Electrical measurements of individual semiconducting single-walled carbon nanotubes of various diameters

Abstract

Individual semiconducting single-walled carbon nanotubes (SWNTs) of various diameters are studied by electrical measurements. Transport through a semiconducting SWNT involves thermal activation at high temperatures, and tunneling through a reverse biased metal–tube junction at low temperatures. Under high bias voltages, current–voltage (I–V) characteristics of semiconducting SWNTs exhibit pronounced asymmetry with respect to the bias polarity, as a result of local gating. SWNT transistors that mimic conventional p-metal-oxide-semiconductor field-effect transistor with similar I–V characteristics and high transconductance are enabled. © 2000 American Institute of Physics.

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Electrical measurements of individual semiconducting single-walled carbon
nanotubes of various diameters
Chongwu Zhou, Jing Kong, and Hongjie Daia)
Department of Chemistry, Stanford University, Stanford, California 94305
?Received 28 October 1999; accepted for publication 28 January 2000?
Individual semiconducting single-walled carbon nanotubes ?SWNTs? of various diameters are
studied by electrical measurements. Transport through a semiconducting SWNT involves thermal
activation at high temperatures, and tunneling through a reverse biased metal–tube junction at low
temperatures. Under high bias voltages, current–voltage (I–V) characteristics of semiconducting
SWNTs exhibit pronounced asymmetry with respect to the bias polarity, as a result of local gating.
SWNT transistors that mimic conventional p-metal-oxide-semiconductor field-effect transistor with
similar I–V characteristics and high transconductance are enabled. © 2000 American Institute of
Physics. ?S0003-6951?00?04612-X?
Carbon nanotubes are molecular wires exhibiting in-
triguing electrical, mechanical, and chemical properties.1–3
Single-walled nanotubes ?SWNT? are ideal systems for
studying the physics in quasi-one-dimension.1,4–6Previous
approaches to addressable SWNT electrical architectures in-
clude depositing SWNTs from liquid suspensions onto pre-
defined electrodes,7–9or onto a flat substrate followed by
locating nanotubes and patterning electrodes.10,11Results ob-
tained with individual single-walled tubes and ropes include
Coulomb charging7,10,11and Luttinger liquid behavior12in
metallic tubes. Semiconducting SWNTs were found to ex-
hibit field-effect transistor-like characteristics at room
temperature.8,9
A recently developed SWNT synthetic method allowed
the growth of individual tubes at controlled sites on
surfaces,13and led to a new approach to obtain large num-
bers addressable SWNTs for systematic studies of various
classes of nanotubes.14,15The current work focuses on eluci-
dating the electrical properties of individual SWNTs that are
semiconducting in nature. We present temperature dependent
transportcharacteristicsof
SWNTs of various tube diameters. Transport mechanisms
through semiconducting SWNTs at various temperatures are
elucidated. SWNT transistors exhibiting current–voltage
(I–V) characteristics resembling that of silicon based
p-metal-oxide-semiconductor
?MOSFET? are obtained, with transconductance two orders
of magnitude higher than previous nanotube transistors.
Sample preparation for metal/individual SWNT/metal
samples involved patterned chemical vapor deposition
growthandmicrofabrication
contacts.13–15Results presented in this letter were obtained
with SWNTs contacted by 20-nm-thick nickel electrodes
with 60-nm-thick gold on top. The lengths of the SWNTs
between electrodes were ? 3 ?m. Degenerately doped sili-
con wafers with 500-nm-thick thermally grown oxide on the
surface were used as the substrates. The heavily doped sub-
strate is conducting at low temperatures and was used as a
back gate. Figure 1 shows tapping mode atomic force mi-
individualsemiconducting
field-effect transistor
formetal-tube electrical
croscopy ?AFM? images of individual SWNTs in two
samples. The diameters of SWNTs were determined from
AFM topographic height data.
I–V curves obtained at room temperature with sample
No. 1 are shown in Fig. 2?a?. The nanotube has a relatively
large diameter of 2.8?0.1nm and exhibits a highly linear
I–V curve with resistance ?340 k? measured at zero gate
voltage (Vg). Positive gate voltages progressively reduce the
linear conductance of the sample ?Fig. 2?a??. At Vg?3 V, the
conductance is suppressed by four orders of magnitude from
that at Vg?0. These I–V characteristics are signatures of
hole-doped semiconducting SWNTs acting as p-type ‘‘tran-
sistors’’ as reported by previous work.8,9,14,15When the gate
voltage is further increased, the conductance of the sample
remains suppressed until the gate voltage reaches ? 40 V
where appreciable recovery in the conductance is observed
?Fig. 2?a? inset?.
The zero-gate linear resistance versus temperature curve
for the d?2.8nm semiconducting tube is shown in Fig. 2?b?
inset. The resistance increases from 340 k? to 1 M? as
temperature is lowered from 300 to 25 K. Below 25 K, the
temperature dependentresistance
?exp(?Ea/KBT) with Ea?4.6meV ?solid line in Fig. 2?b?
inset?. At 4 K, a gap ?20 mV is observed in the I–V curve
and the sample is insulating in the bias range ?V?
??10mV under zero gate voltage ?Fig. 2?b??. The insulat-
ing region is found to be significantly suppressed by apply-
ing a ?1.5 V gate voltage. Applying a positive gate voltage
?e.g., Vg??1 V in Fig. 2?b?? leads to a larger insulating
region in the I–V curve.
canbe fitted into
a?Electronic mail: hdai@chem.stanford.edu
FIG. 1.
?2.8 nm SWNT. ?b? AFM image of sample No. 2, the SWNT diameter
? 1.3 nm.
?a? AFM image of sample No. 1 consisting of a d
APPLIED PHYSICS LETTERSVOLUME 76, NUMBER 1220 MARCH 2000
15970003-6951/2000/76(12)/1597/3/$17.00
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© 2000 American Institute of Physics

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The results obtained with sample No. 1 are interpreted as
the following. First, the nanotube is suggested to be hole
doped along its entire length. Second, each contact is sug-
gested to consist of a serial resistance and a junction formed
with the p-type nanotube bridge. The junction formation
arises from the separation between the nanotube Fermi level
and the valence band EFV?EF?EVand sets a barrier to
electron transport.
The junction barrier is responsible for the observed ther-
mally activated transport shown in Fig. 2?b?, and is deter-
mined to be Ea?4.6meV for sample No. 1 from the tem-
perature dependent linear resistance data. Positive gate
voltages cause the valence band shifting down away from the
Fermi level, leading to higher barriers and thus less conduct-
ing states as seen in Fig. 2?a?. At 4 K where KBT?Ea
?4.6meV, thermally activated transport through the system
is quenched. The sample is in an insulating state near zero
bias as seen in Fig. 2?b?. For bias voltages ?V???10mV,
the sample is turned into a conducting state. Analyses of the
I–V curve after the turn-on find that current increases by
approximately three orders of magnitude in the bias range of
7–14 mV, and can be fitted into I?exp(?c/V) where c is a
constant. These results suggest that electron transport at 4 K
is via a tunneling mechanism. Under a sufficiently high bias
voltage V, electron tunneling occurs through a reverse biased
junction. Similar transport mechanisms were reported in con-
ventional metal–semiconductor–metal systems by Lepselter
and Sze.16
The observed conductance recovery suggests that high
positive gate voltages convert the sample into an n-type sys-
tem from p type, with further increase in gate voltage en-
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hances the conductance of the n-type system. The band gap
can be estimated to be on the order of Eg?150meV,17com-
pared to the theoretically expected Eg?200meV for the d
?2.8nm semiconducting tube.1
Figure 3 shows the results obtained with sample No. 2
consistingofa semiconducting
?0.1nm and length ? 5?m. Linear resistance of the sample
is ? 3.4 M? at room temperature, and increases upon cool-
ing according to ?exp(?Ea/KBT) with Ea?25meV ?Fig. 3
inset?. At 4 K, an insulating gap is observed within ?? 0.6
V in the I–V curve shown in Fig. 3. Within our model, the
junction barrier height is Ea?EFV?25meV, which is com-
parable to the room temperature thermal energy. Note the
expected energy gap for the d?1.3nm tube Eg?0.6eV.1
Beyond the insulating gap in I–V, the current is found to
increase by three orders of magnitude when the bias is in-
creased from 0.5 to 0.9 V, which points to the tunneling
transport mechanism described earlier. Because of a higher
junction barrier than that in sample No. 1, the small diameter
tube sample requires much higher bias voltage to establish
significant tunneling currents through the reverse biased
junction.
We found that at room temperature and zero gate volt-
age, the resistance of semiconducting SWNTs were typically
in the range of 160–500 k? for tube diameters ?2.0 nm.
The resistance of smaller diameter SWNTs with d?1.5nm
were typically on the order of megaohms or higher. Hole
doping to larger diameter tubes led to smaller EFVand ther-
mal activation barriers, as found by temperature dependent
measurements. The lower resistance for larger diameter
semiconducting SWNTs can be attributed to the lower trans-
port barrier at the metal–tube junctions, and better electrical
coupling may have been made with larger diameter tubes and
contributed to their low resistance. For small diameter tubes,
we observed no conductance recovery under gate voltages up
to ?100 V. This can be attributed to the large energy gaps
?? 0.6 eV? relative to the gate efficiency and large band
bending effects at the junctions.
All of our semiconducting nanotube samples exhibit an
interesting feature in the I–V curves under high bias volt-
ages. The I–V curves show remarkable asymmetry with re-
spect to the polarity of the bias voltage when ?V???1 V.
I–V curves obtained at room temperature with sample No. 1
over a bias range of 3 to ?3 V are shown in Fig. 4. In the
SWNT with
d?1.3
FIG. 2. ?a? Room temperature I–V curves of sample No. 1. Inset: current vs
gate voltage recorded at 300 K under a 10 mV bias voltage. ?b? I–V curves
under Vg??1.5, 0, and ?1 V at 4 K. Inset: R vs T. Solid line shows the
exp(?Ea/KBT) fit.
FIG. 3. I–V curve recorded at 4 K with sample No. 2 (Vg?0). Inset: R ?in
log scale? vs 1/T.
1598Appl. Phys. Lett., Vol. 76, No. 12, 20 March 2000 Zhou, Kong, and Dai

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negative bias side, the current initially scales linearly as ?V?
but reaches saturation and stays constant under large nega-
tive biases. In the positive bias side, the current increases
continuously as the bias voltage increases. The asymmetry in
I–V is found to be independent of which metal electrode is
ground ?source? or biased ?drain?. Data recorded after ex-
changing the source and drain electrodes show nearly un-
changed asymmetry in I–V ?Fig. 4 left inset?. Symmetrical
I–V curves can be obtained ?Fig. 4 right inset? under sym-
metrical bias by scanning V in the range of ?3 to 3 V while
biasing the two electrodes at ?V/2 and ?V/2 respectively.
These results suggest that the observed asymmetrical I–V
curves are not caused by asymmetrical parameters such as
different contact resistances at the two metal–tube interfaces,
but are inherent to the metal/tube/metal system.
The I–V asymmetry in bias polarity was consistently
observed in all of the six independent semiconducting
SWNT samples studied. We suggest that the origin of this
asymmetry is local gating of the biased drain electrode. Un-
der a given positive gate voltage ?e.g., Vg?2 V?, the nano-
tube can be considered to have a constant hole density along
its length. In a negative bias configuration ?0,?V?? ?e.g., ?V?
?3 V?, the quasi-Fermi level18shown as dotted line in Fig.
4?c? of the nanotube is further away from the valence band
near the drain where the local gating voltage is more positive
relative to the drain. This results in a reduced hole density in
the tube section near the drain and thus reduced conductance.
Saturation occurs for large ?V? because of the competing
roles of driving and gating of the drain bias voltage. This
phenomenon can be related to local carrier depletion and
channel pinch-off by negative drain bias in a conventional
p-type MOSFET.18In a positive bias configuration ?0,?V??,
local hole enrichment is induced in the nanotube section near
the drain where the quasi-Fermi level is closer to the valence
band as shown in Fig. 4?b?, which results in a more conduct-
ing system.
The results presented in this letter are significant in
terms of enabling high performance nanotube transistors.
First, the I–V curves of our samples resemble those of con-
ventional p-MOSFET.18Second high voltage gain and trans-
conductance are obtained with our devices. Sample No. 1
shownin Fig.2 exhibits
?Vds/?Vg?I?3 ?A?3 compared to the maximum gain of
? 0.35 obtained previously.8
?Ids/?Vg?V?100 mV?200nA/V is obtained with this sample,
which is two orders of magnitude higher than previous re-
sults with SWNTs.9Transconductance normalized by the
tube width is ? 0.1 mS/?m, which is comparable to silicon
based p-MOSFETs. Three independent SWNTs with diam-
eters in the range of 2.5–3 nm are found to exhibit high
transconductance between 100 and 200 nA/V. The high
transconductance is a direct result of the low linear resistance
of these samples ?hundreds of k??. Samples consisting of
small diameter tubes (d?1.5nm? exhibit lower transconduc-
tance in the range of 1–10 nA/V because of their high resis-
tance ?? several M??.
In summary, we presented detailed results of electron
transportmeasurements of
SWNTs. Transport in semiconducting SWNT samples in-
volves thermal activation at high temperatures and tunneling
through a reverse biased metal–tube junction at low tem-
peratures. Electrical properties of SWNTs with various di-
ameters are elucidated. Local gating effects lead to a bias
polarity associated transport phenomenon and high transcon-
ductance SWNT transistors.
positivevoltage gainof
A transconductance of
individualsemiconducting
H. D. acknowledges support by NSF, LAM at Stanford,
DAPRA/ONR, SRC, ACS, and the Camile Henry-Dreyfus
Foundation.
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FIG. 4. ?a? I–V curves recorded at 300 K with sample No. 1 for V?3 to ?3
V. Left inset: I–V curves recorded after exchanging the source-drain elec-
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1599Appl. Phys. Lett., Vol. 76, No. 12, 20 March 2000Zhou, Kong, and Dai
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