www.elsevier.com/locate/carbon

Carbon 44 (2006) 3087–3090

Simulation of carbon nanotube based p–n junction diodes

Jingqi Li a, Qing Zhang a,*, Mary B. Chan-Park b

a Microelectronics Center, School of Electrical and Electronic Engineering, Nanyang Technological University,

Block S2.2, 50 Nanyang Avenue, 639798 Singapore, Singaporeb School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798 Singapore, Singapore

Received 8 November 2005; accepted 4 April 2006Available online 10 July 2006

Abstract

Taking advantage of the unique characteristics of an ambipolar carbon nanotube field effect transistor (CNTFET), a ‘p–n junction’ issimulated along the single-walled carbon nanotube channel using two separate gates close to the source and drain of the CNTFET,respectively. The current–voltage characteristics of the double-gated CNTFET are calculated using a semiclassical method based onthe Schottky barrier field effect transistor mechanism. The calculation results show a good rectification performance of the p–n junction.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Carbon nanotubes; Electrical (electronic) properties

1. Introduction

Switching mechanism of carbon nanotube field effecttransistors (CNTFETs) was initially assumed to be analo-gous to a traditional Si MOSFET. However, by comparingthe transfer characteristics of the CNTFETs exposed to dif-ferent oxygen levels to those doped with different amountsof potassium, Heinze et al. [1] pointed out that the Schottkybarrier (SB) at the contacts between the carbon nanotubes(CNTs) and electrodes plays a key role in controlling theperformance of the devices. In other words, CNTFETscould be operated as ‘‘SB transistors’’, in which the contactresistance, rather than the channel conductance, dominatesthe CNT channel conductance. In addition, the SB mech-anism is also supported by the fact that the inverse sub-threshold slope of the Id–Vg curve is temperature dependentat high temperatures and it levels off at temperatures below200 K [2]. Furthermore, the finding of ambipolar conduc-tion of some CNTFETs [3,4], which is impossible in conven-tional field effect transistors, strongly supports the SBmodel. Lee et al. [5] fabricated a p–n junction on a single

0008-6223/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.carbon.2006.04.041

* Corresponding author. Tel.: +65 679 05601; fax: +65 679 20415.E-mail address: eqzhang@ntu.edu.sg (Q. Zhang).

CNT using a pair of split gate electrodes and showed a verygood diode characteristic by biasing the split gates withopposite potentials. They simulated their experimental find-ings in the frame of the conventional Si MOSFET model.However, since the p–n junction diode was formed on a sin-gle nanotube by electrostatic doping, the CNTFETs couldfunction like a Schottky barrier transistor rather than a con-ventional MOSFET. It would be more convincing to simu-late this phenomenon using the SB-FET mechanism. In thispaper, we analyse the p–n junction diode characteristicsusing the SB-FET mechanism.

2. Methodology

The side-view of the double-gated CNTFET structure isshown in Fig. 1. Carbon nanotube with length of 200 nm isplaced between the 20 nm-thick source and drain elec-trodes. Two back-gate electrodes are close to the sourceand drain, respectively. The gap between them is 20 nm.The length of the source (drain) and gate electrodes are100 nm and 190 nm, respectively. The thickness of theSiO2 layer is 5 nm.

A semiclassical method [6,7] is used to calculate thetransfer characteristics of the CNTFETs. Under an

Fig. 1. A schematic side-view of the double-gated CNTFET. ‘S’ an ‘D’represent the source and drain electrodes, respectively. A single-walledcarbon nanotube as the channel of the CNTFET bridges the source anddrain electrodes. The separate gates are underneath the SiO2 by the sourceand drain, respectively.

-1Vg(V)

I d(A

)

10-10

10-9

10-8

10-7

10-6

10-5

10-4

Vd = 0.25V

0.75V

0.5V

-0.5 0 0.5 1

Fig. 2. Calculated transfer characteristics of the CNTFET at Vd = 0.25,0.5 and 0.75 V when the two gates are commonly swept from �1 to 1 V.

-1.0 -0.5 0.0 0.6 0.8 1.0 1.2-2

0

2

4

6

8

10

12

I d (X

10-6

A)

Vd (V)

-1.0 -0.5 0.0 0.6 0.8 1.0 1.2

-2

0

2

4

6

8

10

12

Blue dash line: Vg1=-Vg2= 0.6V

Black dot line: Vg1=-Vg2= 0.5V

Red solid line: Vg1=-Vg2= 0.4V

Fig. 3. Calculated Id � Vd curves of the CNTFET for a combination ofVg1 and Vg2, or (0.4, �0.4), (0.5, �0.5) and (0.6, �0.6) V.

3088 J. Li et al. / Carbon 44 (2006) 3087–3090

assumption of ballistic transport, the channel current canbe expressed using the Landauer–Buttiker formula asfollows

I ¼ 4e

h

Z½F ðEÞ � F ðE þ eV dÞ�T ðEÞdE; ð1Þ

where Vd is the drain voltage, F(E) is the Fermi functionand T(E) is the energy-dependent transmission throughthe SB between the CNTs and electrodes. T(E) can be esti-mated with the Wentzel–Kramers–Brillouin (WKB)approximation

T ðEÞ ¼ exp �2

Z z2

z1

kðzÞdz� �

; ð2Þ

with the wave number

kðzÞ ¼ 2

3aV 0

Eg

2

� �2

� E þ eV ðzÞ½ �2( )1=2

; ð3Þ

where a = 0.144 nm, Eg = 0.6 eV, and V0 = 2.5 eV are theC–C bond length, the CNT band gap and the tight-bindingparameter, respectively. V(z) is the electrostatic potentialalong the CNT and is obtained by solving the Laplaceequation numerically for the device geometries shown inFig. 1. The integration is performed between the two clas-sical turning points z1 and z2 [6]. Charges on the CNT areneglected in the simulation. The CNT diameter and tem-perature are 1.4 nm and 300 K, respectively. The Fermilevel at the metal–CNT contact is assumed at the middleof the CNT band gap.

3. Results and discussion

If the two gates are biased with a common gate voltage,the transfer characteristics of the simulated CNTFET exhi-bit the typical ambipolar characteristics [3,4,8–10], asshown in Fig. 2. One can see that the drain current (Id)decreases first with increasing gate voltage (Vg) when Vg

is swept from a large negative value, and then increasesagain after reaching a minimum value (Imin). Holes andelectrons dominate the current on the left and right of Imin,respectively. The curves almost overlap for the electroncurrent while they split for the hole current at three differ-

ent drain voltages (Vd). The minimum current occurs atVg = Vd/2 as the electron current rises monotonically withVg exactly as the hole current increases monotonically withVd–Vg [11]. As a result, Imin increases with increasing Vd.The calculated results are consistent with the experimentalobservations for the CNTFETs with a 2 nm or 5 nm thickgate oxide [11], suggesting that this model can be used tointerpret the ambipolar characteristics of the CNTFETs.

When the two gates are biased oppositely, or in otherwords, Vg1 is positively gated and Vg2 is negatively gated,the calculated Id–Vd curves show a typical diode character-istic, as shown in Fig. 3. One can see that Id increases steeplywith increasing Vd when Vd is more than a threshold volt-age, Vth. In contrast, Id varies very little when Vd is sweptfrom 0 to �1 V. Vth is different for different combinationsof Vg1 and Vg2. It shifts rightwards to larger values withincreasing Vg1. In addition, Id at negative drain voltages,for example, Vd = �1 V, decreases apparently with increas-ing Vg1. To understand this phenomenon, we analyze thecurve with Vg1=0.5 V and Vg2=�0.5 V in detail. In thiscase, Vth is found to be about 0.65 V. The energy band dia-grams of the CNT for Vd = 1 and �1 V are shown inFig. 4(a) and (b), respectively. The CNT could be dividedinto two parts according to the band structure caused by

Fig. 4. Energy band diagrams of the CNTFET with Vg1= 0.5 V andVg2 = �0.5 V. The electrodes on the left and right of the CNT are ‘Source’and ‘Drain’, respectively. ‘e’ and ‘h’ represent electrons and holes,respectively. (a) and (b) are for Vd = 1 V and �1 V, respectively.

J. Li et al. / Carbon 44 (2006) 3087–3090 3089

the two gates. The part near the source side (‘n-side’) is‘n-doped’ due to the applied positive gate voltages, whilethe part near the drain side (‘p-side’) is ‘p-doped’ by thenegative gate voltage. Thus, a ‘p–n junction’ is formedalong the single CNT in the CNTFET by electrostatic dop-ing. Electrons could tunnel through the Schottky barrier bythe source into the conduction band of the CNT channel.However, they can not be collected by the drain electrodedue to the high energy barrier in the middle of the CNT.Tunneling from the band to band is not considered in ourcalculation because the tunneling length depends on thegap between the two gates. On the drain side, the Fermilevel of the electrode EFD=�eVd at Vd = 1 V is lower thanthe valence band of the CNT on the source side, holesinjected from the drain thus can tunnel through the thinSchottky barrier on the drain side and consequently arriveat the source electrode. However, if Vd < 0.65 V, EFD isaligned to the forbidden band of the CNT on the sourceside, holes tunneling through the SB on the drain side areblocked by the large energy barrier in the middle of theCNT, leading to a zero channel current. From the aboveanalysis, we conclude that Vth depends on the relative posi-tion of the drain Fermi level and the ‘n-side’ valence band ofthe CNT. Since the ‘n-side’ valence band shifts downwords

with increasing Vg1, the drain voltage at which the drainFermi level is lower than the ‘n-side’ valence band is alsoincreased. As a result, Vth shifts positively with increasingthe absolute values of Vg1and Vg2. The slope change ofthe three different curves in Fig. 3 is caused by the differentvariations of the SB thickness after Vd > Vth. WhenVg1 = �Vg2 = 0.4 V, the SB at Vth is much thicker than thatfor Vg1 = �Vg2 = 0.6 V due to the smaller separationbetween ‘n-side’ valence band and ‘p-side’ valence bandfor the former case than that of the latter case. When theSB is thick, a small decrease in its thickness can not inducea significant increase in hole transmission. As a result, thecurrent changes slowly with increasing Vd, as shown inthe red solid line in Fig. 3. In contrast, if the SB is originallythin enough, like the case of Vg1 = �Vg2 = 0.6 V, a smalldecrease of thickness can lead to a large increase in carriertransmission, resulting in a much steeper slope of the bluedash curve, as shown in Fig. 3.

When a negative Vd is applied, the energy band of theCNT bends upwards by the drain side, as shown inFig. 4(b). In this case, electrons instead of holes are injectedfrom the drain electrode. Once the EFD is higher than theconduction band of the CNT on the drain side, electronscan tunnel through the SB into the conduction band ofthe CNT and subsequently into the source electrode asthe conduction band of the ‘n-side’ CNT is lower than thatof ‘p-side’ CNT. However, the SB in this case is thicker thanthat at a positive Vd. As a result, Id at a revise bias (Vd < 0)is much smaller than that at a forward bias (Vd > 0), a rec-tification characteristic, as shown in Fig. 3. Id also dependson the level of the ‘p-side’ conduction band of the CNT. Thehigher the ‘p-side’ conduction band, the wider the SB at thedrain contact is for a given drain voltage. Since the ‘p-side’conduction band becomes higher with decreasing Vg2, Id atreverse bias decreases with decreasing Vg2, consistent withthe calculated result in Fig. 3.

The main effect of charge on CNT, which is neglected inour calculation, could be to alter the potential of the CNTchannel as reported by Heinze et al. [6]. The source anddrain SBs would be insignificantly affected in the energyrange of considerable tunneling current. With presence ofthe charges, the ‘n-side’ and ‘p-side’ CNT bands inFig. 4(a) should shift upwardly and downwardly, respec-tively. As a result, the separation between ‘n-side’ valenceband and the drain Fermi level decreases, leading to thedecrease of Vth in the rectifying behavior.

Our simulated CNTFET p–n junction is different from aconventional ideal p–n junction in following aspects. Firstof all, our simulated I–V curves strongly depend on thecombination of the two gate voltages so that the simulatedp–n junction is much easily controllable. In contrast, theI–V characteristics of the conventional one are not adjust-able. Secondly, the threshold voltage can be changed by thetwo gate voltages for the simulated junction. For the con-ventional junction, it is a constant at a given temperature[12]. When reversely biased, the current increases very littlewith applied voltage for the conventional diode till the

3090 J. Li et al. / Carbon 44 (2006) 3087–3090

junction breaks down. However, it will increase graduallywhen the revise bias is large enough, say �1 V, in thissimulation, as shown in Fig. 3.

4. Conclusion

The characteristics of an ambipolar carbon nanotubefield effect transistor (CNTFET) with two separate gatesare simulated based on the Schottky barrier transistor mech-anism. Polarities of the two gate voltages play a key role indetermining the characteristics of the CNTFET. The typicalambipolar characteristics are obtained when the two gatesare biased with a common gate voltage. However, the CNT-FET functions as a diode when the two gates are biased withdifferent polarities of the gate voltages. The simulated banddiagrams of the carbon nanotube suggest an on-tube ‘p–njunction’ induced by the corresponding electrostatic poten-tials of the two gates. The output characteristics of the tran-sistor exhibit an excellent rectification characteristic. Theturn-on threshold voltage of the forward conductanceincreases with increasing the positive gate voltage.

Acknowledgement

This research was supported by an A-STAR (Singapore)grant (Project No. 042 114 0041).

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