(Invited) Simulating the Behavior of a Bipolar Filamentary ReRAM Cell for Upcoming Memory Devices
Authors: Wicklein Sebastian , Petti C , Minville T , Bandyopadhyay A , Ilkbahar A 
Published: February 2020

Fundamental research on resistive switches for future non-volatile memories has led to the mass production of resistive random access memory devices (ReRAM)1. In order to realize and design these new memory devices the industry relies on behavioral models of the memory cell. Key aspects to describe these memory cells are still debated. For example, a comprehensive charge transport expression that correlates defect density and conductivity is still missing 2
3. The models for setting and resetting the cell are largely dependent on migration of defects or anions as well as thermal effects4
5. However, these models and concepts for each mechanism are sometimes applicable for one mechanism only or mutually exclusive.

Finite element simulations of a bipolar filamentary ReRAM cell based on a binary oxide are used to model the cell behavior and highlight missing aspects to reliably evaluate the behavior of such a device. The operation of a ReRAM cell can be separated in 3 main aspects, namely, forming, set and reset. The forming (soft breakdown) entails the creation of oxygen vacancies and the conductive filament which can be expressed by a reaction term.  It will be shown that the conductivity definition and the mobility of ions strongly influence the forming event.

The behavioral modeling of the reset-event of a conducting filament by oxygen vacancy migration yields a typical I(V) curve. However, the bipolar characteristic of the device cannot be explained by such a migration of oxygen vacancies alone since it can be applied in either direction. Also, the re-oxidation of the filament results in a very large electric field which would result in return in a soft breakdown event and obstructing the reset. The common expressions for forming generally prevent a successful reset simulation and to simulate the bipolarity of set and reset an anisotropic mobility of the oxygen vacancies is required. Joule heating effects strongly influence the forming, set and reset but without a concrete correlation of conductivity and defect density predictions are difficult to make.

Figure
1
: Finite element simulation of a forming event. The colors represent the density of oxygen vacancies within the dielectric. The metal oxide is sandwiched between two metal electrodes. A positive bias is applied to the top electrode and swept from 0V – 3V (1V/s). a) 0V, b) ~1V, c) ~2V, d) ~2.1V, c) ~2.2V.

Figure 2: a), b), c) normalized color map of oxygen vacancy density. d), e), f) color map of the corresponding electric field. The re-oxidized filament area depicts a very large field that would cause a soft breakdown.

Figure 3: a), b), c) I(V) curve of the corresponding reset event in Figure 2.

In essence, utilizing the known physical characteristics, behavioral models for the ReRAM cell can be realized; however, a coherent behavioral model that is able to simulate all 3 aspects is still problematic to create with the known physical characteristics.

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3.           Park, S., Magyari-köpe, B. & Nishi, Y. Impact of Oxygen Vacancy Ordering on the Formation of a Conductive Filament in TiO 2 for Resistive Switching Memory. 32,2010–2012 (2011).

4.           Waser, R., Dittmann, R., Staikov, G. & Szot, K. Redox-Based Resistive Switching Memories - Nanoionic Mechanisms, Prospects, and Challenges. Adv. Mater.
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5.             Larentis, S. et al. Resistive Switching by Voltage-Driven Ion Migration in Bipolar RRAM — Part II : Modeling. 59, 2468–2475 (2012).

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