Multi-level Random Telegraph Noise Research Articles

Comprehensive physics-based RRAM compact model including the effect of variability and multi-level random telegraph noise

Resistive Random Access Memory (RRAM) technologies are a promising candidate for the development of more energy efficient circuits, for computing, security, and storage applications. However, such devices show stochastic behaviours that not only originate from variations introduced during fabrication, but that are intrinsic to their operation. Specifically, cycle-to-cycle variations cause the programmed resistive state to be randomly distributed, while Random Telegraph Noise (RTN) introduces random current fluctuations over time. These phenomena can easily affect the reliability and performance of RRAM-based circuits. Therefore, designing such circuits requires accurate compact models. Although several RRAM compact models have been proposed in the literature, these are rarely implemented following the programming best-practice for improving the simulator convergence, and a compact model that is able to reproduce the device characteristic including thermal effects, RTN, and variability in multiple operating conditions using a single set of parameters is still missing. Also, only a few works in the literature describe the procedure to calibrate such compact models, and even fewer address the calibration of the variability on experimental data. In this work, we extend the UniMORE RRAM physics-based compact model by developing and validating two variability models, (i) a comprehensive variability model which can reproduce the effect of cycle-to-cycle variability in multiple operating conditions, and (ii) a simplified version that requires fewer calibration data and enables to reproduce cycle-to-cycle variations in specific operating conditions. The model is implemented following Verilog-A programming best-practices and validated on data from three RRAM technologies from the literature and experimentally on TiN/Ti/HfOx/TiN devices, and the relation between experimental data and the variability model parameters is described.

Multilevel RTN Removal Tools for Dynamic FBG Strain Measurements Corrupted by Peak-Splitting Artefacts.

Strain measurements using fibre Bragg grating (FBG) optical sensors are becoming ever more commonplace. However, in some cases, these measurements can become corrupted by sudden jumps in the signal, which manifest as spikes or step-like offsets in the data. These jumps are caused by a defect in the FBG itself, which is referred to as peak-splitting. The effects of peak splitting artefacts on FBG strain measurements show similarities with an additive multi-level telegraph noise process, in which the amplitudes and occurrences of the jumps are related to fibre deformation states. Whenever it is not possible to re-assess the raw spectral data with advanced peak tracking software, other means for removing the jumps from the data have to be found. The two methods presented in this article are aimed at removing additive multi-level random telegraph noise (RTN) from the raw data. Both methods are based on denoising the sample wise difference signal using a combination of an outlier detection scheme followed by an outlier replacement step. Once the difference signal has been denoised, the cumulative sum is used to arrive back at a strain time series. Two methods will be demonstrated for reconstructing severely corrupted strain time series; the data for this verification has been collected from sub-soil strain measurements obtained from an operational offshore wind-turbine. The results show that the proposed methods can be used effectively to reconstruct the dynamic content of the corrupted strain time series. It has been illustrated that errors in the outlier replacements accumulate and can cause a quasi-static drift. A representative mean value and drift correction are proposed in terms of an optimization problem, which maximizes the overlap between the reconstruction and a subset of the raw data; whereas a high-pass filter is suggested to remove the quasi static drift if only the dynamic band of the signal is of interest.

Reduction of random telegraph noise by high-pressure deuterium annealing for p-type omega-gate nanowire FET

In this work, we studied the effect of high-pressure deuterium annealing (HPDA) on a p-type omega-gate nanowire field effect transistor by random telegraph noise (RTN) signal analysis. After HPDA under conditions of 400 °C and 10 atm for 30 min, IOFF decreases by 41.2% and ION increases by up to 5.4%. Also, subthreshold swing (SS) is reduced from 72 mV dec−1 to 70 mV dec−1. In RTN analysis, multi-level RTN is reduced to single-level RTN due to the passivation of a fast trap site by HPDA. ΔID/ID is also decreased 1.3 and 1.1 times at |VOV| = 0.2 V and 0.4 V, respectively. From the low-frequency noise analysis, the reduction of trap density is observed by 86% at |VOV| = 0.4 V after HPDA. Through these results, we found that the HPDA reduces traps of gate dielectric and improves the quality of the interface between gate dielectric and NW channel in p-type OGNW FET.

Impact of Varying Strain Energy in Oxide on Random Telegraph Noise and Associated Time Constants in Silicon Nanowire pMOSFETs

Multilevel random telegraph noise in gate-all-around silicon nanowire pMOSFET shows gate voltage overdrive-dependent interstate transitions, statistical count of which indicates the existence of oxide traps with different time constants. Following the detail extraction of the capture and emission time with gate bias, both have been found to deviate from the usual trend, as predicted by the conventional Shockley–Read–Hall statistics. Two traps in the gate–oxide have been found, in which the near interface is found to respond through the altered RTN activation energy barrier by spatially varying oxide residual strain energy, whereas the farther responds under the weak influence of the oxide strain energy. On the other hand, the emission time of near interface trap has been found to follow similar strain influenced activation barrier, but the magnitude of the emission time of the farther trap shows the hole emission through the p+ polysilicon gate–oxide interfacial trap, while favored by the electrostatic field in oxide. From RTN distributions and time lag plots, interstate transitions and state suppression in RTN are explained under the framework of two-trap postulate, in order to elucidate the unusual gate bias dependence of the measured trap time constants in silicon nanowire pMOSFETs.

Random telegraph noise in 2D hexagonal boron nitride dielectric films

This study reports the observation of low frequency random telegraph noise (RTN) in a 2D layered hexagonal boron nitride dielectric film in the pre- and post-soft breakdown phases using conductive atomic force microscopy as a nanoscale spectroscopy tool. The RTN traces of the virgin and electrically stressed dielectric (after percolation breakdown) were compared, and the signal features were statistically analyzed using the Factorial Hidden Markov Model technique. We observe a combination of both two-level and multi-level RTN signals in h-BN, akin to the trends commonly observed for bulk oxides such as SiO2 and HfO2. Experimental evidence suggests frequent occurrence of unstable and anomalous RTN traces in 2D dielectrics which makes extraction of defect energetics challenging.

RTN in Scaled Transistors for On-Chip Random Seed Generation

Random numbers play a vital role in cryptography, where they are used to generate keys, nonce, one-time pads, and initialization vectors for symmetric encryption. The quality of random number generator (RNG) has significant implications on vulnerability and performance of these algorithms. A pseudo-RNG uses a deterministic algorithm to produce numbers with a distribution very similar to uniform. True RNGs (TRNGs), on the other hand, use some natural phenomenon/process to generate random bits. They are nondeterministic, because the next number to be generated cannot be determined in advance. In this paper, a novel on-chip noise source, random telegraph noise (RTN), is exploited for simple and reliable TRNG. RTN, a microscopic process of stochastic trapping/detrapping of charges, is usually considered as a noise and mitigated in design. Through physical modeling and silicon measurement, we demonstrate that RTN is appropriate for TRNG, especially in highly scaled MOSFETs. Due to the slow speed of RTN, we purpose the system for on-chip seed generation for random number. Our contributions are: 1) physical model calibration of RTN with comprehensive 65- and 180-nm transistor measurements; 2) the scaling trend of RTN, validated with silicon data down to 28 nm; 3) design principles to achieve 50% signal probability by using intrinsic RTN physical properties, without traditional postprocessing algorithms, the generated sequence passes the National Institute of Standards and Technology (NIST) tests; and 4) solutions to manage realistic issues in practice, including multilevel RTN signal, robustness to voltage and temperature fluctuations and the operation speed.

Single vacancy defect spectroscopy on HfO2 using random telegraph noise signals from scanning tunneling microscopy

Random telegraph noise (RTN) measurements are typically carried out at the device level using standard probe station based electrical characterization setup, where the measured current represents a cumulative effect of the simultaneous response of electron capture/emission events at multiple oxygen vacancy defect (trap) sites. To better characterize the individual defects in the high-κ dielectric thin film, we propose and demonstrate here the measurement and analysis of RTN at the nanoscale using a room temperature scanning tunneling microscope setup, with an effective area of interaction of the probe tip that is as small as 10 nm in diameter. Two-level and multi-level RTN signals due to single and multiple defect locations (possibly dispersed in space and energy) are observed on 4 nm HfO2 thin films deposited on n-Si (100) substrate. The RTN signals are statistically analyzed using the Factorial Hidden Markov Model technique to decode the noise contribution of more than one defect (if any) and estimate the statistical parameters of each RTN signal (i.e., amplitude of fluctuation, capture and emission time constants). Observation of RTN at the nanoscale presents a new opportunity for studies on defect chemistry, single-defect kinetics and their stochastics in thin film dielectric materials. This method allows us to characterize the fast traps with time constants ranging in the millisecond to tens of seconds range.

A Complete Statistical Investigation of RTN in HfO<sub>2</sub>-Based RRAM in High Resistive State

In this paper, we investigate the random telegraph noise (RTN) in hafnium-oxide resistive random access memories in high resistive state (HRS). The current fluctuations are analyzed by decomposing the multilevel RTN signal into two-level RTN traces using a factorial hidden Markov model approach, which allows extracting the properties of the traps originating the RTN. The current fluctuations, statistically analyzed on devices with a different stack reset at different voltages, are attributed to the activation and deactivation of defects in the oxidized tip of the conductive filament, assisting the trap-assisted tunneling transport in HRS. The physical mechanisms responsible for the defect activation are discussed. We find that RTN current fluctuations can be due to either the coulomb interaction between oxygen vacancies (normally assisting the charge transport) and the electron charge trapped at interstitial oxygen defects, or the metastable defect configuration of oxygen vacancies assisting the electron transport in HRS. A consistent microscopic description of the phenomenon is proposed, linking the material properties to the device performance.

Statistical analysis of random telegraph noise in HfO2-based RRAM devices in LRS

In this work, we present a thorough statistical characterization of Random Telegraph Noise (RTN) in HfO2-based Resistive Random Access Memory (RRAM) cells in Low Resistive State (LRS). Devices are tested under a variety of operational conditions. A Factorial Hidden Markov Model (FHMM) analysis is exploited to extrapolate the properties of the traps causing multi-level RTN in LRS. The trapping and de-trapping of charge carriers into/out of defects located in the proximity of the conductive filament results in a shielding effect on a portion of the conductive filament, leading to the observed RTN current fluctuations. It is found that both oxygen vacancies and oxygen ions defects may be responsible for the observed RTN. The variations of the current observed at subsequent set/reset cycles are instead attributed to the stochastic variations in the filament due to oxidation/reduction processes during reset and set operations, respectively.

Dedicated random telegraph noise characterization of Ni/HfO2-based RRAM devices

In this work, random telegraph noise (RTN) associated to discrete current fluctuations in the high resistive state of Ni/HfO2-based RRAM devices is investigated. For this purpose, a dedicated software tool has been developed to control the instrumentation and to perform successive and smart RTN measurements in the time domain. After data acquisition, the advanced Weighted Time Lag (WTL) method is employed to accurately identify the contribution of multiple electrically active defects in multilevel RTN signals. Finally, the internal dynamics of trapping and de-trapping processes through the defects close to the filamentary path and its dependence on voltage and time are analyzed.

A study on HfO2 RRAM in HRS based on I–V and RTN analysis

This paper presents a statistical characterization of random telegraph noise (RTN) in hafnium-oxide-based resistive random access memories (RRAMs) in high resistive state (HRS). Complex RTN signals are analyzed exploiting a Factorial Hidden Markov Model (FHMM) approach, which allows to derive the statistical properties of the RTN signals, directly related to the physical properties of the traps responsible for the multi-level RTN measured in these devices. Noise characteristics in different reset conditions are explored through consecutive switching cycles. Noise spectral analysis is also performed to fully support the investigation. An RRAM compact model is also exploited to estimate the physical properties of the conductive filament and of the dielectric barrier from simple I–V data. These tools are combined together to prove the existence of a direct statistical relation between the reset conditions, the volume of the dielectric barrier created during the reset operation and the average number of active traps contributing to the RTN.

Factorial Hidden Markov Model analysis of Random Telegraph Noise in Resistive Random Access Memories


 This paper presents a new technique to analyze the characteristics of multi-level random telegraph noise (RTN). RTN is defined as an abrupt switching of either the current or the voltage between discrete values as a result of trapping/de-trapping activity. RTN signal properties are deduced exploiting a factorial hidden Markov model (FHMM). The proposed method considers the measured multi-level RTN as a superposition of many two-levels RTNs, each represented by a Markov chain and associated to a single trap, and it is used to retrieve the statistical properties of each chain. These properties (i.e. dwell times and amplitude) are directly related to physical properties of each trap.

Observation of Thermally-Activated Electron Traps in GaAs/AlAs/GaAs Heterostructures in Low-Frequency Noise Measurements

-dopinginsidethebarrierwehaveobservedfluctuationsofthetunnelingcurrentwhichexhibited large Lorentzian noise with intensity depending on biasing voltage. We have shown that Lorentziannoise originates from multilevel random telegraph noise of the small number of fluctuators which influence thetunnelingprocess. Time-domainanalysisofthecurrentnoisemeasuredfortemperaturesbetween4.2Kand50Kenabledtodeterminethethermalactivationenergiesofthesefluctuatorslyingbetween0.8and3meV.PACS:73.50.Td,73.40.Gk

Investigation of Random Telegraph Noise in Gate-Induced Drain Leakage and Gate Edge Direct Tunneling Currents of High-$k$ MOSFETs

Random telegraph noise (RTN) in gate-induced drain leakage (GIDL) and gate edge direct tunneling (EDT) leakage currents under GIDL bias conditions were characterized in MOSFETs with a high-k gate dielectric for the first time. The RTNs were analyzed through systematic measurement and calculation. The results indicate that a high-current state in a GIDL current can be attributed to electron capture due to thermal emission. However, electron emission from a trap was mainly affected by gate bias. Both capture and emission times in the RTN of the EDT current had gate bias dependence. Moreover, multilevel RTN waveforms were detected in a device, and our analysis indicated that the multilevel RTN is the result of the combination of the RTNs of the GIDL and EDT currents. The analysis also indicated that two independent traps in the high- k gate dielectric can produce a four-level RTN in the GIDL current. This paper provides the fundamental physics required to understand such leakages in nanoscale MOSFETs and devices that utilize band-to-band tunneling.