Rupture phenomenon

The NDR phenomenon has been observed on SiOx, Ta2O5, Nb2O5, and Al2O3, among others, since the 1960s, and several possible forming process and resistive switching mechanisms have been investigated in the early days. Hickmott et al. [15]

reported that some high-field-dependent processes reduced the number of impurity centers and contributed to conduction (e.g., neutralization from hole centers). The schematic diagram of their proposed model is shown in Fig. 1-10. Simmons and Verderber [16] constructed an impurity band in the center of an insulator film, and proposed that once the impurity band falls below the anode, the current would decrease because only the electrons below the top of the impurity band contribute (Fig.

1-11). Dearnaley et al. [17] reported that filaments are characterized by two important features. The first feature is that the filament may fracture and cease to contribute to conduction; the second is that the filament can re-form under suitable conditions, and the re-forming will be related to the basic forming process of propagation of the filament through the insulator. The fracture of the filament is probably a consequence of Joule heating, which raises the temperature of a part of the filament so that there is local atomic reorganization, as in melting or other phase changes. When continuously operated, the two features exhibit the RS behavior. Dearnaley‘s model has frequently

been adopted to explain switching characteristics; however, the tiny difference between materials is still unknown due to the lack of precise measurement and analysis techniques. Their model is too rough to use in elucidating the development of mainstream NVM in the specific investigation. In the last decade, many groups have deeply investigated and observed the microcrystalline and microstructure of thin films based on the relationship of RS. In the following sections, we examine the occurrence of the thermal Joule heating effect.

(a) Thermal Joule heating

The RESET process of unipolar RRAM devices based on the thermal Joule heating effect is mainly used to explain this mechanism. A high thermal temperature arises from high current density, althrough the existing defects inside the TMO films may induce high Joule heat under applied bias. Resistance change based on thermal Joule heat has been observed in many TMO materials. Kim et al. [18] roughly estimated the temperature of formed filaments using the steady state temperature

model, where the equation for which is given by

4 reaction model of the reset mechanism. The resistance R of the filament is assumed to follow Ohm‘s law. The heating temperature is given for a typical filament by

  R of filament with different resistivity values can be represented, as shown in Fig. 1-12;

for example, for a Ni filament with ρ = 30 μΩ cm and r = 20 nm, the heating temperature is approximately 1000 °C. Chen et al. [20] proposed that the temperature effect can be linked to the thermal release time of trapped charges, and the field effect can be attributed to a field-induced barrier lowering. On the basis of the field-induced barrier lowering effect from qF  eV

E 

 , the erasing temperature can be estimated to be ~800 °C. He et al. [21] studied the switching mechanism of carbon-based RRAM. They simulated the heat generation and propagation driven by an electric current pulse during the switching process; the authors reported that the temperature was approximately 2200 K when set to low resistance, and 4000 K when the state was switched to high resistance. The reported estimated heating temperature is summarized in Table. 1.

(b) Thermal rupture model

Russo et al. constructed a SET and RESET model based on experimental and numerical analysis data; the authors discussed the filament conduction properties and RESET transition kinetics characterization for NiO-based RRAM devices [22]. Using the physics-based numerical modeling of the RESET operation based on conductive filament (CF), they evaluated a statistic characterization of critical filament temperature for the RESET operation. Their results are consistent with a thermally activated RESET mechanism and support a diffusion-based model for RESET. Based on simulation data, the RESET transition was self-accelerated as a consequence of a positive feedback between the thermal dissolution of the CF and local Joule heating in the CF bottleneck, which was used to account for the abrupt resistance transition in

experimental data [23]. The study of Russo et al. [22] was further investigated by Cagli et al. [24], who addressed the analytical modeling of SET and RESET processes in NiO-based RRAM cells. The SET model is based on threshold switching as the initiating mechanism of the transition to low resistance, while the RESET model assumes a thermal dissolution/oxidation of the low-resistance conductive filament.

(c) Where to rupture

Understanding where the filamentary path is to be formed and ruptured is important because the properties of RS during switching depend on the formation and rupture of the conducting filamentary paths. It can be easily divided into two categories: bulk dominates or interface dominates. Russo and Cagli believed that the major heating takes place close to the middle of the CF due to the approximately parabolic temperature profile in the CF during the applied electrical bias. As a result, the disconnection of CF occurs in correspondence with the middle of the filament [20,22,23]. By simulating the heating that takes place within vicinity of the M/O interface, their proposed model can also be well fitted. The simulation on RS has been shown by He et al. [21] to be the illustrated filament breakage and regrowth, as well as its related temperature distribution (Fig. 1-13). A different outlook was proposed to depict where to rupture based on Kinoshita‘s report. Kinoshita et al. [25] investigated the data retention properties of NiO films exposed to sputtered particles and thermal stress. The authors found that the retention of the HRS data is dependent on the polarity of the bias voltage used to program the data, and that RS takes place on the anodic side of the conductive filaments. Kim et al. [26] first compared the RS properties of TiO2, Al2O3, Al2O3/TiO2, and Al2O3/TiO2/Al2O3 thin films by I-V measurements using Pt/insulator/Ru structures. The authors observed that the layer that is secondarily encountered by the injected electrons controls the overall switching

characteristics, suggesting that the first layer always remains in LRS during the entire switching cycle. They further investigated on a Pt/40 nm TiO2/Pt capacitor structure and proposed that the conducting filaments propagate from the cathode interface to the insulator film [27]. Moreover, they argued that RS is induced by the rupture and recovery of the filaments in the localized region approximately 3-10 nm thick near the anode. Their model can also explain well the noisy Ohmic behavior once the voltage bias is applied as opposed to the last operation performed [28]. Only a certain part of the filaments near the anode electrode, and not the whole filament, actively contributes to switching. In their subsequent experiments, they observed that when W and Ir metals were used as top electrodes, the RS property was quite different. They also connected W tip/NiO/Ir/NiO/W tip sample serially and measured the I-V curve, and arrived at the opposite conclusion that the rupture of the conducting filaments occurs at the cathode side while the anodic side is still conducting [29]. Such findings imply that the electrodes may be another dominant factor in the RS operation. Several studies have reported that the oxide film near the anode electrode in some TMO films, such as NiO [18], TiO2 [19], Cu2O [20], HfOx [30] will dominate the RS. However, recent direct experimental results in support of the location of the CF rupture are not available.

(d) Thermal instability

Thermal instability is one of the considerable issues for unipolar RRAM; the main RS mechanism is based on the field induced for SET and thermal Joule heating for RESET process. The applied voltage can be controlled from the measurement setup or a suitable compliance current; however, measuring the accumulated thermal heat during each RESET operation by electronic devices is not possible. Hence, controlling the suitable Joule heat during a RESET process to accomplish a stable

switch to a certain HRS is a critical issue for unipolar RRAM. In 2005, Rohde et al.

[31] first reported the RS of 43 nm-thick TiO2 thin films by electric-pulse-induced operation; the common result obtained was a changing energy but with constant power necessary for one switching event, indicating that RS is a power-induced mechanism. Yun et al. [32] investigated the nanometer-sized localized filaments on the surfaces of NiO films by conductive-AFM; the authors observed the each spot, which is assumed to indicate the beginning of the localized conducting filaments, can be created or destroyed in a random manner (Fig. 1-14). Chang et al. [33] examined the effect of thermal dissipation on RS properties. The thermal instability of the conducting filaments induced the resistance memory switching phenomena to unstable and threshold switching (Fig. 1-15). Variations in CF parameters arise from local variations in material composition – for example, stoichiometric variations in NiOx filaments, metallic impurities, diffused from the electrodes, and structural defects - may as well be a critical issue in causing fluctuations in switching behaviors (Fig. 1-16) [34].