As transistor sizes are downscaled, a single trapped charge has a larger impact on smaller devices and the Random Telegraph Noise (RTN) becomes increasingly important. To optimize circuit design, one needs assessing the impact of RTN on the circuit and this can only be accomplished if there is an accurate statistical model of RTN. The dynamic Monte Carlo modelling requires the statistical distribution functions of both the amplitude and the capture/emission time (CET) of traps. Early works were focused on the amplitude distribution and the experimental data of CETs were typically too limited to establish their statistical distribution reliably. In particular, the time window used has been often small, e.g. 10 sec or less, so that there are few data on slow traps. It is not known whether the CET distribution extracted from such a limited time window can be used to predict the RTN beyond the test time window. The objectives of this work are three fold: to provide the long term RTN data and use them to test the CET distributions proposed by early works; to propose a methodology for characterizing the CET distribution for a fabrication process efficiently; and, for the first time, to verify the long term prediction capability of a CET distribution beyond the time window used for its extraction.

Random Telegraph Noise (RTN) adversely impacts circuit performance and this impact increases for smaller devices and lower operation voltage. To optimize circuit design, many efforts have been made to model RTN. RTN is highly stochastic, with significant device-to-device variations. 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 modelling 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 were integrated to form one dataset for extracting their statistical properties. This allows using the concept of effective charged traps (ECT) and transforms the need for time constant distribution to obtaining the kinetics of ECT, making long term RTN prediction similar to predicting ageing. The proposed methodology opens the way for assessing RTN impact within a window of 10 years by efficiently evaluating the probability of a device parameter at a given level.

The power consumption of digital circuits is proportional to the square of operation voltage and the demand for low power circuits reduces the operation voltage towards the threshold of MOSFETs. A weak voltage signal makes circuits vulnerable to noise and the optimization of circuit design requires modelling noise. Random Telegraph Noise (RTN) is the dominant noise for modern CMOS technologies and Monte Carlo modelling has been used to assess its impact on circuits. This requires statistical distributions of RTN amplitude and three different distributions were proposed by early works: Lognormal, Exponential, and Gumbel distributions. They give substantially different RTN predictions and agreement has not been reached on which distribution should be used, calling the modelling accuracy into questions. The objective of this work is to assess the accuracy of these three distributions and to explore other distributions for better accuracy. A novel criterion has been proposed for selecting distributions, which requires a monotonic reduction of modelling errors with increasing number of traps. The three existing distributions do not meet this criterion and thirteen other distributions are explored. It is found that the Generalized Extreme Value (GEV) distribution has the lowest error and meet the new criterion. Moreover, to reduce modelling errors, early works used bimodal Lognormal and Exponential distributions, which have more fitting parameters. Their errors, however, are still higher than those of the monomodal GEV distribution. GEV has a long distribution tail and predicts substantially worse RTN impact. The work highlights the uncertainty in predicting the RTN distribution tail by different statistical models.

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Random Telegraph Noise (RTN) has attracted much attention, as it becomes higher for smaller devices. Early works focused on RTN in linear drain current, ID,LIN, and there is only limited information on RTN in saturation current, ID,SAT. As transistors can operate in either linear or saturation modes, lack of RTN model in ID,SAT prevents modelling RTN for real circuit operation. Moreover, circuit simulation requires both driving current and threshold voltage, VTH. A common practice of early works is to evaluate the RTN in VTH by ΔVTH=ΔID,LIN/gm, where gm is transconductance. It has been reported that the ΔVTH evaluated in this way significantly overestimates the real ΔVTH, but there is little data for establishing the cumulative distribution function (CDF) of the real ΔVTH. An open question is whether ΔVTH and ΔID,LIN/ID,LIN follow the same CDF. The objectives of this work are three-fold: to provide statistical test data for RTN in ID,SAT; to measure the RTN in real ΔVTH by pulse ID-VG; and, for the first time, to apply the integral methodology for developing the CDF per trap for all four key parameters needed by circuit simulation˗˗ ΔID,LIN/ID,LIN, ΔID,SAT/ID,SAT, ΔVTH,LIN, and ΔVTH,SAT. It is found that the Log-normal CDF is the best for ΔID,LIN/ID,LIN and ΔID,SAT/ID,SAT, while the General Extreme Value CDF is the best for ΔVTH,LIN and ΔVTH,SAT. Both ΔID,SAT/ID,SAT and ΔVTH,SAT are higher than their linear counterparts and separate modelling is required. Finally, the applicability of integral methodology in predicting the long term ΔID,LIN/ID,LIN is demonstrated.