Collective Antenna Effects in the Terahertz and Infrared Response of Highly Aligned Carbon Nanotube Arrays

0.43 MB·English

by  L. Ren

Collective Antenna Effects in the Terahertz and Infrared Response of
Highly Aligned Carbon Nanotube Arrays
L. Ren,1 Q. Zhang,1 C. L. Pint,2,3 A. K. W´ojcik,4 M. Bunney, Jr.,5,6 T. Arikawa,1
I. Kawayama,7 M. Tonouchi,7 R. H. Hauge,2 A. A. Belyanin,4 and J. Kono1,8,∗
1Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA
2Department of Chemistry, Rice University, Houston, Texas 77005, USA
3Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37240, USA
4Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
3 5NanoJapan Program, Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA
1 6Department of Electrical Engineering, Cornell University, Ithaca, New York 14850, USA
0 7Institute of Laser Engineering, Osaka University, Yamadaoka 2-6, Suita, Osaka 565-0871, Japan
2 8Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

n (Dated: December 11, 2013)
a
We study macroscopically-aligned single-wall carbon nanotube arrays with uniform lengths via
J
polarization-dependent terahertz and infrared transmission spectroscopy. Polarization anisotropy
8 is extreme at frequencies less than ∼3THz with no sign of attenuation when the polarization is

perpendicular to the alignment direction. The attenuation for both parallel and perpendicular
]
l polarizations increases with increasing frequency, exhibiting a pronounced and broad peak around
l
a 10THz in the parallel case. We model the electromagnetic response of the sample by taking into
h account both radiative scattering and absorption losses. We show that our sample acts as an
- effective antenna due to the high degree of alignment, exhibiting much larger radiative scattering
s
than absorption in the mid/far-infrared range. Our calculated attenuation spectrum clearly shows
e
m a non-Drudepeak at ∼10THz in agreement with theexperiment.
t. PACSnumbers: 78.67.Ch,63.22.+m,73.22.-f,78.67.-n
a
m
- Carbonnanomaterials—single-wallcarbonnanotubes of their THz polarizers, demonstrating ideal broadband
d (SWCNTs) and graphene — have recently emerged as THzproperties: 99.9%degreeofpolarizationandextinc-
n novel terahertz (THz) systems, offering new opportuni- tion ratios of 10−3 (or 30dB) from ∼0.4 to 2.2THz.
o
ties for basic research and device applications in THz
c Here we present results of our experimental and theo-
[ science and technology.1–4 A variety of proposals exist retical study of the THz and infrared response of highly
for using carbon nanotubes for THz devices, including aligned SWCNT films, similar to the samples used in
1 THzsourcesbasedonballisticquasi-metallicSWCNTs5,6
v Refs. 21 and 26, to elucidate the frequency and polar-
and THz nanoantennas utilizing plasmons in armchair
8 ization dependence of transmission. Specifically, in the
7 SWCNTs.7–10 THz and infrared spectroscopy experi- low-frequency THz regime (<3THz), there is virtually
4 mentsonSWCNTs reportedduringthe pastdecade11–21 no attenuation when the THz polarization is perpendic-
1 haveproducedconflictingresultsaswellascontradicting
ular to the nanotube axis but strong attenuation when
. interpretations, including the controversial origin of the
1 parallel. The attenuation for both parallel and perpen-
0 absorptionpeakobservedaround4THz.12,17–20,22–24 Un- dicularpolarizationsincreaseswithincreasingfrequency,
3 fortunately, there have been considerable uncertainties
exhibiting a pronounced and broad peak around 10THz
1 and shortcomings with the samples used in the previous
in the parallel case. Our theory takes into account both
: studies: not only they were grown by various methods
v the scattering (or radiative) and absorption (or Ohmic)
i andplacedinavarietyofTHz-transparentpolymerfilms, contributions to the total attenuation of THz and in-
X
but also most samples consisted of randomly-oriented
frared waves through the film. Although an individual
r bundles of both semiconducting and metallic nanotubes
a nanotube is an inefficient radiatordue to its small diam-
with a wide distribution of lengths and diameters.
eter, at long wavelengths a large number of aligned nan-
Jeon et al.14,15 and Akima et al.17 used mechani- otubes in the film can be excited coherently and radiate
in phase. The total radiated power is then proportional
callystretchednanotubesampleswithpartialtubealign-
to the square of the number of nanotubes, N, within
ment, observing some polarization anisotropy in THz
thecoherenceareaandcanbelargerthanthe absorptive
transmission experiments. More recently, using ex-
loss, which is proportional to N for any frequency. The
tremely well aligned and ultralong SWCNTs, Ren and
total normalized attenuation clearly shows a non-Drude
co-workersdemonstrated that carbon nanotubes can act
as nearly perfect polarizers in the THz range.21 Kyoung peak at ∼10THz in agreement with the experiment, in-
dicating that the transmission spectra in the THz and
andco-workers,usingwell-alignedmultiwallcarbonnan-
mid-infraredrangeareprimarilydeterminedbythescat-
otubes,alsodemonstratedsimilarlystrongTHzpolariza-
tionanisotropy.25 Renet al.26 hasincreasedthe effective tering (radiative) loss.
thickness of their polarizers to improve the performance Thehighly-alignedSWCNTsamplesusedinthisstudy
2
(a) (b) (a) V
Sapphire
SWNTs
(cid:537)
H
m
22 µµmm 0 (cid:80) THz field
5
(b)
FIG. 1: (color online) (a) Scanning electron microscope im- )
age of a SWCNT film on a sapphire substrate showing the nits1.0 Reference (cid:84)(cid:3)= 90º
high degree of nanotube alignment. (b) Optical microscope u
imageoftheSWCNTfilmshowingthehighuniformityofthe b. (cid:84) = 45°
r
nanotubelengths. a
(
d 0.5 (cid:84) = 30°
el (cid:84) = 0°
Fi
were synthesized via chemical vapor deposition, as de- c
ri
scribed in Refs. 27–31. The as-grown lines of aligned ct0.0
e
SWCNTs are vertically oriented with respect to the El
growth substrate, their length determined by the du-
0 1 2 3 4 5 6
ration of catalyst exposure to the growth conditions.
Time (ps)
A high temperature (750◦C) H O vapor etch was then (c)
2
used to free the catalyst-SWCNT interface,30 allowing 100
(cid:84) = 90°
the resulting aligned film to be efficiently transferred to )
%
80
a host substrate (c-plane sapphire or undoped silicon in (
e
our case). The transfer process results in a homoge- c
neousfilm(initially∼2µmthick)thatremainsas-grown, an 60 (cid:84) = 45°
highly-aligned,andfreeofexposuretoanysolventorliq- mitt
40
uid. Figure 1(a) shows a top-down scanning electron s (cid:84) = 30°
n
microscope image of the SWCNTs showing alignment a
Tr 20 (cid:84)(cid:3)= 0°
present in such a transferred film. Figure 1(b) shows
a top-downopticalmicroscopeimageofthis horizontally
0
aligned SWCNT film, indicating the high uniformity of 0.2 0.6 1.0 1.4 1.8
the nanotube lengths (∼75µm in this case). Frequency (THz)
We used time-domain THz spectroscopy (TDTS) in
the 7–100cm−1 range and Fourier-transform infrared FIG. 2: (color online) (a) Sketch of experimental configu-
spectroscopy (FTIR) in the 100–7000cm−1 range. The ration, showing the interaction between the linearly polar-
TDTS setup used was a typical system based on photo- ized THz electric field and the highly aligned SWCNT film.
conductive antennas made from low-temperature grown The angle between the THz polarization direction and the
GaAs.21,32 The THz beam from the emitter was already nanotube alignment direction, θ, was tuned between 0◦ and
◦
90 . (b) Transmitted THz waveforms in thetime domain for
highly linearly polarized, but a free standing wire-grid
the reference sapphire substrate (black dashed circled curve)
polarizer was placed eight inches from both the emit-
and for the SWCNT film for different angles (colored solid
ter and the sample to increase the polarization degree
curves) between the THzpolarization direction and thenan-
of the incident THz beam. As schematically shown in
otubealignmentdirection. (c)THztransmittancespectrafor
Fig. 2(a), the SWCNT sample was rotated about the four different polarization angles. As the angle between the
propagationdirectionoftheTHzwave. Thisangle,θ,be- THzpolarizationandnanotubealignmentdirectionincreases,
tweenthe nanotube axisandtheTHz polarizationdirec- thetransmittance monotonically increases.
◦ ◦
tion was varied from 0 to 90 . Polarization-dependent
THztransmissionmeasurementswereperformedonboth
the SWCNT film sample on a sapphire substrate and a thatthere is no attenuationwhen the polarizationofthe
referencesapphiresamplewiththesamethicknessasthe incidentbeamisperpendiculartothesample’snanotube
sample substrate. alignment. Whenθ=0◦(parallelpolarization),however,
Figure 2(b) shows the transmitted time-domain wave- strongattenuationoftheTHz waveisseen. The amount
◦ ◦ ◦ ◦
formsforfourdifferentangles(θ=0 ,30 ,45 ,and90 ), ofTHz attentuationismoreevidentinthe frequencydo-
along with the transmitted waveform from the reference main after Fourier-transforming the time-domain wave-
sapphiresubstrate. The90-degreetraceisparticularlyof formsandcalculatingtransmittancespectra,asshownin
note. It closely follows the reference waveform, meaning Fig.2(c). Here,weplotthetransmittance,T =|E˜ /E˜ |2,
s r
3
-4
2.0x10
1.4
1.5
1.2
Real
)
1.0 Parallel S 1.0
(
T) y
(0 0.8 vit
g1 cti 0.5
o u
–l 0.6 nd Imaginary
o 0.0
0.4 C
Perpendicular
0.2 -0.5
0.0
-1.0
2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8
101 102 103 104 101 102 103 104
Frequency (cm-1) Frequency (cm-1)
FIG. 3: THz and infrared attenuation spectra for a highly FIG.4: Real(solidline)andimaginary(dashedline)partsof
alignedSWCNTfilmforpolarizationparallel(black)andper- the surface conductivity of an infinitely-long metallic single-
pendicular (red) to thenanotubealignment direction. wall carbon nanotube with a tube diameter of 2.7nm, calcu-
lated according toRef. 8.
asafunctionoffrequencyinthe0.2-1.8THzrange,where
E˜ and E˜ arethe complex THz signals in the frequency
s r response, for which the contribution of semiconducting
domain for the sample (SWCNT film on sapphire sub-
nanotubes is negligible. The surface conductivity of the
strate) and reference (sapphire substrate only), respec-
nanotubes,σ ,iscalculatednumerically,usingthemodel
tively. Fromthis figure,wesee thatthe transmittanceof c
of rolled-up graphene (see, e.g., Refs. 8 and 9). We
the SWCNT film increases monotonically as the angle θ
◦ ◦ ◦ assume the phenomenological relaxation time, τ, to be
increases from 0 to 90 . When θ = 90 , the transmit-
equalto 10fs inthe THz andmid-infraredrangeand5fs
tance is one in this frequency range. Conversely, when
◦ inthe nearinfrared. Therealandimaginarypartsofthe
θ = 0 , the absorbance is finite and the transmittance
conductivityversusfrequencycalculatedforaninfinitely
is much lower, decreasing with increasing frequency to
◦ ◦ long metallic nanotube with a diameter of 2.7 nm are
a value lower than 10% at 1.8 THz. The 30 and 45
◦ plotted in Fig. 4.
transmittance lines show the same trend as the 0 curve
but with larger amplitudes. Theelectromagneticresponseofananotubeexcitedby
Figure 3 shows the attenuation, −log (T), for θ = a normally incident plane wave is calculated by solving
10
0◦ (parallelpolarization)to 90◦ (perpendicular polariza- the modified Hall´en equation
tion) in the entire range of 7–7000cm−1, combining the
results obtained with TDTS and FTIR, for an aligned L/2
′ ′ ′ ′
SWCNT film on an undoped silicon substrate. Again, (K(z−z )+q(z−z ))I(z ,ω)dz =
Z
highly anisotropic behavior is observed for this SWCNT −L/2
film in this broad frequency region. When the polariza- i4πωε L/2
0 ′ ′
− E sink|z−z |dz
tion is parallel with the nanotube alignment direction, 2k Z−L/2 0
there is strong attenuation exhibiting a prominent and
broad peak at ∼450cm−1 (or ∼13.6THz). When the +C1sinkz+C2coskz, (1)
polarization is perpendicular to the nanotube alignment
direction, the attenuation is significantly suppressed, al- whereI(z,ω)isthecurrentinducedonthenanotube,the
mostzerointheTHzrange(asnotedearlier)andslightly expressionsfor the kernelfunctions K andq aregivenin
increasing with increasing in the infrared range. For Ref. 7, ε is the free space permittivity, k =2π/λ is the
0
both parallel and perpendicular cases, the attenuation free space wavenumber, L is the nanotube length, E is
0
rapidly increases toward the near-infrared range, above the amplitude of the incident plane wave, and the con-
∼3000cm−1, due to interband transitions.31,33 stantsC andC areobtainedfromthe boundarycondi-
1 2
We model the THz and infrared response of highly tions I(±L/2) = 0. This integral equation is solved for
alignedSWCNTs by analyzing the electromagneticscat- I(z,ω) numerically, using the method of moments with
tering and Ohmic losses of a single metallic nanotube. a normalized incident wave, E =1. The current I(z,ω)
0
This is a reasonableapproximationsince the volume fill- is then used to calculate the scattered (or radiated) field
ing factor by nanotubes is only a few percent; also, we as well as the absorbed field due to Ohmic losses. The
are mainly interested in modeling the long-wavelength total power radiated to the far field into all directions is
4
calculated as
(a)
ω2 π L/2 2 -16
Pr(L,ω)= 4ǫ0c3 Z0 dθsin3θ(cid:12)(cid:12)(cid:12)Z−L/2I(z,ω)dz(cid:12)(cid:12)(cid:12) , (2) Ohmic (absorption) loss
(cid:12) (cid:12) -18
(cid:12) (cid:12)
whereas the absorbed power is34 s
s
o
P (L,ω)= 1 Re{σ−1(ω)} L/2 |I(z,ω)|2dz. (3) L -20 Radiative scatering (reflection) loss
o 4πR c Z−L/2
The total attenuation of the incident electromagnetic -22
Single Metallic SWCNT
wave by a film is calculated by adding P and P . A
r o
single nanotube is an inefficient radiatordue to its small 2 4 6 8 2 4 6 8 2 4 6 8
1 2 3 4
radius,7 as also shown in Fig. 5(a). However, at long 10 10 10 10
wavelengths a large number of highly aligned nanotubes 0.0 (b)
Total
in the film can be excited coherently and radiates in
phase. The total radiated power Pr is then proportional -0.5
to the square of the number, N, of nanotubes within the
coherence area which scales roughly as λ2. As a result,
-1.0 Ohmic
the radiatedpowercanbecome largerthan the absorbed s
s
power since the latter Po ∝ N for any frequency.35 We Lo
assumeanN2 dependencefortheradiatedpoweratlong -1.5
wavelengths up to about 20µm, followed by a λ2 cutoff Radiative
to the ∝N dependence. -2.0
The spectrum of Ohmic (absorption) and radiative Aligned SWCNT Film
scattering (reflection) losses for a single metallic nan- -2.5
otube with a diameter of 2.7 nm and a length of 75 µm 2 4 6 8 2 4 6 8 2 4 6 8
1 2 3 4
10 10 10 10
is presented in Fig. 5(a). The spectrum of losses for a
film with a total number of N =5×104 nanotubes con- 1.2 (c)
tributing collectively to scattering at long wavelengths
1.0
is shown in Fig. 5(b); the corresponding total attenu-
ation is given in Fig. 5(c). Note the logarithmic scale 0.8
n
for losses in Figs. 5(a) and 5(b). Both the loss and o
attenuation spectra clearly show a non-Drude peak at ati 0.6
u
∼10 THz, in agreement with the experiment. The peak n
e 0.4
originates from collective radiative scattering. There is Att
a crossover from a radiation-dominated regime to an 0.2
absorption-dominated regime at the lowest frequencies
below ∼2 THz (∼60 cm−1) in Fig. 5(b). This happens 0.0 Aligned SWCNT Film
becauseradiativelossesdroprapidlywithdecreasingfre- -0.2
2 4 6 8 2 4 6 8 2 4 6 8
quency below the peak whereas the absorptionlosses in- 1 2 3 4
10 10 10 10
crease and approach a constant value. This crossover
-1
Frequency (cm )
explains the behavior of the measured attenuation spec-
trum in the lowest frequency range in Fig. 3, which ap-
proaches a plateau. The fact that absorption becomes FIG.5: (a)Thelogarithmofabsorptive(toptrace)andradia-
importantatthelongestwavelengthsisfurthersupported tive(bottomtrace)lossversusfrequencycalculated forasin-
by direct calculations of absorbance based on the com- gle metallic SWCNTwith adiameter of 2.7 nm and alength
plex refractive index in the 0.2-2 THz range extracted of 75 µm. (b) The logarithm of radiative (red line), Ohmic
from our TDTS experiments: the absorbance of the film (blueline),andtotal(blackline)lossesforthefilm,calculated
including the collective antenna effect with N =5×104 and
is more than 50% at frequencies below ∼0.5 THz.
assuming metallic SWCNTs of the same diameter of 2.7nm
Thepresenceofthenon-Drudepeakat∼10THzinour
and a length of 75µm. (c) Total normalized attenuation of
calculations does not depend on the position andprecise
thefilm, calculated from thetotal losses shown in (b).
spectral dependence of the cutoff from N2 to N depen-
denceinthe radiativelossesofthefilm. Theonlyimpor-
tantfactoristhattheattenuationinthemid/far-infrared
wavelength range should be mostly due to collective ra-
diative scattering, not absorptive Ohmic losses; other-
wise, the spectrum of these long nanotubes (L≫1 µm)
5
shouldbe Drude-likeatthese wavelengths.22 Including a allelcase. Our theory, whichtakes into accountboth co-
spread of nanotube lengths and diameters would make herent radiative scattering and absorptive Ohmic losses,
the peak broader and may affect its shape/asymmetry. successfully reproduces the observed spectra. The cal-
The second peak in the near-infrared (>3000 cm−1) is culatedattenuationspectrumclearlyshowsa non-Drude
due to interband transitions. peak at ∼10 THz, which indicates that the transmis-
In summary, polarization dependent THz time- sionspectra in the THz andinfraredrange areprimarily
domain spectroscopy and Fourier-transform infrared determined by radiative scattering losses, reflecting the
spectroscopy of highly-aligned single-wall carbon nan- collective antenna properties of these aligned, ultralong
otube films revealedstrongly anisotropic response in the carbon nanotubes.
entire spectral range. In the low-frequency THz regime
(<3THz),thereisvirtuallynoabsorptionwhentheTHz ThisworkwassupportedbytheDepartmentofEnergy
polarization is perpendicular to the nanotube axis. The (throughGrantNo.DE-FG02-06ER46308),theNational
attenuation for both parallel and perpendicular polar- Science Foundation (through Grants No. OISE-0530220
izations increaseswith increasingfrequency, exhibiting a andEEC-0540832),andtheRobertA.WelchFoundation
pronounced and broad peak around 10 THz in the par- (through Grant No. C-1509).
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