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Abstract
An extensive study on the optical characteristics of vertically aligned single-wall carbon nanotubes (SWCNTs) and engineered multi-wall carbon nanotubes (MWCNTs) using finite-difference time-domain (FDTD) simulation technique is presented in this work. We investigated absorption characteristics for SWCNTs, MWCNTs, dual-diameter MWCNTs, and cone MWCNTs with the changes in the occupation area and incident angle of light in the visible wavelength range. The enhancement of absorption was achieved by changing the geometrical shapes. Our study suggests that 99.569 % of the total light energy is absorbed in SWCNTs and 99.883 % in cone-shaped-top MWCNTs with an occupation area of 20 % and 50 %, respectively, at 450 nm wavelength and 5000 nm tube height. Moreover, for both SWCNTs and MWCNTs, reflectance increases with the increase of the occupation area due to the larger reflecting top surface area. We found that a drastic reduction of absorption occurs as the angle between the tube axis of aligned carbon nanotubes (CNTs) and the incoming light source increases above 30 °. Our study will be valuable for further investigation of the optical properties of shape-engineered CNTs and will promote CNT-based ultra-broadband absorber devices and systems for multifunctional optoelectronic applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since the invention of carbon nanotubes (CNTs) in 1991 [1], there have been reports of diverse applications of CNTs exploiting their unique electrical [2], thermal [3,4] and optical [5,6] properties. In particular, tunable optical properties of CNTs are of prime interest to researchers. Electrical and optical properties of SWCNTs and MWCNTs have been investigated theoretically and experimentally. The versatile application of CNTs stems from their ability to be metallic or semiconducting depending on the chirality. CNTs have applications in the design of on-chip optical interconnect [7], photo-detector [6,8], photovoltaic [9], light emitter [10,11], optical nanoantenna [12] and most importantly CNT based plasmonics [13] that have opened a new avenue in the research of CNT devices and systems. Moreover, literature shows strong absorption of light by aligned CNTs in the whole electromagnetic spectrum makes them a perfect candidate for high efficiency solar cells [14] and photonic crystals [15].
Though CNTs inherently act as a good absorber with a low refractive index [16], numerous studies are still going on for further enhancement of absorption of light. Che $et~ al.$ [17] and Kong $et~al.$ [18] reported mechanisms to enhance absorption of light by incorporating different nanoparticles in CNTs. Ye $et~ al.$ [19] have found that the density of CNTs adversely affects the absorption whereas the increase of the outer diameter of MWCNTs increases absorption. Due to inherent randomness in the arrays of SWCNTs during complex fabrication methods and more homogeneity in the structure of MWCNTs, it is plausible to explore the properties of MWCNTs by further engineering their geometrical shapes, height and spacing in a more controllable way. Though the absorption characteristics of vertically aligned SWCNTs and MWCNTs are already investigated [16,20], exploration of optical properties for engineered MWCNTs such as MWCNTs with dual diameter and nanocone tip are yet to be reported. As cone shape carbon nanotips are already grown experimentally [21,22], engineered MWCNT based nanostructure optical characteristic study will open door for various optoelectronic and metrology applications.
In this study, we explored the optical characteristics of CNTs (by considering each tube identical to a roll of graphite) and emphasized on enhancement of optical absorption through engineering of the tip of MWCNTs. We focused on the enhancement of absorption of vertically aligned arrays of MWCNTs in the visible spectrum by shaping their top surface to reduce the reflecting surface area. We performed a comparative analysis of optical characteristics i.e. absorption, reflection and transmission of SWCNTs and MWCNTs by varying the incident angle of light, occupation area, and the geometry and proposed a near-perfect wideband light absorber. Optimal incidence angle of light with respect to the tube axis and optimal occupation area for vertically aligned CNT array were also determined for maximum absorbance.
2. Methodology
2.1 Nanostructural optimization and optical property analysis methods
Vertically aligned periodic array of CNTs are modeled to study the optical properties of CNTs. CNTs are orderly aligned along the z direction and periodicity exists along x and y directions. The schematics of different structures studied in this work are represented in Fig. 1. Figure 1(a) shows a well-aligned array of SWCNTs, Fig. 1(b) presents the periodic array of MWCNTs, Fig. 1(c) is the array of MWCNT dual diameter structure [23], and Fig. 1(d) illustrates the array of MWCNT cone structure. For SWCNT structure, we used diameter, d = 1.5 nm and center to center distance between SWCNTs, a was taken to be 1.88 nm for the case of an occupation area of 50 %. Occupation area, $A_{OCC}$, for the square lattice structure considered, is calculated using Eq. (1),
For MWCNT, a single MWCNT was consisted of twenty concentric nanotubes with an outer diameter of d = 20.5 nm and 50 % occupation area was ensured in this array by taking a = 25.69 nm. For MWCNT dual diameter configuration, the inner bundle consisted of 10 nanotubes with 5000 nm height for a combined diameter of $d_1 = 10.25$ nm and the outer bundle was comprised of 10 nanotubes with a height of 3500 nm to form the combined outer diameter of $d_2 = 20.5$ nm. Here, center to center distance between MWCNTs, a = 25.69 nm was taken for ensuring 50 % occupation area.
Fig. 1. Schematics of the vertically aligned periodic array of (a) SWCNT with d = 1.5 nm and a = 1.88 nm for 50 % occupation area, (b) MWCNT with d = 20.5 nm consisted with 20 concentric nanotubes and a = 25.69 nm for 50 % occupation area, (c) MWCNT in dual diameter configuration with ${d_1}$ = 10.25 nm, ${d_2}$ = 20.5 nm and a = 25.69 nm for 50 % occupation area, (d) MWCNT cone structure with d = 20.5 nm consisted with 20 concentric nanotubes and a = 25.69 nm for 50 % occupation area.
For MWCNT cone structure, the innermost tube was of 5000 nm height and the outer tubes are reduced in height by 50 nm in each step to form the shape of a cone on the top surface of the array. A bundle of 20 nanotubes with d = 20.5 nm and a = 25.69 nm was used for this case similar to other MWCNT structures. The occupation area was varied from 10 % to 55 % for the case of SWCNT and from 20 % to 50 % for MWCNT, MWCNT dual diameter and MWCNT cone structures with a fixed diameter. Incidence angle of the source with respect to tube axis for each structure was also varied from $0^{\circ }$ to $60^{\circ }$ to study its effect on the absorbance of light.
The complex refractive index of each tube is modelled from the dielectric properties of graphite employing a local dielectric tensor in cylindrical coordinate system and further simplifying using effective medium approximation as described in Bao $et~ al.$ [24]. Lumerical FDTD solution package was used to perform the simulations of all the structures with periodic boundary condition applied along x and y directions and steep angle perfectly matched layer (PML) along the positive and negative z direction shown in Fig. 2. 3D simulation domain with highest possible mesh accuracy was applied with a light source placed 1700 nm above the top surface of the array. A power monitor was placed above the source and another was placed below the bottom surface of the array to study the reflectance (R) and transmittance (T) spectra respectively as illustrated in Fig. 2. Power recorded by reflectance and transmittance monitor being $P_R$ and $P_T$, reflectance (R) and transmittance (T) as a function of wavelength, $\lambda$ are defined as Eq. (2) and (3) respectively, where $P_{in}$ denotes the input power from the source.
TE polarized light of wavelength from 400 nm to 850 nm was used to mimic the solar spectra in the visible range. Absorbance ($A$) and average absorabance ($A_{avg}$) was then calculated using Eq. (4) and (5), respectively.Fig. 2. Cross sectional view of simulation setup (left) indicating perfectly matched layers applied along positive and negative z axis. The reflectance and the transmittance monitors are placed above the source and below the array structure, respectively. The perspective view of CNT array (right) along with source, reflectance monitor and transmittance monitor, where E-field indicates the direction of electric field polarization which is transverse electric (TE) polarized light and the propagation of light is along negative z axis.
2.2 Suggested growth techniques
Vertically aligned SWCNTs with 0.75 nm to 1.5 nm outer diameters can be synthesized by controlling temperature from $650^{\circ }$ C to $800^{\circ }$ C in alcohol chemical vapor deposition (CVD) method [25]. Subnanometer diameters of the SWCNTs were ensured by preventing the Co catalyst from combining into larger groups with the help of Cu nanoparticles. Again, alcohol CVD growth technique can be used with an Ir catalyst to grow vertically aligned SWCNTs with diameters between 0.8 nm to 1.1 nm on SiO$_2$/Si substrates at $800^{\circ }$ C under an ethanol pressure of $10^{-1}$ Pa [26].
Vertically aligned periodic array of MWCNTs can be grown using CVD technique with the help of a metal catalyst, where the tuning of CNT diameter is possible by controlling the particle size of the catalyst used [27,28]. Fe catalyst assisted thermal CVD method with Al$_2$O$_3$ buffer layer was reported by Chakrabarti $et~al.$ to produce vertically aligned MWCNTs with a high percentage of 80 % [28]. Desired periodicity of the array can be ensured by using patterned growth along with the CVD method [29]. In case of Fe catalyst assisted CVD process, further tuning of the diameters of CNTs was reported by Nessim $et~al.$ through catalyst pre–treatment by controlled hydrogen exposure [30]. Catalytic CVD method with the help of Ni catalyst with methane as carbon source and hydrogen as carrier gas at $700^\circ$ C under a pressure of 1.33 kPa was used to grow MWCNTs with diameter ranging from 10 nm to 35 nm as reported by Choi $et~al.$ [31].
Vertically aligned array of MWCNTs with cone-shape-tip can be experimentally grown on nickel dots by plasma-enhanced hot filament chemical vapor deposition (PE-HF-CVD) technique with NH$_3$ catalyst using acetylene (C$_2$H$_2$) as the carbon source [22]. Catalytic CVD method at the presence of metal catalysts results in a sharp tapered tip at the top of vertically aligned CNTs which can be considered identical to the MWCNT cone structure.
Moreover, cap removal and shortening technique of oxidation using mild oxidative conditions of H$_2$O$_2$ solutions can be used to produce MWCNTs with desired height [32]. Dual diameter MWCNTs can be produced by controlled oxidative cutting of regular MWCNTs with the help of piranha solutions for oxidation reaction [33].
3. Results and discussion
Semiconductor CNT arrays are generally very good absorber of light due to their high absorption coefficient and effective refractive index being close to that of air. Reflectance at the air-CNT surface is thus minimized to enhance the absorption of light. So dominance of $\pi -$band optical transitions and high impedance matching with air make CNT arrays suitable candidate for being a perfect absorber [16,34,35]. These absorbance characteristics for both SWCNTs and MWCNTs will be discussed in detail in this section.
3.1 Single wall carbon nanotube (SWCNT)
3.1.1 Effect of the occupation area
Absorbed spectral intensity for AM 1.5 solar irradiance was calculated for 10 %, 20 % and 50 % occupation area with 5000 nm tube height, 1.5 nm outer diameter and $0^{\circ }$ incidence angle of light with the tube axis as shown in Fig. 3. Here, ASTM G-173-03 reference table is used to model the AM 1.5 solar spectra [36]. For all occupation area, SWCNTs showed high absorption though absorption was maximum for 20 % occupation area.
Fig. 3. Absorbed spectral intensity under AM 1.5 solar irradiance for different occupation area for SWCNT with 1.5 nm diameter, 5000 nm tube height and ${0^{\circ }}$ incidence angle of light with respect to the tube axis.
To get a better understanding, the reflectance and transmittance spectra was simulated by varying the occupation area from 10 % to 55 % with interval of 5 %. As indicated in Fig. 4(a), beyond the occupation area of 20 %, reflectance increases significantly due to larger top surface area hence reduction of the absorbance. The inset in Fig. 4(a) shows wavelength spectra of the source used for this simulation. And, the effect of transmittance is not sufficient to dominate reflectance. But the dominance of transmittance occurs for lower occupation area as significant portion of light is transmitted to give a comparatively lower value of absorbance. Average absorbance as a function of occupation area for this SWCNT structure was calculated as shown in Fig. 4(b). The inset graph represents the absorbance spectra for 10 %, 20 % and 50 % occupation area for $0^{\circ }$ incidence angle of light with respect to the tube axis. It is clearly visible from the graph that absorbance increases with occupation area reaching a maximum value of 99.50 % at 20 % occupation area and then decreases.
Fig. 4. (a) Reflectance and transmittance spectra for 10 %, 20 % and 50 % occupation area (Inset shows wavelength spectrum of the source considered). (b) Average absorbance as a function of occupation area for SWCNT with 1.5 nm diameter, 5000 nm tube height and ${0^{\circ }}$ incidence angle of light with the nanotube axis. (Inset graph shows the absorbance spectra for 10 %, 20 % and 50 % occupation area).
3.1.2 Effect of the incidence angle of light
The reflectance and transmittance spectra was simulated by varying the incidence angle of the light from $0^{\circ }$ to $60^{\circ }$ for SWCNT. Each tube was taken to be of 1.5 nm diameter and 5000 nm height, and 20 % occupation area was also maintained for each incidence angle. Figure 5(a) represents absorbance as a function of incident light angle for SWCNT where incident angle is taken with the vertical axis which correspond to tube axis. Absorbance, reflectance and transmittance spectra at different incident angle are presented graphically in Figs. 5(b), 5(c) and 5(d), respectively.
Fig. 5. (a) Average absorbance as a function of incidence angle for SWCNT. (b) Absorbance, (c) Reflectance, and (d) Transmittance spectra for SWCNT at different incidence angle with 20 % occupation area, 1.5 nm diameter and 5000 nm tube height. Inset graph of (b) shows the average reflectance at various incidence angle calculated from both theory and simulation.
It can be easily depicted from the graph that up to $30^{\circ }$ incidence angle, absorbance remains almost same, but beyond that absorbance decreases rapidly along with the increase of incidence angle due to higher reflectance at larger incidence angle. As the effective refractive index ($n_{eff}$) of the array is lower than the average refractive index ($n_{NT}$) of each tube, the value of reflectance is found to be very low. $n_{air}$ is the refracitve index of air in between nanotubes. $n_{eff}$ can be calculated using Maxwell-Garnett model given by Eq. (6) [37],
3.2 Multi wall carbon nanotube (MWCNT)
3.2.1 Effect of the occupation area
To observe the effects of occupation area in MWCNT arrays with 5000 nm tube height, 20.5 nm outer diameter, and $0^{\circ }$ incidence angle of light with respect to the tube axis was considered. Absorbance for different occupation area is plotted in Fig. 6(a), where absorbed spectral power for AM 1.5 solar irradiance is also shown in the inset. From the absorbance plot of Fig. 6(a), we can observe that absorbance increases along with occupation area. However, reflectance also slightly increases which can be seen from Fig. 7(a). This is because of the fact that, the top surface area is larger for larger occupation area. In spite of this increase in reflectance, absorbance is still high due to the fact that transmittance decreases more than the increment in reflectance as presented in Fig. 7(b). Therefore, we can further increase the absorbance at high occupation by reducing the reflectance.
Fig. 6. (a) Absorbance spectra of MWCNT for different occupation area with 5000 nm tube height, 20.5 nm combined diameter and ${0^{\circ }}$ incidence angle of light with the tube axis (inset graph shows absorbed spectra power under AM 1.5 solar irradiance for different occupation area). (b) Average absorbance as a function of occupation area for MWCNT, MWCNT cone and MWCNT dual diameter structures. Inset graph represents the transmittance, reflectance and absorbance spectra for MWCNT, MWCNT cone and MWCNT dual diameter structures at 50 % occupation area.
Fig. 7. (a) Reflectance and (b) Transmittance spectra of MWCNT for different occupation area with 5000 nm tube height, 20.5 nm combined diameter and ${0^{\circ }}$ incidence angle of light with the tube axis.
In order to reduce the reflectance, we need to engineer the the top surface to reduce the top surface area. We introduced MWCNT dual diameter structure as shown in Fig. 1(c) and MWCNT cone structure as shown in Fig. 1(d). And, the enhancement in absorbance for these two structures in comparison with normal MWCNT is illustrated in Fig. 6(b). From the absorbance, reflectance and transmittance spectra at 50 % occupation area represented in the inset graph of Fig. 6(b), it can be interpreted that as the top surface area is smallest for MWCNT cone, reflectance is also lowest. Consequently, it has the highest absorbance. To explain this phenomena, we resort to the effective medium approximation based on Eq. (6). According to this model, nanotube array can be approximated as a uniform medium, where effective refractive index of the array depends on the volume fraction of CNT. In dual-diameter and cone-shaped-top MWCNT arrays, volume fraction of the top surface is less than that of MWCNT array. As a result, effective refractive index of the top surface is reduced in the former two structures, which in turn results in a lower value of reflectance from the air-CNT interface in dual-diameter and cone-shaped-top MWCNT arrays. See Supplement 1 for supporting figures.
3.2.2 Effect of the incidence angle of light
With a constant occupation area of 50 %, 5000 nm tube height and 20.5 nm outer diameter for MWCNT structures, the effects of incidence angle was analyzed. It can be easily depicted from the absorbance, reflectance and transmittance spectra shown in Figs. 8(a), 9(a) and 9(b), respectively that reflectance tends to increase as the incidence angle increases, which in turns decreases the absorbance. And, the transmittance spectra remain same all the time. The reason behind the increment of reflectance and oscillation for MWCNT array is similar to that of SWCNT array as explained in section 3.1.2. The consistency of our observed reflectance with theory from Eq. (6)–(10) is also represented in the inset of Fig. 9(b).
Fig. 8. (a) Absorbance spectra for MWCNT at different incidence angle with 50 % occupation area, 20.5 nm outer diameter and 5000 nm tube height. (b) Average absorbance as a function of incidence angle for MWCNT, MWCNT cone and MWCNT dual diameter structures. Inset graph represents the transmittance, reflectance and absorbance spectra for MWCNT, MWCNT cone and MWCNT dual diameter structures at ${50^{\circ }}$ incidence angle.
Fig. 9. (a) Reflectance and (b) Transmittance spectra for MWCNT at different incidence angle with 50 % occupation area, 20.5 nm outer diameter and 5000 nm tube height. Inset graph in (b) shows the average reflectance at various incidence angle calculated from both theory and simulation.
Moreover, we used cone structure and dual diameter structure to reduce the amount of reflection by reducing the top surface area and the results we found was clearly significant. As we can see from the plot of Fig. 8(b) that pyramid structure has better absorbance than MWCNT dual diameter and normal MWCNT structures.
3.2.3 Effect of the structural parameters
MWCNT array with 15 % occupation area, 20.5 nm outer diameter and $0^{\circ }$ incidence angle of light with the tube axis is considered for studying the effect of tube height. From Fig. 10(a), we can observe that absorbance increases with the increment of tube height. And, absorbance is larger for shorter wavelength as penetration depth for shorter wavelength is smaller compared to longer wavelength. The inset graph of Fig. 10(a) represents the variation of absorbance as a function of wavelength at 5000 nm tube height. The relation of transmitted optical power with tube height (L) is given by Eq. (11),
Here, $\alpha$ is the absorption co-efficient. According to this relation, transmittance is decreased along with the increment of tube length, thus increasing the absorbance exponentially.Fig. 10. (a) Absorbance as a function of tube height at different wavelength for MWCNT array with 20.5 nm outer diameter, 15 % occupation area and ${0^{\circ }}$ incidence angle of light regarding the tube axis (Inset represents the variation of absorbance as a function of wavelength for 5000 nm tube height); (b) Absorbance spectra for MWCNT with variation in height of cone-shaped-top, having 50 % occupation area and 5000 nm tube height (Inset shows the enlarged view); (c) Absorbance spectra for SWCNT with different diameters having 20 % occupation area and 5000 nm tube height. (Inset represents the enlarged view).
Again, reflectance, transmittance, and absorbance spectra of MWCNT array with different diameters (16.5 - 24.5 nm) having identical occupation area and tube height are also observed. It is found that 20.5 nm diameter provides slightly higher reflectance while the transmittance is same for all. As a result, absorbance is minimum for 20.5 nm diameter and almost same for the other two diameters.
In cone-shaped-top MWCNT array, cone height is also varied (from 25 nm to 950 nm) to observe its effect on the optical characteristics. With the increase of cone height reflectance is found to be reduced significantly, while transmittance increases slightly. Thus, increasing cone height from 25 nm to 570 nm enhances the absorption of light in MWCNT array as depicted in Fig. 10(b). However, it is noteworthy to mention that after 570 nm, absorbance becomes almost constant for further increases in cone height.
Varying the height of inner core top region from 1000 - 2000 nm in dual diameter MWCNT array, reflectance, transmittance, and absorbance spectra are observed. While reflectance slightly decreases for larger height of inner-top region, it is countered by the increase in transmittance. As a result, absorbance remains almost same. The overall height of the CNT being constant at 5000 nm, much higher compared to penetration depth, slight variation in inner core height is found to have negligible significance in terms of enhancing absorbance.
Again, to compare our modelled CNTs with cut-flat edge with round edged top (to resemble the shape of CNT with cap when fabricating), reflectance, transmittance, and absorbance spectra for both are observed. It is found that the results for both are comparable with round edge CNTs providing slightly better performance in terms of absorbance as it causes trifle reduction in reflectance.
For SWCNT array, only diameter is varied (from 1.5nm to 3.5 nm) among the structural parameters. And, it is evident from Fig. 10(c) that absorbance is maximum for 3.5 nm diameter, which indicates better performance of SWCNT in terms of absorbing light with higher diameter. See Supplement 1 for supporting content.
3.3 Comparative analysis
The comparison of absorbance, reflectance and transmittance spectra among SWCNT, MWCNT, MWCNT dual diameter and MWCNT cone structures are illustrated graphically in Figs. 11(a), 12(a) and 12(b) respectively. As highest absorbance for SWCNT is found with 20 % occupation area and $0^{\circ }$ incidence angle whereas for MWCNT structures it is found with 50 % occupation area and $0^{\circ }$ incidence angle in our study, these values are used for further comparison. Along with that 1.5 nm diameter for SWCNT and 20.5 nm for MWCNT, MWCNT dual diameter and MWCNT cone structures with 5000 nm tube height is considered for the analysis. We can deduce from the figures that absorbance was highest for MWCNT cone structure and highest reflectance was found for MWCNT structure whereas transmittance is highest for MWCNT dual diameter structure. For having larger top surface area MWCNT array provides greater reflectance. Due to the height of outer bundle of MWCNT dual diameter structure being smaller, it can not absorb longer wavelength and so longer wavelength transmits through resulting in higher transmittance for dual diameter array. R, T, and A at 450 nm wavelength for SWCNT, MWCNT, MWCNT dual diameter and MWCNT cone structures are tabulated in Table 1 for comparison.
Fig. 11. (a) Absorbance (inset shows the enlarged view for 410 nm to 730 nm wavelength) spectra for SWCNT with 20 % occupation area and MWCNT, MWCNT dual diameter and MWCNT cone structures with 50 % occupation area. (b) Electric field distribution in xy cross-section at the middle of the tube height (top) and xz cross-section (bottom) for SWCNT. (c) Electric field distribution in xy cross-section at the middle of the tube height (top) and xz cross-section (bottom) for MWCNT.
Fig. 12. (a) Reflectance, (b) Transmittance spectra for SWCNT with 20 % occupation area and MWCNT, MWCNT dual diameter and MWCNT cone structures with 50 % occupation area. (c) Electric field distribution at reflectance monitor for MWCNT and (d) MWCNT cone structures.
Table 1. Reflectance, Transmittance and Absorbance comparison at 450 nm wavelength
Moreover, E field distributions at xy and xz cross-srction for SWCNT are shown in Fig. 11(b) and similar distributions for MWCNT are shown in Fig. 11(c). Here, xy cross-sections for both SWCNT and MWCNT are taken at the middle of the tube height. As depicted in the figure, the maximum value of E field (0.31 V/m) for SWCNT is found to be greater than that (0.15 V/m) of MWCNT. So, light penetrates deeper into SWCNT prior to being absorbed, and thus, absorption of light for MWCNT occurs within a shorter height than SWCNT. Moreover, Figs. 12(c) and 12(d) represent the E field distribution at the location of reflectance monitor for MWCNT and MWCNT cone respectively. The field distribution here clearly indicates that more light is reflected in MWCNT array compared to MWCNT cone structure.
Again, approximate value of reflectance from the experimental study of multiple authors are presented in Table 2 for comparison with our simulation study. The table suggests that the reflectance of SWCNTs and MWCNTs are almost identical to others, whereas cone shape MWCNTs provide the lowest reflectance due to lowest top surface area.
Table 2. Reflectance comparison of our theoretical study with experimentally reported results of vertically aligned CNT arrays
4. Conclusion
We present here a detailed study of the optical characteristics of single wall and mutli wall carbon nanotubes by engineering their geometrical shapes, occupation area and incident angle of incoming light. Our study suggests by modifying the shape of MWCNT we can achieve absorption of 99.883 %, which is the highest absorbance value found compared to SWCNT and other MWCNT structure, at 450 nm wavelength in cone shape MWCNTs with the occupation area of 50 %. This enhancement of absorption in cone shaped MWCNTs is due to having the lowest reflectance resulting from the reduced top surface area. Moreover, as the angle between the incoming light source and tube axis increases above $30 ^{\circ }$, reflectance in CNTs becomes dominant and reaches up to 14.3 % in MWCNTs. Though an important structural parameter for SWCNT is its diameter, top-surface shape and height are the most influential factors in terms of enhancing absorption for large-diameter MWCNTs. This work suggest that growth of darkest material could be achieved by using MWCNTs with good alignment and cone-shaped-top-surface. Our study would be valuable for the uses of CNTs in diverse devices and systems for energy harvesting and light absorber.
Acknowledgments
The authors would like to thank the department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, for providing necessary facilities for the completion of the work.
Disclosures
The authors declare no conflict of interest.
Supplemental document
See Supplement 1 for supporting content.
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