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Dependency of both source-drain current and current sensitivity of nanosize ISFET biosensor vs. concentration of DNA molecules in aqueous solution theoretically is investigated. In calculations it is carried out effects concerning charge carriers distribution in current channel and concerning carriers’ mobility behavior in high electrical fields in the channel. The influence of DNA molecules on the work of ISFET biosensors is manifested by a change in the magnitude of the gate surface charge. Starting with fairly low concentrations of DNA, ISFET sensors respond to the presence of DNA molecules in an aqueous solution which is manifested by modulation of channel conductance and therefore the source-drain current changes of the field-effect transistor. It is shown that the current sensitivity with respect to concentration of DNA molecules linearly depends on the source-drain voltage and reaches high values.

The ion-sensitive field-effect transistor (ISFET) is one of the most popular semiconductor biosensors, and has been introduced as the first nanosized bio-chemical sensor. Currently, the use of ISFET technology encompasses a wide range of applications in a variety of areas, and those in the bioelectronic monitoring areas are particularly noteworthy. The ISFET sensor has been used to measure H^{+} or OH^{−} ions concentrations in aqueous solution, causing an interface potential on the gate insulator (oxide). Much attention has been paid to silicon based biosensors in the field of bio-analytical applications due to their favorable characteristics (Si-based technology, sensitivity, speed, signal-to-noise ratio, miniaturization, etc.). The introduction of the ISFET biosensor was in 1970 [^{5}. In [

The analysis conducted above shows a high level of experimental research in this area. Very good results have been achieved in the field of sensors fabrication and pH-sensitivity; effective methods have been proposed for lowering the level of low-frequency noise in order to increase the signal-to-noise ratio. However, it seems to us that there are still many open questions when studying the physical mechanisms occurring in a semiconductor and interface semiconductor-insulator that determine and influence on the basic parameters of the sensors.

The aim of this research is the theoretical investigation, simulation and demonstration of the dependency of source-drain current of the silicon nanowire based ISFET biosensor vs. concentration of DNA molecules in aqueous solution. DNA detection mechanism and source-drain current sensitivity depending on the influence of the DNA molecules which occur in an aqueous solution over the Debye screening length will be investigated and discussed.

To study the source-drain current of the ISFET biosensor and its sensitivity to the presence of negatively charged DNA molecules in an aqueous solution, it is necessary to consider the physical processes occurring, in particular, at the interface between the gate insulator and the electrolyte. The main physical processes taking place in the ISFET biosensor for DNA molecule detection are sketched in

Particularly silicon based structures and silicon oxide as an insulator will be discussed. In the

The balance equation for the potentials according to

V g = ϕ s + ϕ S i + ϕ c h + ϕ o x + ϕ d l . (1)

To estimate these potentials as well as the threshold voltage, V t h , and flat-band voltage, V F B , we can use the following relations [

V t h = V F B + 2 φ F + ϕ c h ; V F B = ϕ b u l k , s o l − ϕ c h + ϕ d l − Φ S i − Φ o x q + Q o x C o x ; ϕ b u l k , s o l ≈ 0 ; ϕ S i = ϕ b u l k , S i ≈ 0 ; φ F = 2 φ T ln N A n i ; ϕ c h = 4 q ε 0 ε S i N A φ T C o x 2 ; φ T = k B T q ; ϕ d l = 2 φ T ( ε w ε r N s o l K A K + + H s + ) ; ϕ o x = q N t C o x . (2)

Here q is the elementary charge; k B is the Boltzmann’s constant; T is the absolute temperature; φ T is the thermal voltage; φ F is the Fermi potential; ϕ b u l k , s o l and ϕ b u l k , S i are the electric potentials of the bulk solution and the bulk silicon substrate; ϕ d l is the potential of double layer; Φ S i and Φ o x are the work functions of silicon and silicon oxide (SiO_{2}), correspondingly; Q o x is the oxide layer charge per unit area, C o x is the capacitance of the oxide layer per unit area; ε 0 , ε S i , ε o x , ε w and ε r are the dielectric permittivities of free space, silicon, silicon dioxide, water and electrolyte, respectively; N A is the doping acceptor concentration in p-Si substrate; n i is the intrinsic carrier concentration in bulk silicon; K A K + is the molar concentration of the cations in the solution, H s + is the molar concentration of the hydrogen ions at the oxide surface; N s o l is the molar concentration of the solution; N t is the concentration of surface open electronic binding sites (traps) per oxide unit area. Note that the redox potential E redox is a measure of the ease with which a molecule will accept electrons and double layer in solution consist of IHL (Inner Helmholtz layer), OHL (Outer Helmholtz layer) and GCL (Gouy-Chapman layer) [

The main physical processes occur in the conductive channel. Therefore, for further calculations, it is necessary to determine the surface potential of the interface between the semiconductor layer (channel) and insulator ϕ c h . This can be calculated using Equation (1) and Equation (2) and expressions for the density of minority carriers in semiconductor. For ϕ c h we receive:

ϕ c h = φ T ln ( η C o x φ T N A q t n i 2 ) + φ T ln { ln [ 1 + 1 2 exp ( V g − V t h η φ T ) ] } . (3)

where

η = 1 + C d C o x ≈ 1 + q ε 0 ε S i N A 2 φ T C o x 2

is the factor of the transistor non-ideality ( C d is the capacitance of the silicon depletion layer per unit area).

We consider the case of an inversion n-channel liquid-gated FET (

I s d ( y ) = μ e f w [ Q c h d V s d d y + φ T d Q c h ( y ) d y ] . (4)

Here w is the channel width in Z direction, μ e f is the effective mobility and Q c h is the charge density of the channel mobile carriers ( [ Q c h ] = [ C / cm 2 ] ):

Q c h = ∫ 0 t q n ( x , V g ) d x . (5)

Here t is the thickness of current channel in X direction, n ( x , V g ) is the electron’s concentration in the channel. The behavior of the source-drain current is defined by the distribution of the concentration of the mobile charge carriers over the conducting channel. Obviously, the concentration of mobile carriers in the channel depends on both the coordinate x (see

n ( x , V g ) = n s ( V g ) × f ( x , V g ) . (6)

Here n s ( V g ) is the electron surface concentration per unit area at the oxide interface and f ( x , V g ) in unit of [cm^{−1}] is the function which describes the charge carrier distribution in the X-Z plane of the channel (

The surface concentration can be described using the unified charge control model from expression [

V g − V t h = q C o x ( n s − n s , t ) + η V t h ln ( n s n s , t ) , (7)

where n s , t is the surface density of electrons per unit area at the threshold voltage: n s , t = n s at the V g = V t h . It should be noted that the influence of the charge states of the electrolyte is determined by the value of V t h (see Equation (2)). The concentration n s , t can be expressed as:

n s , t = η C o x φ T 2 q . (8)

Equation (7) has no analytical solution for n s in terms of V g . The following approximate solution is suitable for strong inversion and sub-threshold regimes [

n s = 2 n s , t ln [ 1 + 1 2 exp ( V g − V t h η φ T ) ] . (9)

After determining n s ( V g ) , we must also calculate the function f ( x , V g ) in order to evaluate the influence of peculiarities of the carrier distribution on the physical processes taking place in the channel.

In order to find function f ( x , V g ) for the case of the quasi classical approach, we use the following dependence of n ( x ) [

n ( x ) = N c exp [ − ( E c − q ϕ ( x ) ) − E F k B T ] = n 0 exp [ ϕ ( x ) φ T ] . (10)

Here N c is the density of states in the conduction band of a semiconductor, E c is the semiconductor conduction band energy, ϕ ( x ) is the contact potential at the oxide-channel interface. To determine ϕ ( x ) we have to solve the Poisson equation:

d 2 ϕ ( x ) d x 2 = − ρ ( x ) ε 0 ε S i . (11)

Here ρ ( x ) is the space charge density for the fully ionized acceptor centers in semiconductor (usually it is boron in silicon):

ρ ( x ) = − q ( N A − + n − p ) = − q p 0 [ 1 − exp ( − ϕ φ T ) + n 0 p 0 exp ( ϕ φ T ) ] . (12)

Here n , p and n 0 , p 0 are the concentrations of the non-equilibrium and equilibrium electrons and holes, respectively, N A − is the concentration of negatively charged acceptors. We can use following boundary conditions to solve Equation (11) (see

x → ∞ ⇒ ϕ → 0 , x → 0 ⇒ ϕ → ϕ c h . (13)

Using Equation (12) and boundary conditions (13), we obtain the following solution of Equation (11):

ϕ ( x ) = { ϕ c h + q n 0 ε 0 ε S i [ 1 − exp ( − x l s ) ] } exp ( − x l s ) , (14)

where

l s = L D 1 + n 0 / p 0 , L D = ε 0 ε S i φ T q p 0 , (15)

L D is the Debye screening length.

Then using expression for ϕ c h from Equation (3) finally we have for the function f ( x , V g ) :

f ( x , V g ) = n 0 n s × exp { [ ln ( η φ T C o x N A q t n i 2 ) + ln [ ln ( 1 + 1 2 exp ( V g − V t h η φ T ) ) ] + q t 2 n i 2 ε 0 ε S i φ T N A ] exp ( − x l s ) } . (16)

The field caused by the applied gate voltage in the inversion layer of liquid-gated FETs changes the transport behavior of the charge carriers and results in more frequent scattering events than in the absence of the gate voltage. The carrier’s mobility degrades as the result of scattering processes [

( μ e f ) x = μ 0 − θ ( V g + V t h ) , (17)

where μ 0 is the low-field magnitude of the mobility, θ is the coefficient taken as 28 cm^{2}/(V^{2}s) [

μ ( V g ) = μ 0 + θ ( V g − V t h ) , (18)

where μ 0 = μ | V g = V t h , θ = d μ ( V g ) d V g | V g = V t h , and in general case θ can be positive or negative.

In further calculations we will use expression (17) for the mobility of major carriers in the channel.

Using Equation (4) and Equation (17) we can present the drift component of the source-drain current by following expression:

I s d ( y ) ≈ q w n s V d s l [ μ 0 − θ ( V G + V t h ) ] ∫ 0 t f ( x , V g ) d x ,

where n s is determined from Equation (9).

For the integral

∫ 0 t f ( x , V g ) d x

we have

∫ 0 t f ( x , V g ) d x = n 0 n s ∫ 0 t exp [ G exp ( − x l s ) ] d x ≈ n 0 n s t [ 1 + l s t G ( 1 − e − t / l s ) ] . (19)

Here

G ≡ 1 B + ln B + ln [ ln ( 1 + 1 2 exp ( V g − V t h φ T ) ) ] , B ≡ φ T ε 0 ε o x N A q t 2 n i 2 . (20)

Thus

I s d ( y ) ≈ q w n 0 V d s t l [ μ 0 − θ ( V G + V t h ) ] [ 1 + l s t G ( 1 − e − t / l s ) ] . (21)

Behavior of dependency I s d from number of DNA molecules in solution N DNA can be determined from dependency V t h ( Q o x ) .

For simplicity of further calculations assume that η ≈ 1 and taking account that oxide layer capacitance for unit area

C o x = ε 0 ε o x t . (22)

For V t h from (2) we have:

V t h = 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x . (23)

Substituting (23) into (21) gives:

I s d ( Q o x ) ≈ q w n 0 V d s t l [ μ 0 − θ ( V G + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x ) ] × { 1 + l s t { 1 B + ln B + ln [ ln ( 1 + 1 2 exp ( V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x φ T ) ) ] } ( 1 − e − t / l s ) } . (24)

The influence of the oxide interface on the source-drain current of the transistor can be taken into account by the change of the charge of the oxide interface traps Q o x = q N t ( N t is the surface concentration of oxide interface all proton donors and proton acceptors traps in units cm^{−2},

Q ′ o x = q N t + ( 1 − δ ) , δ ≡ N DNA N t + , (25)

where N t + and N DNA are the surface concentrations of positively charged proton acceptor OH 2 + traps (

near the oxide at a distance of the Debye length. It is clear that (25) is correct for the N DNA ≤ N t + , or δ ≤ 1 . In the case of super compensation when N DNA > N t + the DNA additional molecules do not bind on the surface positively charged sites (proton acceptors,

_{2}-solution, process of negatively charged DNA molecule binding and silicon dioxide tetrahedron structure.

Consider the source-drain current sensitivity of the ISFET biosensor to DNA molecules S as a change in source-drain current Δ I s d for a corresponding change in the proportion of DNA molecules in the solution Δ δ :

S = | Δ I s d Δ δ | , A (26)

As Δ δ is dimensionless parameter sensitivity will be measured by the Ampere.

For numerical computation, we use the following values, which correspond to the sample geometry and the parameters of the materials for the investigated nanosize structure at the room temperature: μ 0 = 260 cm 2 / ( V ⋅ s ) [

pH = − log [ H + ] ,

we get

[ H + ] = 10 − pH = 10 − 7 mol / l .

For the electron concentration in the inversion layer we can assume that it is equal to majority carrier’s concentration in p-Si, e.g. n 0 ( inv ) ≈ p 0 = 10 15 cm − 3 . For the N t + we can do following estimation. It is assumed that traps concentration on the interface silicon oxide-electrolyte is the same as silicon oxide-Si. According to data [_{2} interface is about ( 10 10 - 10 11 ) cm − 2 . In further calculation we will use N t + ≈ 10 11 cm − 2 .

For numerical simulation let’s simplify expression for source-drain current assuming that:

1) At the noted above parameters B ∝ 10 10 and we can ignore term 1 B compared ln B as 1 B ≪ ln B ;

2) [ ln ( 1 + 1 2 exp ( V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x φ T ) ) ] ≈ 1 2 exp ( V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x φ T ) ;

3) ln [ ln ( 1 + 1 2 exp ( V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x φ T ) ) ] ≈ ln 1 2 exp ( V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x φ T ) ;

4) 1 − e − t / l s ≈ 1 − t l s .

Thus source-drain current can be presented as follows:

I s d ≈ q t w n 0 V d s l φ T [ μ 0 − θ ( V G + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x ) ] × [ φ T ( 1 + ln B 2 ) + V g + 2 φ F + ϕ d l − Φ S i − Φ o x q + Q o x C o x ] . (27)

Results of numerical calculations of source-drain current I s d vs source-drain voltage V d s and DNA concentration are presented in Figures 3-5. The error in plotting the dependencies in Figures 3-5 does not exceed (5 - 7)%. In order not to complicate the graphs, these errors are not shown in the figures. Note that fluctuations of values by (5 - 7)% particularly do not affect the course of dependencies and do not change the mechanisms for explaining their behavior. As expected, the dependence of I s d on the source-drain voltage is linear. Dependency I s d vs DNA concentration N DNA (or δ ) is very weak (see

behavior can be explained as follows. Assume that all proton donors (OH^{−}) sites in the interface oxide-electrolyte (^{+}) from solution and changes in their charges are not significant and can be neglected during the sensor operation. At low concentration of DNA molecules 0 < δ < 0.1 , they are bind very weakly or not bind with free proton acceptor sites OH 2 + due to its high diffusion activity and the presence of a Coulomb barrier near proton acceptor sites. With increasing DNA concentration and therefore decreasing their diffusion activity (when 0.1 < δ < 0.8 ) negatively charged DNA molecules overcome Coulomb barrier near the proton acceptor sites and bond with them on the oxide surface. As a result the positive surface charge decreases and correspondingly decreases deepness of current channel and its conductivity (source-drain current). At the super compensation of the proton acceptor sites OH 2 + ( δ → 1 , high concentration of DNA molecules) in oxide-electrolyte interface I s d ( δ ) dependency has increasing behavior. Probably it is conditioned by the ionic Coulomb blockade effect [

The dependence of current sensitivity on source-drain voltage for several values of DNA molecules concentration is presented in

Based on the above reasoning, we can draw the following conclusions.

• ISFET nanosized structures can be used for detecting charged DNA molecules.

• The influence of DNA molecules on the work of ISFET biosensors is manifested by a change in the magnitude of the surface charge of the gate electrode.

• Starting with fairly low concentrations of DNA, ISFET biosensors respond to the presence of DNA molecules in an aqueous solution which is manifested by modulation of channel conductance or the source-drain current.

• Current sensitivity linearly depends on the source-drain voltage and reaches high values.

Thus, ISFET nanosized silicon biosensors can be successfully used to detect very low concentrations of DNA molecules in an aqueous solution with high sensitivity. As an advantage note also the compatibility of silicon based devices with modern CMOS technology.

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

Gasparyan, L., Mazo, I., Simonyan, V. and Gasparyan, F. (2019) ISFET Based DNA Sensor: Current-Voltage Characteristic and Sensitivity to DNA Molecules. Open Journal of Biophysics, 9, 239-253. https://doi.org/10.4236/ojbiphy.2019.94017