Investigation the impact of the gate work-function and biases on the sensing metrics of TFET based biosensors

Field-Effect Transistors (FETs) based biosensors have attracted significant attention in recent times because of the several advantages such as label-free electrical detection, small size and low weight, low-cost mass production, and the possibility of on-chip integration of both sensor and measurement systems [1–5]. FET based biosensor was initially used as Ion Sensitive Field Effect Transistor (ISFET) [1] and became popular for the detection of charged biomolecules. The detection of neutral biomolecules which was a challenge for ISFET [1], could be overcome with the concept of Dielectric Modulated (DM) FET where nanogap cavity, used for biomolecule detection, was embedded in the gate material or gate insulator of a Metal-Oxide-Semiconductor FET (MOSFET) [3, 4]. With the insertion of biomolecules in the nanogap cavity, the effective capacitance of gate oxide changes as it depends on dielectric constant (ε_κ) and charge density (Q) of biomolecules [4–7]. Therefore, DM FET based biosensors can be used to detect charged as well as neutral biomolecules [4].

In past various device topologies such as conventional inversion mode FET [2–4], Junctionless FETs [5, 6], impact ionization MOSFET [6, 7], tunnel FETs [8–16] have been explored for biosensing applications. Tunnel FETs (TFETs) are emerging as potential candidates to overcome the scaling limitation due to their superior performance in terms of speed, power dissipation, and steep switching [8, 9]. TFET based biosensors have shown superior sensitivity and response over their MOSFET counterparts due to carrier transport through Band-to-Band Tunneling (BTBT) mechanism [10, 11]. Thus, TFET based biosensors are drawing greater attention and can be used in the DM topology [12–16], which uses the properties of dielectric modulation and tunneling to detect biomolecules in the cavity.

Sensitivity and Selectivity are essential parameters for FET biosensors [2–4, 6]. Sensitivity (S) is used to measure the presence of biomolecules in the nanogap cavity whereas Selectivity (ΔS) distinguishes between various biomolecules [17]. Previous work on TFET based biosensors to detect the presence of biomolecules through dielectric modulation with the reported drain current sensitivity of 10⁷ for APTES biomolecules (ε_κ = 3.57) [12–16]. While the detection of biomolecules through TFETs is interesting, enhancing the sensing metrics through the optimization of device parameters is a crucial issue for TFET biosensors. In the present work, we address the tunability of sensing metrics through the optimization of gate work-function and back bias for DM p-TFET. As gate work-function and back bias both govern the extent of tunneling through the source-channel junction [18, 19], the optimization of their values is critical for enhancing the performance of TFET biosensors. Our results demonstrate that a low value of gate work-function coupled with a back bias (opposite to the polarity of front gate voltage) should be used to enhance the sensing metrics of TFET based biosensor.

In this work, we have used the Kane model [20] for analyzing BTBT in p-TFET as shown in figure 1(a), along with models for bandgap narrowing, Shockley–Read–Hall (SRH) process [21], concentration and field-dependent mobility with Fermi–Dirac statistics to analyze the performance of devices. Figure 1(b) shows the result of our simulations [22] which agrees reasonably well with the published experimental data for p-TFET with spike anneal process [23]. The parameters values of Kane's Model used in this simulation are bbt.gamma = 1.950, bbt.a_kane = 5.370e + 21 and bbt.b_kane = 1.50e + 7. These parameters values are used after good fitting of simulation data with experimental data. To gain insights into the device behavior, different values of gate work-function and back bias values were analyzed with a single cavity DM p-TFET biosensor, as shown in figure 2(a), using ATLAS simulation software [22]. The device structure consists of a silicon film thickness (T_si) of 10 nm, gate length (L_g) of 200 nm, the oxide thickness (T_ox) of 10 nm and buried oxide thickness (T_box) of 20 nm. A nanogap cavity length (L_cavity) of 75 nm towards the source to channel junction is considered in the front gate oxide (10 nm) for accumulating the biomolecules. A lower value of −0.5 V of drain voltage (V_ds) is selected in the work as it assesses the potential for low power applications.

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The choice of nanogap thickness of 10 nm is governed by the fact that the size [3] of protein lies within the 10 nm range, and the thickness of APTES, biotin, and streptavidin layer are 0.9 nm, 0.6 nm, and 6.1 nm, respectively [24]. Thus, a nanogap thickness of 10 nm is used to retain a higher sensitivity for nanometer-size biomolecules [6, 12, 24]. As shown by Kim et al biomolecules considered in this work i.e. 3-aminopropyltriethoxysilane (APTES), biotin and streptavidin can be represented by dielectric constant (ε_κ) of 3.57, 2.63 and 2.1, respectively [24]. An underlap length (L_un) of 25 nm towards the drain side and asymmetric doping of source (10²⁰ cm⁻³) with lower drain doping (4 × 10¹⁸ cm⁻³) were used to reduce the ambipolar effect [9, 25]. To understand the change in electrical characteristics due to the presence of neutral biomolecules, the cavity was uniformly filled and replaced by a biomolecule corresponding to a specified dielectric permittivity. Figure 2(b) shows an enlarged view of the nanogap cavity when it is empty and filled with biomolecules. This work also reports on the detection of charged biomolecules and the impact of the location of biomolecules in the cavity on sensing metrics. Under the dry environment, the possibility of measurement is higher for various structures, and fabrication process of biosensor structure is also simple as compared to biosensor in a watery environment [2–7]. A sensitivity limitation is observed in the biosensor under aqueous environment due to high ion concentration of the solutions, but this limitation is no longer concern when the biosensor is used in the dry environment [2–7]. Therefore, an air environment is considered in our work to detect bio-molecule. There are various papers [8, 9, 12, 13, 16, 26–28] on TFET and TFET biosensor where BTBT model is included and effect of trap-assisted tunneling (TAT) is not considered. Some authors have also examined the impact of TAT on TFET and TFET biosensor [15, 22, 29, 30]. We have also found that the sensitivity in TFET is higher without TAT; however, a significant value of sensitivity is also observed in TFET biosensor with TAT model, therefore, the inclusion of TAT model will not affect the performance of TFET biosensor. Nevertheless, in this work, to better understand the physics of the TFET biosensor, TAT model is not included.

Figure 2(c) shows drain current (I_ds)—front gate voltage (V_fg) characteristics in absence (ε_κ = 1) and presence of APTES biomolecule (ε_κ = 3.57). We have only included APTES biomolecule in this result for a better understanding of the change in the electrical characteristics due to the presence of biomolecule in the nanogap cavity. The results for other biomolecules (streptavidin and biotin) are similar and not shown here. The three different values of gate work-function (φ_m) correspond to band edge work-function values i.e. 4.2 eV (n-type), 4.6 eV and 5 eV (p-type) were consider for the analysis. As the presence of biomolecule in the nanogap cavity corresponds to an increase in ε_κ of the cavity from 1 to 3.57, the control of the front gate over the source-to-channel tunneling junction increases due to increased gate capacitance. This enhances the electrostatic gate controllability of the front gate electrode over the tunneling junction, and as a result, the minimum tunneling width (W_T) between the conduction band and valence band reduces i.e. W_T2 < W_T1 as shown in figure 2(d). This leads to greater tunneling of carriers from source to the channel and I_ds increases with ε_κ [9]. The drain current is higher at higher φ_m because of greater tunneling of carriers. However, to function as a sensor, an enhanced difference between drain current in presence and absence of biomolecule is required, and not the absolute I_ds value.

The variation of drain current sensitivity (S) with gate work-function (φ_m) has been shown in figure 3(a). Sensitivity (S) is defined as a ratio of drain currents (I_ds,bio / I_ds,air) in the presence and absence of biomolecules [2, 6, 10–13, 31]. Maximum sensitivity is obtained for φ_m = 4.2 eV while minimum sensitivity is exhibited at higher work-function values (5 eV). Peak sensitivity (S_max) obtained for φ_m = 4.2 eV is nearly ×10 and ×550 times higher than that obtained for φ_m = 4.6 eV and 5 eV, respectively. Although, S_max shifts to higher (absolute) front gate voltages, the range of V_fg for achieving S_max is limited to −2 V. Figure 3(b) shows the dependence of S_max on different biomolecules which are represented through various dielectric permittivity (ε_κ) values. Higher sensitivity exhibited by DM TFET based sensor at lower gate workfunction values indicates the enhanced difference between drain currents in the presence and absence of biomolecules in the cavity. The improvement in S_max reflects on the significance of workfunction optimization to enhance the maximum sensitivity of the TFET biosensor. Nearly two orders of improvement in S_max are observed for streptavidin (from 1.6 × 10³ to 1.4 × 10⁵) which increases to about 2.5 orders (from 1.7 × 10⁵ to 9.4 × 10⁷) for APTES biomolecule with φ_m = 4.2 eV, when compared with φ_m = 5.0.

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To further comprehend the variation in S with φ_m, the electrostatic potential (Ψ_S) extracted at 1 nm below the oxide-silicon interface (x, y = 0) along the channel direction is shown in figures 3(c)–(d). The change in electrostatic potential (ΔΨ_S) between absence and presence of biomolecules for φ_m = 4.2 eV is higher than the corresponding change with φ_m = 5 eV. A lower gate workfunction will result in an increased electron concentration at the front surface of silicon film as compared to a device with a higher gate work-function. As a result, the electrostatic potential at the surface of the semiconductor film will be higher in a device with a lower φ_m in the absence of biomolecules. With the insertion of biomolecules in the nanogap cavity, energy bands will bend depending on the change in capacitance as shown in figure 2(d). This will result in the reduction of tunneling width and, hence, greater tunneling of holes from source to the channel which will lead to the lowering of the electrostatic potential at the surface of the semiconductor film. Thus, the relative change in the electrostatic potential (ΔΨ_S) is higher for a lower gate work-function (4.2 eV) as compared to a higher gate work-function (5 eV). The significant change in ΔΨ_S reflects on the suitability of lower gate work-function (∼4.2 eV) for p-TFET based biosensor.

The impact of back gate bias (V_bg) on the performance of conventional FET based biosensor have been investigated in the literature [31–33]. Therefore, we also have investigate the significance of V_bg to tune the sensitivity of TFET biosensor to higher values. Figure 4(a) shows maximum drain current sensitivity (S_max) as a function of back bias. The dependence of S_max on V_bg can be explained from the I_ds–V_fg graph shown in figure 4(b). Applying a negative back bias (for p-TFET) reduces the tunneling width and results in greater tunneling of carriers from source to the channel. This results in a higher drain current even in the absence of biomolecules and, therefore, the relative difference in current due to the presence of biomolecules in the cavity is reduced. Hence, sensitivity is degraded by applying negative back gate bias. A positive back bias, until 1.0 V, reduces drain current due to a wider tunneling width and, hence, I_ds in the absence of biomolecules is reduced. Therefore, the relative change in the drain current due to the presence of biomolecules in the cavity is maximized and sensitivity improves. As shown in figure 4(a), S_max improves from 10⁸ to 10⁹ for V_bg varying from 0 V to 0.5 V. Although S_max increases until 1 V, the change is only marginal for V_bg varying from 0.5 V to 1 V. Hence, V_bg = 0.5 V is selected as an optimal bias for the TFET based biosensor. Beyond V_bg = 1 V, S_max again decreases due to an increase in the ambipolar current which is bias dependent [25]. The increase in ambipolar current as shown in figure 4(c) results in a higher drain current even in the absence of biomolecules and, hence, lower S_max values for V_bg > 1 V are obtained.

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Figure 4(d) shows the variation of minimum tunneling width (W_T) with back gate bias for biomolecules (ε_κ = 3.57, 2.63 and 2.1) and air (ε_κ = 1). W_T is the minimum separation distance between the conduction band of source and valence bands of the channel [9] and is maximum in the absence of biomolecules (figure 2(d)). This figure shows that the variation in W_T with V_bg is prominent in the absence of biomolecules than in their presence because of the direct proportionality on gate capacitance (through ε_κ) on biomolecules. Also, a maximum difference (in absence and presence of biomolecule) in W_T is obtained for V_bg within the range 0.5 V to 1.0 V, which confirms the dependence of I_ds and S_max on V_bg as shown in earlier graphs.

The behavior of S_max on V_bg can also be analyzed by extracting the hole concentration (n_h) as a function of V_bg at the front surface of the semiconductor film. Applying a negative bias enhances tunneling of holes from source to channel region while a positive back bias reduces the degree of tunneling more significantly in the absence of biomolecules in the cavity. When the cavity is empty, the front gate is unable to modulate the energy bands to influence the tunneling of carriers. As a consequence, the application of a positive back bias can result in a decrease in the hole concentration at the front surface of semiconductor film as shown in figure 4(e). In the presence of biomolecules in the cavity, the modulation of the bands is primarily being governed by the front gate bias and application of a lower back gate voltages (−0.5 V to 0.5 V) is unable to significantly modulate the energy bands, and hole concentration does not change appreciably (figure 4(f)). Thus, the maximum change in hole concentration, which also reflects a maximum change in the drain current occurs at V_bg ∼ 0.5 V. This change in hole concentration, as shown in figures 4(e)–(f) reflects on the enhancement in S_max as compared to that achieved at V_bg = 0 V. In order to see the impact of V_bg on energy band profile, lateral energy band diagrams from source to drain near the front surface and back surface with applied negative back gate voltage is shown in figures 4(g) and (h), respectively. Figures 4(g) and (h) shows that for V_bg from 0 V to −0.5 V and to −1.0 V, minimum tunnelling width (W_T) at the front surface and back gate of silicon decreases due to improved electrostatics over the channel this leads to the higher value of drain current of APTES biomolecules for V_bg = −1.0 V.

In order to examine the characteristics and sensitivity performance of p-TFET biosensor for various biomolecules, a I_ds–V_fg and Sensitivity −V_fg plots are shown in figures 5(a) and (b), respectively for biomolecule (ε_κ) = 2, 4, 6, 8, 10 and 12. In figure 5(a), I_ds increases as dielectric constant of biomolecules increases from 2 to 12 and this is attributed due to increased gate controllability over the channel [8–10]. Similar to figure 5(a), in figure 5(b) Sensitivity increases with an increase in the dielectric constant of biomolecules, and this occurs because ratio between of I_ds,bio/I_{ds, air} changed to a higher value. The peak value of sensitivity (S_max) in figure 5(b) are ∼5 × 10⁵, 3 × 10⁹, 5 × 10¹⁰, 2 × 10¹¹, 8 × 10¹¹ and 2 × 10¹² for biomolecules (ε_κ) = 2, 4, 6, 8, 10 and 12, respectively.

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Apart from enhancing the Sensitivity (S) through gate work-function and back bias, another important metric is the distinguishability or separation of various types of biomolecules [2, 3, 17] which is known as Selectivity (∆S), and defined as the ratio of drain currents in the presence of biomolecules in the cavity i.e. (I_ds,bio1)/(I_ds,bio2). The dependence of maximum Selectivity (∆S_max) with gate workfunction (φ_m) is shown in figures 6(a)–(b). ∆S_1,max and ∆S_2,max are defined as the ratio of (I_ds,APTES) / (I_ds,Biotin) and (I_ds,Biotin) / (I_{ds,Streptavidin}), respectively. A higher value of ∆S is advantageous as different biomolecules can be distinguished from each other. Results indicate that a lower work-function of 4.2 eV and a positive back bias of 0.5 V are advantageous to improve Selectivity apart from Sensitivity. Selectivity is enhanced by ×(1.8 − 2) by V_bg. ∆S_1,max is higher than ∆S_2,max due to the greater change in the dielectric permittivity (Δε_κ = 3.57–2.63 = 0.94) for APTES and Biotin as compared to that between Biotin and Streptavidin (Δε_κ = 2.63–2.1 = 0.53). The improvement in both Selectivity and Sensitivity through the appropriate choice of gate work-function and back bias reflects on the tunability of the sensing metrics through device optimization.

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After optimizing the value of φ_m = 4.2 eV and V_bg = 0.5 V for achieving higher sensing metrics for neutral biomolecules, we investigate the sensing capability of TFET biosensor for charged biomolecules. The biomolecule can have a positive or negative charge and the same is evaluated by the Henderson–Hasselbalch equation. The charge on the biomolecule depends on the pH of the solution, molar concentration and isoelectric point (pI) [17]. The charge on the biomolecule can be negative for pI < pH and positive if pI > pH. A significant difference between the pI of the biomolecule and pH of the solution is preferred to improve the detection of the biomolecule [34]. The value of pI of biomolecule used in this work i.e. APTES, streptavidin and biotin, are 8.73 [35], 5–6 [36] and 3.5 [36], respectively. As specific charge densities for each biomolecule, for different molar concentration and pH values, have not been reported in the literature [24]. It is not possible to model a biomolecule with certain fix charge density. Also, the charge on the biomolecule is not constant and it varies with the pH and molar concentration [37]. Therefore, charged biomolecules are considered and have been analyzed through a fixed value of interface charge [4, 6]. To understand the change in sensitivity due to the presence of negatively charged biomolecules, we have shown the results for Streptavidin (ε_κ = 2.1). The impact of the charge is simulated by considering negative fixed charge density (−Q) at the Si/SiO₂ interface.

The presence of charge on the biomolecule allows for the additional change in I_ds–V_fg characteristics apart from that due to the presence of biomolecules in the cavity for a fixed φ_m and V_bg. As a result, drain current sensitivity is expected to improve with an increase in the charge on the biomolecule. The same is shown in figure 7(a) where I_ds–V_fg characteristics are plotted for various charge densities. The value of −Q is varied from −10¹⁰ Ccm⁻² to −10¹² Ccm⁻² with ε_κ of 2.1 [4, 6, 12, 13, 16, 38]. The variation of maximum Sensitivity (S_Q,max) of a charged biomolecule with charge density is shown in figure 7(b). The S_Q,max can be understood as a linear combination of sensitivity due to the presence of biomolecules in the cavity (S_Neutral) and due to the charge of biomolecules (S_Charged). For lower values of charge densities i.e. ≤ ∣10¹¹∣ Ccm⁻², Sensitivity does not change appreciably and total Sensitivity (S_Total) is governed by S_Neutral. For values of charge density greater than ∣10¹¹∣ Ccm⁻², S_Total increases appreciably to ∼3 × 10⁸ with V_bg = 0.5 V for Streptavidin biomolecule (ε_κ = 2.1) due to an appreciable contribution of S_Charged. Variation for other biomolecules (Biotin and APTES) will be similar and is not shown in this graph.

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In practical applications of the FET based biosensor, the accumulation of biomolecules can be disordered, random and complex due to the low binding probability of biomolecules in a nanogap cavity [6, 12, 39]. Therefore, the location of the biomolecule in the partially filled cavity is expected to be important for the functioning of a biosensor. To analyze the same, we have considered 25% and 50% filled cavity or fill-in factor (r) [6, 39] with APTES biomolecule as a function of distance from the source-channel tunneling junction (figure 8(a)). As shown in figure 8(b), S_max is strongly dependent on the distance from the source-channel interface and reduces very sharply as the location of biomolecule shifts to the interior of the cavity. A 50% filled cavity with biomolecule at the source-channel junction achieves nearly the same S_max as a filled cavity while a reduction of an order is observed for 25% filled cavity at a position at the tunneling junction. Results indicate that the fill-in factor is not crucial for the detection of biomolecules in TFET biosensor but the location of the biomolecule is critical for the functioning of the biosensor. As biomolecule shifts away from the source-channel tunneling junction, the controllability of the gate to modulate the energy bands is diminished and, hence, S_max reduces. To achieve S_max ≥ 10⁴, APTES biomolecules must be positioned within to 12 nm from the source-channel tunneling junction for a 50% filled cavity. As shown in figure 8(c), drain current reduces with an increase in a and, hence, S_max reduces. Selectivity shows a stronger dependence on the location of biomolecules within the cavity (figure 8(d)). To obtain reasonable values of ΔS_1,max and ΔS_2,max biomolecules must be limited to a region 5 nm from the source-channel junction. Selectivity, primarily governed by the ratio of drain currents, depends on the effective gate oxide capacitance which depends on the location and dielectric permittivity of the biomolecules. Therefore, a cavity with two different biomolecules such as APTES and Biotin within the cavity will exhibit different values of total gate capacitance even at the same location due to the difference in permittivity. As the location of the biomolecule shifts away from the tunneling junction, the peak values of ΔS_1,max and ΔS_2,max reduces.

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To further explain the sensitivity degradation with a tunneling width as a function of the varied location of biomolecules is shown in figures 8(e)–(f) where r = 50% APTES biomolecules are considered in the cavity. Where tunneling width (W_T) is defined as the minimum distance between the conduction band (CB) of the source to valence band (VB) of the channel. It is well known that I_ds current will be higher in TFET for narrow (minimum) tunneling width and will be low for wider tunneling width [10–12]. In figure 8(e) tunneling width is extracted just below the 0.5 nm from the front oxide-silicon interface along the channel direction at V_fg = −3.0 V, V_bg = 0.5 V and V_ds = −0.5 V and a similar approach have been also used for extraction of W_T in figure 8(f). Figure 8(f) shows a minimum W_T ∼16 nm for a = 0 nm to 12 nm as a result of a higher value of I_ds for APTES leads into a sensitivity value from 10⁹ to 10⁴ (figure 8(c)). However, for a ≥ 12 nm, W_T (≥16 nm) increases due to loss of front gate over the tunneling junction, owing to this I_ds for APTES reduces and sensitivity value below 10⁴ is achieved for a ∼12 nm. Thus to achieve the considerable value of sensitivity (10⁴) in TFET biosensor, biomolecules must be positioned at (a = 0 nm) or near to (a ≤ 12 nm) tunneling junction within nanogap cavity. Since selectivity is also a ratio of I_ds,bio1/I_ds,bio2 thus above explanation of sensitivity degradation can also be used for degradation of selectivity with biomolecules varying locations (a).

To overcome the location dependence sensitivity degradation of TFET, choosing a lower length cavity (10 nm–15 nm) is not feasible due to the length of biomolecules that lies up to the range of 50 nm [40]. This can be overcome by the use of advanced structures of TFET [41, 42] which incorporate vertical as well as lateral tunneling phenomenon for current conduction. Such design would be relatively less sensitive on the location of a biomolecule in a cavity as both lateral and vertical tunneling components would contribute to the current in the presence of biomolecules in the cavity.

In TFET biosensor we used a single cavity at source-channel junction due to the presence of tunnelling junction and to get the higher sensitivity in TFET an underlap region at the drain to channel junction is used to reduce the ambipolar conduction [8–13, 27]. A double cavity (DC) TFET biosensor is shown in figure 9(a) and its corresponding I_ds−V_fg in presence and absence of biomolecules is compared with a single cavity (SC) TFET biosensor (used TFET structure in this work) as can be seen in figure 9(b). Since in TFET biosensor, tunnelling junction (source-channel junction) is a more sensitive region to detect the biomolecules [3–5] and second cavity located at the drain side is far away from the tunnelling junction, thus I_ds current is nearly same for SC TFET and DC TFET biosensor (figure 9(b)) and sensitivity value will also be same for both the devices. Hence, a single cavity TFET structure is used for biomolecules detection, which can be fabricated easily as compared to the double cavity TFET structure [43]. A detailed description of fabrication for the proposed device architecture is reported in our previous work [43].

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In order to compare our results with previous work of TFET biosensor [10, 12, 13, 15, 16, 26, 29, 44, 45], maximum drain current sensitivity (S_max) of APTES biomolecules (ε_κ = 3.57) is shown in figure 10. In our case, S_max ∼10⁹ is observed after proper optimizing the value of gate work function and back gate bias voltage in p-TFET biosensor.

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In this work, we have investigated the tunability of sensing metrics i.e., Sensitivity and Selectivity by appropriate choice of gate work-function and back gate bias for p-TFET biosensors. It has been observed that a lower gate workfunction (φ_m) ∼4.2 eV and a positive back gate bias (V_bg) of 0.5 V have considerably enhanced the sensing metrics of a p-TFET biosensor. A high sensitivity value ∼10⁹ for APTES along with a selectivity value ∼200 for Biotin biomolecule is obtained in an optimized device. It is also highlighted that the location of the biomolecule in the cavity is critical than a fill-in factor (r) of the cavity for TFET based biosensor. To obtain the S_max ≥10⁴ and appreciable value of ΔS_max for 50% filled cavity, biomolecules should be accumulated within 12 nm and 5 nm from the tunneling junction, respectively. The present work highlights new opportunities to tune the sensing metrics to higher values and also identifies the constraints in terms of location of the biomolecule in the cavity in TFET based biosensors.

This work is partially supported by DST SERB Project (file no. SRG/20l9/001l03, dated December 04, 2019).