Large variation in basic memory properties is a serious issue that hinders the practical use of ReRAMs. This study revealed that one of the main factors causing variation is the presence of multiple filaments in each memory cell. An operating filament switches to another filament having the smallest set voltage at each instant of switching. We propose a resistive switching model that takes the presence of multiple filaments into consideration. A Monte Carlo simulation based on the resistive switching model reproduces the Vset distribution. The dependence of <Vset> on the number of switching cycles was predicted by the model and confirmed experimentally.

A hypothesis that probability giving Δ(1/V set ) [= 1/V set (n) -1/V set (n+1) ] > 0, P[Δ(1/V set ) > 0], increases with increasing the number of filaments contained in one memory cell, N fila , and decreases with increasing switching cycle, n, was made to validate a multi-filament model (MFM) as a mechanism causing the cycle to cycle dispersion of V set in ReRAM. Here, Δ(1/V set ) is the difference between the inverse of set voltages after n-th and (n+1)-th reset processes. This in turn means that V set will decrease with increasing N fila and will increase with increasing n. In addition, another hypothesis that probability giving Δ(1/R) [= 1/R n -1/R n+1 ] > 0, P[Δ(1/R) > 0], agrees with P[Δ(1/V set ) > 0] was made by incorporating the assumption that v set depends on d with the MFM. Here, R n , v set , and d represent resistance in high resistance state after the n-th reset process, the set voltage of each filament, and the thickness of a gap between the electrode and the edge of the filament. The validity of these two hypotheses were confirmed by measuring the dependence of P[Δ(1/V set ) > 0], P[Δ(1/R) > 0], and the mean value of V set , , on both the length of the perimeter, L, and n of Pt/NiO/Pt structures to which filaments were introduced by etching the NiO layer. INTRODUCTIONLarge dispersion of switching characteristics has hindered ReRAM from being put into practical use. The dispersion of memory characteristics such as cycle to cycle dispersion of V set have been reported to be related to the plurality of filaments [1][2][3][4]. However, the relationship between switching characteristics and the number of filaments which are contained in one memory cell, N fila , is still an open issue due to the difficulty in controlling N fila . Recently, Yoda et al. [5] reported that filaments, which are generally received as the gathering of oxygen vacancies [6][7][8], can be introduced on the etched surface of a NiO film due to the reduction effect of the bombardment by the etching gas, Ar + [9, 10]. Tanaka et al. [11] reported N fila -dependence of V set -distribution by measuring the size-dependence of V set -distribution for etched Pt/NiO/Pt structures, in which N fila is proportional to the length of the perimeter of the cell, 4L. A multifilament model (MFM), which detail will be described below, was proposed to reproduce the N fila -dependence of V set -distribution by the Monte Carlo simulation based on the model [11].In this paper, we formed a hypothesis, which is led if the MFM is valid as the mechanism causing V set -dispersion. This hypothesis, probability that Δ(1/V set ) (= 1/V set (n) -1/V set

Two hypotheses were formulated to validate a multi-filament model (MFM) as a mechanism for the cycle-to-cycle dispersion of Vset in resistive random-access memory. The first is that the probability of Δ(1/Vset) > 0, P[Δ(1/Vset) > 0], increases with the number of filaments in one memory cell, Nfila, and decreases with increasing switching cycle, n. Here, Δ(1/Vset) is the difference between the inverse of the set voltages after the n-th and (n + 1)-th reset processes [1/Vset(n) − 1/Vset(n + 1)]. Thus, Vset decreases with increasing Nfila and increases with n. The second hypothesis is that the probability of Δ(1/R) > 0, P[Δ(1/R) > 0], agrees with P[Δ(1/Vset) > 0], assuming that vset depends on d in the MFM. Here, Δ(1/R) = 1/Rn − 1/Rn + 1, and Rn, vset, and d represent the resistance in the high-resistance state after the n-th reset process, the set voltage of each filament, and the thickness of a gap between the electrode and the end of the filament, respectively. The validity of these two hypotheses was confirmed by measuring the dependence of P[Δ(1/Vset) > 0], P[Δ(1/R) > 0], and the mean value of Vset on both n and the length of the perimeter for Pt/NiO/Pt structures into which filaments were introduced by etching the NiO layer.

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Large variation in basic memory properties is a serious issue that hinders the practical use of ReRAM. This study revealed that one of the main factors causing variation is the presence of multiple filaments which have distinct set voltages in each memory cell. An operating filament switches to another filament having the smallest set voltage at each instant of switching. We propose a resistive switching model that takes the presence of multiple filaments into consideration. A Monte Carlo simulation based on the resistive switching model reproduces the set voltage distribution. Improvement of accuracy of the simulation can be also expected considering the fact that Vset increases at a certain probability at each instant of set switching.