Chapter 2 Low Frequency Noise Theory and Measurement Method
2.2 Low Frequency Noise Theory
In the past several decades, the origins and physical mechanisms underlying flicker noise remain an open question, with lot of debates and arguments in the experimental results and modeling to match the measurement. Number fluctuation model and mobility fluctuation model appear as two most popular mechanisms to explain and predict the measured flicker noise [11,12]. In 1957, McWhorter published a flicker noise model based on quantum mechanical tunneling transitions of electrons between the gate oxide and channel . In practice, the tunneling time varies exponentially with distance, and it is assumed that trap density is uniform in both energy and distance from the channel interface to extract the time constants for generating flicker noise. The McWhorter model, namely number fluctuation model may be useful due to its simplicity and good agreement with experimental, particularly for n-channel MOSFETs [12,13]. However, the mobility fluctuation model appears to better explain the flicker noise measured from p-channel MOSFETs [14,15]. As compared to surface channel MOSFETs, buried-channel MOSFETs or bipolar junction transistors (BJT) demonstrate significantly lower flicker noise [16-21]. The published results are in favor of the number fluctuation model that the flicker noise is originated from the traps in the oxide or at oxide/channel interface. However, the surface carrier mobility is reduced compared to the bulk value due to additional surface scattering (acoustic phonon and surface roughness), which has an impact on the mobility fluctuation. Hooge mobility noise , which is sensitive to the crystalline quality, can be employed to explain the higher flicker noise for surface channel devices in which the carriers are in close proximity to the gate oxide and may suffer aggravated mobility fluctuation. In the following, the number fluctuation and mobility fluctuation models will be described in more detail.
2.2.1 Number Fluctuation Theory 
The physical mechanism underlying the number fluctuation noise is the interaction between the channel carriers and slow traps in the gate oxide, which is illustrated in Fig. 2.2.
The dynamic exchange of carriers between the gate oxide and channel causes a fluctuation in the surface potential (S) and then gives rise to fluctuations in the inversion carrier density
Qinv. This in turn leads to noise in the drain current. Note that Qinv (the fluctuation in the inversion carrier density) can occur even without a current flowing the channel and the channel current is only used to sense the fluctuations. The mathematical formulas for expressing number fluctuation model in different operation regions are provided as follows In weak inversion region
-Nt the density of traps at quasi Fermi level
The frequency dependence with the exponent may deviate from 1 under the condition that the trap density Nt is not uniform in depth. For the case when the trap density near the gate oxide/channel interface is higher than that in the interior of the gate oxide, tends to be
smaller than 1. For the opposite case, may become larger than 1. As for the bias dependence predict by the number fluctuation model, the normalized drain current noise SIDS/IDS2 varies with approximately as 1/IDS2 or 1/(VGS-VT)2 in strong inversion region given by (2.2)~(2.5) while is nearly independent of bias in weak inversion region, shown in (2.1). In this work, the LFN in terms of SIDS/IDS2 measured from n-channel MOSFETs just follows number fluctuation model and varied with IDS according to the relationship of 1/IDS2.
Fig.2.2 Schematical illustration of electrons in the channel of MOSFET moving in and out of the traps giving rising to fluctuations in the inversion carrier density and thereby the drain current.
2.2.2 Mobility Fluctuation Theory
Mobility fluctuation is another mechanism, which can contribute flicker noise. The mobility fluctuation model was first proposed by F.N. Hooge with an empirical formula given for the resistance fluctuation . According to the Hooge empirical formula, the drain current noise generated by fluctuation in the channel carrier mobility can be written as (2.6).
where H is a dimensionless parameter and referred as Hooge parameter. The typical values of
H range between 10-3 and 10-6 for surface channel transistors. H may be down to 10-7 for buried channel transistors like N+ gate pMOSFETs and even lower to the order of 10-8 for JFETs. Note that phonon scattering was proposed as the primary source generating mobility
fluctuation noise . The effective mobility eff of the channel carriers is determined by different scattering mechanisms, which vary in different ways with the effective normal field E⊥eff as a function of inversion carriers density QINV and body depletion charge QB. As a result,
H is not only dependent on technology but also on the bias conditions. In general, each scattering process generates mobility fluctuation noise with the amount given by each respective Hooge parameter, denoted as Hj. Assume the scattering processes are independent of each other and then Matthiessen’s rule can be applied as follows
eff j j
(2.7) The fluctuations in different scattering processes are assumed independent. Then the variation applied to (2.7) can lead to
The power spectral density can be derived as
It can be understood from (2.11) that H varies with biases due to the bias dependent factor
2. The total drain current noise is evaluated by adding the noise contribution from each channel segment derived for linear region as follows.
2 2 0 2