Filamentary RRAM Research Articles

Excellent Pattern Recognition Accuracy of Neural Networks Using Hybrid Synapses and Complementary Training

To overcome the performance degradation in hardware neural networks (NNs) with non-ideal synapse devices, we proposed a novel neuromorphic architecture with both TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> -based interfacial RRAM and CBRAM-based filamentary RRAM for highly accurate NN training and long-term inference reliability. We used a threshold-triggered training scheme, in which interfacial and filamentary RRAMs were programmed in a complementary fashion. This took advantage of the long retention time of the filamentary RRAM and the high-resolution, symmetric weight update in the interfacial RRAM. Additional evaluation of device parameters, such as linearity, precision, variation, and retention time, was conducted. An excellent pattern recognition accuracy of ~97% was achieved during training with the MNIST dataset. Thus, reliable inference accuracy after training was maintained using the filamentary RRAM.

OFF State Conduction in Filamentary RRAM

In spite of extensive research, the physics of electric transport in the OFF (high resistance) state of resistive random access memory remains poorly understood. Here, we propose a theory that explains the observed activation nature of that transport, its exponential non-ohmicity, variations between nominally identical structures, and failure trends. Our theory proceeds from the finding that the diffusion transport mechanisms must be ruled out as leading to nonphysically high temperatures ( $T\sim 4000-5000$ K) well above melting. The Schottky emission remains acceptable due to its underlying ballistic transport by ~1 eV electrons spreading the Joule heat over much larger distances without melting. Taking into account, the random fields of charged defects the Schottky emission enables one to describe the device variability and failures.

Mimicking Synaptic Behaviors with Cross-Point Structured TiOx/TiOy-Based Filamentary RRAM for Neuromorphic Applications

This paper presents the fabrication and characterization of the cross-point structure 20 × 20 μm2 RRAM with TiOx/TiOy bi-layer insulator for synaptic application in neuromorphic systems. The measured oxygen concentration of the TiOx/TiOy switching layers of the fabricated devices using X-ray photoelectron spectroscopy analysis showed that the oxygen concentration ratio between TiOx and TiOy is ~ 1.5. After electroforming at ~ 5.62 V, the on/off ratio was ~ 76 at 0.2 V with the DC sweep voltage scheme. Synaptic behaviors including long-term potentiation (LTP) and long-term depression (LTD) were performed with 50 identical pulses for the implementation of RRAM into neuromorphic systems based on convolutional neural networks. Also, linearly increased (or decreased) 25 pulses were applied to the device so that the conductance changes linearly. The resulting linear LTP and LTD characteristics were mirror-symmetric, which could maximize the accuracy. For Hebbian learning, the device also mimicked the spike-timing-dependent plasticity properties with a conductance change from − 77.79% to 96.07% using a time-division multiplexing approach.

Endurance and Retention Degradation of Intermediate Levels in Filamentary Analog RRAM

The understanding of the retention and endurance degradation behavior of different levels of filamentary analog RRAM is critical for the development of the neuromorphic computing. This paper investigates the conductance distribution of different levels during retention and endurance tests. The low conductance states and high conductance states change from the normal distribution at the beginning to asymmetric skewed distribution with baking time increasing. But intermediate states remain the normal distribution. A model is proposed to predict the conductance evolution of different levels. It is also found that endurance lifetime depends on the ratio and position of endurance window. The longer endurance lifetime is attributed to switching in a smaller high-C window. Physical mechanism of endurance degradation is discussed.

Parasitic engineering for RRAM control

The inevitable current overshoot which follows forming in filamentary RRAM devices is often perceived as a source of variability that should be minimized. This sentiment has led to efforts to curtail the overshoot by decreasing the parasitic capacitance using highly integrated 1T-1R or 1R-1R device structures. While this is readily achievable in single device test structures, it poses an intricate design constraint for memory array designs. Several papers (Degraeve et al., 2010, 2014; Fantini et al., 2013; Raghavan et al., 2013; Padovani et al., 2015) suggest that there is insufficient current to form stable filaments for small parasitic capacitances and/or low current compliance levels. Thus, the relationship between minimizing overshoot current and improved filament stability is tenuous. In this study, we utilize the forming energy-based understanding of filamentary forming to reveal that the parasitic capacitance should be optimized, rather than minimized for better filament control.

Heat Transfer in Filamentary RRAM Devices

We study the heat transport in filamentary RRAM nano-sized devices by comparing the accurate results of COMSOL modeling with simplified analytical models for two complementary mechanisms: one neglecting the radial heat transfer from the filament to the insulating host, while the other describing the radial transport through the dielectric in the absence of the filament heat transfer. For the former, we find that the earlier assumed simplification of the electrodes being ideal heat conductors is insufficient; a more adequate approximation is derived where the heat transport is determined by the adjacent proximities of the filament tips in the electrodes.We find that both complementary mechanisms overestimate the maximum temperature yet offering acceptable results. However, the two in parallel provide a better analytical approximation. In addition, we show that the Wiedemann-Franz-Lorenz law helps the analysis when the Lorenz parameter is chosen from the actual data. We present an approximate expression for the SET voltage possessing a high degree of universality and predicting that filament materials with low Lorenz numbers can be good candidates for the future low set voltage devices.

Log-Normal Statistics in Filamentary RRAM Devices and Related Systems

We present a phenomenological theory of the log-normal statistics commonly observed in filamentary resistive memory and related devices. Based on the central limit theorem that statistics are shown to emerge regardless of the underlying material properties when the processes are dominated by thermal activation or tunneling. That takes place in particular for the read-out resistances in the high-resistive (OFF) state, and the random telegraph noise amplitudes, but can be observed in the low-resistive (ON) state as well. We show that the statistics of switching times becomes log-normal when the switching is due to the field induced nucleation.

Improving Analog Switching in HfO&lt;italic&gt;x&lt;/italic&gt;-Based Resistive Memory With a Thermal Enhanced Layer

Analog RRAM with hundreds of resistance levels is an attractive device for neuromorphic computing. However, it is still very challenging to realize good analog behavior in filamentary RRAM cells. In this letter, we developed a novel methodology to improve the analog switching in filamentary RRAM. The impact of local temperature on analog switching behavior is elucidated. The transition from abrupt switching to analog switching is found at higher temperature. Based on this result, a thermal enhanced layer (TEL) is proposed to confine heat in switching layer for realizing analog RRAM. The HfO x /TEL RRAM shows analog switching characteristics with more than ten times window using 50-ns pulses. Finally, a 1-kb analog RRAM array is demonstrated with uniform analog switching, fast speed, excellent resistance window, and excellent retention properties.

Self-Heating During submicrosecond Current Transients in Pr0.7Ca0.3MnO3-Based RRAM

In filamentary RRAM, the role of self-heating in set/reset (by ion transport) is well established. However, in nonfilamentary Pr0.7Ca0.3MnO3 (PCMO) RRAM, self-heating during set/reset has not been explored. Recently, we have shown self-heating to explain nonlinearity in dc IV characteristics. In this paper, we present the observation of self-heating using transient current during pulses. We show that the cooling timescale is limited by measurement system timescale (~30 ns). The self-heating-based experimental current transient timescale is longer (50–100 ns) and is not described by simple exponential decay. To explain this behavior, self-heating in PCMO RRAM (where Joule heating and current increase create a positive feedback) is implemented into technology computer aided design simulations. Simulations produce excellent agreement with experiments. Eventually, simulations deviate from experiments when thermally assisted ionic transport during set/reset is not included in the model. To interrupt the continuous self-heating, an n-pulse-train with cooling time between pulses versus single pulse-based set/reset experiment was designed with the same peak bias time. Set/reset effectiveness degrades as n increases while effect of increasing cooling time confirmed a cooling timescale of ~30 ns. Overall, self-heating provides a consistent explanation of the transient currents. Thus, this paper establishes that self-heating considerations must be included for PCMO-based RRAM modeling and design.

Thermometry of Filamentary RRAM Devices

Since thermal effects play a major role in filamentary RRAM devices, we compare the two localized thermometry methods developed for such devices. One method is based on short-pulsed measurements and the other on the measurement of minority-carrier injection from the filament into a semiconductor electrode by thermionic emission. We carried out and compared the measurements on the same functional oxide layer. Both methods indicate that the filament temperature is at least $\sim 550$ K during device operation. Furthermore, comparison between the measured thermal resistance and the thermal simulations of both techniques shows that under the conditions of low forming current compliance ( $\sim 10~\mu \text{A}$ ), the filament dimensions are below $\sim 5$ nm. We show that the thermionic emission method is useful for high-resistance ( $>100~\text{k}\Omega )$ devices operating at low-power conditions ( $ ), whereas the pulsed thermometry is more suitable for lower resistance devices ( $ operated above 1 $\mu \text{W}$ . The average thermal resistance measured by the pulse technique decreases with applied power. Our simulations indicate that the expansion of the heated zone surrounding the filament can explain the observed reduction in thermal resistance with applied power. The underlying physics of the two methods is discussed.

Causes and consequences of the stochastic aspect of filamentary RRAM

Filamentary resistive RAM devices are affected by various sources of instability and variability. Stochastic fluctuations, caused by variability of the RRAM-driving transistor and process-induced device-to-device variations, affect both forming and set/reset transients. Also the intrinsic stochastic mechanisms that control the filament growth and shrinkage complicate the set and reset operation. In particular, RRAM operated at low current shows very broad distributions of both the low and high resistive state. Furthermore, at low read voltage a large amplitude Random Telegraph Noise is measured, caused by both electrostatic modulation of the constricted current flow and by random perturbation of the vacancies in the filament. Additional variability arises from the stochastic probability of finding an intact or a ruptured filament in high resistive state at low current compliance.