On the Accuracy in Modeling the Statistical Distribution of Random Telegraph Noise Amplitude

Mehzabeen Mehedi,Zhigang Ji,Zengliang Ye,Weidong Zhang,Kean Hong Tok,John S Marsland,Jian Fu Zhang

doi:10.1109/access.2021.3065869

Mehzabeen Mehedi, Zhigang Ji + Show 5 more

Open Access

https://doi.org/10.1109/access.2021.3065869

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Abstract

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.

Highlights

Random telegraph noise (RTN) is a step-like fluctuation of drain current under constant gate and drain voltages
PROBLEMS WITH THE PROPOSED STATISTICAL DISTRIBUTIONS For the RTN amplitude per trap, two popular statistical distributions used in early works are Lognormal [1], [5]–[8], and Exponential [3]–[6], [28], [29]
This work assesses the accuracy of the statistical distributions for the RTN amplitude per trap

Summary

Introduction

Random telegraph noise (RTN) is a step-like fluctuation of drain current under constant gate and drain voltages. It has received many attentions, as it adversely affects the operation of electronic circuits [1]–[15]. As MOSFETs become smaller, RTN becomes increasingly important, driven by an increased impact of a single charge on smaller devices and an increase in the number of devices in a system [1]–[8]. A large number of devices in a system will contain more devices in the tail of statistical distributions, which can cause errors. The minimization of overdrive voltage, (Vg-Vth), in the future leaves little room to tolerate the RTN induced jitter [5], [16], [18]

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Conclusion