ELEC2550, DECEMBER 2016 1 Low-Frequency Noise in MOSFETs Léopold Van Brandt, Student Member, IEEE, Abstract —As soon as inherent noise of MOSFET becomes an issue in the design of ICs, accurate physics- based models are necessary. The present paper reviews the different noise sources responsible for MOSFET drain current fluctuation. The long-running question of the physical origin of 1/f noise is briefly addressed. Special attention is paid to the Random Telegraph Noise (RTN) since it gets as significant as statistical variability in deeply-scaled CMOS technologies. Due to the extreme complexity of the underlying physical mechanism, which is capture and emission of carrier by an oxide defect, we adopt a phenomenological ap- proach. A stochastic model is firstly derived. Then, the fundamental physical parameters are discussed based on the simple Shockley-Read-Hall theory and the charge sheet approximation. Index Terms—MOSFET noise, oxide defects, charge trapping, RTN, stochastic modelling, 1/f noise. I. Introduction E LECTRICAL NOISE can be defined as a randomly time-fluctuation electrical signal. We are interested in the inherent noise, resulting from discrete and random movement of charge in a wire or device [1]. The study of the noise in MOSFETs becomes a topic of greatest interest as soon as this noise limits the design margins of CMOS Integrated Circuits (ICs) [2]. For about a decade, statistical variability is a serious issue for circuit designers [3]–[5]. Current fluctuations due to Low-Frequency Noise (LFN), that we discuss in details in this paper, was found to be more significant than the Random Dopant Fluctuation (RDF) for MOSFETs scaled beyond 22nm [6], [7]. This provide a clear motivation for in-depth analysis of LFN. The scope of this paper is firstly to review the different noise sources in MOSFET (section II). Then, we further investigate the Random Telegraph Noise (RTN) in section III, as it is the dominant LFN source in deeply-scaled technology [2], [8]. The very traditional two-state model is presented, as well as a physical discussion of the important parameters. Section IV then concludes. II. Noise sources in MOSFET MOSFET drain current noise The total MOSFET drain current I D (t) is the sum of both the deterministic DC component I D,ref , resulting Léopold Van Brandt is with the Department of ELectrical EN- gineering (ELEN), part of the Institute of Information and Com- munication Technologies, Electronics and Applied Mathematics (ICTEAM) in the Université Catholique de Louvain (UCL), Belgium. E-mail: leopold.vanbrandt@student.uclouvain.be from the applied bias (V G ,V D ), and the randomly time- fluctuating quantity ΔI (t), which also depends on the bias. Mathematically, we have I D (V G ,V D ,t)= I D,ref (V G ,V D )+ΔI D (V G ,V D ,t). For the sake of convenience, we will omit the D subscript, as we are only dealing with the drain current. Further- more, as we limit ourself to the transient study of a device under DC-bias, the (V G ,V D )-dependence of both the reference current and the noise will be implied. We simply write I (t)= I ref +ΔI (t). We emphasized that ΔI (t), written with a capital letter, denotes the stochastic process itself and not some realization of it. From the experimental point of view, we indeed measure one single noise trace Δi (t). We point out that the full knowledge of ΔI (t) would a priori require an infinite number of realizations of the noise {Δi 1 (t) , Δi 2 (t) ,... } . Consequently, a stochastic process such as ΔI (t) is more conveniently described by its statistical properties. We briefly summarize the two fundamental quantities that are essential to describe an electrical noise. Details can be found in a dedicated textbook about probabilities and stochastic processes (our preference is Papoulis’s book [9]). • the mean-square, or variance of the noise, is denoted by σ 2 ΔI and basically represents the average power contained in the noise signal. • the noise Power-Spectral Density (PSD) S ΔI (f ) is a deterministic function of frequency f , whose units are  A 2 /Hz  and tells us how the current noise power is spread along the frequency axis: σ 2 ΔI =  f2 f1 S ΔI (f )df , (1) [f 1 ,f 2 ] being the bandwidth of interest. The rest of the current section is dedicated to the description of the different noise sources that impact the MOSFET drain current. A. Thermal noise The thermal (or Johnson [10] or Nyquist [11]) noise is caused by the random Brownian motion of electrons in conductors. In 1928, Johnson, one of the very early pioneers in electrical noise, described the phenomenon in the following words [10]: