On the Thermal Models for Resistive Random Access Memory Circuit Simulation
Juan B. Roldán,
Gerardo González-Cordero,
Rodrigo Picos,
Enrique Miranda,
Félix Palumbo,
Francisco Jiménez-Molinos,
Enrique Moreno,
David Maldonado,
Santiago B. Baldomá,
Mohamad Moner Al Chawa,
Carol de Benito,
Stavros G. Stavrinides,
Jordi Suñé,
Leon O. Chua
Affiliations
Juan B. Roldán
Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, Avd. Fuentenueva s/n, 18071 Granada, Spain
Gerardo González-Cordero
Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, Avd. Fuentenueva s/n, 18071 Granada, Spain
Rodrigo Picos
Industrial Engineering and Construction Department, University of Balearic Islands, 07122 Palma, Spain
Enrique Miranda
Department Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q., 08193 Bellaterra, Spain
Félix Palumbo
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290, Buenos Aires C1425FQB, Argentina
Francisco Jiménez-Molinos
Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, Avd. Fuentenueva s/n, 18071 Granada, Spain
Enrique Moreno
UJM-St-Etienne, CNRS, Laboratoire Hubert Curien UMR 5516, Institute of Optics Graduate School, University Lyon, F-42023 St-Etienne, France
David Maldonado
Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, Avd. Fuentenueva s/n, 18071 Granada, Spain
Santiago B. Baldomá
Unidad de Investigación y Desarrollo de las Ingenierías (UIDI), Facultad Regional Buenos Aires, Universidad Tecnológica Nacional, Medrano 951, Buenos Aires C1179AAQ, Argentina
Mohamad Moner Al Chawa
Institute of Circuits and Systems, Technische Universität Dresden, 01062 Dresden, Germany
Carol de Benito
Industrial Engineering and Construction Department, University of Balearic Islands, 07122 Palma, Spain
Stavros G. Stavrinides
School of Science and Technology, Thermi University Campus, International Hellenic University, 57001 Thessaloniki, Greece
Jordi Suñé
Department Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q., 08193 Bellaterra, Spain
Leon O. Chua
Electrical Engineering and Computer Science Department, University of California, Berkeley, CA 94720-1770, USA
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.
