Negative Differential Resistance in Bidirectional Threshold Switching of Ag/HfO x /Pt Device

In this work, the dependence of negative differential resistance (NDR) on compliance current ( I cc ) was investigated based on Ag/HfO x /Pt resistive memory device. Tunable conversion from bidirectional threshold switching (TS) to memory switching (MS) were achieved through enhancing I cc . NDR can be observed in TS as I cc is below 800μA but vanishes in MS. The switching voltages and readout windows of TS evolve with I cc . Furthermore, the dynamic conductance ( dI/dV ) as a function of time in NDR can be well illustrated by capacitor-like relaxation equation, and the relaxation time constant is significantly dependent on I cc . These phenomena were elucidated from viewpoint of nanofilament evolution controlled by I cc as well as nanocapacitor effects originated from nanofilament gap. The I cc -dependent NDR as well as conversion between TS and MS on Ag/HfO x /Pt resistive memory device indicates its potential application as a multifunctional electronic device.


Introduction
Resistance random accessory memory (RRAM) based on the resistive switching (RS) phenomenon in capacitor-like metal-insulator-metal (MIM) devices has attracted significant attention due to its simple structure, easy fabrication, fast switching speed and superior scaling property. [1][2][3] Two basic switching modes were generally included according to the electrical switching behaviors of RRAM, namely memory switching (MS) and threshold switching (TS). [4][5][6] The MS is a kind of nonvolatile behavior, both high resistance state (HRS) and low resistance state (LRS) can be maintained after removing the external bias, enabling the application in the nonvolatile memories， reconfigurable logic and neuromorphic computing, which has been intensively investigated in various transitional metal oxides, such as HfO2, [7] Al2O3, [8] SrTiO3, [9] and so on. On the contrary, the TS is a type of volatile behavior with an S-shape I-V curve that works in limited voltage range between two critical values called the holding voltage (VH) and threshold voltage (VTH). Differing from nonvolatile MS, LRS in TS will switch back to HRS as applied bias is below VH, that is, HRS retains below VH and only LRS is displayed above VTH. Many investigations have demonstrated the excellent selector function of TS to suppress the sneak problem of high-density crossbar arrays as connected with RRAM in series [10][11][12][13] . Even conversion between MS and TS under the suitable external excitation was also reported. [5,6,14,15] Lately, an important nonlinear carrier-transport phenomenon-negative differential resistance (NDR), referring to a decrease in current with increasing 3 voltage or vice versa, has been discovered accompanying with various RS, such as unipolar RS on Ag/SiO2/Pt device, [16] multilevel RS on Pt/BaSrTiO3/SrTiO3:Nb device, [17] bipolar RS on Ag/ZnO/Zn device [18] and flexible organic memristive memory [19] . However, the origin of NDR in RS is controversial. Discharging electrons from metal nanocrystals, charge storage processes between interfaces, separation of oxygen vacancies and trapped electrons, and different work functions of materials have been proposed to contribute to NDR. Furthermore, the compliance current (Icc) is a vital parameter for RRAM to understand and manipulate RS, but the effects of Icc on NDR are still insufficient. In this work, conversion from bidirectional TS to MS were achieved on Ag/HfOx/Pt device through controlling Icc. NDR can be observed in TS with Icc lower than 800μA. The dependence of NDR on Icc was also investigated by manipulating TS via Icc. The phenomena can be elucidated in the view of conductive filaments model as well as nanocapacitor effects originated from filament gap.

Experimental section
The HfOx films were directly deposited on the available Pt/TiO2/SiO2/Si

Results and discussion
A pristine Ag/HfOx/Pt device stays HRS. To get the switching effects, an electroforming process was generally needed. It has been reported that the resistive switching performances are well dependent on the electroforming process like polarity, sequence of Icc. [20][21] Also, double and asymmetric two-step electroforming are reported to be beneficial to stabilize the resistive switching. [7] Here, an incomplete electroforming process with Icc of 10μA was applied by performing a positive sweeping 0 ~+8V. As Fig. 1(a) indicates, the current is far lower than 10μA and there is no abrupt current rise in this process. After that, the sweeping setup of 0V→−0.4V→0V→0.4V→0V was subsequently performed. Whether the voltage sweeps from VH + or VHto 0V, current increases gradually, while dynamic conductance degrades. Similar NDR was achieved in all TS curves.
Moreover, it is of significant importance to emphasize that negative current was detected in positive NDR bias but positive current emerges in negative NDR bias.
For this sake, the bidirectional TS with NDR was further purchased and systematically compared under various Icc of 1μA, 10μA, 20μA, 50μA, 100μA, 150μA, 500μA and 800μA. Fig. 2(a) and 2(b) show some typical I-V curves and corresponding evolution of switching voltages with Icc, including VH + , VH -, VTH + and VTH -. As Fig. 2(a) indicates, Ag/HfOx/Pt device evidently manifests the bidirectional TS with NDR as Icc is below 800μA. With enhancing Icc from 1μA to 800μA, all threshold voltages VTH + and VTHevolve towards the lower value ( Fig. 2(b)).
Although the holding voltage VH + and VHincrease slightly in small Icc, both descend eventually as Icc rises up. Meanwhile, the readout windows, defined as the voltage gap 6 between VH and VTH, drop gradually with increasing Icc (Inset in Fig. 2(b)). However, TS of Ag/HfOx/Pt device becomes unstable when Icc is over 800μA, and converses to MS as Icc is larger than 1mA. Fig. 2(c) displays I-V curves within continuous 600 cycles with Icc of 5mA, featuring with typical nonvolatile MS. The corresponding evolution of Reset/Set voltages and resistance at 0.05V, shown in Fig. 2(d) Many investigations have directly observed growth and annihilation of Ag nanofilaments via electrochemical redox process in Ag-based programmable metallization cells that causes Set and Reset switching in MS. [25,26] The tiny Ag nanofilaments, especially in a low Icc, are not stable due to Rayleigh instability.
Therefore, the tiny nanofilaments will be dissolved spontaneously under surface energy as well as the diffusion into matrix due to the concentration gradient and thermal effects, [26,27] resulting in the volatile TS accordingly. For both MS and TS, Icc plays a particularly important role in manipulating nanofilaments morphology. [16,18,[25][26][27] Therefore, on basis of abovementioned analysis, the Icc-dependent NDR in this work can be understood from viewpoint of the evolution of Ag conductive nanofilaments coupling with the capacitive effects of nanocapacitor resulted from nanofilaments gap. Fig. 4 schematically illustrates the overall evolution of Ag nanofilaments and nanocapacitor as well as the corresponding equivalent circuits in TS and MS. Initially, incomplete electroforming did not switch Ag/HfOx/Pt device to LRS. As the negative bias was applied on the Pt electrode, Ag nanofilaments grew along the old one and switched device to LRS as bias came to VTH - (Fig. 4(a)). But tiny nanofilaments formed due to the limitation of low Icc. The tiny Ag nanofilaments can be equivalently considered as a resistance and are unstable in nano scale, which 8 dissolved spontaneously under surface energy, resulting in switching back to HRS at VH - (Fig. 4(b)). Then, the residual nanofilaments in HfOx films were disconnected with nanogap. Due to high conductivity of Ag nanofilaments, the overall device resembles nanocapacitor with two resistances in series, the equivalent circuit is shown in right side of Fig. 4(b). As the applied bias was below VH -, the nanocapacitor discharged, enhancing current of circuit, namely NDR. It also created the reverse current owing to the opposite electric field direction between nanocapacitor and applied bias. Similar processes occurred in the positive bias region, as shown in Fig.

4(c) and 4(d).
According to the model of a

Conclusions
In summary, we investigated the dependence of NDR on Icc based on Ag/HfOx/Pt resistive memory device. In addition to bipolar memory switching in large Icc, the as-fabricated device exhibit bidirectional threshold switching with NDR in low Icc.
This NDR is significantly dependent on Icc, and the dynamic conductance dI/dV-t plot in NDR is good accordance to the capacitor-like relaxation equation. These phenomena were attentively elucidated from viewpoint of filaments evolution controlled by Icc as well as nanocapacitor effects resulted from filaments gap.