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Dual Dielectrically Modulated Electrostatically Doped Tunnel-FET for Biosensing Applications

Authors:
  • Vidya Pratishthan’s, Kamalnayan Bajaj Institute of Engineering and Technology , Baramati

Abstract and Figures

For next-generation biosensing applications, a dual dielectrically modulated tunnel field effect transistor based on electrostatically doping (DDM-EDTFET) has been proposed. The proposed device is implemented with the aim of reducing the fabrication complexity and cost of TFET based biosensor with nanoscale dimensions. For this, the proposed biosensor device utilizes polarity gate concept based on electrostatic doping to form the source-drain region. Moreover, a nanogap cavity is stacked between the gate electrode and HfO2 layer for detection of target biomolecules. In this pursuit, the proposed biosensor device offers significant sensing performance along with superior doping control over channel with minimum process variability issues and thermal budget. Based on extensive two-D TCAD device level simulations, sensing performance of the proposed biosensor device has been evaluated for both the charged (k>1, ρ0) and charge-neutral (k>1, ρ = 0) biomolecules. Furthermore, the sensing capability has been analyzed through distinct dielectric constant (k) and negative charge density (ρ−) of biomolecule at a specific gate and drain bias conditions.
shows the cutaway view of a DDM-EDTFET structure [12] with embedded nanogap cavity within the gate dielectric towards the source end. The simulation parameters adapted from [12] are silicon film thickness (TSi = 10 nm), oxide layer (Tox = 1 nm), gate length (Lg= 50 nm) and Control Gate (CG) metal work function (= 4.5 eV). The formation of n+ and p+ D/S regions in an intrinsic Si film, is achieved through electrostatically doping i.e with the application of appropriate positive (+1.2 V)/negative (-1.2V) bias at polarity gates, PG-1/PG-2, respectively. Silicon thickness is kept within the Debye length for uniform distribution of the charge carrier [17]. Moreover, work functions of all gate electrodes (ϕm = 0.45 eV) are compound of nickel silicide (NiSi) [10]. Both spacer lengths are of 5 nm. In Fig. 1, the nanogap cavity formed between the gate electrode and HfO2 layerand have the same process steps that are described in [2]. To avoid the sensitivity degradation due to gate-to-channel leakage current, a thin layer 1nm of dielectric material (HfO2 is considered in this work) as an insulator within the nanogap cavity is essential [1]. In the event of biomolecules conjugation within the nanogap cavity under the gate, the gate capacitance increases which in turn, helps in an enhancement in drain current in DDM-EDTFET. The term biomolecule conjugation depicts the variation of biomolecules accumulation when considered a distinct dielectric and/or charge density beneath cavity region [1]. When there is no biomolecule (k = 1) i.e. air cavity, there is no formation of channel beneath the HfO2 layer. However, paralyzed biomolecules in cavity result change in the cavity capacitance and biomolecules having k>1 results in channel inversion. Therefore, the electron concentration rises below the cavity and in this way, magnitude of drain current enhanced [2]. The simulations have been carried out assuming that the nanogap cavity completely occupied by the biomolecules (k>1), and the influence of charged biomolecules (ρ0) is simulated by considering negative charge density at the silicon-oxide interface [18].
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Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 153
e
t
International Journal on Emerging Technologies 10(4): 153-159(2019)
ISSN No. (Print): 0975-8364
ISSN No. (Online): 2249-3255
Dual Dielectrically Modulated Electrostatically Doped Tunnel-FET for Biosensing
Applications
L.K. Bramhane
1
, P.K. Kadbe
1
, B.H. Patil
1
, S.D. Chede
2
and S.B. Lande
2
1
Assistant Professor, Department of E & TC VPKBIET, Baramati, Pune (Maharashtra), India.
2
Professor, Department E & TC VPKBIET, Baramati, Pune (Maharashtra), India.
(Corresponding author: L.K. Bramhane, lokesh.bramhane@vpkbiet.org, Whatsapp no. 7000972760)
(Received 29 August 2019, Revised 25 October 2019, Accepted 04 November 2019)
(Published by Research Trend, Website: www.researchtrend.net)
ABSTRACT: For next-generation biosensing applications, a dual dielectrically modulated tunnel field effect
transistor based on electrostatically doping (DDM-EDTFET) has been proposed. The proposed device is
implemented with the aim of reducing the fabrication complexity and cost of TFET based biosensor with
nanoscale dimensions. For this, the proposed biosensor device utilizes polarity gate concept based on
electrostatic doping to form the source-drain region. Moreover, a nanogap cavity is stacked between the gate
electrode and HfO
2
layer for detection of target biomolecules. In this pursuit, the proposed biosensor device
offers significant sensing performance along with superior doping control over channel with minimum
process variability issues and thermal budget. Based on extensive two-D TCAD device level simulations,
sensing performance of the proposed biosensor device has been evaluated for both the charged (k>1, ρ0)
and charge-neutral (k>1, ρ = 0) biomolecules. Furthermore, the sensing capability has been analyzed through
distinct dielectric constant (k) and negative charge density (ρ) of biomolecule at a specific gate and drain
bias conditions.
Keywords: Polarity control, Doping-less, Band-to-band Tunneling (BTBT), Biosensor, Biomolecules, Dielectrically
modulated.
Abbreviations: DDM-EDTFET, Dual Dielectrically Modulated Electrostatically Doped Tunnel-Field Effect Transistor;
ISFETs, ion-sensitive FETs; DM-FET, dielectric modulated FET; T
Si,
Silicon Thickness; T
ox
, Oxide Thickness; ϕ
m
,
Metal Work function.
I. INTRODUCTION
Biosensors are the strong candidate for their ability to
detect the charged molecules as well as the neutral
molecules (species). In literature, the electrochemical
based biosensors are the strong contender for the
supervision of infectious agents due to their high
sensitivity and cost effectiveness [1-8]. However, for
early-stage electrochemical detection, a highly specific,
sensitive, selective and reliable biosensor can play a
crucial role due to their ability to convert biological
information directly into a processable electrical signal.
Moreover, with the combination of surface physics and
bioengineering, ion-sensitive FETs (ISFETs) was
proposed for the fast detection of charged biomolecules
that exist between the dielectric gate and electrolyte
solution [5]. However, ISFETs have parasitic sensitivity
to temperature and light. Moreover, unable to detect the
neutral biomolecules and have the compatibility issue
with the CMOS process. In [8–10], to solve the problem
of detecting neutral biomolecules and to modulate
electrostatic properties, a cavity based dielectric
modulated FET (DM-FET) has been proposed. The
nanogap cavity can be formed using the process steps
reported in [4, 7]. But these devices have low binding
probability in carved cavity region [4-6]. However, tunnel
FET-based biosensors investigated widely for their
superior sensitivity and quick response time when it is
compared to biosensors based on FET [1, 2, 11,12].
But, these devices postulate different metals to doped
the regions.
Also, ion implantation, annealing for damage removal
and dopant activation process make fabrication of these
devices complex and expensive. Hence, doping less
devices that are based on charge plasma (work function
engineering) have been recently proposed to eliminate
the requirement of different processes used to doped
the targeted regions [13-16]. Although, in these devices,
the problem of choosing different work function metal or
formation of alloys having a desired work function is still
persisting and needed to resolve. Hence, to solve the
problem of selecting different work function metals and
to increase the ability to detect a species correctly, a
way of dealing with the issues needed to optimize
further to fulfill the requirements of next-generation
biosensing applications [17]. In this paper, DDM-
EDTFET is proposed to detect the different types of
biomolucules and to resolve the issues of doping
requirements and selecting an appropriate metal work
function. For this, an electrostatic polarity control doping
has been adopted in the proposed DDM-EDTFET in
which a positive or negative supply voltage is applied to
the polarity control electrodes to induce the charge
carriers (electrons or holes) in targeted silicon region.
For example, a positive supply voltage applied to
polarity control electrode results in an accumulation of
electrons while a negative voltage on polarity control
electrode accumulates holes.
Moreover, HfO
2
has been introduced between the silicon
and cavity region to modulate the electrical properties of
the proposed device.
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 154
Furthermore, the nanogap cavity on top of or beneath
HfO
2
is used to sense both charged and neutral
biomolecules. Apart from this, the impact on sensitivity,
ON-current, sub-threshold slope, and electron tunneling
rate have been studied with variation in density of
charged and neutral biomolecules.
II. DEVICE DIMENSIONS AND MODELS
Fig. 1. Cross-sectional structural view of dual
dielectrically modulated electrostatically doped tunnel-
FET (DDM-EDTFET).
Fig. 1 shows the cutaway view of a DDM-EDTFET
structure [12] with embedded nanogap cavity within the
gate dielectric towards the source end. The simulation
parameters adapted from [12] are silicon film thickness
(T
Si
= 10 nm), oxide layer (T
ox
= 1 nm), gate length (L
g
=
50 nm) and Control Gate (CG) metal work function (=
4.5 eV). The formation of n+ and p+ D/S regions in an
intrinsic Si film, is achieved through electrostatically
doping i.e with the application of appropriate positive
(+1.2 V)/negative (-1.2V) bias at polarity gates, PG-
1/PG-2, respectively. Silicon thickness is kept within the
Debye length for uniform distribution of the charge
carrier [17]. Moreover, work functions of all gate
electrodes
m
= 0.45 eV) are compound of nickel
silicide (NiSi) [10]. Both spacer lengths are of 5 nm. In
Fig. 1, the nanogap cavity formed between the gate
electrode and HfO2 layerand have the same process
steps that are described in [2]. To avoid the sensitivity
degradation due to gate-to-channel leakage current, a
thin layer 1nm of dielectric material (HfO
2
is considered
in this work) as an insulator within the nanogap cavity is
essential [1]. In the event of biomolecules conjugation
within the nanogap cavity under the gate, the gate
capacitance increases which in turn, helps in an
enhancement in drain current in DDM-EDTFET. The
term biomolecule conjugation depicts the variation of
biomolecules accumulation when considered a distinct
dielectric and/or charge density beneath cavity region
[1]. When there is no biomolecule (k = 1) i.e. air cavity,
there is no formation of channel beneath the HfO
2
layer.
However, paralyzed biomolecules in cavity result
change in the cavity capacitance and biomolecules
having k>1 results in channel inversion. Therefore, the
electron concentration rises below the cavity and in this
way, magnitude of drain current enhanced [2]. The
simulations have been carried out assuming that the
nanogap cavity completely occupied by the
biomolecules (k>1), and the influence of charged
biomolecules (ρ0) is simulated by considering negative
charge density at the silicon-oxide interface [18].
Fig. 2. Transfer characteristics of DDM-EDTFET with
and without high-k material, HfO
2
as an insulator in the
nanogap cavity filled with biomolecules with dielectric
constant, k=5 at V
DS
= 1.0 V and V
GS
= 1.2 V.
III. RESULTS AND DISCUSSION
Atlas Silvaco V5.19.20 [19], a Two-Dimensional device
simulator is used to accomplish the parameters of n-
channel DDM-EDTFET. However, band-to-band
tunneling model, drift-diffusion current transport model,
concentration dependent Shockley-Read-Hall (SRH)
generation and recombination model are used to extract
different parameters. In n channel DDM-EDTFET, the
band-to-band tunneling (BTBT) current via junction form
between the source and channel is examined under the
influence of biomolecule conjugation. The simulations
have been carried out as target biomolecules are
present in cavity region and keeping consistent
difference in between theses different values. There are
two parameters named dielectric constant and density
of charge carrier that can be used for sensitivity analysis
of DDM-EDTFET biosensor.
A. Impact of biomolecules conjugation on band profile
and surface potential
In this section, primarily, we have shown the influence of
biomolecule conjugation on the lateral energy-band
profile parallel to the tunneling path. The energy-band
profiles in the DDM-EDTFET biosensor for the different
values of negative charge densities ) as well as
dielectric constants (k) of the biomolecules are shown in
Fig. 3 (a) and (b), respectively, under the ON-state
considering V
GS
= 1.2 V and V
DS
= 0.5 V to ensure the
noteworthy contributions from both these terminals.
From, Fig. 3 (a), it is observed that as dielectric constant
increases the band bending enhances, and thereby,
reduces the minimum tunneling length or barrier width in
the event of biomolecule conjugation.
Moreover, Fig. 3 (b) shows energy band profiles for
charged biomolecules i.e. the biomolecules with ρ in
the cavity. It is observed that with enhancement in ρ,
the barrier height increases in the nanogap cavity and
hence decreasing surface potential and lateral electric
field that degrades ON-state current.
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 155
Fig. 3. Energy band diagrams of DDM-EDTFET along
the X-axis with distinct values of (a) k when ρ = 0 and
(b) ρ when k = 5 and 7 under ON-state conditions (V
DS
=
0.5V and V
GS
= 1.2V)
In this regard, we have also shown the impact of
biomolecules conjugation with varying dielectric
constants and ρ on the electron tunneling rate and
hence on the ON-state current in Fig. 4 (a) and (b),
respectively. The lateral electric field enhances at the
tunnel junction due to the presence of biomolecules
(k>1) underneath the cavity region, which governs the
BTBT generation rate of charge carriers and the
tunneling probability. Hence, the generation rate or
tunneling rate increases exponentially with the increase
in the electric field and leads to an increase in ON-state
current of the device as verified from Fig. 4 (a) and (b).
Similarly, to investigate the impact of biomolecules
conjugation on electrostatic potential of DDM-EDTFET
biosensor, we have analyzed the surface potential in
ON-state bias condition (V
DS
= 0.5V and V
GS
= 1.2V)
with varying k and ρ as shown in Fig. 5 (a) and (b),
respectively along the X-axis. It is observed from Fig. 5
(a), that absence of biomolecules (k=1) results in
minimum surface potential. However as the value of k
increases, it reaches to higher values in the presence of
biomolecules conjugation (k>1) beneath the nanocavity.
This accounts for the fact that the biomolecules with
higher values of k enhance the coupling between gate
and channel and thereby active capacitance [20]. As a
result, the barrier width at the source-channel junction
decreases and results in a steep rise in the potential
profile underneath the cavity [2]. Similarly, from Fig. 5
(b), effective surface potential decreases when density
of negative charge increases. Since, with the negative
charge of the biomolecules, the flat band voltage (V
fb
) is
directly proportional to charge density (eρ/C), this, in
turn, reduces the effective gate bias (V
GSeff
), followed by
a decrease of the surface potential beneath the
nanogap cavity [2]. However, a low value of charged
biomolecules (-10
11
cm
−2
) has negligible impact in
comparison with higher charged molecules that cause a
significant lowering of the surface potential as confirmed
from Fig. 5 (b).
Fig. 4. Electron tunneling rate and ON-state current of
DDM-EDTFET with different (a) k when ρ=0 and (b) ρ
when k= 5 and 7 under ON-state conditions (V
DS
= 0.5V
and V
GS
= 1.2V).
Fig. 5. Surface potential profile of DDM-EDTFET with
different (a) k when ρ=0) and (b) ρ when k= 5 and 7
under ON-state conditions (V
DS
= 0.5V and V
GS
= 1.2V).
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 156
B. Impact of biomolecules conjugation on drain current
Fig. 6 shows the transfer characteristics of the
DDMEDTFET with varying (a) dielectric constants and
(b) negative charge densities in an event of biomolecule
conjugation with biasing V
GS
= 1.2 V and V
DS
= 1 V.
From Fig. 6 (a), with the value of k = 1 (air cavity), it is
clear that the DDM-EDTFET exhibits a very low value of
ON-state current (10
11
A/µm). As the value of k
increases from 1 (presence of biomolecules), then
significant improvement in the value of ON-state current
is observed. On the other hand, from Fig. 6 (b), an
opposite behavior with the increase in the value of
negative charge densities in the transfer characteristics
of DDM-EDTFET is observed. This is due to the fact
that with increase in negative charge densities, the
surface potential decreases (Fig. 5 (b)) which causes
the degradation in the ON-state current of the device. It
is worthwhile to mention that at k =7, DDM-EDTFET
attains higher value of ON-State current (10
7
A/µm)
with minimum degradation with ρin comparison with k
= 5 (Fig. 6 (b). Fig. 7 show the output characteristics of
the DDMEDTFET for different values of (a) dielectric
constant and (b) negative charge densities. The output
characteristics depict the same behaviorial changes with
respect to variation in dielectric constant and negative
charge densities as that shown by the transfer
characteristics.
Fig. 6. Transfer characteristics of DDM-EDTFET with
different (a) k when ρ=0) and (b) ρ when k= 5 and 7 at
V
GS
= 1.2V and V
DS
= 1V.
Fig. 7. Output characteristics of DDM-EDTFET with
different (a) k when ρ=0) and (b) ρ when k= 5 and 7 at
V
GS
= 0.5V and V
DS
= 1V.
C. Sensitivity analysis with respect to biomolecule
conjugation
The effectiveness of the DDM-EDTFET biosensor can
be assessed by the drain current sensitivity S
Drain
[7];
higher S
Drain
indicates better detection of molecules and
can be defined as:
S
Drain
= (I
BioDrain
- I
Drain
)/ I
Drain
Where, I
Drain
and I
BioDrain
are drain currents in the
absence of biomolecules and in the presence of
biomolecules, respectively. However, S
Drain
demonstrates the inverse relationship with V
GS
.
Therefore, biasing the device at optimum voltage isalso
a key factor to attain higher sensitivity. Fig. 8 (a) and (b)
demonstrate that the sensitivity of drain current of
DDMEDTFET biosensor with the increasing values of
dielectric constants and negative charge densities,
respectively with respect to the variation in V
GS
at a
fixed V
DS
= 0.5V. From Fig. 8 (a), it reaches maximum
up to 10
7
for a dielectric constant of k = 7. While it
reaches to 10
6
for dielectric constant of k=5. However,
degradation has been observed in S
Drain
with the
increase in the value of negative charge densities as
shown in Fig.8 (b). Inspite of this degradation, the DDM-
EDTFET with significant variation in SDrain predicts its
detectability ranging from -1×10
11
to -1×10
12
cm
−2
with
both k=5 and 7. Similarly, Fig. 8 (c) and (d) shows the
drain current sensitivity with the increasing values of
dielectric constants and negative charge densities,
respectively with respect to the
variation in V
DS
at a fixed V
GS
= 1.2V.
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 157
Fig. 8 (c) shows that S
Drain
reaches to maximum
sensitivity of 10
5
for dielectric constant of k=7 and 10
4
for dielectric constant of k=5. Fig. 8 (d) indicates that the
sensing efficiency decreases with the increasing ρ,
associated with the biomolecules conjugation.
Fig. 8. Drain current sensitivity of DDM-EDTFET with
different (a) k but ρ=0 and (b) ρ but k=5 and 7; with V
GS
variation at a fixed V
DS
= 0.5V. Drain current sensitivity
of DDM-EDTFET with different (a) k but ρ=0 and (b) ρ
but k=5 and 7 with V
DS
variation at a fixed V
GS
= 1.2V.
The observed maximum sensitivity for charged
molecules with respect to drain bias are 10
5
. While, with
respect to gate bias is 10
4
for ρ = –1×10
12
at k=7. It can
be observed from the transfer characteristics of
DDMEDTFET based biosensor, the relative change in
I
ON
and V
th
with increasing values of k is very high. The
impacts of charged (k>1, ρ= 0) as well as charged-
neutral (k>1, ρ= 0) biomolecules have been also derived
from Fig. 6 (a) and (b) as shown in Fig. 9 (a) and (b).
More precisely, for sensitivity analysis of DDM-EDTFET,
we have considered the following parameters
individually as follows: 1) I
ON
, 2) I
ON
/I
OFF
ratio and 3)
subthreshold slope (SS). Fig. 9 (a) shows tremendous
rise in I
ON
with changes in k. Also, in the presence of
charged biomolecules (ρ=10
12
cm
−2
) in the cavity, ION
reduces by ten times at low value of k(= 0. 5). We have
also shown I
ON
/I
OFF
ratio of DDM-EDTFET biosensor
with variation in dielectric constant values and negative
charge densities in Fig. 9 (b). It can be understood that
the increase/decrease in I
ON
/I
OFF
ratio with k/ρ is on
account of increase/decrease in the value of ON-state
current (Fig. 6 (a) and (b)). Also, Vth also changes at
different dielectric constant with charged biomolecules
as can be verified from Fig. 6 (a) and (b). From the
sensitivity analysis, it is worthwhile to mention that the
effect of biomolecule charge weakens as k increases
and is quite sensible for low values of k, thus confirmed
the high sensitivity of DDM-EDTFET based biosensor.
Fig. 9. Impact of charged biomolecules on (a) I
ON
and
(b) I
ON
/I
OFF
for a range of dielectric constant (k=5, and
7) for a DDM-EDTFET based biosensor at V
GS
= 1.2 V
and V
DS
= 0.5 V.
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 158
Fig. 10. (a) Subthreshold slope and (b) subthreshold
slope sensitivity of the proposed device for ρ=0 and
dielectric range from k= 1 to 7 at V
GS
= 1.2V and V
DS
=
0.5V.
In addition, we have also analyzed subthreshold slope
for the DDM-EDTFET based biosensor. The
subthreshold slope is proportional to gate biasing [21],
thus, subthreshold slope is resting on gate biasing that
quantify the effectiveness of gate voltage in controlling
the channel region. Fig.10 (a) and (b) show the variation
in SS with respect to the increasing values of the
dielectric constant. It is verified from Fig.10 (a) that with
biomolecules conjugation (k>1), the gate controlling
increases, and which in turn results in reduction in SS.
Consequently, a significant improvement in SS
sensitivity is achieved with increasing values of k as
shown in Fig. 10 (b). Thus, this reduction in SS depicts
better detection capability of DDM-EDTFET based
biosensor.
D. Effect of parameter variation on device performance
In this section, we have discussed the effect of
parameter variation i.e variation in length (L
C
) and
thickness (t
C
) of cavity. Fig.11 (a) demonstrates the
transfer characteristics with variation in L
C
.
It is observed that as L
C
increases then no significant
improvement in I
ON
and I
OFF
is observed with L
C
above
15 nm. It is due to the reason that the drain current in
TFET depends on tunneling and not in diffusion
process. Likewise, Fig.11 (b) shows the variation in
cavity thickness on the transfer characteristics of the
DDM-EDTFET biosensor.
Fig. 11. Effect of variation in (a) the length of cavity (L
C
)
and (b) the thickness of cavity (t
C
) on the transfer
characteristics of DDM-EDTFET at V
GS
= 1.2V and V
DS
= 0.5V.
Here, the drain current decreases with the increase in
t
C
. Since the increment in t
C
causes the reduction in the
gate field controlling the tunneling of charge carriers and
hence the current. This also imposes a requirement for
higher gate voltage for better conduction of the device
with thicker cavity. Therefore, for better electrical
performance of DDM-EDTFET based biosensor, the
optimum values are 15nm and 5nm for L
C
and t
C
,
respectively.
IV. CONCLUSION
The performance of dual dielectrically modulated
electrostatically doped tunnel-FET has been
investigated for biosensing applications in detail. We
have explored the underlying physics of DDM-EDTFET
and estimated its sensing performance. In addition with
significant sensitivity improvement in comparison with
other conventional biosensors, the proposed DDM-
EDTFET based biosensor offers less fabrication
overhead due to the doping-less architecture. Therefore,
it is expected to be immune from random dopant
fluctuations problems as well as other doping related
issues. In this work, the sensing performance of DDM-
EDTFET has been evaluated for charged (k>1, ρ0) as
well as charged-neutral (k>1, ρ=0) biomolecules
conjugation through extensive device-level simulation.
Bramhane et al., International Journal on Emerging Technologies 10(4): 153-159(2019) 159
In addition, the impact of biomolecule dielectric constant
and charge density on both the electrical and sensing
performance of EDTFET based biosensor has been
studied. Hence, from the studied, it is confirmed that
DDM-EDTFET can be used as an emerging highly
sensitive label-free bioequipment in biosensing
applications.
V. FUTURE SCOPE
This work will pave the path for the implimentation of
dual dielectric materials in sensing devices to enhance
drain current that results in identification of different
charged or nuetral biomolucules.
Conflict of Interest. The authors declare that there is
no conflict of interest of any sort on this research.
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How to cite this article:
Bramhane, L. K. Kadbe, P. K. Patil, B. H. Chede,
S. D. and Lande,
S.B. (2019). Dual
Dielectrically Modulated Electrostatically Doped Tunnel-FET for Biosensing Applications. International Journal on
Emerging Technologies, 10(4): 153–159.
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