**7.1. Fully filled nanogap**

Firstly, we assume that the entire embedded nanogap of the CG TFET in **Figure 2b** is filled with biomolecules, and observe the influence of different factors on its sensitivity. The Fill Factor of an embedded nanogap is defined as the ratio of the area covered by immobilized biomolecules to the total area of the nanogap, and is generally expressed in percentage. For a fully filled nanogap, the Fill Factor is 100%.

## *7.1.1. Negatively charged biomolecules*

The sensitivity of the CG TFET as a biosensor with fully filled nanogap is plotted for negative charge of biomolecules for *k* = 5, 7, 10 and 12 in **Figure 3a**. With the increase in magnitude of negative charge, the sensitivity decreases. The presence of negatively charged biomolecule-SiO2 interface prevents depletion of the p-type channel, thus requiring a higher gate voltage than a neutral interface to deplete the p-type substrate, and cause reduction in tunnel width. The voltage balance equation of a metal-oxide-semiconductor structure is represented as [54].

$$V\_{\mathcal{L}} = \psi\_s + \mathfrak{O}\_{\text{MS}} - \frac{qN\_{\text{inv}}}{\overline{C}\_m'} \tag{6}$$

where, *VG* is the gate voltage, *Ψ<sup>s</sup>* is the electrostatic potential at the surface, Φ*MS* is the difference between the work functions of metal and semiconductor, *q* is the value of electronic charge, *Nbio* denotes the number of charges per unit area, and *Cox* / is resultant capacitance per unit area. Furthermore,

$$\mathbf{C}'\_{\alpha} = \frac{k}{t\_m(\mathbf{x})} \tag{7}$$

**Figure 2.** 2-D schematic of dielectric-modulated biosensors: (a) CG TFET, (b) decreasing step profile of biomolecules, (c) increasing step profile of biomolecules, (d) concave step profile of biomolecules, (e) convex step profile of biomolecules,

Dielectric-Modulated TFETs as Label-Free Biosensors http://dx.doi.org/10.5772/intechopen.76000 25

(f) MOSFET, and (g) legend for all the 2D schematics.

where *k* is the dielectric constant, and *t ox*(*x*) is the dielectric thickness as a function of lateral position due to the circular gate.

form of a semi-circle. This gate engineering introduces flexibility into the architecture of the device, and aids in optimization of chief electrical parameters, primarily the ambipolar current and ratio of on and off currents [53]. One of the techniques of reducing ambipolar current in a TFET apart from asymmetric source-drain doping is the introduction of gate-drain underlap [3, 45, 53]. In case of Circular Gate TFET, the gate being circular in shape, the gate dielectric thickness is dependent on the radius of the circle. A gate-drain underlap in the architecture shall decrease the thickness of the gate dielectric, which shall, in turn, increase the influence of the gate on the channel. Therefore, reduced ambipolar current can be achieved with appropri-

A circular gate TFET as a DM biosensor is depicted in **Figure 2a**. The total length of the Silicon body TFET is 100 nm, where the source and drain are 30 nm each. An embedded nanogap is incorporated into the geometry to immobilize the biomolecules. The embedded nanogap is usually etched out of a dielectric formed by a native oxide. We have considered a native oxide

Firstly, we assume that the entire embedded nanogap of the CG TFET in **Figure 2b** is filled with biomolecules, and observe the influence of different factors on its sensitivity. The Fill Factor of an embedded nanogap is defined as the ratio of the area covered by immobilized biomolecules to the total area of the nanogap, and is generally expressed in percentage. For a

The sensitivity of the CG TFET as a biosensor with fully filled nanogap is plotted for negative charge of biomolecules for *k* = 5, 7, 10 and 12 in **Figure 3a**. With the increase in magnitude of negative charge, the sensitivity decreases. The presence of negatively charged biomolecule-

ence between the work functions of metal and semiconductor, *q* is the value of electronic

/ = \_\_\_\_ *<sup>k</sup> t*

 interface prevents depletion of the p-type channel, thus requiring a higher gate voltage than a neutral interface to deplete the p-type substrate, and cause reduction in tunnel width. The voltage balance equation of a metal-oxide-semiconductor structure is represented as [54].

> *q Nbio Cox*

is the electrostatic potential at the surface, Φ*MS* is the differ-

/ (6)

*ox*(*x*) (7)

*ox*(*x*) is the dielectric thickness as a function of lateral

/ is resultant capacitance per

of 1 nm in the nanogap, which is assumed to remain after the gap is etched out.

ate ratio of on and off current simultaneously.

24 Design, Simulation and Construction of Field Effect Transistors

fully filled nanogap, the Fill Factor is 100%.

*VG* <sup>=</sup> *<sup>ψ</sup><sup>s</sup>* <sup>+</sup> *<sup>Φ</sup>MS* <sup>−</sup> \_\_\_\_\_

charge, *Nbio* denotes the number of charges per unit area, and *Cox*

*7.1.1. Negatively charged biomolecules*

where, *VG* is the gate voltage, *Ψ<sup>s</sup>*

*Cox*

where *k* is the dielectric constant, and *t*

position due to the circular gate.

unit area. Furthermore,

**7.1. Fully filled nanogap**

SiO2

**Figure 2.** 2-D schematic of dielectric-modulated biosensors: (a) CG TFET, (b) decreasing step profile of biomolecules, (c) increasing step profile of biomolecules, (d) concave step profile of biomolecules, (e) convex step profile of biomolecules, (f) MOSFET, and (g) legend for all the 2D schematics.

source-channel tunnel junction has an impact on the drain current. However, as the dielectric constant increases, the minimum value of drain current shifts to the left, thus, verifying the increase in gate capacitance. This corresponds to a decrease in the threshold voltage as shown in **Figure 3d**. The threshold voltage exhibits a high shift with increasing negative charge for low-*k* biomolecules as compared to high-*k* cases. For *k* = 5, the threshold voltage increases by

Like Section 7.1.1, similar plots are presented here for positive charge of biomolecules. The variation of sensitivity with increasing positive charges for *k* = 5, 7, 10 and 12 is shown in **Figure 4a**. The positive charge of biomolecules depletes the p-type channel, and causes more tunneling of electrons at the source-channel tunnel junction. Hence, the sensitivity increases. For *k* = 5, the sensitivity increases by a factor of 11 when the charge changes from

plot can be made in a similar manner as in Section 7.1.1 with the help of Eqs. (6) and (7).

**Figure 4.** (a) Sensitivity versus positive charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12; (b) transfer

characteristics of CG TFET as biosensor for *k* = 1 (air), 5, 7, 10 and 12 at fixed negative charge, *Nbio*= 10<sup>11</sup> cm−2

voltage versus positive charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12.

, whereas for *k* = 12, the factor is 2.29. The explanation for the trend of the

as com-

27

Dielectric-Modulated TFETs as Label-Free Biosensors http://dx.doi.org/10.5772/intechopen.76000

; (c) threshold

3.56% as the charge of the immobilized biomolecules change from neutral to −1012 cm−2

pared to *k* = 12 where the increase is relatively small, that is, 2.49%.

*7.1.2. Positively charged biomolecules*

neutral to 1012 cm−2

**Figure 3.** (a) Sensitivity versus negative charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12; (b) surface potential versus position from source to drain at gate voltage 2 V, drain voltage 0.5 V, and *Nbio* = −10<sup>11</sup> cm−2 for dielectric constant, *k* = 1, 5, 7, 10 and 12; (c) transfer characteristics of CG TFET as biosensor for *k* = 1 (air), 5, 7, 10 and 12 at fixed negative charge, *Nbio* = −10<sup>11</sup> cm−2 ; (d) threshold voltage versus negative charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12.

Considering a fixed gate voltage, as the negative charge of biomolecules increases, *Ψ<sup>s</sup>* must decrease in order to satisfy the potential balance in Eq. (6). As a result, the drain current decreases, thus reducing the sensitivity.

The change in sensitivity of the sensor with increasing magnitude of negative charge is more in case of a low dielectric constant and reduces as the dielectric constant of the nanogap increases. At *k* = 5, the sensitivity decreases by a factor of 25 when the charge of the immobilized biomolecules changes from neutral to −1012 cm−2 as compared to *k* = 12, where it drops by 2.61. In Eq. (6), at fixed negative *Nbio* and *VGS*, as *k* in Eq. (7) increases, the potential −\_\_\_\_\_ *q Nbio Cox* / decreases, resulting in a corresponding increase in *Ψ<sup>s</sup>* . This increases the drain current, and hence, the sensitivity of the biosensor. This effect is demonstrated in **Figure 3b**.

**Figure 3c** shows the plots of transfer characteristics of a fully filled nanogap CG TFET biosensor at drain voltage 1 V and charge of biomolecules equal to −10<sup>11</sup> cm−2 . The absence of biomolecules corresponds to *k* = 1 with no charge at the air-SiO2 interface as the nanogap remains devoid of biomolecules. Due to the presence of unaltered gate dielectric towards the channel-drain junction of the geometry, therefore, the ambipolar current is same for all dielectric constants of the nanogap. The dielectric constant of the fully filled nanogap closer to the source-channel tunnel junction has an impact on the drain current. However, as the dielectric constant increases, the minimum value of drain current shifts to the left, thus, verifying the increase in gate capacitance. This corresponds to a decrease in the threshold voltage as shown in **Figure 3d**. The threshold voltage exhibits a high shift with increasing negative charge for low-*k* biomolecules as compared to high-*k* cases. For *k* = 5, the threshold voltage increases by 3.56% as the charge of the immobilized biomolecules change from neutral to −1012 cm−2 as compared to *k* = 12 where the increase is relatively small, that is, 2.49%.

## *7.1.2. Positively charged biomolecules*

Considering a fixed gate voltage, as the negative charge of biomolecules increases, *Ψ<sup>s</sup>*

potential versus position from source to drain at gate voltage 2 V, drain voltage 0.5 V, and *Nbio* = −10<sup>11</sup> cm−2

at fixed negative *Nbio* and *VGS*, as *k* in Eq. (7) increases, the potential −\_\_\_\_\_

biomolecules corresponds to *k* = 1 with no charge at the air-SiO2

sensor at drain voltage 1 V and charge of biomolecules equal to −10<sup>11</sup> cm−2

decreases, thus reducing the sensitivity.

26 Design, Simulation and Construction of Field Effect Transistors

ecules changes from neutral to −1012 cm−2

biosensor. This effect is demonstrated in **Figure 3b**.

corresponding increase in *Ψ<sup>s</sup>*

negative charge, *Nbio* = −10<sup>11</sup> cm−2

*k* = 5, 7, 10 and 12.

decrease in order to satisfy the potential balance in Eq. (6). As a result, the drain current

**Figure 3.** (a) Sensitivity versus negative charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12; (b) surface

constant, *k* = 1, 5, 7, 10 and 12; (c) transfer characteristics of CG TFET as biosensor for *k* = 1 (air), 5, 7, 10 and 12 at fixed

The change in sensitivity of the sensor with increasing magnitude of negative charge is more in case of a low dielectric constant and reduces as the dielectric constant of the nanogap increases. At *k* = 5, the sensitivity decreases by a factor of 25 when the charge of the immobilized biomol-

**Figure 3c** shows the plots of transfer characteristics of a fully filled nanogap CG TFET bio-

remains devoid of biomolecules. Due to the presence of unaltered gate dielectric towards the channel-drain junction of the geometry, therefore, the ambipolar current is same for all dielectric constants of the nanogap. The dielectric constant of the fully filled nanogap closer to the

as compared to *k* = 12, where it drops by 2.61. In Eq. (6),

. This increases the drain current, and hence, the sensitivity of the

; (d) threshold voltage versus negative charge of biomolecules for dielectric constant,

*q Nbio Cox*

/ decreases, resulting in a

interface as the nanogap

. The absence of

must

for dielectric

Like Section 7.1.1, similar plots are presented here for positive charge of biomolecules. The variation of sensitivity with increasing positive charges for *k* = 5, 7, 10 and 12 is shown in **Figure 4a**. The positive charge of biomolecules depletes the p-type channel, and causes more tunneling of electrons at the source-channel tunnel junction. Hence, the sensitivity increases. For *k* = 5, the sensitivity increases by a factor of 11 when the charge changes from neutral to 1012 cm−2 , whereas for *k* = 12, the factor is 2.29. The explanation for the trend of the plot can be made in a similar manner as in Section 7.1.1 with the help of Eqs. (6) and (7).

**Figure 4.** (a) Sensitivity versus positive charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12; (b) transfer characteristics of CG TFET as biosensor for *k* = 1 (air), 5, 7, 10 and 12 at fixed negative charge, *Nbio*= 10<sup>11</sup> cm−2 ; (c) threshold voltage versus positive charge of biomolecules for dielectric constant, *k* = 5, 7, 10 and 12.

**Figure 4b** depicts the transfer characteristics of the CG TFET for *k* = 5, 7, 10, and 12 at *Nbio* = 10<sup>11</sup> cm−2 . The on current in case of positive charged biomolecules is higher than that in case of negatively charged biomolecules as evident from **Table 1**.

In **Figure 4c**, for *k* = 5, the threshold voltage decreases by 4.03% when the charge changes from neutral to 1012 cm−2 , whereas for k = 12, the drop is 2.68%.
