Telegraph Noise Research Articles

AC RTN: Testing, Modeling, and Prediction

Random telegraph noise (RTN) adversely induces time dependent device-to-device variations and requires modeling to optimize circuit design. Many early works were focused under dc test conditions, although digital circuits typically operate under ac conditions and it has been reported that ac RTN is substantially different from dc RTN. Tests on ac RTN were carried out mainly on individual traps, and a reliable statistical distribution of trap time constants for ac RTN is still missing. This prevents verifying the statistical accuracy of Monte Carlo ac RTN simulation based on compact models, especially in terms of their ability to predict ac RTN as time window increases. Recently, an integral methodology has been proposed for dc RTN, which can not only model it at short time but also predict it at long time. By introducing the concept of effective charged traps, the need for statistical distribution of trap time constants is removed, making RTN prediction similar to aging prediction. The objectives of this work are to report statistical experimental ac RTN data and to test the applicability of integral methodology to them. For the first time, it will be shown that a model extracted from a time window of 7.8 s can be used to predict the statistical distribution of long-term ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 10^{{4}}$ </tex-math></inline-formula> s) ac RTN. The dependence of ac RTN on frequency and time window is analyzed, and the contributions of carrier tunneling from gate and substrate are assessed.

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.

Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching

Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states.

Energy landscape study by telegraph noise of domain wall motion

The energy barrier landscape in-between two adjacent pinning sites of magnetic domain wall was investigated by telegraph noise of domain wall motion. The telegraph noise provided numerous depinning times for each pinning site, from which the depinning energy barrier characteristics were extracted. By generating the telegraph noise under application of magnetic field and electric current, the energy barrier landscape could be reconstructed with the barrier height and lateral size of the adjacent pinning sites. The lateral size fits well with other independent estimation based on the signal level with the focused laser beam, providing the validity of the present approach.

Disentanglement Dynamics in Nonequilibrium Environments.

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Long-time protection of thermal correlations in a hybrid-spin system under random telegraph noise.

The engineering features of transmitting mediums and their impact on different characteristics of a quantum system play a significant role in the efficient performance of nonlocal protocols. For this purpose, the dynamics of open quantum systems and coupling mediums remain a pathway. In this work, we investigate the dynamics of quantum correlations using negativity, uncertainty-induced nonlocality, and local quantum Fisher information in a hybrid qubit-qutrit thermal state when coupled with a magnetic field and influenced by random telegraph noise. Different features of the system parameters are taken into account while designing longer preservation of qubit-qutrit correlations. We show that the temperature has an inverse impact on the initial values of negativity, uncertainty-induced nonlocality, and local quantum Fisher information. When the magnetic field is characterized by different features, the entanglement, nonlocality, and Fisher information show a variety of dynamical maps, assuring their distinct nature. In addition, the qubit-qutrit correlations undergo repeated revivals when the configuration is restricted to the non-Markovian regime. On the other hand, an exponential drop with a single minimum is observed in the Markovian regime of the coupled field. Most importantly, our findings reveal that the present coupled fields have several advantages that can be leveraged to generate the optimal degree of entanglement, nonlocality, and local quantum Fisher information preservation in quantum dynamical maps.

Entropic uncertainty and quantum correlations dynamics in a system of two qutrits exposed to local noisy channels

We address the dynamics of the lower bound of geometric quantum discord and quantum-memory-assisted entropic uncertainty in a two-qutrit system when exposed to classical channels characterized by power-law (PL) and random telegraph (RT) noises. The system-channel coupling strategy is examined in two contexts: common qutrit-environment (CQE) and different qutrit-environment (DQE) configurations. We show that the geometric quantum discord functions remain anti-correlated with entropic uncertainty and decline as uncertainty appears in the system. The rate of entropic uncertainty appearance seems more prevalent than the decline rate of quantum discord function, suggesting that uncertainty causes the quantum correlations to fade in quantum systems. We find that non-local correlations estimated by the lower bound of geometric quantum discord are not destroyed even at the maximum entropic disorder and entropic uncertainty. In addition, the efficacy of entropic uncertainty and the lower bound is strongly influenced by the state’s purity factor, with the former being more robust at higher purity values and the latter at lower purity values. All the parameters impact entropic uncertainty, however, the mixedness of the state is noticed to greatly alter the generation of quantum memory. Besides, PL noise caused Markovian behavioral dynamics, and the RT noise allowed non-Markovian dynamics, while the latter remains more resourceful for the quantum correlations preservation and entropic uncertainty suppression. We also demonstrate how to model longer quantum correlations and provide optimal parameter settings for suppressing the dephasing and entropic uncertainty effects.

A Novel Encrypted Computing-in-Memory (eCIM) by Implementing Random Telegraph Noise (RTN) as Keys Based on 55 nm NOR Flash Technology

A novel encrypted Computing-in-Memory (eCIM) architecture is proposed based on 55nm NOR Flash memory technology, wherein the current fluctuations caused by random telegraph noise (RTN) in flash cells are utilized as the intrinsic encryption source. Furthermore, aiming at the low-power consumption with high bit-density, the near-subthreshold region of the flash cell is used for 2-bit/cell operation. It is demonstrated that, in the designed 32-bit floating-point (FP) calculation architecture, ultra-low power dissipation (0.24 pJ/bit) can be achieved with high calculation accuracies after the decryption.

Single- Versus Multi-Step Trap Assisted Tunneling Currents—Part II: The Role of Polarons

Using the framework developed in the first part of this work, we demonstrate the capabilities of the extended two-state nonradiative multi-phonon (NMP) model by reproducing leakage current characteristics of two selected technologies. First, we identify the temperature-activated leakage mechanism in SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stacks using a tens of nanometer thick thermally grown oxide as trap-assisted tunneling (TAT) through defects. Interestingly, this effect can be reproduced with the same parameters in a SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stack with deposited oxide. Our simulations demonstrate that these charge transition centers are distributed within only a few nanometers from the SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface. The low thermal activation of the leakage current is linked to the low relaxation energies of the involved traps compared with those typically involved in bias temperature instability (BTI) and Random Telegraph Noise (RTN). Second, a similar mechanism can explain TAT characteristics and transient charge trapping currents in Metal–Insulator–Metal (MIM) capacitors with a ZrO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> insulating layer. By comparison of our model parameters to theoretical density functional theory (DFT) calculations, we identify self-trapped electrons (polarons) as a likely cause for these effects, as they have the required low relaxation energies.

Strong increase in ultrasound attenuation below Tc in Sr2RuO4 : Possible evidence for domains

Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using resonant ultrasound spectroscopy (RUS). We find that the attenuation for compressional sound increases by a factor of seven immediately below T$_\mathrm{c}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-T$_\mathrm{c}$ ($d$-wave) superconductors. We find our observations to be most consistent with the presence of domain walls between different configurations of the superconducting state. The fact that we observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally-degenerate superconducting order parameters that are not related to each other by symmetry. Whatever the mechanism, a factor of seven increase in sound attenuation is a singular characteristic with which any potential theory of the superconductivity in Sr$_2$RuO$_4$ must be reconciled.

Spatially Controlled Generation and Probing of Random Telegraph Noise in Metal Nanocrystal Embedded HfO2 Using Defect Nanospectroscopy

Random telegraph noise (RTN) is often considered a nuisance or, more critically, a key reliability challenge for miniaturized semiconductor devices. However, this picture is gradually changing as recent works have shown emerging applications based on the inherent randomness of the RTN signals in state-of-the-art technologies, including true random number generator and IoT hardware security. Suitable material platforms and device architectures are now actively explored to bring these technologies from an embryonic stage to practical application. A key challenge is to devise material systems, which can be reliably used for the deterministic creation of localized defects to be used for RTN generation. Toward this goal, we have investigated RTN in Au nanocrystal (Au-NC) embedded HfO2 stacks at the nanoscale by combining conduction atomic force microscopy defect spectroscopy and a statistical factorial hidden Markov model analysis. With a voltage applied across the stack, there is an enhanced asymmetric electric field surrounding the Au-NC. This in turn leads to the preferential generation of atomic defects in the HfO2 near the Au-NC when voltage is applied to the stack to induce dielectric breakdown. Since RTN arises from various electrostatic interactions between closely spaced atomic defects, the Au-NC HfO2 material system exhibits an intrinsic ability to generate RTN signals. Our results also highlight that the spatial confinement of multiple defects and the resulting electrostatic interactions between the defects provides a dynamic environment leading to many complex RTN patterns in addition to the presence of the standard two-level RTN signals. The insights obtained at the nanoscale are useful to optimize metal nanocrystal embedded high-κ stacks and circuits for on-demand generation of RTN for emerging random number applications.

Local bifurcation with spin-transfer torque in superparamagnetic tunnel junctions

Modulation of the energy landscape by external perturbations governs various thermally-activated phenomena, described by the Arrhenius law. Thermal fluctuation of nanoscale magnetic tunnel junctions with spin-transfer torque (STT) shows promise for unconventional computing, whereas its rigorous representation, based on the Néel-Arrhenius law, has been controversial. In particular, the exponents for thermally-activated switching rate therein, have been inaccessible with conventional thermally-stable nanomagnets with decade-long retention time. Here we approach the Néel-Arrhenius law with STT utilising superparamagnetic tunnel junctions that have high sensitivity to external perturbations and determine the exponents through several independent measurements including homodyne-detected ferromagnetic resonance, nanosecond STT switching, and random telegraph noise. Furthermore, we show that the results are comprehensively described by a concept of local bifurcation observed in various physical systems. The findings demonstrate the capability of superparamagnetic tunnel junction as a useful tester for statistical physics as well as sophisticated engineering of probabilistic computing hardware with a rigorous mathematical foundation.

Readout of Parafermionic States by Transport Measurements

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.

Quantum Conductance in Memristive Devices: Fundamentals, Developments, and Applications.

Quantum effects in novel functional materials and new device concepts represent a potential breakthrough for the development of new information processing technologies based on quantum phenomena. Among the emerging technologies, memristive elements that exhibit resistive switching, which relies on the electrochemical formation/rupture of conductive nanofilaments, exhibit quantum conductance effects at room temperature. Despite the underlying resistive switching mechanism having been exploited for the realization of next-generation memories and neuromorphic computing architectures, the potentialities of quantum effects in memristive devices are still rather unexplored. Here, a comprehensive review on memristive quantum devices, where quantum conductance effects can be observed by coupling ionics with electronics, is presented. Fundamental electrochemical and physicochemical phenomena underlying device functionalities are introduced, together with fundamentals of electronic ballistic conduction transport in nanofilaments. Quantum conductance effects including quantum mode splitting, stability, and random telegraph noise are analyzed, reporting experimental techniques and challenges of nanoscale metrology for the characterization of memristive phenomena. Finally, potential applications and future perspectives are envisioned, discussing how memristive devices with controllable atomic-sized conductive filaments can represent not only suitable platforms for the investigation of quantum phenomena but also promising building blocks for the realization of integrated quantum systems working in air at room temperature.

An Integral Methodology for Predicting Long-Term RTN

Random telegraph noise (RTN) adversely impacts circuit performance and this impact increases for smaller devices and lower operation voltage. To optimize the circuit design, many efforts have been made to model RTN. RTN is highly stochastic, with significant device-to-device variations (DDVs). Early works often characterize individual traps first and then group them together to extract their statistical distributions. This bottom-up approach suffers from limitations in the number of traps it is possible to measure, especially for the capture and emission time constants, calling the reliability of extracted distributions into question. Several compact models have been proposed, but their ability to predict long-term RTN is not verified. Many early works measured RTN only for tens of seconds, although a longer time window increases RTN by capturing slower traps. The aim of this work is to propose an integral methodology for modeling RTN and, for the first time, to verify its capability of predicting the long-term RTN. Instead of characterizing properties of individual traps/devices, the RTN of multiple devices was integrated to form one dataset for extracting their statistical properties. This allows using the concept of effective charged traps (ECTs) and transforms the need for time constant distribution to obtain the kinetics of ECT, making long-term RTN prediction similar to predicting aging. The proposed methodology opens the way for assessing RTN impact within a window of ten years by efficiently evaluating the probability of a device parameter at a given level.

Intrinsic variation effect in memristive neural network with weight quantization

To analyze the effect of the intrinsic variations of the memristor device on the neuromorphic system, we fabricated 32 × 32 Al2O3/TiO x -based memristor crossbar array and implemented 3 bit multilevel conductance as weight quantization by utilizing the switching characteristics to minimize the performance degradation of the neural network. The tuning operation for 8 weight levels was confirmed with a tolerance of ±4 μA (±40 μS). The endurance and retention characteristics were also verified, and the random telegraph noise (RTN) characteristics were measured according to the weight range to evaluate the internal stochastic variation effect. Subsequently, a memristive neural network was constructed by off-chip training with differential memristor pairs for the Modified National Institute of Standards and Technology (MNIST) handwritten dataset. The pre-trained weights were quantized, and the classification accuracy was evaluated by applying the intrinsic variations to each quantized weight. The intrinsic variations were applied using the measured weight inaccuracy given by the tuning tolerance, RTN characteristics, and the fault device yield. We believe these results should be considered when the pre-trained weights are transferred to a memristive neural network by off-chip training.

Understanding random telegraph noise in two-dimensional BP/ReS2 heterointerface

Black phosphorus (BP)-based broken gap heterojunctions have attracted significant attention mainly owing to its wide thickness-dependent Fermi level, offering opportunities to demonstrate various carrier transport characteristics and high performing optoelectronic applications. However, the interfacial effects on the carrier scattering mechanism of the two-dimensional (2D) broken gap heterojunctions are unclear. Herein, we discuss the origin of random telegraph noise of multilayer BP/ReS2 heterojunction diode, in particular, at the direct tunneling (DT) conduction regime. The gate-tunable diode characteristic of BP/ReS2 heterojunction allows one to unveil systematically the transition of the charge fluctuation mechanism from drift-diffusion to the DT regime. Unlike individual BP and ReS2 devices, the current noise histogram obtained from the BP/ReS2 heterojunction device exhibits exclusively two dominant peaks at the DT regime. We ascribed this distinct low-frequency noise feature representing the presence of random telegraph signal to the BP/ReS2 interfacial traps by taking into account of the inherent direct tunneling current conduction mechanism. In addition, the electrostatic bias-dependent power spectrum density manifests clearly that the dominant scattering mechanism is the carrier number fluctuation rather than tunneling barrier height fluctuation at the BP/ReS2 heterointerface. This study elucidates the carrier transport and the charge fluctuation mechanism at the 2D heterostructure interface.

Extinction and positive recurrence of a regime‐switching HIV/AIDS model with treatment and standard incidence

In this paper, we investigate the dynamics of a high‐dimensional human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) model with treatment and standard incidence, which is perturbed by telegraph noise. The switching is formulated by a continuous time Markov chain. Firstly, we show the existence and uniqueness of the global positive solution. Then, conditions for extinction of the disease are established. Moreover, through constructing suitable Lyapunov functions, we derive sufficient conditions for the existence of positive recurrence of the solutions. Positive recurrence implies all the individuals can coexist and persist in the long term. Finally, numerical experiments are performed for supporting the theoretical results.

Investigation of Random Telegraph Noise Under Different Programmed Cell Vt Levels in Charge Trap Based 3D NAND Flash

As an important constraint on the threshold voltage (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ) distribution, the random telegraph noise (RTN) has attracted much attention due to the widely used multi-bit-per-cell technology in 3D NAND flash. This work investigated the physical mechanisms of RTN in charge- trap-based 3D NAND flash. According to statistical 3D TCAD simulation analysis, the fringing field from the control gate and the random discrete nitride trapped charges, two competitive mechanisms, are proposed to be responsible for the non-monotonic RTN behavior. As the programmed cell V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> level increases, the increasing fringing field from the control gate reduces the current-path percolation effect and the RTN amplitude. However, once the random discrete nitride trapped charges start to dominate the percolation current path, the RTN amplitude increases significantly. Instructively, the clarification of RTN competitive mechanisms contributes to compacting V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> distributions specifically in multi-level 3D NAND flash.

On the chaotic nature of random telegraph noise in unipolar RRAM memristor devices

Random telegraph noise (RTN) owns its very name to its assumed stochastic nature. In this paper, we follow up previous works that questioned this stochastic nature, and we investigate this assumption using experimentally measured noise coming from properly biased Ni/HfO2 unipolar Resistive RAM memristor nanodevices. We have used established, well–known tools from nonlinear theory to examine the current–noise temporal series. Evaluation results show that this series appears to exhibit not a stochastic, but a deterministic chaotic behavior, also demostrating interesting fractal characteristics in 2D and 3D phase space projections. The presented results clearly advocate for a strong component of complex (chaotic) fluctuation of deterministic origin, instead of a typical (fully stochastic) RTN. This result could pave the path for an enhanced understanding of the mechanisms behind RTN emergence, as well as improve its noise models.