Multi-scale SimulationTunn

Larkhoon Leem1, Ashutosh SrivasJ

1Department of Electrical Engineering Stanford U

4Dipartimento di Ingegneria

Abstract

Band-to-band Tunneling Field Effe(TFETs) are emerging as a solution to b60mV/dec sub-threshold slope limit ofMOSFETs. In this work, we present for multi-scale simulation results of partiaCarbon Nanotube heterojunction TFET. the CNT and GNR homojunction TFETheterojunction TFETs demonstratsub-threshold region characteristics − 1061% smaller Subthreshold Swing (SS) whrange of 22~26mV/dec and the I-V amcompletely eliminated.

Introduction

With all the fruits harvested from tCMOS design tree, it has become cleaimprovements in energy efficiency will onthrough novel and revolutionary changedesign [1]. Band-to-band Tunneling Transistors (TFETs) have recently attracted the research community because of sub-threshold slope (SS). Conventional MOby thermal injection over channel barrier lim60mV/decade. In contrast, TFETs expquantum mechanical tunneling as the demechanism, leading to small SS and reducedvoltage for digital logic applications. Whilband-to-band tunneling transistors have beachieve SS < 60mV/dec [2], their potential alimited by: 1) small Ion current as compared tMOSFETs, 2) ambipolar I-V characteristic60mV obtained only in a very limited Vgs iwork, we present for the first time, multi-consisting of Density-Functional Theory (DHückel Theory (EHT), Molecular Dynamatomistic Tight-Binding (TB) calculationCarbon nanostructure-based TFETs with typbarriers that results from partially unziNanotubes (CNTs). The concept of unzippin(Fig. 1,2) is promising because one can obtaGNRs with reduced roughness [3]. In addunzipped CNT has been shown to significthe tunneling barrier [6]. In this work, wdemonstrate for the first time that partially ucan induce type-II heterojunction betwe

ns of Partially Unzipped CNT Heteeling Field Effect Transistor

stava2, Shuang Li3, Blanka Magyari-Köpe1, GiusJames S. Harris1, Gianluca Fiori4

g, 2Department of Materials Science and Engineering, 3DepUniversity, 420 Via Palou, 94305, Stanford, U.S.A. dell�’Informazione, Universita di Pisa, via Caruso, 56122, P

ect Transistors break classical f conventional

the first time ally unzipped Compared to

Ts, GNR/CNT te superior 4× smaller Ioff, hich lies in the mbipolarity is

the low-power ar that further nly be realized s in MOSFET

Field Effect deep interest in

their small OSFETs operate miting the SS to ploit interband evice operation d power supply le a number of een reported to applications are to conventional s, and 3) SS < interval. In this -scale approach DFT), Extended mics (MD) and ns to simulate pe-II tunneling ipping Carbon ng CNT [3,4,5] ain high quality dition, partially cantly diminish we numerically unzipping CNT een GNR and

primitive CNT to overcome thmentioned above.

Device operating

The I-V curve ambipolarityresults from the symmetric energOFF states: the energy bandgap ajunction becomes narrower whbandgap at the drain and channe

(a) GNR(source)-CNT(channel)-GNR(drai

(c) GNR-CNT-CNT

Figure 1. Partially unzipped CarbonTunneling FET (TFET) Cross-sectionaNanoribbon (GNR)/CNT heterojunctions tFET performance (a)~(d).

Figure 2. Energy-relaxed configurationsfrom Molecular Dynamics (MD) simustabilized configuration (d).

(a) Figure 3. Symmetric energy bands ofdiagrams of a homojunction TFET whenTunneling happens for both Vgs >0 and Vg(b) of homojunction CNT TFET. Ambipolmolar fractions) in drain region were optim

ero-junction

eppe Iannaccone4,

artment of Physics,

Pisa, Italy

he limitations of TFETs

principle

y of homojunction TFETs ybands at device ON and at the source and channel en Vgs >0. The energy el junction symmetrically

in) (b) CNT-GNR-CNT

(d) CNT-GNR-GNR

n Nanotube (CNT) Heterojunction al schematics of simulated Grapheneto study their effects on the Tunneling

s of partially unzipped CNT obtained ulations. Initial (a) and final energy

(b) f Homojunction TFETs. Energyband

n Vgs >0 and Vgs < 0, respectively (a). gs <0, which leads to I-V ambipolarity in arity prevails even the doping levels (in

mized as in [7].

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gets narrow to incur large OFF current whe3(a)). A well-defined approach based osuppress this ambipolarity is to break the asymmetric doping (Fig. 3(b)) or gate electroHowever, these techniques do not ambipolarity and the effectiveness is limitedrange (Fig. 3(b)) [7]. Interestingly, heterfundamentally break this symmetry, leadinsub-threshold region characteristics: large bais used for the channel and drain region ttunneling at the drain-channel junction bandgap material is selected for the souincrease the tunneling Ion. Among various types (Fig. 4 i~iii), type-II is preferred over of smaller bandgap overlap or effectivefacilitate Ion tunneling and higher energy baIoff current flow [8]. This type-II heterojuncnanostructure can be easily achieved by partthe CNTs. When CNTs are partially unzippedifference in energy bandgaps and workfunthe primitive and unzipped CNT, which canheterojunctions.

Device simulation process

The flow diagram of our multi-scal

Figure 4. Band diagram (white solid lines) and lCNT-GNR-CNT (center) and GNR-CNT-CNT (right) ccreate GNR n=16 at source/drain or channel regions.heterojunctions are formed. Notably, the symmetric ene

CNT (N,0)

GNR (n)

Eg_CNT (DFT)

Eg_CNT (EHT) φ(CNT) φ

[R

14 24 0.612eV 0.64 eV 3.783 eV

~13 22 0.7364 0.77 3.8215 11 16 0.766 0.79 3.745 10 16 0.937 1.01 3.813 8 16 0.57 1.054 4.017 7 14 0.497 1.184 4.201

Table 1. Calculated electronic structures of partiadifference between the vacuum level and the Fermi levTheory (EHT) and the rest from Density Functional T

en Vgs <0 (Fig. on physics to symmetry with ode location [7]. eliminate I-V d to narrow Vgs rojunctions can ng to excellent andgap material to suppress the

while, small urce region to

heterojunction type-I because e bandgap to

arrier to impede ction in carbon tially unzipping ed, there exist a nctions between n lead to type-II

le approach is

shown in Fig. 5. Electronic stbandgap and workfunctions of calculated using DFT, EHheterostructure was energy-rsimulation at T=0K. Then, the 3Dthe Non-Equilibrium Green�’s funand Tight-Binding methods wercharacteristics of the device. DFdone using Atomistix ToolKit veand 10.08.0 [10], I-V characteexploited the open-source Nano[11] and MD simulation used LFor bandgap, workfunction and I-no curvature and abrupt junction were assumed. This was to reducDFT calculations but also, our Ithat TFETs with �“completely rolleas the channel region had the Ids d(Fig. 6). More realistic curvature CNTs was obtained from MD includes long range Coulombic (2507 C, H atoms). This result wof the simulation process in a fudevice configurations (Fig. investigated for optimal device p

local density of states (LDOSs) of GNR/CNT tunneling FETs. configurations are shown for ON (top row) and OFF state (bottom row). C. Due to the workfunction and bandgap differences between the GNRergyband diagrams as in Fig. 3(a) are not found in our GNR/CNT hetero

φ(CNT)Ref. 14]

Eg_GNR(DFT)

Eg_GNR(EHT) φ(GNR) φ(GNR)

[Ref. 15]φ(GNR)- φ(CNT)

~4.7eV

0.295eV 0.352 eV 3.628 eV

~4.58 eV

-0.0111 eV0.491 0.46 3.618 -0.0485

0.672 0.624 3.582 -0.08 -0.038

4.8 -0.22 5.1 0.12 0.047 3.567 -0.0655

ally unzipped CNT using first principles methods. Eg: energy bandvel. For I-V calculations, we used the energy bandgaps of CNT and GNR

Theory (DFT). *Eg_eff is an overlap between two bandgaps (Fig. 4 (ii)).

tructure such as energy GNR and CNTs were

HT [9]. Carbon-based relaxed through DFT D-Poisson equation within nction Formalism (NEGF) re used to calculate I-V FT/EHT calculation was

ersion 2008.10.0, 2010.02 eristics calculation fully TCAD ViDES simulator

LAMMPS simulator [12]. V calculations, GNR with between GNR and CNT

e the number of atoms in I-V calculations indicated ed GNR�” and �“flat GNR�” difference of 4.6% or less information on unzipped simulation (Fig. 2) that interaction among atoms

will be included in the rest uture work. Four different

1(a)~(d)) have been performance according to

GNR-CNT-GNR (left column), CNT(8,0) is partially unzipped to R and CNT, type-II (staggered) ojunction TFETs.

)

Type -II

Type-III

Eg_eff,* effective bandgap

V 0.3409 eV 0.4115 0.544 0.586 0.404

-0.0185 dgap, φ: workfunction, the energy R obtained from Extended Hückel

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ITRS requirements [13]. The nominaldouble-gate geometry with 1.7 nm thick SiThe channel length, Lch=15nm, the source/dLS|D is 10nm. The source/drain used <=3e-levels in molar fractions.

Device simulation results

Table 1 shows the energy bworkfunctions of CNTs and unzipped CNfrom DFT and EHT methods in this work. Cpossible loss of Carbon atoms during unzicontrolling etching time), a number of difGNRs can be produced from a single chiCalculated results indicate that the workfunca function of nanotube diameter. On thunzipped CNTs are found to have alworkfunctions because zero curvature GNRExample combinations of zig-zag CNTs GNRs that make type-II heterojunctions are1. Among these combinations, CNT (8,0) anare chosen for further I-V calculations becaubandgap overlap between CNT and GNR whis large. The DFT calculations were dogeometrical relaxation to a force toler0.05eV/Angstrom. Difference in this limit to slight variations in the workfunction valuother related works [14,15].

Fig. 2 illustrates the energy relaxatipartial unzipping of CNT (8,0) through MCompletely stabilized configuration showcurved GNR region before GNRs becoming c

Figure 6. I-V characterisitics of heterojunction TFEGNR (�“flat�”) vs. completely rolled GNR. I-VCNT-GNR-CNT with unrolled and rolled GNRs are cin linear scale and the right plot in log scale). Festimation, CNT(source)-GNR(channel)-CNT(drain) used, whose device turns on at Vgs <0 as shown in the p

Figure 5. Flow chart simulations for heterojuDeliverables from each step inner boxes.

l device has iO2 gate oxide. drain extension, -3/atom doping

bandgaps and NTs calculated Considering the pping (e.g., by

fferent types of rality of CNT. ction of CNT is he other hand, lmost constant

Rs are assumed. and armchair

listed in Table nd a-GNR n=16 use of its small

while Eg of CNT one using the

rance limit of could have led

ues compared to

ion process of MD simulations. wed 3~4nm of completely flat.

In Fig. 4, the Density-of-StatGNR/CNT heterojunction TFETsrow) and OFF state (bottom rowunzipped to create a-GNR n=16 aregions. Due to the heterojuncbands present in homojunction Texample, in GNR(source)-CTFET, tunneling is enhanced in theffective bandgap (Fig. 4(e)). In thstrongly suppressed by larger band high energy barrier of typ4(f)).

Compared to the CNT and GGNR/CNT heterojunction TFETsub-threshold region characteristicsmaller SS=22~26mV/dec (comand I-V ambipolarity is completThis is because of 1) the availamaterial for the channel (CNT heterojunction, Eg=1.054eV) 2)material (a-GNR n=16, Eg=0.624and 3) type-II heterojunction forinterface (effective Eg=0.44eV). FGNR/CNT heterojunction TFEhomojunction TFETs were operformance. Doping levels (in drain region were reduced (as region) to suppress the ambipo(14,0) (Eg=0.64eV) was chosen the Eg=0.624eV of GNR n=16.

Among four heterojunctio1(a)~(d)), GNR-CNT-GNR demonstrate better substhreshold This is due to large energy bandgaand drain region (GNR-CNT-CNTat the channel-drain junction (were no significant differencesbetween the two configurations (F

ETs with unrolledV curves of thecompared (left plotor the worst case

configuration isplot.

Figure 7. Comparison of I-V curves FETs. The workfunction of the gate elIds=10-11A is at Vgs=0V. Compared theterojunction TFET shows smaller Ioff

completely suppressed while they show cGNR TFET.

of multi-scale unction TFETs. are shown in the

te (DOS) plots of the s are shown for ON (top

w). CNT (8,0) is partially at source/drain or channel tions, symmetric energy TFETs are removed. For NT(channel)-CNT(drain)

he ON state due to smaller he OFF state, tunneling is

bandgap channel material pe-II heterojunction (Fig.

GNR homojunction TFETs, Ts demonstrate superior cs - 104× smaller Ioff, 61%

mpared with CNT-TFET) tely suppressed (Fig. 7).

ability of larger bandgap (8,0) in the GNR/CNT

) the smaller bandgap eV) for the source region r the source and channel For fair comparisons with ETs, CNT and GNR ptimized for the best molar fractions) in the

compared to the source olarity. In addition, CNT for CNT TFET to match

on configurations (Fig. and GNR-CNT-CNT

slope and Ioff than the rest. ap material in the channel T) and high energy barrier GNR-CNT-GNR). There s in I-V characteristics Fig. 7), indicating that it is

of Carbon based tunnelinglectrode is adjusted to haveto CNT TFET, GNR/CNTf ,SS and I-V ambipolaritycomparable performance with

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sufficient to have the unzipping of CNT at source/channel interface only for this particular device dimension and operation voltage range. When unzipped region (GNR) is used as a channel material (Fig. 1(b),(d)), device turns ON at Vgs <0 and OFF at Vgs >0, which effectively works as PMOS device. However, due to smaller bandgap of GNR (n=16) in the channel region, weak ambipolarity is witnessed (Fig. 8).

Subthreshold characteristics of GNR/CNT heterojunction TFET also depend on the channel length, doping and Vds (Fig. 9). Direct tunneling between the source and drain dramatically increases with shorter channel length (< 15nm). Furthermore, large Vds increases the device off-state tunneling through the channel-drain junction. This tunneling disappears when Vds 0.4V and removes the ambipolarity (Fig. 9).

Ion of GNR/CNT heterojunction TFETs strongly depends on the injecting states from the source region. GNR-CNT-GNR and GNR-CNT-CNT configurations show comparable Ion as those of GNR homojunction TFETs. On the other hand, CNT-GNR-CNT and CNT-GNR-GNR show similar Ion to CNT TFETs. However, this is a conservative estimation, since it can be further improved by an inherent stress developed in the junction region due to the partial unzipping of the CNT [16,17].

Conclusion

We have investigated the performance of partially unzipped CNT heterojunctions, by means of a multi-scaled approach based on DFT, EHT, MD and self-consistent TB simulations of carrier transport. GNR/CNT heterojunctions demonstrated to be good candidates for low voltage logic applications and show better performance in terms of low subthreshold slope and strongly suppressed ambipolar behavior as compared to CNT and GNR TFETs.

Acknowledgment G.F. and G.I. gratefully acknowledge the EC 7FP

Project GRAND (Contract 215752), and the MIUR-PRIN for �“Modeling and simulation of graphene nanoribbon FETs for high-performance and low-power logic applications�” project (Prot. 2008S2CLJ9).

Reference 1. J. Rabaey, �“Low Power Design Essentials,�” Springer, DOI 10.1007

(2009) 2. W. Choi, B. Park, J. Lee, T.K. Liu, �“Tunneling Field-Effect

Transistors with Subthreshold Swing (SS) less than 60mV/dec,�” IEEE Electron Device Lett., vol. 28, no. 8, pp.743-745 (2007)

3. L. Jiao, L. Zhang, X. Wang, G. Diankov and H. Dai, �“Narrow Graphene Nanoribbons from Carbon Nanotubes,�” Nature, vol. 458, pp877-880 (2009)

4. D. Kosynkin, et al., �“Longitudinal Unzipping of Carbon Nanotubes to form Graphene Nanoribbons,�” Nature, vol. 458, pp. 872-877 (2009)

5. K. Kim, A. Sussman, and A. Zettl, �“Graphene Nanoribbons Obtained by Electrically Unwrapping Carbon Nanotubes,�” ACS Nano, vol.4, no.3 (2010)

6. Y. Yoon, S. Salahuddin, �“Barrier-free tunneling in a carbon heterojunction transistor,�” Appl. Phys. Lett., vol. 97, 033102 (2010)

7. P. Zhao, J. Chauhan and J. Guo, �“Computational Study of Tunneling Transistor Based on Graphene Nanoribbon,�”, Nano Lett., vol.9, no. 2, pp.684-688 (2009)

8. D. Kim, et al., �“Low Power Circuit Design based on Heterojunction Tunneling Transistors (HETTs),�” Proc. Intl. Symp. Low Power Electronics and Design, pp.219-224 (2009)

9. D. Kienle, J.I. Cerda and A.W. Ghosh, �“Extended Hückel theory for band structure, chemistry, and transport. I. Carbon nanotubes,�” J. Appl. Phys, vol. 100, 043714 (2006)

10. M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Phys. Rev. B vol. 65, 165401 (2002)

11. G. Fiori, G. Iannaccone, "NanoTCAD ViDES," DOI: 10254/nanohub-r5116.5, (2008)

12. S. Plimpton, �“Fast Parallel Algorithms for Short-Range Molecular Dynamics,�” J Comp Phys, vol. 117, pp.1-19 (1995)

13. ITRS http://public.itrs.net 14. B. Shan, K. Cho, �“First Principles Study of Work Functions of

Single Wall Carbon Nanotubes,�” Phys. Rev. Lett. vol. 94, 236602 (2005)

15. Q. Yan, et. al., �“Intrinsic Current-Voltage Characteristics of Graphene Nanoribbon Transistors and Effect of Edge Doping,�” Nano Lett., vol.7, no.6 pp.1469-1473 (2007)

16. J. Zhang, K. Ong and P. Wu, �“The Influence of Out-of-Plane Deformation on the Bandgap of Graphene Nanoribbon,�” J. Phys. Chem. C, vol. 114, pp.12749-12753 (2010)

17. Y. Li, X. Jiang, Z. Liu and Z. Liu, �“Strain Effects in Graphene and Graphene Nanoribbons: The Underlying Mechanism,�” Nano Res., vol. 3, no. 8, pp. 545-556 (2010) Figure 9. Vds (left) and channel length (right) dependence of

GNR/CNT Heterojunction TFETs. Subthreshold slope (SS) and Ioff

show dependencies on the Vds (left) and the channel length (right).

Figure 8. CNT-GNR-CNT heterojunction TFET I-V characteristics.When unzipped region (GNR) is used as a channel region, device turnson at Vgs <0, effectively working as a PMOS device. However, due to smaller bandgap of GNR in the channel region, weak ambipolarity iswitnessed.

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