RTNinja: A generalized machine learning framework for analyzing random telegraph noise signals in nanoelectronic devices

TL;DR

The paper tackles the challenge of random telegraph noise (RTN) in nanoelectronics by introducing RTNinja, a generalized, fully automated framework for unsupervised RTN analysis. It combines LevelsExtractor (Bayesian level identification and de-noising with BIC-based model selection) and SourcesMapper (generation and evaluation of candidate N-source decompositions using Markov transitions and affinity clustering) to deconvolve RTN signals without prior knowledge of source count or distributions. Extensive Monte Carlo validation on 7,000 synthetic datasets shows RTNinja can reconstruct signals and extract source amplitudes and activities across varying SNRs and complexities, though performance degrades with high noise and many sources. This framework enables large-scale RTN benchmarking, reliability assessment, and defect-physics exploration in state-of-the-art nanoelectronics and emerging quantum technologies.

Abstract

Random telegraph noise is a prevalent variability phenomenon in nanoelectronic devices, arising from stochastic carrier exchange at defect sites and critically impacting device reliability and performance. Conventional analysis techniques often rely on restrictive assumptions or manual interventions, limiting their applicability to complex, noisy datasets. Here, we introduce RTNinja, a generalized, fully automated machine learning framework for the unsupervised analysis of random telegraph noise signals. RTNinja deconvolves complex signals to identify the number and characteristics of hidden individual sources without requiring prior knowledge of the system. The framework comprises two modular components: LevelsExtractor, which uses Bayesian inference and model selection to denoise and discretize the signal, and SourcesMapper, which infers source configurations through probabilistic clustering and optimization. To evaluate performance, we developed a Monte Carlo simulator that generates labeled datasets spanning broad signal-to-noise ratios and source complexities; across 7000 such datasets, RTNinja consistently demonstrated high-fidelity signal reconstruction and accurate extraction of source amplitudes and activity patterns. Our results demonstrate that RTNinja offers a robust, scalable, and device-agnostic tool for random telegraph noise characterization, enabling large-scale statistical benchmarking, reliability-centric technology qualification, predictive failure modeling, and device physics exploration in next-generation nanoelectronics.

Figures (9)

• Figure 1: (a) Schematic illustration of RTN signal analysis, a descriptive type of unsupervised learning problem, using the RTNinja machine learning framework. Input to the framework is a convoluted RTN signal resulting from the activity of a hidden number of individual sources, along with intrinsic noise fluctuations. Without any predefined estimates of the underlying information, RTNinja analyzes the signal and outputs the total number of individual sources and their corresponding activity. Ideally, the output is an exact reproduction of the input sources ($N = N'$) with their corresponding activity. (b) Monte Carlo-based RTN simulator. The number of sources ($N$) is sampled from a Poisson distribution, where each source has three attributes: amplitude ($\Delta^n$), on-state activity, and off-state activity. Both state activities follow exponential distributions with the primary distribution parameters, on-state mean value ($\langle\tau_{on}^{n}\rangle$) and off-state mean value ($\langle\tau_{off}^{n}\rangle$), are sampled from a log-normal distribution. Extrinsic noise is added to the RTN signal in proportion to the overall signal magnitude. (c) The example dataset is simulated for a total time of $10^{3}$ units (e.g., seconds) at a sampling rate of 50 samples per unit. This particular signal constitutes four sources, with amplitudes within the range ($4\times10^{-1}$, $3$) and mean activities within the range ($3\times10^{-1}$, $5\times10^{2}$). (d) Workflow of the RTNinja machine learning framework. Observable information, that is, an experimental RTN signal, is provided as input data to the framework. RTNinja analyzes this information and outputs the hidden individual RTN sources and their corresponding progression characteristics. The framework consists of two modules: LevelsExtractor and SourcesMapper. LevelsExtractor identifies discrete constant levels and builds an optimal model of the input data. SourcesMapper finds the most likely solution, that is, the number of sources along with their amplitudes and activities, that explains the optimal model produced by LevelsExtractor. Each module consists of three sub-modules, with the objectives and underlying approaches of each sub-module clearly outlined.
• Figure 2: Working details and results of the LevelsExtractor module. (a) Flowchart of the Bayesian algorithm, which identifies the most suitable hypothesis (number of levels and their model parameters) based on observed data using Bayes' theorem. The hypothesis is updated if the posterior probability falls below a user-defined threshold ($10^{-15}$ in this case). The conditional probability, $P(d_t \mid H)$, is calculated using a custom CDF-based proximity estimator, representing the likelihood of a data point belonging to its nearest level ($P = 1$ if $d_{t} = \mu_{i}$). (b) Flowchart of the De-noiser, which assigns data points to their nearest levels, applying a custom continuity condition (hyperparameter set to $c$ = 3 data points) to ensure statistical significance for transitions identified as RTN signatures. (c) The Bayesian algorithm extracts 11 levels, with the total weighted distribution of these levels (red) overlapping the dataset histogram (blue), and $\mu$ values of levels represented by dashed lines. (d) Input data are successfully reconstructed, with $\mu$ values of the 11 levels represented by dashed lines. (e) Standard deviation is estimated a priori using a median moving range method ($\sigma_{MMR}$). While a minority of the input data contains the RTN transition information, the remaining portion corresponds to experimental noise at a constant level, leading to $\sigma_{MMR}$ estimation. Multiple feature models are built by varying the initial $\sigma$ value input to the Bayesian algorithm. BIC values are computed for all models, where the optimal $\sigma$ value and the corresponding feature model are determined by the lowest BIC value. This does not necessarily coincide with $\sigma_{MMR}$ since fast and small-amplitude RTN sources might remain undetectable.
• Figure 3: (a) Flowchart illustrating the generation of multiple $N$-source sets. The output information from the LevelsExtractor module is used to extract transition probabilities between levels and all possible source amplitudes. Clusters and their representative amplitudes are identified in the normalized $P_{T}-\Delta$ space, enabling the combinatorial generation of $N$-sized $\Delta$ sets. (b) Markov transition matrix depicting the transition probabilities between the 11 Bayesian levels. Diagonal elements are masked for clarity, as they represent the high likelihood of remaining at the same level. The limited observability of transitions is evident in the broad distribution of activity rates associated with the hidden sources. (c) Result of the AP clustering algorithm applied to the normalized $P_{T}-\Delta$ space, revealing 13 clusters and their representative points (indicated with bold markers). (d) Flowchart for baseline estimation. For each candidate solution, the corresponding $2^{N}$-configuration set is generated. A range of baseline values is tested for each set, with the optimal baseline defined as the one that best matches the total distribution of Bayesian levels, determined using a maximum log-likelihood approach. (e) Example of a 16-configuration set with a specific baseline value derived from a candidate solution (4-source set), mapped onto the Bayesian levels distribution. The intersectional probability density values are used to compute the log-likelihood. Since only 11 levels are observed, some configurations may not align with any level, which does not pose an issue.
• Figure 4: (a) Cost function designed to evaluate candidate solutions, incorporating both static and dynamic metrics. The static metric maps each Bayesian level to its closest state configuration, quantifying the goodness of match based on proximity. The dynamic metric involves data reconstruction using these mapped state configurations, where simultaneous switching of multiple sources during a transition is treated as a violation. This process is exemplified for a 2-source system with four possible configurations, illustrating that transitions involving both sources changing their activity state are counted as violations. (b) Data reconstruction results for the optimal candidate solution, demonstrating successful signal reconstruction with only 5 violations out of a total of 1086 transitions. (c) Deconvolution of the optimal candidate solution into its four hidden sources, compared with the ground truth. The slow-activity sources (#1 and #3) are accurately extracted, with amplitude deviations within $\pm 0.5\%$. For the fast-activity sources (#2 and #4), the extracted amplitudes are within $\pm 1.7\%$, although some activity signatures are either not captured or shifted in occurrence instances. These discrepancies may arise from the de-noiser, where continuity constraints affect the quantized data, and/or from cost function constraints related to violated transitions.
• Figure 5: Performance of the RTNinja framework at 1%, 5%, and 30% noise levels across all dataset complexities. (a) Matrix showing the number of datasets corresponding to each combination of true and estimated source counts, with diagonal entries indicating correct matches. (b) Activity match accuracy for mapped input--output sources, grouped by dataset complexity. The number of detected sources and probability of achieving $>$95% activity match is indicated. (c) Accurate amplitude extraction is demonstrated, independent of noise level and data complexity. Blue squares indicate noise bounds; dashed lines mark $0.5\times$ and $2\times$ amplitude thresholds, with percentages showing sources within bounds. (d) Off-state and (e) on-state mean durations, with the percentage of estimates within $0.5\times$$-$$2\times$ of true values. Accuracy is affected by inherent statistical sampling limitations and increasing noise, which can lead to underestimation.