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An ab-initio approach to the optical properties of CxNy single wall nanotubes
Diamond & Related Materials 18 (2009) 1002–1005
Contents lists available at ScienceDirect
Diamond & Related Materials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d i a m o n d
An ab-initio approach to the optical properties of CxNy single wall nanotubes Debnarayan Jana a,⁎, Li-Chyong Chen b,⁎, Chun Wei Chen c, Kuei-Hsien Chen d a
Department of Physics, University College of Science and Technology, University of Calcutta, Kolkata-700 009, West Bengal, India Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan c Department of Material Science and Engineering, National Taiwan University, Taipei 10617, Taiwan d Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan b
a r t i c l e
i n f o
Available online 24 February 2009 Keywords: Nanotube and fullerenes Doping Ab-initio DFT calculations Optical properties
a b s t r a c t We investigate the optical properties of (8,0) single wall carbon nanotubes (SWCNTs) alloyed with nitrogen (N) using relaxed carbon\carbon (C\C) bond length ab-initio density functional theory (DFT) calculations in the long wavelength limit. The Fermi energy of this doped system shows a unique maximum (7.52 eV) at 75% doping. This is in contrast with boron (B) doped system wherein a minimum is observed at the same doping concentration. It is observed that the magnitude of the static dielectric constant essentially depends on the nitrogen doping concentration as well as the direction of polarization. The static refractive index (real as well as imaginary) shows a unique maximum at 50% doping concentration in all three cases of electromagnetic field. All these factors may shed light on the nature of collective excitations in boron–carbon–nitrogen (B–C–N) nanotubules and other nanotube composite systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Since 1991 [1], carbon nanotubes (CNTs) have been attracted the attention of theoretical and experimental research groups [2,3] because of owing to their unique one-dimensional structure, that shows unusual physical, chemical and mechanical properties. In particular, single walled carbon nanotubes (SWCNTs) have been the subject of interest because of its potential applications in nanoelectronic devices [2,3]. The electronic properties of single walled carbon nanotubes (SWCNTs) depend strongly on size as well as chirality. However, in experimental synthesis of the CNTs, the above properties cannot be easily tailored. But there have been quite a few attempts to control the properties by incorporating extrinsic foreign atom doping. In most of these doping, the natural choices have been boron (B) or N, due to two specific reasons. These substitutions in CNT significantly modify the chemical binding configuration, physical, chemical and optical properties in comparison to pure CNTs. Recent examples have been the N doping in multi-walled carbon nanotubes (MWCNTs), which introduces an appreciable atomic scale deformation [4–6] in the local network of (5,5) and (9,0). Moreover, it is well known that pure SWCNTs are unable to detect highly toxic gases, water molecules and bio-molecules [7]. To improve the nano sensor reliability and quality, the importance of substitutional alloying of impurity atoms such as B, N has been discussed [8,9]. These studies are also important from the technological point of view as it helps to
⁎ Corresponding authors. Jana is to be contacted at Fax: +91 33 23509755. Chen, Fax: +886 2 23655404. E-mail addresses: [email protected] (D. Jana), [email protected] (L.-C. Chen). 0925-9635/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2009.02.020
control the device design in molecular electronics and sensors. The various aspects of the doping of N in the CNTs have been reviewed recently [10–12]. Theoretically, the metallic character [13] of CN has been predicted by first principle calculation. Also, the optical properties of 4 Å diameter pure SWCNT have been investigated [14–16] recently by first principles calculation to explain the experimental results. Most recently, ab-initio calculations of the linear and non-linear optical properties of pure SWCNTs have shown that [17] the dielectric function depends essentially on chirality, diameter and the nature of polarization of incident electromagnetic field. Thus, the N substitutions in nanotubes strongly modify the electronic band structure and hence the optical properties as it depend on the band structure. In this paper, we would like to investigate the optical properties, in particular refractive index of (8,0) CxNy nanotubes as a function of N doping concentration under the action of a uniform electric field with various polarization direction through relaxed C\C bond length ab-initio DFT. 2. Numerical methods An extensive account of the numerical computation dealing with optical properties [18], optical conductivity [19], reflectivity and refractive index [20] associated with B doped system. The detailed simulation of optical properties of N-doped system has been done [21] recently to find out the significant changes in compared to B-doped system. Here we briefly summarize some of the salient features of this computation. In this numerical simulation, the imaginary part of the dielectric function has been computed by using first order time dependent perturbation theory. In the simple dipole approximation
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005
1003
modifications) used mostly in electronic band structure calculation, the optical properties of the system are normally standardized by spin un-polarized GGA. A cutoff energy of 550 eV for the grid integration was adopted for computing the charge density of the doped system. For Brillouin zone (BZ) integration along the tube axis, we have used 6 Monkhorst [25] k-points. The smearing broadening in computing the optical properties was kept fixed at 0.5 eV. The atomic positions are relaxed until the forces on the atoms are less than 0.01 eV/Å. The typical convergence was achieved till the tolerance in the Fermi energy is 0.1 × 10−6 eV. The geometrical structure of impure system was built by replacing one of the C atom(s) in the hexagonal ring by N atom(s). The preferred N sites were chosen having lowest total formation energy. This is in agreement with the electronic structure calculation of N-doped SWCNT [26]. The typical computational super cell used here (which includes typically single unit of CNT) is the 3d triclinic crystal (a = 9.40 Å, b = 9.50 Å, c = 4.219 Å and angles α = β = 90°,γ = 120°) having P1 symmetry. The energy cut-off, k-point sampling, geometry, GGA/norm-conserving pseudo-potential are same in all CxNy systems.
3. Results and discussion
Fig. 1. Ball and stick model of (8,0) CN tube in 3d triclinic structure.
used in Cambridge Serial Total Energy Package (CASTEP) code [22], the imaginary part is given by 2e2 π X C → → V 2 C V jhψk j u · r jψk ij δ Ek − Ek −E e2 ðqY0→u ; h ωÞ = Xe0 k;V;C
ð1Þ
Ω and ε0 represent respectively the volume of the super-cell and the →→ dielectric constant of the free space; u , r respectively represent the polarization vector of the incident electric field and position vector. Except the k sums, the other two sums take care of the contribution of the unoccupied conduction band (CB) and occupied valence band (VB). In computing the imaginary part of the above dielectric function, typically [1/2 (total number of electrons +4] number of bands were taken. The matrix element between the VB and CB is computed in terms of pseudo-potential [23] given by c → → v hψk j u · r jψk i =
Before we discuss the optical properties, the typical ball and stick models of pure (8,0) and CN system are shown in Fig. 1. All the results presented in this numerical calculation have same set of parameters as indicated in earlier section. Fig. 2 shows the variation of Fermi energy with N-doping concentration. It is clear from the Fig. 2 that the Fermi energy shows a maximum value of 7.22 eV for CN3 tube. The shifting of Fermi energy with doping has been noticed for B doping [21] and p type doping [27] in SWCNT. This has profound implication in analyzing Raman spectra [27]. It has been earlier noticed [24] that the band gap at the most symmetric point of BZ shows a maximum at 50% doping. This engineering of band gap at the most symmetric point (known as Γ point) in BZ may be useful in device and sensor applications. However, with B doping, we noticed a minimum of the band gap [21] at Γ point for 55% doping. These observations are required later on to understand some of the features of the optical properties of the doped CNT systems. In Fig. 3, we show the typical behavior of both real and imaginary part of the refractive index of pure and CN SWNTs as a function of frequency. By definition, both values are positive throughout the range
h i 1 → 1 → → v c → v c u · hψk j P jψk i + u · hψk j jVnl j; r jψk i imω hω ð2Þ
→ Here, P is the momentum operator and Vnl is the appropriate pseudo-potential of the system. Once ε2 is calculated as a function of frequency in the long wavelength limit, the real part (ε1(ω)) is obtained via Krammers– Kronig relation. In fact, knowing these two quantities ε1(ω) and ε2 (ω), system's optical properties such as absorption, reflectivity, optical conductivity and the loss function can be specified as a function of frequency. The refractive indexes are related to the dielectric constants via the relations (as implemented in CASTEP [22]) given by N = n + ik =
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e1 + ie2
ð3Þ
For the exchange and correlation term in DFT, the generalized gradient approximation (GGA) as proposed by Perdew et al. [24] is adopted. The standard norm-conserving pseudo-potential in reciprocal space is invoked for the optical calculation. Compared to the standard local density approximation (LDA) (with appropriate
Fig. 2. Variation of Fermi Energy with N doping concentration.
1004
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005
Fig. 3. Schematic variation of refractive index with frequency for parallel polarization of the electromagnetic field; (a) (8,0) CN SWNT and (b) (8,0) SWCNT.
of frequency. The maximum value of the imaginary part of the refractive index is increased in the doped case. This is probably due to the increase of free electrons in the doped case. The behavior of real static refractive index for all three cases with N doping is shown in Fig. 4. It is to be noted that in our simulation, the static values have been computed at ω = 0.0150 Hz. It is evident from the figure that for all three cases, the static value of the real part of refractive index shows a unique maximum at 50% N doping. Moreover, in parallel polarization, the maximum static value reaches the highest value in compared to other cases while in perpendicular case, the maximum value is the lowest one. This behavior of the refractive index is reminiscent of the non-linear behavior of the static dielectric electric constants reported in the literature [21]. It is to be noted that irrespective of the nature of polarization of the electromagnetic field, for B doping case, the minimum values of the real part of the static refractive index occur 31% doping concentration. In Fig. 5, we show the typical variation of static imaginary refractive index with N doping concentration for all three cases of electromagnetic field. As usual, the imaginary part shows a maximum
Fig. 5. Variation of imaginary static refractive index with nitrogen doping concentration.
at 50% doping concentration irrespective of the nature of the electromagnetic field. However, it has been observed that [20] both the real and imaginary part shows an existence of a minimum value for a unique concentration of B doping in all three cases. The anisotropic behavior in optical properties is a common phenomenon in low dimensional system. Here, we can clearly distinguish the various maximum values in three polarization cases. In fact, one can control the static values of the refractive index with nitrogen doping concentration so that one can use this system for two layer anti-reflection coating. Since, the reflectivity is related to refractive index, it has been noticed that [21] at some particular nitrogen concentration, the reflectivity at normal incidence vanishes. Hence, this study may be helpful in potential application to some optical devices. The brightness of the image can be controlled by the vanishing reflectivity value. The present study may provide some valuable guidance for CNT based chemical sensors for water, cyanides, carbon-monoxide and formaldehyde. 4. Conclusions and perspectives From the first principles relaxed C\C bond length DFT calculation of the optical property of (8,0) CxNy SWNT systems, we have observed significant changes in the optical behavior for different CNT systems (radius b1 nm) with different polarizations. Both the static refractive index and reflectivity depend on nitrogen doping concentration in a non-linear way having a unique maximum at particular concentration (0.5). It will be interesting to explore these aspects in N doped quasimetallic and metallic SWNT system. Acknowledgements One of the authors (DJ) would like to thank the National Science Council (NSC) of the Republic of China for financially supporting him as a visiting researcher under Contract No. NSC93-2811-M-002-034. Discussions with Dr. C. L. Sun are gratefully acknowledged. References
Fig. 4. Variation of real static refractive index with nitrogen doping concentration.
[1] S. Iijima, Nature (London) 354 (1991) 56. [2] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical properties of carbon nanotubes, Imperial College Press, London, 1998. [3] S. Reich, C. Thomsen, J. Maulzsch, Carbon nanotubes: basic concepts and physical properties, Wiley-VCH, Weinheim, 2004.
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005 [4] C.-L. Sun, H.-W. Wang, M. Hayashi, L.-C. Chen, K.-H. Chen, J. Am. Chem. Soc. 128 (2006) 8368. [5] L.-C. Chen, et al., Adv. Func. Mater. 12 (2002) 687. [6] C.-L. Sun, et al., Chem. Mater. 17 (2005) 3749. [7] J. Kong, et al., Science 287 (2000) 622. [8] S. Peng, K. Cho, Nano Lett. 3 (2003) 513. [9] L. Bai, Z. Zhou, Carbon 45 (2007) 2105. [10] C.P. Ewels, M. Glerup, J. Nanosci. Nanotechnol. 5 (2005) 1345. [11] M. Terrones, et al., Mater. Today 7 (2004) 30–45. [12] M. Terrones, A.G.S. Filho, A.M. Rao, in: A. Jorio, G. Dresselhaus, M.S. Dresselhaus (Eds.), Carbon Nanotubes, Topics Appl. Physics, vol. 111, Springer-Verlag, 2008, p. 531. [13] Y. Miyamoto, M.L. Cohen, S.G. Louie, Solid State Commun. 102 (1997) 605. [14] M. Machon, S. Reich, C. Thomsen, D. Sanchez-Portal, P. Ordejon, Phys. Rev. B 66 (2002) 155410. [15] X.P. Yang, H.M. Weng, J. Dong, Euro. Phys. J. B 32 (2003) 345. [16] H.J. Liu, C.T. Chan, Phys. Rev. B 66 (2002) 115416.
1005
[17] G.Y. Guo, K.C. Chen, D.-S. Wang, C.-G. Duan, Phys. Rev. B 69 (2004) 205416. [18] D. Jana, L.-C. Chen, C.W. Chen, S. Chattopadhyay, K.-H. Chen, Carbon 45 (2007) 1482. [19] D. Jana, L.-C. Chen, C.W. Chen, K.-H. Chen, Ind. J. Phys. 81 (2007) 41. [20] D. Jana, L.-C. Chen, C.W. Chen, K.-H. Chen, Asian J. Phys. 17 (2008) 105. [21] D. Jana, A. Chakrabarti, L.-C. Chen, C.W. Chen, K.-H. Chen, First principle calculations of the optical properties of CxNy single walled carbon nanotubes, Nanotechnology 20 (2009) 175701. [22] M.D. Segall, et al., J. Phys. Cond. Matter., 14 (2002) 2717. [23] A.J. Read, R.J. Needs, Phys. Rev. B 44 (1991) 13071. [24] J.P. Perdew, K. Berke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [25] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1992) 5188. [26] S.S. Wu, Q.B. Wen, W.T. Zheng, Q. Jiang, Nanotechnolgy 18 (2007) 165702. [27] W. Zhou, J. Vavro, N.M. Nemes, J.E. Fischer, et al., Phys. Rev. B 71 (2005) 205423.
Contents lists available at ScienceDirect
Diamond & Related Materials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d i a m o n d
An ab-initio approach to the optical properties of CxNy single wall nanotubes Debnarayan Jana a,⁎, Li-Chyong Chen b,⁎, Chun Wei Chen c, Kuei-Hsien Chen d a
Department of Physics, University College of Science and Technology, University of Calcutta, Kolkata-700 009, West Bengal, India Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan c Department of Material Science and Engineering, National Taiwan University, Taipei 10617, Taiwan d Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan b
a r t i c l e
i n f o
Available online 24 February 2009 Keywords: Nanotube and fullerenes Doping Ab-initio DFT calculations Optical properties
a b s t r a c t We investigate the optical properties of (8,0) single wall carbon nanotubes (SWCNTs) alloyed with nitrogen (N) using relaxed carbon\carbon (C\C) bond length ab-initio density functional theory (DFT) calculations in the long wavelength limit. The Fermi energy of this doped system shows a unique maximum (7.52 eV) at 75% doping. This is in contrast with boron (B) doped system wherein a minimum is observed at the same doping concentration. It is observed that the magnitude of the static dielectric constant essentially depends on the nitrogen doping concentration as well as the direction of polarization. The static refractive index (real as well as imaginary) shows a unique maximum at 50% doping concentration in all three cases of electromagnetic field. All these factors may shed light on the nature of collective excitations in boron–carbon–nitrogen (B–C–N) nanotubules and other nanotube composite systems. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Since 1991 [1], carbon nanotubes (CNTs) have been attracted the attention of theoretical and experimental research groups [2,3] because of owing to their unique one-dimensional structure, that shows unusual physical, chemical and mechanical properties. In particular, single walled carbon nanotubes (SWCNTs) have been the subject of interest because of its potential applications in nanoelectronic devices [2,3]. The electronic properties of single walled carbon nanotubes (SWCNTs) depend strongly on size as well as chirality. However, in experimental synthesis of the CNTs, the above properties cannot be easily tailored. But there have been quite a few attempts to control the properties by incorporating extrinsic foreign atom doping. In most of these doping, the natural choices have been boron (B) or N, due to two specific reasons. These substitutions in CNT significantly modify the chemical binding configuration, physical, chemical and optical properties in comparison to pure CNTs. Recent examples have been the N doping in multi-walled carbon nanotubes (MWCNTs), which introduces an appreciable atomic scale deformation [4–6] in the local network of (5,5) and (9,0). Moreover, it is well known that pure SWCNTs are unable to detect highly toxic gases, water molecules and bio-molecules [7]. To improve the nano sensor reliability and quality, the importance of substitutional alloying of impurity atoms such as B, N has been discussed [8,9]. These studies are also important from the technological point of view as it helps to
⁎ Corresponding authors. Jana is to be contacted at Fax: +91 33 23509755. Chen, Fax: +886 2 23655404. E-mail addresses: [email protected] (D. Jana), [email protected] (L.-C. Chen). 0925-9635/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2009.02.020
control the device design in molecular electronics and sensors. The various aspects of the doping of N in the CNTs have been reviewed recently [10–12]. Theoretically, the metallic character [13] of CN has been predicted by first principle calculation. Also, the optical properties of 4 Å diameter pure SWCNT have been investigated [14–16] recently by first principles calculation to explain the experimental results. Most recently, ab-initio calculations of the linear and non-linear optical properties of pure SWCNTs have shown that [17] the dielectric function depends essentially on chirality, diameter and the nature of polarization of incident electromagnetic field. Thus, the N substitutions in nanotubes strongly modify the electronic band structure and hence the optical properties as it depend on the band structure. In this paper, we would like to investigate the optical properties, in particular refractive index of (8,0) CxNy nanotubes as a function of N doping concentration under the action of a uniform electric field with various polarization direction through relaxed C\C bond length ab-initio DFT. 2. Numerical methods An extensive account of the numerical computation dealing with optical properties [18], optical conductivity [19], reflectivity and refractive index [20] associated with B doped system. The detailed simulation of optical properties of N-doped system has been done [21] recently to find out the significant changes in compared to B-doped system. Here we briefly summarize some of the salient features of this computation. In this numerical simulation, the imaginary part of the dielectric function has been computed by using first order time dependent perturbation theory. In the simple dipole approximation
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005
1003
modifications) used mostly in electronic band structure calculation, the optical properties of the system are normally standardized by spin un-polarized GGA. A cutoff energy of 550 eV for the grid integration was adopted for computing the charge density of the doped system. For Brillouin zone (BZ) integration along the tube axis, we have used 6 Monkhorst [25] k-points. The smearing broadening in computing the optical properties was kept fixed at 0.5 eV. The atomic positions are relaxed until the forces on the atoms are less than 0.01 eV/Å. The typical convergence was achieved till the tolerance in the Fermi energy is 0.1 × 10−6 eV. The geometrical structure of impure system was built by replacing one of the C atom(s) in the hexagonal ring by N atom(s). The preferred N sites were chosen having lowest total formation energy. This is in agreement with the electronic structure calculation of N-doped SWCNT [26]. The typical computational super cell used here (which includes typically single unit of CNT) is the 3d triclinic crystal (a = 9.40 Å, b = 9.50 Å, c = 4.219 Å and angles α = β = 90°,γ = 120°) having P1 symmetry. The energy cut-off, k-point sampling, geometry, GGA/norm-conserving pseudo-potential are same in all CxNy systems.
3. Results and discussion
Fig. 1. Ball and stick model of (8,0) CN tube in 3d triclinic structure.
used in Cambridge Serial Total Energy Package (CASTEP) code [22], the imaginary part is given by 2e2 π X C → → V 2 C V jhψk j u · r jψk ij δ Ek − Ek −E e2 ðqY0→u ; h ωÞ = Xe0 k;V;C
ð1Þ
Ω and ε0 represent respectively the volume of the super-cell and the →→ dielectric constant of the free space; u , r respectively represent the polarization vector of the incident electric field and position vector. Except the k sums, the other two sums take care of the contribution of the unoccupied conduction band (CB) and occupied valence band (VB). In computing the imaginary part of the above dielectric function, typically [1/2 (total number of electrons +4] number of bands were taken. The matrix element between the VB and CB is computed in terms of pseudo-potential [23] given by c → → v hψk j u · r jψk i =
Before we discuss the optical properties, the typical ball and stick models of pure (8,0) and CN system are shown in Fig. 1. All the results presented in this numerical calculation have same set of parameters as indicated in earlier section. Fig. 2 shows the variation of Fermi energy with N-doping concentration. It is clear from the Fig. 2 that the Fermi energy shows a maximum value of 7.22 eV for CN3 tube. The shifting of Fermi energy with doping has been noticed for B doping [21] and p type doping [27] in SWCNT. This has profound implication in analyzing Raman spectra [27]. It has been earlier noticed [24] that the band gap at the most symmetric point of BZ shows a maximum at 50% doping. This engineering of band gap at the most symmetric point (known as Γ point) in BZ may be useful in device and sensor applications. However, with B doping, we noticed a minimum of the band gap [21] at Γ point for 55% doping. These observations are required later on to understand some of the features of the optical properties of the doped CNT systems. In Fig. 3, we show the typical behavior of both real and imaginary part of the refractive index of pure and CN SWNTs as a function of frequency. By definition, both values are positive throughout the range
h i 1 → 1 → → v c → v c u · hψk j P jψk i + u · hψk j jVnl j; r jψk i imω hω ð2Þ
→ Here, P is the momentum operator and Vnl is the appropriate pseudo-potential of the system. Once ε2 is calculated as a function of frequency in the long wavelength limit, the real part (ε1(ω)) is obtained via Krammers– Kronig relation. In fact, knowing these two quantities ε1(ω) and ε2 (ω), system's optical properties such as absorption, reflectivity, optical conductivity and the loss function can be specified as a function of frequency. The refractive indexes are related to the dielectric constants via the relations (as implemented in CASTEP [22]) given by N = n + ik =
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e1 + ie2
ð3Þ
For the exchange and correlation term in DFT, the generalized gradient approximation (GGA) as proposed by Perdew et al. [24] is adopted. The standard norm-conserving pseudo-potential in reciprocal space is invoked for the optical calculation. Compared to the standard local density approximation (LDA) (with appropriate
Fig. 2. Variation of Fermi Energy with N doping concentration.
1004
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005
Fig. 3. Schematic variation of refractive index with frequency for parallel polarization of the electromagnetic field; (a) (8,0) CN SWNT and (b) (8,0) SWCNT.
of frequency. The maximum value of the imaginary part of the refractive index is increased in the doped case. This is probably due to the increase of free electrons in the doped case. The behavior of real static refractive index for all three cases with N doping is shown in Fig. 4. It is to be noted that in our simulation, the static values have been computed at ω = 0.0150 Hz. It is evident from the figure that for all three cases, the static value of the real part of refractive index shows a unique maximum at 50% N doping. Moreover, in parallel polarization, the maximum static value reaches the highest value in compared to other cases while in perpendicular case, the maximum value is the lowest one. This behavior of the refractive index is reminiscent of the non-linear behavior of the static dielectric electric constants reported in the literature [21]. It is to be noted that irrespective of the nature of polarization of the electromagnetic field, for B doping case, the minimum values of the real part of the static refractive index occur 31% doping concentration. In Fig. 5, we show the typical variation of static imaginary refractive index with N doping concentration for all three cases of electromagnetic field. As usual, the imaginary part shows a maximum
Fig. 5. Variation of imaginary static refractive index with nitrogen doping concentration.
at 50% doping concentration irrespective of the nature of the electromagnetic field. However, it has been observed that [20] both the real and imaginary part shows an existence of a minimum value for a unique concentration of B doping in all three cases. The anisotropic behavior in optical properties is a common phenomenon in low dimensional system. Here, we can clearly distinguish the various maximum values in three polarization cases. In fact, one can control the static values of the refractive index with nitrogen doping concentration so that one can use this system for two layer anti-reflection coating. Since, the reflectivity is related to refractive index, it has been noticed that [21] at some particular nitrogen concentration, the reflectivity at normal incidence vanishes. Hence, this study may be helpful in potential application to some optical devices. The brightness of the image can be controlled by the vanishing reflectivity value. The present study may provide some valuable guidance for CNT based chemical sensors for water, cyanides, carbon-monoxide and formaldehyde. 4. Conclusions and perspectives From the first principles relaxed C\C bond length DFT calculation of the optical property of (8,0) CxNy SWNT systems, we have observed significant changes in the optical behavior for different CNT systems (radius b1 nm) with different polarizations. Both the static refractive index and reflectivity depend on nitrogen doping concentration in a non-linear way having a unique maximum at particular concentration (0.5). It will be interesting to explore these aspects in N doped quasimetallic and metallic SWNT system. Acknowledgements One of the authors (DJ) would like to thank the National Science Council (NSC) of the Republic of China for financially supporting him as a visiting researcher under Contract No. NSC93-2811-M-002-034. Discussions with Dr. C. L. Sun are gratefully acknowledged. References
Fig. 4. Variation of real static refractive index with nitrogen doping concentration.
[1] S. Iijima, Nature (London) 354 (1991) 56. [2] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical properties of carbon nanotubes, Imperial College Press, London, 1998. [3] S. Reich, C. Thomsen, J. Maulzsch, Carbon nanotubes: basic concepts and physical properties, Wiley-VCH, Weinheim, 2004.
D. Jana et al. / Diamond & Related Materials 18 (2009) 1002–1005 [4] C.-L. Sun, H.-W. Wang, M. Hayashi, L.-C. Chen, K.-H. Chen, J. Am. Chem. Soc. 128 (2006) 8368. [5] L.-C. Chen, et al., Adv. Func. Mater. 12 (2002) 687. [6] C.-L. Sun, et al., Chem. Mater. 17 (2005) 3749. [7] J. Kong, et al., Science 287 (2000) 622. [8] S. Peng, K. Cho, Nano Lett. 3 (2003) 513. [9] L. Bai, Z. Zhou, Carbon 45 (2007) 2105. [10] C.P. Ewels, M. Glerup, J. Nanosci. Nanotechnol. 5 (2005) 1345. [11] M. Terrones, et al., Mater. Today 7 (2004) 30–45. [12] M. Terrones, A.G.S. Filho, A.M. Rao, in: A. Jorio, G. Dresselhaus, M.S. Dresselhaus (Eds.), Carbon Nanotubes, Topics Appl. Physics, vol. 111, Springer-Verlag, 2008, p. 531. [13] Y. Miyamoto, M.L. Cohen, S.G. Louie, Solid State Commun. 102 (1997) 605. [14] M. Machon, S. Reich, C. Thomsen, D. Sanchez-Portal, P. Ordejon, Phys. Rev. B 66 (2002) 155410. [15] X.P. Yang, H.M. Weng, J. Dong, Euro. Phys. J. B 32 (2003) 345. [16] H.J. Liu, C.T. Chan, Phys. Rev. B 66 (2002) 115416.
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