Download X. Xie, S.H. Jin, M.A. Wahab, A.E. Islam, C. Zhang, F. Du, E. Seabron

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Received 29 May 2014 | Accepted 19 Sep 2014 | Published 12 Nov 2014
DOI: 10.1038/ncomms6332
Microwave purification of large-area horizontally
aligned arrays of single-walled carbon nanotubes
Xu Xie1,*, Sung Hun Jin2,*, Muhammad A. Wahab3,*, Ahmad E. Islam1, Chenxi Zhang4, Frank Du1, Eric Seabron1,
Tianjian Lu5, Simon N. Dunham1, Hou In Cheong6, Yen-Chu Tu1, Zhilin Guo6, Ha Uk Chung1, Yuhang Li7,
Yuhao Liu1, Jong-Ho Lee8, Jizhou Song9, Yonggang Huang7, Muhammad A. Alam3,
William L. Wilson1 & John A. Rogers1
Recent progress in the field of single-walled carbon nanotubes (SWNTs) significantly
enhances the potential for practical use of this remarkable class of material in advanced
electronic and sensor devices. One of the most daunting challenges is in creating large-area,
perfectly aligned arrays of purely semiconducting SWNTs (s-SWNTs). Here we introduce a
simple, scalable, large-area scheme that achieves this goal through microwave irradiation of
aligned SWNTs grown on quartz substrates. Microstrip dipole antennas of low work-function
metals concentrate the microwaves and selectively couple them into only the metallic SWNTs
(m-SWNTs). The result allows for complete removal of all m-SWNTs, as revealed through
systematic experimental and computational studies of the process. As one demonstration of
the effectiveness, implementing this method on large arrays consisting of B20,000 SWNTs
completely removes all of the m-SWNTs (B7,000) to yield a purity of s-SWNTs that corresponds, quantitatively, to at least to 99.9925% and likely significantly higher.
1 Department
of Materials Science and Engineering, Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA. 2 Department of Electronic Engineering, Incheon National University, Incheon 406-772, Republic of Korea. 3 School of Electrical and Computer
Engineering, Purdue University, West Lafayette, Indiana 47907, USA. 4 Department of Mechanical and Aerospace Engineering, University of Miami, Coral
Gables, Florida 33146, USA. 5 Department of Electrical Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. 6 Department of
Chemical Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. 7 Department of Mechanical Engineering, Northwestern
University, Evanston, Illinois 60208, USA. 8 Department of Electrical Engineering, Seoul National University, Seoul 151-600, Republic of Korea. 9 Department
of Engineering Mechanics and Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China. * These authors contributed equally to this work.
Correspondence and requests for materials should be addressed to J.A.R. (email: [email protected]).
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he extraordinary electrical properties1–3 of semiconducting
single-walled carbon nanotubes (s-SWNTs) make them
uniquely attractive for use in logic transistors/circuits4–10,
radiofrequency (RF) transistors11–16, optoelectronic devices17–19
and sensors20–22. The required horizontally aligned array
configurations in SWNTs are possible through chemical vapour
deposition (CVD)-based growth on quartz substrates23,24. A
long-standing challenge for use of such arrays in demanding
applications arises from the need to remove all of the metallic
tubes (m-SWNTs), which typically comprise B1/3 of all of the
SWNTs. Techniques for selective growth25,26 and for post-growth
purification via chemical etching/separation27–29, optical
ablation30,31 or electrical breakdown32 provide some capabilities
in yielding s-SWNTs in CVD arrays, but none approaches the
daunting requirements in purity for applications in low-power
digital circuits (499.9999% s-SWNTs)33.
A recently described alternative method referred to as
thermocapillary-enabled purification34 can exceed these targets.
Here a partial top-gate transistor structure allows selective current
injection into the m-SWNTs. The resulting local Joule heating
creates increases in temperature (a few degrees) that lead to
gradients (tens of degrees per mm) sufficiently large to drive
thermocapillary flow in an overcoat of an amorphous smallmolecule material (thermocapillary resist, Tc-resist). This flow
forms local trenches above the m-SWNTs, thereby exposing them
for complete elimination by reactive ion etching (RIE), without
damaging the s-SWNTs. Although effective, this method has
several practical disadvantages, such as: the need for multiple
deposition and etching steps to form the necessary electrodes and
gating structures; the requirement of physical contact with these
electrodes to allow selective current injection; and residue and
other contamination that often remains, even after removal of
these materials following the purification process. To avoid these
issues, here we implement a different scheme in which microwave
radiation selectively heats the m-SWNTs to levels that initiate the
thermocapillary flows. Microwave radiation represents a
noninvasive heating technique, which is simple and scalable.
For low cost, desktop sources of microwaves, the intensity below
the level required for non-negligible direct heating of SWNTs,
because of their extremely small absorption cross-sections35.
Antennas can, however, simultaneously amplify the microwave
power and selectively transfer the radiation energy into heating of
m-SWNTs. Systematic experimental studies demonstrate the
effectiveness of this simple process by complete and selective
removal of m-SWNTs from large and small arrays of SWNTs,
including examples that include tens of thousands of SWNTs.
Measurements and computational results reveal all of the
fundamental aspects of interactions between the microwaves,
antennas and SWNTs. The results represent substantial progress
towards the large-scale, economical production of well-aligned
arrays of purely s-SWNTs.
T
Results
Microwave purification of large-area arrays of aligned SWNTs.
Schematic illustrations and corresponding images for each step of
the microwave purification process appear in Fig. 1a,b (i–iii).
Patterning narrow strips of iron catalyst particles on a quartz
substrate followed by CVD growth23 yields nearly perfectly
aligned, horizontal arrays of SWNTs that include both metallic
and semiconducting types. A second patterning step defines
collections of microstrip dipole antennas (typically 50 nm Ti) that
amplify the microwave field and effectively transfer incident
power into current flows selectively in the m-SWNTs. Without
the antennas, the heating of the SWNTs is negligible
(Supplementary Fig. 1). Although other antenna geometries can
2
be considered36, the designs used here are attractive because of
their simple planar layouts. Increasing the lengths of the strips
and decreasing their separations improve the field enhancement.
The lengths, widths and separations for experiments reported
here are LA ¼ 500 mm (length of one arm in the dipole),
WA ¼ 1 mm (width of an arm) and L0 ¼ 15 mm (gap between
the arms), respectively. Details appear in Supplementary Fig. 2a.
Deposition of a uniform overcoat of Tc-resist (typically B30 to
40 nm thick) followed by microwave irradiation (300 W, 70 °C,
3 h) in a small, desktop single-mode cavity (Supplementary Fig. 3)
initiates mild heating selectively in the m-SWNTs and resulting
thermocapillary flows at these locations (increases in microwave
power can enable reductions in LA and increases in L0, for singlestep, rapid purification over areas larger than those described
here). The open trenches that form as a result of the flows allow
complete removal of the m-SWNTs by RIE, without affecting the
s-SWNTs. Washing away the Tc-resist with acetone completes
the purification process.
Figure 1c shows the normalized average trench depth (h/H,
where h is the average trench depth and H is thickness of the Tcresist; see inset schematic in Fig. 1c) along each SWNT (387
SWNTs investigated across an array with density B0.5 SWNTs
per mm) in the form of a cumulative distribution function (CDF).
The results exhibit two distinct regions, that is, no trenches or
deep trenches, with a cutoff at CDFB0.64, corresponding to fully
developed trenches at B36% of the SWNTs in the array. This
number is close to the expected population (B33%) of
m-SWNTs derived from CVD growth. Transistors that utilize
the microstrip antennas as source-drain contacts (channel length
Lch ¼ B15 mm, channel width Wch ¼ B1 mm; see Supplementary
Fig. 2a) exhibit collective transfer curves and output characteristics (Fig. 1d,e, from 40 transistors added together; individual
transistor responses in Supplementary Fig. 2b) consistent with
complete removal of m-SWNT, that is, ratio of on to off currents
of 41,000. High-output currents (B25 mA) are consistent with
retention of a large majority of the s-SWNTs. This demonstration
involves both large areas (15 mm 40 mm ¼ 0.6 mm2) and
numbers of SWNTs (B20,000). The expected current from a
single m-SWNT in this device structure (B2–3 mA for VDS ¼
1 V (refs 37,38) is much larger than the observed off current
(B0.5 mA), thereby suggesting a purity in s-SWNTs of
499.9925% (when one m-SWNT exists among the s-SWNTs,
the purity is 1-1/(20,000*2/3) ¼ 99.9925%).
Effectiveness of microwave purification. Criteria for effectiveness of this process include33,39 the elimination of all of the
m-SWNTs, and the preservation of all of the s-SWNTs, without
change in their intrinsic properties33,39. To quantify the
effectiveness, we exploit detailed imaging (scanning electron
microscopy (SEM) and atomic force microscopy (AFM)) and
electrical measurements on small arrays of SWNTs (each with
between 10 and 31 SWNTs, for easy imaging) before and after the
purification (for direct comparisons). The test structures
(Supplementary Fig. 4a,b) use Ti microstrip antennas
(Supplementary Fig. 5) as the source-drain contacts, where
poly(methyl methacrylate) (PMMA) serves as the gate dielectric
(for easy removal after characterization) and Ti (50 nm) as the
gate metal.
Figure 2a shows representative transfer characteristics evaluated before and immediately after purification (implemented here
in three cycles of Tc-resist deposition and microwave irradiation
to improve the yields; details in the Supplementary Note 1). In
this example, the process removes 8 of 25 SWNTs in the device,
thereby increasing the on/off ratio from B2.2 to B4.2 103. If
we assume, as a rough estimate, that the on currents in the
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(i)
(ii)
(iii)
(i) Pattern catalyst strips;
grow SWNT arrays
(ii) Pattern microstrip antennas;
deposit Tc-resist; use microwave
radiation to selectively heat the
m-SWNTs for inducing local
thermocapillary flow
2.45 GHz
H
E
1.25
10–3
Tc-resist
1.00
0.50
0.25
lD (mA)
h
H
–lD (A)
h/H
0.75
10–4
10–5
Qz
10–6
0.00
0.0 0.2 0.4 0.6 0.8 1.0
CDF of SWNTs
VDS = –1 V
–20
0
20
0.000
–0.125
–10
–0.250
Density:
~0.33 SWNTs/μm
–15
–0.375
VGS
–0.500
from 30 V to –40 V.
–0.625
–10 V step
–20
Purified region: 15 μm × 40 mm
10–7
–40
0
–5
–25
40
–10
–8
VGS (V)
–6 –4
VDS (V)
–2
lD (μA μm–1)
(iii) Etch exposed m-SWNTs;
remove Tc-resist;
leave all s-SWNTs
0
Figure 1 | Microwave-based purification of large arrays of aligned SWNTs. (a) Schematic illustration of the key steps in the process. (i) CVD growth
yields aligned SWNTs of both metallic and semiconducting types. (ii) Microstrip antennas (Ti) defined on this substrate convert incident microwave
irradiation into Joule heating selectively in only the m-SWNTs. The resulting heating causes local thermocapillary flow of a thin overcoat (B35 nm) of an
amorphous organic material (thermocapillary resist, Tc-resist), thereby opening trenches at the m-SWNTs. (iii) Etching away the exposed m-SWNTs and
removing the Tc-resist leaves arrays of pure, unmodified s-SWNTs. (b) AFM and SEM images at each step: (i) pristine arrays of SWNTs before the
purification; (ii) topography associated with formation of trenches at the m-SWNTs and (iii) s-SWNTs after the purification. Scale bar, 15 mm. (c) Statistics
of the normalized average trench depths (h/H) along each SWNT, plotted as a function of the cumulative distribution fraction (CDF) of the SWNTs (387 in
total). The results indicate that B36% of the SWNTs yield deep trenches. The inset provides a schematic illustration of the geometry for extracting the
trench depth, with key parameters defined. (d,e) Cumulative transfer curves and output characteristics for 40 transistors built with purified arrays of
SWNTs. The transistors utilize the Ti microstrip antennas as source and drain contacts, with channel lengths B15 mm and channel widths B1 mm, to
achieve an on/off ratio B103 and large output current B25 mA.
s-SWNTs are similar to those of the m-SWNTs at similar bias
conditions, then even a single remaining m-SWNT would lead to
on/off ratios of o17 (o2.6 if the on currents in the s-SWNTs are
ten times smaller than the m-SWNTs40, as might be expected
because of poor contacts to the s-SWNTs associated with the Ti
electrodes). The measured on/off ratio is therefore consistent with
complete removal of all m-SWNTs. The relatively large reduction
in on current in Fig. 2a (B13.9 to B0.8 mA) is a consequence of
the large Schottky barriers that form at the contacts between the
s-SWNT and the Ti40,41 (Supplementary Fig. 6), rather than the
degradation of s-SWNTs. Currents measured at high source/drain
bias (Imax at VDS ¼ 10 V; Fig. 2b), where contact effects are
minimal (Supplementary Fig. 7 and Supplementary Table 1),
indicate a reduction of only B60%, at various gate voltages (VGS).
This value is within a range expected for complete retention of
the s-SWNTs, with unmodified electrical properties34. For 20
transistors studied in this manner, the process removes 143 of 409
SWNTs (Supplementary Table 2). The corresponding percentage
(B35%) is consistent with the results of Fig. 1, and the expected
population of m-SWNTs. Moreover, the on-off ratios (Ion/Ioff)
and the ratios of the numbers of SWNTs before and after
purification (Na/Nb) are consistent with effective operation of the
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10–3
0
VDS= –1 V
10–8
–150
–20
0
20
VGS (V)
–200
–10
40
10–2
–lD (A)
lon /loff
100
Before
After
104
102
100
0.0
–8
10–4
10–6
0.4
0.6
Na/Nb
0.8
1.0
10–12
0.4
10–7
0.2
–2
0
10–9
0.0
1,800
0.2
0.4
0.6 0.8
Na/Nb
0.0
1.0
0.0
0
1,600
1,400
1,200
–3
–2
–1
0
VG-VT (V)
10–8
–3
–2
–1
0
1
2
–0.5
–25
–1.0
–50
–75
VDS = 0.1 V
VDS = –1 V
10–10
0.2
0.6
10–6
10–8
–6 –4
VDS (V)
–1 –1
108
106
Before
0.8
2
–40
After
–100
μ (cm V s )
10–10
–lD (A)
10–6
10–5
lD (μA)
lD (μA)
–lD (A)
–50
1.0
Imax_b
Imax_a
Imax_a/Imax_b
10–4
Imax_a/Imax_b
Before
After
Density:
0.44 SWNTs/μm
–100
–3
VGS (V)
–1.5
VGS is changed
from 0 V to –3 V, – 0.5 V step
–2
–1
lD (μA μm–1)
10–4
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6332
–2.0
0
VDS (V)
Figure 2 | The effectiveness of the microwave-based purification process. (a,b) Typical transfer curves and output characteristics (near the on
state region) for transistors built on small arrays of SWNTs before and after purification. The transistors use Ti metal as the source and drain electrodes,
which also serve as the antennas during the purification. The on/off ratio of the transistors increases from B2.2 to B4.2 103, and the maximum output
current decreases by only B41%. (c) The maximum output current before and after (Imax_b and Imax_a, respectively) purification, as a function of
the ratio of the number of SWNTs after purification to the value before purification (Na/Nb). Imax_a/Imax_b ranges from 0.1 to 0.6, and increases with Na/Nb.
The results indicate that the s-SWNTs are well preserved. (d) Statistics of the on/off ratios (Ion/Ioff) of transistors based on the SWNTs before and after the
purification, respectively. The Ion/Ioff increases from o5 to 1 103B106, suggesting complete removal of the m-SWNTs. (e,f) Typical transfer
curve and output characteristics of a transistor built on a small array of purified SWNTs with Pd contacts and a gate dielectric of SU8 (50 nm)/HfO2 (5 nm).
The low hysteresis, p-type behaviour facilitates extraction of the device mobility, which is B1,600 cm2 V 1 s 1 as shown in the inset graph.
process (Fig. 2d and Supplementary Table 2). The ratio of Imax
before and after purification (Imax_b/Imax_a) ranges from 0.1 to
0.6, and increases with Na/Nb (Fig. 2c). The large current
retention (weighted average value of Imax_a/Imax_b B0.35)
together with the expected, large percentage of remaining
SWNTs (65%), provide additional evidence that the process
preserves all, or nearly all, of the s-SWNTs.
Effectively assessing the performance of purified arrays benefits
from ohmic contacts (Pd) and high-capacitance gate dielectrics
(SU8 (50 nm)/HfO2 (5 nm)). Transistors with such designs
(Supplementary Fig. 4c) show p type characteristics with low
hysteresis (Fig. 2e,f). The results allow quantitative extraction of
mobilities. The average values that use rigorous calculations of the
gate capacitance42–45 (Supplementary Note 2) and neglect contact
resistances are B1,600 cm2 V 1 s 1 as shown in the inset of
Fig. 2e (weighted average B1,100 cm2 V 1 s 1 for various
devices, Supplementary Fig. 8). Mobilities in this range are
comparable to those reported from pristine SWNTs2 on quartz,
as well as s-SWNTs purified via TcEP with direct current (DC)
injection34.
Heating mechanisms and origins of selectivity. Three-dimensional (3D) finite element analysis (FEA), calculations using an
equivalent circuit model and experimental measurements illustrate the mechanisms that underlie the conversion of microwave
radiation into selective heating of the m-SWNTs. The first part of
the process involves interactions between the microwave fields
and the microstrip dipole antennas. Figure 3a shows simulated
distributions of the magnitude of the electrical field (E-field) near
the gap between the antenna arms for normally incident plane
waves polarized along the arms (see Supplementary Fig. 9a,b for
4
other polarizations). The results show that large-field enhancements are possible (line plots across the gap appear in
Supplementary Fig. 9c). For the range of dimensions studied here,
FEA modelling establishes (Fig. 3b) that the enhancement of the
average E-field in the X direction (EX) increases approximately
linearly with LA and decreases slightly with increasing WA and
decreasing thickness (Supplementary Fig. 9d). The field is
inversely proportional to L0 (Supplementary Fig. 9c), consistent
with expectation based on simple electrostatics.
This E-field initiates movements of free carriers in the SWNTs
(Supplementary Fig. 9e). The resulting current leads to Joule
heating. The wavelength of the microwave radiation (B12.2 cm)
is much larger than the dimensions of the system (that is, the
antennas, and the SWNTs). As a result, an equivalent circuit
model can be implemented under the quasi-static approximation
(Fig. 3c and Supplementary Fig. 10a,b) to obtain physical insights
into the heating mechanisms. Here the electrically small antenna
is equivalent to a voltage source (VA) with internal resistance (RA,
mainly from resistance of the metal strip) and reactance (XA,
mainly from the capacitance of the antenna), the values of which
can be extracted from FEA simulations or analytical calculations
(Supplementary Fig. 10c). The simplest case corresponds to the
presence of a single m-SWNT, treated as a series of lumped
resistors (r, defined as kO mm 1) and inductors (L, defined as
H m 1)46. The length of physical overlap between the m-SWNT
and the antenna (LC) allows electrical coupling through the
associated capacitances (geometric and quantum capacitance Cg
and Cq, respectively) and a shunt conductance (G). The resulting
network of elements has an impedance that can be calculated
analytically. By ignoring capacitive coupling between the exposed
region (L0) and the antenna, this segment of the m-SWNT can be
treated as a pure load, with impedance of Z0 ¼ (r þ ioL)L0,
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m–1
30
20
10
X
20
2
10
1
Exp.
FEA.
Circuit
0
X (μm)
30
10
10
20
Exp.
FEA.
Circuit
3
20
10
2
10
–10
30
20
30
1
Exp.
FEA.
0
0
5
Trench depth (nm)
3
40
4
4
Power (μW μm–1)
Trench depth (nm)
4
–5
.8
0.6 0
0.4
)
m
m
WA (
40
5
30
–10
0
0.2
LC
L0
1.0
Qz
40
0
LC
Antenna
SWNT
Z
RC
Lr
0
1.0
0.8
0.6
0.4
L
A (m
0.2
m)
0
–5
0
0
X (μm)
5
LC
30
LC
3
20
2
L0
10
0
10
1
Exp.
Circuit
–40
–20
0
20
X (μm)
Power (μW μm–1)
Antenna
Cg
Cq
20
0
Z
Trench depth (nm)
40
Trench depth (nm)
X
VA XA RA
60
Power (μW μm–1)
Y
80
Power (A.U)
V
Magnitude of average
Ex (V m–1)
Plane wave incident
E-field: 1 V m–1
Along x
0
40
(μW μm–1)
4
2
(μW μm–1)
Antenna area
0
4
0
0
0.00
0.03
0.06
0.09
–1
Conductivity of SWNT (μm kΩ )
2
0
Antenna area
Figure 3 | Coupling between the microwave field, the antennas and the SWNTs. (a) Finite element analysis (FEA) of the distribution of the electric
field around a microstrip dipole antenna, revealing a strong enhancement near the gap between two antenna arms. Scale bar, 65 mm. (b) FEA of the
field enhancement as a function of the length and width of the antenna. The enhancement scales approximately linearly with the length of the antenna,
whereas it is relatively insensitive to the width. (c) An equivalent circuit for the antenna and SWNT system. (d) Schematic illustration of an individual
m-SWNT in contact with both arms of the antenna. The AFM topography image and the plot below show a relatively constant trench depth along the
length of the SWNT. The green and red curves correspond to heating profiles from the FEA and circuit models, respectively. Scale bar, 5 mm. (e) Schematic
illustration of an individual m-SWNT in contact with only one arm of the antenna. The AFM topography image and trench profile show a decrease
in the depth of the trench, starting from the edge of the antenna arm in contact with the SWNT to its opposite end, where the trench gradually vanishes.
This trend matches the heating profile predicted by the FEA simulation. Scale bar, 5 mm. (f) Schematic illustration of an m-SWNT under an antenna without
direct contact. The AFM topography image and plot of the trench profile are from an m-SWNT in an array of well-separated SWNTs. The trench
not only exists in between the two antenna arms, but also extends underneath both arms. The heating profile computed using the circuit model with the
resistivity of the SWNT as the only fitting parameter (70 kO mm 1) matches the trench profile. Scale bar, 20 mm. (g) Average trench depth along the
SWNT, for 16 individual m-SWNT devices, as a function of the resistivity of the SWNT. The open circles and the red curve are heating profiles from the FEA
and circuit model, respectively. (h,i) SEM, AFM topography and FEA images of arrays of SWNTs with only one side in contact and without contact,
respectively. Scale bars, 15 mm.
dominated by the resistance rL0. Details of each value are in
Supplementary Note 3.
The geometry used for the purification process summarized in
Figs 1 and 2 (Supplementary Fig. 5) appears in the schematic
illustration near the top of Fig. 3d. The AFM topography image
and the graph illustrate the trench morphology and its depth as a
function of position along the m-SWNT, respectively. The
microwave conditions are 160 W, 70 °C, 3 h and the Tc-resist
has a thickness of B40 nm. Here the trench has a depth that is
independent of position along the m-SWNT. The linear relationship between trench depth and heating power (Supplementary
Fig. 11) implies a spatially uniform heating profile. Quantitative
calculations of the power density from FEA and the circuit model
follow from use of the resistance of the m-SWNT (r ¼ 80
kO mm 1) measured under DC conditions, and simulated
microwave radiation (equivalent voltage for the circuit) as the
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source (Supplementary Fig. 12). The DC value of r provides a
good approximation of the corresponding AC value because ot
oo1, where t (B10 12 s)38 is the characteristic scattering time
in SWNTs and o is the angular frequency of the microwaves
(2p 2.45 GHz). The simulations show a nearly constant heating
profile, consistent with experimental observations of the trench
depth. Based on the similarity in flow profiles, the temperature
increase associated with microwave irradiation can be assumed to
be similar to that associated with DC injection reported
previously34. Microwave heating power densities between 3 and
30 W m 1, therefore, correspond to temperature increases at the
top-surface of Tc-resist of between 2 and 15 °C (ref. 34).
In rare cases, the SWNTs make contact only to one side of the
antenna, as shown in the Fig. 3e. The corresponding AFM
topography image and profile of the trench depth associated with
a m-SWNT in this type of configuration (metallic type inferred
from the formation of the trench; Tc-resist B40 nm; microwave
conditions: 300 W, 70 °C, 3 h) reveal a spatial decrease in depth,
starting from the edge of the antenna arm that contacts the
m-SWNT and extending continuously to its tip end. This trend
matches the heating profiles calculated by FEA, as shown here in
arbitrary units (The profile is nearly invariant with r, for values
between 10 and 100 kO mm 1.). This behaviour indicates that the
current flow in the SWNT decreases continuously to zero at the
tip, as required by the boundary conditions at that location.
Another case of interest, as described subsequently, occurs when
the SWNTs span the gap but do not directly contact the antenna,
as shown in Fig. 3f. Here only capacitive coupling is important.
The AFM topography image and trench depth correspond to a
m-SWNT (determined by Raman microscopy) in a sparse array
(distances from adjacent SWNTs 43 mm) on a sapphire substrate
to facilitate Raman measurements47 (Supplementary Note 4 and
Supplementary Fig. 13). Here microwave exposure (160 W, 70 °C,
3 h) occurs, while antennas (LA ¼ 1,000 mm, WA ¼ 80 mm and
L0 ¼ 8 mm) on a cover glass are separated by a B1.1-mm air gap
above the SWNTs (see Methods). The results show that the
trench depth is largest at the centre region (L0) and gradually
decreases to zero within a distance shorter than the overlap length
(LC). With r ¼ 70 kO mm 1, the circuit model yields a spatial
variation in heating power that matches the observed trench
depth (Fig. 3f).qThese
variations take the form of |sinh2(x/LT)|,
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where LT 1=Cg þ 1=Cq =ior is the transfer length
(magnitude B9.5 mm in this case, Supplementary Note 3). As
the capacitive coupling mechanism does not require the antennas
to contact the SWNTs, it provides an interesting option in
purification, as described subsequently. On the other hand, direct
contact offers significant benefits in selectivity, also as described
subsequently.
By comparison to individual SWNTs, implementation with
arrays involves additional considerations related to wide variations in the electrical properties of the SWNTs48,49 (chiralities,
resistivities) and coupling (electrical, thermal, flow) between
them. The circuit model treats each SWNT (the centre part with
length L0) as a load with impedance Z0, which is dominated by
the resistance of the SWNT. Experimental validation of this
approach can be accomplished through studies of trenches
formed in isolated SWNTs with different resistances. The antennas
for these measurements use the structure in Supplementary Fig. 5
with Ti (2 nm)/Pd (48 nm) and L0 ¼ B8 mm. The experiments
involve Tc-resist with thickness of B50 nm, and microwave
conditions of 80 W, 60 °C and 3 h. Figure 3g plots the average
trench depth formed with 16 different m-SWNTs as a function of
their conductivity evaluated at a bias of 1 V (Supplementary
Fig. 14). The linear relationship is consistent with a dominant role
of the load impedance, as in the FEA simulation and the
6
equivalent circuit model. Arrays of SWNTs can be viewed as
individual SWNTs, electrically connected in parallel. Figure 3h,i
shows results obtained with arrays (160 W, 70 °C, 3 h, Tc-resist
thicknessB40 nm) for the cases of contact on one side and for no
contact with the antennas, respectively (contacts on both sides
appears in Fig. 1b). The depths of the trenches are different for
each of the SWNTs, likely due to variations in their conductances,
per results of Fig. 3g. FEA simulations of the heating power along
the lengths of the SWNTs provide some insights. Here the FEA
modelling treats the SWNTs as uniform resistors, with overall
magnitudes that incorporate the contact effects (quantum contact
resistances and Schottky barriers at the contacts) in an ad hoc
manner. Quantitative treatments using 1D drift diffusion models,
described subsequently, capture the detailed physics of these
barriers. The results in Fig. 3h include 7 SWNTs with a small r
(53.3 kO mm 1, derived from the total resistance measured on
the entire array before isolation from one contact), and 15
SWNTs with large r (5,330 kO mm 1 to represent the SWNTs
that do not form trenches17,50). The magnitudes of the computed
power inside each SWNT in the array are directly related to the
values of r. For this particular geometry, SWNT–SWNT coupling,
although present44, does not have a significant effect on the
results. The non-contact case (Fig. 3i) also shows a distribution
of trench depths. Here assignments of SWNTs with various
resistivity (50 kO mm 1 to represent the most conducting
SWNTs37; 150 kO mm 1 to represent moderate conducting
ones51; 5,000 kO mm 1 to represent the least conducting
ones50) in the FEA allow correlation of the conductances of the
SWNTs with the magnitudes of heating, as also expected from the
equivalent circuit results.
The purification process relies critically on selective heating in
the m-SWNTs. The discussions above relate the resistance of the
SWNTs to the heating power imparted into the SWNTs.
Although s-SWNTs are generally more resistive than m-SWNTs,
unintentional doping51,52 and other effects can diminish these
differences. Selectivity in such cases can be greatly enhanced by
the Schottky barriers that form at the contacts between the
antenna metal and the s-SWNT. These barriers lead to large
impedances that block the flow of current (that is, reflect
microwave power). Systematic experimental and computational
studies of trench formation with antennas constructed using
different metals reveal the underlying physics. The investigation
begins with a comparison of average currents measured under
DC conditions using two terminal test structures (channel length
B15 mm, width B50 mm, Supplementary Fig. 5) formed with
various metal contacts, as a means to assess the magnitudes of the
Schottky barriers. Figure 4a shows the results, scaled on a per tube
basis (each data point averages more than 100 SWNTs) at bias
voltages of 1, 5, 10 and 20 V, for different metals (Ti (1 nm)/Pd
(49 nm), Au (50 nm), Mo (50 nm), Ti (50 nm), Al (50 nm) and Ti
(1 nm)/Mg (70 nm)). The most prominent trend is a decrease in
current with work-function, consistent with an increase in the
magnitude of the Schottky barriers between the metals and the
s-SWNTs. Intrinsic s-SWNTs have a Fermi level at the middle
bandgap level B4.78 eV (ref. 53). In practice, s-SWNT often are
unintentionally doped (for example, oxygen or water)17,51, in a
way that shifts the Fermi level towards the valence band, to favour
hole transport (schematic of band diagram in Supplementary
Fig. 15a). High work-function metal contacts (Pd and Au) are
therefore almost transparent to hole injection (schematic band
diagram in Supplementary Fig. 15b). As the work-function
decreases, Schottky barriers increase in significance, with an effect
of restricting the current flow (schematic band diagram of Mo, Ti,
Al, Mg in Supplementary Fig. 15c,d). Quantitative self-consistent
DC drift-diffusion transport simulations support these trends
(Fig. 4b,c, Methods section and Supplementary Note 5). The
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20 V
4
6 10 V
3
5V
2
2
0
1
1V
8
10 V
4
5V
2
Ti/Pd Au Mo Ti
Al Ti/Mg
Metal antenna
1.00
h/H
0
1V
0.50
Au (5.0 eV)
0.50
0.00
0.00
0.00
–0.25
–0.25
–0.25
1.25
1.25
1.00
Exp.
Sim.
1.00
0.0
0.2 0.4 0.6 0.8
CDF of SWNTs
h/H
0.50
1.0
Ti (4.3 eV)
0.25
Al (4.1 eV)
0.50
0.2 0.4 0.6 0.8
CDF of SWNTs
1.0
1.00
Exp.
Sim.
0.75
0.50
Mg (3.7 eV)
0.25
0.25
0.00
0.00
0.00
–0.25
–0.25
–0.25
0.0 0.2 0.4 0.6 0.8 1.0
CDF of SWNTs
0.0
1.25
Exp.
Exp. Tc half thick
Sim.
Sim. Tc half thick
0.75
0.75
Mo (4.6 eV)
0.25
0.25
0.0 0.2 0.4 0.6 0.8 1.0
Exp.
Sim.
0.75
CDF of SWNTs
h/H
5V
1.00
h/H
h/H
Pd (5.1 eV)
1
1.25
Exp.
Sim.
0.75
0.25
20 V
2 10 V
Ti/Pd Au Mo Ti
Al Ti/Mg
Metal antenna
1.25
Exp.
Sim.
0.75
0.50
1V
Sim.: s-SWNTs
3
Al Ti/Mg
Ti/Pd Au Mo Ti
Metal antenna
1.25
1.00
20 V
6
0
0
4
Sim.: m-SWNTs & s-SWNTs
h/H
4
10
Average current (μA)
5
Average current (μA)
8
6
Exp.: m-SWNTs & s-SWNTs
Work-function (eV)
Average current (μA)
10
0.0 0.2 0.4 0.6 0.8 1.0
CDF of SWNTs
0.0 0.2 0.4 0.6 0.8 1.0
CDF of SWNTs
Figure 4 | Study of the mechanism for selective current injection into the m-SWNTs. (a) Average current per SWNT (black symbols) evaluated in two
terminal test structures at bias voltages of 1, 5, 10 and 20 V, for different metals. Data for each metal type correspond to results averaged from more than
100 SWNTs. The average current decreases as the work-function of the metal decreases. (b,c) Simulations of the average current per SWNT for different
metal contacts. The simulation averages the currents from SWNTs with different diameters consistent with experimental measurements. For b, the
simulation assumes that one-third of the SWNTs are metallic. For c, the results involve only s-SWNT. The general trends from simulations match the
experimental observations. As the work-function of the contacts decreases, the current in the s-SWNTs decreases due to the formation of the Schottky
barriers at the contacts of the s-SWNTs. The slight increase of the current for Mg contact arises from band-to-band tunnelling effects. (d–i) Experimental
and simulated statistics of the normalized trench depths for different metals as the antennas during the microwave process, (d) Pd (113 SWNTs), (e) Au
(229 SWNTs), (f) Mo (159 SWNTs), (g) Ti (311 SWNTs), (h) Al (337 SWNTs), (i) Mg (170 SWNTs). For metals with relatively high work-function, such as
Pd and Au, both the m-SWNTs and some fraction of the s-SWNTs create trenches. For metals with low work-function, such as Mo, Ti, Mg, a distinct onset
in the trench depth statistics separate the m-SWNTs from the s-SWNTs. The Al antenna results in a continuous distribution of trench depths, and a gap
appears when the thickness of the film decreases to B20 nm. This result suggests insufficient heating for the m-SWNTs, possibly due to the poor
wettability of Al on the SWNTs. The simulations match the experimental results, thereby verifying that the Schottky barrier plays a key role in the selective
heating of the m-SWNTs.
simulations average the currents from SWNTs with different
diameters (Supplementary Fig. 16a). The results of Fig. 4b assume
that one-third of the SWNTs are metallic; Fig. 4c shows results
that include only s-SWNTs. As in experiment, decreases in the
work-functions increase the Schottky barriers, thereby decreasing
the average currents in the s-SWNTs. A slight increase in current
for the case of Mg arises from band-to-band tunnelling. The
simulations treat the m-SWNTs as the same, in terms of contact
properties (the quantum contact resistance h/4e2), for all metal
types. Additional effects such as wettability of the metals on the
SWNTs54 may account for the differences between the measured
and simulated current values. To illustrate the significant effects
of Schottky barriers on the microwave heating characteristics,
squares in Fig. 4d–i show the experimentally measured statistics
associated with the normalized trench depths observed in arrays
of SWNT with different metal antennas (250 W, 73 °C and 3 h for
all metals except Pd, which used 300 W, 70 °C, 3 h; TC-resist
thicknessB35 nm). The sharp transitions between 0.62 and 0.68
in the CDF for the low work-function metals (Mo, Ti, Al, Mg) are
consistent with the experimentally demonstrated selectivity for
the case of Ti. The CDF shows smooth variations for high workfunction metals (Pd, Au). Al represents an exception to these
trends, where sharp and smooth variations occur for Tc-resist
thicknesses of B20 and B40 nm, respectively. We associate these
behaviours with poor wetting of the Al onto the m-SWNT,
thereby leading to high contact resistances. Simulation of the
heating power (proportional to the trench depth) includes
Schottky barriers (derived from the DC transport, see Methods
section and Supplementary Note 5) in the total impedance
calculation (for s-SWNTs). The simulated statistics (stars in
Fig. 4d–i, plotted as normalized trench depth) match the observed
distribution of trench depths for various metal types investigated
here (with the exception of Al, for reasons described above).
Detailed studies of the effects of the diameter distributions of
s-SWNTs in the grown arrays indicate efficacy in purification
across the entire range of diameters when the antennas involve
low work-function metals (for details, see Supplementary Fig. 16).
These experimental and computational studies support the
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ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6332
assertion that metals with high work-function (Pd and Au) allow
current injection, and therefore Joule heating, in both the
m-SWNTs and a portion of the s-SWNTs. Metals with low
work-function such as Mo, Ti, Mg, allow current only in the
m-SWNTs. The Schottky barriers at the contacts are, therefore,
beneficial to selectivity in the purification process.
purification; an optical image of the antenna mask in contact with
the SWNT substrate (quartz); AFM topography image of the
trenches and the SWNTs after etching. The separation between
the antennas (LA ¼ 1,500 mm, WA ¼ 80 mm, Ti (2 nm)/Pd
(48 nm)) and the quartz substrate is B1.1 mm during the exposure (Tc-resist B50 nm; microwave conditions: 80 W, 60 °C, 3 h).
The CDF of the trench depths (averaged on the centre segment
L0 ¼ 8 mm) for 112 SWNTs appears in Fig. 5c. The smooth distribution is consistent with the absence of Schottky barriers that
would result from physical contact. In this case, the heating
characteristics depend mainly on the values of r and the capacitive coupling strength between the antenna and the SWNTs, as
estimated from the equivalent circuit model (Supplementary
Fig. 17). As a result, trenches form at some portion of the
s-SWNTs. In a practical sense, all m-SWNTs and some of the
s-SWNTs can be removed completely; different regions of
operation correspond to complete removal (judged by AFM and
SEM), partial removal (judged by SEM and empirical evidences
from electrical probing) and complete preservation, as illustrated
in Fig. 5c. Measurements on transistors built using small arrays of
SWNTs (channel length ¼ 30 mm, width ¼ 35 mm, source-drain
contacts Ti (2 nm)/Pd (48 nm), dielectric SU8 2002 ¼ 2 mm)
purified in this manner verify these behaviours (Fig. 5d). The
extent of removal of s-SWNT can be minimized by eliminating
any unintentional doping55, a capability that is likely important,
in any case, for practical use of s-SWNTs in electronic circuits.
Purification based on removable antennas. Even without the
Schottky barriers, however, some level of effectiveness in purification is possible, mainly based on differences between r for
m-SWNTs and s-SWNTs (Supplementary Fig. 17). An important
opportunity that emerges is the ability to use non-contact,
capacitive coupling (Fig. 3f,i) with removable and reusable
antenna structures (Supplementary Fig. 18). Figure 5a shows a
schematic illustration of such a process. Microstrip dipole
antennas patterned on a glass substrate with micropillars of
poly(dimethylsiloxane) (PDMS) form an ‘antenna mask’. This
mask can be laminated on a substrate that supports an array of
SWNTs with an overcoat of Tc-resist. Exposure to microwave
radiation leads to heating at sufficient levels to create deep
trenches at the m-SWNTs for their removal by RIE. The
micropillars hold the antenna mask and substrate together at a
constant separation distance (set by the height of the micropillars) during the exposure. The mask can be peeled away for reuse (Supplementary Fig. 19). Figure 5b shows a corresponding
series of images, including an SEM of the SWNTs before
E
a
a
nn
nn
te
An
e
nt
H
A
PDMS
micropillars
PDMS pillar
Antenna area
Antenna
Antenna
Antenna area
Marker on the
receiving substrate
50
10–6
Full elimination
10–7
Partial damage
30
20
10–8
–ID(A)
h (nm)
40
10–9
10–10
10
Full preservation
10–11
0
0.0
0.2 0.4 0.6 0.8
CDF of SWNTs
1.0
10–12
–90 –60 –30 0 30
VGS (V)
60
90
Figure 5 | Purification based on removable antennas. (a) Schematic illustration of a process that uses removable antennas formed on a glass
substrate with PDMS micropillars. Laminating this type of antenna mask on a substrate with aligned SWNTs coated with Tc-resist, followed by microwave
irradiation results in sufficient heating to create deep trenches at the m-SWNTs. The micropillars hold the antenna mask and substrate together at a
constant distance during the process. The mask can be removed afterward, for reuse. (b) Images corresponding to each step shown in the schematic
illustrations: SEM image of the SWNTs before the purification (scale bar, 15 mm); optical image of the antenna mask after contacting the quartz substrate
(scale bar, 50 mm); AFM topography image of the trench formation and SEM image after the etching and washing away the Tc-resist (scale bars, 15 mm).
(c) Cumulative distribution function of the average trench depths (averaged on L0 ¼ 8 mm) for 112 SWNTs. The continuous distribution of trench
depths suggests that both m-SWNTs and some fraction of the s-SWNTs generate heat to create trenches. As a result, all m-SWNTs and a portion of
s-SWNTs can be removed, depending on the trench depths, which are marked in regions that correspond to full elimination (judged by AFM and SEM),
partial elimination (judged by SEM and empirical evidence from electrical probing) and full preservation. (d) Transfer curve from a typical transistor
that uses arrays of SWNTs purified with an antenna mask.
8
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The removable antenna is advantageous, because it eliminates the
need to perform any processing on the SWNT substrate. Further
improvements in its selectivity will make this approach the
technique of choice for microwave purification.
Discussion
The schemes presented here provide straightforward, scalable and
effective routes to aligned arrays of purely s-SWNTs, with
minimal processing. The significant reduction and, for removable
antenna approaches, the complete elimination of processing on
the nanotube substrate for microwave purification represent
significant simplifications compared with previously described
Joule heating approaches34 using electrode structures for gate
modulation. The method here is uniquely well suited for use with
aligned arrays of SWNTs on solid substrates, where the
nanotubes are optimally configured for direct integration into
devices with conventional designs. Although not directly
applicable to bulk SWNTs, the levels of purity in s-SWNTs that
can be achieved significantly exceed those currently possible with
other techniques, and there is no need for any solution separation
or chemical modification of the SWNTs56. All aspects of the
purification process are scalable to large areas, and we did not
observe any residues associated with etching the m-SWNT
(Residue can sometimes arise from photoresist processing and
removal of the Tc-resist.). The resulting arrays are well configured
for use in various applications, ranging from sensors to low noise
RF amplifiers. With sufficiently powerful microwave sources, it
may be possible to eliminate the antenna structures entirely
(Supplementary Fig. 1), thereby further simplifying the process.
Under optimized conditions trench widths of 100–200 nm
(ref. 34) should be possible (Supplementary Fig. 20), thereby
enabling arrays with densities up to B5 SWNTs per mm.
Significantly improved densities should be possible with arrays
that have enriched content of semiconducting SWNTs realized by
selective growth techniques25,26.
Methods
Growing horizontally aligned SWNTs. The growth process began with preparation of substrates by cutting quartz wafers (ST-cut; Hoffman) into dies
(1.65 cm 6.5 cm; Disco DAT-6TM dicing saw), and annealing them for 16 h at
900 °C in air. Photolithographic patterning of resist (AZ 5214 positive photoresist),
deposition of metal (Fe, 0.2B0.8 nm; electron-beam evaporation, AJA) and lift-off
processing defined strips of catalyst (10 mm wide, spaced by 200 mm) oriented
perpendicular to the preferred growth direction on the quartz. Annealing the
substrate at 950 °C in air for 1 h, cooling to room temperature and then heating to
925 °C again under a flow of H2 (200 s.c.c.m.) prepared the catalysts for growth.
Finally, introducing ethanol (bubbled from a flask at 0 °C by 30 s.c.c.m. H2 and
30 s.c.c.m. Ar) into the growth tube at 925 °C for 30 min yielded horizontally
aligned arrays of SWNTs.
Purification via microwave induced thermocapillary flows. Photolithography
(AZ 2020 negative photoresist), electron-beam evaporation (Ti 50 nm, AJA) and
lift-off defined arrays of microstrip antennas. RIE (100 mTorr, 19.6 s.c.c.m. O2,
100 W, 45 s; Plasma-Therm RIE) through a photoresist mask (AZ 5214) removed
SWNTs everywhere except for regions between the gaps of the microstrip antennas.
Thermal evaporation (Kurt Lesker) yielded a uniform, thin layer (typically
30–50 nm) of Tc-resist a,a,a’-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene
(TCI International). Placing the coated substrate into a 10-ml vial purged with inert
gas (Ar) provided a consistent environment for microwave exposure. Transferring
the vial to the microwave oven (CEM discovery SP) enabled exposure under
controlled conditions (power, maximum temperature and time; a summary of
microwave exposure conditions for all experiments described in the main text
appears in Supplementary Fig. 21). An infrared sensor monitored the temperature
of the vial during the experiments. Cooling the vial with a constant flow of nitrogen
during exposure helped to maintain a constant temperature. A set of schematic
illustrations and optical images of the reactor and the position of the sample and
the temperature sensor appear in Supplementary Fig. 3. After microwave radiation
and associated thermocapillary flow, RIE (10 mTorr, 1 s.c.c.m. O2, 1 s.c.c.m. CF4,
60B80 W, 17 s; Plasma-Therm RIE) removed the exposed m-SWNTs, without
affecting the s-SWNTs. Stripping away the Tc-resist with acetone completed the
process of forming arrays of purely s-SWNTs.
Fabrication and measurement of transistors. Fabrication of large-scale transistors (channel length Lch ¼ 15 mm, channel width Wch ¼ 1 mm) based on largearea, purified arrays of SWNTs used Ti microstrip antennas as the source-drain
electrodes. Spin-coating PMMA (950 A7, 1,500 r.p.m. for 45 s and then 4,000 r.p.m.
for 30 s, baking 10 min at 110 °C) as the dielectric, and depositing Ti (50 nm) as the
top-gate through a shadow mask completed the fabrication processes.
Forming transistors (Lch ¼ 15 mm, Wch ¼ 50 mm) with pristine, small arrays of
SWNTs followed the same procedures described above. After measurements
(semiconductor parameter analyzer; Agilent, 4155C), immersing the transistors
into acetone removed the PMMA and lifted-off the top-gates. Microwave and
etching processes eliminated the m-SWNTs from the arrays. After purification,
transistors fabricated with the s-SWNTs facilitated direct comparisons of electrical
properties with those from the as-grown, unpurified SWNTs.
To obtain transistors with low hysteresis and low operating voltages,
photolithography (AZ 2020 negative photoresist) and electron-beam evaporation
(2 nm Ti, 48 nm Pd) defined fresh contacts (Lch ¼ 5 mm, Wch ¼ 65 mm) on the
purified arrays. Spin-casting a thin layer of an epoxy photoresist (diluted SU8, SU8
2000.5: cyclopentanone ¼ 1:7; 3,000 r.p.m. for 30 sB50 nm), then baking at 175 °C
for 1 h in glove box formed the first layer of the dielectric. Atomic layer deposition
(120 °C; Cambridge NanoTech) of HfO2 (5 nm) formed the second layer. Finally,
lithography (AZ 5214), electron-beam evaporation (50 nm Ti) and lift-off defined
the gate electrode.
Forming two-terminal (2T) devices with individual SWNTs derived from arrays
of SWNTs with low density (0.1–0.3 SWNTs per mm) followed similar procedures.
After forming the contacts, photolithography (AZ 5214) and subsequent RIE
(100 mTorr, 19.6 s.c.c.m. O2, 100 W, 45 s) removed all of the SWNTs except those
protected by narrow regions (B3 mm in width). Scanning electron microscopy
(SEM, Hitachi, S-4800) and electrical analyses (Agilent, 4155C) further defined a
subset of devices with only a single SWNT bridging the electrodes. Fabricating and
characterizing transistors based on such 2T devices used gates on PMMA gate
dielectrics, as described previously, to identify the m-SWNTs and s-SWNTs from
the electrical responses.
Fabricating and applying removable antenna masks. Removable antenna masks
used cover glass (gold seal, No.1, 0.13–0.17 mm thick; Fisher Scientific) as the
supporting substrates, and molded micropillars of PDMS as the adhesive media.
The fabrication began with patterning the metal antennas (Ti 50 nm or Ti 2 nm/Pd
48 nm), and then depositing a thin overcoat of SiO2 (40 nm). Subsequent photolithography defined square windows on another cover glass to form the mold. Spincasting (4,000 r.p.m., 60 s) a layer of diluted PDMS (two components mixed with
1:30 weight ratio, then diluted by Hexane with 1:16 volume ratio) onto the base, and
then attaching the mold to the base in a mask aligner (MJB 4, Suss Microtec)
enabled the molding process. The base and mold were transferred into a vacuum
chamber (1 10 4 Torr, 10 min) to release trapped air bubbles. Baking on a hot
plate (120 °C, 8 h) fully cured the PDMS. Immersion in acetone for overnight
dissolved the photoresist on the mold. Peeling off the base and cutting it into
dimensions to match the quartz substrates formed the antenna mask. Application of
a mask to a substrate with arrays of SWNTs (patterned into lengths of 80 mm) and
Tc-resist relied on aligned transfer-printing. The PDMS micropillars held the mask
and the sample together with a constant distance (determined by the height of the
micropillars and the thin PDMS layer underneath, Supplementary Fig. 18) during
microwave exposure. After exposure, the antenna mask was simply removed.
Modelling of thermocapillary flow. The physics of thermocapillary flow can be
described by the one-dimensional lubrication equation,
2 @h
@ th2
h3 @
@ h
þ
¼0
ð1Þ
þ
g 2
3Z @x
@t
@x 2Z
@x
where h(x,t) is the film thickness, g is the surface tension, which usually depends
linearly on the surface temperature T of film (that is, g ¼ g0 g1(T 273)) where g0
is the surface tension at 273 K and g1 is the temperature coefficient of surface
tension, t ¼ (qg)/(qT)(qT)/(qx) is the thermocapillary stress, and Z is the film
viscosity. The initial condition is h(x,t ¼ 0) ¼ h0, where h0 is the initial film
thickness, and the boundary conditions are h(x ¼ ±N,t) ¼ h0 and q2h/
qx2(x ¼ ±N,t) ¼ 0 (zero pressure).
The power absorbed by the SWNTs is the summation of a steady-state component
Q0 (power per unit length) and a time-oscillating component Q(t)pwith
the frequency
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
on the order of GHz. The thermal diffusion length is defined by a=ð4pf Þ, where a
is the thermal diffusivity of the film and f is the frequency of microwave radiation. a is
usually on the order of 10 7 m2 s 1 for a polymer. For f on the order of 1 GHz, the
thermal diffusion length is less than 1 nm, which is much smaller than the film
thickness (B30 nm) such that the time-oscillating component of power yields a
negligible surface temperature rise. Therefore, the surface temperature in equation (1)
is mainly from the steady-state power Q0 and is given by34
1
TðxÞ ¼
2ks p
LZ=2
Z1
du
- L=2
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0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Q0 J0 x u2 þ x2
dx þ T0 ;
coshðxh0 Þ þ kkfs sinhðxh0 Þ
ð2Þ
9
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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6332
where T0 is the background heating, L is the SWNT length, ks and kf are the thermal
conductivity of substrate and film, respectively, and J0 is the 0th order Bessel function
of the first kind. Here kf ¼ 0.2 W m 1 K 1 and ks ¼ 6 W m 1 K 1 (refs 34,57). As
the Tc-resist used in the experiment exhibits similar behaviour as polystyrene with a
molecular weight 1,215 g mol 1, we take polystyrene’s surface tension with g0 and g1
as 47.4 10 3 N m 1 and 0.078 10 3 N m 1 K 1 (ref. 58), and viscosity
1640
Z ¼ 1:3810 4 eT 253 Pa s, where T has the unit of K, in our calculations. The Fortran
solver PDE_1D_MG can be used to solve equation (1) to yield the evolution of the
film thickness h(x,t).
FEA of the microwave field distributions. Three-dimensional finite element
simulations (COMSOL, RF module) yielded distributions of the microwave field
around the antennas. Implementation of the scattering field formalism with plane
waves (normalized E-field 1 V m 1, polarized along the length of the dipole
antenna) as the background field served as the platform for calculations of individual antennas. Treating the microstrip antenna and the SWNT with transition
boundaries (thickness 50 nm) simplified the meshing while retaining the essential
physics. Because of practical constraints in meshing, the SWNTs were modelled as
50 or 200 nm wide strips (with resistivity scaled to match the resistance of the
SWNTs per unit length). Perfectly matched layers enclosing the simulation domain
ensured no reflections of the scattered waves. Calculations of antenna arrays utilized the perfect electrical conductor and perfect magnetic conductor conditions for
the boundaries perpendicular to the background E-field and M-field, respectively,
to guarantee periodicity. Scattering boundary conditions imposed at the upper and
lower boundaries absorbed the scattered waves. The calculated E-field (within the
middle gap L0) of the antenna arrays differed by B2% from that of individual
antenna for the typical structure (LA ¼ 500 mm, WA ¼ 65 mm, L0 ¼ 15 mm, spacing
between antennas in the array ¼ 1,200 mm).
DC transport simulation for different metals as contacts. The average current
and total resistances of the SWNTs are determined by solving self-consistently the
3D electrostatics and the 1D drift-diffusion transport through the SWNTs. The 3D
electrostatics accounts of the full device geometry: the SWNTs on the quartz
substrate are terminated by source (S) and drain (D) contacts, and covered by
insulating material Tc-resist. The results show that carrier transport depends
sensitively on (i) the diameter of the tubes within the as-growth array, (ii) the
work-function of the contact materials (Pd (5.1 eV), Au (5.0 eV), Mo (4.6 eV), Ti
(4.33 eV), Al (4.1 eV), and Mg (3.7 eV))40,54,59 and (iii) effective applied bias, VDS
(extracted by correlating the equivalent trench depths in Tc-resist for DC and
microwave inputs). The source to drain of this two-terminal device is separated by
L0 ¼ 15 mm. These S/D contacts to the s-SWNTs may involve Schottky barriers
(work function of the contacto(electron affinity þ band gap) of the s-SWNT) or
they can be ohmic (work function of the contact4(electron affinity þ band gap) of
the s-SWNT). For the s-SWNTs, irrespective of the contact type, we solve the
electrostatics and charge density self-consistently17,50. We find that for the ohmic
contact, the electrostatic potential drops linearly through the channel, as expected;
whereas, for the Schottky contact, the potential drop depends on the contact
resistance and a self-consistent solution between electrostatic potential and charge
density is essential. For low Schottky barriers (related to high work function
contacts), the current is primarily thermionic; for very high Schottky barriers
(related to low work function contacts), the band-bending close to the source
contact can be significant enough to induce additional band-to-band tunnelling
current50. We note that the model is predictive because each component of the
model has been validated against independent experiments17,50. A detailed
description of the model follows.
Carrier transport in s-SWNT. The electrostatics potential, V, is a solution of
Poisson equation,
r:ðerV Þ ¼ r:
ð3Þ
Here the dielectric constant of the medium is e. The charge density, r, is a
function of the density of carriers (electron and hole), and fixed interface charges
(4.4 1019 cm 3)17. The fixed charges are determined by fitting the I–V
characteristics for one SWNT and subsequently kept constant for all other
simulations involving different diameters and contact work function. The electron
and hole concentrations must be calculated as a solution of the continuity and the
drift-diffusion equations, as follows.
1 dIn
1 dIp
R þ GSBT;n þ GBTBT;n ¼ 0;
þ R GSBT;p GBTBT;p ¼ 0:
q dX
q dX
ð4Þ
Where R is the direct band-to-band recombination rate, q is the electron charge,
X is the position variable along the SWNTs, and GSBT,n(p) and GBTBT,n(p) are the
generation rate in the channel for electron (hole) because of Schottky-barrier
tunnelling and band-to-band tunnelling, respectively, from the source and drain
contacts. The expressions for GSBT,n(p) and GBTBT,n(p) along the s-SWNT are
GSBT;nðpÞ ðXÞ ¼
10
h
2
exp pdV
dX ATtd 4
h
kB
exp pffiffiffiffiffi R
2 2m X
0
‘
pffiffiffiffiffi R
2 2m L
X
‘
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i h 1 þ expZnðpÞ i 3
þ
ErX;CðVÞ dr ln 1 þ expZ
nðpÞ;S
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i h 1 þ expZnðpÞ i 5;
ErX;CðVÞ dr ln 1 þ expZ
nðpÞ;D
ð5Þ
5 jdV=dX j2 td
EG2
:
ð6Þ
exp 2
d‘ vF jdV=dX j
9 p‘ vF
2
2
2
Here A ¼ 1.5 10 EGA cm K
is the Richardson constant, kB is the
Boltzmann constant, T is the lattice temperature and r is a position variable along
the SWNTs. Effective mass of electron and hole is m ¼ EGm0/20, where m0 is the
mass of free carrier. Zn,S(D) ¼ (EF,S(D) EC)/kBT, Zp,S(D) ¼ (EV EF,S(D))/kBT,
ErX,C ¼ EC(r) EC(X), ErX,V ¼ EV(X) EV(r), where EF,S(D) is the Fermi energy for
carriers in S(D) contact. From equation (6), : is the reduced Planck’s constant, t is
the wall thickness of the SWNT, |dV/dX| is the local electric field along SWNT. The
Fermi velocity (vF ¼ 108 cm s 1) depends the band structure of the SWNTs17. The
band gap of s-SWNTs is related to the diameter of the tubes (d) as EG ¼ 0.7/d eV
and d is the ideality factor. The drift-diffusion currents for electron (hole), In(p)in
equation (4) is represented as,
GBTBT;nðpÞ ðXÞ ¼
dV
dn
dV
dp
þ qDn
; Ip ¼ qpmFE
qDp
:
ð7Þ
dX
dX
dX
dX
Here ID ¼ In þ Ip is the current through the s-SWNT. The field-dependent
mobility is mFE ¼ mpeak/(1 þ mpeak|(dV/dX)|/vs), where the peak mobility,
mpeak ¼ 1,600(300/T)(d/1 nm)2, and vs is the carrier’s saturation velocity60. Dn(p) is
the electron (hole) diffusion coefficient. Additional information including
boundary conditions for Poisson and charge continuity and simulation procedures
is provided in Supplementary Note 5.
Carrier transport in m-SWNT. Regardless the S/D work function, metallic
carbon nanotubes form ohmic contact with source and drain. The electrostatic
potential drops linearly within the channel and charge carriers drift in this
potential profile. The current through the m-SWNT can be calculated as
ID ¼ (4q2/h)(leff/L0)VDS (ref. 38), where leff is the effective mean free path and h is
the Planck’s constant. The parameter leff can be expressed through Mathiessen’s
1 ¼ l 1 þ l 1, where l is the elastic scattering mean free path and
rule as leff
e
T
e
lT is the distance an electron must travel in the electric field to reach threshold
scattering energy (:O) to emit an optical phonon (:O ¼ 0.2 eV) or zone boundary
phonon (:O ¼ 0.16 eV)38. Specifically, lT ¼ :O/qEX, where EX ¼ VDS/L0 is
the average electric field along the m-SWNT. The current flow through the
m-SWNT, therefore, is ID ¼ (4q2/h)(leEX/(1 þ qleEX/:O)). The elastic scattering
mean free path is proportional to the m-SWNT diameter through the relation
le ¼ 300 d (ref. 37).
Once we know the current through each s-SWNT and m-SWNT (discussed
above), we calculate the average current for as-grown array SWNTs using
the diameter distribution obtained from experiments (Supplementary Fig. 7a
of
The average current for the as-grown array is computed as
P ref.s 17).
SWNT*PDF *0.67 þ Im SWNT*PDF *0.33]/P [PDF *0.67 þ PDF *0.33],
i[ID(i)
i
D(i)
i
i
i
i
where, i is the P
SWNT index. The P
average current of an array composed exclusively
SWNT*PDF /
of s-SWNT is iIsD(i)
i
iPDFi. We compute the total power dissipation
due to joule heating by integrating of the product of the current and local-field
along the SWNT, and assume that the heating and the trench-depth are linearly
correlated to the power dissipation along the channel. Finally, to differentiate
between s-SWNTs versus m-SWNTs, we obtain the CDF of diameter distribution
of the as-grown array SWNTs by integrating the probability density function
(Supplementary Fig. 7a of ref. 17) and normalizing it to 1. We subdivide CDF in a
2:1 ratio and assign the corresponding fractions to s-SWNTs (0–67%) and
m-SWNTs (68–100%).
In ¼ qnmFE
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Acknowledgements
We thank Wei Wang, To Wang and Pandu Wisesa for helping with the sample preparations, Hage Ali Sami and Slava V. Rotkin for helpful discussions. The experiments
were carried out in part in the Frederick Seitz Materials Research Laboratory Central
Research Facilities, University of Illinois at Urbana-Champaign. The work on the
microwave apparatus was in part supported by an NRO Director’s Innovation Initiative
award (NRO000-13-C0056). The research on fundamental understanding of the process
and demonstrations in transistors was supported in part by Systems on Nanoscale
Information fabriCs (SONIC), one of the six SRC STARnet Centers, sponsored by
MARCO and DARPA. The Purdue group acknowledges computational resources from
Network of Computational Nanotechnology and the financial support from the NSF
Center for Nanoengineered Electronic Devices for calculations of the effects of selectivity
associated with contacting antennas. J.S. acknowledges the supports from the National
Natural Science Foundation of China (Grant nos 11372272 and 11321202), and the
Thousand Young Talents Program of China.
Author contributions
X.X., A.E.I., W.L.W. and J.A.R. conceived and designed the experiments; X.X., S.H.J.,
A.E.I., F.D., S.N.D., H.I.C., Y.-C.T., Z.G., H.U.C., Y.Liu, J.-H.L., J.S., Y.H., M.A.A.,
W.L.W. and J.A.R. performed the experiments and analysis; X.X., M.A.W., C.Z., A.E.I.,
E.S., T.L., Y.Li, J.S., Y.H., M.A.A., W.L.W. and J.A.R. performed modelling and simulations; J.S., Y.H., M.A.A, W.L.W. and J.A.R. provided technical guidance; X.X., M.A.W.,
J.S., A.E.I., S.H.J. and J.A.R. wrote the paper.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests: The authors declare no competing financial interests.
Reprints and permission information is available online at http://npg.nature.com/
reprintsandpermissions/
How to cite this article: Xie, X. et al. Microwave purification of large-area
horizontally aligned arrays of single-walled carbon nanotubes. Nat. Commun. 5:5332
doi: 10.1038/ncomms6332 (2014).
NATURE COMMUNICATIONS | 5:5332 | DOI: 10.1038/ncomms6332 | www.nature.com/naturecommunications
& 2014 Macmillan Publishers Limited. All rights reserved.
11
a
b
c
80
60
2
µm
0
nm
40
500 μm
10nm Tc-resist
-2
20
Microwave 80
300W 1h 60C
-4
0
60
20
40
µm
60
80
0
30 μm
40
2
nm
µm
30 μm
0
-2
20
SWNT arrays on quartz
-4
0
e
Plane wave incident
E-field: 1 V/m
Along x
V/m
30
20
10
0
15 µm long SWNT
Abs (Ex) (V/m)
d
0.6
0
20
40
µm
60
80
0.4
0.2
Abs (Ex)
0.0
-10
-5
0
5
10
Position along the SWNT (μm)
Supplementary Figure 1. Microwave heating of SWNTs without antennas. (a) Schematic
illustration of arrays of SWNTs on quartz substrate with lengths up to 500 µm. These SWNTs
were grown by using catalyst strips with width of 40 µm and spacing of 600 µm.
Photolithographic patterning and RIE etching isolated the SWNTs from the catalyst regions.
(b) SEM image of a portion of the SWNT arrays. (c) AFM topography image of the same area
of the sample after microwave radiation (300 W, 1h, 60 0C, without any antennas). Very
shallow trenches (0 nm~3 nm) can be observed. The sample was coated with ~10 nm Tcresist. (d) E-field distribution around a SWNT (represented by a metal strip with Length=15
µm, width=50 nm, height=50 nm, and r=50 kΩ/μm in the FEA simulation). (e) Magnitude of
the E-field inside the SWNT, as a function of position along the SWNT.
a
C1 C2
C3 C4
C5
C6 C7 C8 C9 C10
6.5 mm
R1
1 mm
R2
R3
R4
16.5 mm
1.015 mm
Sample layout on a die
Basic unit
5
2.0
10
On current (mA)
On-off ratio
1.5
4
10
3
10
1.0
On current
2
10
1
10
0.5
On-off ratio
b
0
10
-1
0.0
10
0 1 2 3 4 5 6 7 8 9 10 11
Column
Supplementary Figure 2. Purification of large-area arrays of SWNTs. (a) Schematic
layout of the antenna structures. 40 blocks (4×10 array) of microstrip dipole antennas were
patterned on a centimeter-sized die. The inset shows one such blocks, which consists a pair
of rectangular metal strips spaced by 15 µm. (b) On-current and on-off ratio statistics of 40
transistors based on the purified SWNTs. Non-uniform distribution of the on-currents arises
from the variations in temperature induced by the microwaves. These variations lead to
degradation of the Tc-resist at some locations, resulting in insufficient protection of the SSWNTs during the RIE etching afterwards. The large temperature rise is caused by
simultaneously heating a large number of m-SWNTs (estimated as ~7000), and its nonuniformity is likely due to the insufficient heat dissipation at these high power levels.
10 ml vial
a
b
Nitrogen cooling
outlet
IR temperature
sensor
Cavity
IR temperature
sensor
Nitrogen cooling
outlet
c
d
Quartz
substrate
Side view
Front view
Supplementary Figure 3. Components of the microwave exposure systems. (a)-(b)
Schematic illustration and optical image of the various components in the main chamber of
the microwave oven. The IR temperature sensor is located in the center at the bottom. (c)-(d)
Schematic illustration and optical image of the position of the substrate inside the vial during
microwave irradiation.
c
b
a
PMMA
Before purification
PMMA
After purification
SU8/HfO2
New SD and dielectrics
Supplementary Figure 4. Steps to verify the effectiveness of the purification process.
(a)-(b) Fabrication and measurement of transistors built on small arrays of SWNTs before
and after the purification enables direct comparisons. The source and drain of the transistors
also serve as the antennas during the purification. Utilizing PMMA as the dielectric facilitates
the removal of the top gate structure after characterization. (iii) Patterning Ohmic contacts
(Pd) and high capacitance gate dielectrics of SU8/HfO2 yields transistors with performance
suitable for extracting intrinsic properties.
16.5 mm
b
a
0.9 mm
6.5 mm
0.6 mm
c
1 mm
Basic unit
• Sample size: 16.5 mm x 6.5 mm
• Physical dimension (W/L=65/15 um)
• Antenna contact metal: Ti
Supplementary Figure 5. Layout of antennas with small arrays of SWNTs. (a) Optical
microscope image of samples with Ti antenna structures (also serve as contacts for the
transistors). (b, c) Schematic illustration and SEM image for the basic unit and SWNTs,
respectively.
-2
10
-4
VDS=-0.1V
-4
10
-6
10
-8
10
-10
-12
-20
0
20
VGS(V)
10
40
d
0
-40
-20
0
20
VGS(V)
40
0
-20
-20
ID(A)
-8
-10
-40
-40
VGS=40V
VGS=20V
VGS=0V
VGS=-20V
VGS=-40V
-60
-80
-100
-120
-6
10
-12
c
Before TcEP
After TcEP
10
10
10
VDS=-1.0 V
10
-ID(A)
-ID(A)
10
-2
b 10
Before TcEP
After TcEP
-10
-5
VDS(V)
0
 Ion retention difference from transfer
curve:
•
VDS=-0.1V 2.6%
•
VDS=-1V 5.7%
•
More than 100% variation can
happen depending on drain
bias
-40
VGS=40V
-60
VGS=20V
VGS=0V
VGS=-20V
VGS=-40V
ID(A)
a
-80
-100
-120
-10
-5
VDS(V)
0
 Fully accumulation region in output
characteristics
•
VDS=-10V
•
-10V < VGS <-40V
•
Average value extraction
Supplementary Figure 6. Ion retention estimated from transfer curves and output
characteristics. (a, b) Transfer curves before and after purification at (a) VDS=-0.1V and (b)
VDS=-1V; (c, d) Output characteristics of (c) before and (d) after the purification.
0
ID(A)
After
-50
Before
-100
-150
VGS is changed from -10V to -40V
, with -10V step
-10
-5
VDS(V)
0
Supplementary Figure 7. Output characteristics before and after purification. Contact
resistance effects are mitigated when retention of the on current is estimated from output
characteristics before and after purification at the bias conditions of VDS=-10 V, for VGS from 10 V to -40 V.
b
2200
2000
1800
1600
1400
1200
1000
800
600
-2.0
1150
1100
µ (cm2/V/s)
µ (cm2/V/s)
a
Average mobility
1050
1000
950
-1.5
-1.0
VGS-VT (V)
-0.5
900
-2.0
-1.5
-1.0
-0.5
VGS-VT (V)
Supplementary Figure 8. Mobilities of purified SWNTs. (a) Extracted field effect mobility
from devices consisting of purified small-arrays of SWNTs, as a function of gate overdrive
(VGS - VT) and at Vds=-0.1V. Those devices use Ti/Pd as the new contacts, and SU8/HfO2 as
the dielectrics. (b) Average field effect mobility of all of the devices. Data are weighted
averages determined by the number of remaining SWNTs in each device.
a
b
90
120
Incident field: 1 V/m
Along Y direction
60
30
150
V/m
180
5
Y
X
0
240
d
30µm
70µm
20
120µm
10
150µm
0
100
50
0
50
100
14
12
10
8
6
4
2
0
0
270
1
2
300
3
4
5
Antenna thickness (μm)
X (µm)
e
Field enhancement factor (A.U.)
Field enhancement factor (A.U.)
30
330
210
Z
c
0
Incident field: 1 V/m
Along X direction
V/m
30
20
Y
X
Z
65 μm
10
0
Supplementary Figure 9. Operation of microstrip dipole antennas. (a) E-field distribution
induced by an incident wave polarized perpendicular to the lengths of antennas (E-field along
the Y direction). Dimensions of the antenna are LA=500 µm, WA=65 µm, tA=50 nm. (b) Polar
plot of the E-field enhancement for incident wave polarized in different directions. Only the
microwave component polarized along the length of the antenna contributes to the heating of
the SWNTs. (c) Line plots of E-field enhancements across the gap, for different gap
distances L0. Simulation results correspond to the case where no SWNTs are present in
between the antenna arms. (d) FEA result of E-field enhancement as a function of the metal
thickness. Data is from the center point within the gap between the two antenna arms.
Dimensions of the antenna are WA=65 µm, LA=500 µm. (e) Distribution of E-field when a
single m-SWNT bridges the two antenna arms. A strong induced E-field appears within the
SWNT. Dimensions of the antenna are WA=65 µm, LA=500 µm , tA=50 nm.
a
b
c
LA---Length of one antenna arm
WA---Width of the antenna
tA---Thickness of the antenna
λ---Wavelength of the microwave
σ---Conductivity of the antenna metal
Rr---Radiation resistance of the antenna
Ro---Ohmic resistance of the antenna
RA---Rr+Ro
XA---Reactance of the antenna
ε0εr---permitivity
Cg---Geometric capacitance between the
SWNT and metal antenna
Cq---Quantum capacitance of the SWNT
d---Distance between the SWNT and antennas
W---Spacing between SWNTs in the arrays
Vf---Femi velocity of m-SWNT
Lm ---Mutual inductance between the SWNT
and metal antenna
Lk ---Kinetic inductance of the SWNT
r --- Resistance of the SWNT per unit length
λeff --- effective mean free path
LT---Transfer length
RC---half of the quantum contact resistance
Supplementary Figure 10. Equivalent circuit model for the m-SWNT and antenna. (a)
Schematic illustration of the system. (b) Corresponding equivalent circuit. (c) Analytical
expressions and definitions for the key parameters of the equivalent circuit model.
400 min
200 min
0.8
0.8
70 min
h/H
0.6
0.4
1.0
15 (W/m)
0.6
5 (W/m)
0.4
10 min
0.2
0.0
0
3
6
9
12
0.0
0
100
Power density (W/m)
0.2
300
0.0
0
200
400
Right dipole arm
Left dipole arm
90 min
180 min
3
6
9
12
15
f
0
-15
30 min
65 0C
Power density (W/m)
e
2 μm
80 W 60 0C
2 (W/m)
1 (W/m)
Time (min)
40
30 min
-30
h (nm)
d
75 0C
0.6
0.4
0.2
15
85 0C
0.8
10 (W/m)
h/H
1.0
0
-15
90 min
-30
Trench depth (nm)
1.0
h/H
c
b
a
30
Theory fit: 𝝁𝟎 𝒌𝒇 𝑯/(𝜸𝟏 𝑸𝟎 )=60
H~35 nm
10 (W/m)
8 (W/m)
20
6 (W/m)
4 (W/m)
10
2 (W/m)
0
-15
180 min
-30
-1
0
0
0
50
100
Time (min)
150
200
1
Position (μm)
Supplementary Figure 11. Trench depths as a function of power, time and background
temperature. (a) Simulated trench depth versus power density at different times with the
background temperature T=65oC; (b) Simulated trench depth versus time at different power
densities at t=70min. (c) Simulated trench depth versus power density at different
background temperatures at time t=70min; The film is considered to similar to polystyrene,
with a temperature dependent viscosity of A*exp(B/(T-T)) where A=1.38e-4 Pas, B=1640K
and T =253K and surface tension of 47.4e-3-0.078e-3*(T-273) N/m (extracted from
supplementary Fig. 9d). (d, e) AFM topography images (d) and cross section plots (e) of
trench profiles from the same SWNT at different time intervals. (f) Trench depths at various
time intervals, extracted from different SWNTs under the same expose condition (80W 60oC).
Computational results on the same plot verify the scaling law.
a
b
10
0
h (nm)
15 µm
SEM
-10
4
2
0
-2
-4
10
-30
5
0
0
nm
µm
Microwave_160W
DC_70 µW_65C
DC_142 µW_65C
DC_220 µW_65C
-20
15
-0.5
Microwave_160W_70C(IR camera)_70min
10
20
25
30
µm
40
50
0.0
0.5
Position (μm)
60
c
20
10
4
15
nm
µm
2
0
10
-2
DC_16V(142μW)_65C_70min
0
20
0
10
20
30
40
50
60
70
µm
15
-10
4
Microwave_160W
DC_26 µW_75C
DC_43 µW_75C
DC_53 µW_75C
DC_83 µW_75C
2
0
-20
nm
µm
0
-4
h (nm)
5
25
10
-2
5
-4
-30
DC_8V(53μW)_75C_70min
0
0
10
20
30
40
50
60
-0.5
70
µm
0.0
Position (μm)
d
e
35
0.5
V/m
50
25
y=0.36x+1.22
30
0
h (nm)
25
20
15
T=75 C
T=65 C
10
5
0
0
y=0.15x-5.08
40
80 120 160 200
Power (μW)
Oven:160W ; Equivalent DC voltage: 8V
Equivalent AC voltage=11.3V;
Local equivalent Ex-field=11.3V/15um=7.5 ×105 (V/m)
Equivalent incident field: 7.5 ×105 (V/m)/46.6=1.6×104 (V/m)
Equivalent incident microwave intensity:
P=1/2*E^2/376.73=3.4×105 (W/m2)
Supplementary Figure 12. Estimation of the microwave intensity. (a) SEM image of an
individual m-SWNT and corresponding AFM topography images of trenches that form at
various conditions. (b,c) Comparisons of average cross-sectional trench profiles generated
by microwave radiation (160 W, 700C, 70min) with those generated by DC Joule heating at
various power levels at 650C (b) and 750C (c) for the same time 70min, respectively. For (b),
when the trench formed by DC Joule heating is deeper than that which originates from
microwave radiation, the width is noticeably smaller, which indicates a smaller background
heating. Trenches from DC heating at 53µW (8V) in (c) match well with those created by
microwave exposure, in both width and depth, suggesting a similar power level and
background heating. (d) Plot of the average trench depth as a function of DC Joule heating
power, showing a linear dependence. The slope is strongly affected by the background
temperature. (e) FEA analysis of the E-field distribution around the antenna and calculations
of the equivalent incident microwave intensity (total power of 160W).
80
a
SEM
60
40
AFM
20
20 μm
c
A.U.
RBM signal for 785 nm
Raman shift (cm-1)
250
0
200
0
20
40
µm
60
80
150
100
d
Raman Intensity (A.U.)
µm
b
2000
SWNT-15
1500
166 cm-1
1000
500
0
100
150
200
250
Raman shift (cm-1)
Supplementary Figure 13. Raman spectroscopy of SWNTs transferred onto sapphire
substrate . (a) SEM image of the aligned SWNTs after being transferred onto the sapphire
substrate. (b) AFM topography image of trench formations (microwave using removable
antenna LA=1000 μm, WA=80 µm and L0=8 μm, condition at 160W, 700C, 3h). (c) Raman line
scan across the center of the SWNT arrays (indicated by the dashed line in (a)) by 785nm
laser excitation. (d) Spectrum of the SWNT showing strong resonance in (c) (SWNT number
15, which is also the one shown in Fig. 2f). The peak ~166 cm-1 in the RBM region indicates
this SWNT is metallic.
a
b
5um
5um
VDS=- 0.1V
VDS=-1 V
10
-6
10
-7
-50
0
50
10
-100
100
VGS (V)
16
VDS=- 0.1V
VDS=-1 V
-5
-ID (A)
-ID (A)
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-100
-50
0
50
100
VGS (V)
12
10
14
4
8
5um 6
c
4
2
0
2
2
0
d
0
30
0
4
0
M-SWNT
S-SWNT
20
10
10
20
µm
0
30
h (nm)
6
5um
6
-
-2
20
µm-4
10
30
4
40
2
0
0.0 2.0µ 4.0µ 6.0µ 8.0µ 10.0µ
2T current (A)
100p
1n
10n
100n
1µ
2T current (A)
Supplementary Figure 14. Trench formations of Individual SWNTs in direct contact
with antennas . (a,b) Typical SEM image, transfer curve and AFM topography image of the
trench formation for the individual s-SWNT(a) and m-SWNT(b), respectively. The metals for
the antennas are Ti (2nm) / Pd (48 nm). (c) Statistics of the average trench depth along the
SWNTs, plotted against the two terminal currents (measured at 1V). (d) Magnified view of the
s-SWNT data in the dashed square in (c).
0
-
nm
8
h (nm)
µm
10
2
4
µm
12
40
b
a
Vacuum
 Mg
SWNT
Pd & Au
EFS
 Al
Ti
EC
 Mo
 Au
EG~1/d
Thermionic
 Pd
EV
EFD
Pd and Au, hole thermionic current
c
d
EFS
SBT
EC
Mo, Ti, & Al
EV
EFS
EC
Mg
EV
EFD
SBT
Mo, Ti, and Al, SBT current
EFD
BTBT, SBT, & Recomb
Mg, SBT, BTBT and recombination current
Supplementary Figure 15. Band diagrams for different metal as contacts. (a) Schematic
illustration of the Fermi levels of Mg, Al, Ti, Mo, Au, Pd, with respect to the band diagram of
the SWNT. (b-d) Schematic band diagram of the SWNT contacted by metals with relatively
high work-function (Pd, Au), intermediate work-function (Mo, TI, Al), and low work-function
(Mg). For Pd and Au contacts, thermionic current dominates; for Mo, Ti and Al contacts,
Schottky barrier tunneling is the major mechanism for current conduction, resulting a low
current level. For Mg contacts, band-to-band tunneling begins to play an important role,
thereby increasing the current slightly.
EG [eV]
(a)
(b)
1.4 0.64 0.41 0.3 0.24
Diameter distribution
Log-normal Fit
CDF of s-SWNTs
1.2
[a.u.]
1
0.8
Mo
0.6
0.4
Pd
0.2
0
0
1
2
d [nm]
3
Ti, Al, &
Mg
Au
4
Supplementary Figure 16. Diameter distribution of the SWNTs before and after the
purification. (a) Distribution of diameters of SWNTs in a typical array measured by atomic
force microscopy [ref.17 and ref. 48 in main text]. This diameter distribution is assumed to
characterize the distribution for both the metallic and semiconducting SWNTs. The bandgap
energy (EG) of corresponding s-SWNTs appears on the top axis, computed as 0.7/d (nm).
The cumulative distribution function (CDF) of the s-SWNTs is computed from a log-normal fit
of the diameter distribution by integration and then normalization to 67%. (b) Fraction of the
remaining s-SWNTs (relative to all of the SWNTs) as a function of the maximum diameter of
the remaining s-SWNTs, extracted from Figure 4d-i. Metals investigated in the experiments
are highlighted by the data points.
Heating power (A.U.)
in contact
5nm HfO2
1.1 µm air
1
10
0
10
-1
10
2
10
3
10
4
10
Resistivity (kΩ/µm)
Supplementary Figure 17. Simulation of microwave heating of SWNTs without
Schottky barriers. The circuit model shows that the heating power decreases as the
resistivity of the SWNTs increase. For removable antennas, decreasing the distance and
increasing the dielectric constant of the materials between the antennas and the SWNTs can
increase the capacitive coupling, thereby increasing the level of heating. Other parameters in
the calculations are: L0=8 µm, LC=36 µm, diameter of the SWNT=1.2 nm, and spacing
between SWNTs=2 µm.
Microstrip
antenna
a
b
Cover glass
Micropillar
PDMS
Photoresist
Cover glass
(Micropillar molding)
SWNTs
Quartz substrate
(Aligned transfer-printing)
Supplementary Figure 18. Fabrication process for the removable antennas. (a) Crosssectional schematic illustration of molding micropillars by PDMS. (b) Schematic illustration of
the structure after transfer printing, where the microstrip antennas are held at a constant
distance from the SWNTs.
PDMS Pillar
a
b
Antenna
Markers
on the
quartz
substrate
Antenna
80 µm
c
8080
d
80
6060
60
0 0
0
nm
nm
µm
µm
-2 -2
4040
-2
-4
nm
µm
-4 -4
40
-6 -6
2020
-6
-8 -8
20
-8
0 0
first expose
0 0
0
2020
Second
4040Expose6060
8080
µmµm
0
20
40
µm
60
80
Supplementary Figure 19. Multiple exposures using removable antennas. (a,b) Optical
microscope images of the antenna masks when in contact with the quartz substrates, for the
first and second exposures, respectively. The microstrip antenna is shifted upwards for the
second exposure. (c,d) AFM topography images of the trenches formed after the first and
second exposure, respectively. Arrows mark the vertical position of the center of the
microgap. Trenches extend as the removable antennas shift, proving the effectiveness of this
multiple exposure process.
a 20
b 20
c 20
15
15
10 (W/m)
10
WT/H (A.U.)
15
WT/H (A.U.)
WT/H (A.U.)
5 (W/m)
10
H=25 nm
H=40 nm
5
5
0
0.0
0.2
0.4
h/H
0.6
0.8
1.0
0
0.0
0.2
0.4
0.6
h/H
0.8
10
T=65 C
T=75 C
5
1.0
0
0.0
0.2
0.4
0.6
0.8
h/H
Supplementary Figure 20. Computational results for trench widths under various
conditions. The dependence of trench profile on (a) power density with background
temperature T=65oC and film thickness 40 nm, (b) film thickness with background
temperature T=65oC and power density 5 W/m, and (c) background temperature with film
thickness 40 nm and power density 5 W/m. The results are obtained at t=70 min. The film
is similar to polystyrene with a temperature dependent viscosity of A*exp(B/(T-T)) with
A=1.3810-4 Pas, B=1640 K and T =253 K and surface tension of 47.4 10-3-0.078 10-3
*(T-273) N/m.
1.0
Temperature (0C)
74
3h expose
72
70
68
66
64
62
60
58
50 100 150 200 250 300 350
Large array
purification condition
Small array
purification condition
Removable antenna
based purification
condition
Power (W)
Supplementary Figure 21. Summary of microwave conditions described in the main
text. The conditions used for purification used exposure times of 3 hours.
VGS=-10V
VGS=-20V
VGS=-30V
VGS=-40V
Before TcEP
-9.68E-05
-1.04E-04
-1.07E-04
-1.09E-04
After After TcEP
-2.94E-05
-3.68E-05
-4.15E-05
-4.47E-05
Ratio
3.03E-01
3.53E-01
3.86E-01
4.11E-01
Average Ratio
0.36
STD
0.05
Supplementary Table 1. Ion retentions based on the output currents at VDS=-10 V. Data
in this table is extracted from Supplementary Fig. 7. The average value is calculated from 4
data points, including VGS=-10 V, VGS=-20 V, VGS=-30 V and VGS=-40 V.
on_off ratio (VDS=-1V)
Ion retention
Device No.
Total SWNTs
Removed SWNTs
Removed Ratio
output
Before
After
1
16
6
0.38
0.43
3.20E+00
5.27E+03
2
24
9
0.38
0.41
2.19E+00
4.16E+03
3
27
9
0.33
0.19
1.94E+00
1.34E+03
4
15
4
0.27
0.36
1.96E+00
8.04E+03
5
24
4
0.17
0.57
1.71E+00
4.77E+04
6
21
4
0.19
0.17
1.72E+00
2.30E+04
7
18
8
0.44
0.06
2.60E+00
3.39E+04
8
9
10
25
25
14
11
8
5
0.44
0.32
0.36
0.22
0.41
0.43
1.78E+00
2.19E+00
3.20E+00
5.32E+03
4.16E+03
5.27E+03
11
13
5
0.38
0.35
2.46E+00
3.73E+04
12
23
8
0.35
0.29
2.32E+00
2.02E+05
13
18
4
0.22
0.51
1.94E+00
1.26E+04
14
16
8
0.50
0.21
2.30E+00
2.09E+03
15
23
10
0.43
0.26
1.69E+00
4.03E+04
16
21
9
0.43
0.23
1.46E+00
1.55E+04
17
20
5
0.25
0.61
3.11E+00
8.53E+04
18
20
5
0.25
0.59
4.34E+00
1.47E+04
19
15
6
0.40
0.39
1.85E+00
3.78E+05
20
31
15
0.48
0.32
1.88E+00
2.07E+03
143
0.35
0.35
2.29E+00
4.63E+04
0.09
0.15
7.13E-01
9.24E+04
409
STD
Supplementary Table 2. Statistical data of SWNTs before and after purification. The
average fraction of SWNTs removed is 0.350.09, determined by SEM and AFM analysis
before and after the purification. The fractional current retention (i.e. Ion retention) is
0.350.15, as estimated from the output characteristics. The average current on/off ratio after
purification is (4.63 9.24) x 104.
Supplementary Note 1: Multi-cycles of Tc-resist deposition and microwave radiation
Three cycles of Tc-resist deposition and microwave irradiation ensure the full protection of the
unexposed s-SWNTs, even when processing conditions of the etching tools vary slightly. Details
of the processes are: (1) deposition of Tc-resist (~35 nm), and microwave irradiation at 250 W,
73 0C, 3 h; (2) deposition of Tc-resist (~20 nm), and microwave irradiation at 200 W, 65 0C, 3 h;
(3) deposition of Tc-resist (~20 nm), and microwave irradiation at 200 W, 65 0C, 3 h. This
multiple layer scheme enhances the etch resistance by increasing the thickness of the Tc-resist.
Furthermore, the multiple depositions also help to eliminate the effects of pinholes that form in
single layers.
Supplementary Note 2: Mobility extraction
The characterization of average field effect mobility () per SWNT within a device at
different VGS involves modeling of ID-VGS characteristics, measured at VGS >> VT and at small
VDS ~ 0.1V, using the following expression:
I D  CG W L VGS  VT VDS
(1)
Here, W = 50 μm is the width and L = 5 μm is the length of the transistor. Threshold voltage (VT)
for equation (1) is calculated from the x-axis intercept of the slope on ID-VGS curve, drawn at
maximum transconductance (gm,max ≡ max of ∂ID/∂VGS) point. Gate to channel capacitance (CG)
is calculated by considering the effect of SWNT density (DSWNT = 1/λ0, where is the average
spacing between two SWNTs) and quantum capacitance (CQ)1:
CG  0  Cox1  CQ1 
In equation (2), oxide capacitance (Cox) is defined using –
(2)
Cox 
2 SiO2
(3)
  sinh  2 EOT / 0  
ln  0

 rSWCNT


where εSiO2 is the dielectric constant of SiO2, rSWNT is the radius of SWNT, and EOTSU8, EOT are
the effective oxide thickness for SU8 and the entire dielectrics, respectively: 2
EOTSU 8  rSWNT [(1 
TSU 8 ( SiO2 / SU 8 )
)
 1]
rSWNT
EOT  EOTSU 8  EOTSU 8 [(1 
THfO2
(4)
( SiO2 /  HfO2 )
 1] (5)
EOTSU 8
Here, the definition of EOT allows simplification of the electrostatics within the dielectric
)
stack that contains 50 nm SU-8 and 5 nm HfO2, where T(…) and ε(…) are the nominal thickness
and dielectric constant (~ 25 for HfO23 and ~ 4 for SU-84,5) for respective dielectrics. (Dielectric
constants for the dielectrics may vary depending on the deposition recipe for HfO26, or the
dilution/coating recipe for SU-8. However, even a 20% variation in dielectric constant results
only a ~5% variation in extracted . Finally note that the effect of contact resistance ~ 28 kΩ7 is
ignored during mobility extraction for these long-channel length devices.)
Supplementary Figure 8a plots extracted average mobility per SWNT for a set of devices as
a function of gate overdrive (≡ VGS - VT). Extracted mobility reduces at higher gate overdrive for
all the devices because of the availability of higher scattering centers or density of states.
Mobility values populated at ~ 1100 cm2/V-sec at lower gate overdrive and reduces to ~ 900
cm2/V-sec at higher gate overdrive, as also evident from the average mobility (averaged over all
the measured devices) plot in Supplementary Fig. 8b. Extracted mobility is slightly higher than
the values (~ 1000 cm2/V-sec) that we reported in our previous report on sorted SWNTs8.
Simplicity of the sorting process is believed to the origin for this improvement.
Supplementary Note 3: Discussion of equivalent circuit model
Equivalent circuit in Fig. 2c and Supplementary Fig. 10a-c show three major regions, namely the
antenna region, the contact region, and the load region.
For the antenna region, the equivalent voltage is inferred from FEA simulation and associated
experiments (Supplementary Fig.12). The resistance (~120 Ω) of the antenna is negligible
compared to the contribution of capacitance to the impedance (~-4×103 Ω, or ~-1×104 Ω if
assuming surroundings of antennas are all air), for the typical antenna structure LA=1000 µm,
WA=65 µm, tA=50 nm.
Regarding the contact region, we assume that the shunt conductance G is infinite (perfect
contact) if the SWNTs are in direct contact with the antennas. Without direct contact, G is set to
be 0. Both the mutual inductance and kinetic inductance are small for the SWNTs, resulting in
negligible impedance (~60 Ω/µm). Therefore, the resistances of the SWNTs dominate the total
impedance. The current transfers from the antenna to the SWNTs within a characteristic length
(LT), take the form sinh(x/LT) /sinh(LC/LT) (where the end of the antenna is at the origin of the xaxis).
For the load region, only the resistance and inductance are considered. Ignoring the capacitive
coupling between the center segments of the SWNT to the surroundings simplifies the
calculation.
Supplementary Note 4: Transfer printing of SWNTs for Raman spectroscopy
Transfer printing of the aligned arrays of SWNTs from the quartz substrate to an ɑ-plane
sapphire substrate facilitates the Raman spectroscopy (to determine the type of the SWNTs
without electrical contacts), due to absence of peaks (below ~378 cm-1) associated with the
sapphire in the radial breathing mode (RBM) region of SWNTs (Supplementary Fig. 13). To
perform the transfer, a thin layer of poly(vinyl alcohol) (PVA, Sigma-Aldrich, dissolved in water
~ 5% as percentage by weight) was first drop-casted on the quartz substrate. Baking the substrate
at 60 0C for 10 min eliminated the solvent. Thermal tape allowed retrieval of the PVA film (with
the SWNTs) and release onto the a-plane sapphire substrate at 110 0C. Immersion of the
sapphire/SWNTs/PVA substrate in hot water (700C) for 3 h washed away the PVA film. Raman
spectroscopy was carried out on a Raman confocal imaging microscope (Horiba LabRAM HR
3D, equipped with four lasers, 532nm, 633nm, 785nm and 830nm) under ambient conditions.
Supplementary Note 5: Model for charge transport
Simulation of average current and power dissipation of s-SWNT involves a self-consistent
solution of spatially-resolved 3D electrostatics potential and charge density distributions. The 3D
electrostatics accounts for the complete device geometry: the SWNTs on the quartz substrate are
terminated by source (S) and drain (D) contacts, and covered by insulating material Tc-resist. To
calculate the potential from Eq. (3) of main text, we use the Dirichlet boundary conditions at the
source and the drain metallic contacts and assign fixed potentials, namely, ФS and VDS - ФD, to
the respective contacts. Here, ФS and ФD are the work functions of the source and drain,
respectively, and VDS is the applied drain bias. The Neumann boundary conditions on the
exposed surfaces of the quartz substrate and Tc-resist9 ensure that the normal component of the
electric field is zero.
The solution of the Eq. 3 in the main text depends on the charge density   q  p - n - N a  ;
the charge density along the channel is obtained by calculating carrier densities (electron (n) and
hole (p)) through drift-diffusion equations (Eqs. (4)-(7) of main text), and through independent
determination of the ionized impurity ( N a ) concentrations.
We follow two different ways to calculate carrier concentrations depending on biasing
arrangement. First, at VDS = 0, the device is in equilibrium, therefore, the Fermi level is flat
throughout the device and is aligned with source and drain. Electron and hole concentrations are
computed as,

n  p   NC 1/2 n p 
where, effective density of states are NC 
integral of order one-half, n 

(6)
8  EG  k BT  k BT 10
, 1/ 2 is the Fermi-Dirac


a  EG  4 0  3 EG
EV  EFp
EFn  EC
, p 
, α = 1-2 is the zone degeneracy
k BT
k BT
coefficient, the graphene lattice constant is a = 0.246 nm, γ0 ~ 3 eV is the π-bond energy, EFn ( p )
is quasi-Fermi energy for electrons (holes), and EC(V) is the conduction (valence) band energies.
Second, when VDS ≠ 0, Fermi-level are no longer constant along the channel of the s-SWNT,
therefore, carrier concentrations must now be calculated by solving continuity equation. The
electron and hole boundary currents ( I sn and I sp ) of the continuity equation have the following
expressions:



I sn  qvsn n S , D  nequi ; I sp  qvsp p S , D  pequi
where, nequi  NC 1/2 n,S or , n, D  ,

(7)
pequi  NC 1/2  p ,S or ,  p , D  , vsn ( sp ) is the surface
recombination velocity of electron (hole), equal to half of the thermal velocity11, n( p) S , D is the
concentration of electron (hole) at the interfaces of Source/SWNT and Drain/SWNT and is
obtained by solving Eqs. (4)-(7) of the main text. Note that the diffusion coefficients (Dn(p)) used
in Eq. (7) of the main text appropriately account for the Fermi-Dirac distribution,
k T

Dn p    B FE ,n p   1/2 n p 
 q




1/2 n p 

(8)
Ionized impurity concentration, N a , represents the influence of negatively charged interface
defect12 on the electrostatics of s-SWNT through the relation
Na  Na 1  4exp  EV  EFp  0.045 / kBT   (9)


where, Na = 4.4x1019 cm-3 is the uniform concentration of the impurity throughout the s-SWNT9.
Supplementary References:
1
2
3
4
5
6
7
8
9
10
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