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aANIC Lab, King Abdullah University of Sc
23955-6900, Kingdom of Saudi Arabia. E-mbPhysical Science and Engineering Division,
Technology (KAUST), Thuwal 23955-6900, KcSchool of Electrical and Electronic Engineeri
Nanyang Avenue, Singapore 639798dSchool of Chemical and Biomedical Engine
62 Nanyang Drive, Singapore 637459
Cite this: Nanoscale, 2013, 5, 2476
Received 20th October 2012Accepted 21st January 2013
DOI: 10.1039/c3nr33263b
www.rsc.org/nanoscale
2476 | Nanoscale, 2013, 5, 2476–248
Influence of contact height on the performance ofvertically aligned carbon nanotube field-effecttransistors
Jingqi Li,a Yingchun Cheng,b Zaibing Guo,a Zhihong Wang,a Zhiyong Zhu,b
Qing Zhang,c Mary B. Chan-Park,d Udo Schwingenschloglb and X. X. Zhang*a
Vertically aligned carbon nanotube field-effect transistors (CNTFETs) have been experimentally
demonstrated (J. Li et al., Carbon, 2012, 50, 4628–4632). The source and drain contact heights in vertical
CNTFETs could be much higher than in flat CNTFETs if the fabrication process is not optimized. To
understand the impact of contact height on transistor performance, we use a semi-classical method to
calculate the characteristics of CNTFETs with different contact heights. The results show that the drain
current decreases with increasing contact height and saturates at a value governed by the thickness of
the oxide. The current reduction caused by the increased contact height becomes more significant when
the gate oxide is thicker. The higher the drain voltage, the larger the current reduction. It becomes even
worse when the band gap of the carbon nanotube is larger. The current can differ by a factor of more
than five between the CNTEFTs with low and high contact heights when the oxide thickness is 50 nm.
In addition, the influence of the contact height is limited by the channel length. The contact height
plays a minor role when the channel length is less than 100 nm.
1 Introduction
Carbon nanotube eld-effect transistors (CNTFETs) have beenextensively studied in the last decade. Most of these studiesfocused on planar CNTFETs.2–7 Vertical transistors require lessspace than planar ones, resulting in a large integration inten-sity. It is very important for some special applications in whichthe transistor area is critical for performance. Vertical organictransistors8,9 have been successfully used in display technology.With the goal of achieving high integration density, includingsimple short channel fabrication, we recently experimentallydemonstrated a vertical CNTFET.1 In this new structure, theplanar arrangement of the source, gate and drain is turned 90�,so that they are positioned on top of each other and the carbonnanotube (CNT) channel is perpendicular to the surface. Thisconguration could give rise to some different characteristicscompared with planar CNTFETs. For example, the source anddrain contact lengths in vertical CNTFETs can be easilycontrolled by the metal deposition time without using litho-graphic or etching techniques. A contact length of less than
ience and Technology (KAUST), Thuwal
ail: [email protected]
King Abdullah University of Science and
ingdom of Saudi Arabia
ng, Nanyang Technological University, 50
ering, Nanyang Technological University,
1
10 nm can be fabricated without difficulty. As a result, the gate-to-source and gate-to-drain overlap capacitance could be verysmall. A decrease in the parasitic capacitance could signicantlyincrease the cutoff frequency in radio frequency applications.10
However, a simplied fabrication of the short contact length isobtained at the cost of increasing the source and drain contactheight. The contact height could be very high if an advancedtechnique, such as electron beam lithography, is not used in thefabrication process. An increased contact height could inu-ence the electric eld distribution at the contact, which in turncould change the Schottky barrier (SB) between the CNT and thesource and drain. As we know, SB plays a key role in SB tran-sistors. By using an appropriate source SB, a source-gated pol-ysilicon thin lm transistor11,12 can operate at lower voltageswith larger gain and lower power dissipation. CNTFETs work asSB transistors. The current is controlled by thermally assistedtunneling through the SBs at the contacts. The SB shape (heightand thickness) plays a key role in the performance of theCNTFETs. The SB height for electron/hole depends on the line-up of the contact metal Fermi level and the conduction/valenceband of carbon nanotubes, and the gate voltage. The SB thick-ness is controlled by the gate voltage through the electric eld atthe contacts. The current is blocked by the thick SB if anappropriate gate voltage is not applied. Increasing/decreasingthe gate voltage leads to a large electric eld at the contact,reducing the thickness of the SB and allowing thermal assistedtunneling of electrons/holes. A sharper contact leads to eldfocusing, and hence a large eld at the contact.13 Since the
This journal is ª The Royal Society of Chemistry 2013
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geometry of the contact can inuence the electric eld at thecontact, an increased contact height could signicantly affectthe SB thickness and the direct current (DC) performance ofvertical CNTFETs. To understand the effect of the contact heighton CNTFETs, we use a semi-classical method to calculate thecharacteristics of vertical CNTFETs with different contactheights and channel lengths.
2 Methodology
The structure of the vertical CNTFET under consideration isshown in Fig. 1. From le to right, the structural elementsinclude a side gate, a SiO2 gate dielectric layer, and a verticalstack of a drain contact, an isolation dielectric layer and asource contact. A semiconducting carbon nanotube (CNT) isvertically connected to the source and drain contacts, which areisolated by the SiO2 layer. A grounded right gate electrode (notshown here) is used for the calculations. It is 190 nm away fromthe SiO2 gate dielectric layer.
We used a semi-classical method14–17 to simulate the char-acteristics of the CNTFETs. The current is calculated using theLandauer–Buttiker formula with the assumption that thetransport in the CNT is ballistic. This formula is expressed asfollows:
I ¼ 4e
h
ð�FðEÞ � FðE þ eVdÞ
�TðEÞdE; (1)
where Vd is the drain voltage, F(E) is the Fermi function and T(E)is the energy-dependent transmission through the SB betweenthe CNTs and electrodes. T(E) can be estimated using theWentzel–Kramers–Brillouin (WKB) approximation
TðEÞ ¼ exp
264� 2
ðz2z1
kðzÞdz
375; (2)
with the wave number
kðzÞ ¼ 2
3aV0
(�Eg
2
�2
��E þ eVðzÞ�2
)1 =
2
; (3)
where a ¼ 0.144 nm, Eg ¼ 0.6 eV, and V0 ¼ 2.5 eV are the C–Cbond length, the CNT band gap and the tight-binding param-eter, respectively. V(z) is the electrostatic potential along the
Fig. 1 Schematic structure of a vertical CNTFET. A single-walled carbon nano-tube is vertically connected to the source and drain contacts.
This journal is ª The Royal Society of Chemistry 2013
CNT and is obtained by numerically solving the Laplace equa-tion for the device geometries shown in Fig. 1. The integration isperformed between the two classical turning points, z1 and z2.14
The temperature considered here is 300 K. The Fermi level, EF,of the source and drain contacts is assumed to be at the middleof the CNT band gap. Charges on the carbon nanotube, whichhave a main effect on altering the potential within the CNTchannel, are neglected in our calculation. It is a good approxi-mation14 for Schottky barrier (SB) CNTFETs in which the sourceand drain SBs would be insignicantly affected in the energyrange of considerable tunneling current.
3 Results and discussion
The transfer characteristics of the vertical CNTFETs withdifferent source and drain contact heights, h, are shown inFig. 2. The channel length and oxide thickness are 200 nm and50 nm, respectively. It can be seen that all three transistorsexhibit apparent ambipolar characteristics. The drain current,Id, decreases with increasing gate voltage at rst, and thenincreases again aer reaching a minimum current. Thisbehavior is consistent with our experimental results1 for theCNTFETs with the Fermi level of the source and drain contactsaligning to the middle of the CNT band gap. The n-branchcurrent at positive gate voltage, Vg, and the p-branch current atnegative Vg are caused by electron injection from the source tothe drain and hole injection from the drain to the source,respectively. The minimum current occurs when Vg is one-halfthe drain voltage (Vd) because the electron current risesmonotonically with Vg exactly as the hole current increasesmonotonically with Vd� Vg.18 The increased contact height doesnot change the ambipolar characteristics. However, the Id � Vgcurve gradually shis lower as h increases from 5 nm to 190 nm,i.e., the device current corresponding to the same Vg decreasesgradually as the contact height increases. The subthreshold
Fig. 2 Calculated transfer characteristics of the CNTFETs with different contactheights at Vd ¼ 0.5 V. The black, red and blue curves are for contact heights h ¼5 nm, 20 nm and 190 nm, respectively.
Nanoscale, 2013, 5, 2476–2481 | 2477
Fig. 4 Electrostatic potential contour lines for the CNTFETs at Vd ¼ 0.5 V andVg ¼ �1 V for (a) h ¼ 5 nm and (b) h ¼ 190 nm, respectively. Adjacent contourlines differ by 0.2 V. The yellow squares represent source and drain contacts. Thegate oxide thickness is 5 nm.
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slope, S ¼ dVg/d(log Id), increases from 410 mV dec�1 for h ¼5 nm to 470 mV dec�1 for h¼ 190 nm in the p-branch. The largeS obtained here is due to the thick oxide (tox ¼ 50 nm) used inthe calculation. It is 140 mV dec�1 for the CNTFETs with tox ¼5 nm and there is almost no difference between the lowercontact and higher contact heights.
To understand the effect of contact height, we calculate thecurrent for the CNTFETs with different contact heights. Thechannel length and electrode length are 200 nm and 100 nm,respectively. The drain currents as a function of the electrodeheight for tox ¼ 5 nm and tox ¼ 100 nm are shown in Fig. 3. Fortox ¼ 5 nm, we can see that the current decreases rapidly from1.68 � 10�5 to 1.52 � 10�5 when h changes from 5 nm to 40 nmand it saturates at h ¼ 50 nm. When the oxide thickness isincreased from 5 nm to 100 nm, the saturation occurs at h¼ 100nm, suggesting that the saturation height increases with theoxide thickness. The variation of drain current with the contactheight can be analyzed through the electric eld in the vicinityof the drain contact. The electric eld determines the shape ofthe SB between the CNT and the contacts, and the SB plays a keyrole in the transistor performance. Fig. 4(a) and (b) show thedistribution of the electrostatic potential for the CNTFETs withh ¼ 5 nm and h ¼ 190 nm, respectively. We can see that theposition of the equal-potential lines apparently changes.Compared with the lines from �0.2 V to �1 V for h ¼ 190 nm inFig. 4(b), the lines for h ¼ 5 nm in Fig. 4(a) shi signicantly tothe right grounded gate electrode, leading to more dense equal-potential lines near the bottom le corner of the drain contact,indicating that the potential gradient in that part of the devicewith h¼ 5 nm is larger than that with h¼ 190 nm. The potentialgradients on the CNT at 1 nm away from the drain contact are76 mV nm�1 and 62 mV nm�1 for h ¼ 5 nm and h ¼ 190 nm,respectively. The larger potential gradient results in a thinnerSB at the drain contact. The thinner the SB is, the larger thetransmission probability for the electrons or holes is. As aresult, the drain current for h ¼ 5 nm is larger than that forh ¼ 190 nm.
Fig. 3 Drain currents as a function of contact height at Vd¼ 0.5 V and Vg¼�1 V.The black and red curves are for tox ¼ 5 nm and tox ¼ 100 nm, respectively. Theycorrespond to the left and right Y-axis, respectively.
2478 | Nanoscale, 2013, 5, 2476–2481
We dene R as the ratio of the drain current for h ¼ 5 nm tothat for h ¼ 190 nm. It is found that R falls in the range of 1.1 to1.6 when tox ¼ 5 nm. We note that R is different at different Vgalthough the oxide thickness is the same. The distribution of Ras a function of Vg is shown in Fig. 5. The maximum ratio, Rmax,is at Vg ¼ 0.1 V. R decreases as |Vg| increases. To understand theresults, the energy band diagrams (inset of Fig. 5) are used. TheCNT energy band shis its center part upward at Vg < 0 V relativeto that at Vg ¼ 0 V, and it bends downward at the drain contactwhen a positive Vd is applied. If Vg is small enough, the drain SBbecomes very thin and the transmission probability of the holeis very large. The drain SB is almost transparent at Vg¼�1 V. Asa result, a slight change in the SB thickness caused by the highercontact results in a negligible current decrease. That is why theratio is very small at around Vg ¼ �1 V. Similarly, positive Vgleads to a downward shi of the center of the CNT band gap.The current comes mainly from the electron injection fromthe source contact. The larger the gate voltage, the thinner thesource SB and the smaller the current variation caused by the
This journal is ª The Royal Society of Chemistry 2013
Fig. 5 Distribution of the current ratio of the CNTFETs with h¼ 5 nm to that withh ¼ 190 nm as a function of gate voltage at Vd ¼ 0.5 V. The left and right insetsshow band diagrams at Vg < 0 and Vg > 0 V, respectively. EFS and EFD represent theFermi level of the source and drain contacts, respectively.
Fig. 6 The maximum current ratio of the CNTFETs with h ¼ 5 nm to that withh ¼ 190 nm as a function of tox
1/6. The blue, red and green lines are for Vd ¼0.75 V, 0.5 V and 0.25 V, respectively. The insets are schematic triangular SBs atdifferent oxide thicknesses and gate voltages.
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change of the contact height. As |Vg| decreases, the SB becomesthicker (but much thinner than the limit for a negligibletransmission because tox ¼ 5 nm) and a smaller SB thicknesschange may cause a relatively larger current change. This is whyR increases as |Vg| decreases, as shown in Fig. 5. The drop atVg ¼ 0.3 V is due to the thick SB, which results in almost thelowest current at Vd ¼ 0.5 V. The interesting thing is that Rmax
increases gradually as the oxide thickness increases and Rmax
corresponds to a different Vg at different oxide thicknesses, aslisted in Table 1.
We rst consider why Rmax increases with oxide thickness.The scaling rules of oxide thickness for different device struc-tures are different.14 With a negligible contact thickness, thepotential in the vicinity of the contact is inversely proportionalto tox
1/2 and the current is expected to scale in the same way. Incontrast, if the contact is quite thick, the electrostatic potentialdepends on tox
�2/3, and the drain current also depends ontox
�2/3. We therefore suggest that R is proportional totox
2/3/tox1/2 ¼ tox
1/6. Fig. 6 shows the change of Rmax as a functionof tox
1/6 for Vd ¼ 0.75 V, 0.5 V and 0.25 V. The linear increase ofRmax with the increase of tox
1/6 for all the three cases are inagreement with our suggestion.
The dependence of Rmax on Vg can be explained from thechange of the SB with oxide thickness. For simplicity, we use atriangle SB model to represent the SB obtained from
Table 1 The current ratios of the CNTFETs with h ¼ 5 nm to that with h ¼190 nm at different oxide thicknesses and their corresponding Vg and Vd � Vg
tox
Vd ¼ 0.75 V Vd ¼ 0.5 V Vd ¼ 0.25 V
R Vg Vd � Vg R Vg Vd � Vg R Vg Vd � Vg
5 1.62 0.3 0.45 1.58 0.1 0.4 1.45 �0.2 0.4510 2.22 0.2 0.55 2.04 0 0.5 1.8 �0.3 0.5520 3.23 0.1 0.65 2.73 �0.2 0.7 2.31 �0.5 0.7535 4.23 �0.1 0.85 3.44 �0.4 0.9 2.81 �0.8 1.0550 4.94 �0.3 1.05 3.93 �0.7 1.2 3.15 �1 1.2575 5.69 �0.6 1.35 4.45 �1 1.5 3.49 �1.4 1.65
This journal is ª The Royal Society of Chemistry 2013
calculations. In the inset of Fig. 6, the SB for h ¼ 5 nm at Vd ¼0.5 V and Vg ¼ 0.1 V (the Rmax conditions at tox ¼ 5 nm) isrepresented by a blue triangle. Its height is equal to Vd � Vg andits width is proportional to the oxide thickness. At the samedrain voltage and gate voltage, the SB for h ¼ 190 nm (notshown) has the same height as for h¼ 5 nm, but is thicker. Thisthickness difference results in the large current ratio underthese conditions. As tox increases, the two SBs expand hori-zontally and the blue SB turns into the large green triangle. TheSB difference between h ¼ 5 nm and h ¼ 190 nm is larger thanthat for tox ¼ 5 nm. However, the probability of hole trans-mission is signicantly reduced due to the increased barrierthickness. As a result, the change in SB thickness caused by theincreased contact height would not result in the largest currentratio as at tox ¼ 5 nm. Since the drain voltage does not changewhen the oxide is thick and the current depends, to a largeextent, on the hole transmission of the SB between EF + Eg/2(EF ¼ �Vd is the Fermi level of the drain contact) and EF � Eg/2(the position of the valence band at the drain), the SB shape inthis range is critical to achieving a large current ratio. BeyondEF + Eg/2, the transmission decreases signicantly due to thethick barrier at energies far away from the Fermi energy. It isreasonable to suggest that the SB that satises the maximumcurrent ratio at a thick tox has a sharp part similar to the blue SBfor tox ¼ 5 nm. This kind of SB can be achieved by reducing thegate voltage. In this way, the height of the SB increases and thegradient of the SB decreases at the same time. The green SBtends to be the red one at an appropriate Vg. Under thiscondition, the SBs for the thick tox are similar to that for tox ¼5 nm. As a result, the SB differences between h ¼ 5 nm and h ¼190 nm give rise to the largest R at a thick tox. This is why Rmax isat different Vg for different tox and Vg shis to smaller values astox increases, as can be seen in Table 1. To reach this condition,a lower Vd requires a smaller Vg because the SB height is equal toVd� Vg, being in agreement with the calculation data in Table 1.The increasing trend of Rmax with tox
1/6 accounts for the largesubthreshold difference between the high contact and lowcontact height with the thick tox and the small subthreshold
Nanoscale, 2013, 5, 2476–2481 | 2479
Fig. 8 The current ratio of the CNTFETs with h¼ 5 nm to that with h¼ 190 nm asa function of the channel length. The green, red and blue curves are for Vg ¼�0.1V, �0.5 V and �1 V, respectively. The source and drain contact length, oxidethickness and drain voltage are 100 nm, 10 nm and 0.5 V, respectively.
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difference with the thin tox. In addition, the increase of Rmax
with tox1/6 means that the current reduction due to high contact
height is serious when the oxide is thick, being consistent withthe low current obtained in the experiment.1
At a given oxide thickness, the difference between Vd and Vgthat meet the conditions of the Rmax increases with decreasingVd, indicating that the electric eld in the vicinity of the bottomle drain contact increases by following the same trend. Thestronger electric eld weakens the inuence of the contactheight effect, resulting in a smaller SB thickness change. Theenergy band diagrams of the CNTFETs for Vd¼ 0.75 V, 0.5 V and0.25 V at tox ¼ 50 nm are shown in Fig. 7. The order of the SBthickness changes from large to small are at Vd ¼ 0.75 V, 0.5 Vand 0.25 V, which agrees with our expectations. The larger SBthickness change at Vd ¼ 0.75 V leads to a larger current ratiothan at Vd ¼ 0.5 V. Similarly, the ratio at Vd¼ 0.5 V is larger thanthat at Vd ¼ 0.25 V. These differences lead to the differentgradients of the current increasing with tox
1/6, as can be seenin Fig. 5.
We now turn to the impact of the channel length, Lch, on thetransistor performance. ACNTFETwith tox¼ 10nm,VD¼ 1V anda contact length of 100 nm is considered here. The change ofR asa function of channel length is shown in Fig. 8. The green, redandblue curves are forVg¼�0.1V,�0.5 V and�1V, respectively.We nd that R increases as the channel length increases from20 nm to 100 nm in all the three cases. The ratios saturate at100 nm. For a very short channel, say 20 nm, the contact heighthas almost no effect on the current and the ratio R is close to 1.This result canbeunderstood from the electricelddistribution.If the channel length is shorter than the contact length, the gate-generated electric eld in the region above the two contacts isdrastically screened by the two contacts. As a result, the contactheight has a small effect on the current. As the channel lengthincreases, the contact screening effect gradually diminishes andthe contact height could inuence the current. The band
Fig. 7 Band diagrams of the CNTEFTs with tox¼ 50 nm at the drain side. The top,middle and bottom two bands are for Vd ¼ 0.25 V, 0.5 V and 0.75 V, respectively.In each of the couples, the lower band is for h¼ 5 nm and the upper one is for h¼190 nm. The SB thickness differences at their corresponding drain Fermi levels forthe three couples are indicated by three double arrows.
2480 | Nanoscale, 2013, 5, 2476–2481
diagrams for different channel lengths and contact heights atVd¼ 1 V and Vg¼�0.5 V are shown in Fig. 9. The inner and outertwo bands are for Lch ¼ 20 nm and Lch ¼ 200 nm, respectively. Itcanbe seen clearly that the inner two bands aremuch closer thanthe outer two bands, leading to a smaller current ratio for Lch ¼20 nm than that for Lch ¼ 200 nm. The reason for different Rs atdifferent Vg is the same as that explained for the distribution of Rvs. Vg at tox ¼ 5 nm.
Although the selective growth of enriched semiconductingSWNTs (up to 97%) has been successfully reported,19–21 SWNTgrowth with identical chirality is still not possible. There isalways a diameter (band energy) distribution in the SWNTproduct. Fig. 10 explores the role of a carbon nanotube bandgap. The green, red and blue curves are for Eg¼ 0.8 eV, 0.6 eV and0.4 eV, respectively. The height of SB between the carbon nano-tube and the source/drain contact is directly proportional to theband gap of the carbonnanotube. The current for aCNTFETwitha smallEg (small SB) is larger than thatwith a largeEg (large SB) atthe same Vd and Vg. For a small Eg, the change of SB thickness
Fig. 9 Band diagrams of the CNTFETs with different channel lengths at Vd ¼ 1 Vand Vg ¼ �0.5 V. The inner two (black and red) bands and the outer two (greenand blue) bands correspond to Lch ¼ 20 nm and Lch ¼ 200 nm, respectively.
This journal is ª The Royal Society of Chemistry 2013
Fig. 10 The maximum current ratio of the CNTFETs with h ¼ 5 nm to that withh ¼ 190 nm as a function of tox
1/6at Vd ¼ 0.5 V. The green, red and blue lines arefor Eg ¼ 0.8 eV, 0.6 eV and 0.4 eV, respectively.
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caused by the contact height gives rise to a relatively smallcurrent change. In contrast, a large Eg leads to a large currentvariation with a contact height change, as can be seen in Fig. 10.All the three curves show a linear relationship between Rmax andtox
1/6, but the gradients are different. The larger the Eg, the largerthe gradient. This result indicates that the high contact heightfor a CNTFET with a larger Eg will cause more serious currentdegradation than that with a small Eg at the thick oxide.
4 Conclusion
The inuence of the source and drain contact height on theperformance of vertical CNTFETs has been studied using asemi-classical method. The drain current decreases withincreasing contact height and it saturates at a certain heightbeyond which the contact height has no further effect on thecurrent change. This saturation height depends on the oxidethickness. The thicker the oxide, the larger the saturationheight. The current ratio of a CNTFET with a low contact height(5 nm) to that with a high contact height (190 nm) changes withthe gate voltage at the same oxide thickness and drain voltage.The maximum current ratio increases linearly with tox
1/6
because of the different scaling rules for low and high contactheights. The increasing gradient for a high drain voltage islarger than that for a low drain voltage. In addition, thisincreasing gradient is larger for a large band gap of the carbonnanotube than that for a small band gap. The channel lengthcan also affect the current ratio. The shorter the channel, thesmaller the current ratio. The current ratio saturates at amaximum value when the channel length is 100 nm.
This journal is ª The Royal Society of Chemistry 2013
Notes and references
1 J. Li, C. Zhao, Q. Wang, Q. Zhang, Z. Wang, X. X. Zhang,A. I. Abutaha and H. N. Alshareef, Carbon, 2012, 50, 4628–4632.
2 S. J. Tans, A. R. M. Verschueren and C. Dekker, Nature, 1998,393, 49–52.
3 R. Martel, T. Schmidt, H. R. Shea, T. Hertel and Ph. Avouris,Appl. Phys. Lett., 1998, 73, 2447–2449.
4 Ph. Avouris, Phys. Today, 2009, 62, 34–40.5 Q. Cao and J. A. Rogers, Nano Res., 2008, 1, 259–272.6 J. Li, Q. Zhang, D. Yang and J. Tian, Carbon, 2004, 42, 2263–2267.
7 M. A. Wahab and K. Alam, Nano-Micro Lett., 2010, 2, 126–133.
8 M. A. McCarthy, B. Liu, E. P. Donoghue, I. Kravchenko,D. Y. Kim, F. So and A. G. Rinzler, Science, 2011, 332, 570–573.
9 M. A. McCarthy, B. Liu and A. G. Rinzler, Nano Lett., 2010, 10,3467–3472.
10 J. Guo, S. Hasan, A. Javey, G. Bosman and M. Lundstrom,IEEE Trans. Nanotechnol., 2005, 4, 715–721.
11 R. A. Sporea, M. J. Trainor, N. D. Yong, J. M. Shannon andS. R. P. Silva, IEEE Trans. Electron Devices, 2010, 57, 2434–2439.
12 J. M. Shannon and E. G. Gerstner, IEEE Electron Device Lett.,2003, 24, 405–407.
13 S. Heinze, J. Tersoff, R. Martel, V. Derycke, J. Appenzeller andPh. Avouris, Phys. Rev. Lett., 2002, 89, 106801.
14 S. Heinze, M. Radosavljevic, J. Tersoff and Ph. Avouris, Phys.Rev. B: Condens. Matter Mater. Phys., 2003, 68, 235418.
15 S. Heinze, J. Tersoff and Ph. Avouris, Appl. Phys. Lett., 2003,83, 5038–5040.
16 W. Zhang, C. Chen and Y. Zhang, Microelectron. J., 2009, 40,1681–1685.
17 J. Li, Q. Zhang and M. Chan-Park, Carbon, 2006, 44, 3087–3090.
18 M. Radosavljevic, S. Heinze, J. Tersoff and Ph. Avouris, Appl.Phys. Lett., 2003, 83, 2435–2437.
19 W. Zhou, S. Zhan, L. Ding and J. Liu, J. Am. Chem. Soc., 2012,134, 14019–14026.
20 L. Ding, A. Tselev, J. Y. Wang, D. N. Yuan, H. B. Chu,T. P. McNicholas, Y. Li and J. Liu, Nano Lett., 2009, 9, 800–805.
21 Y. Che, C. Wang, J. Liu, B. Liu, X. Lin, J. Parker, C. Beasley,H.-S. P. Wong and C. Zhou, ACS Nano, 2012, 6, 7454–7462.
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