Editorís note: This work was first presented at the 2011 IEEE International Electron Devices Meeting (IEDM) and appears here courtesy of the IEEE. For more information about IEDM 2012 (San Francisco, CA; December 10-12), click here.
The origin of switching parameter variations in metal-oxide resistive-switching random access memory (RRAM) is studied. The stochastic formation/rupture of the conductive filaments (CFs) is modeled and incorporated with a trap-assisted-tunneling (TAT) current solver. The experimental DC I-V characteristics and pulse transient waveform featuring the current fluctuation during the reset process are reproduced by Monte Carlo simulations.
It is found that the wide spread of high resistance states (HRS) are due to the variation of tunneling gap distances, and the tail bits of the HRS are due to the newly generated traps near the electrode at the end of the reset process. To solve the over-reset and tail bits problems, a device structure with active/buffer bi-layer oxides combined with the reset-verify technique is proposed. Our model is corroborated by measured experimental data of hafnium oxide (HfOx) based RRAM.
Metal oxide RRAM is one of the most promising candidates for future non-volatile memory applications. Among the RRAMs reported, HfOx-based devices have shown excellent performance such as scalability (better than 30 nm), switching speed (on the order of nanoseconds), endurance (approximately 1010 cycles), and data retention (better than 10 years extrapolated at 200ļ C) . A 4-Mb array macro circuit was demonstrated . However, poor uniformity of the switching parameters has been the major challenge for the large-scale manufacturing . The physical origin of the variation is still not well understood so far. In this study, we aim to obtain new insights on this problem through modeling and comparison with experiment. The device fabrication and principal electrical characteristics of the TiN/HfOx/Pt devices are reported in our previous work .
In the widely recognized bipolar switching mechanism, the set process from HRS to low resistance state (LRS) is the formation of CFs by generation of oxygen vacancies (Vo), while the reset process from LRS to HRS is the rupture of CFs by recombining Vo with the oxygen ions that migrate from the oxygen reservoir at the electrode/oxide interface  (see figure 1). The insensitivity of the measured current to temperature suggests that TAT is the dominate conduction mechanism . Recent measurements and analysis of the lowfrequency noise and AC conductance provide additional evidence of the TAT conduction process .
Figure 1: In the set, oxygen atoms are pulled out of the lattice, generating oxygen vacancies (Vo) and leaving behind CFs in the bulk oxide. O2- drift to TiN, and are stored at the interface, where TiN acts as an oxygen reservoir. In the reset under a reversed bias, O2- migrate from the interface back to the bulk oxide and recombine with Vo, leading to the rupture of CFs near TiN; O2- migration is field- and temperature-assisted.
TAT includes three steps electrode to trap tunneling, trap-to-trap tunneling, and trap-to-electrode tunneling (see figure 2). We developed a TAT solver that calculates the electron occupation probability of all the traps based on equation 1, which accounts for all the possible tunneling paths between the traps, and between the traps and the electrodes.
where fn is the nth trap's electron occupancy, r is the hopping rate between traps, and R is the tunneling rate between the electrodes and the traps.
Mott hopping (equation 2)  and WKB approximation (equation 3) are used for calculating the transition rates between the traps, and between the electrodes and the traps, respectively.
is the distance between traps, ? is the electron wavefunction localization length ~0.3 nm, v0
is the electronic charge, and ?V
is the voltage difference.
is the distance between trap and electrode, m*
is the effective mass for HfO2
Hz, and V
is the applied voltage.
The steady state current is given by equation 4:
Figure 2: Schematic of the trap-assisted-tunneling (TAT) conduction mechanism shows (1) electrode to trap tunneling, (2) trap to rap tunneling, (3) trap to electrode tunneling. Current insensitivity on temperature  suggests TAT dominates instead of thermal activation conduction processes.
Take a 1-D Vo chain with a tunneling gap between the electrode and the filament as an example. Figure 3 shows an exponential decrease of the tunneling current with the increasing gap distance. Thus any variation of the gap distance would cause a significant variation of the HRS resistance.
Figure 3: I-V of 1-D filament for different gap distances . The inset shows current exponentially decreases with increasing gap distance, which is the main cause of the HRS variation.
Figure 4 shows that increasing the applied voltage reduces the electron occupancy probability in the traps near the cathode, and the electrode to trap tunneling becomes the bottleneck of the conduction.
Figure 4: Electron occupancy probability along 1-D filament under different bias voltages. With the increase of voltage, the occupancy near the cathode decreases and the electrode to trap tunneling becomes the bottleneck of the whole conduction.
To simulate the randomness of Vo configuration, we extended our TAT solver to a 2-D case (see figure 5). The results of this paper are based on 2-D simulation.
Figure 5: An example of 2-D electron occupancy probability, and the following simulations are based on 2-D.
The stochastic nature CF formation/rupture is considered as the following: In the forming/set process, the probability of Vo generation is determined by the attempt-to-escape rate that oxygen jumps over its barrier as: