J Comput Electron (2010) 9: 146–152 DOI 10.1007/s10825-010-0317-8 Stochastic modeling of bipolar resistive switching in metal-oxide based memory by Monte Carlo technique Alexander Makarov · Viktor Sverdlov · Siegfried Selberherr Published online: 7 October 2010 © Springer Science+Business Media LLC 2010 Abstract A stochastic model of the resistive switching mechanism in bipolar metal-oxide based resistive random access memory (RRAM) is presented. The distribution of electron occupation probabilities obtained is in agreement with previous work. In particular, a low occupation region is formed near the cathode. Our simulations of the temperature dependence of the electron occupation probability near the anode and the cathode demonstrate a high robustness of the low occupation region. This result indicates that a decrease of the switching time with increasing temperature cannot be explained only by reduced occupations of the vacancies in the low occupation region, but is related to an increase of the mobility of the oxide ions. A hysteresis cycle of RRAM switching simulated with the stochastic model including the ion dynamics is in good agreement with experimental re- sults. Keywords Resistive switching mechanism · Stochastic model · Monte Carlo method · RRAM 1 Introduction The resistive switching phenomenon is observed in differ- ent types of insulators, such as metal oxides, perovskite oxides, and chalcogenide materials. Because the electrical A. Makarov ( ) · V. Sverdlov · S. Selberherr Institute for Microelectronics, Vienna University of Technology, Vienna, Austria e-mail: makarov@iue.tuwien.ac.at V. Sverdlov e-mail: sverdlov@iue.tuwien.ac.at S. Selberherr e-mail: selberherr@iue.tuwien.ac.at conductance of the insulator can be set at different levels by the application of an electric field, this phenomenon be- comes attractive for advanced memory concepts. Indeed, a state with high resistance can be interpreted as logical 1 and a state with low resistance as logical 0, or vice versa, de- pending on the technology. The concepts of memory using the resistive switching phenomenon can be conveniently di- vided into the following three categories: Conductive Bridge RAM (CBRAM), Phase Change RAM (PCRAM), and Re- sistive RAM (RRAM). CBRAM is based on a solid-state electrolyte in which mobile metal ions create a conductive bridge between the two electrodes under the influence of an electric field. PCRAM employs the difference in resistivity between the crystalline and amorphous phases of a chalco- genide compound. RRAM is based on metal oxides, such as TiO x [1–4], HfO 2 [5], Cu x O[6], NiO [7], ZnO [8], and perovskite oxides, such as doped SrTiO 3 [9], doped SrZrO 3 [10], Pr 1−x Ca x MnO 3 [11], and employs the electric field induced difference in resistivity between the high and low current carrying states. The increasing demand for miniaturization of microelec- tronic devices has significantly accelerated the search for new concepts of nonvolatile memory during the last few years. Memory based on charge storage (such as flash mem- ory, and others) is gradually approaching the physical lim- its of scalability, and conceptually new types of memories based on a different storage principle are gaining momen- tum. Apart from good scalability, a new type of memory must also exhibit low operating voltages, low power con- sumption, high operation speed, long retention time, high endurance, and simple structure [12, 13]. In addition to RRAM, PCRAM, and CBRAM there ex- ist several other concepts as potential replacements of the charge memory. Some of the technologies are already avail- able in prototype form (such as carbon nanotube RAM