Nanofabrication of top-gated carbon nanotube-based
transistors: Probing electron-electron interactions in
one-dimensional systems
J.A. Sulpizioa)
Department of Physics, Stanford University, Stanford, California 94305
Z.Z. Bandić
Hitachi San Jose Research Center, San Jose, California 95120
D. Goldhaber-Gordon
Department of Physics, Stanford University, Stanford, California 94305
(Received 31 March 2006; accepted 8 August 2006)
Carbon nanotubes are interesting for studying the remarkable electronic properties of
one-dimensional (1D) quantum systems. Electron flow in such systems is not described
by Fermi liquid theory—restricted dimensionality leads to the appearance of collective
excitations—or Luttinger liquid behavior. Previous studies have probed Luttinger liquid
behavior by tunneling into or between one-dimensional systems. We propose to extend
these studies by using narrow top gates to introduce tunable tunnel barriers within
nanotubes. We report on the scalable fabrication of carbon nanotube-based transistors
with nanowire top gates. We have used electron-beam lithography (EBL) to create
single-walled carbon nanotube (SWNT) transistors with source-drain spacings down to
200 nm and with sub-30 nm metal top gates for creating tunable tunnel barriers. The
top metal gate is isolated from the nanotube by a thin aluminum oxide layer deposited
by atomic layer deposition. We fabricated chips with 100 devices using multiple
electron-beam lithography alignment steps and achieved overall placement better than
30 nm. The details of top-gated SWNT transistor fabrication are presented, and initial
transport measurements on fabricated devices are discussed.
I. INTRODUCTION
Carbon nanotubes have attracted significant interest
for studying electronic properties of one-dimensional
(1D) electron systems.1–5 Electron flow in three dimensional systems has been successfully described by
Landau Fermi liquid theory,6 in which there exists a oneto-one correspondence between non-interacting and interacting electron states (quasiparticle excitations). In
these systems, the important electron scattering processes
occur around the Fermi level, significantly simplifying
quantitative analysis [Figs. 1(a) and 1(b)]. The approximations of Landau Fermi liquid theory are correct when
the electron–electron relaxation time ␶ee is much larger
than both the relaxation times for scattering of electrons
with phonons and impurities, ␶e−ph and ␶e−imp respectively.7 Essentially, quasiparticle excitations in higher dimensional systems behave as nearly free particles (i.e.,
the particles can “move past each other”). However, the
Landau Fermi liquid theory description of many-body
systems is not valid for interacting systems in 1D. The
restricted dimensionality in 1D changes the nature of
electron–electron scattering so that only collective excitations exist in interacting systems [Fig. 1(c)].
The theoretical description of the interacting 1D quantum state, first developed by Tomonaga and Luttinger,8,9
involves plasmon-like excitations that behave as bosons.10–12 In such a Luttinger liquid, a highly correlated
many-electron state emerges as a consequence of the
reduced dimensionality and electron–electron interactions. This correlated state is characterized by a parameter
␣=
冉 冊
1 1 ␯共0兲 2
,
2 4 2␲␯F
where ␯(k) ⳱ f [Vee(r)], Vee(r) is the electron–electron
interaction, and ␯(0) ⳱ ␯(kF). The parameter ␣ clearly
reflects the strength of the electron-electron interactions.
For a Luttinger liquid, the tunneling density of states ␳
has a power law behavior ␳ ∼ ␳(␮ − ⑀)␣ as a function of
energy ⑀. This leads to power law behavior of conductance G across a tunnel barrier as a function of temperature and bias voltage:
a)
再
dI
T ␣, eV Ⰶ kBT linear regime
∼ ␣
dV
V , eV Ⰷ kBT high bias regime
Address all correspondence to this author.
e-mail: jopizio@stanford.edu
DOI: 10.1557/JMR.2006.0361
G=
2916
© 2006 Materials Research Society
J. Mater. Res., Vol. 21, No. 11, Nov 2006
.
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J.A. Sulpizio et al.: Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in 1D systems
FIG. 1. Failure of Fermi liquid theory for 1D electron gas. In Fermi liquid theory for three-dimensional systems, (a) single electron energy levels
and (b) interacting electron energy levels exhibit a one-to-one correspondence; quasiparticle excitations behave as nearly free particles (i.e., the
particles can “move past each other”).1 (c) Such a description is not valid in a 1D electron system, since the nature of electron-electron scattering
changes, and only collective excitations may exist.
For a normal Fermi liquid, energy-independent tunneling
is expected and the tunneling conductance is independent
of bias and temperature.1,2 As predicted theoretically,
nanotubes have been shown to exhibit Luttinger liquid
behavior in transport measurements.1,2 Previous experimental efforts include tunneling between two Luttinger
liquids in a kinked nanotube system. In these experiments, only the extreme cases of no tunnel barrier and
strong tunnel barrier were studied. Additionally, the onset of Coulomb blockade due to poorly transmitting contacts prevented Luttinger liquid measurements at very
low temperatures. Interesting experimental questions remain about how the conductance behaves in the other
tunneling regimes and at lower temperatures.
We propose to study tunneling between Luttinger
liquids in a single-walled carbon nanotube (SWNT) device across a tunable tunnel barrier induced by narrow
(20–30 nm) metal top-gate electrodes. Local gating of
nanotube devices with top gates has recently been
achieved.3 Although Luttinger liquid behavior has only
been previously observed via transport measurements in
metallic nanotubes,1,2 Luttinger liquid behavior may be
expected in both metallic and semiconducting nanotubes.
The Luttinger liquid may emerge in any 1D electronic
system where the electronic band structure can be linearized around the Fermi level; the presence of a band gap
would not change this as long as the Fermi level lies
above the gap (which is the case for the gated nanotube).
By measuring
G=
dI
dV
between the source and drain contacts as a function of
narrow gate voltage, we aim to achieve tunneling between Luttinger liquids in various regimes of barrier
transmission, and to quantitatively measure the strength
of electron-electron interactions. Most of the previous
studies of carbon nanotube transistors3 have involved
locating individual nanotubes by atomic force microscopy (AFM) and contacting them individually, whereas
our approach is more scalable, as we rely on the probabilistic placement of the nanotubes using lithographically
defined catalyst fields. Specifically, this probabilistic approach allows us to pre-define regions in which carbon
nanotubes will grow, and therefore fabricate many topgated devices at once. In addition, such a probabilistic
approach has not been used before for nanofabricaton of
carbon nanotube devices with several narrow top gates.
II. CARBON NANOTUBE GROWTH
AND CHARACTERIZATION
Prior to the carbon nanotube growth, catalyst regions
were lithographically defined on the substrate surface.
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J.A. Sulpizio et al.: Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in 1D systems
FIG. 2. (a) Nanotube emerging from the catalyst pad made of iron
oxide nanoparticles embedded in alumina and (b) carbon nanotube
visible in the finished device. The highlighted sections indicate the
position of the nanotube.
The substrate was spincoated with poly(methyl methacrylate) (PMMA) electron beam (e-beam) resist, and
4 ␮ × 4 ␮ regions were exposed and developed in resist.
The formulation of catalyst used was 20 mg ferric nitrate
monohydrate and 15 mg alumina dissolved in 15 ml of
methanol, ultrasonicated for 2 h prior to deposition. The
catalyst solution was deposited by pipette directly onto
the PMMA-coated and patterned substrate. Catalyst regions were lifted off by allowing the solvent to evaporate
under nitrogen, heating the substrate to 70 °C, and lifting
off residual catalyst on PMMA resist in acetone. This
procedure effectively creates iron oxide nanoparticles
embedded in an alumina matrix.13
Single-walled carbon nanotubes were grown in a
quartz tube furnace at temperatures between 800 °C and
950 °C. Before initiating growth, the furnace was ramped
to growth temperature over a period of approximately
15 min under flow of 500 sccm of hydrogen. The standard gases and flow rates used during growth were methane (1000 sccm), hydrogen (500 sccm), and ethylene
(25 sccm). Typical growth time varied between 5 and
10 min. Figure 2(a) shows nanotube emerging from the
catalyst pad.
Growth conditions were tuned to optimize for the
growth of SWNTs as opposed to multiwalled nanotubes.
AFM was used to verify nanotube diameter. Measured
diameters of approximately 1 nm were considered as
strong indicators of single-walled nanotubes. Figure 3(a)
shows an AFM image of a nanotube emerging from an
iron oxide nanoparticle catalyst pad, while Fig. 3(b)
shows the cross-section AFM profile of the same nanotube measured in the labeled region. The measured diameter of the nanotube is 1.2 nm. Figures 3(c) and 3(d)
show another example of a nanotube emerging from the
catalyst pad with a measured diameter of 0.8 nm.
FIG. 3. (a) Nanotube emerging from the catalyst pad made of iron oxide nanoparticles embedded in alumina. (b) Cross-section profile of the
nanotube shown in (a). The diameter of the nanotube is 1.2 nm. (c) Nanotube emerging from the catalyst pad. (d) Diameter of the tube shown in
(c) is measured as 0.8 nm.
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J. Mater. Res., Vol. 21, No. 11, Nov 2006
J.A. Sulpizio et al.: Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in 1D systems
FIG. 4. Fabrication of carbon nanotube-based transistors.
III. CARBON NANOTUBE
TRANSISTOR FABRICATION
Figure 4 shows steps used in the fabrication of CNT
chips. The substrate used for fabrication was a degenerately doped Si substrate with 100 nm-1 ␮m thick thermally grown SiO2 film. A Leica VB6 e-beam tool was
used for the aligned lithographic steps in the fabrication.
The typical alignment achieved was 15–20 nm for 3␴. In
the first step, alignment marks were lithographically defined in PMMA resist, then transferred by CHF3-based
reactive ion etching into the SiO2 film. These alignment
marks were then used in all subsequent EBL steps.
Following alignment mark definition, we defined catalyst regions for individual devices, and lifted off iron
oxide/alumina catalyst material solution in methanol,
as described in Sec. II. Each individual SWNT device
employs two 4 × 4 ␮m catalyst regions separated by 7
␮m. After iron oxide/alumina catalyst regions were defined, SWNTs were grown as described in Sec. II. The
catalyst regions on the SWNT chips were intentionally
positioned in the growth furnace so that the gas
FIG. 5. Fabricated SWNT transistor with top gates.
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J.A. Sulpizio et al.: Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in 1D systems
flow direction was parallel with the line connecting two
catalyst marks. Following SWNT growth, EBL with
alignment, followed by e-beam evaporation and lift-off
of Pd were used to define 40-nm–thick Pd low Schottky
barrier (ohmic) contacts to the nanotubes.13 The spacing
between contacts, which defined the length of the active
region of the carbon nanotube, varied between 200 nm
and 5 ␮m. These channel lengths were chosen to compromise between finite-size effects and the probability of
point defects in the nanotubes. After Pd ohmic contacts
were defined, Ti(10 nm)/Au(35 nm) large area source
and drain contacts were lifted off and aligned to Pd contacts. The devices were then annealed in Ar at 220 °C for
10 min to improve the contact resistance. Prior to definition of narrow top gates, a 6–30-nm–thick alumina
layer was deposited by atomic layer deposition to isolate
the electrically contacted nanotube. Finally, EBL with
alignment and lift-off process was used to define 20 nm
wide Ti(5 nm)/Au(20 nm) nanowire gates between the
region defined by Pd contacts. One of the final device
structures is shown in Fig. 5.
IV. PRELIMINARY TRANSPORT MEASUREMENTS
Figures 6(a) and 6(b) show room temperature conductance traces
G=
dI
dV
as a function of the back-gate voltage (applied to the bulk
of the conductive silicon substrate) for two representative
devices. The contacts are highly transmitting, and the
devices can be fully depleted, suggesting semiconducting
SWNTs. Such devices are promising candidates for local
gating experiments. The top gates will be characterized
carefully by low temperature transport measurements to
avoid potential room temperature damage to the devices.
Preliminary conductance measurements (down to T ⳱
4 K) as a function of top-gate voltage on similar devices
with 30 nm alumina top-gate insulation suggest that the
top gate does not locally electrostatically couple to the
nanotube, but instead couples to the entire channel (for
channel lengths down to 200 nm). However, we expect to
achieve local gating with the thinner alumina insulation
of 6 nm.
V. CONCLUSIONS
Interacting electron systems in 1D cannot be effectively described with the Landau Fermi liquid model.
SWNTs are potentially interacting 1D systems exhibiting
Luttinger liquid behavior and can be locally gated with
the fabrication of top gates. We have fabricated narrow
gate nanotube transistor devices using scalable methods
to study tunneling transport in a Luttinger liquid, with the
carbon nanotubes grown from lithographically defined
2920
FIG. 6. (a) and (b) Room temperature conductance versus back-gate
voltage of representative devices with channel lengths of 500 nm. The
devices have highly transmitting contacts and can be fully depleted.
This suggests the devices contain semiconducting SWNTs, and are
promising candidates for future local gating experiments.
catalyst regions. This approach allowed for parallel fabrication of a large number of devices.
Multiple e-beam exposure and alignment steps were
used to define device geometry, low-barrier Pd contacts,
and dielectrically insulated 20-nm–wide top gates. Preliminary transport measurements indicate semiconducting devices that are deplete-able with highly transmitting
contacts, suggesting the devices are well suited for Luttinger liquid tunneling measurements with local narrow
top gates.
ACKNOWLEDGMENTS
This work was partially supported by The Air Force
Office of Scientific Research. JAS acknowledges support
from a National Science Foundation Graduate Research
Fellowship.
J. Mater. Res., Vol. 21, No. 11, Nov 2006
J.A. Sulpizio et al.: Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in 1D systems
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