Results in Physics 6 (2016) 879–883

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Results in Physics

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Gate dielectric strength dependent performance of CNT MOSFET andCNT TFET: A tight binding study

http://dx.doi.org/10.1016/j.rinp.2016.11.0022211-3797/� 2016 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding author.E-mail address: sarkershamimbd@gmail.com (Md. Shamim Sarker).

Md. Shamim Sarker ⇑, Muhammad Mainul Islam, Md. Nur Kutubul Alam, Md. Rafiqul IslamDepartment of Electrical and Electronic Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 September 2016Received in revised form 23 October 2016Accepted 1 November 2016Available online 4 November 2016

Keywords:CNT TFETSubthreshold slopBarrier width, Conduction band (C.B) andValance band (V.B)Oxide dielectric strengthTight binding approach

This paper presents a comparative study between CNT MOSFET and CNT TFET taking into account of dif-ferent dielectric strength of gate oxide materials. Here we have studied the transfer characteristics, on/offcurrent (ION/IOFF) ratio and subthreshold slope of the device using Non Equilibrium Greens Function(NEGF) formalism in tight binding frameworks. The results are obtained by solving the NEGF andPoisson’s equation self-consistently in NanoTCADViDES environment and found that the ON state perfor-mance of CNT MOSFET and CNT TFET have significant dependency on the dielectric strength of the gateoxide materials. The figure of merits of the devices also demonstrates that the CNT TFET is promising forhigh-speed and low-power logic applications.

� 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction

Silicon oriented CMOS technology are very much popular insemiconductor industries due to their extraordinary matured pro-cess technology and low cost. However, when the existing CMOStechnology enters into nanometer regime (below 100 nm) thistechnology hits a plateau [1]. This is because in this scaling limit,the semiconductor industry faces some serious problem regardingthe fabrication process and some adverse size effect includingshort channel effects, parasitic capacitance, and leakage currentsetc., and these effects become more severe when gate length isscaled continuously [2,3]. In recent years, extensive researcheshave been carrying out to explore new materials and as well asnew technology to replace the existing CMOS technology and sup-press its drawbacks. Tunneling field effect transistor (TFET), whichworks on the basis of band to band tunneling are drawing massattention due to their lower subthreshold slop and low off stateleakage current [4–10]. Since the basis of operation of TFET is bandto band tunneling, TFET is more immune to short channel effectsthan its MOSFET counterpart [11–13]. However, in spite of severaladvantages of TFET over conventional MOSFET, TFET suffers from aserious problem to overcome, which is its low ON state current dueto presence of tunneling barrier. Existing Si-based TFET devicesprovides very low ON current [14], it is therefore very much impor-

tant to search proper material system for TFET. Carbon nanotubehas a potential to be the appropriate channel material to replaceSi in this new technology due to its unique quasi one dimensionalproperty such as high electron mobility and high Fermi velocity[15]. Since the tunneling transistor is a new type of device, it isof utmost important to explore the performance of this device withdifferent parameters.

It is to be noted here that the conventional scaling rule of MOS-FET (which is constant electric field) is not blindly followed to scaledown the TFET. In a previous study Bhuwalka, et al. [16] haveexplained about the rule of scaling down of Si TFET and concludedthat constant field scaling rule is not applicable for TFET, thoughthey have some works where the channel length and oxide thick-ness are decreased simultaneously [11,16], following the Den-nard’s scaling rule [17]. However, when studying TFET, it is moreconvenient to vary one parameter at a time, in order to get com-plete understanding of the effect of each change and isolate theeffect.

In this article we report the gate-oxide dielectric strengthdependent performance comparison for CNTMOSFET and CNTTFETconsidering double gate structure. We have shown that the effectof different high-k dielectrics is not similar in these two cases.The physics behind their dissimilar behavior is also explained withtheir respective band diagram and electric field. The currentvoltage (I-V) characteristics are obtained by solving the NEGFand Poisson’s equation self-consistently in NanoTCADViDESenvironment. Other performances of the device like ION/IOFF ratio

880 Md. Shamim Sarker et al. / Results in Physics 6 (2016) 879–883

and subthreshold slope are studied from the transfer characteris-tics in conjunction with band diagram.

This article is organized as follows: device structure and simu-lation methods are explained under section II, while section IIIdemonstrate the details results and discussion, and section IV con-tains the summery.

Simulation details

Device structure

The double gate device structure used in our simulation isshown in ‘‘Fig. 1”. We have used CNT in the channel of the deviceswith chirality of (13,0), having a length of 15 nm. CNT in this chi-rality has a band gap of 0.75 eV. Source and drain are the extensionof the channel doped with n-type dopant for the MOSFET. For theTFET source is doped with p-type while the drain is doped with n-type dopant. The doping density of the source and drain reservoirsis taken f ¼ 5� 10�3. On the top and bottom of the channel weused gate insulator that is extended over the source, and drain aswell. For suppressing the ambipolar conduction in TFET, weapplied a small body bias in the bottom gate and it is also appliedfor MOSFET for fair comparison between them.

Simulation approach

The transfer characteristics of CNT MOSFET and TFET are deter-mined by solving Schrodinger equation using NEGF formalism,which are solved self consistently with 3-D Poison’s equation.The 3D Poison’s equation is given by [18,19]

r½eð~rÞr/ð~rÞ� ¼ �q½pð~rÞ � nð~rÞ þ NþDð~rÞ � Nþ

A ð~rÞ þ qfix� ð1Þ

where /ð~rÞ is the electrostatic potential, eð~rÞ is the dielectric con-stant, Nþ

D and NþA are the concentration of ionized donors and accep-

tors, respectively, and qfix is the fixed charge. Remaining terms arethe electron and hole concentration, nð~rÞ and pð~rÞ, respectively.These are evaluated by solving the Schrodinger equation using openboundary condition considering the tight binding Hamiltonian withan atomistic (pz)basis.

The greens function can be expressed as [12,13]

GðEÞ ¼ ½EI � H � RS � RD��1 ð2Þ

where ‘E’ is the energy, ‘I’ the identity matrix, ‘H’ is the Hamiltonianof the GNR written in tight binding approach and RS and RD are theself-energies of source and drain contacts, respectively. Here trans-port is assumed completely ballistic and charge is considered aspoint charge.

Assuming that the chemical potential of the reservoirs arealigned at equilibrium with the Fermi level of the GNR, and given

Source reservoirs

CNT Channel

Drain reservoirs

Dielectric

Bottom Gate

Dielectric

Top gate15 nm 15 nm

15 nm

Fig. 1. Proposed CNT MOSFET/CNT TFETstructure.

that there is no confined states. The electron and hole concentra-tions in the channel are

nð~rÞ ¼ 2Z þ1

Ei

dE½jwSðE;~rÞj2f ðE� EFSÞ þ jwDðE;~rÞj2f ðE� EFDÞ� ð3Þ

and

pð~rÞ ¼ 2Z Ei

1dEf½jwSðE;~rÞj2½1� f ðE� EFSÞ� þ jwDðE;~rÞj2½1� f ðE� EFDÞ�g

ð4ÞHere ‘~r’ is the coordinate of carbon site, ‘f ’ is the Fermi-Dirac

occupation factor, and jwSj2ðorjwDj2Þ is the probability that statesinjected by the source (or drain) reach the carbon site (~r) andEFSðorEFDÞ is the Fermi level of the source (or drain)

The current is computed by

I ¼ 2qh

Z þ1

�1dETðEÞ½f ðE� EFSÞ � f ðE� EFDÞ� ð5Þ

where ‘q’ is the electron charge, ‘h’ is the planks constant and ‘T(E)’is the transmission coefficient that is given as-

T ¼ �Tr

XS

�Xþs

!GXD

�XþD

!Gþ

" #ð6Þ

Here Tr is the trace operator. The simulation is carried out attemperature 300 K.

Result and discussion

The dielectric materials used in our study are listed in ‘‘Table 1”along with their dielectric constants:

As the attempt to compare the performance between the CNTMOSFET and CNT TFET, we first present the oxide dielectricstrength dependent transfer characteristics of the CNT MOSFETshown in ‘‘Fig. 2”, where the thickness of the gate insulator isassumed as 2 nm. The results are evaluated varying the gate biasVgs from 0 to 0.4 V, while keeping the drain bias Vds fixed at0.4 V. The curves is plotted in logarithmic and as well as linearscale to understand the difference between ION and IOFF clearly.

From ‘‘Fig. 2” it is seen that the ON current is the lowest for thesmallest dielectric strength and gradually increases with increasein dielectric strength although the variation of OFF current is neg-ligible. These results can be explained from the respective ON stateand OFF state band diagram shown in ‘‘Figs. 3 and 4”. It is seen in‘‘Fig. 3” that the magnitude of barrier height for both low-K andhigh-K gate dielectric are almost similar. That means the channelis equally resistive for electron to flow for both cases. As a resultthe variation of OFF state current is almost negligible. While inON state, ‘‘Fig. 4” shows that high-K gate oxide paves the lowerenergy path for electron. As a result ON state current for high-Kgate oxide become higher than the low-K gate oxide and theseobservation is consistent with the results reported by other groupsas well [20].

Table 1Lists of dielectric materials with their dielectric strengths.

Dielectric material Dielectric strength

Silicon dioxide (SiO2) 3.9Silicon nitride (Si3N4) 7.0Hafnium silicate (HfSiO4) 11Yttrium Oxide (Y2O3) 16Hafmium oxide (HfO2) 25

0.0 0.1 0.2 0.3 0.4

101

102

103

104

Dra

in C

urre

nt,I

D(

Aµ)

Dielectric Constants, kD

rain

Cur

rent

,ID

(A

/mµ

µ)

Gate Voltage (V)

k=3.9 k=7.0 k=11 k=16 k=25

2

4

6

8

10

12

14

16

18

Fig. 2. ID-Vgs characteristics of the proposed CNT MOSFET as a function differentgate oxide materials having thickness of 2 nm.

0 5 10 15 20 25 30 35 40 45

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Dielectric Constants, k

C.B

V.B Vgs

= 0.0 VV

ds=0.4 V

Ene

rgy

(eV

)

Position alone the channel (nm)

k=3.9 k=16 k=25

Fig. 3. OFF state band diagram of CNT MOSFET for SiO2 (k = 3.9), Y2O3(k = 16) andHfO2 (k = 25). Physical oxide thickness is kept constant at 2 nm.

0 5 10 15 20 25 30 35 40 45

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Position alone the channel (nm)

Ene

rgy

(eV

)

C.B

V.B

Dielectric Constants, k

k=3.9 k=16 k=25

Vgs

= 0.0 VV

ds=0.4 V

Fig. 4. ON state band diagram of CNT MOSFET for SiO2 (k = 3.9), Y2O3(k = 16) andHfO2 (k = 25). Physical oxide thickness is kept constant at 2 nm.

Md. Shamim Sarker et al. / Results in Physics 6 (2016) 879–883 881

On the other hand, the gate oxide dielectric constants depen-dent transfer characteristics of CNT TFET is shown in ‘‘Fig. 5” whereall the conditions (oxide thickness, gate voltage, drain voltage) aremaintained equally as CNT MOSFET for fair comparison. It is seenthat the ON current is the highest for the smallest dielectric con-stant and gradually decreased with increase in dielectric constant,which is the reverse trends of the CNT MOSFET as seen in ‘‘Fig. 2”.The results can be explained from the respective ON state energyband diagram and distribution of the electric field for the CNT TFETshown in ‘‘Figs. 6 and 7”, respectively. It is observed in ‘‘Fig. 6(a)”that the energy band obtained for the gate oxide with the lowestdielectric constant offers the smallest tunneling distance, that is,the barrier width, W indicated by arrows in the solid square box.The expanded view of this region is shown in the inset of ‘‘Fig. 6(a)”. The variation of the barrier width, W as a function of gate-oxide dielectric strength is plotted in ‘‘Fig. 6(b)”. It is found thatthe barrier width increases with increasing oxide dielectricstrength. Since the tunneling probability is inversely related withthe width of tunneling barrier, therefore, gradual fall of ON statecurrent is found in ‘‘Fig. 5” with increasing the oxide dielectricstrength.

This falling nature of ION can also be explained from the distri-bution of electric field at the tunneling junction (source-channeljunction) shown in ‘‘Fig. 7”. Here the peak amplitude of electricfield at the tunneling junction is reduced with increase in oxidedielectric constants. This electric fields is related with the trans-mission co-efficient of the TFET by the ‘‘Eq. (7)” [21]:

TðEÞ1exp �4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m � E3=2

g

q3q�hF

0@

1A ð7Þ

where m⁄ is the effective electron mass of the material, Eg is theband gap of the channel material and F is the electric field in thesource channel junction. Eq. (7) implies that, the lower electric fieldwill result in lower transmission coefficient and finally lower ONcurrent. That is why the ION is gradually reduced with the increasein dielectric strength.

In addition, sharpness of the band bending at the tunnel junc-tion of ‘‘Fig. 6(a)” can also be described from the electric field dis-tribution at ON-state as shown in ‘‘Fig. 7”. Electric fields at thetunneling junction is very much pointy and possess highest valuefor k = 3.9. So it affects the band at the tunneling junction moreprecisely. As a result the band bending at the tunneling junctionis very sharp. But as the dielectric constant increases the electric

0.0 0.1 0.2 0.3 0.4

10-3

10-2

10-1

100

101

102

103

Dra

inC

urre

nt,

I D(

A)

Dielectric Strength, k

Dra

inC

urre

nt,

I D(

A/

m µ

µ

µ)

Gate Voltage, (V)

k=3.9k=7.0k=11k=16k=25

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Fig. 5. ID-Vgs characteristics of the proposed CNT TFET as a function different gateoxide materials having thickness of 2 nm.

0 10 20 30 40

-1.2

-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

8 12 16 20 24-0.6-0.4-0.20.00.20.40.6

Vgs

=0.4 VV

ds=0.4 V (a)

W

C.B

V.B

Dielectric Constant, k

Ener

gy (e

V)

Gate Voltage (V)

k=3.9 k=16 k=25

5 10 15 20 252

4

6

(b)

Bar

rier

Wid

th,

W(n

m)

Dielectric Strength, k

Fig. 6. (a) ON state band diagram for k = 3.9, k = 16 and k = 25 (b) dielectric strengthdependent barrier width. Physical oxide thickness is kept constant at 2 nm.

0 5 10 15 20 25 30 35 40 450

1x108

2x108

3x108

4x108

5x108

Dielectric Constant, k

Elec

tric

field

(V/m

)

position along the channel

k=3.9 k=16 k=25

Fig. 7. Distribution of electric field in ON state: for k = 3.9, k = 16 and k = 25.Physical oxide thickness is kept constant at 2 nm.

0 5 10 15 20 25 30 35 40 45

-1.0

-0.5

0.0

0.5

1.0

Vgs

=0.0 VV

ds=0.4 V

V.B

C.B

Dielectric Constant, k

Transition

Ene

rgy

(eV

)

Position along the Channel (nm)

k=3.9 k=16 k=25

Fig. 8. OFF state band diagram for k = 3.9, k = 16 and k = 25. Physical oxidethickness is kept constant at 2 nm.

0.0

0.5

1.0

07

142128

4x104

6x1048x104

105

5 10 15 20 2514

16

(b)

(c)

(d)

(a)

I ON

(Aµ

)

I OFF

(nA

)S t

(mV

/dec

)

S t(m

V/d

ec)

I ON

/IO

FF

I ON

/IO

FFI O

FF

(pA

)

I ON

(Aµ

)

Dielectric Strength, k

3691215

1.6

2.0

2.4

3.0x103

6.0x103

9.0x103

60646872

Fig. 9. Dielectric strength dependent (a)ION/IOFF ratio (b) ION(c)IOFF(d) subthresholdslop of CNT TFET (blue line) and CNT MOSFET (black line) for oxide thickness of2 nm. (For interpretation of the references to colour in this figure legend, the readeris referred to the web version of this article.)

882 Md. Shamim Sarker et al. / Results in Physics 6 (2016) 879–883

field at the tunneling junction get broadened shown in ‘‘Fig. 7” andreaches inside the channel and source region. As a results, a portionof bands inside the channel and source region is also get affectedby the electric field and become pushed down a little. As a result,the overall sharpness of the band is reduced.

Now in OFF state condition, we can see that IOFF also have fallingcharacteristics with increase in dielectric constants and it can beexplained from the respective OFF state band diagram shown in‘‘Fig. 8”. Here it is seen that the tunneling distance increases grad-ually with increase in dielectric constants. As a result the OFF statecurrent reduces gradually.

A comparison of ION, IOFF, and ION/IOFF ratio of CNT TFET and CNTMOSFET is shown in ‘‘Fig. 9” as a function of dielectric constant.Here left hand scale indicates the results obtained for the CNT TFETand right hand scale for the CNT MOSFET. The ION/IOFF ratioincreases with the oxide dielectric constants for the CNT TFET

shown in ‘‘Fig. 9(a)” in spite of having falling characteristics of bothION and IOFF shown in ‘‘Fig. 9(b) and (c)”. This is because the IOFFreduces more drastically than the ION in their individual scale withthe variation of oxide dielectric constants. So ION/IOFF ratio is foundto be increased gradually with increase in dielectric constants.

In contrast, the ION/IOFF ratio also found to have rising trendswith dielectric constants for the CNT MOSFET shown in ‘‘Fig. 9(a)” which can be clearly understood from ‘‘Fig. 9(b) and (c)”. Inaddition to them subthreshold slope is strongly correlated withthe performance of a logic device. Fig. 9(d) shows subthresholdperformance of the CNT TFET along with the CNT MOSFET.

It is found that the subthreshold slope decreases with increas-ing dielectric constant for both of the devices. The minimum valueof subthreshold slope is found to be about 14 mV/dec and 60 mV/dec, respectively, for the CNT TFET and CNT MOSFET, indicatingthat the CNT TFET shows excellent subthreshold performance.Finally except ON current, CNT TFET shows much better resultsthan the CNT MOSFET with excellent subthreshold performance.

Md. Shamim Sarker et al. / Results in Physics 6 (2016) 879–883 883

But this low ON current also has an advantage in switching andlow power application.

Conclusion

Oxide dielectric strength dependent performance is studied fordouble gate CNT MOSFET and CNT TFET. The ON current perfor-mance of CNT MOSFET improves with increase in oxide dielectricconstants, but in case of TFET this performance deteriorates. TheOFF state current decreases with increasing dielectric constantfor the CNT TFET, although it is almost constants for the CNT MOS-FET. The ION/IOFF ratio and the subthreshold performance of bothdevices improve with increase in dielectric constants. Our studydemonstrates that except ON current, TFET has much better per-formance than MOSFET in other performance parameters andseems to be a potential candidate for high-speed and low-powerswitching devices.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.rinp.2016.11.002.

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