Electromagnetic modelling of bundle of singlewalled carbon nanotubes with circular geometry for antenna applications

Transcription

1 University o Wollongong Research Online University o Wollongong in Dubai - Papers University o Wollongong in Dubai 017 Electromagnetic modelling o bundle o singlewalled carbon nanotubes with circular geometry or antenna applications Yaseen Jurn University Malaysia Perlis MohamedFareq AbdulMalek University o Wollongong in Dubai Hasliza Rahim University Malaysia Perlis Sawsen Mahmood University o Mustansiriyah Wei Liu University Malaysia Perlis, wliu@ustc.edu.cn Publication Details Jurn, Y. N., AbdulMalek, M., Rahim, H. A., Mahmood, S. A. & Liu, W. 017, 'Electromagnetic modelling o bundle o single-walled carbon nanotubes with circular geometry or antenna applications', Applied Computational Electromagnetics Society Journal, vol. 3, no. 6, pp Research Online is the open access institutional repository or the University o Wollongong. For urther inormation contact the UOW Library: research-pubs@uow.edu.au

2 ACES JOURNAL, Vol. 3, No. 6, June Electromagnetic Modelling o undle o Single-walled Carbon Nanotubes with Circular Geometry or Antenna Applications Yaseen N. Jurn 1,, Mohamedareq Abdulmalek 3, Hasliza A. Rahim 4, Sawsen A. Mahmood 5, and Wei-Wen Liu 6 1 School o Computer and Communication Engineering University Malaysia Perlis (UniMAP), 0000 Arau, Perlis, Malaysia yaseen_nasir@yahoo.com Minister o Science and Technology, aghdad, Iraq 3 Faculty o Engineering and Inormation Sciences University o Wollongong in Dubai (UOWD), Dubai, United Arab Emirates mohamedareqmalek@uowdubai.ac.ae 4 ioelectromagnetics Research Group (ioem), School o Computer and Communication Engineering University Malaysia Perlis (UniMAP), Pauh Putra, Arau, Perlis 0600, Malaysia hrahim3@gmail.com 5 Computer Science Department, College o Education University o Mustansiriyah, aghdad, Iraq mahmood_sawsan@yahoo.com 6 Institute o Nano Electronic Engineering University Malaysia Perlis (UniMAP), Kangar, Perlis, Malaysia vwenliu@yahoo.com Abstract This paper aims to present an eective electromagnetic (EM) modelling approach or circular bundle o single-walled carbon nanotubes (CSWCNTs), based on the electrical conductivity, relative complex permittivity and linear distribution impedance by applying General Ohm s law or this bundle. The equivalent single conductor material (ESCM) model or personiication the C-SWCNTs is presented in this paper. The main target o this modelling approach is to estimate and investigate the EM properties o CSWCNTs using common EM engineering tool solver CST (MWS). For this purpose, the C-SWCNTs and ESCM dipole antennas will be designed and implemented using CST (MWS). Mathematically, the equivalent conductivity model, relative complex permittivity and other parameters o the C-SWCNTs will be derived in this paper and considered as equivalent material parameters or the ESCM. This modelling technique is expected to provide new avenues or designing dierent antenna structures. Index Terms undle o SWCNTs, C-SWCNTs, CSubmitted On: May 4, 016 Accepted On: February 6, 017 SWCNTs dipole antenna, CNTs dipole antenna, nanodipole antenna. I. INTRODUCTION In recent years, the carbon nanotubes composite (CNTs-composite) have been an eicient candidate material or dierent applications due to their unique electrical and physical properties. However, the CNTscomposite material is still at the oreront o research today. It is also considered as promising material or nano-scale applications. The essential investigations o the CNTs antenna model have been conducted by many researchers using dierent comprehensive techniques [1-8]. A lot o research had been presented by Hanson et al. [9-15], in order to investigate and study the undamental electrical properties as well as the EM behavior o the SWCNT dipole antenna. In the context o these studies, in [6] Hanson provided an equivalent model or SWCNT using a common solid conducting material as nanowire, which will be adopted in this work to present the simple equivalent modelling approach or the SWCNT in the ACES

3 53 ACES JOURNAL, Vol. 3, No. 6, June 017 CST (MWS). The bundle o SWCNTs (-SWCNTs) structure was proposed by many researchers instead o individual SWCNT to mitigate the problems related to the SWCNTdipole. Thereore, several studies used the circuit modelling technique or modelling the -SWCNTs, in order to investigate its electrical and EM properties with dierent cross-sectional area (rectangular and circular cross-section) [17-5]. For this purpose, the -SWCNTs dipole antenna coniguration was utilized by many researchers to investigate the EM properties o - SWCNTs [6-30]. Previous research was implemented -SWCNTs dipole antenna using an equivalent circuit modelling approach and numerical mathematical approach. In contrast, it is very diicult to implement these modelling approaches in the available EM engineering tool solver. The most important issue o the nanotechnology devices was represented by conducting a communication between the devices themselves and the outside world. For this reason, this work presents an attempt to get beneits rom the advantages o the C-SWCNTs properties to mitigate this issue by designing nanoantennas. Thereore, the estimation o the EM behavior o C-SWCNTs with several cross-sectional areas through available EM engineering sotware package is a signiicant matter. Thereore, this paper presents equivalent modelling approach (ESCM) or the bundle o SWCNTs with a circular cross-sectional area (C- SWCNTs). As well as, the simple modelling approach or the SWCNT is presented or the purpose o design the multi conductors C-SWCNTs. These modelling approaches will be utilized to exhibit the EM properties o the C-SWCNTs structure and to validate the equivalent modelling approach o C-SWCNTs. The equivalent single conductor material model (ESCM) is proposed to personiication the C-SWCNTs, based on applying the electrical conductivity, relative complex permittivity, linear distribution impedance, and General Ohm s law. Also, the nano-solid tube material model (NSTM) is utilized to represent the SWCNT by applying the same rules and conditions. The purpose o ESCM modelling approach is to investigation and prediction the EM properties o this bundle with dierent numbers o SWCNTs. To validate this modelling approach, the dipole antenna coniguration o multi conductors C- SWCNTs based on NSTM model and the corresponding ESCM model will be designed and implemented in the CST (MWS). The comprehensive perormance comparisons between the ESCM modelling approach results and the results o related corresponding works will be perormed. Finally, the matching input impedance issue o SWCNT dipole antenna and C-SWCNTs dipole antenna is discussed. II. FRAMEWORK For the purpose o EM modelling o C-SWCNTs, the progress o this ramework is presented as ollows: First, explain the general coniguration o C-SWCNTs. Second, the C-SWCNTs is represented by an equivalent single conductor material (ESCM) model and then implemented in the CST (MWS) with a circular crosssectional area by inserting the material parameters o C-SWCNTs into CST (MWS). A mathematical analysis related to an equivalent complex conductivity, complex permittivity and other important parameters o the C- SWCNTs is presented in this work. Third, the nanoscale solid tube material model (NSTM) which is an equivalent to the SWCNT is presented to design the multi conductors C-SWCNTsdipole antenna. Finally, the ESCM dipole antenna is utilized to predict the EM properties o C- SWCNTs structure in dierent geometrical size and dimensions. A. Coniguration o C-SWCNTs The C-SWCNTs is constructed o several identical numbers (N) o armchair-swcnts which has a radius (r), which are arranged in parallel and aligned along the axis o bundle. The number o SWCNTs in this bundle depends on its circular cross-sectional area. Figure 1 shows the sketch o C-SWCNTs. This coniguration is presented in this work based on neglecting the eects o wrapping and twisting o the SWCNTs in the bundle by assuming that all SWCNTs are parallel aligned along the same axis [31]. In addition, the electron transport along individual SWCNT is slightly aected by the nearest SWCNTs in the bundle because the inter-tube conductance is slightly compared to the conductance along the SWCNT [3]. In this coniguration, the cross-section speciic area o C-SWCNTs is calculated as a unction o their characteristics (radius o SWCNT r, lattice constant, and number o SWCNTs in the bundle N) and vice versa: R = r+ ( r+ )( N 1). (1) x Due to the hexagonal geometric structure o this bundle, the total number (N) o SWCNTs included in the bundle depending on the number o outer side SWCNTs (Nx) that orms the outer side o the hexagonal structure. Where, the radius o C-SWCNTs (R ) represents the radius o the ESCM model: R r N = 1, x + () ( r + ) N x N =1+ 6 (j-1). (3) j=

4 JURN, ADULMALEK, RAHIM, ET AL.: ELECTROMAGNETIC MODELLING OF UNDLE OF SINGLE-WALLED CARON NANOTUES 533 Fig. 1. Cross section o C-SWCNTs with equivalent radius (R ) and identical SWCNTs with radius (r).. Mathematical analysis o C-SWCNTs In this section, the key material parameters o C- SWCNTs are derived based on the mathematical analysis o this bundle. The eective conductivity model o the C-SWCNTs is derived mathematically or the purpose o simulation and modelling approach. The equivalent conductivity model o the C-SWCNTs is represented by a general orm bellow: σ x σ = σ I = σ bundle scalar y σ z (4) σ 0 0 = 0 σ σ z Where (I) is the identity matrix, ( σ bundle ) is the eective complex conductivity model o C-SWCNTs and ( σ scalar ) is the scalar unction consist o dierent components o the conductivity with dierent directions (x, y, and z-direction). When the bundle is oriented along the z-direction, thereore, the main component o the conductivity is the ( σ z ); whereas the other components ( σx and σy ) are not taken into account in this work. The embedded medium o this bundle which is assumed has a very small conductivity ( σ 0 ) or ideal dielectric med medium. Thereore, at σ, and bundle >> σ σ 0 med med σx= σ y = 0, the conductivity o the bundle is deduced as shown below: σ bundle j zj j = 1 k x y = m σ. (5) Where, k is the number o materials constructed the bundle and m j is the volume raction actor o the material. In this work, the number o materials is two (which are SWCNTs and dielectric material o the medium). Thereore, the mentioned Equation (5) is given by the general ormula below: = bundle m = m + m. (6) j zj 1 z1 z j = 1 σ σ σ σ Where, ( σ ) is the conductivity o SWCNTs ( z1 σ ), SWCNT and ( σ ) is the conductivity o the imbedded material z (dielectric medium). σ = m σ + m σ bundle 1 SWCNT med. (7) At σ med 0, the conductivity o the C-SWCNTs is deduced by this ormula: NASWCNT σ = σ. (8) bundle SWCNT A Where A is a cross-sectional area o the individual SWCNT SWCNT (circumerence o the SWCNT), and A is the cross-sectional area o the bundle. The ormula mentioned in Equation (8), can be utilized with bundle has (circular or rectangular) cross-sectional area. From the relation between the two areas o SWCNT and C-SWCNTs ( A and SWCNT A ) the volume raction V FR or this NASWCNT structure is represented by the orm ( VFR = ). A Then, this leads to: rn σ = σ. (9) bundle SWCNT R ased on the conductivity o the SWCNT presented in [9], the Equation (9) is given by the orm below: 4Ne V σ = - j. (10) bundle π R h( w jv) Where, e is the electron charge, h is the reduced 34 Plank s constant ( h= Js. ), V is the 5 Fermi velocity o CNT ( V = m/s ), v is a phenomenological relaxation requency o SWCNT ( v = 6T ), so, F, where (T=300) is temperature r v = v π in kelvin, and w is the angular requency. From Equation (10), the complex conductivity o the bundle depends on the number o SWCNTs and the cross-sectional area o the bundle. Hence, this conductivity represents the equivalent conductivity o the ESCM model: = σ. (11) σbundle ESCM In addition to the eective conductivity model o the C-SWCNTs structure, the plasma requency is considered as a remarkable parameter or the EM modelling and simulation o the C-SWCNTs structure in dierent 3D EM simulation sotware package or

5 534 ACES JOURNAL, Vol. 3, No. 6, June 017 antenna applications. On the bases o the eective conductivity model mentioned in Equation (10) and the bulk conductivity model presented by Hanson [9], the plasma requency ( w ) o the C-SWCNTs and ESCM P model is deduced as ollows: e Neq, V w = P o π R ε h. (1) 4NmeV Where Neq, = is the number o electrons π Rr per unit volume o the bundle; also, the phenomenological relaxation requency (v ) o the C-SWCNTs is given by this ormula below: 6T v =. (13) R ' On the other hand, the real part ( ε ) and imaginary '' part ( ε ) o the relative complex permittivity o C- SWCNTs ( ε ) are concluded based on the plasma requency ' wp ε = 1 (14) w + v '' wpv ε = (15) 3 w + wv In another context, according to the general admitted deinition o the complex permittivity demonstrated in the previous research [33], the permittivity and conductivity o C-SWCNTs are linked by the ollowing relation σbundle, i σbundle, r ε = j o o wε wε, (16) σ ' bundle, i ε = 1+, (17) o wε σ '' bundle, r ε =. (18) o wε As a result, the relative complex permittivity o C- SWCNTs is modeled with Equations (14 and 15) or Equations (17 and 18), the both equation sets provide the same results. Thereore, the EM parameters o C- SWCNTs which are extracted (or estimated) in this work is utilized to represent this composite material in the dierent 3D EM simulation sotware packages including CST (MWS) and HFSS and other. C. Modelling approach o C-SWCNTs The material parameters o C-SWCNTs extracted in the mathematical analysis above are make to possible to represent the C-SWCNTs by an equivalent single conductor material model (ESCM) through CST (MWS). This modelling approach contributes to investigate the EM behavior o this bundle with dierent geometrical structures. Thereore, by inserting the material parameters o C-SWCNTs into the CST (MWS) sotware package, the ESCM model can be designed and implemented. For the purpose o modelling approach, the schematic o the ESCM model is an equivalent to the C-SWCNTs Fig.. The dipole antenna or both C-SWCNTs and ESCM was employed to validate this modelling approach depending on the comparison between their results. Fig.. Schematic coniguration o: (a) C-SWCNT and (b) equivalent ESCM model. D. Modelling o SWCNT To overcome the diiculty to dealing with the hollow cylinder o SWCNT, the solid cylinder model was adopted to represent the SWCNT. The transormation actor TRF between these structures was presented in previous works [9, 34]. In this work, the nano-solid tube material (NSTM) model is presented to model the SWCNT. The raw material o NSTM is derived rom original material o SWCNT. This modelling approach aims to design and predict the EM properties o multi conductors C-SWCNTs through design the C- SWCNTs dipole antenna in the CST (MWS) sotware package. The conductivity o the NSTM model ( σ ) NSTM is deduced rom the surace conductivity o SWCNT ( σ SWCNT ) presented in [9], as shown in the ormula below: 4eV σ j SWCNT r π hr w jv w psw σ = = NSTM. (19) ( ) The plasma requency ( ) o SWCNT can be estimated based on the bulk conductivity model presented in [9]. As well as, the relative complex permittivity o SWCNT ( ε ) is possible to estimate as shown below e V wpsw =, (0) o π r ε h ' ε = 1 w w psw + v vw psw 3, (1) ε '' =. () w + wv ' Where ( ε ) the real part and ( ε '' ) the imaginary part o the SWCNT relative complex permittivity. Hence,

6 JURN, ADULMALEK, RAHIM, ET AL.: ELECTROMAGNETIC MODELLING OF UNDLE OF SINGLE-WALLED CARON NANOTUES 535 in order to implement the simulation technique o this modelling approach, the material parameters o the SWCNT are inserted in the CST (MWS) as a new normal. III. APPLICATION OF C-SWCNTS AND ESCM MODEL In order to estimate the EM properties o C- SWCNTs, the dipole antenna o both multi conductors C-SWCNTs and corresponding ESCM model were applied and solved through CST (MWS). Furthermore, provide a comparison between these structures, in order to validate the ESCM model. The schematics o the C- SWCNTs and ESCM dipole antennas are shown in Fig. 3. With regard to both C-SWCNTs and ESCM dipole antennas, in the CST (MWS) environment, the SWCNT material and C-SWCNTs material were set up as new, normal materials in Drude method. Their parameters were inserted in the CST (MWS) to represent the equivalent NSTM model or SWCNTs and ESCM model to C-SWCNTs. These parameters were previously extracted in this work. This process represents the modelling approaches or both SWCNT and C- SWCNTs in the CST (MWS) sotware package in order to preace the design o dierent types o CNT antennas in the simulation mode. That means, a raw material o the equivalent NSTM model and ESCM model is derived rom SWCNTs and C-SWCNTs materials instead o deriving rom other material. (a) (b) Fig. 3. Dipole antenna structure or both: (a) C- SWCNTs and (b) ESCM model. IV. MATCHING IMPEDANCE OF C- SWCNT DIPOLE ANTENNA In order to implement the C-SWCNTs dipole antenna, the matching input impedance issue is demonstrated in this paper. Mathematically, based on the antenna concepts, the surace impedance is considered as an input impedance or dipole antenna [35]. Hence, according to the equivalent circuit diagram o the SWCNT presented by urk [1-4], the input impedance o SWCNT antenna, which is equal to the input impedance o the equivalent nanowire model o SWCNT ( Z in, equvl ) which presented in previous work [34], can be estimated. For simplicity, with regards to the SWCNT, the quantum parameters are given below: L L Zin, equvl =, πσ r = πrσ (3) equvl SWCNT in, equvl. Z = Rq + jwζ (4) Here, Rq is the quantum resistance, and ζ is the quantum inductance. These quantities are mathematically presented as ollows: πhvl πhl Zin, equvl = + jw, (5) 4eV 4eV πhvl 3πhLT Rq = =, (6) 4eV rev 4eV π hl ζ =. (7) On the other hand, with regards to the C-SWCNTs dipole antenna, the quantum resistance and quantum inductance can be estimated based on the general ormula o the eective impedance o the bundle ( Z ) bundle according to the impedance o SWCNT: Zin, equvl Z = bundle. (8) N For simplicity, the eective impedance o C- SWCNTs based on the assumption that all SWCNTs are metallic, identical and arranged in the parallel structure. Thus, the quantum parameters o C-SWCNTs are computed as given below: πhvl 3πhLT R = =, (9) q 4Ne V Nre V π hl ζ =. (30) 4 Ne V The one o the main problems o C-SWCNTs dipole antenna is the matching issue between this antenna and the eeding source (discreet port). In this work, the simple matching approach is presented to mitigate this problem in simulation mode. This matching approach depends on adaptation the Normalized Fixed Impedance (NFI) value, which is one parameter o the s11 parameters setting window, in order to balancing the eectiveness o the input impedance o this dipole

7 536 ACES JOURNAL, Vol. 3, No. 6, June 017 antenna with the internal impedance o the eeding source. The NFI option o the s11 parameters in CST (MWS) sotware package is very important when the initial value o the NFI is selected based on computing the value o R q rom Equation (9). This value represents the impedance value that the system is needed to realize the matching between eeding source and dipole antenna (load). In another context, this value represents a starting value to obtain a well value o matching impedance between source and C-SWCNTs dipole antenna to obtain the optimum result o s11 parameters. Indeed, the simple matching approach presented in this work is implemented or design C- SWCNTs dipole antenna. As well as, this matching process is beneits or achieving the matching situation or dierent nanoelectronic antennas. V. SIMULATION RESULTS AND DISCUSSION In this work, the CST (MWS) sotware package is utilized to implement both equivalent modelling approaches, namely the NSTM or the SWCNT material to design multi conductors C-SWCNTs, as well as ESCM to design single conductor which is corresponding to C-SWCNTs, in which the dipole antenna coniguration was employed to achieve this purpose. To design C- SWCNTs dipole antenna, each packed o SWCNTs bundle will be connected to a square contact to make a eeding source touch all SWCNTs. The dimensions o this contact (length width) are equal to (W D t) and thickness is equal to (r). The discreet port was used as a eeding source or all dipole antennas designed in this work. The simulation results o this work could be implemented as ollows. A. Simulation results o C-SWCNTs and ESCM model In this section, both structures o C-SWCNTs and ESCM modelling approach are implemented, in order to investigate the important material parameters o the C-SWCNTs and to validate the ESCM modelling approach, based on comparison o their results. In addition, estimate the EM properties o C-SWCNTs in dierent cross-section area (small and large cross section area) which contains dierent numbers o SWCNTs. 1. Investigation o C-SWCNTs material parameters In order to estimate and study the perormance o the conductivity o the C-SWCNTs ( σ bundle ), which represent the conductivity o the equivalent ESCM model, the C-SWCNTs included various numbers o the identical SWCNTs (N = 7, 19, 36, and 61) were implemented or this purpose. Figure 4 represent the behavior o the conductivity versus requency, based on increases the number o SWCNTs in the bundle. Also, the plasma requency o the bundle ( w P ) is aected by increases the number o SWCNTs (N) in the bundle, as shown in Fig. 5. As a presented in these igures, the behavior o the conductivity o C-SWCNTs was illustrated with increases the number o SWCNTs in this bundle (N). This mean, with increases the equivalent radius o the bundle. The plasma requency o this bundle was decreased due to increases the radius o SWCNT. In contrary, the plasma requency was increased due to increases the number o SWCNTs included in this bundle.. Validation o ESCM model To validate the ESCM modelling approach, the dipole antenna coniguration was designed based on the multi conductors C-SWCNTs structure and the ESCM model. The C-SWCNTs with dierent number o SWCNTs (N = 7, 19, 36 and 61) are mainly used with those corresponding cross-sectional area o ESCM model, in order to investigate the comparison between these structures. In addition, these two structures have the same lengths or designing the dipole antenna. All o the SWCNTs included in the bundle are identical, have the same radius (r =.71 nm). Similarly, the lattice distance ( ) between the two adjacent SWCNTs is equally and equal to (0.34 nm). The length o dipole antenna is (L = 30 µm). The details o C-SWCNTs and ESCM model are described in Table 1, in order to design the dipole antennas associated with these structures. The two types o dipole antennas centered by a eeding gap (d = R ). The results o these antennas are shown in Fig. 6 or C-SWCNTs and corresponding ESCM dipole antennas. Conductivity (S/m) Imag part Realm part 1.5 x 107 N=7 N= N=37 N= Frequency (GHz) σ bundle Fig. 4. The conductivity o -SWCNTs ( ) versus the requency with various number o SWCNTs (N).

8 JURN, ADULMALEK, RAHIM, ET AL.: ELECTROMAGNETIC MODELLING OF UNDLE OF SINGLE-WALLED CARON NANOTUES 537 Plasma Frequency in THz N=7 N=19 N=37 N= Radius o SWCNT, (r) nm Fig. 5. Plasma requency o C-SWCNTs ( w P ) versus the radius o SWCNT with various number o SWCNTs (N). Table 1: Details o -SWCNTs and corresponding ESCM structures Number o Cross-Section Total Number Corresponding SWCNTs in the Area o Co SWCNT-s Radius o C- Outer Side o SWCNTs and in the undle SWCNT-s and the undle ESCM A N ESCM R (nm) Structure Nx (Micrometer ) As a result, by increasing the number o SWCNTs included in the bundle, the resonant requency increases and the s11 parameters improved. Meanwhile, by increasing the cross-sectional area o the ESCM model, the same behavior was shown with related to resonant requency and s11 parameters. In another context, the two structures, multi conductors C-SWCNTs and ESCM model have the same response to changing the corresponding design parameters. These simulation results represent the EM behavior o C-SWCNTs with a small cross-sectional area. 3. Veriy the accuracy o modelling results In order to veriy the accuracy o the simulation results in this work, the comparisons between the results o C-SWCNTs and ESCM modelling approach have been presented. The comparison between these structures was carried out based on the behaviour o the resonant requency versus dierent number o the SWCNTs included in the bundle. Where, both dipole antennas have same length (L = 30 μm) and same cross-sectional area, which are changed based on the number o SWCNTs in the bundle. The comparison o these simulation results or both dipole antennas was illustrated in Fig. 7. Likewise, the other comparison or both dipole antennas has been implemented based on the eiciency o them, at the same length (L = 30 μm) and same cross-sectional area where (N = 7) S11-parameters (d) N = 1 N = 7-50 N = 7 N = N = 19 N = N = 37 N = 61 N = Frequency (GHz) Fig. 6. Simulation results o multi conductor C- SWCNTs at N = (7, 19, 37 and 61) and an equivalent ESCM dipole antennas. The solid lines are the C- SWCNT results and the dotted lines are the ESCM results. The simulation results o C-SWCNTs and corresponding ESCM dipole antennas exhibited in Fig. 8, indicate the good conormity between the multi conductors C-SWCNTs structure and ESCM model. Frequency (GHz) N Fig. 7. Comparison results between C-SWCNT and ESCM dipole antennas, based on the resonant requency versus the number o SWCNTs included in the bundle at N = (7, 19, 37 and 61). From the comparisons results presented in Fig. 7 and Fig. 8, a well accuracy results and compatibility can be observed between both C-SWCNTs and ESCM dipole antennas. That means, the ESCM modelling approach has a good validation to represent the C-SWCNTs material structure.

9 538 ACES JOURNAL, Vol. 3, No. 6, June SWNTs dipole antenna ESCM dipole antenna 0-10 N = 71 N = 1141 N = 611 Eiciency S11-parameters (d) Frequency (GHz) Fig. 8. Comparison results between C-SWCNT and ESCM dipole antennas, based on the eiciency versus requency at N = (7). 4. Electromagnetic behaviour o C-SWCNTs with large cross-section area The equivalent ESCM model or the C-SWCNTs area was utilized to predict the electromagnetic properties o C-SWCNTs with a large cross-section area, based on designing and implementing the ESCM dipole antenna into CST (MWS). The details o dierent crosssectional areas o the C-SWCNTs and corresponding ESCM model are described in Table, the crosssectional areas were selected based on the number o SWCNTs (N) included in the bundle, which is related to the corresponding number o outer SWCNTs o hexagon or the original structure o C-SWCNTs (N x = 10, 0 and 30). With regard to these details, the dipole antennas are designed and implemented in CST (MWS), in order to investigate the EM properties o C-SWCNTs at large scales geometric structures. The results o these antennas were shown in Fig. 9. Table : Simulation details o ESCM that are equivalent to C-SWCNTs structures Number o Radius o Corresponding Cross-Section SWCNTs in Equivalent Number o Area o ESCM the Outer ESCM Model to SWCNTs in the A Side o the the C-SWCNTs (Micrometer undle Nx R (Nanometre) C-SWCNTs ) N (Tube) From this result, the resonant requency o ESCM dipole antenna was increased by increasing the crosssectional area o ESCM model. Likewise, the s11 parameters o these dipole antennas improved. This result represents the starting phase to deal with a large geometrical structure o the C-SWCNTs or the irst time Frequency (GHz) Fig. 9. Simulation results o ESCM dipole antenna with large cross-section areas, which are equivalent to N = (71, 1141, and 611). VI. CONCLUSION In this paper, the two modelling approaches or SWCNT and C-SWCNTs were presented and carried out into CST (MWS). To validate the ESCM modelling approach, the several numbers o SWCNTs which constructs the bundle with speciic cross-section areas were designed and their results are also compared with those o similar cross-section area o the corresponding ESCM model. From these comparisons, a consistency o results was ound between ESCM model and C- SWCNTs. The simulation results o ESCM and C-SWCNTs dipole antennas demonstrated using o ESCM model to represent the C-SWCNTs instead o C-SWCNTs with hollow or solid cylinder SWCNTs structure. This led to reduce the overall complexity and solving the simulation time problem or estimation o EM properties or C-SWCNTs with large number o SWCNTs. The main goal o the ESCM modelling approach is to make a computation analysis less complicated at the simulation mode. The designing o ESCM model with a small and large cross-sectional areas corresponded to C-SWCNTs with dierent numbers o SWCNTs make the estimation o the EM properties o C-SWCNTs with a short time be compared with the traditional method o multi conductors C-SWCNTs. Actually, the perormance evaluation indicators o C-SWCNTs dipole antenna are dependent on the diameter and length o C-SWCNTs, as well as the number o SWCNTs included in this bundle. Further optimization can be done to achieve better radiation perormance, based on these perormance indicators. The contribution o this paper is to provide and validate the equivalent single conductor material (ESCM) model approach or the C-SWCNTs using the CST (MWS) sotware package. The raw material o ESCM

10 JURN, ADULMALEK, RAHIM, ET AL.: ELECTROMAGNETIC MODELLING OF UNDLE OF SINGLE-WALLED CARON NANOTUES 539 model is derived rom the material properties o C- SWCNTs. Moreover, with regards to the antenna applications, the presented modelling approach or C-SWCNTs is very useul and make possible to design antenna uses in on-chip wireless communication. This leads to make the CNTs is a candidate promising material or this purpose. REFERENCES [1] P. J. urke, Lüttinger liquid theory as a model o the gigahertz electrical properties o carbon nanotubes, IEEE Trans. Nanotechnology, vol. 1, no. 3, pp , 00. [] P. J. urke, Correction to Lüttinger liquid theory as a model o the gigahertz electrical properties o carbon nanotubes, IEEE Trans. Nanotechnology, vol. 3, no., p. 331, 004. [3] P. J. urke, An RF circuit model or carbon nanotubes, IEEE Trans. Nanotechnology, vol., no. 1, pp , 003. [4] P. J. urke, Correction to an RF circuit model or carbon nanotubes, IEEE Trans. Nanotechnology, vol. 3, no., pp. 331, 004. [5] P. urke, S. Li, and Z. Yu, Quantitative theory o nanowire and nanotube antenna perormance, IEEE Transactions on Nanotechnology, vol. 5, no. 4, pp , 006. [6] L. Nougaret, G. Dambrine, S. Lepilliet, H. Happy, N. Chimot, V. Derycke, and J.-P. ourgoin, Gigahertz characterization o a single carbon nanotube, Appl. Phys. Lett., vol. 96, no. 4, pp , 010. [7] A. Naeemi and J. D. Meindl, Physical modeling o temperature coeicient o resistance or singleand multi-wall carbon nanotube interconnects, IEEE Electron Device Letters, vol. 8, no., pp , 007. [8] A. Naeemi, R. Sarvari, and J. D. Meindl, Perormance modeling and optimization or singleand multi-wall carbon nanotube interconnects, 44 th ACM/IEEE Design Automation Conerence, pp , 007. [9] G. W. Hanson, Fundamental transmitting properties o carbon nanotube antennas, IEEE Trans. Antennas. and Propag., vol. 53, no. 11, pp , 005. [10] G. W. Hanson and Jin Hao, Inrared and optical properties o carbon nanotube dipole antennas, IEEE Trans. Nanotechnol., vol. 5, no. 6, pp , 006. [11] G. W. Hanson. Current on an ininitely-long carbon nanotube antenna excited by a gap generator, IEEE Trans. Antennas. and Propag., vol. 54, no. 1, pp , 006. [1] G. W. Hanson and Jay A. erres, Multiwall carbon nanotubes at RF-THz requencies: Scattering, shielding, eective conductivity and power dissipation, IEEE Trans. Antennas and Propag., vol. 59, no. 8, pp , 011. [13] N. Fichtner, X. Zhou, and P. Russer, Investigation o carbon nanotube antennas using thin wire integral equations, Advances in Radio Science, vol. 6, pp , 008. [14] N. Fichtner, X. Zhou, and P. Russer, Investigation o copper and carbon nanotube antennas using thin wire integral equations, IEEE Proceedings o Asia-Paciic Microwave Conerence, pp. 4, 007. [15] J. Hao and G. W. Hanson, Electromagnetic scattering rom inite-length metallic carbon nanotubes in the lower IR bands, Physical Rev.., vol. 74, pp. (035119,1)-(035119,6), 006. [16] G. W. Hanson, A common electromagnetic ramework or carbon nanotubes and solid nanowires Spatially dispersive conductivity, generalized Ohm s law, distributed impedance, and transmission line model, IEEE Trans. Microwave Theory Tech., vol. 59, no. 1, pp. 9 0, 011. [17] M. S. Sarto, A. Tamburrano, and M. D Amore, New electron-waveguide-based modeling or carbon nanotube interconnects, IEEE Transaction on Nanotechnology, vol. 8, pp. 14-5, 009. [18] M. S. Sarto and A. Tamburrano, Multiconductor transmission line modeling o SWCNT bundles in common-mode excitation, IEEE International Symposium on Electromagnetic Compatibility, vol., pp , 006. [19] M. Sabrina Sarto and A. Tamburrano, Electromagnetic analysis o radio-requency signal propagation along SWCN bundles, 6th IEEE Conerence on Nanotechnology, pp , 006. [0] M. D Amore, M. S. Sarto, and A. Tamburrano, Signal integrity o carbon nanotube bundles, IEEE International Symposium on Electromagnetic Compatibility, pp. 1-6, 007. [1] M. D Amore, M. Ricci, and A. Tamburrano, Equivalent single conductor modeling o carbon nanotube bundles or transient analysis o highspeed interconnects, 8th IEEE Conerence on Nanotechnology, Arlington, Texas, pp , 008. [] M. D Amore, M. S. Sarto, and A. G. D'Aloia, Equivalent single conductor or modeling near ield radiated emission o carbon nanotube bundles, 9th IEEE Conerence on Nanotechnology, Genoa, pp , 009. [3] M. D Amore, A. G. D Aloia, M. S. Sarto, and A. Tamburrano, Near ield radiated rom carbon nanotube bundles, IEEE Transactions on Electromagnetic Compatibility, vol. 54, pp , 01. [4] Q. Libo, Z. Zhangming, D. Ruixue, and Y. Yintang, Circuit modeling and perormance analysis o SWCNT bundle 3D interconnects,

11 540 ACES JOURNAL, Vol. 3, No. 6, June 017 Journal o Semiconductors, vol. 34, pp. ( ) ( ), 013. [5] M. D'Amore, F. Maradei, S. Cruciani, and M. Feliziani, High requency perormance o carbon nanotube-based spiral inductors, Conerence o International Symposium on Electromagnetic Compatibility (EMC Europe), rugge, elgium, pp , 013. [6] Y. Huang and W.-Y. Yin, Perormance predication o carbon nanotube bundle dipole antenna, Proceedings o Asia-Paciic Microwave Conerence, pp. 1-4, 007. [7] Y. Huang, W.-Y. Yin, and Q. H. Liu, Perormance prediction o carbon nanotube bundle dipole antennas, IEEE Transactions on Nanotechnology, vol. 7, pp , 008. [8] Y. Wang, Y. M. Wu, L. L. Zhuang, S. Q. Zhang, L. W. Li, and Q. Wu, Electromagnetic perormance o single walled carbon nanotube bundles, Microwave Conerence, Asia Paciic, pp , 009. [9] A. M Attiya, Lower requency limit o carbon nanotube antenna, PIER 94, pp , 009. [30] S. Choi and K. Sarabandi, Perormance assessment o bundled carbon nanotube or antenna applications at terahertz requencies and higher, IEEE Transactions on Antennas and Propagation, vol. 59, pp , 011. [31] M. S. Sarto and A. Tamburrano, Multiconductor transmission line modeling o SWCNT bundles in common-mode excitation, IEEE International Symposium on Electromagnetic Compatibility, vol., pp , 006. [3] H. Stahl, J. Appenzeller, R. Martel, P. Avouris, and. Lengeler, Intertube coupling in ropes o singlewall carbon nanotubes, Phys. Rev. Lett., vol. 85, no. 4, pp , 000. [33] S. J. Oranidis, Maxwell s Equations. Chapter 1, Electromagnetic Waves and Antennas, 010. [34] G. W. Hanson, A common electromagnetic ramework or carbon nanotubes and solid nanowiresspatially distributed impedance, and transmission line model, IEEE Transaction on Microwave Theory and Techniques, vol. 59, pp. 9-0, 011. [35] C. A. alanis, Antenna Theory Analysis and Design. 3rd edition, John Wiley and Sons, USA, 005. Yaseen Naser Jurn was born in aghdad, Iraq. He received the.sc. degree in Communication Engineering rom the University o Technology, aghdad, Iraq, in 1995, the M.Sc. degree in Communication Engineering (Direction o Arrival) rom the Universiti Technology, aghdad in 00 and the Ph.D. degree in Communication Engineering (Nano Antenna Design) rom the University Malaysia Perlis (UniMap), Perlis, Malaysia, in 017. Currently he is a Senior Engineer in Minister o Science and Technology, aghdad, Iraq, where he has been an Engineer since 1995 in Ministry o Science and Technology. His main personal research interests are modelling, simulation, and antenna design, antennas and propagations, electromagnetics, modern nanomaterial structure design, nano antenna design, modelling and simulation o nano antenna. Mohamedareq Abdulmalek obtained his.eng. (Hons.) - Electronic and Communication Engineering rom the University o irmingham, U. K. in He received his M.Sc. (Eng.) in Microelectronic Systems and Telecommunications at The University o Liverpool, U. K. in 004 and Ph.D. Electrical Engineering (Radio Frequency and Microwave) in 008 rom The University o Liverpool, U. K. Recently, he is an Associate Proessor in Faculty o Engineering and Inormation Sciences, University o Wollongong in Dubai. His main research interests are antenna design, embedded computing, microwave absorbers rom agricultural waste and eects o RF on human s health. Hasliza inti A. Rahim received the achelor degree in Electrical Engineering rom University o Southern Caliornia (USC), Los Angeles, USA in 003. Later, she received the Master in Electronics Design System rom the University Sains Malaysia, Transkrian, Pulau Pinang, Malaysia in 006 and Ph.D in Communication Engineering rom the University Malaysia Perlis, Perlis, Malaysia in 015. She joined the School o Computer and Communication Engineering, UniMAP in 16th August 006 as Lecturer and now as Senior Lecturer. She is the Head and Principle Researcher o ioelectromagnetic Excellence Research Group (ioem). Her extensive research area covers a range o applied engineering including advanced technologies or 4G/5G, antennas, wireless body area networks (WAN), eects o RF on health, electromagnetics, and bioelectromagnetics. Several research unds were granted nationally such as Fundamental Research Grant Scheme, National ScienceFund, and Malaysian Communications and Multimedia Commission. She has authored and coauthored more than 50 peer reviewed scientiic publications, including articles in Nature Publishing Group journal (Scientiic Reports), 3 patents, and book chapters. She has been awarded with the Excellence

12 JURN, ADULMALEK, RAHIM, ET AL.: ELECTROMAGNETIC MODELLING OF UNDLE OF SINGLE-WALLED CARON NANOTUES 541 Woman Inventor by the University Malaysia Perlis in 010. Sawsen Abdulahadi Mahmood was born in aghdad, Iraq. She obtained her.sc. in Mathematics rom the University o aghdad, aghdad, Iraq, in 199, the M.Sc. degree in Computer Science rom the University o Technology, aghdad, Iraq, in 00. She received her Ph.D. in Computer Science at the Faculty o Computer Science in 015 at University o Technology, aghdad, Iraq. Recently, she is an Associate Proessor in Faculty o Computer Science, University o Mustansiriyah, in aghdad, Iraq. Her main personal research interests are Pattern Recognition and Machine Learning, 3D image analysis recognition, 3D video analysis, Surveillance System based on Internet o things environment, and Voice Recognition. Liu Wei Wen obtained the.sc. with Education (.Sc. Hons.) in Physics, 00, rom Physics Department, Faculty o Science, University Putra Malaysia (UPM), Serdang, Selangor. The M.Sc. in Materials Science, 005 Physics Department, Faculty o Science, University Putra Malaysia (UPM), Serdang, Selangor. He received the Ph.D. in Nano Materials, 01, rom School o Materials and Mineral Resources Engineering, Universiti Sains Malaysia (USM), Nibong Tebal, Penang. His main personal research interest is in synthesis o carbon nanotubes and graphene and their application in biosensor.

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