**3. Noise in MOS devices**

It is very significant to study the sources of noise as noise degrades the quality of the desired signal. In MOSFET, the various noise sources are: (a) thermal noise introduced by the channel/polysilicon gate resistance/source-drain resistance/ distributed substrate resistance, (b) flicker noise from the channel. In MOSFET device thermal noise dominates at high frequency and in the channel, it further gives rise to both drain channel noise and induced gate noise. In the nMOS structure, excess thermal noise exhibits in the channel. As drain to source voltage is increased, the noise in the channel increases [17].

D.P. Triantis et al. presented a systematic formulation of the high frequency noise in short-channel MOSFET. The reported MOSFET structure was operating in the saturation region [18]. The small-signal behavior and noise analysis of nanoscale MOSFET at RF was reported by M.A. Chalkiadaki and C.C. Enz [19]. A.G. Mahmutoglu and A. Demir presented an idealized trap model to encounter the behavior of traps present in the gate oxide [20]. H. Tian and A. EL. Gamal proposed a nonstationary extension noise model to analyze flicker noise in MOSFET circuits more accurately [21]. C. Hu et al. studied the lowfrequency noise characteristics of MOSFET to investigate the effect of noise by changing metal interconnect perimeter length, device W/L ratio, and gate-biasing voltage [22].

Renuka Jindal developed noise mechanisms in MOSFET for both intrinsic and extrinsic noise. The study of intrinsic noise mechanisms is essential to study the effect of channel thermal noise, induced gate noise, and induced substrate noise on device operation [23].

#### **4. Noises in tunnel FETs**

In Tunnel FETs, different types of noise from low-frequency to high-frequency must be considered. Low-frequency noise can be further classified into random telegraph noise (RTN)/burst noise and flicker noise, while high-frequency noise can be further classified into shot noise and thermal noise.

#### **4.1 Low frequency noise sources**

#### *4.1.1 Random telegraph noise*

Random telegraph noise (RTN) is a non-white noise that mainly occurs due to the presence of impurities in semiconductors and thin gate-oxide films. The trapping and de-trapping of carriers in the channel are the source of RTN [24]. If the trap is located on the source-channel interface, RTN is more pronounced because the trapped charge can change the junction electric field which in turn affects BTBT [25]. It is a function of temperature, radiation, and induced mechanical stress. In audio amplifiers, the burst noise sounds as random shots, which are similar to the sound associated with making popcorn. The noise spectral density is given by RTN is given by Eq. (1) [26]:

$$\mathcal{S}\_{\text{RTN}}(f) = \mathcal{C} \frac{4(\Delta I)^2}{\mathbf{1} + \left(\frac{2uf}{f\_{\text{RTN}}}\right)^2} \tag{1}$$

*f RTN* is RTN noise corner frequency. The intensity of RTN noise depends upon the site at which the trap center is located concerning the Fermi level and the center area of the Fermi level is responsible for the generation of RTN noise.

#### *4.1.2 Flicker noise*

Flicker noise is a low-frequency noise that arises from the trapping and detrapping of charge carriers in the trap states in the gate oxide around the quasifermi level. It is mostly generated at the interface of Si-substrate and gate oxide. At the interface of Si substrate, there exist dangling bonds. These dangling bonds give rise to extra energy states. The charge carriers that move across these energy states, get trapped in these sites. The noise spectral density is given by surface model is given by Eq. (2) [26]:

$$\,\_1S\_{\frac{1}{2}}\alpha \left(\overline{\Delta N}\right)^2 \int\_{\tau\_1}^{\tau\_1} \frac{4\tau}{1+\alpha\tau^2}d\tau = \left(\overline{\Delta N}\right)^2 \frac{1}{f} \tag{2}$$

where, <sup>1</sup> *<sup>τ</sup>*<sup>2</sup> <sup>≪</sup> *<sup>ω</sup>* <sup>≪</sup> <sup>1</sup> *<sup>τ</sup>*<sup>1</sup> and the noise spectral density for surface model remains constant up to *<sup>f</sup>* <sup>2</sup> <sup>¼</sup> <sup>1</sup> 2*πτ*<sup>2</sup> .

#### **4.2 High frequency noise sources**

Thermal noise and shot noise are the two types of noise sources that degrade the device's performance operating at high frequency. For the analysis of thermal noise effect on TFET structure, the thermal noise model of MOSFET in ON-state is used, when the applied drain-source voltage is zero [27]. Though, shot noise is the dominant form of high-frequency noise/white noise in heterojunction TFET. The modeling of shot noise can be done in the same way as it is done in tunnel diodes [28].

#### *4.2.1 Shot noise*

In electronic devices, the noise that arises due to the unavoidable random fluctuations of electric current when the charge carriers travel a gap is known as shot noise [29]. Shot noise exhibits since the current is not a continuous flow but it is the sum of discrete pulses in time where each pulse corresponds to the transfer of electron through a conductor. Shot noise is caused by the thermal motion of electrons and occurs in any conductor having resistance R. The most dominant white noise is shot noise and in TFET, it can be modeled similarly as it is modeled in tunnel diode.

$$
\dot{a}\_{\text{shot}}^2 = 2qI\_D \Gamma \tag{3}
$$

where, Γ is Fano factor that indicates the deviation in the magnitude of shot noise from the nominal value *ID*. Fano factor value depends upon applied voltage and it is frequency independent [30].

#### *4.2.2 Thermal noise*

In electronic devices, the noise generated inside a conductor at equilibrium due to the thermal agitation of charge carriers is known as thermal noise. In 1928, Johnson experimentally verified the theory of the fluctuating movement of charges in thermal equilibrium that was initially proposed by Einstein in 1905 [31]. The magnitude of random motion of free electrons and resistance of elements increases with an increase in temperature. Due to this thermal motion of charge carriers, a fluctuating voltage is created at the terminals of the conductor [12].
