developed. In addition to standard electrical characterization by means of I-V curves, scanning thermal microscopy was employed to localize the hot spots on the top device surface (linked to conductive nanofilaments, CNFs) and perform in-operando tracking of temperature in such spots. In this way, electrical and thermal responses can be simultaneously recorded and related to each other. In a complementary way, a model for device simulation (based on COMSOL Multiphysics) was implemented in order to link the measured temperature to simulated device temperature maps. The data obtained were employed to calculate the thermal resistance to be used in compact models, such as the Stanford model, for circuit simulation. The thermal resistance extraction technique presented in this work is based on electrical and thermal measurements instead of being indirectly supported by a single fitting of the electrical response (using just I-V curves), as usual. Besides, the set and reset voltages were calculated from the complete I-V curve resistive switching series through different automatic numerical methods to assess the device variability. The series resistance was also obtained from experimental measurements, whose value is also incorporated into a compact model enhanced version.

TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing: from synaptic plasticity to stochastic resonance.

We characterize TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing. We analyze different features that allow the devices to mimic biological synapses and present the models to reproduce analytically some of the data measured. In particular, we have measured the spike timing dependent plasticity behavior in our devices and later on we have modeled it. The spike timing dependent plasticity model was implemented as the learning rule of a spiking neural network that was trained to recognize the MNIST dataset. Variability is implemented and its influence on the network recognition accuracy is considered accounting for the number of neurons in the network and the number of training epochs. Finally, stochastic resonance is studied as another synaptic feature. It is shown that this effect is important and greatly depends on the noise statistical characteristics.

Thermal Characterization of Conductive Filaments in Unipolar Resistive Memories.

A methodology to estimate the device temperature in resistive random access memories (RRAMs) is presented. Unipolar devices, which are known to be highly influenced by thermal effects in their resistive switching operation, are employed to develop the technique. A 3D RRAM simulator is used to fit experimental data and obtain the maximum and average temperatures of the conductive filaments (CFs) that are responsible for the switching behavior. It is found that the experimental CFs temperature corresponds to the maximum simulated temperatures obtained at the narrowest sections of the CFs. These temperature values can be used to improve compact models for circuit simulation purposes.

On the Thermal Models for Resistive Random Access Memory Circuit Simulation.

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.