1 Introduction

The unprecedented outbreak of the novel coronavirus, which is termed as “Coronavirus Disease-2019 (COVID-19)” by the World Health Organization (WHO), has laid hold of the entire world in a great dilemma, forcing lockdown and straining public health care systems. This led to the precarious positions of numerous governments around the globe facing economic recession. COVID-19 is a respiratory disease caused by a contagious virus known as the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) [1]. It is a member of coronaviridae family, a single-stranded positive-sense RNA virus. Similar to the influenza virus, it also blitzed the human respiratory system giving rise to minor ailments like cough, fever, fatigue, and breathlessness in serious case [2]. Although the exact source of this virus is not known to us, scientists have discovered that its gene sources are typically derived from bats and rodents, and found it to be a member of the β-CoV genera of the coronavirus family. This β-CoV is familiar to the world since there were already two different zoonotic disease outbreaks happened before [4], i.e., SARS-CoV (2002–2003) and MERS-CoV (2012). The COVID-19 was first reported in Wuhan, China's Hubei province in December 2019. Since then, the disease has spread globally like a wildfire due to human-to-human transmission and on January 30, 2020 [3], WHO (World Health Organization) declared it to be a Public Health Emergency of International Concern (PHEIC) [5]. The lifestyles of people all over the world have changed attributable to the outbreak of coronavirus-2019. To control this transmission to some extent, many governments were forced to undertake countrywide lockdowns, recommend to maintain social distancing and self-isolation, and also advice to work from home. Mass testing of the population at large were conducted [6]. Many countries are struggling to produce an efficient vaccine/treatment for this virus. Early diagnosis and management are one of the important means to contain the spread of this contagious virus [7]. The understanding of the structural information along with the pathological information of COVID-19 are required to design various diagnostic methods. The image of this virus was displayed by the Centers for Disease Control and Prevention (CDC), USA [8], and it is round shaped consisting of a thin membrane where envelope and spike proteins are attached as shown in Fig. 1. Its genetic material is RNA rather than a DNA and is covered by the Nucleocapsid proteins (N-Protein). The envelope and spike proteins are termed as E-Protein and S-Protein, respectively [9]. It is also essential to understand the mechanism of the virus involved in recognizing the receptor. COVID-19 causative virus SARS-CoV-2 recognizes the receptor named angiotensin-converting enzyme 2 (ACE2) present in humans. The virus-surface spike protein acts as a mediator for the arrival of coronavirus into host cells. This spike protein consists of receptor-binding domain (RBD) which specifically accepts ACE2 as its receptor. From their crystal structures, it is determined that SARS-CoV RBDs have two parts—a core and a receptor-binding motif (RBM). The RBM conciliates the interactions with ACE2. The ACE2 surface also possesses two hotspots for binding SARS-CoV virus [10, 11]. Jian Shang et al. determined the structural basis of receptor recognition by SARS-CoV-2 through crystallization of SARS-CoV-2 RBD–ACE2 complex [12].

Fig. 1
figure 1

Structure of SARS-CoV-2

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The methodologies adopted for detecting SARS-CoV-2 in human at present are real-time reverse transcription-polymerase chain reaction (RT-PCR) and Enzyme-Linked Immunosorbent Assays (ELISA) IgG antibody test. In ELISA test, the related antibodies from the blood serum of patient’s body are detected rather than the actual virus [13, 14]. Currently, the primary method for diagnosis is the real-time RT-PCR where the specimen from interior nasal swab is taken to detect the gene of E-protein, RNA (N-Protein) along with open frame reading b1 (OFRb1) and OFRb2. The detection process starts by placing the sample or virus RNA in the testing kit. Next, a replica of this virus RNA is produced by depositing primer over it. Further, this virus RNA is converted to complementary DNA (c-DNA) through reverse transcriptase process and by using DNA polymerization technique, various copies are formed [15]. c-DNA is the synthetic DNA in which the sequence of bases is complementary to that of a given example of DNA. RNA serves as a template for c-DNA synthesis. The final step is to denature and break the DNA into two strands by heating. After this, the primer and reporter molecules which are fluorescent in nature and quencher, collectively known as probe, are added to the denatured DNA helix using annealing processes. The Thermus Aquaticus (TAQ) enzyme removes the reporter from the probe. As the reporter gets detached from the quencher, it produces light. In this way, the rRT-PCR kit detects SARS-CoV-2 [16]. Molecular diagnosis using this technique takes at least 3 h which includes the virus RNA preparation. Furthermore, the diagnostic accuracy can also be affected by these RNA preparation steps. Nowadays, the rapid antigen test (RAT) is also performed where viral antigen is detected. However, since this kind of detection process is also based on label sensor, it is also less accurate. Therefore, highly sensitive diagnostic techniques whose detection processes directly depend on viral antigens in the clinical samples are required for an accurate and rapid detection of COVID-19 [17, 18]. Of all the currently available diagnostic methods, the FET-based biosensors can be a promising candidate with various advantages such as high sensitivity providing instantaneous measurements with a very less quantities of analytes [19, 20]. Such biosensors have great potential in clinical diagnosis, point-of-care testing, and on-site detection. Tunnel field effect transistor (TFET)-based biosensors have the ability to give higher sensitivity and better performance with faster response [21,22,23,24,25]. This transistor is a gated reverse bias p-i-n diode and it works on the principle of band-to-band tunneling giving sub-threshold swing (SS) steeper than that of MOSFET [26,27,28].

In this work, TFET-based biosensor is studied for diagnosing SARS-CoV-2 through the investigation of electrical property (dielectric constant) of C-DNA and S-protein of the virus. The S-protein of COVID-19 is composed of glycoproteins like biotin-streptavidin and folded proteins whose general dielectric constant approximately ranges from 1 to 4. As per the literature [29, 30], the dielectric constant of DNA lies between 1 and 64. Hence, two ways of virus detection methods are adopted and these are the detection using S-protein and the DNA detection where the virus RNA is converted into its C-DNA. Sensitivities of the proposed TFET-based biosensor are analyzed for both the detection methods. Several FET-based biosensors have been reported in the literature for sensing SARS-CoV-2 [31,32,33,34]. However, the proposed biosensor in our work is based on the Tunnel FET which works on the principle of quantum mechanical tunneling and it is well known for its steeper sub-threshold swing characteristics providing faster switching. This peculiar property of TFET is responsible for the impressively high sensitivity when being used in the sensing applications. Also, the sensing process is done by immobilizing the target molecules inside the nanogaps which is created by etching some part of the oxide layer. Two types of metal are used for gate. This can avoid the chances of alteration of the chemical properties of the target molecules due to the reaction with the solution of ionic liquid gate.

2 Device structure and simulation strategy

Figure 2 shows the 2D schematic of Vertical TFET (VTFET)-based label-free biosensor designed for sensing SARS-CoV-2. It consists of a SiGe pocket with 30% Ge concentration allowing both vertical and lateral tunneling of the device. This N + pocket has a doping concentration of 1 × 1019 cm−3 throughout these analyses. The dimensions of the device are indicated in Fig. 2. Two metal gates, Φm1  = 3.8 eV (source side) and Φm1  = 5.1 eV (drain side), are utilized in this sensor design to obtain better ION/IOFF ratio. The doping concentration of source, channel, and drain regions are, respectively, 5 × 1019 cm−3, 1 × 1015 cm−3, and 1 × 1018 cm−3. The fixed dielectric material (HfO2) is 10 nm long. A layer of SiO2 having 1 nm thickness is embedded in the structure to account for the immobilization of receptor molecules as well as for minimization of the leakage current. The entire sensing process is assumed to occur in a dry environment.

Fig. 2
figure 2

2D cross-sectional view of Vertical TFET-based SARS-CoV-2 sensor

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All the simulations are done using 2D Sentaurus TCAD tool [35]. The band-to-band tunneling (BTBT) mechanism occurring within the device is executed using non-local BTBT model. The forbidden energy bandgap narrowing due to the higher doping level in the drain and source regions is accounted in the simulation process by the bandgap narrowing model. Shockley Read Hall (SRH) model is included to handle the recombination mechanisms due to indirect bandgap materials. The working principle of this type of biosensor depends on the gate and channel coupling. This coupling is less when the cavities are empty and it increases when the biomolecules are incubated inside the cavities as in this case effective gate capacitance increases. Consequently, the concentration of electron in the channel rises significantly giving higher drain current. In order to carry out this action in the simulation process, the biomolecule to be detected is replaced by an insulator with same value of dielectric constant. Thus, the nanogaps are occupied by this insulator. The condition when the cavities are empty is represented by an insulator having k = 1 (air). The fabrication aspects are not much focused in this work. However, such type of FET-based dielectric modulated label-free biosensors are successfully fabricated in other reported works. Giwan Seo et al. fabricated an FET-based biosensor for the detection of COVID-19 causative virus in human nasopharyngeal swab specimens where they used SARS-CoV-2 spike antibody for the hybridization process [17]. The detection process of the proposed vertical TFET-based COVID-19 sensor is given in Fig. 3.

Fig. 3
figure 3

Operation procedure of vertical TFET-based COVID-19 sensor

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3 Results and discussion

The fundamental characteristics of the proposed sensor concerning the S-protein and C-DNA are investigated in this section for better understanding of its operation and physics. Although the exact value of dielectric constant of this virus is not declared till now, it is known to us that the dielectric of S-protein ranges from 1 to 4, while the dielectric constant of DNA lies constant between 1 and 64. Therefore, in this work, k = 4, 10, and 12 are used to represent S-protein and C-DNA.

3.1 Sensitivity analysis concerning neutral charge

Figure 4 investigates the ID–VGS characteristics of the VTFET-based sensor for various value of dielectric constants (k) of the virus protein and C-DNA assuming that they are neutral charged. The amount of drain current rises when the nanogaps are filled with biomolecules (k = 4, 10, 12) and its value is less in the empty state of the nanogaps. This is because the hybridization of the biomolecules due to the immobilized receptors inside the nanogaps imparts a measurable change in the channel conductivity as the effective gate capacitance increases.

$$C_{eff} = \frac{{\varepsilon_{bio} \varepsilon_{SiO2} }}{{\varepsilon_{bio} t_{SiO2} + \varepsilon_{SiO2} t_{bio} }},$$
(1)
Fig. 4
figure 4

Transfer characteristics of Vertical TFET-based label-free biosensor for sensing SARS-CoV-2

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where Ceff is the effective capacitance per unit area assuming that the filled factor of nanogaps is 100%. It is understood from Eq. (1) that Ceff increases with \({\varepsilon }_{bio}\) (value of k). This increases the electric field lines in the channel region and causes the accumulation of more charges. Consequently, the drain current enhances. The corresponding energy band diagrams in both lateral and vertical directions for different values of k representing the biomolecules are, respectively, plotted in Fig. 5a and b. Band bending is more at k = 12 which explains the higher drain current characteristics in comparison with other k under consideration. The drain current sensitivity of the proposed SARS-CoV-2 sensor is measured with respect to k = 1 (air), i.e., the state when the nanogaps are empty. The sensitivity is measured using Eq. (2).

$$Sensitivity, S_{n} = \left. {\frac{{I_{D,k} }}{{I_{{D,Air\left( {k = 1} \right)}} }}} \right|_{{V_{GS,} V_{DS} }},$$
(2)
Fig. 5
figure 5

Conduction and valence band energy distribution over a lateral direction and b vertical direction at various value of k

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where ID,k and ID,Air(k=1), respectively, indicates the drain current at a fixed gate (VGS) and drain voltage (VDS) for filled nanogaps (S-proteins or C-DNA) and empty nanogaps. Figure 6a depicts the plot for calculated drain current sensitivity for the three different neutral charged biomolecules under consideration. The sensitivity is found to be in the order of 106 at k = 12, which is quite high as compared to the existing devices because of the presence of the SiGe n + pocket at the source–channel junction. This shows the viability of this biosensor as a superior one. The response time of the proposed biosensor is specified as time to rise to 90% of final value, measured from onset of step input change in the measured variable. From Fig. 6b, the response time is found to be tpLH = 12 ps which is very less. This is due to the steeper sub-threshold swing characteristics of TFET. Furthermore, ID–VGS characteristics shown in Fig. 4 clearly display the variation in certain DC characteristics like ION, Vth, SS, and ION/IOFF for the virus protein and DNA within the nanogaps. The variation of SS and ION/IOFF at various value of k representing S-protein and C-DNA is depicted in Fig. 7. The rise in ION/IOFF is about 30% and SS drops by a factor of 1% when the value of k under consideration increases.

Fig. 6
figure 6

a Drain current sensitivity of VTFET-based biosensor for neutral charged biomolecules. b Time-dependent response of the VTFET-based biosensor at dielectric constant, k = 12

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Fig. 7
figure 7

Variation of sub-threshold swing (SS) and ION/IOFF at various value of k representing S-protein and C-DNA

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3.2 Sensitivity analysis concerning DNA charge density

The method of virus detection using its DNA is done by converting the RNA of the virus into DNA using reverse transcriptase process. The DNA molecules can possess charges and hence it can alter the sensitivity of the sensor depending on the density of the charges. In this section, the responses of the proposed sensor to the positively and negatively charge DNA which are immobilized within the nanogaps are studied. Figure 8a shows the difference in drain current from maximum negative to maximum positive charge density of DNA considered in the simulation. The transfer characteristics is plotted assuming that the nanogaps are fully filled with DNA molecule having k = 10. To visualize the difference in current characteristics with charge density more clearly, the transfer characteristics is plotted in linear scale in Fig. 8b. The ON-state current and threshold voltage in both the cases depend on the charge density of the DNA under test. Drain current increases as the positive charge density enhances while it is observed to be declining as the density of negatively charged analytes rises. The threshold voltage (Vth) is also observed to be declining from maximum value of negative to maximum value of positive charges of the DNA molecules under consideration. Therefore, another method of determining sensitivity is in terms of Vth as it is a function of dielectric constant and charge of the analytes at the interface.

$$Sensitivity, S_{n} = V_{th,k = 1} - V_{th, k},$$
(3)
Fig. 8
figure 8

Variation of transfer characteristics at different DNA charge density where drain current is in a log scale and b linear scale

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where Vth,k=1 and Vth,k are the Vth of the ID–VGS characteristics for empty nanogaps and filled nanogaps, respectively.

The ID–VGS characteristics of the proposed sensor at k = 1, 4, 10, and 12 having fixed negative charge density, Nbio =  − 1 × 1012 C/cm2 are plotted in Fig. 9a. The drain current is observed to be shifted towards the right when the density of the negatively charged DNA molecules rises from neutral to − 2 × 1012 C/cm2. The change in Vth is plotted in Fig. 9b for various values of k considered in this analysis. But, for a particular density of charged DNA, Vth reduces with the increase in k. Equation 2 is used to calculate the drain current sensitivity. From Fig. 9c, it is clear that the sensitivity declines for the improved values of the negative charge densities of the DNA molecules. This can be explained using the potential balanced equation given in Eq. 4.

$$V_{GS} = \Psi_{S} + \Phi_{MS} - \left( {\frac{{q\left( { \mp N} \right)}}{{C_{eff} }}} \right),$$
(4)
Fig. 9
figure 9

a Transfer characteristic of VTFET sensor for the detection of SARS-CoV-2 when the DNA charge density is − 1 × 1012 C/cm2. b Threshold voltage (VT) versus various negative charge densities of DNA. c Sensitivity (Sn) versus various negative charge densities of DNA

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where ΨS represents the surface potential, ΦMS is the contact potential, q gives the unit charge, \(\mp \mathrm{N}\) is the biomolecules’ charge per unit area (Nbio), and Ceff is the effective capacitance per unit area. In Eq. (4), for fixed values of VGS and k, the increase in the value of − N will reduce ΨS. The reduction in ΨS is the reason behind the degradation of drain current and ultimately a reason for the sensitivity reduction. Additionally, at constant VGS and –N, the rise in k value results in the improvement of ΨS which enhances the drain current and thus sensitivity. This explains the improvement of Sn with the increase in k value. Again, the term –qN/Ceff in Eq. (4) takes into account the impact of negatively charge biomolecules. The depletion of the channel is limited by this term. Therefore, a higher gate voltage (greater than the case of neutral charged biomolecules) is needed to deplete the channel and hence, Vth rises (Fig. 9b).

Similarly, the impacts of positively charged DNA on the characteristics of the sensor are studied in Fig. 10. Figure 10a shows the ID–VGS characteristics of the proposed sensor at k = 4,10, and 12 considering the effect of positive charges keeping Nbio = 1 × 1012 C/cm2. Reduction of Vth with the increase in the density of the positive charge is observed in Fig. 10b. This is because, the increase in positive charge density (+ N) in the term qN/Ceff of Eq. (4) leads to the rise in surface potential (ΨS) at a given VGS. Thus, the channel conductance of the sensor increases. Likewise, the increase in density of positive charges of DNA improves the sensitivity of the device which can be seen from Fig. 10c.

Fig. 10
figure 10

a Transfer characteristic of VTFET sensor for the detection of SARS-CoV-2 when the DNA charge density is 1 × 1012 C/cm2. b Threshold voltage (VT) versus various positive charge densities of DNA. c Sensitivity (Sn) versus various positive charge densities of DNA

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3.3 Effect of scaling on noise in TFET-based biosensor

A semiconductor device faces reliability problems due to the inherent defects like interface trap charges (ITCs) present in the device physics [36]. Hence, the models that explicitly take into account the occupation and the charge stored on traps must be considered in the simulation. Acceptor-type traps at the interfaces are examined in this section. This type of traps does not possess any charge when it is not occupied and carry the charge of an electron when fully occupied.

Uniform and Gaussian type of distribution are investigated in this work [37].

$$\begin{gathered} {\text{Uniform}}:\;N_{0} ; for E_{0} - 0.5E_{S} < E < E_{0} + 0.5E_{S} \hfill \\ {\text{Gaussian}}:\;N_{0} exp\left( { - \frac{{\left( {E - E_{0} } \right)^{2} }}{{2E_{S}^{2} }}} \right) \hfill \\ \end{gathered}$$

Here, N0 is set with the concentration of traps (1 × 1013 eV−1 cm−2), E0 (0 eV) and ES (0.1 eV) are given in eV by EnergyMid and EnergySig. The trap charge density distributions against energy are plotted in Fig. 11a. Figure 11b depicts the transfer characteristics curves of VTFET biosensor at k = 12 showing the effect of ITCs. The traps located near the tunneling junction are mainly responsible for the degradation of drain current. They are plotted in Fig. 11a. Figure 11b depicts the transfer characteristics curves of VTFET biosensor at k = 12 showing the effect of ITCs. The traps located near the tunneling junction are mainly responsible for the degradation of drain current. The process of random trapping and detrapping are also one of the major reasons of the fluctuation in the total number of carriers available for current transport [38]. The trapped charges can instigate fluctuation in carrier mobility and electric field too. The noise produced by such traps are studied. This type of noise cannot be completely eliminated since it is inherited in the device physics. Therefore, it has to be minimized by clever choice of device material and geometry. Effect of pocket length scaling on drain current noise spectral density (Sid) is shown in Fig. 12a and b for f = 1 MHz and 10 GHz, respectively. Furthermore, the distribution of net Sid over frequency is plotted in Fig. 13. The Sid is higher at lower frequency and its value diminishes for elevated frequency. Hence, this type of noise is known as the low-frequency noise. Net Sid is observed to be higher at LPocket = 10 nm as compared to 15 nm and 20 nm. Hence, considering the noise as well as drain current aspect, LPocket = 20 nm is considered for all the analyses. Figure 14 shows the sensitivity variations with and without traps at k = 12. The sensitivity slightly decreases in the presence of traps but it is high enough to surpass the sensitivity of the state-of-the-art biosensors. The lower limit of detection (LOD) is measured by considering the signal-to-noise ratio (SNR) extracted from a combination of noise and I–V characterization. The SNR for bioFET devices in terms of number fluctuation model is presented as [39]

$$SNR = \frac{{g_{m} }}{{\sqrt {S_{id} } }} = \frac{1}{{\sqrt {S_{VFB} } }} = \sqrt {\frac{{WLC_{ox}^{2} f}}{{\lambda kTq^{2} N_{T} }}},$$
(5)
Fig. 11
figure 11

a Distribution of trap charges over energy b Influence of uniform and Gaussian type of trap distributions on drain current characteristics

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Fig. 12
figure 12

Drain current noise spectral density of TFET-based biosensor at a f = 1 MHz b f = 10 GHz

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Fig. 13
figure 13

Net Sid with respect to frequency

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Fig. 14
figure 14

a Sensitivity of VTFET-based biosensor in the presence and absence of traps at k = 12. b Plot of SNR as a function of solution gate voltage

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where W and L are the widths and lengths of the device, respectively. λ is the tunneling parameter for electrons in silicon oxide, k is the Boltzmann constant, T is the temperature, f is the frequency at which the power of the noise density (Sid) is measured, and Cox is the oxide capacitance per unit area. NT is the trap density including surface states and interface traps/defects. The LOD follows the minimum detectable surface potential change and it is given by 1/SNR, which is limited by the flat-band voltage fluctuations due to the effects of traps and interface states [39, 40]. Figure 14b shows the plot of SNR as a function of solution gate voltage. The peak SNR value of 11,200 is obtained which translates to a minimum detectable voltage of ~ 89 µV. SNR is maximum at the point of peak transconductance (gm). Hence, the LOD is significantly low for this very less minimum detectable voltage.

3.4 Benchmarking against various reported work

The proposed VTFET-based biosensor for the detection of SARS-CoV-2 is benchmarked in this section against the parameters such as sensitivities, response time and limit of detection of various simulated, analytically modeled, and fabricated works published till date. Table 1 shows the status map of various FET-based sensors. The term ‘approximate sensitivity’ is used in Table 1 as they are extracted from the published work.

Table 1 Status map of fet-based biosensors
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4 Conclusion

Developing a highly sensitive and rapid biosensor for the detection of SARS-CoV-2 has become extremely important to contain the COVID-19 pandemic to some extent. In this work, a vertical TFET-based dielectric modulated biosensor for sensing COVID-19 causative virus (SARS-CoV-2) is proposed. The utilization of n + pocket at the source side provides better drain current of the device. The simulation data clearly remark a very high sensitivity for different dielectric virus proteins (S-protein and DNA) which are hybridized within the nanogaps. An optimum sensitivity of 1.56 × 106 is obtained for fully filled neutral biomolecules when k = 12 which is quite high. Further, investigation has been done on the change in sensitivity due to the effect of virus DNA charge density. The sensitivity increases when the nanogaps are filled with positively charged biomolecules while it is observed to be declining when the analytes are negatively charged. The sensitivity of this sensor is also studied in the presence of noises induced by the interface trap charges. Finally, a status map of published FET-based sensors is studied and it reveals the viability of the proposed VTFET-based biosensor to be a superior one with low operating power and better sensitivity.