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The results of a comparative literature analysis of internal electrical noises and signal-to-noise ratio for nanoscale BioFET (biological field-effect transistor) and DNA (deoxyribonucleic acid) sensors based on different architectures MIS (metal-insulator-semiconductor), EIS (electrolyte-insulator-semi-conductor) and ISFET (ion-selective field-effect transistor) are presented. Main types, models and mechanisms of internal noises of bio- & chemical field-effect based sensors are analyzed, summarized and presented. For the first time, corresponding detail electrical equivalent circuits were built to calculate the spectral densities of noises generated in the active part of a solid (semiconductor, dielectric) and in an aqueous solution for MIS, EIS and ISFET structures based sensors. Complete expressions are obtained for the rms (root mean square) value of the noise current (or voltage), as well as the noise spectral densities for the architectures under study. The miniaturization of biosensors leads to a decrease in the level of the useful signal-current. For successful operation of the sensor, it is necessary to ensure a high value of the SNR (signal-to-noise ratio). In case of weak useful signals, it is necessary to reduce the level of internal electrical noise. This work is devoted to a detailed study of the types and mechanisms of internal electrical noises in specific biosensor architectures.

The field-effect transistor-based biosensors (BioFETs) [ion sensitive field effect transistors (ISFET), electrolyte-insulator-semiconductor (EIS) structures, its modifications] are a potential candidate for future bioassay applications due to its low cost, fast response, high sensitivity and small sensing size. The pH-sensitive ISFETs are very important sensors for in vivo continuous monitoring application of physiological and environmental system. The accuracy of ISFET output measurement is greatly affected by the presences of internal noise, drift and slow response of the device. Although the noise analysis of BioFETs so far performed in different literature relates only to sources originated from FET structure which is almost constant for a particular device, the pH-dependent electrochemical noise has not been substantially explored and analyzed in detail. Reliable ways of DNA sequencing by ionic and tunneling current require low-noise and high-speed measurements of current in aqueous environments [

Previous works showed the four DNA nucleotides possess statistically distinguishable electronic signatures [

A solid-state nanopore platform with a low noise level and sufficient sensitivity to discriminate ssDNA homopolymers of poly-A40 and poly-T40 using ionic current blockade sensing are proposed and demonstrated in [

1) highly insulating dielectric substrates that are used to mitigate the effect of parasitic capacitance elements, which decrease the ionic current root mean square (rms) noise level to sub-10 pA and

2) ultra-thin silicon nitride membranes with a physical thickness of 5 nm (an effective thickness of 2.4 nm estimated from the ionic current) are used to maximize the SNR and the spatial depth resolution.

The reliable formation of small nanopores (<2 nm in diameter), fabrication of an extremely thin sensing zone with a thickness comparable to the spacing of each nucleotide, decrease of the noise level, and control of the translocation speed that would guarantee sufficient time to sense each nucleotide are the few challenges that limit the performance of solid-state nanopores. Among these issues, the excess noise level in solid-state nanopores (a few tens of pA to 100 pA, 10 times larger than that of protein counterparts [_{x} membrane directly on top of highly dielectric substrates proposed in [

In [^{2} Hz. This feature is

naturally interpreted as stemming from the voltage noise in the current amplifier coupled to the net capacitance of the mechanically controllable break junction (MCBJ) system. Morikawa reported also a use of insulator-protected nanoprobes for achieving 7.6 pA rms noise at 50 kHz sampling rates in an electrolyte solution [

The LF pH-dependent electrochemical noises that originate from the ionic conductance of the electrode-electrolyte-FET structure of the device and that the noise depends on the concentration of the electrolyte and 1 / f in nature are investigated in [

In [

Syu with coauthors discusses how BioFET sensor can be designed by CMOS platform and the integration with sample processing and data processing apparatus for clinical sample testing [

With the increased use of ISFET as a commercial micro- and nano-BioFET sensor for accurate biomedical measurements, noise factors will determine the performance limits of the system. The total noise comes from the ISFET sensor itself, as well as from the read-out circuit. The important noise components are present in a MOS transistor. The first one is the thermal noise, and the other 1 / f -noise.

The study of noise in BioFETs is important for the reason that any source of noise present in the sensor will impose a fundamental limit on the resolution and accuracy of the measurements and, hence, sensitivity of BioFETs limited by the sensor noise. In BioFET sensors presents several intrinsic and extrinsic rms noise sources [

1) Intrinsic noise i d 1 2 ¯ generated by the electronic device itself ( 1 / f -noise, channel thermal noise, source and drain diffusion resistance thermal noises, substrate resistance noise, shot noise).

2) Extrinsic electrochemical noise i d 2 2 ¯ generated by ion-membrane interactions, in the solution and at the reference electrode.

3) Extrinsic noise source i d 3 2 ¯ coming from biasing elements (power supplies, reference electrode biasing, external biasing resistances). These noise sources can generally be filtered.

The BioFET total noise spectrum can be presented as

i n d 2 ¯ = i d 1 2 ¯ + i d 2 2 ¯ . (1)

Extrinsic electrochemical noise has been modeled in [

The trend towards miniaturization of biosensors leads to a decrease in the level of the useful signal current. A high signal-to-noise ratio must be ensured for the sensor to work successfully. In case of weak wanted signals, it is necessary to reduce the level of internal electrical noise. As follows from the analysis of literature data, many types of internal electrical noises with different generation mechanisms and with different frequency behavior arise in biosensors. To improve the performance of sensors and increase the SNR value, it is necessary to study in detail the mechanisms of these noises and identify their effect on the operation of the sensors.

This work is devoted to a detailed study of the types and mechanisms of internal electrical noises, especially low-frequency noise, in specific biosensor architectures. For this purpose, the corresponding electrical equivalent circuits will be constructed and expressions for the rms noise value will be obtained.

Note that BioFETs several structures (ISFET, EIS, etc.) tend to be operated at low frequencies, where 1 / f -noise is dominated, therefore, our main attention in the next parts of the paper will be focus mainly on low frequency noise.

Main types of semiconductor based BioFET sensors operated using peculiarities of field-effect, especially properties of depletion layer near the interface of semiconductor-insulator. Those are field-effect biosensors: MIS, EIS and ISFET structures.

Electrical noises both in solids and in aqueous solutions have been well studied. Despite this, when considering specific biosensor architectures, it becomes necessary to take into account some specific factors that are usually not taken into account in well-known formulas for noise. These factors are associated with miniaturization (size effects), with the generation of complex physical processes at the interfaces and surfaces of specific materials, etc. In this section, for a complete understanding of the problem, in addition to the already known formulas, we will also present expressions obtained and modernized by us for specific designs of sensors operating in different modes and frequency ranges.

Obvious that sensitivity, selectivity and detectivity of electronic devices determined in general by the internal electrical noise’s types, its level and frequency behavior, and consequently by the SNR [

V 2 ¯ = S V Δ f , i 2 ¯ = S i Δ f . (2)

Here Δ f is the elementary frequency bandwidth. Usually one assumes Δ f = 1 Hz.

Equivalent schematic analogy of a noisy resistor presented in

Below we will shortly characterize the NSD and sources of the main types of noises in metals, semiconductors, dielectrics, bio liquids and electrolyte mediums.

The detailed analysis shows that main types of noises in bio- and chemical sensors can be classified as follows [

1) Noise generated in solid state region:

· Thermal noise;

· Generation-recombination (g-r) noise in the space charge region at the substrate-channel interface;

· 1 / f and g-r noises generated due to trapping and detrapping on the semiconductor/insulator interface;

· Hooge’s bulk 1 / f -noise;

· Channel 1 / f -noise.

2) Electrochemical noise associated with the ion/membrane interactions:

· Thermal noise;

· Shot or Schottky noise;

· 1 / f -noise in corrosive interfaces;

· Spurious noise.

3) Noise generated in the solution and at the reference electrode as well as noise resulting from the fluctuations of the biasing elements:

· Bulkthermal noise;

· Diffusion layer thermal noise;

· Biological noise.

Thermal noise is the electronic noise generated by the thermal motion of the charge carriers (electrons in conductors, electrons and holes in semiconductors, ions in aqueous solution, bio liquids, electrolytes and dielectrics) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment such as sensors can drown out weak signals, and can be the limiting factor on sensitivity of electrical devices. In an ideal resistor it is approximately white, meaning that the power spectral density is nearly constant throughout the frequency spectrum [

S V T = 4 k T R or S i T = 4 k T G , (3)

where T is the thermodynamic temperature, R is the resistance and G is the conductance of the sample.

Those frequency independent noise spectra represent a simplification. An accurate calculation based on a quantum mechanics model gives

S V T ( f ) = 4 R h f ( 1 2 + 1 e h f / k T − 1 ) ,

so that Equation (3) is basically only valid for h f ≪ k T , i.e. for “low” frequencies and high temperatures ( h is the Plank’s constant). However, the quantum noise for h f ≫ k T has to be considered basically only for frequencies very much higher than in radio frequency and microwave application of concentration of non-equilibrium carriers during the random g-r and trapping-detrapping processes as on the interface impurity states and site bindings, as a result of the bulk random g-r processes.

Generation-recombination noise. NSD of the g-r noise determined by the following expression:

S V g − r = S 0 1 + ( ω τ ) 2 .

Here S 0 is the some constant depending on the semiconductor bulk and surface properties, ω = 2 π f is the cyclic frequency, τ is the time constant (for bulk semiconductors usually fluctuating minority carriers’ life time). Generation-recombination noises spectra are described by the Lorentzians.

Biological noise conditioned by the random fluctuation of the number of captured particles/molecules in acqeous solution. Biological processes, such as protein synthesis or trafficking, undergo random fluctuations, “noise”, that are often detrimental to reliable information transfer, but can also constitute opportunities for more efficient cellular computations.

Cellular noise is often investigated in the framework of intrinsic and extrinsic noise. Intrinsic noise refers to variation in identically-regulated quantities within a single cell: for example, the intra-cell variation in expression levels of two identically-controlled genes. Extrinsic noise refers to variation in identically-regulated quantities between different cells: for example, the cell-to-cell variation in expression of a given gene. The main source of stochastic variability on the cellular level is the intrinsic thermal fluctuations of biochemical reactions driving gene expression, signaling, cell cycle, motility, etc. These reactions occur through random collisions and transient binding of various molecular species within a single cell. Cellular noise is random variability in quantities arising in cellular biology. For example, cells which are genetically identical, even within the same tissue, are often observed to have different expression levels of proteins, different sizes and structures. These apparently random differences can have important biological and medical consequences [

Shot noise.Shot noise is a form of noise that arises because of the discrete nature of the charges carried by charge carriers, electrons, holes or ions. When looking at what is shot noise, it can be seen that it is particularly obvious when current levels are low. This is because the statistical nature of the current flow together with the discrete charge levels is more apparent. The continuous flow of these discrete pulses gives rise to almost white noise. There is a cut-off frequency which is governed by the time it takes for the electron or other charge carrier to travel through the conductor. This noise depends on the current flowing and is independent of temperature. The current through the space charge areas of a semiconductor junction (source-channel or drain-channel in BioFET sensors) are composed of many individual current impulses, due to the transport of individual charge carriers. Since this motion of carriers is statistical, we always have, besides the expected dc currentI, also an ac noise component. With the assumption of individual, rectangular current impulses of the width τ for every charge component, we can calculate an NSD as following:

S i S − N = 2 e I × sin 2 ( π f τ ) ( π f τ ) 2 .

For low frequencies, there is sin ( x ) / x ∝ 1 and we get the commonly used expression for the shot noise

S i S − N = 2 e I . (4)

Spurious noise. To discuss digitally-based noise, we need to modify the traditional definition of noise. “Noise is almost always defined as being random, while digitally-based “noise” is deterministic, that is, it can be computed mathematically” [

Usually the time constants involved in the detection of biological and chemical species in bio-liquid or electrolyte medium via field effect are relatively large. Therefore, it would be expected that LF (or flicker) noise is more critical than other types of noises in FET based bio- and chemical sensors.

Heerema with coauthors present an extensive study of the 1 / f -noise in the ionic current through graphene nanopores and compare it to noise levels in silicon nitride pore currents [

Low frequency noise conditioned by the random fluctuations of concentration or mobility of non-equilibrium carriers, ions and charged molecules in aqueous solution, by the trapping-detrapping processes on the free energetic states on the interface surface, as well as by the electron-phonon interactions in the bulk of semiconductor, and by the fluctuation of electron’s and phonon’s distribution functions. For the BioFET sensors LF NSD can be determined by the Hooge’s model, McWhorter or correlated number-mobility fluctuation model and charge fluctuation model.

The main mechanisms of the formation of 1 / f -noise in semiconductors (active part of FETs) presented in [

1) Hooge model [

In his paper [

R n 2 = α H N R 2 f .

Here N is the total number of free carriers in the bulk, and α H is known as “Hooge’s constant” an empirical parameter. This equation fits his data for metal films very well. In [

I n 2 = μ 0 μ e f f ( μ 0 μ l ) 2 q α H I D 2 w l ( V G S − V t h ) 1 f , (5)

where μ 0 is the low-field mobility of the carriers, μ l is the mobility if only lattice scattering exists,

μ e f f = μ 0 1 + θ ( V G S − V t h ) ,

θ is the mobility attenuation factor, V G S and V t h are gate-source and threshold voltages. Again, significant bias dependences can be explained by changes in the assorted mobility parameters.

For modeling S i ( f ) dependencies barely will be useful Hooge’s universal formula of current noises for materials and structures with macroscopically homogeneous current density [

S i ( f ) = α H I 2 N t o t f γ , (6)

where Hooge’s parameter α H for semiconductors typically α H ≈ 2 × 10 − 3 [

2) McWhorter’s or Correlated Number-Mobility Fluctuation Model

McWhorter, working with germanium filaments at MIT Lincoln Laboratory in 1957 proposed that flicker noise is primarily a surface effect [

In the correlated number-mobility fluctuation theory NSD of the flat-band voltage fluctuation can be described as [

S V , F B ( f ) = e 2 k T N t w l β C 2 1 f . (7)

Here, w and l are width and length of the insulator gate, β = 2 ℏ 2 m ∗ Φ B is the McWhorter’s or tunneling parameter ( m ∗ is the effective mass of electrons, Φ B is the tunneling barrier height seen by electron at the interface), N t is the oxide equivalent trap density in eV^{−}^{1}cm^{−}^{3}, C is the cumulative capacitance.

The McWhorter’s model attributes the origin of 1 / f -noise to the random fluctuation on the number of carriers in the channel due to fluctuations in the surface potential^{1}. The fluctuations are caused by rapping and detrapping of carriers by energetic traps located near the Si-SiO_{2} interface [

S i d ( f ) = K F I d s C o x L 2 1 f .

where K F is a quality independent on bias but dependent on sensor fabrication process.

The Hooge’s empirical model attributed 1 / f -noise to carriers’ mobility fluctuations, due to carrier interactions with crystal lattice fluctuations [

S i d ( f ) = α H q μ f I d s ( V g s − V t h ) L 2 1 f ,

where α H is Hooge 1 / f -noise parameter (Hooge’s parameter), μ f is carriers’ effective mobility.

For low noise applications the level of thermal and 1 / f -noises must be sufficiently low.

Based on the number fluctuation noise model [

S i d ( f ) = q 2 μ N o t I d s a t C o x L 2 1 f ,

and at sub-threshold

S i d ( f ) = q 4 N o t I d s 2 C i n v 2 ( C o x + C D ) 4 ( k T ) 2 W L 1 f .

Here C i n v , C o x and C D are the inversion, oxide and depletion layers capacitances per unit area, N o t is the effective oxide traps density per unit area.

Problems of minimization of ISFET noises and results of LF noise measurements are detailed discussed in [

3) Charge Fluctuation Model

We can consider 1 / f -noise source, V 2 ¯ , via fluctuation of the oxide traps (free bonds of proton donors O − and proton acceptors OH 2 + ,

Q t = e N o t w l , (8)

where N o t is the number of occupied traps. Then the NSD of the charge fluctuation of occupied traps is:

S Q ( f ) = ( e w l ) 2 S N o t ( f ) . (9)

Spectral density of the number fluctuations of occupied traps can be determined as [

S N o t ( f ) = w l N f . (10)

The voltage-fluctuation noise spectral density can be calculated using the expression:

S V ( f ) = S Q ( f ) C e f 2 = e 2 N w l C e f 2 1 f . (11)

In expressions (10) and (11) N is the equivalent density of traps per unit area at the SiO_{2}/electrolyte interface, C e f = C i C d C i + C d , C i is the capacitance of the insulator (oxide) layer and C d is the capacitance of the semiconductor depletion layer.

SNR is a measure for comparison of the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power P_{S} to the noise power P_{N}. For linear devices SNR can be calculated from expressions:

SNR = P S P N = I S I N = I S S i Δ f (12a)

= V S V N = I S R t o t S V Δ f . (12b)

Here I S ( V S ) and I N ( V N ) are useful signal current (voltage) and noise equivalent current (voltage), correspondingly, R t o t is the total resistance of the sample.

In review [_{2}-based transistors quantify. The combined sensitivity enhancement and noise rejection guarantee a high SNR of the NCBioFET, making this device a promising candidate for realizing advanced integrated nano-biosensors. Most importantly, NCFETs can improve the SNR compared to traditional MOSFETs by reducing the LF flicker noise related to carrier number fluctuations. The results of the analysis show that despite the fundamental limits of charged-based BioFETs, the NCBioFET can improve the limits of label-free detection of biomolecules.

McAndrew with coauthors shows how correlated noise can be implemented in Verilog-A, and presents a new and simple technique to simulate the noise correlation coefficient using only the standard Space noise analyses [

S i ( f ) = 4 k T G + K F I 2 W L 1 f .

Numerical and analytical theory of signal and noise of double-gated pH-sensors was provided in [_{min}) of such devices. It is defined ΔpH_{min} as being the minimum change in pH above the noise ﬂoor that can be continuously (without signal averaging) detected by the FET-sensor. In this article, authors offer a comprehensive theoretical analysis of double-gated pH sensors, with emphasis on the “so-called” amplified Nernstian response and the SNR. Authors combine the classical theory of the MOSFET [

In [_{ID} shows a typical 1 / f α behavior with the exponential slope α ∝ 1 in a 3-dec frequency bandwidth of f 1 − f 2 = 1 − 1000 Hz. The SNR was extracted based on the following equation [

SNR = Δ I / ∫ f 1 f 2 S I D ( f ) d f ,

where ΔI is the drain current change in the range of pH = 4 − 10. In range 1 − 1000 Hz S I D ( f ) ∝ ( 10 − 20 ÷ 10 − 25 ) A^{2}/Hz ( V g ∝ 0.8 ÷ 1.2 V), SNR max ∝ 3000 A/A at V g ∝ 1.0 V.

Our research in the field of mechanisms of LF noise in semiconductors, semiconductor devices and BioFET sensors is devoted to a number of works (e.g. [

The main sources of electron mobility fluctuations in semiconductors were analyzed in [

Brief overview of the basic tendencies of development of nanoscale (bio-)chemical sensors is presented in [

· Low-frequency noise spectral density generally expressed as

S v = A V 2 + β f γ .

· The noise amplitude (parameter A) reflects the sample quality and increases with decreasing device size and depends on many parameters of material, its structure, sizes, NTs bulk and surface physical and chemical conditions, from its fabrication method.

A ∝ R , A ∝ 1 N , A ∝ 1 L .

where R is the device resistance, N is the number of atoms or carriers in the system, L is the sample length ( N ∝ L ). A = 1 × 10 − 11 R .Parameter A varies within 10^{−}^{13} up to 4 × 10^{−}^{4}.

· The size scaling is incorporated in Hooge’s empirical law A = α H N .

· In the linear regime 1 / A ∝ | V g − V t h | if noise is due to mobility fluctuations and 1 / A ∝ | V g − V t h | 2 if noise is due to number fluctuations.

· Parameter β = 0 is expected for pure resistance fluctuation in ohmic conductors. The γ ≠ 1 behavior is associated with nonlinear characteristics.

· Excess noise with a slope different from unity ( γ ≠ 1 ) can be explained by a superposition of a few Lorentzians.

In [

LF noise spectroscopy at nanoscale and noise reduction in BioFET sensors functionalized with carbon NT multilayers areee detailed analyzed in [

In this section, for the first time, complete equivalent electrical circuits of some biosensors are constructed, taking into account the characteristics of a semiconductor, dielectric, aqueous solution, analyte and reference electrode. On the basis of these schemes, the spectral densities of the internal electrical noises (or rms values) were calculated. In these calculations, we used both well-known formulas (for example, for thermal noise) and formulas that we have modernized and obtained for specific investigated cases and operating modes. We also used the results of studies by other authors. These expressions and formulas can be found both in ours and in articles by other authors listed in the cited references.

For analyzing the noise properties, we need model equivalent electrical schemes of the elements of investigated structures. Below we will use the standard equivalent schematic analogy of a noisy resistor R consisting serial connected voltage generator via average square of the fluctuating voltage V 2 ¯ , or by the parallel connected current generator via average square of the fluctuating current i 2 ¯ (

On

Electrical equivalent scheme for noises analyses for this case can be presented as the serial connection of semiconductor and insulator layers (see

V M I S 2 ¯ = V i 2 ¯ + V S 2 ¯ + V F B 2 ¯ ,

where

V S 2 ¯ = 4 k T R S b + 4 k T R S d 1 + ( ω R S d C d ) 2 , V i 2 ¯ = 4 k T R i , V F B 2 ¯ = e 2 k T N γ w l C e f 2 1 f , R S = R S b + R S d ,

R S b and R S d are resistances of the bulk region and depletion layer of the semiconductor, correspondingly. Note that second term in right hand of V S 2 ¯ is the g-r part of the noises, conditioned by the g-r processes in the depletion region. The noise source V F B 2 ¯ characterizes fluctuation processes which take part on the interface of the depletion region and insulator. Thus

V M I S 2 ¯ = 4 k T ( R S b + R i ) + e 2 k T N t γ w l C e f 2 1 f + 4 k T R S b 1 + ( ω R S d C d ) 2 ≈ 4 k T R i + e 2 k T N t γ w l C e f 2 1 f + 4 k T R S b 1 + ( ω R S d C d ) 2 ,

as R i ≫ R S . Therefore, noises consist of the thermal, flicker and g-r components.

Schematic picture of EIS structure and its electric equivalent scheme are presented in

V c h 2 ¯ = e 2 N A C e f 2 1 f ; V D 2 ¯ = 4 k T R D ; V R E 2 ¯ = 4 k T R R E ; V b 2 ¯ = 4 k T R b ; V D N A 2 ¯ = K D V D α f b .

Here V c h 2 ¯ is the spectral density of the charge fluctuation on the insulator-electrolyte interface [

Therefore, for EIS structure we can write

V E I S 2 ¯ = 4 k T ( R S b + R i + R b + R D + R R E ) + K D V D α f b + e 2 N w l C e f 2 ( 1 + k T N t γ N ) 1 f + 4 k T R S b 1 + ( ω R S d C d ) 2 .

Taking into account that

R i ≫ R S + R b + R D + R R E ,

for the NSD of the EIS biosensor we get

V E I S 2 ¯ ≈ 4 k T R i + K D V D α f b + e 2 N w l C e f 2 ( 1 + k T N t β N ) 1 f + 4 k T R S b 1 + ( ω R S d C d ) 2 .

For the sensors on the base of such structures we have important difference. Schematic picture and electrical scheme of the ISFET/MOSFET structure presented on

Source-drain current noise can be successfully described by the Hooge’s 1 / f -noise, flat-band voltage fluctuation, semiconductor potential fluctuation and depletion region resistance fluctuation.

The NSD of the drain current noise in MOSFETs using also results of [

i D S 2 ¯ = 4 k T μ e f C e f w l ( V ′ F B + φ S 0 − V A − φ 00 − 2 e ε S N D C i ) + e 2 k T N t γ w l C e f 2 ( g m + α μ e f C e f I D ) 2 1 f + ω τ I 0 2 1 + ( ω τ ) 2 . (13)

Here first term describes thermal, second term, flicker and third term, g-r part of the noise.

The NSD of the drain current noise in a load resistor R L connected between source and drain in the linear regime approximated as [

i D S 2 ¯ = i C h 2 ¯ + g C h 2 R D S 2 i R d S 2 ¯ [ 1 + g C h ( R d S + R L ) ] 2 . (14)

According to Hooge’s empirical mobility fluctuation model for elementary bandwidth Δ f = 1 Hz

S i ( f ) = i D S , 1 / f 2 ¯ = e α H i D S w l C o x ( V G S − V T ) 1 f = e α H μ e f i D S V D S l 2 1 f . (15)

In (12)-(13) α is Coulomb scattering coefficient; C d is the capacitance of the diffusion layer; C e f is the effective capacitance per unit area, consisting of the insulator and any functionalization layer; C d l is the depletion layer capacitance; I 0 in (13) is the any parameter; R L is the load resistor resistance; R S d is the resistance of semiconductor bulk and depletion layer; R d S is the series resistances; i C h 2 ¯ is the noise contribution from the channel with conductance g C h , V S 2 ¯ is the semiconductor bulk resistance voltage noise; R c t = k T Z e | 1 i T | is the charge transfer resistance [

As we can see noise spectral density for all investigated cases consist three obligatory components: thermal, low-frequency and generation-recombination. Depending on the special experiment conditions either type of noises will be dominated in the appointed frequency interval. For example in EIS functionalized with PAMAM SWNT 1 / f -noise dominates over thermal noise lower 10 Hz [^{4} Hz [

All authors participated in the statement of the problem and discussion of the results. L. Gasparyan and F. Gasparyan conducted literature review. F. Gasparyan and V. Simonyan built equivalent circuits and participated in writing the text of the article.

The authors declare no conflicts of interest regarding the publication of this paper.

Gasparyan, L., Gasparyan, F. and Simonyan, V. (2021) Internal Electrical Noises of BioFET Sensors Based on Various Architectures. Open Journal of Biophysics, 11, 177-204. https://doi.org/10.4236/ojbiphy.2021.112006