Analytical modeling of split-gate junction-less transistor for a biosensor application

A B S T R A C T This paper represents the analytical modeling of split-gate Dielectric Modulated Junction Less Transistor (JLT) for label free electrical detection of bio molecules. Some part of the channel region is opened for providing the binding
of 6
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
  Contents lists available at ScienceDirect Sensing and Bio-Sensing Research  journal homepage: Analytical modeling of split-gate junction-less transistor for a biosensorapplication Shradhya Singh a , Balwinder Raj a, ⁎ , S.K. Vishvakarma b a  Nanoelectronics Research Lab, Department of Electronics & Communication Engineering, National Institute of Technology (NIT), Jalandhar 144011, India b  Nanoscale Devices, VLSI Circuit and System Design Lab, Discipline of Electrical Engineering Indian Institute of Technology (IIT), Indore, MP, India A R T I C L E I N F O  Keywords: Dielectric modulationConformal-mappingSplit-gate junction less transistorBiomolecule sensor A B S T R A C T This paper represents the analytical modeling of split-gate Dielectric Modulated Junction Less Transistor (JLT)for label free electrical detection of bio molecules. Some part of the channel region is opened for providing thebinding sites for the bio molecules unlike conventional MOSFET which is enclosed with the gate electrode. Dueto this open area, the surface potential of this region a ff  ected by the charged and neutral bio molecules im-mobilized to the open region of channel. Surface potential of the channel region obtained by solving two-Dimensional Poisson's equation by potential pro fi le having parabolic nature through channel region usingtechnique called conformal mapping. By deriving the surface potential model, derivation of threshold model canalso be done. For the detection of bio molecule, variation in to the threshold voltage due to binding of biomolecule in the gate underlap region is the sensing metric. 1. Introduction Scaling down the conventional MOSFET dimension to the nano levelcontinuously giving rise to the Short Channel e ff  ects (SCEs) and it in- fl uence the performance of the device which cannot be ignored. Toreduce the impact of SCEs, many nano devises are introduced likeDouble gate MOSFET, Fin-FET, Si nanowire, CNTFET, Gate All Around,TFET, Junctionless Transistor etc. These devices can suppress the e ff  ectSCEs on the characteristic and also increases the gate controllabilityover the channel. It is also very di ffi cult to create ultra sharp dopingpro fi le between source/drain (S/D) regions with body region at na-noscale level. Several novel MOSFETs design has been developed todefeat the fabrication issue. Colinge et al. [1,2,3], reported Junction less Transistor, this transistor is having lower Drain Induced BarrierLowering(DIBL) and enhanced on-state and transfer characteristics thanthat of the usual MOSFETs [4,5,6,7,21,22]. In the recent work, the focus is on the sensor application of Junction less transistor for labelfree electrical detection of biomolecule. The detection is done by as-suming the dry environment. Split-gate devices are also reported inliterature [27 – 29]. Split-gate means in the device the middle part of thegate oxide etched away to form a cavity in between the gate oxides of either sides. This cavity i.e. a gate underlap region is utilizes as thesensing site for the biomolecules. When the bio-molecules are bindedwith the sensing area i.e. cavity region the characteristics of the tran-sistor get shifted in comparison to the characteristics get in the absenceof the biomolecule in the cavity [13,15 – 19].In this paper focus is on derivation of an analytical model for split-gate dielectric modulated Junction less transistor that is utilized as abio-sensor for the label free electrical recognition of biomolecules likecell, enzyme, DNA, protein etc. Etching of gate electrode is done frommiddle region of channel of DG-JL-MOSFET. The interaction of bio-molecule is occurring in the cavity area. The biomolecules eithercharged or neutral are bind with the gate underlap region, due to whichthe deviation in the electrical characteristic i.e. drain current, thresholdvoltage(V th ) and surface potential occurs [20,23,24]. For detection of  bio molecule, variation in the threshold voltage because of binding of bio molecule in the gate under lap region is the sensing metric [25,26]. Analytical modeling of the split-gate dielectric modulated JLT is done atMATLAB Tool (Table 1). 2. Device architecture used in simulation  2.1. Parameters of split-gate dielectric modulated Junctionless transistor  L g  is de fi ned as the length of the region which is enclosed by gateelectrode, L cavity  is de fi ned as length gate underlap (cavity) region.t cavity , t ox , tsi are de fi ned as thickness of region where cavity is createdwhich is gate underlap, gate and channel oxide respectively. t ox1  is thethickness of SiO 2  layer, the value is 1nm only. It is used to prevent thefurther oxidation in the open cavity region. When Si substrate is 15 November 2017; Received in revised form 7 February 2018; Accepted 7 February 2018 ⁎ Corresponding author.  E-mail address: (B. Raj). Sensing and Bio-Sensing Research 18 (2018) 31–362214-1804/ © 2018 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (    uncovered towards air ambient [8] the SiO 2  layer work as the adhesivelayer for binding of biomolecules. The gate underlap region acts as thesensing location, in that location the neutral and charged bio-moleculesare binded.This structure is designed by utilizing process simulation tool i.e. “ ATLAS ”  of Silvaco. The characteristic of simulation a ff  ected withneutral biomolecules consisting of di ff  erent dielectric constant i.e.K > 1. As reported in literature APTES=3.57 [11]), biotin=2.63[10], protein=2.50 and streptavidin=2.1 [9].For charged biomole- cule, the simulation is done by assuming the  fi xed positive or negativecharge (N f  =+5*10 15 /m 2 ) in the cavity region at the boundary of SiO 2  and gate underlap region. 3. Two dimensional potential model The proposed device structure given in Fig. 1 will be considered formodel development. In device the whole channel region is separatedinto three regions. Region-1 & region-3 are gate overlap region andregion-2 is named as gate underlap region i.e. cavity. The lateral axisexplanation of all 3 regions are; region-1 (0 < y < L g ), region 2(L g  < y < L g +L cavity ), region-3 (L g +L cavity  < y < 2L g +L cavity ).The 2-Dimensional Poisson's equation for channel region of the abovedevice can be written as + = −∈ d φ x ydx d φ x ydyqN  ( , ) ( , ) i i dSi 2222 (1)where  i =1, 2, 3 for all the three regions. N d  is the channel dopingconcentration of and  ∈  Si  is de fi ned as the  Si  permittivity. Quantum ef-fect does not consider in order simplifying the analysis of surface po-tential. Potential distribution of all 3 regions can be written as = + + φ x y C y C y x C y x  ( , ) ( ) ( ) ( ) i i i i 0 1 2 2 (2)As the region-1 and region-3 have same e ff  ective gate oxide capa-citance and the  fl at band voltages of both the regions are same as boththe regions are symmetric and can be written as: ∈ = C t  ox ox ox   (3) = = − − − V V φ χ  E φ 2  fb fb m Si g  f  1 3 (4)where  ∈ ox   is the gate oxide permittivity i.e. HfO 2 ,  t  ox   is the thickness of the gate oxide,  ф m  is the gate metal work function,  χ si  is de fi ned aselectron a ffi nity, E g  is the energy band gap of the Si.  φ  f   is the Fermipotential of the intrinsic semiconductor which can be represented as: ⎜ ⎟ = ⎛⎝⎞⎠ φ KT q N n ln  f di 3.1. Surface potential for region 1 Below boundary conditions must be satis fi ed in the region 1 to makesure the continuity of the surface potential and electric  fi eld displace-ments at the interface of region-1 and region-2 ==∂∂ = ∈∈ ⎡⎣⎢− −⎤⎦⎥∂∂ = −∈∈ ⎡⎣⎢− −⎤⎦⎥ == φ y φ yφ t y φ yφ x y x φ y V V t φ x y x φ y V V t  (0, ) ( )( , ) ( )( , ) ( ) ( )( , ) ( ) ( )  fsSi bs x ox Si fs gs fbox  x t ox Sibs gs fbox  1 11 1101 11 1 1 Si where  φ  fs 1 (  y  ) de fi nes surface potential of front-gate x and  φ bs 1 (  y  ) is thesurface potential back gate.By applying the above mentioned boundary conditions into the Eq.(2), coe ffi cients must be expressed as a function of surface potential of the front-gate i.e.  φ  fs 1 (  y  ) = C φ y ( )  fs 01 1  (5a) Table 1 Parameters of the device.S. No. Parameter Values1 Channel length 225nm2 HfO 2  thickness 10nm3 SiO 2  thickness 1nm4 Si thickness 10nm5 Doping 10 25 /m 3 6 Length of HfO 2  25nm Fig. 1.  Schematic of split-gate DM-Junctionless transistor with binding biomolecules in the cavity region.  S. Singh et al.  Sensing and Bio-Sensing Research 18 (2018) 31–36 32  = ∈∈ ⎡⎣⎢− −⎤⎦⎥ C φ y V V t  ( ) ( ) ox Si fs gs fbox  111 1 (5b) = −∈∈ ⎡⎣⎢− −⎤⎦⎥ C φ y V V t t  ( ) ( ) ox Sibs gs fbox Si 211 1 (5c)By using Eqs. (5a), (5b), (5c) and (2), the relationship between surface potential of front gate and back gate can be derived: = + ∈∈ ⎡⎣⎢− −⎤⎦⎥− ∈∈ ⎡⎣⎢− −⎤⎦⎥ φ x y φ yφ y V V t t φ y V V t t t  ( , ) ( )( ) ( )( ) ( )  fsox Si fs gs fbox Siox Sibs gs fbox SiSi 1 11 11 12 (6)As the devise is symmetric the front gate and back gate surfacepotentials are same i.e. = φ y φ y ( ) ( )  fs bs 1 1 As in junction less transistor the Si thickness is very less, so that atany point in channel region derivative of tangential electric  fi eld (E.F.)can be related to the tangential electric  fi eld at the front boundary of Si-SiO 2  as ∂∂ = ∂∂ φ x y y K φ y y ( , ) 1 ( ) s fs 212212 (7)where  Ks  parameter is used for the correlation between derivative of the electric  fi eld at one point of Si thin  fi lm to the derivative of theelectric  fi eld at back Si-SiO 2  boundary and  K   s  must be lie in the range of 0 to 1.By solving the di ff  erential equation, the surface potential of thefront gate can be obtained as. = + + − φ y A e B e σ  ( )  fs λ y λ y 1 1 1 1 1 1 (8)where = −= ∈∈ = ⎡⎣⎢−∈ − ∈∈−⎤⎦⎥ σ  βαα K t t  β K qN  V V t t  2 2( ) ox Sisox SisdSiox Si gs fbox Si 1111 11 =  λ α 1 1 A 1  & B 1  can be represent as the term of the length of the region = − − += − −  BV σ e ψ σ  λ L A V σ B ( )2sinh( ) bi λ L g bi 11 0 111 1 1  g  1 (9)where  ψ  0  is de fi ned as intermediate potential on the interface of region1 and 2. It will be derived in the next part. 3.2. Surface potential for region 2 Below boundary conditions must be satis fi ed in region 2 to makesure the continuation of the electric  fi eld and potential displacements atboundary of region 1 and 2 & also at region 2 and region 3. ==∂∂ = ∈∈ ⎡⎣⎢− −⎤⎦⎥∂∂ = −∈∈ ⎡⎣⎢− −⎤⎦⎥ == φ y φ yφ t y φ yφ x y x φ y V V t yφ x y x φ y V V t y (0, ) ( )( , ) ( )( , ) ( ) ( )( )( , ) ( ) ( )( )  fsSi bs x ox Si fs gs fb x t ox Sibs gs fb 2 22 2202 22 2 2 Si where = −  ( ) V V   fb fbqN C  2 1  f eff  of region 2. N f   is the charge possessed by thecharged biomolecule in gate underlap region. =+ C C C C C  eff ox fr ox fr  11 here, C ox1  is the oxide capacitance of the SiO 2  in region 2. C fr  is fringingcapacitance of gate electrode. t(y) is de fi ned as the distance betweenright side periphery of bottom and top gates to the back and frontsurface channel. t(y) is variable obtained because of the fringing elec-tric  fi eld e ff  ect and it is also very di ffi cult to derive its value directly Sothe technique called Conformal-Mapping has been utilized to calculateC fr  and t(y).The mapping function is as below: − + = +  y L jnx M u jv ( ) sinh( )  g   (10)where  L  g  =  L ch −  L cavity  =− ⎛⎝ ⎞⎠ − − +− ( ) n Lt t  ( ) sinh cosh cavityox ox t t t t t  1 1 ( )( ) ox ox g ox ox  11 = −⎛⎝ ⎞⎠ − − +− ( )  M  L sinh cosh cavityt t t t t  1 ( )( ) ox ox g ox ox  11 By using Eq. (10), ABCD points on the device in the x-y coordinate isconverted into A ′ B ′ C ′ D ′  on the device in u-v coordinate as shown in theFig. 2. That is why, the arc like electric  fi eld curve in the cavity area inthe x-y coordinate has now transformed in a straight line in u-v co-ordinate. Due to this conversion, the t(y), which is de fi ned as the dis-tance from the gate electrode and gate underlap and it is not having the fi x value, but converted into the m π /2, i.e. the distance in between thepoints C ′  and A ′  in u-v coordinates and also satisfying this condition i.e. = ( ) sin 1 mπ  2  . Because of the conformal-mapping technique, a correla-tion among x-y and converted u-v coordinates is derived by solving Eq.(10). = −  x t t u v ( ) sin cosh ox ox  1  (11a) = +  y L v u sinh cos  g   (11b)Now, fringing capacitance must be as: = ∈ −− ′ ′ ′ ′′ ′ ′ ′ C  u uv v  fr  D B C BC B A B 1 (12)where  ∈ 1  shows the biomolecule's dielectric constant in cavity regionwhich is vary from K=1 (for free space) to K > 1 (existence of bio- Fig. 2.  Field lines due to gate fringing e ff  ect a) prior to conformal-mapping and b) later to conformal-mapping.  S. Singh et al.  Sensing and Bio-Sensing Research 18 (2018) 31–36 33  molecules). By replacing the points A(L g ,0), B(L g +L cavity ,0), C(L g , t ox ),and D(L g , t ox +t g ) de fi ned in x-y coordinate system in the Eq. (10), theequivalent points in u-v coordinate system should be written as: A ′ (Lg,0), B ′ (M, 0), C ′ (0,m π /2) , and D ′ (M, m π /2). Replacing each points intoEq. (12), the fringing capacitance of gate electrode can derived as: ⎜ ⎟ ⎜ ⎟ = ∈ ⎛⎝⎛⎝− +− ⎞⎠⎞⎠ − C mπLt t t t t  2·sinh cosh( )( )  fr cavityox ox g ox ox  1 1 11 here  ∈ 1  shows the biomolecule's dielectric constant i.e. binded in thecavity region 2.Now again by transforming the u, v coordinates into srcinal, sur-face potential for the second segment can be expressed as = + + − − − φ y A e B e σ  ( )  fsγ  M  y Lg  γ  M  y L 2 2( )1( )2  g  (13)where  = − = = = ⎡⎣ + ⎤⎦ −∈ γ D σ D K M α D K M β  D D s sqN  0 2 0 22 1 22 dSi 10 = −∈ = −∈ − αC t  βC t V V  2 2 ( ) eff Si Sieff Si Si gs fb 2 2 2 = − − − ( )  Bψ σ e ψ σ  L ( ) ( )2sinh  Lγ  M  cavity 20 2 1 1 γ  M  Cavity 3.3. Surface potential for region 3 Similar to the region-1, surface potential of region 3 can be ex-pressed as = + + − + − − + φ y A e B e σ  ( )  fs λ y L L λ y L L 3 3 ( ( ))3 ( ( ))3  g cavity g cavity 3 3 (14)As the region-1 and region-3 are symmetric, so the parameters. = = = = α α β β λ λ σ σ  1 3 1 3 1 3 1 3 = − − + −= − −  Bψ σ e V V σ  λ L A ψ σ B ( ) ( )2sinh( )( )  λ Lbi ds g  30 1 ( )313 1 3 3  g  3 At the boundary of gate covered area i.e. region 1 and gate un-covered area i.e. region 2, the  fi eld must be continuous, i.e., = == dφ ydydφ ydy ( ) ( )  fs y L fs y L 1 2  g  g  Similarly, electric  fi eld should also be continuous at the interface of region 2 and region 3, so = = += + dφ ydydφ ydy ( ) ( )  fs y L L fs y L L 2 3  g cavity g cavity By the electric  fi eld continuity at both the boundaries, the inter-mediate potential  ψ  0  and  ψ  1  at the boundary of region-1 and region-2and at the interface of region-2 and region-3 can be obtained. 4. Result & discussion 4.1. Surface potential Fig. 3(a) and (b) show the variation in the surface potential acrossthe channel length. The part of gate is etched away to create the site inwhich the neutral as well as charged bio molecules are immobilized,which changes the minimum surface potential. When dielectric con-stant increases from unity to higher values, the minimum surface po-tential increase. In Fig. 3(a) the comparison of surface potential withchannel length of JLT based sensor is done with the FET based sensor atchannel length of 800nm [14]. It can be observed from  fi gure that thedeviation in surface potential is more in JLT based sensor. Fig. 3(b)shows the surface potential variation with channel length of 225nm.When charged bio-molecules are bind in the cavity region theminimum surface potential decreases with the negatively charged bio-molecules but increases for positively charged bio-molecules with re-spect to the neutral bio-molecules. The increase and decrease in thesurface potential is for the reason that of the change in the  fl at bandvoltage that is ( Δ V   fb ) in the gate underlap region, it depends on thenature of the bio-molecules bind in gate cavity region i.e. dielectricconstant for the neutral bio-molecules and charge for the charged bio-molecules.As  = V  ∆  fbqN C   f eff  , here  C  e  ff   rely on the dielectric constant of the bio-molecule. Fig. 4(a) represents the comparison of surface potential withchannel length of JLT based sensor is done with the FET based sensor atchannel length of 800nm and variation is more in the proposed deviceas shown in  fi gure. Fig. 4(b) shows the surface potential variation withchannel length of 225nm. 4.2. Threshold voltage Threshold voltage is the sensing metric for the biomolecules de-tection purpose. Neutral bio-molecules (having speci fi c dielectric con-stant) and neutral bio-molecules in the gate underlap cavity of the splitgate DM-JLT shows an impact on the V th  is shown in Fig. 5. This  fi gureshows the e ff  ect of neutral bio-molecules on the V th . As all the bio-molecules have speci fi c dielectric constant, that is why the cavity re-gion has di ff  erent dielectric constant to examine the impact of neutralbiomolecules in gate underlap area, and if the neutral biomolecule isbinded in the gate underlap area, the dielectric constant varies from 1to advanced values i.e. (K=1, 3, 7, 10), the V th  increases of the device.From Fig. 2(b), the variation in V th  due to charged biomolecules in thegate underlap region. One can observed that negatively (positively)charged bio molecule is binded in the gate underlap area the V th  in-creases (decreases). Ref [12]. -0.6-0.51-0.42-0.33-0.24-0.15- 0 200 400 600 800 1000    S   u   r    f   a   c   e   P   o   t   e   n      a    l    (   V    ) Channel Length(nm) Kref=1K=1Kref=3K=3Kref=7K=7Kref=10K=10 DashLine: Reference ModelSolid Line: Proposed Model (a) -0.5-0.4-0.3-0.2- 0 50 100 150 200 250 300 350    S   u   r    f   a   c   e   P   o   t   e   n      a    l    (   V    ) Channel Length(nm) K=1K=3K=7K=10 (b) Fig. 3.  variation in surface potential across the channel length between source to drain of split-gate DM-JLT. (a)the comparison between the impact of the dielectric constant of corresponding neutral bio-molecules bind in cavity of JLT based sensor with FET basedsensor at L channel =800nm for di ff  erent dielectric constant and (b) the impact of thedielectric constant of corresponding neutral bio-molecules of JLT based sensor of L channel =225nm. Other parameters are V ds =0V, V gs =0.5V.  S. Singh et al.  Sensing and Bio-Sensing Research 18 (2018) 31–36 34  4.2.1. Sensitivity  The mathematical formula for evaluating the sensitivity of theasymmetric DM- JLT when it is considered that the charged and neutralbio-molecules are binded into the gate underlap region is shown as: = = − >= S  V K V K V K  ( 1) ( 1)( 1)Sensitivity of neutral biomolecules  NBth thth = − S  V V V  (NeutralBiomolecules) (ChargedBiomolecules)(NeutralBiomolecules)Sensitivity of charged biomolecules CBth thth Sensitivity (S NB ) of neutral biomolecules binded into the cavity re-gion is shown in Fig. 6(a). The sensitivity of neutral biomolecules in-creases linearly with the dielectric constant for asymmetric split gateDM-JLT based sensor. Sensitivity (S CB ) of charged bio-molecules in thegate underlap region is shown in Fig. 6(b). From Fig. 1 can observed that, the positively charged biomolecule consisting charge density of (10*10^15m^( − 2)) shows sensitivity factor as 150mV and the posi-tively charged bio-molecule consisting charge density of ( − 10*10^15m^( − 2)) shows sensitivity factor of 360mV with respectto the neutral biomolecules consisting dielectric of (K=5) binded inthe cavity region. Hence negative biomolecules shows higher sensitivitythan the positive biomolecules. 5. Conclusion In this paper, analytical modeling of split-gate Junctionless tran-sistor for label free detection of charged and neutral bio-molecules hasbeen proposed. The impact of bio-molecules in the gate underlap regionhas been studied on electrical characteristic such as the surface po-tential and V th  of the device. By observing the impact of bio-moleculeon the electrical characteristic i.e. threshold voltage, sensitivity factor itis found that the sensitivity is good for negatively charged bio-mole-cules. Acknowledgement We thanks to VLSI Design research group of NIT Jalandhar for theirinterest in this work and their useful comments to draft the fi nal form of the paper. The support of DST SERB Project (ECR/2017/000922) isgratefully acknowledged. We should like to thanks NIT Jalandhar forlab facilities and research environment to carry out this work. Con fl ict of interest None. -0.6-0.4- 0 200 400 600 800 1000    S   u   r    f   a   c   e   P   o   t   e   n      a    l    (   V    ) Channel Length(nm) Nfref=5*10^(11)Nf=5*10^11m^(-2)Nfref=0Nf=0Nfref=-5*10^11m^(-2)Nf=-5*10^11m^(-2) DashLine: Reference ModelSolid Line: Proposed Model (a)(b) -0.6-0.4- 0 50 100 150 200 250 300 350    S   u   r    f   a   c   e   P   o   t   e   n      a    l    (   V    ) Channel Length(nm) Nf=5*10^11m^(-2)Nf=0Nf=-5*10^11m^(-2) Fig. 4.  Variation in surface potential across the channel length from source to drain forasymmetric split-gate DM-JLT. (a) the comparison between the impact of the presence of charges of equivalent charged bio-molecules of JLT based sensor with FET based sensor atL channel =800nm on surface potential and (b) the impact of the presence of charge of corresponding charged bio-molecules of JLT based sensor of L channel =225nm on thesurface potential. Other parameters are V ds =0V, V gs =0.5V. 0.50.520.540.560.580.60.620.640.660.680 2 4 6 8 10 12    T    h   r   e   s    h   o    l    d   V   o    l   t   a   g   e    (   V    ) Dielectric Constant Vth_proposedVth_reference (a) Solid line: Proposed DeviceDash line: Reference Device -7 -2 3 8 13    T    h   r   e   s    h   o    l    d   V   o    l   t   a   g   e    (   V   t    h    ) charged biomolecules(*10^15m^-2) Vth_ref Vth Solid line: Proposed ModelDash line: Reference Model (b) Fig. 5.  Threshold voltage for di ff  erent dielectric constant of related neutral biomolecules& charged biomolecules. (a) Impact on threshold voltage because of the presence of neutral bio-molecules in the gate underlap region having speci fi c dielectric constants. (b)Impact on V th  because of the existence of charged bio-molecules in the gate underlapregion for di ff  erent charge values from positive to negative. 2 4 6 8 10 12    S    N   B Dielectric Constant SSref  Solid line: Proposed ModelDash line: Reference Model(a) -10 -5 0 5 10 15    S    C   B Charged Biomolecule(*10^15m^(-2)) Sref S Solid line: Proposed ModelDash line: Reference Model (b) Fig. 6.  Sensitivity factor (a) shows sensitivity of neutral biomolecules (b) shows sensi-tivity of charged biomolecules.  S. Singh et al.  Sensing and Bio-Sensing Research 18 (2018) 31–36 35
Similar documents
View more...
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks