This is the accepted version of the article: Saraza-Canflanca, Pablo; Martin Martinez, Javier; Castro-Lopez, Rafael; [et al.]. «Statistical characterization of time-dependent variability defects using the maximum current fluctuation». IEEE Transactions on Electron Devices, Vol. 68, issue 8 (Aug. 2021), p. 4039-4044. DOI 10.1109/ted.2021.3086448 This version is available at https://ddd.uab.cat/record/249148 under the terms of the license Statistical characterization of Time-Dependent Variability defects using the Maximum Current Fluctuation P. Saraza-Canflanca, J. Martin-Martinez, R. Castro-Lopez, E. Roca, R. Rodriguez, F. V. Fernandez, M. Nafria  distributed. BTI is also associated to the same kind of Abstract— This paper presents a new methodology to phenomena, though, in this case, charge de-trapping is mainly extract, at a given operation condition, the statistical observed when gate bias is decreased (a phase known as distribution of the number of active defects that contribute recovery). However, some of the carriers may not be de- to the observed device Time-Dependent Variability, as well as their amplitude distribution. Unlike traditional trapped, leading to a permanent shift of the threshold voltage, approaches based on complex and time-consuming consequently degrading the device performance [6]. In ultra- individual analysis of thousands of current traces, the scaled devices, the recovery phase is observed as sudden proposed approach uses a simpler trace processing, since increments in the drain current, similar to RTN current shifts. only the maximum and minimum values of the drain current In fact, there is a general consensus that RTN and the during a given time interval are needed. Moreover, this recoverable component of BTI are caused by the same type of extraction method can also estimate defects causing small current shifts, which can be very complex to identify by defects [4],[7], and the observation of one phenomenon or the traditional means. Experimental data in a wide range of gate other actually depends on the operation conditions (voltage, voltages, from near-threshold up to nominal operation time, temperature). conditions, are analyzed with the proposed methodology. Then, nowadays both phenomena are usually described in the context of defect-centric models [7]-[10], which account for the Index Terms—Time-Dependent Variability (TDV), Random variations in the transistor threshold voltage caused by the Telegraph Noise (RTN), Bias Temperature Instability (BTI), trapping/detrapping of charge carriers in/from defects present transistor, Maximum Current Fluctuation (MCF) in the devices. To assess the impact on circuit performances it I. INTRODUCTION is crucial to characterize these phenomena and extract the statistical distributions of the main parameters that describe T IME-Dependent Variability (TDV), caused by phenomena such as Random Telegraph Noise (RTN) and them. The characterization of RTN and BTI defects traditionally Bias Temperature Instability (BTI) has become a subject of relies on the detailed analysis of individual current traces [11]- increasing concern in deeply-scaled CMOS technologies [1], [13]. This analysis detects the number of transitions with a due to its role as a source of device and circuit performance distinct amplitude, each one of them corresponding to a variability [2], [3]. At device level, RTN is observed as discrete different defect, or the total number of current levels. From any jumps of the drain current. It is generally accepted that these of these values, the number of defects can be easily calculated. current shifts are caused by the stochastic trapping/detrapping However, these conventional approaches are convoluted and of charge carriers in/from defects. In particular, when charge error-prone to the point that they are unable to correctly extract carriers are trapped in defects, they change the density of charge the number of defects and associated current shifts when: (1) located at the silicon-oxide interface, which causes an increase the trace is very complex (i.e., with a large number of distinct in the threshold voltage of the device, thus decreasing its drain transitions, particularly if some of these transitions have similar current [4],[5]. Detrapping of carriers from defects has associated current amplitudes); (2) some of the defects produce therefore the opposite impact on the device current. Because of current shifts with an amplitude below the noise level; or, (3) the stochastic nature of the phenomenon, the threshold voltage the defect characteristics are around the measurement shifts (or, equivalently, current jumps), are statistically This work was supported by the VIGILANT Project (PID2019- P. Saraza-Canflanca, R. Castro-Lopez, E. Roca and F. V. Fernandez 103869RB / AEI / 10.13039/501100011033) and the TEC2016-75151- are with Instituto de Microelectrónica de Sevilla, (Universidad de Sevilla, C3-R Project (AEI/FEDER, UE). Pablo Sarazá Canflanca also CSIC), Sevilla, Spain (email: Francisco.Fernandez@imse-cnm.csic.es). acknowledges MICINN for supporting his research activity through the J. Martin-Martinez, R. Rodriguez and M. Nafria are with the Department predoctoral grant BES-2017-080160. of Electronic Engineering. Universitat Autonoma Barcelona, 08193, Bellaterra, Spain (email: javier.martin.martinez@uab.cat). equipment resolution. In this paper, we propose a method based on a new metric, the Maximum Current Fluctuation (MCF), to obtain the distribution of the number of active TDV-related defects (i.e., defects that suffer at least one trapping/detrapping event) and their associated current shifts, δI, that i) accounts for all active defects, and ii) does not require any complex analysis of the experimental current traces, since only a very rough estimation of the current shift distribution (easier to obtain) and the upper and lower bounds of the current are required. This model describes the experimental data accurately at gate voltages ranging from the near-threshold region to the nominal operation voltage of the technology. The rest of this paper is structured as follows. First, in Section II, the MCF methodology used in this work is explained. Then, in Section III, the results obtained using this methodology are presented. Finally, in Section IV, conclusions are drawn. II. METHODOLOGY DESCRIPTION Fig. 1. a) Experimental current trace and current bounds from which the In the following, a metric is introduced to easily extract the MCF is computed. The arrow indicates the MCF at around t=41s. b) MCF(t) obtained from 20 current traces (the one in Fig.1a is highlighted defect-centric model parameters, i.e., the number of active in green). c) The cumulative distribution functions (cdf) of the MCFs for defects and their associated current jumps, from experimental t=1s and t=50s for a set of 500 transistors. current traces. Consider the current trace shown in Fig. 1a corresponding to where N represents the number of active defects (i.e., defects a PMOS device of W/L=80nm/60nm biased with |𝑉 | 1.2V that have captured/emitted a charge carrier at least once) from and |𝑉 | 0.1V . We define the cumulative maximum current the beginning of the time window up to time t, and 𝛿𝐼 (CMAXC) at any time instant 𝑡′ within the experimental represents the current shift associated to the trapping/detrapping window as the maximum current within the interval 0 𝑡 𝑡′: in/from each of those defects. The term 𝜀 accounts for the contribution of the background noise to the MCF. 𝐶𝑀𝐴𝑋𝐶 𝑡 max 𝐼 𝑡 (1) ∀ ∈ , Fig. 1b shows the temporal evolution of the MCFs of 20 CMOS transistors. From these data, the cumulative distribution function (cdf) of the MCF can be obtained for a particular time CMAXC is plotted in the same figure with the orange line. instant, as shown in Fig. 1c. Notice how, in Fig. 1c, the Similarly, the cumulative minimum current (CMINC) at any distribution of the MCF values shift to larger values when time instant 𝑡′ within the experimental window is defined as: longer times are considered. This is expected, since a larger 𝐶𝑀𝐼𝑁𝐶 𝑡 min 𝐼 𝑡 (2) number of active defects may be present in longer measurement ∀ ∈ , windows (e.g., 50s) than in shorter ones (e.g., 1s). In fact, the MCF for a single device depends on the number of active and is plotted in the same figure with a lower blue line. Finally, defects, N, and their current shifts, δI, associated to their the metric proposed in this paper, the maximum current occupancy state, as shown in equation (4). Therefore, at each fluctuation (MCF), is defined as the difference between both: time t, there is a unique distribution of N that, together with the δI distribution, correctly describes the experimental MCF 𝑀𝐶𝐹 𝑡 𝐶𝑀𝐴𝑋𝐶 𝑡 𝐶𝑀𝐼𝑁𝐶 𝑡 (3) distribution. The extraction of both distributions is the goal of this work. Note that the parameters (N and δI) that are needed by the Notice that, although current transitions caused by TDV MCF-based methodology to describe and predict the impact of defects are bipolar (i.e., charge trapping/de-trapping events TDV defects on the transistor characteristics, can be easily decrease/increase the drain current), the MCF metric is, related to those of defect-centric TDV models, such as the according to its definition, unipolar (i.e., the difference between Probabilistic Defect Occupancy (PDO) model [9]. The the maximum and minimum values of the current will always necessary parameters to construct such model are the total be a positive value and MCF(t) an ever-increasing function). number of defects in the device (NT), the distribution of the Due to the TDV stochasticity, each device shows a different capture and emission time constants of the defects (c, e), MCF trace. In fact, the MCF value for a given device at a time which determine for each defect its probability of being t can be expressed as: occupied or empty, and the distribution of the amplitudes of the shifts associated to each defect when occupied, δI. These 𝑀𝐶𝐹 𝑡 𝛿𝐼 𝜀 (4) variables can be easily related to those used in our work. First, the number of active defects N extracted through the MCF- based methodology depends on the total number of defects in experimental cdfs obtained for the δI distributions for the the device, NT, and on the time constants (c, e). For each different biasing voltages, which can be correctly fitted defect, its time constants determine if the device will be active considering two lognormal distributions. Fig. 2b displays the (i.e., suffer at least one trapping/detrapping event) during a corresponding pdfs of the fitted two-lognormal model. The given time window, in particular, during the time interval inset in Fig. 2b shows the experimental histogram constructed between the start of the measurement and the time instant in with the values of δI extracted at one of the bias conditions, which the cdf of the MCF is calculated (e.g., a defect with c  which reinforces the suitability of a two lognormal model. The e  1s will surely be accounted as an active defect during a two lognormal function in the RTN amplitude distribution measurement yielding the calculation of MCF at 50s). Finally, could originate from two categories of traps, located above the the distribution of the amplitudes of the shifts considered in percolation path or not, which cause larger or smaller RTN defect-centric models is equivalent to the δI distribution amplitudes, respectively [18]. In any case, notice that no considered in this work. assumption has been done for the selection of this type of A related but different metric, the Within Device Fluctuation distribution, but rather has been found to properly fit the (WDF), has been presented in [14],[15]. However, though experimental data. In fact, only by using high resolution somehow related, they should not be confused, since they have equipment, which allows the measurement of current jumps in been defined with different goals. The WDF metric for a time the nanoampere range, the lognormal corresponding to the instant 𝑡′ is given by the difference between 𝑀𝑎𝑥 𝑡′ and smaller amplitudes shows up. 𝑀𝑖𝑛 𝑡′ . 𝑀𝑎𝑥 𝑡′ is given by the maximum current increase Using these distributions and assuming a Poisson from the start of the measurement up to 𝑡′ (hence, it is directly distribution with mean value for the number of defects related to our definition of CMAXC), and 𝑀𝑖𝑛 𝑡′ is given by [19], the experimental MCF distributions can be fitted. An the minimum current variation from the end of the measurement example is shown in Fig 3 (blue line) for |𝑉 | 1.2V and 𝑡 window down to 𝑡′ [14] (thus different from CMINC). A major difference between both metrics is that the WDF value at intermediate time instants depends on the size of the measurement time window, e.g., the value of 𝑀𝑖𝑛 𝑡 for the trace in Fig. 1a for time instants between 18s and 30s is different if the measurement window extends to 30s or to 50s. This brings along an important consequence: the value of the WDF metric is only reliable for time instants sufficiently below the measurement window [14]. In any case, the WDF metric is, in itself, not appropriate for our purposes in this paper, since the 𝑀𝑖𝑛 𝑡′ values at intermediate time instants would be determined by the current variation at the later time instants. Hence, it cannot be related to the number of active defects and associated current jumps at those intermediate time instants, which is the goal of this paper. To expose the limitations of time-consuming conventional approaches, an attempt has been made to extract the amplitudes of the current shifts caused by the trapping/de-trapping events of individual defects from experimental data. In order to get statistically relevant data, RTN traces have been measured in 500 PMOS transistors of W/L = 80nm/60nm (integrated into an IC fabricated in a commercial 65nm planar CMOS technology specifically designed for TDV characterization) with |𝑉 | 0.1V and different gate voltages, |𝑉 | 0.6V, 0.7V, 0.8V, 1.0V and 1.2V, for 50s. Details about the IC and the measurement set-up can be found in [16] and [17]. Fig. 1a shows an example of noise-free RTN trace (red trace), obtained using the method in [11]. Noise-free trace here refers to the result of a mathematical processing that eliminates small current shifts due to background noise including e.g., thermal Fig. 2. a) δI cdf and fitted two-lognormal model (black lines). b) noise of the devices or noise of the measurement equipment, Corresponding probability density functions (pdf) of the fitted two- hence, obtaining a clean trace that clearly shows the effect of lognormal model. The inset in b) displays the histogram for the RTN. From the noise-free RTN traces, the δI caused by each experimentally-extracted amplitudes for one of the bias conditions defect is extracted. Using this procedure, hundreds of δI values (|VGS| = 1.V). were determined for each bias condition. Fig. 2a depicts the 100ms, which has made use of the 1.2V- δI distribution in Fig. and small, in every current trace, as required to get the 2. Clearly, the larger values (above 50nA) of the MCF distributions in Fig. 2. distribution can be properly described using this approach. An additional fact must be considered when trying to fit the However, it fails to describe the smaller MCF values, because experimental cdf of the MCF in Fig. 3: so far, devices without the δI distribution is obtained from the experimental current defects lead to simulated MCF = 0, while, experimentally, MCF traces (as that in Fig. 1a), where, as mentioned in Section I, a will be always higher than zero due to the background noise. To portion of defects, especially those with small δI, have not been solve this discrepancy, a Gaussian background noise with detected (due to experimental limitations) and yet these affect standard deviation obtained from the experimental data is added the MCF calculation, and are therefore accounted for by the to the generation of the MCF values. Then, the experimental MCF-based methodology. In fact, low-δI detection problem is MCF distribution can be more accurately fitted (black line in a common issue of any method extracting δI, and consequently Fig. 3) in the whole range. In summary, the experimental MCF N, from experimental RTN traces [11], [19], [20], which are not distribution can be correctly described by just considering a able to detect defects that have an associated low-amplitude Poisson distribution of N with mean value (1.8, for the case current shift. This reinforces the idea that conventional shown in Fig. 3), the corrected δI distribution (red line in inset processing techniques may not only require a complex and of Fig. 3) originated from an easy-to-attain, rough δI time-consuming analysis, but may also lead to an erroneous distribution approximation, and a Gaussian background noise. characterization of the distribution of the number of defects and their associated amplitudes. III. RESULTS To solve this inaccuracy, we postulate here that the MCF Once the MCF-based methodology has been explained, the metric can be useful even without a detailed, time-consuming next step is to analyze the MCF time dependence. Fig. 4 shows analysis of the traces to attain a δI distribution (as in Fig. 2). In the MCF distributions for different measurement intervals fact, these painstakingly-derived δI distributions are not really considering sections of the measured traces up to 10ms, 100ms, required. To illustrate this, the N distribution and a corrected δI 1s, 10s and 50s. As expected, the MCF distributions shift to distribution (red curve in the inset in Fig. 3) have been obtained higher values for longer times. This is attributed to the fact that by minimizing the difference between the MCF cdf in Fig. 3 in longer current traces more defects can be activated, and, (red curve) and the experimental one (grey dots). Notice that therefore, higher MCF values are encountered from the traces. the δI distributions in Fig. 2 are not used for this MCF Interestingly enough, the experimental MCF distributions can distributions fittings. Instead, for proper convergence of the be well reproduced with our approach by simply varying the fitting procedure, a very rough initial approximation (green mean value of the active defects, , without any modification curve in the inset in Fig. 3) is obtained from those traces (150 of the previously corrected δI distribution or the background out of 500) that contain one clear defect (only two current levels noise. This implies that there is no correlation between the separated by at least 5nA). This approximated δI distribution is current shift associated to a defect and its time constants [21]. faster and easier to extract and does not require a detailed, The approach illustrated above for |𝑉 | 1.2V has been complex, and painstakingly processing of every shift, both large applied to other operation conditions. Fig. 5a shows the evolution of with time for all the applied values of 𝑉 , which can be described using a bias-dependent lognormal-type distribution. Fig. 5b shows the Poisson distribution for the number of defects for t=50s at different bias conditions. Fig. 3. MCF experimental distribution (grey symbols) and fitting (lines) Fig. 4. Experimental MCF distributions obtained at different times considering the extracted and corrected δI distributions. The inset shows (symbols) and fittings using the proposed technique (solid lines). (green) the initial guess of the δI distribution considered for the MCF distribution fitting and (red) δI distribution that better fits the distribution. Fig. 6. a) Experimental τe and τc values obtained from the analysis of individual RTN traces. The size of the symbols represents the δI associated to each defect. b) Portion of the total active defects at a given time interval, ΔN, extracted using the MCF-based method, versus the relative number of defects, ΔNτ, obtained from the analysis of individual traces (Fig. 6a). mean and standard deviation of the lower and upper lognormal function and 𝐾 represents the relative amplitude of both distributions. And for the number of defects: Fig. 5. a) Time evolution of (symbols), which can be described 𝑁 log 𝑡 𝜇 using a lognormal-type distribution (lines). b) Poisson distributions at N t 1 𝑒𝑟𝑓 (6) t=50s. 2 𝜎 √2 Table I displays the main parameters extracted through the Using these parameters, it is possible to predict the impact of MCF-based procedure, namely the distribution of the current the current fluctuations on the overall device drain current, as shifts associated to the trapping/detrapping of defects, and the when using other defect centric models such as the Probabilistic number of such active defects with respect to the operation Defect Occupancy (PDO) model [9]. time. Specifically, the parameters correspond to fitting the Finally, to further illustrate the proposed methodology, the following distribution for the current shifts: following test has been performed. From the detailed analysis cdf 𝛿𝐼 𝐾 1 𝑒𝑟𝑓 log 𝛿𝐼 𝜇𝑙 1 𝐾 1 𝑒𝑟𝑓 log 𝛿𝐼 𝜇𝑢 (5) of hundreds of individual RTN traces measured at |𝑉 | 1V 2 𝜎𝑙 √2 2 𝜎𝑢 √2 and 1.2V, many emission (τe)/capture (τc) times have been Where erf() is the error function, 𝜇 , 𝜇 , 𝜎 and 𝜎 , represent the extracted (Fig. 6a). With these data the number of defects Nτ TABLE I. PARAMETERS EXTRACTED FOR THE 𝛿𝐼 DISTRIBUTION OF RTN DEFECTS AND THE TIME EVOLUTION OF 𝑉 𝐾 𝜇 𝜎 𝜇 𝜎 𝑁 𝜇 𝜎 0.6V 0.86 -7.95 0.07 -7.25 0.26 9.77 4.14 2.93 0.7V 0.77 -7.94 0.09 -7.16 0.22 9.87 3.21 2.51 0.8V 0.64 -8.05 0.13 -7.18 0.29 10.20 3.02 2.56 1V 0.76 -8.07 0.21 -7.15 0.25 9.85 1.59 2.14 1.2V 0.80 -7.91 0.12 -7.18 0.25 10.37 0.78 1.84 that will be active within a given time window has been [7] T. Grasser, K. Rott, H. Reisinger, M. Waltl, J. Franco, B. Kaczer, “A unified perspective of RTN and BTI”, in Proc. Reliability Physics calculated, assuming that defects will be active within a given Symposium (IRPS), IEEE International, pp. 4A-5, 2014. DOI: time window t if their corresponding τe and τc are smaller than 10.1109/IRPS.2014.6860643. t. When the relative variation of the number of defects, Nτ, in [8] B. Kaczer, J. Franco, P. Weckx, Ph. J. Roussel, E. Bury, M. Cho, R. a given time interval is plotted against the equivalent variation Degraeve, D. Linten, G. Groeseneken, H. Kukner, P. Raghavan, G. Rzepa, W. Goes and T. Grasser, "The defect-centric perspective of device and evaluated using the MCF-based method, ΔN, a linear relation circuit reliability — From individual defects to circuits," 2015 45th between them for the voltages cot5yinsidered is observed (Fig. European Solid State Device Research Conference (ESSDERC), 2015, pp. 218-225, doi: 10.1109/ESSDERC.2015.7324754. 6b). This result indicates that the same temporal trend is [9] J. Martin-Martinez, B. Kaczer, M. Toledano-Luque, R. Rodriguez, M. obtained for the number of defects that will be active, whether Nafria, X. Aymerich and G. Groeseneken, "Probabilistic defect predicted by the novel MCF-based technique presented in this occupancy model for NBTI," 2011 International Reliability Physics paper or extracted by performing a time-consuming, massive Symposium, 2011, pp. XT.4.1-XT.4.6, doi: 10.1109/IRPS.2011.5784605. analysis of individual current traces. However, the procedure [10] N. Ayala, J. Martin-Martinez, R. Rodriguez, M. Nafria and X. Aymerich, "Unified characterization of RTN and BTI for circuit performance and here presented is much simpler and more straightforward than variability simulation," 2012 Proceedings of the European Solid-State the identification of individual defects from a large set of traces, Device Research Conference (ESSDERC), 2012, pp. 266-269, doi: while accounts for all the active defects in the device within the 10.1109/ESSDERC.2012.6343384. experimental time window, regardless of their amplitude. [11] P. Saraza-Canflanca, J. Diaz-Fortuny, R. Castro-Lopez, E. Roca, J. Martin-Martinez, R. Rodriguez, M. Nafria, F. V. Fernandez, "A robust and automated methodology for the analysis of Time-Dependent IV. CONCLUSIONS Variability at transistor level", Integration, vol. 72, pp. 13-20, 2020. DOI: 10.1016/j.vlsi.2020.02.002 In deeply-scaled CMOS technologies, TDV phenomena, [12] T. Nagumo, K. Takeuchi, S. Yokogawa, K. Imai, Y. Hayashi, "New such as RTN and BTI, display a stochastic nature, caused by the analysis methods for comprehensive understanding of random telegraph trapping/de-trapping of charge carriers in/from individual noise", in2009 IEEE International Electron Devices Meeting (IEDM), IEEE, pp. 1-4. 2009. DOI: 10.1109/IEDM.2009.5424230 defects. To account for this stochastic behavior, it is [13] J. Martin-Martinez, J. Diaz-Fortuny, R. Rodriguez, M. Nafria, X. fundamental to develop accurate and automated methods to Aymerich, “New weighted time lag method for the analysis of random accurately characterize those phenomena. telegraph signals”, IEEE Electron Device Letters, vol. 35, pp. 479-481, 2014. DOI: 10.1109/LED.2014.2304673. This paper presents a novel methodology using a new metric, [14] M. Duan, J.F. Zhang, Z. Ji, W.D. Zhang, B. Kaczer, T. Schram, R. MCF, to evaluate the distributions of the number of active Ritzenthaler, G. Groseneken and A. Asenov, "New analysis method for TDV-related defects and their associated current shifts within a time-dependent device-to-device variation accounting for within-device given time window and under given operation conditions. fluctuation," IEEE Trans. on Electron Devices, vol. 60, no. 8, pp. 2505- 2511, Aug. 2013. Unlike conventional methods that analyze current traces, this [15] M. Duan, J. F. Zhang, Z. Ji, W. Zhang, B. Kaczer, T. Schram, R. method relies on a rather uncomplicated processing. It has also Ritzenthaler, A. Thean, G. Groeseneken, A. Asenov, "Time-dependent been shown that the MCF-based methodology is able to obtain variation: A new defect-based prediction methodology", in Symposium a more precise distribution of the defect current amplitudes than on VLSI Technology: Digest of Technical Papers, IEEE, pp. 1-2, 2014. DOI: 10.1109/VLSIT.2014.6894373. conventional techniques, often failing at detecting defects with [16] J. Diaz-Fortuny, J. Martin-Martinez, R. Rodriguez, R. Castro-Lopez, E. low-amplitude current shifts. Roca, X. Aragones, E. Barajas, D. Mateo, F. V. Fernandez, M. Nafria, "A versatile CMOS transistor array IC for the statistical characterization of time-zero variability, RTN, BTI and HCI", IEEE Journal of Solid-State REFERENCES Circuits, vol. 54, no. 2, pp. 476-488, 2018. DOI: [1] N. Tega, H. Miki, F. Pagette, D. J. Frank, A. Ray, M. J. Rooks, W. 10.1109/JSSC.2018.2881923 Haensch, K. Torii, "Increasing threshold voltage variation due to random [17] J. Diaz-Fortuny, P. Saraza-Canflanca, R. Castro-Lopez, E. Roca, J. telegraph noise in FETs as gate lengths scale to 20 nm", in Symposium on Martin-Martinez, R. Rodriguez, F. V. Fernandez, M. Nafria, “Flexible VLSI Technology, IEEE, pp. 50, 2009. setup for the measurement of CMOS time-dependent variability with [2] N. Tega, H. Miki, M. Yamaoka, H. Kume, T. Mine, T. Ishida, Y. Mori, array-based integrated circuits”, IEEE Transactions on Instrumentation R. Yamada, K. Torii, "Impact of threshold voltage fluctuation due to and Measurement, 2019. DOI: 10.1109/TIM.2019.2906415 random telegraph noise on scaled-down SRAM", in Reliability Physics [18] Z. Zhang, S. Guo, X. Jiang, R. Wang, Z. Zhang, P. Hao, Y. Wang, R. Symposium (IRPS), IEEE International, pp. 541-546, 2008. DOI: Huan, "New insights into the amplitude of random telegraph noise in 10.1109/RELPHY.2008.4558943 nanoscale MOS devices," in International Reliability Physics Symposium [3] M. Luo, R. Wang, S. Guo, J. Wang, J. Zou, R. Huang, "Impacts of random (IRPS), IEEE International, pp. 3C-3, 2017. DOI: telegraph noise (RTN) on digital circuits", IEEE Transactions on Electron 10.1109/IRPS.2017.7936288. Devices, vol. 62, pp. 1725-1732, 2015. DOI: 10.1109/TED.2014.2368191 [19] P. Weckx, B. Kaczer, C. Chen, P. Raghavan, D. Linten, A. Mocuta, [4] T. Grasser, H. Reisinger, W. Goes, T. Aichinger, P. Hehenberger, P. J. "Relaxation of time-dependent NBTI variability and separation from Wagner, M. Nelhiebel, J. Franco, B. Kaczer, "Switching oxide traps as RTN," in Reliability Physics Symposium (IRPS), IEEE International, pp. the missing link between negative bias temperature instability and random XT-9.1-XT-9.5, 2017. https://doi.org/10.1109/irps.2017.7936423. telegraph noise," in International Electron Devices Meeting (IEDM), [20] F. M. Puglisi, P. Pavan, "RTN analysis with FHMM as a tool for multi- IEEE, pp. 1-4, 2009. DOI: 10.1109/IEDM.2009.5424235. trap characterization in HfOx RRAM", in International Conference of [5] T. Grasser, “Stochastic charge trapping in oxides: From random telegraph Electron Devices and Solid-State Circuits, IEEE, pp. 1-2, 2013. DOI: noise to bias temperature instabilities”, Microelectronics Reliability, vol. 10.1109/EDSSC.2013.6628059. 62 (1), pp. 39-70, 2012, doi: 10.1016/j.microrel.2011.09.002. [21] K. Abe, A. Teramoto, S. Sugawa and T. Ohmi, " Understanding of traps [6] T. Grasser, T. Aichinger, G. Pobegen, H. Reisinger, P. J. Wagner, J. causing random telegraph noise based on experimentally extracted time Franco, M. Nelhiebel, B. Kaczer, " The ‘Permanent’ Component of NBTI: constants and amplitude," in International Reliability Physics Symposium Composition and Annealing," in International Reliability Physics (IRPS), IEEE International, 2011. DOI: 10.1109/IRPS.2011.5784503 Symposium (IRPS), IEEE International, 2011. DOI: 10.1109/IRPS.2011.5784543.