Comprehensive numerical modeling of filamentary RRAM devices including voltage ramp-rate and cycle-to-cycle variations

Abstract

The equilibrium ON and OFF states of resistive random access memory (RRAM) are due to formation and destruction of a conducting filament. The laws of thermodynamics dictate that these states correspond to the minimum of free energy. Here, we develop a numerical model that, through the minimization of free energy at a given voltage, determines the filament parameters and thus the electric current. Overall, it simulates the current-voltage (I-V) characteristics of RRAM. The model describes mutual transformations of RRAM states through SET (ON→OFF) and RESET (OFF→ON) processes. From the modeling perspectives, these states and processes constitute four programming modules constructed here in COMSOL Multiphysics software tackling the electrodynamic and heat transfer equations and yielding RRAM energy and I-V. Our modeling uniquely reproduces the observed I-V varying with voltage ramp-rates. That is achieved by accounting for the ramp-rate dependent activation energy of conduction. The underlying mechanism is due to the deformation interaction caused by the double well atomic potentials universally present in amorphous materials and having exponentially broad distribution of relaxation times. As another unique feature, our modeling reproduces the observed cycle-to-cycle variations of RRAM parameters attributed to the lack of self-averaging in small ensembles of double well potentials and electronic states in geometrically small (nano-size) RRAM structures. * Electronic address: dipesh.niraula@rockets.utodeo.edu † Electronic address: victor.karpov@utoledo.edu FIG. 1: Top left: Schematic of the circuitry where input voltage source VS, load resistor RL and a simple RRAM device RD are connected in series. Bottom left: plot of input voltage pulse where λ is the voltage ramp-rate and Vamp is the amplitude. Top right: Representation of a typical I-V characteristics of RRAM [4-7]. VD is the voltage drop across RRAM device. The SET current ISET is the maximum current limited by the Vamp. Bottom right: Customary representation of the I-V with absolute valued current axis. The dashed domain represents very fast nucleation processes.the source voltage ramping; they represent the SET and RESET processes. Their characteristic features are voltage snapback A-B followed by the vertical domain B-C for SET, and voltage snapforward D-E followed by the horizontal domain E-F for RESET. arXiv:1806.01397v2 [cond-mat.mes-hall]

Structural and Parametric Identification of Knowm Memristors

“…In [ 31 ], the research was extended to Al 2 O 3 devices, and the conductance quantization description was refined as a quantum point-contact model. D. Niraula and V. Karpov in [ 32 ] proposed a comprehensive model, adopted for the low-current snapforward and snapback effects, as well as cycle-to-cycle switching variability, which was represented as particle dynamics in a finite number of double-well potentials. Unfortunately, operating with the description of processes in partial derivatives, these models are quite complex and not suitable for use in software circuit simulation environments.…”

Filamentary physics and modelling in redox-based resistive devices

“…This is likely attributed to Joule heating as the filament and the surrounding regions heats up due to the high voltage applied. The temperatures are consistent with those reported at corresponding reset voltages [195]. Further analysis of the FEM model can be found in Appendix A5 Numerical Model Parameter Investigations.…”

“…[128,193] Fantini et al also explored the impact of load resistances and ramp rates on the output current of the TiN/HfO2/Hf/TiN device models, [194] which was further improved by Niraula et al more recently to incorporate filament evolution, gap dynamics, temperature and energy as a comprehensive FEM model. [195] Finite element model (FEM) simulations such as COMSOL and TCAD would also be useful in analyzing and predicting the transistor behavior. [196] As the Pt/HfO2/Ti devices were shown experimentally to exhibit hopping conduction in Chapter 3, a variation of hopping, i.e.…”

“…Properties of materials used in the Pt/HfO2/Ti model[195] Pt/HfO2/Ti Model parameters of the 4 fittings shown in Figure5.17[195] …”

Operando Direct Observation of Filament Formation in Resistive Switching Devices Enabled by a Topological Transformation Molecule

“…For the parameters of HfO 2x conductive filament and TT molecule layer, the parameters of them were summarized as following table S1. [1][2][3] (TT is an organic semiconducting small molecule. Hence, using another common organic semiconducting material P3HT to replace TT because of the high similarity.)…”