key: cord-0074056-9z500tbl authors: Das, Rahul; Chattopadhyay, Ankush; Chanda, Manash; Sarkar, Chandan K.; Bose, Chayanika title: Analytical Modeling of Sensitivity Parameters Influenced by Practically Feasible Arrangement of Bio-Molecules in Dielectric Modulated FET Biosensor date: 2022-01-28 journal: Silicon DOI: 10.1007/s12633-021-01617-z sha: 0edb789542d9069c5ae97ec87ac01934dd1f25a3 doc_id: 74056 cord_uid: 9z500tbl In this paper, analytical modeling of a Dielectric Modulated Double Gate Field Effect Transistor (DM-DGFET) for biosensing application is presented with extensive data analysis. Firstly, the size of the nanogaps and arrangements of biomolecules in those gaps are optimized with respect to the sensitivity of the above sensor. The optimized DM-DGFET is next analyzed on the basis of its modeling and simulation. This paper addresses novel issues arising from arrangements of biomolecules, especially from practical point of view. Effect of probe placement due to steric hindrance and random nature of biomolecules, are also considered. The capacitances associated with the nanogaps occupied by biomolecules, following various arrangements, are modeled. Expressions of the threshold voltage, drain current and its sensitivity in terms of variations are also derived using the capacitance model. A comparative study of the proposed and the existing architectures is made. The influence of process variation on the sensitivity of the sensor is also studied. The results from the proposed analytical model are validated with the simulated data obtained from TCAD device simulator. In conclusion, the proposed DM-DGFET based biosensor architecture will emerge as an optimal model, very useful for the study on this field in future. Biosensor research is one of the most developing fields in last few decades. Biosensor works on the principle of detection of biomolecules and gets significant importance for clinical diagnostic, defense, and in several environmental applications. Apart from the above mentioned fields, biosensor is also having a wide range of application areas, viz., in the field of optics [1] , electrochemical sensors [2] , nanomechanics [3] etc. However such biosensors suffer from some serious shortcomings, like requirements of costly equipment, high manufacturing cost, and low sensitivity. Semiconductor based biosensor has evolved in order to overcome these issues. Field effect transistor (FET) based biosensor has several advantages, such as, cost effectiveness, better sensing mechanism, greater precision along with higher sensitivity. Ion Sensitive Field Effect Transistor (ISFET) was invented in around 1970s. Initially, it was widely used for the detection of pH level in any type of solution [6] [7] [8] . The concentration of the ions in the analytes controls the performance of the device. From the deviation of the threshold voltage the concentration of ion or the pH value was detected [9] [10] [11] . In spite of its good performance for the detection of ionic solution or charged molecules, the sensitivity of ISFET degrades for the neutral biomolecules [12] . Therefore, researchers felt the need to design biosensor that can be equally sensitive for charged as well as neutral biomolecules. Dielectric Modulated FET (DMFET) appears as the perfect solution for this issue. In DMFET, the change in the gate capacitance occurs due to the change in dielectric constant of the materials to be tested, and (that) results in (the) deviation in the threshold voltage and drain current of (from) the device w.r.t. those with no material i.e. with air filled nanogaps [12] . On the basis of such deviations, the target material can be characterized. The basic 3D structure of DMFET was proposed by Lm et al. in [12] . In this type of biosensor devices, formation of a nanogap involves a thin film deposition and subsequent wet etching processes. This reduces the complications in lithographic process associated with the planar nanogap FETs [13] [14] [15] [16] [17] . As sensitivity is the prime concern of biosensors, search for highly sensitive biosensor is still in progress. Various unique structures have been proposed to improve the sensitivity. Narang et al. [18] proposed a DG-MOSFET based Dielectric modulated structure for better response. As this structure comprises of two nanogaps for trapping biomolecules, its sensing range is expected to be much wider. As far as the modeling is concerned, significant developments took place in last few years. Narang et al. presented a tunnel FET based bio-sensor considering dielectric-modulation [19] . They also reported a comparative analysis between dielectric modulated FET and TFET in the context of biosensors [20] . Choi et al. modeled the nanogap-embedded FET for bio-sensor applications [21] . Bhattacharyya et al. assessed the performance of a dual-pocket vertical heterostructure tunnel FET-based biosensor [22] . In all the above articles, dielectric modulation has been considered. But, the various possible filling patterns generated by the bio-molecules trapped in nanogap are believed to influence the sensitivity of the biosensor. Unfortunately, this problem is not yet addressed. In this work, some practical surface profiles of organic fluids appeared in biomolecule-filled nanogaps in DG MOSFET will be considered for analytical modeling, for the first time. The silanization process of surface functionalization will be considered in this work, in which the hybridization of bio-molecules with SiO 2 takes place [22] . The structure of the nanogap and its surrounding material will be optimized in order to improve the sensitivity. A detail analytical model of surface potential, threshold voltage, drain current and sensitivity will be presented considering various surface profiles of biomolecules filling the nanogaps created in both sides of the gates. Considering such four patterns (increasing/decreasing inward pattern, concave and convex pattern), the threshold voltage and ON-current sensitivity will be determined. The deviations in threshold voltage and ON-current sensitivity will also be studied. In addition, the effects of process variations on bio-sensing parameters will be analyzed in detail. The analytical modeling of the proposed device structure will be validated with the simulated results obtained from Silvaco TCAD. The device structure is based on traditional n-channel DGMOSFET with a dielectric modulated nanogap embedded gate insulator as shown in Fig. 1 . SiO 2 layer underneath the gate has divided into hydroxyl (-OH) bond and acted as a biomolecule receptor. For a better operation and sensitivity, a thin layer of 1 nm SiO 2 on the top of the nanogap is also kept untouched during the etching process. T ox , T G and t si denote the thickness of the oxide layer, gate and Si-film respectively. In past few decades, researchers realised nanogaps by partly etching out various materials used in the dielectric layer. Amongst several materials, Silicon Di-oxide (SiO 2 ), Hafnium Di-oxide (HfO 2 ), and Poly-Si are used most frequently. In this literature, a comparative analysis of these three materials, considering the biomolecules of distinct permittivities, has been performed based on the threshold voltage and current sensitivity. Most popular biomolecular materials used nowadays are APTES ( k = 3.57 ), biotin ( k = 2.63 ), Keratin ( k = 5 − 10 ), amino acids ( k = 11 − 25 ), in which the permittivity ( k ) varies in the range of 2 − 25 . Here, the materials of three different permittivity values ( k = 2, 11, 22 ) are examined in detail. Figures 2 and 3 depict that the device with SiO 2 as the nanogap surrounding material yields the best performance judged on the basis of both type of sensitivities. The sensitivity increases 2 to 4 times with k = 11, 22 respectively for the change in surrounding materials of nanogap, i.e., SiO 2 as a replacement of Poly − Si . The value of V th in case of SiO 2 increases with the increment of permittivity of the biomolecules due to the increase in associated field lines. On the other hand, Poly-Si being a good conductor, does not cause any significant change in V th due to the change of biomolecules ; it has thus similar V th for all k(= 2, 11, 22) . Therefore, the simulation results firmly establish the fact that the device with SiO 2 as nanogap lining material is the best performer among the three materials for bio sensing applications. Therefore, the device with SiO 2 is chosen for further optimization. Optimization of nanogap structure, based on its height and width, is performed in this literature for the first time. The maximum length of the nanogap in each side is chosen as one third of the gate length ( L = 75 nm ). in order to maintain proper functionality. Thus a minimum of 25 nm I-shaped layer is maintained. The width of the nanogap in each side is considered as 25 nm, 22.5 nm and 20 nm. Along with that, the height of the nanogap is also optimized with four trial values −25 nm, 30 nm, 35 nm and 40 nm. Larger the nanogap height, greater the gate-metal separation from the channel yields poorer gate control. The ON-current and the ON-current sensitivity ( I ON ) are found to increase with the increase in permittivity of biomolecules. The present study particularly aimed at the detection of DNA structure ( k ∼ 11 ) [23] . Table 1 and Fig. 4 present the current and threshold voltage sensitivity of the biosensor with different combinations of width and height of nanogap structure fully occupied by the biomolecules. It is observed that with the increase in nanogap height, higher voltage is needed to switch ON the device and the threshold voltage sensitivity also increases ( V th ). Around 15% decrement in I ON is observed for the increase in the height of the nanogap from 25 nm to 40 nm. It is due to the narrowness of the gate dielectric and increment of the distance between channels and gate-metal, which in turn reduces the gate control over the channel. For the similar change in nanogap height, V th increases upto 2 times (width = 20nm ) and 2.5 times (width = 25nm ). Hence, it will be a healthy tradeoff, in which the device with 3 times higher V th is chosen, ignoring the negligible reduction in I ON . Thus, nanogap The 2D potential profile ( (x, y) ) of the channel underneath the gate is determined from the Poisson's Equation, given by, where, q, N a and si represent charge of an electron, doping concentration of the channel and permittivity of Si-film respectively. The solution of Eq. 1 is a parabolic function of y, [24] and is expressed as follows, The expressions of P 1 (x) , P 2 (x) and P 3 (x) are derived using the boundary conditions, as follows, i) Putting y = 0 in Eq. 2 yields surface potential of the top surface i.e., ii) Electric field at the top channel is expressed as, iii) In the bottom channel, the electric field is calculated as, Due to the symmetrical nature of the device with respect to both the gates, top and bottom channels are having same potential while operating in shorted gate mode, i.e., Hence, from Eqs. 4, 5 and 6, P 3 (x) can be expressed as, Therefore, the generalized expression of potential function becomes, Putting y = 0 in Eq. 8 yields, Replacing the expressions of second order partial fractions from Eqs. 9a, 9b in Eq. 1 yields, . The solution of Eq. 10 is, In DM-DGFET, various bio-fluids are characterized through variations in capacitance associated with the nano-gaps filled with those fluids. In real situation, nano-gaps are hardly completely filled rather bio-fluids containing long biomolecules may follow different surface profiles within the nanogaps,and therefore offer different capacitances. Here, we will consider four basic filling patterns that ma be generated by the fluids confined in nanogaps. These are schematically presented in Fig. 5 . In order to estimate the capacitance associated with the nanogaps, we first concentrate on the smallest column containing minimum numbers of bio-molecules, as depicted in Fig. 6 (a). The part of the bio-molecules occupies nanogap contribute capacitance C BM , whereas the rest of the nanogaps contributes capacitance C VA . Thus, the equivalent capacitance of the smallest column ( C 1 = C VA ||C BM ) can be expressed as, Similarly, capacitance associated with other columns are calculated for various patterns of bio-molecules in the nano-gap. Few of them are analyzed in the following sub-sections. Increasing and decreasing inward patterns are shown in Fig. 5(a) . These patterns comprise of two symmetrical sections of dielectric modulated nano-gaps. Each section consists of five columns in which the height of the bio-molecule filled portion of the individual column increases with a step size of T ox ∕5 . C i , i ( i = 1 to 5 ) denote the capacitance and area associated with the i th column respectively. The smallest value of i corresponds to the column that consists of minimum number of bio-molecules. Therefore, the capacitances are calculated as follows, Two sections of dielectric modulated nano-gaps are separated by a column and enclosed by two thin layers (top and bottom) of dielectric. The capacitance associated with the column is mathematically expressed as, C col = ox1 col ∕T ox ; where, ox1 , col are the permittivity of the dielectric and area of the column respectively. Therefore, the total capacitance ( C z ) per unit area associated with two nano-gaps and column is expressed as, t is the total area associated with the nano-gaps and column. Capacitances per unit area associated with the top and bottom layers that enclose the nao-gaps, are denoted by C x and C y , respectively (as shown in Fig. 6 ); and expressed mathematically as, C x = ox1 ∕T oxpad1 , C y = ox1 ∕T oxpad2 ; where, T oxpad1 and T oxpad2 are the thicknesses of the two layers. Therefore, the total oxide capacitance per unit area ( C ox ) is expressed as, In concave and convex pattern of dielectric modulated nanogap (as shown in Fig. 5(b) ), each side consists of five columns assumed to be partly or fully filled with bio-molecules. The smallest height of bio-molecules filled column is assumed to be T ox ∕3 and the rest portion of height 2T ox ∕3 is vacant (filled by air). The height of bio-molecules increases/decreases by a step height of T ox ∕3 . Assuming, the capacitance and area (13) Expressions of constants such as, A 1 , A 2 can be derived from the continuity equations and built-in potential developed at the interface of two different regions. Built-in potentials developed at the source-channel and drain-channel interfaces are denoted by P 4 and P 5 respectively. The expressions of P 4 and P 5 are given by, The continuity equations of potential at the source/drainchannel interface are expressed as, From Eqs. 11, 19a and 19b, the expressions of A 1 and A 2 are derived as, Threshold voltage is defined as the minimum gate-to-source voltage to make the surface potential equal to the twice of the Fermi potential ( f ,si ) of the channel. It is expressed mathematically as [25] , where, x min is the location of the minimum surface potential from the source-channel interface [26] , obtained from the following equation, Sensitivity(S) has been defined as the change in the threshold voltage with biomolecules trapped in nanogap cavities with respect to the empty cavity [18] , given as, It is found that the S bio increases with the increase in the height of the cavity as its permit larger number of molecules to get into it. The literature [18] concludes that larger molecules offer better sensitivity. Streptavidin and other larger molecule of size around 6-7 nm is the best molecule to fit in this device. It is also reported that the device with completely full cavity offers better sensitivity. However, in the full cavity structure as the gate is floating, it should have fabrication issues. It requires body support during fabrication, that in turn nullify the effect of down-scaling. Drain current model of the DG MOSFET based structure can be represented for its various operating regions, i.e., subthreshold, linear and saturation. Liang et al. in [27] had presented the subthreshold current model which can be used to obtain the I DS,sub . In linear and saturation regions of operation, the drain current model proposed in [28] is used in the present study as follows, where, a and c represent the effect of velocity overshoot [29] and channel length modulation factor [30] respectively. The saturation voltage ( V Dsat ) is calculated from the formula, where, v sat denotes the saturation velocity of electron [28] . Values of , are given in [31, 32] . In this section, the proposed model is compared with the simulated data. The transfer characteristics of cocave convex and increasing decreasing patterns considering both the model and simulated data are shown in Fig. 7 . Perfect (28) S bio = (V T(empty) − V T(bio) )∕V T(empty) (29) matching between the two is observed, which validates the proposed model. The results obtained from the modeling and simulations (using SILVACO TCAD) of the DM DGFET with Fully Filled Nanogap considering the effects of different biomolecular patterns have been thoroughly analyzed. The threshold voltage and the ON-current sensitivity have been calculated for four different patterns of bio-molecules confined in the nano-gaps. The deviation of the above parameters from the fully filled structure has also been calculated. In the mirror image pattern, the top and bottom nanogaps are assumed to be exactly same. In Fig. 8 , the transfer characteristics of four different patterns have been depicted. It is clearly observed from the figure that the concave pattern exhibits the highest ON-current leading to a deviation margin of 13%. It also produces the lowest OFF-current. The other three patterns generate 6-9 times larger OFF-current than the concave counterpart. Although, the fully filled structure of DG-MOSFET based bio-sensor has been analyzed in various literatures, partially (half and quarterly) filled nano-gap may describe the real situation better, which needs special attention. In partially filled nano-gap structure, mirror-like pattern of top and bottom nanogaps has been studied in various reports. However, this pattern is totally dependent on the orientation of biosensor arising from its placing. It may vary depending on placement of the sensor in the bio-molecular solution. For this reason, along with conventional mirror pattern in the bottom nanogap, the same pattern both in the top and bottom nanogaps has also been tested. The mirror type pattern architecture is termed as Dielectric modulated DGMOSFET with Mirror Structure (DM DGMOSFET-MS), whereas the same type architecture is termed as Dielectric modulated DGMOSFET with Same Structure (DM DGMOSFET-SS); these are depicted in Fig. 9(a), (b) , respectively. Both of these nano-gap architectures are analyzed in detail and the values of various parameters are given in Tables 2 and 3 , as follows. In Fig. 10 , the transfer characteristic of the DM-DGMOS-FET-SS is presented. It also exhibits a similar trend as that of the DM-DGMOSFET-MS. The concave pattern yields the lowest OFF-current and highest ON-current in both the device architectures. ON-Current Sensitivity ( I ON ) for the same type of devices with similar patterns is depicted in Fig. 12 . It is found that both the architecture offer almost the same sensitivity. However, in between four patterns, the concave pattern for both DM-DGMOSFET-MS and DM-DGMOSFET-SS shows almost 26-35% higher sensitivity compared to other three patterns. Researches had mostly considered the ideal situation where the nano-gap is fully filled. However, in reality due to the steric hindrance, probe placement and other fabrication disorders, the nanogap may not be completely filled. The deviation of the threshold voltage ( V th ) in reference to the device with a full-filled cavity is termed as "error", which is The biomolecular pattern having the least error is supposed to be the most perfect i.e., closest to the ideal case. Depending upon the highest sensitivity and lowest error values, a trade-off should be done, which can be used in future. Figure 13 illustrates the V th,Error of DM-DGMOS-FET-MS and DM-DGMOSFET-SS devices for four different patterns. From the figure, it is quite clear that the DM-DGMOSFET-SS follows the same trend as that of the DM-DGMOSFET-MS, but the magnitude of error is almost 60-65% lower for the former device, which is highly appreciable. Among the four patterns, decreasing and concave patterns yield lower V th,Error values in both the cases. The concave pattern showcases the minimum value for DM-DGMOSFET-MS, whereas the decreasing pattern exhibits the minimum value for DM-DGMOSFET-SS. However, their difference is almost negligible. The concave pattern shows a maximum of 33% and 60% lower V th,Error in case of DM-DGMOSFET-MS and DM-DGMOSFET-SS, respectively. However, the decreasing pattern shows a negligible 4 mV lower error than the concave pattern when used in DM-DGMOSFET-SS configuration. In Fig. 14, I ON Tables 2 and 3 respectively. It has been found from the study that DM-DGMOSFET-SS depicts better performance than DM-DGMOSFET-MS in every aspect, and the concave pattern emerges as the preferable one in most of the cases. Therefore, DM-DGMOSFET-SS with concave pattern has been chosen for further studies. So far, the study has been carried out assuming the symmetrical device structure. It is evident that the DM-DGMOSFET-SS with concave biomolecular pattern and optimised nanogap offers the best performance in terms of sensitivity and error analysis. In contemporary researches, mainly in H. Im et al. [12] , it is stated that the nanogap used in the biosensing process, is an outcome of sensible wet etching procedure. Although the fabrication process are performed with extreme precision, the influence of process variation can not be made totally absent. In this section, a structure which may appear due to the variation in the wet etching process has been studied. Four types of structural variations due to the variation in etching process are considered below. (a) Nanogaps wider in drain side under both top and bottom gates, (b) Nanogaps wider in source side under both top and bottom gates, (c) Nanogaps wider in drain side under only one gate, (d) Nanogaps wider in source side under only one gate. The structures are schematically presented in Fig. 15 . All these structures are considered to be Asymmetric as they deviate from the ideal symmetric structure. In case Firstly, the sensitivity parameters of the above structures are investigated with the optimized nanogaps, each filled with biomolecules following the concave pattern as described earlier. As both the gates are shorted, variation in gate bias will equally influence the nanogaps under top and bottom gates. In Fig. 16 , the threshold voltage sensitivity ( V th ) of the four devices is exhibited. The figure suggests that the device in Fig. 15(a) and (c), i.e. the devices with wider nanogap in drain side offer ∼ 100% and ∼ 40% higher V th for aligned structure and misaligned structures respectively than its source side counterpart. Therefore, more the vertical SiO 2 layers (shaded Blue in Fig. 15 ) shift towards source end, stronger gate control and in turn, a higher sensitivity for a biosensor are achieved. Figure 17 depicts the variation in I ON for all the above structures. However, the variations in this biosensing parameter are less than 10%, and thus not much significant. It may be concluded that I ON is quite insensitive to process variation related to formation of the nanogap cavities. Results related to Figs. 16 and 17 are presented in Table 4 . In this paper, an extensive study has been carried out on Dielectric Modulated DGFET to view its suitability as a biosensing device by modifying the structure based on the orientation of the biomolecules within the nanogaps. A novel approach has been made by optimizing the device with respect to the nanogap forming material along with the height and width of it. SiO 2 emerges as the best one for creating the nanogaps by obtaining 200-400% ΔV th than its nearest contender. The largest nanogap height (40 nm) and width (25 nm) taken for optimization, have been selected based on the sensitivity. The effect of different profiles arising from distribution of biomolecules in nanogap cavities has also been studied in this paper. A mirror type profile (DM-DGFET-MS) and the same type profile (DM-DGFET-SS) have been studied. Results show that for both DM-DGFET-MS and DM-DGFET-SS, concave surface profile of biomolecular solution in the nanogap is having respectively 26% and 35% better sensitivity than the other cases studied here. Its preformation deviation ( ΔV th,Error , ΔI ON,Error ) from ideal sensor with fully-filled nanogaps has been also calculated and concave profile yields 33% lower error value than its nearest counterpart for both DM-DGFET-MS and DM-DGFET-SS configurations. Therefore, the study suggests that this type of FET based biosensor can be a good option for the solution, which follows a concave profile in a confined region due to its liquid property like viscosity and surface tension. Influence of changing the degree of asymmetry on the biosensor performance and finding the solutions that can offer concave profiles has also been studied. The devices with wider drain side nanogap offers ∼ 100% and ∼ 40% higher ΔV th for aligned structure and misaligned structures respectively than its source side counterpart. Therefore, more the vertical SiO 2 layers shift towards source end, stronger gate control and in turn, a higher sensitivity for a biosensor. In case of presently found SARS COV-2 virus (Coronavirus) detection, the nanogap structure and the dielectric constant should be modified and optimized according to the size of the Coronavirus (60-140 nm) for better sensitivity and efficient detection with the same structure. si + fb − P 6 P 9 =1 − P 7 ; P 10 = 2 qNa si + fb P 11 =4P 7 P 9 − 1 P 12 =2P 10 + 4 f ,si − 4P 6 P 9 − 4P 7 P 8 P 13 =4P 6 P 8 − 4 2 f ,si − P 2 10 − 4 f ,si P 10 Conceptualization, Methodology, Supervision, Correction of manuscript, Reviewing and Editing. Funding No funding is available for this work. Availability of data and materials Authors are not willing to disclose the data and materials related to this research, as this work is a part of thesis. Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Ethics Approval For this type of study formal consent is not required. Not applicable for this type of study. Not applicable for this type of study. Not applicable for this type of study. Informed consent Not applicable for this type of study. 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