Antenna resonances in terahertz photoconductivity of single wall carbon nanotube fibers

Diamond & Related Materials 27–28 (2012) 36–39

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Antenna resonances in terahertz photoconductivity of single wall carbon nanotube fibers☆ M.V. Shuba a, D. Seliuta b, c,⁎, P.P. Kuzhir a, S.A. Maksimenko a, V.K. Ksenevich d, I. Kašalynas b, J. Macutkevič b, G. Valušis b a

Institute for Nuclear Problems, Bobruiskaia 11, 220030 Minsk, Belarus Centre for Physical Sciences and Technology, Goštauto 11, LT-01108, Vilnius, Lithuania Vilnius Gediminas Technical University, Naugarduko 41, LT-03227 Vilnius, Lithuania d Belarus State University, Nezalezhnastsi Av. 4, 220030 Minsk, Belarus b c

a r t i c l e

i n f o

Available online 27 May 2012 Keywords: Carbon nanotubes Absorption factor Photoconductivity Terahertz

a b s t r a c t Electromagnetic properties of single wall carbon nanotube (SWCNT) film on the surface of silica fibers have been studied numerically and experimentally. Optical properties of SWCNT layers are strongly influenced by the interference effects and antenna resonances in SWCNTs. Experimentally, the antenna resonances have been verified with low temperature photoconductivity measurements in terahertz range. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Development of single wall carbon nanotube (SWCNT) synthesis and device engineering has been rapid during the last decade. Area of potential applications is broad because of SWCNT superior mechanical, thermal and electrical properties. Photodetection is a promising sphere of SWCNT applications originating from sensitivity of SWCNT conductivity to electromagnetic waves [1,2]. In the infrared, light absorption induces interband optical transitions in semiconducting SWCNT giving rise to photoconductivity and photovoltage [3]. On the other hand, small specific heat of SWCNT allows one to create relatively fast and sensitive bolometric (thermal) detector. Especially high detection sensitivity was achieved using SWCNT films suspended in vacuum [4]. Recently it was reported [5] that in SWCNT fibers, slow bolometric signal is accompanied by a fast component related with the terahertz-assisted hopping which is potentially useful for pulsed THz radiation detection. At high frequencies it is appropriate to consider SWCNTs as dipole antennas in one-dimensional limit. However, in many practical SWCNT structures (films, fibers) large number of SWCNTs are employed, since, in contrast to individual SWCNT devices, it allows fabrication of large active area devices. Moreover, ensemble averaging over large number of SWCNTs makes the device characteristics much more predictable. As a rule, individual properties of SWCNTs in SWCNT structures are retained, however, modified. Antenna effects in isolated finite☆ Presented at the Diamond 2011, 22nd European Conference on Diamond, DiamondLike Materials, Carbon Nanotubes, and Nitrides, Garmisch-Partenkirchen. ⁎ Corresponding author at: Centre for Physical Sciences and Technology, Goštauto 11, LT-01108, Vilnius, Lithuania. E-mail addresses: dalius@pfi.lt, [email protected] (D. Seliuta). 0925-9635/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2012.05.012

length SWCNTs [6–9] and CNT-based composite material [10,11] were studied during the last decade. In this work, we investigate electromagnetic properties of SWCNT film within the terahertz range. For optimization of experimental measurements of antenna effects we analyze dependence of the absorption spectra of SWCNT films on various parameters - SWCNT volume fraction, film thickness, SWCNT length. We demonstrate that peaks observed in frequency characteristic of the detected photoconductive signal are associated with the antenna effects in metalic CNTs. Experimental results are evidenced by calculations of light absorption in dielectric media containing various types of SWCNTs. 2. Material and methods SWCNTs were fabricated with laser ablation technology. Silica fibers after removal of the cladding layers were silanized and coated with SWCNTs dispersed in water. SWCNT coating layers of thickness≈ 20 μm were deposited on fibers of diameter 130 μm. Average length of SWCNTs (around 2 μm) was found from scanning electron microscopy imaging of SWCNT layers. For low temperature photoconductivity measurements in SWCNT structures samples were attached to dielectric substrate and contacted with silver paste. DC electric field in the SWCNT layers was kept around 3 V/cm. Negligible heating of SWCNT layers by DC current was verified by proportionality of the signal to the electric field strength. The photoconductive signal was measured in the terahertz range as a response to optically pumped gas laser FIRL-100 (Edinburgh Instruments) delivering THz radiation power of 1–10 mW. Laser spot diameter in the sample position was 1–2 mm. SWCNT-silver paste contacts were screened from THz illumination. The photoconductive signal was insensitive to THz polarization implying that SWCNTs are not oriented.

M.V. Shuba et al. / Diamond & Related Materials 27–28 (2012) 36–39

To describe the electromagnetic energy absorption in SWCNT thin film we consider a dilute composite material comprising of different randomly dispersed types of randomly dispersed and oriented SWCNTs in the matrix with dielectric permeability equal to 1. For low volume fractions of SWCNT inclusions in a host medium we estimated the effective relative permittivity εeff and the effective conductivity σeff of SWCNT composite media. Using the Fresnel formulas we calculated reflectance R = Ir/Io, transmittance T = It/Io and absorption factor A = 1 − T − R of a plate with a given thickness when a plane wave falls normally on the plate, where Ir, It and Io denote intensity of reflected, transmitted and incident electromagnetic waves, respectively. 3. Theory For comparison with experiments, we first find parameters of SWCNT film, corresponding to the interaction of terahertz frequency plane wave with SWCNTs. We assume that the strongest interaction corresponds to the strongest energy absorption in SWCNT film. The ~ n ~) chosen type of SWCNTs is described by the chiral indexes ( m; and we designate the single index j to identify the type of SWCNT. For calculations of εeff and σeff of SWCNT composite media we applied adopted Waterman-Truell formula [11]: ∞

εeff ðωÞ ¼ 1 þ

1 ∑ ∫ α ðω; LÞNj ðLÞdL; 3ε0 j 0 j

ð1Þ

h i σ eff ðωÞ ¼ −iωε0 εeff ðωÞ−1

ð2Þ

where ω = 2πf and f are angular frequency and frequency of the electromagnetic field, respectively; ε0 = 8.85 × 10 − 12 F/m; the function Nj(L) describes the number density of SWCNTs of type j, length L and radius Rj; the factor 1/3 in Eq. (1) is due to the random orientations of the SWCNTs; αj(ω, L) is the axial polarizability of an isolated SWCNTs of type j and can be calculated using the integral equation technique described in [6,7,12]. Assuming the electromagnetic response of semiconducting tubes in terahertz range to be small compared to electromagnetic response of metallic tubes, we do not take into consideration the semiconducting tubes in Eq. (1). Let us nj denote the volume fraction occupied by the j-type SWCNTs (conceived ∞

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s = 1 and s =2 are for first and the second peaks, respectively, Re(β) ≈ 0.02 is retardation coefficient for surface waves in the SWCNT [14]. Frequency dependences of the plate absorption factor A and real part of effective permittivity Re(εeff) at different SWCNT length L0 are presented in Fig. 1b and c, respectively. It is seen that the plate with thickness 5 μm is practically non-transparent in high frequency part of the spectra (> 3 THz) (thick lines in Fig. 1b) and the spectrum of absorption factor of this plate is coincident with the spectrum of thick (2000 μm) plate (thin lines in Fig. 1b). Note that the absorption peaks bellow 3 THz in Fig. 1b are determined by interference effects of plane wave in thin plate (the interference peak positions are different due to different effective permittivities of the plates, see Fig. 1c). The spectra of absorption factor (Fig. 1b) have dips around 2.5, 4.8 and 8.5 THz for SWCNTs with average length 2, 1, and 0.5 μm, respectively. These dips lie between the first and the second antenna resonances of SWCNT and correspond to reduced current excitation in SWCNTs. The second antenna resonances lead to broad peaks in absorption coefficient spectra (indicated by arrows), meanwhile, the first antenna resonances are suppressed because of weak penetration of electromagnetic wave inside the modeled plate due to high value of Re(εeff) (see Fig. 1c). Note that at the same SWCNT volume fraction the penetration depth is larger for film with shorter tubes than that with longer ones. The reason is smaller effective permittivity of short tubes film than that of long tubes film. Fig. 2 shows the frequency dependence of the absorption coefficient of SWCNT films with different film thickness. The second antenna resonance at frequency around 4 THz leads to maximum in absorption spectra (see Fig. 2) in all the considered film thicknesses. Spectra of thick SWCNT layers is distorted below 1 THz due to the interference effects. As it is seen in Fig. 2, the absorption factor of thick (d>1μm) SWCNT films does

2

as cylinders of volume πRj2L) nj ¼ π∫ Rj Lj Nj ðLÞdL, then the volume 0

fraction occupied by all metallic tubes is n ¼ ∑ nj . As was shown in j

Ref. [12], the axial polarizability of all metallic tubes depends slightly on nanotube radius, therefore, we do not take variations in radius into account and instead modeled all metallic SWCNTs as being of a single type. Quantum energy of terahertz radiation is much less than the interband transition energy in metalic SWCNT M11 (1.9 eV [13]). In metallic SWCNTs, intraband electron transitions are responsible for the electrical conductivity which is assumed to satisfy Drude-law [14]. In terahertz region, electron relaxation time is determined by electron-acoustic phonon scattering and was taken 150 fs, which is close to electron relaxation time in graphite [15]. In numerical calculations we consider diluted composite of (12,0) metallic zigzag carbon nanotubes with Gaussian distribution of the nanotube length N(L)~exp[−(L − L0)2/ 2Δ2]; where L0 is average SWCNT length and the parameter Δ will be taken as Δ = 0.3L0. The real part of the effective conductivity presented in Fig. 1a contains two peaks. The first (more intense) peak located at 1.39 THz, 2.42 THz and 4.51 THz; and the second peak (indicated by arrows) at 4.2 THz, 7.2 THz and 13.4 THz occur for average SWCNT length 2 μm, 1 μm, and 0.5 μm, respectively. These peaks are due to antenna (geometrical) resonances of surface waves in the SWCNTs [6–9] at frequencies determined by the condition L0k ≈ π(2s− 1)Re(β), where

Fig. 1. Frequency dependence of the real part of effective conductivity (a), the absorption factor (b) and the real part of effective permittivity (c) for SWCNT film with thickness 5 μm and SWCNT volume fraction 0.01 at different average nanotube length L0 = 0.5 μm (solid line), L0 = 1 μm (dashed line), L0 = 2 μm (dotted line). Thin lines in (b) correspond to SWCNT film with thickness 2000 μm. Electron relaxation time is τ = 150 fs. Arrows indicate the second antenna resonance position.

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tunneling [16]. Each of these mechanisms dominates in specific temperature region and has characteristic relation between SWCNT layer resistance and temperature. We found that at low temperatures (4–10 K), resistivity of SWCNT layers can be approximated by Mott equation for VRH [17]:  1 4 T R ¼ R0 exp M T

Fig. 2. Frequency dependence of the absorption factor A of SWCNT film at different film thickness d (given in micrometers). L0 = 2 μm, τ = 150 fs, n = 0.01.

not exceed 0.1, meanwhile, strong energy dissipation in thin (db 1μm) SWCNT films occurs even at relatively small value of SWCNT volume fraction n=0.01 (see Fig. 2), since electromagnetic wave reflection is small and electromagnetic field easily penetrates into SWCNT film. Fig. 3 demonstrates frequency dependence of the absorption factor of SWCNT film of thickness 0.2 μm at different SWCNT volume fractions and different SWCNT length values. As shown in Fig. 3, absorption of thin SWCNT film increases with decrease of SWCNT volume fraction from 0.08 to 0.005. In such a thin film the absorption spectra is not distorted by the interference and the spectra of absorption factor is similar to the conductivity spectra (compare Figs. 1a and 3). Moreover, at small values of n the first antenna resonance is well pronounced and contributes strongly to the SWCNT film absorption. Calculations show that the effective absorption of terahertz radiation (about 50%) is realized in SWCNT thin films with thickness as small as 0.2 μm and SWCNT volume fraction as low as 0.005. This may be applied in thin SWCNT containing layers designed for shielding of high frequency electromagnetic radiation. 4. Results and discussion SWCNT layers demonstrated activation-type electrical conductivity: exponential decrease of resistance with temperature. In principal, two mechanisms contribute to electrical conductivity of SWCNT films: variable range hopping (VRH) and fluctuation induced

Fig. 3. Frequency dependence of the absorption factor of SWCNT film at different SWCNT volume fractions n and SWCNT length values. The film thickness is 0.2 μm. Electron relaxation time τ = 150 fs.

ð3Þ

where TM is a constant depending on the localization length and density of the localized states. In VRH mode, electric charge transfer originates from hopping of electrons between localized states which are located at the intratube defects or intertube contacts. Photoconductivity in VRH mode originates from generation of excess electrons from the localization centers. In principal, generation of electrons may be related to SWCNT heating (thermal effect) [4] as well as direct excitation of electrons by terahertz photons (terahertzinduced hopping) [5,18]. In case of short terahertz pulses thermal signal and photoexcitation signal can be observed and measured separately due to different characteristic time constants [18]. However, both mechanisms demonstrate practically identical spectral dependencies which may be interpreted in terms of the aforesaid calculations. The photoconductivity signal gradually decreases with temperature increase and vanishes above 80 K. In Fig. 4 we plotted the photoconductivity signal as a function of excitation frequency at temperature 4 K assuming that all the incident power is absorbed by the SWCNT layer. The calculated absorption factor is given by solid line. For calculations SWCNT volume fraction n was taken 0.01. As far as only metallic SWCNT were considered, volume fraction n = 0.01 was evaluated by dividing total volume of metallic SWCNTs by volume of SWCNT layer including SWCNTs of all types and also voids between SWCNTs. For interpretation of the experimental results we assume that higher absorption factor indicates stronger interaction of SWCNTs with terahertz radiation and is related to the stronger photoconductive signal. At the antenna resonancies excess carriers are released and maxima in the photoconductivity spectra are observed (Fig. 4). Second antenna resonance near 4 THz and the dip between the resonancies at around 2.5 THz are clearly visible, however, the first resonance is obscured by weak penetration of electromagnetic wave due to high value of Re(εeff) at low frequencies (see Fig. 1c) as well as by interference effects. Interference effects in the experimental curve do not follow calculation results probably due to nonhomogeneity of SWCNT film. It should be noted that the calculation results can also be applied for optical measurements at room temperature provided by sufficiently large area SWCNT films are prepared with reasonable homogeneity. The only parameter that noticeably changes with temperature is the

Fig. 4. Frequency dependence of the calculated absorption factor (solid line) and experimental photoconductivity signal (dots). Calculation parameters: L0 = 2 μm, τ = 150 fs, d = 20 μm, n = 0.01.

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relaxation time. In terahertz range the electron relaxation time 33 fs at temperature 300 K was estimated in Ref. [11] on the basis of experimental results given in [19]. Calculated spectra of the absorption factor demonstrate that the antenna resonance position does not depend on the relaxation time. 5. Conclusions Terahertz absorption peaks in SWCNT layers are determined by the antenna resonances of SWCNTs and can be varied with SWCNT length variation. The first antenna resonance occurs in the absorption spectra only at small SWCNT concentration and small SWCNT film thickness. Calculation results have been verified by the low temperature photoconductivity measurements at discrete laser lines. Strong energy absorption in thin SWCNT films allows application in electromagnetic shielding layers at high frequencies. Acknowledgements This research was partially supported by EU FP7 under Projects: No. FP7-230778 TERACAN, No. FP7-247007 CACOMEL, No. FP7-266529 BY-NanoERA; Collaborative linkage grant under project CBP.EAP.CLG 983910; ISTC under project No. B-1708; and grant No. MIP-097/2011 from the Research Council of Lithuania. References [1] R.J. Chen, N.R. Franklin, J. Kong, J. Cao, T.W. Tombler, Y. Zhang, H. Dai, Appl. Phys. Lett. 79 (2001) 2258–2260.

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