Controlled inter-state switching between quantized conductance states in resistive devices for multilevel memory

A detailed understanding of quantization conductance (QC), the correlation with resistive switching phenomena and controlled manipulation of quantized states is crucial for realizing atomic-scale multilevel memory elements. Here, we demonstrate highly stable and reproducible quantized conductance states (QC-states) in Al/niobium oxide/Pt resistive switching devices. Three levels of control over the QC-states, required for multilevel quantized state memories, like, switching ON to different quantized states, switching OFF from quantized states, and controlled inter-state switching among one QC state to another has been demonstrated by imposing limiting conditions of stop-voltage and current compliance. The well-defined multiple QC states along with a working principle for switching among various states show promise for implementation of multilevel memory devices.

Driven by the demand for improved computing capability, the semiconductor industry is following the extension of Moore's law which says that the density of transistors in an integrated circuit doubles every two years. However the current technology, charge based flash memory, has reached its limits of miniaturization. [1][2] Also, all existing devices are limited to two stable memory states (i.e., "0" and "1"). Increasing the number of stable states, from bi-stability to multi-stability, will be an effective method for producing high-density and efficient memory devices.
As one for the most promising candidate for future non-volatile memories, resistive random access memory (ReRAM) with simple two-terminal sandwiched structured devices exhibit attractive performances due to their scalability down to atomic level, CMOS compatibility, low-power consumption, and high-speed features. [3][4] It has been proposed that the multiple stable states available in the resistive switches can be used for multilevel storage for ultrahigh density memories. 5 Existence of stable multistates has been demonstrated in resistive switching, [6][7][8][9][10][11][12][13][14] ferroelectric [15][16][17][18][19][20] and phase change [21][22][23][24][25] memory devices. Atomic point contact based QC observed in resistive switching devices has also been demonstrated for memory applications. [26][27][28][29][30][31] However, controlled manipulation of multiple stable states for potential application in multilevel memory is yet to be achieved. Several kinds of control over stable QC-states in a resistive switching device are required to achieve multilevel quantized state memories. These particular kinds of devices have not been fully explored, partly because of the lack of appropriate materials and lack of design & working principles. Many groups have demonstrated quantization in several ReRAM [32][33][34][35][36] as well as in atomic switch 29,[37][38][39] devices. The conditions to achieve different quantized states either with current compliance [40][41] or with stop voltage 37,40 have been reported. Also, there is some understanding about the stability of these states with respect to time. 35,37,[42][43] However, conditions for controlled inter-QC-state switching, essential for multilevel memory, have not been reported.
Here, we demonstrate control over the events of switching ON to different QC-states, switching OFF from QC-states, and inter-QC-state switching in Al/Niobium oxide/Pt device.
Firstly, stable and reproducible QC-states with integer and half-integer multiples of quantum of conductance (G 0 = 2e 2 /h ~77.4 S) were achieved, indicating formation of well-controlled atomic point contacts in the conducting filaments. Then, the devices were manipulated to exhibit hundreds of different inter-QC-state switching, both in the direction of SET (higher G 0 ) or RESET (lower G 0 ) starting from any particular QC-state. The initial and final QCstates, for each switching event, were found to be stable. The device exhibited longer retention times for higher QC-states. Rules for controlled switching are evolved with stopvoltage and current compliance limits during current-voltage (I-V) measurements. The working principles demonstrated in this work, to achieve QC-states and to induce inter-QCstate switching, is a crucial step towards realization of multilevel memory devices.
Switching ON to QC-state: The resistive switching and QC characteristics are demonstrated using I-V measurements on Al/Nb 2 O 5 /Pt devices in air at room temperature. These devices, in their pristine state, were found in high resistance OFF state (HRS) of the order of ~10 9 Ω.
Initially, the device was switched to low resistance ON state (LRS) at a forming voltage ~4 V with current compliance (I c ) of 5 µA, as shown in the inset of Figure 1a. After forming, with voltage sweeps, the device showed reproducible switching between LRS to HRS (RESET; voltage ~ -0.4 to -1.2 V) and vice-versa (SET; voltage ~1.6-2.5 V), shown as semilogarithmic I-V plots in Figure 1a. These devices show both unipolar as well as bipolar switching characteristics in either polarities of the voltage ( Figure S1). In our previous work, 34 unipolar switching behaviour of the Al/Nb 2 O 5 /Pt devices were presented and it was demonstrated that the conducting filament, after making the atomic point contact, grows in thickness atom-by-atom during SET voltage sweep. Here, in this work, conducting filaments were stabilized to achieve various QC-states. During the SET process, the LRS was controlled by applying voltage sweeps with different current compliance values of 100, 200, 300, 400 and 500 µA ( Figure 1b) and different resistance states of 9 kΩ, 6 kΩ, 4 kΩ, 2.9 kΩ and 2.3 kΩ, respectively, were achieved. These resistance states were stable and correspond to quantized conductance states of ~1.5 G 0 , ~2 G 0 , ~3.5 G 0 , ~4.5 G 0 , and ~5.5 G 0 , respectively ( Figure 1c).  Different QC-states were achieved in different SET sweeps and their retention time was measured at 100 mV read voltage. Figure 2h shows the retention time of >500 s for QCstates corresponding to 1 G 0 , 2 G 0 , 3.5 G 0 , 4.5 G 0 , and 5.5 G 0 . The retention time of different QC-states were observed to be increasing with increase in G 0 . In general, QC-states below 3 G 0 were stable for less than 800 s, while the QC-states higher than 3 G 0 were stable for more than 1000 s. However, on some occasions, stability over 1000 s were also observed for states <3 G 0 . Retention data of various other QC-states are shown in supplementary Figure S2a.
The stability of a particular QC-state depends on the strength of the corresponding conducting filament. The conducting filament diameter increases as the G 0 of QC-states increase, thus making them more and more robust. The magnitude of applied read voltage during retention measurement was also found to influence the stability of QC-states (supplementary fig2b).
Inter-QC-state switching: Once a device is switched ON to a particular QC-state, voltage sweep and current compliance conditions could be controlled to exhibit many different inter-QC-state switching in the device, be in the direction of SET (higher G 0 ) or RESET (lower G 0 ). Figure 3 shows one set of four successive switching steps of inter-QC-state in SET direction of a particular device along with the corresponding QC-state retention time up to 100 s. The device was, firstly, SET to ~2.5 G 0 with I c = 200 µA (Figure 3a). In the subsequent voltage sweep with I c = 300 µA, we induced an inter-QC-state switching from 2.5 G 0 to ~3 G 0 state (Figure 3b). Here, during the second sweep, the starting QC-state was found to be at 0.5 G 0 instead of 2.5 G 0 . This change in state can be understood as instability of states below 3 G 0 , as discussed above. Further, the QC-state was successively switched from 3 G 0 to 3.5 G 0 (Figure 3c)  The inter-QC-state switching where the I c values were increased in steps of 400 A and 800 A were also performed. In Figure 3k, the device was switched to ~3 G 0 state with I c = 300 A (black trace) and then in subsequent voltage sweep with I c = 700 A, the device switched to ~7 G 0 state (red trace). Further, as another voltage sweep was performed with I c = 1.5 mA, the device switched from 7 G 0 to 15 G 0 . While switching from 3 G 0 to 7 G 0 , the device showed indications to stop at different intermediate QC-states, however, due to higher I c limit, the devices stopped only at 7 G 0 . It appears that an I c of more than 300 A and less than 700 A would have possibly stabilized the device at some intermediate QC-state.
During the voltage sweep with I c = 1.5 mA, the device exhibited instability around 12 G 0 state (Figure 3k, blue trace). Since, the device can switch in both unipolar and bipolar modes, it can be understood as the device's tendency to RESET in unipolar mode due to very high currents, however, the voltage was in the range of SET (1.5-2.5 V), thus the device switched to 15 G 0 . The inter-QC-state switching was also controlled and reproducibly performed in RESET direction. Figure 4 shows three successive steps of inter-QC-state switching of a device, where different stop voltages are used to control switching to different QC levels. The device was, firstly, SET to ~20 G 0 state. Then, an inter-QC-state switching from 20 G 0 to 6 G 0 was induced by a voltage sweep, where -1.0 V was kept as the stop-voltage (V s ), shown in Figure 4a. In the subsequent sweeps, the QC-state switched from 6 G 0 to 4.5 G 0 (Figure 4b) and from 4.5 G 0 to 3.5 G 0 (Figure 4c), with V s = -1.1 V and -1.2 V, respectively. In another subsequent sweep, the QC-state switched from 3.5 G 0 to a very high resistance state (i.e. complete RESET) with V s = -1.5 V, as shown in Figure 4d. Each QC-state, after every switching, was found to be stable with time (Figure 4e-h).
During RESET switching, the critical parameter was the stop-voltage instead of the current compliance limit. For example, during the voltage sweep in Figure 4a Hundreds of inter-QC-state switching events in both SET and RESET directions were performed. The SET and RESET inter-QC-state switching (Figure 3 and 4) are distinguished by the limiting conditions of current compliance and stop-voltage during voltage sweep cycles, respectively. However, to ensure complete RESET from any QC-state, both current compliance as well as stop-voltage needs to be kept high.
In summary, stable and reproducible QC-states were achieved in Al/Nb 2 O 5 /Pt devices by limiting current compliance during the current-voltage measurements. All the states were stable at least for 500 s, and the higher conductance states exhibited longer retention times.
The stable quantized states could be controllably switched to higher G 0 (SET direction) or to NiCr alloy strip of width ~0.7 mm to make Pt available for bottom electrode contact. Then, Nb 2 O 5 thin films were grown using reactive dc magnetron sputtering at a pressure of 2.0×10 -2 mbar in gas mixture of Ar (94%) and O 2 (6%), while the base pressure was evacuated at ~6 ×10 -7 mbar. Thereafter, the top electrode of Al was deposited with areas ranging from 100 to 500 µm 2 using a shadow mask by thermal evaporation technique. The current-voltage (I-V) characteristics were measured on two probe station with Agilent 2450 source-measure unit.
All the measurements were performed at room temperature by applying the voltage source on the Al top electrode with the Pt bottom electrode grounded. The voltage was swept keeping a current compliance for all electrical measurements. This method of fabricating device and electrical measurement was also followed in our previous report. s1