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Terahertz-infrared electrodynamics of single-wall carbon nanotube films
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Download details: IP Address: 128.83.63.20 This content was downloaded on 28/08/2017 at 11:27 Manuscript version: Accepted Manuscript Zhukova et al To cite this article before publication: Zhukova et al, 2017, Nanotechnology, at press: https://doi.org/10.1088/1361-6528/aa87d1 This Accepted Manuscript is: © 2017 IOP Publishing Ltd During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period. After the embargo period, everyone is permitted to copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by-nc-nd/3.0 Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. When available, you can view the Version of Record for this article at: http://iopscience.iop.org/article/10.1088/1361-6528/aa87d1
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Terahertz-infrared electrodynamics of single-wall carbon nanotube films
E S Zhukova1, A K Grebenko1, A V Bubis1, A S Prokhorov1,2, M A Belyanchikov1,
A P Tsapenko3, E P Gilshteyn3, D S Kopylova3, Yu G Gladush3, A S Anisimov4, V B Anzin1,2, A G Nasibulin3,5,6 and B P Gorshunov1,2 1
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Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow Region, 141700 Russia 2
A.M. Prokhorov General Physics Institute, RAS, Moscow, 119991 Russia
3
Skolkovo Institute of Science and Technology, Nobel str. 3, 143026, Moscow, Russia 4
Canatu Oy, Konalankuja 5, FI-00390 Helsinki, Finland
Department of Applied Physics, Aalto University, School of Science, P.O. Box 15100, FI-00076 Espoo,
an
5
Finland
6
National University of Science and Technology “MISIS”, Leninsky Ave, 4, Moscow, 119049, Russia
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E-mail: [email protected] (E.S. Zhukova); [email protected] (B.P. Gorshunov); [email protected] (A.G.Nasibulin)
Abstract
Broad-band (4 to 20 000 cm-1) spectra of real and imaginary conductance of a set of high-quality pristine and AuCl3-dopped single-walled carbon nanotube (SWCNT) films with different transparency are systematically
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measured. It is shown that while the high-energy (≥1 eV) response is determined by well-known interband transitions, the lower-energy electrodynamic properties of the films are fully dominated by unbound charge carriers. Their main spectral effect is seen as the free-carrier Drude-type contribution. Partial localization of these carriers leads to a weak plasmon resonance around 100 cm-1. At the lowest frequencies, below 10 cm-1, a gap-like feature is detected whose origin is associated with the energy barrier experienced by the carriers at
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the intersections between SWCNTs. It is assumed that these three mechanisms are universal and determine the low-frequency terahertz-infrared electrodynamics of SWCNT wafer-scale films.
PACS: 73.25.+I; 73.63.Fg; 78.67.Ch;
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AUTHOR SUBMITTED MANUSCRIPT - NANO-114632.R2
AUTHOR SUBMITTED MANUSCRIPT - NANO-114632.R2
1. Introduction Carbon nanotubes (CNTs) still attract considerable attention due to their extraordinary fundamental properties and potential applications in electronics and optics [1; 2; 3]. Along with the individual tubes, many applications require macro-scale thin wafers composed of large set of the CNTs [4; 5; 6]. Electronic and optical properties
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of such objects are unique since they are determined not only by specific intrinsic characteristics of the electronic system within the tubes but also by extrinsic factors like the CNTs alignment, presence of intertrube contacts, distribution of the CNT lengths, diameters and doping levels, presence of defects/kinks within separate tubes, folding of CNTs into bundles; controlling these factors allows, in principle, to “tune” the wafers’ properties and adjust them in accordance with practical needs. Recently, potential applications in photonics has triggered significant research interest towards developing highly both transparent and conductive single-walled carbon nanotube (SWCNT) films for various spectral regions [7; 8; 9]. Post-processing methods,
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such as chemical doping with AuCl3, allow to vary the properties of the films in a most significant way [10]. Thus, depending on the used dopant, spectral transmission and conductance can be effectively "tuned" to modify the wide-range optoelectronic properties of SWCNT films. Low-frequency (infrared, terahertz) optical spectroscopy provides an effective tool to monitor the properties of the macro-scale films. Despite vigorous
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activity, however, no consensus has been achieved during the past decades on the mechanisms that determine their low-energy electrodynamic response. Various groups presented results that sometimes are in contraction between each other. For example, the so-called terahertz conductivity peak is observed at frequencies from 0.4
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THz [11] to 30 THz [12] and its origin is assigned either to a small energy gap in the density of states caused by the finite curvature of the quasimetallic tubes [13; 14; 15; 16; 17] or to the plasmonic oscillations of charge carriers within the finite-length SWCNTs [11; 18; 19; 20; 21; 22]. Reports on the metal-like conductivity, that is expected to govern the dc and the low-energy ac electronic properties of the wafers, are very rare [23; 24] and the conclusions are rather vague. The current situation is due to the fact that the majority of spectroscopic experiments were performed on different samples of CNT films, their purity and quality were not always high enough and investigated spectral ranges were not sufficiently broad to identify the microscopic mechanisms
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that determine the terahertz-infrared electrodynamics of the CNT films. Here, we address this issue by performing measurements of broad-band (sub-terahertz, terahertz, infrared and visible) spectra of films composed by high-quality SWCNTs. We show that the low-energy (frequencies lower than 1000 cm-1, energies below ≈0.15 meV) electrodynamics of all films is determined by three phenomena: a) contribution from delocalized charge carriers that is described within the Drude conductivity model; b) the plasmon excitation
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coming from longitudinal oscillations of the charge carriers partly localized within SWCNTs and c) a pseudogap-like feature caused by tunneling of the carriers through the intertube contacts.
2. Experimental details The films were synthesised by an aerosol CVD (floating catalyst) method, which allows to obtain high-
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quality, highly conductive and optically transparent films of SWCNTs [25; 26]. These films can subsequently be easily transferred to almost any substrate or made freestanding, which makes them very promising material for flexible, stretchable, transparent electronics, photovoltaics and other applications [6; 27]. We have 2
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systematically studied a series of pristine and AuCl3 doped freestanding films with different transparencies measured at the wavelength of 550 nm: 65%, 75%, 80%, 90%, 95% (approximate values). Films were fixed on plastic frames with clear aperture of about 8 mm. Doping was performed by aerosol spraying of 15 mM ethanol solution of AuCl3. This dopant allows to increase significantly the conductivity of SWCNT films while
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maintaining transparency.
Transmission electron microscope (TEM) FEI Tecnai G2 F20 was used to investigate the structure of SWCNTs. To minimize the destructive influence of electron irradiation all measurements were performed at the acceleration voltage of 80 kV and with minimal possible electron illumination time. SWCNTs were directly collected at the reactor outlet onto carbon coated gold TEM grids. The morphology was characterized by scanning electron microscopy (SEM) FEI Helios Nanolab 660. SEM and TEM images of the pristine SWCNTs
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shown in Figure 1a,b confirm their high quality.
Figure 1. (a) SEM and (b) TEM images of (a) pristine SWCNT films. (с) Raman spectra of pristine SWCNTs (black) of 90% transmittance (at the wavelength of 550 nm) and after AuCl3-doping (red). Raman spectroscopic measurements were carried out with help of Thermo Scientific DXRxi Raman Imaging Microscope together with diode-pumped solid state laser operating at 532 nm. The output power was set to 0.1 mW. The laser spot was focused with a long working distance 50x objective (numerical aperture of
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0.50). The signal accumulation time of 20 s, and laser exposure time of 60 Hz were used. Raman spectra confirmed our microscopy observation, the formation of SWCNTs of a high quality. Figure 1c shows the clearly distinguishable SWCNT peaks (black) related to radial breathing mode (RBM), small intensity D mode and high intensity G modes (with G/D ratio of 155), 2D mode. As seen from the AuCl3-doped SWCNTs spectrum (red), there are several doping-related features present. Chemical doping in SWCNTs involves
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charge transfer between gold chloride and the nanotubes [28; 29; 30; 31]. That changes the work function and Fermi level of the nanotubes. As a result, the corresponding peak changes are seen in Raman spectra of the doped nanotubes. The strong p-type doping shift and change in shape of G-band peak take place due to the charge transfer and phonon stiffening, correspondingly [28]. The intensity change in 2D-band peak happens
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due to the change of the metallicity of the SWCNTs [28]. Following previous studies [27;29], we believe that solution of AuCl3 forms amorphous deposits and gold chloride on the SWCNT walls. On average, the bundles in our samples are small in diameters and consist of several nanotubes only (Figure 1b). The effect is seen in Raman spectra as the RBM-band peaks suppression, as supported additionally by TEM images [27]. SWCNTs 3
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covered with the deposits still retain their tubular structure even after doping. Gold chloride and deposits are found on the tubes and between the bundles. Figure 2 presents Kelvin probe force microscopy scans of the 80% transparency pristine and AuCl3 doped films. The work-function scans clearly demonstrate uniform distribution of the potential over the film
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area testifying only minor role of intertube contacts. Nanometer size inclusion is seen in the doped film that should be ascribed to gold residual. Electrodynamic response of the freestanding films was measured in the range of wavenumbers from few cm-1 up to 20 000 cm-1 using three different spectrometers. One film (65%) was selected to study the spectra in a wide temperature interval, from 300 K down to 5 K. All films were studied in the transmission geometry. The terahertz-subterahertz spectra of the films were measured by continuous-wave spectrometer based on backward-wave oscillators (BWOs) [32] and by the commercially available pulsed time-domain spectrometer (TDS) TeraView. Both these terahertz spectrometers operate in a
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quasi-optical regime (no waveguides used) and allow for direct determination of the spectra of real σ1 and imaginary σ2 parts of the optical (ac) conductivity, without use of the Kramers-Kronig analysis that is a regular procedure in the Fourier-transform infrared spectroscopy where just one quantity is determined experimentally - reflection or transmission coefficient. The BWO-spectrometer operates in two modes [32] In the transmission
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amplitude mode, the frequency-tunable monochromatic radiation passes through an empty aperture that is covered afterwards by a plane sample under study; the division of the two recorded spectra provides with the transmission coefficient Tr of the sample. The transmission phase mode utilizes the Mach-Zehnder interferometric scheme. During frequency scanning, at each frequency the position of the movable mirror in
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the reference channel of the interferometer is recorded that provides minimum of the interference. This is done when there is no sample in the measurement channel and with the sample placed in it; the difference between the two data arrays provides with the spectra of the phase shift, φ, of the radiation passed through the sample. Two measured quantities, Tr and φ, allow to determine the two required optical parameters, σ1 and σ2, using standard Fresnel equations for a layer. In TDS spectrometers, the sample is subject to a picosecond pulse that contains frequency components from about 0.3 THz up to several terahertz. The position and the amplitude of
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the pulse are detected when the measurement channel is empty or “blocked” with the sample. The difference in time between the two peaks is a measure of the radiation delay caused by the sample, and the amplitudes of the peaks give the measure of radiation absorption in the sample. Going from time domain to frequency domain is realized with the Fourier transformation, and results, again, with the spectra of transmission coefficient amplitude Tr and phase φ, with a subsequent determination of the σ1 and σ2, spectra of the sample under study.
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Above terahertz (THz) frequencies, in the infrared (IR) range, spectra of amplitude of the transmission coefficient were measured with a standard Fourier-transform spectrometer Bruker Vertex 80v. 3.
Results and discussion
Due to friability of pristine films their thickness cannot be precisely specified. In the following, we
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discuss our results without assigning certain thickness to all films and without specifying their internal structure. This approach allows to compare the effective optical properties of pristine and doped films. We use the model of complex conducting surface developed in [33] for conducting layers whose thickness is smaller than the skin depth. The complex conductance Y of such layer is given by 4
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𝑌 = 𝜎1 𝑑 + 𝑖𝜎2 𝑑,
(1)
where 1 and 2 are the real and imaginary parts of the layer conductivity and d is its thickness if the layer is homogeneous. Figure 3 presents spectra of real and imaginary parts of conductance of 65% transparency pristine (b,c) and doped (e,f) films measured at two different temperatures; we first discuss the room
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temperature data.
Figure 2. Kelvin probe force microscopy of SWCNT film with 80% transparency (at the wavelength of 550
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nm): (a) topography and (b) work-function maps of the pristine film; (c) topography and (d) work-function maps of the AuCl3 doped film.
Above 3000 cm-1, pronounced minima are seen that are connected with the interband transitions (van Hove singularities) [34]. Strong decrease below 1000 cm-1 of the THz and IR transmissivity (Figure 3a,d) and corresponding behavior of the directly determined real and imaginary THz conductance spectra (Figure 3b,c,e,f) have to be associated with the response of delocalized charge carriers since: a) the spectra of THz real
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and imaginary conductances have the form predicted by the Drude model of free-carrier conductivity – real conductance shows increase towards low frequencies and imaginary conductance displays distinct signs of a characteristic broad peak [35, 36]; b) the low-frequency extrapolations of real conductance are in reasonable agreement with the published dc values [23; 24; 37]; c) the real conductance shows metal-like temperature dependence – increase while cooling down (figure 3b and e). We have obtained the broad-band THz-IR spectra
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of 1d and 2d by fitting the merged THz and IR transmission coefficient spectra (dots and lines in Fig.3a,d, respectively). Minima seen in transmissivity above ≈3000 cm-1 were modeled with regular Lorentzians. Lowerfrequency spectra were modeled on the basis of the Drude expressions for the complex conductivity [35, 36]:
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2 * ( ) d 1 ( ) d i 2 ( ) d 2 dc 2 i 2 dc 2 d ,
(2)
where 𝜎dc is the dc conductivity and is the charge-carrier scattering rate. It is important to stress that the lowfrequency (below ≈100 cm-1) spectra of transmission coefficients were processed together with the directly
5
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measured real and imaginary conductances that determine the transmissivity at these frequencies; such approach allowed us to unambiguously define charge carriers parameters that enter expression (2) (see below). We note that in order to consistently describe the transmissivity and conductance spectra we had to introduce additional term in the form of absorption band located around 100 cm-1. It is indicated by a shaded area in
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middle panels of figure 3 and was modeled by a Lorentzian. One more peculiarity detected in the spectra of all pristine films was a decrease of real conductance towards lowest frequencies below ≈ 10 cm-1 at 300 K
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(figure 3b).
Figure 3. Room temperature (black dots, black lines) and 5 K (blue dots) spectra of (a, d) transmission coefficients and (b, e) effective real and (c, f) effective imaginary parts of conductance of (a, b, c) pristine and
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(d, e, f) AuCl3 doped CNT films with 65% transparency (at the wavelength of 550 nm). Dots correspond to direct measurements on THz pulsed time-domain and cw backward-wave oscillator based spectrometers. Grey-shaded areas in (b) and (e) show absorption peaks due to plasmon resonance. Dashed lines in (a) and (d) correspond to fitting when the absorption resonances at 100 cm-1 in 1d spectra (grey-shaded area in (b) and (e)) are not taken into account.
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To analyze the nature of the absorption band around 100 cm-1, we plot its spectral shape for all pristine and doped films (insets in figure 4). It is seen that the band intensity or spectral weight (area under the 1d curves) is larger for the doped films and quickly decreases with the increase of the films transparency (inset in figure 4b). This is a strong indication that the origin of the bands should be related to the presence of delocalized charge carriers. We associate these absorption peaks with plasmonic oscillations of charge carriers
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that are partly localized by defects, impurities and intersections of tubes. Corresponding excitations have been previously observed in numerous experiments [11; 12]. The amplitude of the bands is significantly smaller than the free-carrier Drude component (characterized by the 1d value at about 10 cm-1) making them not so 6
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clearly pronounced in the present experiments; we believe that the reason is an effective screening by delocalized carriers and by only a small fraction of localized carriers compared with the amount of delocalized carriers. The fact that the position of the bands is basically unchanged in all studied films means that the carriers’ localization distance is determined not by the SWCNTs’ ends [11], but by certain defects within the
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tubes or tubes crossings. We can estimate the distance L between those defects as L = Vp(p)-1, where Vp is the plasmon velocity that is several times larger than the Fermi velocity. With p ≈ 100 cm-1, Vp ≈ 4VF [18] and the Fermi velocity VF ≈ 108 cm/s we obtain L ≈ 0.4 μm. With the mean-free path in our films l ≈ 0.1 μm (see below) we have l/L ≈ 0.25 meaning that our films are rather “clean” [18]. The value L ≈ 0.4 μm correlates well with the average distance between intersections of CNTs, as can be seen from figure 2a-d. We thus assume that the plasmonic excitations occur due to reflections of the charge carrier plasma at the CNT intersections. Wavelength (nm) 105
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1 Pristine
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Figure 4. Room temperature spectra of real parts of effective conductance of (a) pristine and (b) AuCl3 doped SWCNT films of different transparency (at the wavelength of 550 nm). Dots correspond to direct measurements on THz pulsed time-domain and cw backward-wave oscillator based spectrometers. Lines correspond to the least-square fit results, as described in the text. Insets show absorption peaks due to plasmon
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resonances in (a) pristine and (b) AuCl3 doped films and the dependence of the peaks oscillator strengths (area under the spectra) on the films transparency (lower inset in frame (b)). To account for the lowest-frequency downturn of the real conductance (that is proportional to
absorption) observed in pristine SWCNTs we recall that their response is determined by two contributions to
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the dc/ac conductivity, one connected with the intrinsic conductivity of a separate SWCNTs or SWCNT bundles, and the other governed by the fluctuation-assisted tunneling (FAT) of charge carriers through the energy barriers at the intertube contacts [38; 39; 40]. The total resistivity is given by 7
AUTHOR SUBMITTED MANUSCRIPT - NANO-114632.R2
−1 (𝑇) 𝑅𝑑𝑐 (𝑇) = 𝜎𝑑𝑐 = 𝐴 𝑒𝑥𝑝 (−
𝑇𝑚 ) 𝑇
𝑇
𝑡 + B exp(𝑇 +𝑇 ).
(3)
𝑠
Here, the temperature Tm accounts for the backscattering of the charge carriers within the SWCNT (SWCNT
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bundle), kBTt corresponds to the typical energy barrier for the carrier tunneling, the ratio Tt/Ts determines the tunneling in the absence of fluctuations, A and B are temperature independent factors and kB is the Boltzmann constant. The values of the tunnel gaps can be estimated as 1.4-1.6 meV (corresponding to the temperatures Tt = 16-18 K [37]) for pristine SWCNT films and as 0.2-0.25 meV (Tt = 2-3 K [37]) for doped films (this estimation corresponds to CuCl3 doped films, but we expect that it does not differ much from films doped with AuCl3). Let h be the energy of the electromagnetic radiation that probes the response of the film (h is the Planck’s constant). Then, for this energy being much larger than the tunnel gap (h >> kBTt) the radiation does not “feel” the presence of the small gap, and the charge carriers respond as if they were free. For the other
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case, h < kBTt, the carriers experience the impeding tunnel gap leading to lower ac and the dc conductivities [41]. Exactly this behavior is observed around 10 cm-1 for pristine films, where the tunnel gap energy corresponds to the frequency 11 - 13 cm-1. Similarly, no signs of the tunnel gaps of 0.2 - 0.25 meV
measured at significantly higher frequencies. 60
40
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Pristine
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Drude (cm-1)
80
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(corresponding frequencies are 1.4 - 2 cm-1) are detected in the spectra of doped SWCNT films that are 90
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AuCl3 doped T=300 K
(a)
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Figure 5. Effective parameters of charge carriers in pristine and AuCl3 doped SWCNT films as dependent on the films transparency: (a) the charge carriers scattering rate, (b) the mobility, (c) the collision time and (d) the mean-free path.
Having identified the Drude-like component in the response of the films one can extract effective
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parameters of corresponding charge carriers. Typical downturn towards high frequencies in the real conductance or peak position of the imaginary conductance (figures 3 and 4) provide with the carriers’ 𝑒
scattering rate γ that, in turn, allows calculation of effective mobility 𝜇 = 2π𝑚∗ 𝛾 (e is the electron charge and 8
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m* = 0.2 me [42] is its effective mass), the collision time of τ = (2)-1 and the mean-free path of l = VF (with the Fermi velocity of VF = 8∙107 cm/s [43]). These quantities are plotted in figure 5 where it is seen that they are practically independent on the films transparency. As expected, the obtained values of mobility and meanfree path are much smaller than those of individual SWCNTs, = 1000 - 30 000 cm2V-1s-1 [44; 45; 46; 47], l
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= 1 - 2 μm [48], due to the effect of intertube contact phenomena.
We now turn to the temperature dependences of the charge carriers’ effective parameters that were determined for the 65% transparency film (figure 6). The scattering rates for the pristine and AuCl3 doped films show similar behaviors with the values for the doped film being slightly larger. This can be due to the increase in the charge carrier concentration in the doped films and thus higher collision frequency and additional scattering on the impurities introduced by doping, or due to the involvement in the scattering processes of small wave vector phonons in the doped films, where the Fermi level is shifted down into the
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valence band [37]. The overall temperature variation of the charge carriers’ parameters (scattering rate, mobility, scattering time, mean-free path) is similar to that observed in semiconductors for free carriers in conduction or valence band where they reveal metal-like frequency dependences of complex conductivity spectra (like those in figure 3). While cooling down from the room temperature down to ≈100 K the scattering
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weakens due to freezing out of the phonon scattering while at lower temperatures impurity/defects scattering mechanism dominates.
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Figure 6. Temperature dependences of (a) the effective charge carriers scattering rate, (b) the mobility, (c) the collision time and (d) the mean-free path of pristine and AuCl3 doped CNT films with 65% transparency (at
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the wavelength of 550 nm).
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Extrapolating the conductance of SWCNT films to the zero-th wavenumber (figure 4), one can calculate that the sheet resistance of the 90% transmittance films after doping lowered from 167 to 67 Ohm/sq. This low value of the sheet resistance for the SWCNT film tells about high level of doping, which leads to significant shift of the Fermi level after the doping compared to the pristine SWCNTs. This results in the increase of the
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number of charge carriers and in the reduction of the Shottky barrier between the SWCNTs and bundles [49; 50].
We finally note that knowing the exact value of the film thickness would allow us to calculate the conductivity dc=ne=ne2(2m*)-1 and hence the effective free charge carriers’ concentration. With m* = 0.2 me [42] and taking the thickness of d = 20 nm [51] of the pristine and AuCl3-doped 90% transparency films we would obtain the concentration values of 1.9*1019 cm-3 and 4.8*1019 cm-3, respectively.
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4. Conclusions
By measuring the broad-band spectra of complex conductance of a set of high-quality SWCNT films we show that their terahertz-infrared electrodynamic response is mostly determined by unbound charge carriers that provide three main contributions: a) contribution from delocalized carriers described by the Drude
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conductivity model; b) weak resonance-like absorption band around 100 cm-1 connected with plasmonic oscillations of carriers localized by intersections of SWCNTs in the films; c) gap-like feature at or below ≈10 cm-1 caused by tunnel barriers experienced by the carriers at the SWCNTs contacts. We estimated effective
and the mean-free path.
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parameters of the charge carriers that determine the films optical response: the mobility, the scattering rate,
Acknowledgements
The work was supported by the Russian Ministry of Education and Science (Program ‘5top100’). Russian Science Foundation is greatly acknowledged for a financial support (agreement No 17-19-01787) for the
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synthesis, doping and characterisation of SWCNTs. The work was carried out with financial support from the Ministry of Education and Science of the Russian Federation as part of Improve Competitiveness Program of NUST MISiS, implemented by a governmental decree dated 16th of March 2013, No 211.
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433-442
[3] Avouris P, Freitag M and Perebeinos V 2008 Carbon-nanotube photonics and optoelectronics. Nature Photonics 2 341- 350 10
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[4] Cao Q, Rogers J A 2009 Ultrathin films of single-walled carbon nanotubes for electronics and sensors: a review of fundamental and applied aspects Adv. Mater. 21 29-53 [5] Aitolaa K, Kaskelaa A, Halmea J, Ruiza V, Nasibulin A G, Kauppinen E I and Lunda P D 2010 Single-
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[6] Hecht D S, Hu L, Irvin G 2011 Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures Adv. Mater.23 1482–1513
[7] Chae, S. H., Lee, Y. H. 2014 Carbon nanotubes and graphene towards soft electronics. Nano Convergence, 1(1), 1-26
[8] He, L., Tjong, S. C. 2016 Nanostructured transparent conductive films: fabrication, characterization and
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[9] Hu, L., Hecht, D. S., Gruner, G. 2010 Carbon nanotube thin films: fabrication, properties, and applications. Chemical reviews, 110 (10), 5790-5844
[10] Kim, K. K., Yoon, S. M., Park, H. K., Shin, H. J., Kim, S. M., Bae, J. J., et al. 2010 Doping strategy of
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[12] Tae-In Jeon et al. 2004 Optical and electrical properties of preferentially anisotropic single-walled
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carbonnanotube films in terahertz region. Journal of Applied Physics 95 5736-5740 [13] Pekker A and Kamaras K 2011 Wide-range optical studies on various single-walled carbon nanotubes: Origin of the low-energy gap Phys. Rev. B 84 075475
[14] Itkis M E, Niyogi S, Meng M E, Hamon M A, Hu H, and Haddon R C 2002 Spectroscopic study of the fermi level electronic structure of single-walled carbon nanotubes Nano Lett. 2 155-159 [15] Borondics F, Kamarás K, Nikolou M, Tanner D B, Chen Z H and Rinzler A G 2006 Charge dynamics in transparent single-walled carbon nanotube films from optical transmission Phys. Rev. B 74 045431
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[16] Ugawa A, Rinzler A G, and Tanner D B 1999 Far-infrared gaps in single-wall carbon nanotubes Phys. Rev. B 60 R11305-R11308
[17] Ruzicka B, Degiorgi L, Gaal R, Thien-Nga L, Bacsa R, Salvetat J-P, and Forro L 2000 Optical and dc conductivity study of potassium-doped single-walled carbon nanotube films Phys. Rev. B 61 R2468-R2471 [18] Nakanishi T and Ando T 2009 Optical response of finite-length carbon nanotubes J. Phys. Soc. Jpn. 78
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[19] Morimoto T and Okazaki T 2015 Optical resonance in far-infrared spectra of multiwalled carbon nanotubes Applied Physics Express 8 055101 [20] Akima N et al. 2006 Strong anisotropy in the far-infrared absorption spectra of stretch-aligned single-
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walled carbon nanotubes Adv. Mater. 18 1166–1169 [21] Zhang Q, Hároz E H, Jin Z, Ren L, Wang X, Arvidson R S, Lüttge A and Kono J 2013 Plasmonic nature of the terahertz conductivity peak in single-wall carbon nanotubes Nano Lett. 13 5991−5996
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[22] Morimoto T, Joung S K, Saito T, Futaba D N, Hata K, and Okazaki T 2014 Length-dependent plasmon resonance in single-walled carbon nanotubes ACS Nano 8 9897–9904
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[26] Kaskela A. et al. 2010 Aerosol-synthesized SWCNT networks with tunable conductivity and transparency by a dry transfer technique Nano Lett. 10 4349-4355
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[28] Kim S M et al. 2011 Role of anions in the AuCl3-doping of carbon nanotubes Acs Nano 5 1236-1242. [29] Kim K K et al. 2008 Fermi level engineering of single-walled carbon nanotubes by AuCl3 doping.
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[31] Goak JC, Lee SH, Han JH, Jang SH, Kim KB, Seo Y, Seo YS. and Lee N 2011 Spectroscopic studies
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[46] Martel R, Schmidt T, Shea H R, Hertel T and Avouris Ph 1998 Single- and multi-wall carbon nanotube field-effect transistors Appl. Phys. Lett.73 2447-2449
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[50] Mustonen K, Laiho P, Kaskela A, Susi T, Nasibulin A G and Kauppinen E I 2015 Uncovering the
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Terahertz-infrared electrodynamics of single-wall carbon nanotube films
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Download details: IP Address: 128.83.63.20 This content was downloaded on 28/08/2017 at 11:27 Manuscript version: Accepted Manuscript Zhukova et al To cite this article before publication: Zhukova et al, 2017, Nanotechnology, at press: https://doi.org/10.1088/1361-6528/aa87d1 This Accepted Manuscript is: © 2017 IOP Publishing Ltd During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period. After the embargo period, everyone is permitted to copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by-nc-nd/3.0 Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. When available, you can view the Version of Record for this article at: http://iopscience.iop.org/article/10.1088/1361-6528/aa87d1
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Terahertz-infrared electrodynamics of single-wall carbon nanotube films
E S Zhukova1, A K Grebenko1, A V Bubis1, A S Prokhorov1,2, M A Belyanchikov1,
A P Tsapenko3, E P Gilshteyn3, D S Kopylova3, Yu G Gladush3, A S Anisimov4, V B Anzin1,2, A G Nasibulin3,5,6 and B P Gorshunov1,2 1
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Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow Region, 141700 Russia 2
A.M. Prokhorov General Physics Institute, RAS, Moscow, 119991 Russia
3
Skolkovo Institute of Science and Technology, Nobel str. 3, 143026, Moscow, Russia 4
Canatu Oy, Konalankuja 5, FI-00390 Helsinki, Finland
Department of Applied Physics, Aalto University, School of Science, P.O. Box 15100, FI-00076 Espoo,
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5
Finland
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National University of Science and Technology “MISIS”, Leninsky Ave, 4, Moscow, 119049, Russia
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E-mail: [email protected] (E.S. Zhukova); [email protected] (B.P. Gorshunov); [email protected] (A.G.Nasibulin)
Abstract
Broad-band (4 to 20 000 cm-1) spectra of real and imaginary conductance of a set of high-quality pristine and AuCl3-dopped single-walled carbon nanotube (SWCNT) films with different transparency are systematically
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measured. It is shown that while the high-energy (≥1 eV) response is determined by well-known interband transitions, the lower-energy electrodynamic properties of the films are fully dominated by unbound charge carriers. Their main spectral effect is seen as the free-carrier Drude-type contribution. Partial localization of these carriers leads to a weak plasmon resonance around 100 cm-1. At the lowest frequencies, below 10 cm-1, a gap-like feature is detected whose origin is associated with the energy barrier experienced by the carriers at
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the intersections between SWCNTs. It is assumed that these three mechanisms are universal and determine the low-frequency terahertz-infrared electrodynamics of SWCNT wafer-scale films.
PACS: 73.25.+I; 73.63.Fg; 78.67.Ch;
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AUTHOR SUBMITTED MANUSCRIPT - NANO-114632.R2
1. Introduction Carbon nanotubes (CNTs) still attract considerable attention due to their extraordinary fundamental properties and potential applications in electronics and optics [1; 2; 3]. Along with the individual tubes, many applications require macro-scale thin wafers composed of large set of the CNTs [4; 5; 6]. Electronic and optical properties
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of such objects are unique since they are determined not only by specific intrinsic characteristics of the electronic system within the tubes but also by extrinsic factors like the CNTs alignment, presence of intertrube contacts, distribution of the CNT lengths, diameters and doping levels, presence of defects/kinks within separate tubes, folding of CNTs into bundles; controlling these factors allows, in principle, to “tune” the wafers’ properties and adjust them in accordance with practical needs. Recently, potential applications in photonics has triggered significant research interest towards developing highly both transparent and conductive single-walled carbon nanotube (SWCNT) films for various spectral regions [7; 8; 9]. Post-processing methods,
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such as chemical doping with AuCl3, allow to vary the properties of the films in a most significant way [10]. Thus, depending on the used dopant, spectral transmission and conductance can be effectively "tuned" to modify the wide-range optoelectronic properties of SWCNT films. Low-frequency (infrared, terahertz) optical spectroscopy provides an effective tool to monitor the properties of the macro-scale films. Despite vigorous
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activity, however, no consensus has been achieved during the past decades on the mechanisms that determine their low-energy electrodynamic response. Various groups presented results that sometimes are in contraction between each other. For example, the so-called terahertz conductivity peak is observed at frequencies from 0.4
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THz [11] to 30 THz [12] and its origin is assigned either to a small energy gap in the density of states caused by the finite curvature of the quasimetallic tubes [13; 14; 15; 16; 17] or to the plasmonic oscillations of charge carriers within the finite-length SWCNTs [11; 18; 19; 20; 21; 22]. Reports on the metal-like conductivity, that is expected to govern the dc and the low-energy ac electronic properties of the wafers, are very rare [23; 24] and the conclusions are rather vague. The current situation is due to the fact that the majority of spectroscopic experiments were performed on different samples of CNT films, their purity and quality were not always high enough and investigated spectral ranges were not sufficiently broad to identify the microscopic mechanisms
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that determine the terahertz-infrared electrodynamics of the CNT films. Here, we address this issue by performing measurements of broad-band (sub-terahertz, terahertz, infrared and visible) spectra of films composed by high-quality SWCNTs. We show that the low-energy (frequencies lower than 1000 cm-1, energies below ≈0.15 meV) electrodynamics of all films is determined by three phenomena: a) contribution from delocalized charge carriers that is described within the Drude conductivity model; b) the plasmon excitation
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coming from longitudinal oscillations of the charge carriers partly localized within SWCNTs and c) a pseudogap-like feature caused by tunneling of the carriers through the intertube contacts.
2. Experimental details The films were synthesised by an aerosol CVD (floating catalyst) method, which allows to obtain high-
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quality, highly conductive and optically transparent films of SWCNTs [25; 26]. These films can subsequently be easily transferred to almost any substrate or made freestanding, which makes them very promising material for flexible, stretchable, transparent electronics, photovoltaics and other applications [6; 27]. We have 2
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systematically studied a series of pristine and AuCl3 doped freestanding films with different transparencies measured at the wavelength of 550 nm: 65%, 75%, 80%, 90%, 95% (approximate values). Films were fixed on plastic frames with clear aperture of about 8 mm. Doping was performed by aerosol spraying of 15 mM ethanol solution of AuCl3. This dopant allows to increase significantly the conductivity of SWCNT films while
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maintaining transparency.
Transmission electron microscope (TEM) FEI Tecnai G2 F20 was used to investigate the structure of SWCNTs. To minimize the destructive influence of electron irradiation all measurements were performed at the acceleration voltage of 80 kV and with minimal possible electron illumination time. SWCNTs were directly collected at the reactor outlet onto carbon coated gold TEM grids. The morphology was characterized by scanning electron microscopy (SEM) FEI Helios Nanolab 660. SEM and TEM images of the pristine SWCNTs
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shown in Figure 1a,b confirm their high quality.
Figure 1. (a) SEM and (b) TEM images of (a) pristine SWCNT films. (с) Raman spectra of pristine SWCNTs (black) of 90% transmittance (at the wavelength of 550 nm) and after AuCl3-doping (red). Raman spectroscopic measurements were carried out with help of Thermo Scientific DXRxi Raman Imaging Microscope together with diode-pumped solid state laser operating at 532 nm. The output power was set to 0.1 mW. The laser spot was focused with a long working distance 50x objective (numerical aperture of
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0.50). The signal accumulation time of 20 s, and laser exposure time of 60 Hz were used. Raman spectra confirmed our microscopy observation, the formation of SWCNTs of a high quality. Figure 1c shows the clearly distinguishable SWCNT peaks (black) related to radial breathing mode (RBM), small intensity D mode and high intensity G modes (with G/D ratio of 155), 2D mode. As seen from the AuCl3-doped SWCNTs spectrum (red), there are several doping-related features present. Chemical doping in SWCNTs involves
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charge transfer between gold chloride and the nanotubes [28; 29; 30; 31]. That changes the work function and Fermi level of the nanotubes. As a result, the corresponding peak changes are seen in Raman spectra of the doped nanotubes. The strong p-type doping shift and change in shape of G-band peak take place due to the charge transfer and phonon stiffening, correspondingly [28]. The intensity change in 2D-band peak happens
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due to the change of the metallicity of the SWCNTs [28]. Following previous studies [27;29], we believe that solution of AuCl3 forms amorphous deposits and gold chloride on the SWCNT walls. On average, the bundles in our samples are small in diameters and consist of several nanotubes only (Figure 1b). The effect is seen in Raman spectra as the RBM-band peaks suppression, as supported additionally by TEM images [27]. SWCNTs 3
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covered with the deposits still retain their tubular structure even after doping. Gold chloride and deposits are found on the tubes and between the bundles. Figure 2 presents Kelvin probe force microscopy scans of the 80% transparency pristine and AuCl3 doped films. The work-function scans clearly demonstrate uniform distribution of the potential over the film
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area testifying only minor role of intertube contacts. Nanometer size inclusion is seen in the doped film that should be ascribed to gold residual. Electrodynamic response of the freestanding films was measured in the range of wavenumbers from few cm-1 up to 20 000 cm-1 using three different spectrometers. One film (65%) was selected to study the spectra in a wide temperature interval, from 300 K down to 5 K. All films were studied in the transmission geometry. The terahertz-subterahertz spectra of the films were measured by continuous-wave spectrometer based on backward-wave oscillators (BWOs) [32] and by the commercially available pulsed time-domain spectrometer (TDS) TeraView. Both these terahertz spectrometers operate in a
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quasi-optical regime (no waveguides used) and allow for direct determination of the spectra of real σ1 and imaginary σ2 parts of the optical (ac) conductivity, without use of the Kramers-Kronig analysis that is a regular procedure in the Fourier-transform infrared spectroscopy where just one quantity is determined experimentally - reflection or transmission coefficient. The BWO-spectrometer operates in two modes [32] In the transmission
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amplitude mode, the frequency-tunable monochromatic radiation passes through an empty aperture that is covered afterwards by a plane sample under study; the division of the two recorded spectra provides with the transmission coefficient Tr of the sample. The transmission phase mode utilizes the Mach-Zehnder interferometric scheme. During frequency scanning, at each frequency the position of the movable mirror in
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the reference channel of the interferometer is recorded that provides minimum of the interference. This is done when there is no sample in the measurement channel and with the sample placed in it; the difference between the two data arrays provides with the spectra of the phase shift, φ, of the radiation passed through the sample. Two measured quantities, Tr and φ, allow to determine the two required optical parameters, σ1 and σ2, using standard Fresnel equations for a layer. In TDS spectrometers, the sample is subject to a picosecond pulse that contains frequency components from about 0.3 THz up to several terahertz. The position and the amplitude of
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the pulse are detected when the measurement channel is empty or “blocked” with the sample. The difference in time between the two peaks is a measure of the radiation delay caused by the sample, and the amplitudes of the peaks give the measure of radiation absorption in the sample. Going from time domain to frequency domain is realized with the Fourier transformation, and results, again, with the spectra of transmission coefficient amplitude Tr and phase φ, with a subsequent determination of the σ1 and σ2, spectra of the sample under study.
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Above terahertz (THz) frequencies, in the infrared (IR) range, spectra of amplitude of the transmission coefficient were measured with a standard Fourier-transform spectrometer Bruker Vertex 80v. 3.
Results and discussion
Due to friability of pristine films their thickness cannot be precisely specified. In the following, we
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discuss our results without assigning certain thickness to all films and without specifying their internal structure. This approach allows to compare the effective optical properties of pristine and doped films. We use the model of complex conducting surface developed in [33] for conducting layers whose thickness is smaller than the skin depth. The complex conductance Y of such layer is given by 4
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𝑌 = 𝜎1 𝑑 + 𝑖𝜎2 𝑑,
(1)
where 1 and 2 are the real and imaginary parts of the layer conductivity and d is its thickness if the layer is homogeneous. Figure 3 presents spectra of real and imaginary parts of conductance of 65% transparency pristine (b,c) and doped (e,f) films measured at two different temperatures; we first discuss the room
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temperature data.
Figure 2. Kelvin probe force microscopy of SWCNT film with 80% transparency (at the wavelength of 550
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nm): (a) topography and (b) work-function maps of the pristine film; (c) topography and (d) work-function maps of the AuCl3 doped film.
Above 3000 cm-1, pronounced minima are seen that are connected with the interband transitions (van Hove singularities) [34]. Strong decrease below 1000 cm-1 of the THz and IR transmissivity (Figure 3a,d) and corresponding behavior of the directly determined real and imaginary THz conductance spectra (Figure 3b,c,e,f) have to be associated with the response of delocalized charge carriers since: a) the spectra of THz real
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and imaginary conductances have the form predicted by the Drude model of free-carrier conductivity – real conductance shows increase towards low frequencies and imaginary conductance displays distinct signs of a characteristic broad peak [35, 36]; b) the low-frequency extrapolations of real conductance are in reasonable agreement with the published dc values [23; 24; 37]; c) the real conductance shows metal-like temperature dependence – increase while cooling down (figure 3b and e). We have obtained the broad-band THz-IR spectra
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of 1d and 2d by fitting the merged THz and IR transmission coefficient spectra (dots and lines in Fig.3a,d, respectively). Minima seen in transmissivity above ≈3000 cm-1 were modeled with regular Lorentzians. Lowerfrequency spectra were modeled on the basis of the Drude expressions for the complex conductivity [35, 36]:
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2 * ( ) d 1 ( ) d i 2 ( ) d 2 dc 2 i 2 dc 2 d ,
(2)
where 𝜎dc is the dc conductivity and is the charge-carrier scattering rate. It is important to stress that the lowfrequency (below ≈100 cm-1) spectra of transmission coefficients were processed together with the directly
5
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measured real and imaginary conductances that determine the transmissivity at these frequencies; such approach allowed us to unambiguously define charge carriers parameters that enter expression (2) (see below). We note that in order to consistently describe the transmissivity and conductance spectra we had to introduce additional term in the form of absorption band located around 100 cm-1. It is indicated by a shaded area in
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middle panels of figure 3 and was modeled by a Lorentzian. One more peculiarity detected in the spectra of all pristine films was a decrease of real conductance towards lowest frequencies below ≈ 10 cm-1 at 300 K
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(figure 3b).
Figure 3. Room temperature (black dots, black lines) and 5 K (blue dots) spectra of (a, d) transmission coefficients and (b, e) effective real and (c, f) effective imaginary parts of conductance of (a, b, c) pristine and
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(d, e, f) AuCl3 doped CNT films with 65% transparency (at the wavelength of 550 nm). Dots correspond to direct measurements on THz pulsed time-domain and cw backward-wave oscillator based spectrometers. Grey-shaded areas in (b) and (e) show absorption peaks due to plasmon resonance. Dashed lines in (a) and (d) correspond to fitting when the absorption resonances at 100 cm-1 in 1d spectra (grey-shaded area in (b) and (e)) are not taken into account.
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To analyze the nature of the absorption band around 100 cm-1, we plot its spectral shape for all pristine and doped films (insets in figure 4). It is seen that the band intensity or spectral weight (area under the 1d curves) is larger for the doped films and quickly decreases with the increase of the films transparency (inset in figure 4b). This is a strong indication that the origin of the bands should be related to the presence of delocalized charge carriers. We associate these absorption peaks with plasmonic oscillations of charge carriers
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that are partly localized by defects, impurities and intersections of tubes. Corresponding excitations have been previously observed in numerous experiments [11; 12]. The amplitude of the bands is significantly smaller than the free-carrier Drude component (characterized by the 1d value at about 10 cm-1) making them not so 6
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clearly pronounced in the present experiments; we believe that the reason is an effective screening by delocalized carriers and by only a small fraction of localized carriers compared with the amount of delocalized carriers. The fact that the position of the bands is basically unchanged in all studied films means that the carriers’ localization distance is determined not by the SWCNTs’ ends [11], but by certain defects within the
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tubes or tubes crossings. We can estimate the distance L between those defects as L = Vp(p)-1, where Vp is the plasmon velocity that is several times larger than the Fermi velocity. With p ≈ 100 cm-1, Vp ≈ 4VF [18] and the Fermi velocity VF ≈ 108 cm/s we obtain L ≈ 0.4 μm. With the mean-free path in our films l ≈ 0.1 μm (see below) we have l/L ≈ 0.25 meaning that our films are rather “clean” [18]. The value L ≈ 0.4 μm correlates well with the average distance between intersections of CNTs, as can be seen from figure 2a-d. We thus assume that the plasmonic excitations occur due to reflections of the charge carrier plasma at the CNT intersections. Wavelength (nm) 105
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10000
Wavenumber (cm-1)
Figure 4. Room temperature spectra of real parts of effective conductance of (a) pristine and (b) AuCl3 doped SWCNT films of different transparency (at the wavelength of 550 nm). Dots correspond to direct measurements on THz pulsed time-domain and cw backward-wave oscillator based spectrometers. Lines correspond to the least-square fit results, as described in the text. Insets show absorption peaks due to plasmon
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resonances in (a) pristine and (b) AuCl3 doped films and the dependence of the peaks oscillator strengths (area under the spectra) on the films transparency (lower inset in frame (b)). To account for the lowest-frequency downturn of the real conductance (that is proportional to
absorption) observed in pristine SWCNTs we recall that their response is determined by two contributions to
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the dc/ac conductivity, one connected with the intrinsic conductivity of a separate SWCNTs or SWCNT bundles, and the other governed by the fluctuation-assisted tunneling (FAT) of charge carriers through the energy barriers at the intertube contacts [38; 39; 40]. The total resistivity is given by 7
AUTHOR SUBMITTED MANUSCRIPT - NANO-114632.R2
−1 (𝑇) 𝑅𝑑𝑐 (𝑇) = 𝜎𝑑𝑐 = 𝐴 𝑒𝑥𝑝 (−
𝑇𝑚 ) 𝑇
𝑇
𝑡 + B exp(𝑇 +𝑇 ).
(3)
𝑠
Here, the temperature Tm accounts for the backscattering of the charge carriers within the SWCNT (SWCNT
cri pt
bundle), kBTt corresponds to the typical energy barrier for the carrier tunneling, the ratio Tt/Ts determines the tunneling in the absence of fluctuations, A and B are temperature independent factors and kB is the Boltzmann constant. The values of the tunnel gaps can be estimated as 1.4-1.6 meV (corresponding to the temperatures Tt = 16-18 K [37]) for pristine SWCNT films and as 0.2-0.25 meV (Tt = 2-3 K [37]) for doped films (this estimation corresponds to CuCl3 doped films, but we expect that it does not differ much from films doped with AuCl3). Let h be the energy of the electromagnetic radiation that probes the response of the film (h is the Planck’s constant). Then, for this energy being much larger than the tunnel gap (h >> kBTt) the radiation does not “feel” the presence of the small gap, and the charge carriers respond as if they were free. For the other
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case, h < kBTt, the carriers experience the impeding tunnel gap leading to lower ac and the dc conductivities [41]. Exactly this behavior is observed around 10 cm-1 for pristine films, where the tunnel gap energy corresponds to the frequency 11 - 13 cm-1. Similarly, no signs of the tunnel gaps of 0.2 - 0.25 meV
measured at significantly higher frequencies. 60
40
70
80
Pristine
dM
Drude (cm-1)
80
an
(corresponding frequencies are 1.4 - 2 cm-1) are detected in the spectra of doped SWCNT films that are 90
100
AuCl3 doped T=300 K
(a)
(cm2V-1s-1)
0
1200
800
(b)
(fs)
400
150
100
(c)
l (m)
pte
50
0.1
0.0
60
(d) 70
80
90
100
Film transparency (%)
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Figure 5. Effective parameters of charge carriers in pristine and AuCl3 doped SWCNT films as dependent on the films transparency: (a) the charge carriers scattering rate, (b) the mobility, (c) the collision time and (d) the mean-free path.
Having identified the Drude-like component in the response of the films one can extract effective
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Page 8 of 13
parameters of corresponding charge carriers. Typical downturn towards high frequencies in the real conductance or peak position of the imaginary conductance (figures 3 and 4) provide with the carriers’ 𝑒
scattering rate γ that, in turn, allows calculation of effective mobility 𝜇 = 2π𝑚∗ 𝛾 (e is the electron charge and 8
Page 9 of 13
m* = 0.2 me [42] is its effective mass), the collision time of τ = (2)-1 and the mean-free path of l = VF (with the Fermi velocity of VF = 8∙107 cm/s [43]). These quantities are plotted in figure 5 where it is seen that they are practically independent on the films transparency. As expected, the obtained values of mobility and meanfree path are much smaller than those of individual SWCNTs, = 1000 - 30 000 cm2V-1s-1 [44; 45; 46; 47], l
cri pt
= 1 - 2 μm [48], due to the effect of intertube contact phenomena.
We now turn to the temperature dependences of the charge carriers’ effective parameters that were determined for the 65% transparency film (figure 6). The scattering rates for the pristine and AuCl3 doped films show similar behaviors with the values for the doped film being slightly larger. This can be due to the increase in the charge carrier concentration in the doped films and thus higher collision frequency and additional scattering on the impurities introduced by doping, or due to the involvement in the scattering processes of small wave vector phonons in the doped films, where the Fermi level is shifted down into the
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valence band [37]. The overall temperature variation of the charge carriers’ parameters (scattering rate, mobility, scattering time, mean-free path) is similar to that observed in semiconductors for free carriers in conduction or valence band where they reveal metal-like frequency dependences of complex conductivity spectra (like those in figure 3). While cooling down from the room temperature down to ≈100 K the scattering
an
weakens due to freezing out of the phonon scattering while at lower temperatures impurity/defects scattering mechanism dominates.
50
0
100
150
200
250
300
-1
dM
(cm )
80
40
65%
Pristine AuCl3 doped
(a)
(cm2V-1s-1)
0
1200
800
400
(b)
0
pte
(fs)
160
80
(c)
0
l (m)
0.15 0.10
ce
0.05
(d)
0.00 0
50
100
150
200
250
300
Temperature (K)
Figure 6. Temperature dependences of (a) the effective charge carriers scattering rate, (b) the mobility, (c) the collision time and (d) the mean-free path of pristine and AuCl3 doped CNT films with 65% transparency (at
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the wavelength of 550 nm).
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Extrapolating the conductance of SWCNT films to the zero-th wavenumber (figure 4), one can calculate that the sheet resistance of the 90% transmittance films after doping lowered from 167 to 67 Ohm/sq. This low value of the sheet resistance for the SWCNT film tells about high level of doping, which leads to significant shift of the Fermi level after the doping compared to the pristine SWCNTs. This results in the increase of the
cri pt
number of charge carriers and in the reduction of the Shottky barrier between the SWCNTs and bundles [49; 50].
We finally note that knowing the exact value of the film thickness would allow us to calculate the conductivity dc=ne=ne2(2m*)-1 and hence the effective free charge carriers’ concentration. With m* = 0.2 me [42] and taking the thickness of d = 20 nm [51] of the pristine and AuCl3-doped 90% transparency films we would obtain the concentration values of 1.9*1019 cm-3 and 4.8*1019 cm-3, respectively.
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4. Conclusions
By measuring the broad-band spectra of complex conductance of a set of high-quality SWCNT films we show that their terahertz-infrared electrodynamic response is mostly determined by unbound charge carriers that provide three main contributions: a) contribution from delocalized carriers described by the Drude
an
conductivity model; b) weak resonance-like absorption band around 100 cm-1 connected with plasmonic oscillations of carriers localized by intersections of SWCNTs in the films; c) gap-like feature at or below ≈10 cm-1 caused by tunnel barriers experienced by the carriers at the SWCNTs contacts. We estimated effective
and the mean-free path.
dM
parameters of the charge carriers that determine the films optical response: the mobility, the scattering rate,
Acknowledgements
The work was supported by the Russian Ministry of Education and Science (Program ‘5top100’). Russian Science Foundation is greatly acknowledged for a financial support (agreement No 17-19-01787) for the
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synthesis, doping and characterisation of SWCNTs. The work was carried out with financial support from the Ministry of Education and Science of the Russian Federation as part of Improve Competitiveness Program of NUST MISiS, implemented by a governmental decree dated 16th of March 2013, No 211.
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