Single- and multi-wall carbon nanotube field-effect transistors
R. Martel, T. Schmidt, H. R. Shea, T. Hertel, and Ph. Avouris
a)
IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598
~Received 1 July 1998; accepted for publication 24 August 1998!
We fabricated field-effect transistors based on individual single- and multi-wall carbon nanotubes
and analyzed their performance. Transport through the nanotubes is dominated by holes and, at
room temperature, it appears to be diffusive rather than ballistic. By varying the gate voltage, we
successfully modulated the conductance of a single-wall device by more than 5 orders of magnitude.
Multi-wall nanotubes show typically no gate effect, but structural deformations—in our case a
collapsed tube—can make them operate as field-effect transistors. © 1998 American Institute of
Physics. @S0003-6951~98!00143-0#
Carbon nanotubes ~NTs! are a new form of carbon with
unique electrical and mechanical properties.
1
They can be
considered as the result of folding graphite layers into carbon
cylinders and may be composed of a single shell–single wall
nanotubes ~SWNTs!, or of several shells—multi-wall nano-
tubes ~MWNTs!. Depending on the folding angle and the
diameter, nanotubes can be metallic or semiconducting.
Simple theory also shows that the band gap of semiconduct-
ing NTs decreases with increasing diameter. These predic-
tions have been verified in recent scanning tunneling spec-
troscopy experiments.
2,3
Their interesting electronic structure makes carbon nano-
tubes ideal candidates for novel molecular devices. Metallic
NTs, for example, were utilized as Coulomb islands in
single-electron transistors
4,5
and, very recently, Tans and co-
workers built a molecular field-effect transistor ~FET! with a
semiconducting nanotube.
6
In this letter, we report on the fabrication and perfor-
mance of a SWNT-based FET and explore whether MWNTs
can be utilized as the active element of carbon-based FETs.
Despite their large diameter, we find that structurally de-
formed MWNTs may well be employed in NT-FETs. Based
on the output and transfer characteristics of our NT devices,
we evaluate their carrier density and discuss the transport
mechanism.
The SWNTs used in our study were produced by laser
ablation of graphite doped with cobalt and nickel catalysts.
7
For cleaning, the SWNTs were ultrasonically treated in an
H
2
SO
4
/H
2
O
2
solution. MWNTs were produced by an arc-
discharge evaporation technique
8
and used without further
treatment. The NTs were dispersed by sonication in dichlo-
roethane and then spread on a substrate with predefined elec-
trodes. A schematic cross section of a NT device is shown in
Fig. 1. They consist of either an individual SWNT or
MWNT bridging two electrodes deposited on a 140 nm thick
gate oxide film on a doped Si wafer, which is used as a back
gate. The 30 nm thick Au electrodes were defined using elec-
tron beam lithography. For imaging, we used an atomic force
microscope operating in the noncontact mode. The source–
drain current I through the NTs was measured at room tem-
perature as a function of the bias voltage V
SD
and the gate
voltage V
G
.
Figure 2~a! shows the output characteristics I –V
SD
of a
device consisting of a single SWNT with a diameter of 1.6
nm for several values of the gate voltage. At V
G
5 0 V, the
I–V
SD
curve is linear with a resistance of R5 2.9 MV. For
V
G
, 0 V, the I –V
SD
curves remain linear, whereas they be-
come increasingly nonlinear for V
G
@ 0 V up to a point
where the current becomes unmeasurably small, indicating a
controllable transition between a quasimetallic and an insu-
lating state of the NT. Figure 2~b! shows transfer character-
istics I–V
G
of our NT device for different source–drain volt-
ages. The behavior is similar to that of a p-channel metal–
oxide–semiconductor FET.
9
The source–drain current
decreases strongly with increasing gate voltage, which not
only demonstrates that the NT device operates as a field-
effect transistor but also that transport through the semicon-
ducting SWNT is dominated by positive carriers ~holes!. The
conductance modulation of our SWNT-FET exceeds 5 orders
of magnitude @see inset of Fig. 2~b!#. For V
G
, 0 V, the
I– V
G
curves saturate indicating that the contact resistance
R
C
at the metal electrodes starts to dominate the total resis-
tance R5 R
NT
1 2R
C
of the device. Here, R
NT
denotes the
gate-dependent resistance of the NT. The saturation value of
the current corresponds to R
C
'1.1 MV. Similar contact re-
sistances were previously found for metallic SWNTs.
4
The origin of the holes is an important question to ad-
dress. One possibility is that the carrier concentration is in-
herent to the NT. Another possibility is that the majority of
carriers are injected at the gold–nanotube contacts. The
higher work function of gold leads to the generation of holes
in the NT by electron transfer from the NT to the gold
a!
Electronic mail: avouris@us.ibm.com
FIG. 1. Schematic cross section of the FET devices. A single NT of either
MW or SW type bridges the gap between two gold electrodes. The silicon
substrate is used as back gate.
APPLIED PHYSICS LETTERS VOLUME 73, NUMBER 17 26 OCTOBER 1998
24470003-6951/98/73(17)/2447/3/$15.00 © 1998 American Institute of Physics
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electrodes.
2
Assuming that the band-bending length in their
SWNT is neither very short nor very long, Tans et al. have
argued that the FET operation can be explained based on this
charge transfer.
6
At V
G
5 0 V, the device is ‘‘on’’ and the
Fermi energy is close to the valence-band edge throughout
the NT. If indeed the band-bending length is comparable to
the length of the SWNT, a positive gate voltage would gen-
erate an energy barrier of an appreciable fraction of eV
G
in
the center of the tube ~since the gate/NT distance is shorter
than the source/drain separation!. The threshold voltage V
G,T
required to suppress hole conduction by depleting the tube
center would be determined by the thermal energy available
for overcoming this barrier. Thus, V
G,T
should be much
lower than the 6 V observed in Fig. 2~b!. Therefore, it is
important to explore the other possibility, namely, that the
carriers are an inherent property of the tube.
In this case, we expect a fairly homogeneous hole distri-
bution along the NT independent of the gate voltage. An
estimate of the hole density can then be obtained by writing
the total charge on the NT as Q5 CV
G,T
, where C is the NT
capacitance and V
G,T
the threshold voltage necessary to
completely deplete the tube. The NT capacitance per unit
length with respect to the back gate is C/L
'2
p
ee
0
/ln(2h/r), with r and L being the NT radius and
length, and h and
e
the thickness and the average dielectric
constant of the device.
10
Using L5 300 nm, r5 0.8 nm, h
5 140 nm, and
e
'2.5, we evaluate a one-dimensional hole
density of p5 Q/eL'9310
6
cm
21
from V
G,T
5 6 V. This
value corresponds to about 1 hole per 250 carbon atoms in
the NT. For comparison, in graphite there is only 1 hole per
10
4
atoms.
11
The large hole density suggests that the NT is
degenerate and/or that it is doped with acceptors, for ex-
ample, as a result of its processing.
12
Assuming that transport in our NT is diffusive at room
temperature ~as in SWNT bundles
13
!, we can estimate the
mobility of the holes from the transconductance of the FET.
In the linear regime, it is given by dI/dV
G
5
m
h
(C/L
2
)V
SD
. Subtracting the contact resistance, we ob-
tain a NT transconductance of dI/dV
G
51.73 10
2 9
A/V at
V
SD
510 mV, corresponding to a hole mobility of
m
h
'20 cm
2
/V s. This value is close to the mobility in heavily
p-doped silicon of comparable hole density,
9
but consider-
ably smaller than the 10
4
cm
2
/V s observed in graphite.
11
The low value of the NT mobility is consistent with our
initial assumption of diffusive transport and suggests that the
SWNT contains a large number of scatterers, possibly related
to defects in the NT or disorder at the NT/gate–oxide inter-
face due to roughness. SWNTs are known to conform to the
topography of the surface so as to increase their adhesion
energy. Such deformations can lead to local electronic struc-
ture changes,
14
which may act as scattering centers. The low
mobility is surprising in view of the coherence length of
more than 1
m
m reported on the basis of energy quantization
along a metallic SWNT at low temperature.
4
However, we
note that there have been no transport experiments on indi-
vidual SWNTs that provide evidence for ballistic transport at
room temperature ~e.g., by observing conductance
quantization!.
15
Having demonstrated FET operation for a SWNT, we
move on to explore whether transport through MWNTs can
be controlled by a gate electrode. The band gap of NTs has
been predicted to decrease with increasing tube diameter.
1
Therefore, MWNTs with diameters of 10 nm or more are
expected to show metallic rather than semiconducting behav-
ior at room temperature. We fabricated a number of MWNT
devices with resistances of R;100 kV. Most of these de-
vices showed no gate action, and a typical I –V
G
curve is
plotted in Fig. 3 ~curve A!.
Structural deformations of NTs change their electronic
properties. Curve B in Fig. 3 shows that this can lead to a
significant gate effect in MWNTs. As is the case for the
SWNT-FET, the source–drain current of this MWNT-FET
decreases with increasing gate voltage, i.e., the dominant
conduction process is hole transport. In contrast to the
SWNT device, this MWNT-FET could not be completely
depleted. The I –V
SD
curve remained linear independent of
the gate voltage ~not shown!. Between V
G
5235 and 25 V,
the resistance increased only from R5 76 to 120 kV, corre-
sponding to a conductance modulation by about a factor 2.
FIG. 2. Output and transfer characteristics of a SWNT-FET: ~a! I –V
SD
curves measured for V
G
526, 0, 1, 2, 3, 4, 5, and 6 V. ~b! I–V
G
curves for
V
SD
5 10–100 mV in steps of 10 mV. The inset shows that the gate modu-
lates the conductance by 5 orders of magnitude (V
SD
5 10 mV).
FIG. 3. I –V
G
curve of a typical MWNT device ~curve A! in comparison
with that of a collapsed MWNT of similar cross section ~curve B!.
2448 Appl. Phys. Lett., Vol. 73, No. 17, 26 October 1998 Martel
et al.
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The gate effect reaches a sharp maximum between V
G
5215 and 0 V.
16
To explain this peculiar behavior, we consider the AFM
image, Fig. 4~a! of the MWNT-FET. The device consists of
a collapsed MWNT, which bridges the gap between two Au
electrodes separated by about 1
m
m. This nanostripe is 3 nm
high—from which we conclude that it has four or five
shells—and it exhibits a number of twists @Figs. 4~b! and
~c!#—which allow us to determine its width to be 12 nm.
Based on the structural information summarized in Fig.
4~d!, we propose the following explanation for the behavior
of the MWNT-FET. Since the intershell interaction in
MWNTs is weak, it is reasonable to assume that transport is
confined to the outermost shell of the nanostripe.
15
The con-
ductance modulation of about 2 indicates that the bottom
‘‘plate’’ of the outermost shell is depleted by the gate,
whereas the top layer is less affected due to screening by the
inner shells ~and the bottom layer as long as it is conduct-
ing!. Our model implies that the bottom ‘‘plate’’ is decou-
pled from the top layer, which may be the consequence of
lateral quantization effects perpendicular to the tube axis.
Using R5 R
NT
1 2R
C
for the ‘‘on’’ state (V
G
5215 V) and
R5 2R
NT
1 2R
C
for the ‘‘off’’ state of the MWNT-FET
(V
G
5 0 V), we estimate a resistance of R
NT
5 32 kV for the
outer shell of the NT and deduce a contact resistance of R
C
5 23 kV.
Finally, we proceed analogously to the SWNT-FET
analysis to evaluate the hole density and mobility of the col-
lapsed MWNT. Numerical calculations show that the capaci-
tance per unit length is reasonably well described by C/L
5 2
p
ee
0
/ln(2h/r) despite the slab-shaped geometry of the
collapsed tube. Using L5 1.1
m
m, r5 5 nm, and a threshold
voltage of V
G,T
'8 V to deplete the bottom layer, we obtain
p'1.73 10
7
cm
21
for its hole density. From the transcon-
ductance of dI/dV
G
53.53 10
2 8
V/A at V
SD
5 50 mV, we
estimate a mobility of
m
h
'220 cm
2
/V s. The hole density is
similar to the SWNT but the mobility is higher, which sug-
gests a reduced number of scatterers. This may arise from the
fact that the MWNTs were not ultrasonically treated in acids.
Furthermore, they do not deform as much as SWNTs in or-
der to conform to roughness at the NT/gate–oxide interface.
In conclusion, we fabricated molecular field-effect tran-
sistors with single- and multi-wall carbon nanotubes. Trans-
port in the NTs is dominated by holes and, at room tempera-
ture, it appears to be diffusive. Using the gate electrode, the
conductance of a SWNT-FET could be modulated by more
than 5 orders of magnitude. An analysis of the transfer char-
acteristics of the FETs suggests that the NTs have a higher
carrier density than graphite and a hole mobility comparable
to heavily p-doped silicon. Large-diameter MWNTs show
typically no gate effect, but structural deformations can
modify their electronic structure sufficiently to allow FET
behavior.
The authors thank A. G. Rinzler, R. E. Smalley, and H.
Dai for providing the NTs, and they gratefully acknowledge
S. Koester and M. J. Rooks for assistance with the electron-
beam lithography, F. Stern for capacitance calculations, and
P. Solomon for helpful discussions. T.S. and T.H. thank the
Alexander von Humboldt Foundation for support.
1
For a review, see M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund,
Science of Fullerenes and Carbon Nanotubes ~Academic, San Diego, CA,
1996!.
2
J. W. G. Wildo
¨
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Dekker, Nature ~London! 391,59~1998!.
3
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391,62~1998!.
4
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and C. Dekker, Nature ~London! 386, 474 ~1997!.
5
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6
S. J. Tans, A. R. M. Verschueren, and C. Dekker, Nature ~London! 393,
49 ~1998!.
7
T. Guo, P. Nikolaev, A. Thess, D. T. Colbert, and R. E. Smalley, Chem.
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8
D. T. Colbert, J. Zhang, S. M. McClure, P. Nikolaev, J. H. Hafner, D. W.
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9
S. M. Sze, Physics of Semiconductor Devices ~Wiley, New York, 1981!.
10
This expression was inferred from P. M. Morse and H. Feshbach, Methods
of Theoretical Physics ~McGraw–Hill, New York, 1953!, p. 11. The NT is
considered as a metallic cylinder, which is a good approximation as long
as the density of states at the Fermi level is high. Similar expressions were
used to estimate Coulomb-blockade energies of NTs.
11
N. B. Brandt, S. M. Chudinov, and Ya. G. Ponomarev, Semimetals, 1.
Graphite and its Compounds ~North-Holland, Amsterdam, 1988!.
12
H. He, J. Klinowski, M. Forster, and A. Lerf, Chem. Phys. Lett. 287,53
~1998!.
13
J. E. Fischer, H. Dai, A. Thess, R. Lee, N. M. Hanjani, D. L. Dehaas, and
R. E. Smalley, Phys. Rev. B 55, R4921 ~1997!.
14
A. Rochefort, D. Salahub, and Ph. Avouris, Chem. Phys. Lett. ~to be
published!.
15
Only in freely suspended MWNTs without NT/substrate interaction has
evidence for ballistic room-temperature transport been found @S. Frank, P.
Poncharal, Z. L. Wang, and W. A. de Heer, Science 280, 1744 ~1998!#.
16
The position of the sharp drop in the I–V
G
curve was found to depend on
the sweep direction, but the voltage range over which the drop occurs
showed no hysteresis.
FIG. 4. ~a! Noncontact AFM image of the MWNT-FET. ~b! and ~c! Close
up views showing three twists in the collpased NT ~see arrows!. ~d! Sche-
matic cross section of the collapsed MWNT.
2449Appl. Phys. Lett., Vol. 73, No. 17, 26 October 1998 Martel
et al.
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