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Electron energy loss study of plasmon excitations in curved carbon network
ELSEVIER
ELECTRON
SyntheticMetals 103(1999) 2502-2503
ENERGY
LOSS
STUDY
OF PLASMON NETWORK
EXCITATIONS
IN CURVED
CARlBON
L. Henrard”, 0. Stephanb,C. Colliexb ‘Groupe de Dynamique des Phases Condensees. Universitt de Monpellier II. Place E. Bataillon CC026 34095 Montpellier, France Taboratoire de Physique du solide. B8t 5 10. UniversitB de Paris&d. 91405 Orsay, France
Abstract In the present contribution, we focus on the plasmon excitations of curved carbon sp2 bonded materials : onion-like fullerenes and nanotubes. Experimental spatially resolved transmission Electron Energy Loss Spectroscopy (EELS)-data are analysed within a dielectric approach where the anisotropy of particles is fully treated. Combination of-theoretical simulation and experimental results allows the differentiation of tangential radial (12.8 eV) and tangential (16-19 eV) surface plasmon and of volume (23-27 eV) plasmons. A shift of the surface plasmon resonance energy with the electron impact parameter is attributed to a change of relative contributions of multipolar modes.
For several years and following fullerene discovery [ 11, carbon multishell compounds (onion-like fullerenes and carbon nanotubes) brought attention of material scientists. Carbon nanotubes were first observed in the soot resulting from an electrically produced arc between carbon electrodes [2] and carbon spherical multishell onions were first observed by electron bombardment of carbon soot in electron microscope [3]. These findings put the question of the relative stability of, thermodynamically most stable, graphite and diamond and the dangling bonds free new forms of carbon cited above. Even if carbon nanotubes are now well known for their potential application (electron emitters, i-dimension quantum conductors, ...)[4] and onion-like fullerenes have been proposed as carriers for interstellar dust extinction [S], the role of the special ‘curved anisotropy’ in electronic structure and polarisability is also of fundamental interest [ 131. Here we report an energy electron loss (EELS) study of dielectric response of onion-like fullerene and we stress the effect of the anisotropy on collective excitations of dielectric shells. Details of the model we used for the simulation of plasmon excitation cross section (both optical and for EELS) were presented elsewhere [6]. There are based on a semi-analytical resolution of Maxwell equations for dielectric shells formed with anisotropic material described by a dielectric tensor diagonal in spherical coordinates and boundary conditions matching. Dielectric functions of graphite are used throughout this paper. high Experimental spatial resolution EELS measurement in the low-loss region were performed on onion-like fullerenes produced by carbon ions implatation into silver polycrystalline substrate 171. Collections of
spectra were acquired using a 100 KV STEM VG -FIB 501 equipped with a field emission gun tind a parallel detector providing a 0.7 eV energy resolution, The 0.5 nm probe was scanned point to point across the nanoobject. In the first figure, we used a losntzian model for the dielectric tensor [6] so that excitations modes dearly show UP* In fig. 1, we would emphasised the analogy between the two modes of dielectric shells (called tangential and radial) and the symmetric and anti-symmetric modes of a selfsupported dielectric film (see fig. lb for a schematic representation of these modes). If we look at a film as a dielectric shell of infinite radius, we can make the following analogy :
lJRtiQ;R-rwd;l(l-p)eQd In fig la, we show the resonance energy of the plasmon excitation modes with respect to 1 (I-p) where 1 is the multipolar order of the excitation (I=I for dipolar modes, 1=2 for quadrupolar modes, ...) and p is the r/R ratto with r and R the inner and outer radius of the dielectric shell, respectively. The inset of fig. la display the dispersion relation of the excitation energy of a film with Qd where Q is the transfer momentum and d the thickness of the film . We have shown [S] that this two modes structure is no more valid for anisotropic shells. In this case, a multi-mode spectrum is obtained with maxima corresponding to resonance in both in plane and out of plane component of the dielectric tensor, We call former excitations ta@entiirl modes and the latter radial modes. Fig 2a presents experimental spatially resolve&EELS spectra acquired for different impact parameters. The two upper curves are obtained for an electron beam penetrating
0379~67791996 - seefront matter0 1999 Elsevier ScienceS.A. All rights reserved. PII: SO379-6779(98)01072-S
L. Henrard
et al. 1 Synthetic
the carbon shells. Volume plasmon modes are then mainly observed at 28 eV and 25 eV depending on the orientation of the carbon layers regarding the electron beams [8]. The other three curves are for external electrons and then only surface long range plasmons are excited. Comparison with theoretical simulation based on ref [6] (fig 2b) leads to the following assignment of the peaks : e-n* collective excitation is found at 12.8 eV (The simulated spectra show this radial resonance at 14.2 eV. This small disagreement is due to the chosen input dielectric function 191). It corresponds to radial (out of plane) excitation. The large resonance around 17 eV is attributed to a tangential excitation of the surface o-o*plasmon.
Metals
103 (1999)
2503
25024503
dipolar field. The dispersion of the resonance energy with respect to I can be seen in fig la. For a planar surface, this effect of the dispersion on the impact parameter dependence of the resonance energy can only be described by a relativistic theory [IO]
Energy CC”)
Enqy (cV)
Fig. 2 : Experimental (a) and theoretical (b) EELS loss probabilities of a carbon onion for various impact parameter.
Tangential +
Symmetric
In conclusion, we have compared the plasmon excitation of a dielectric film and of a dielectric shell and the crucial role of anisotropy for the interpretation of the experimental analysis of the onion polarisability by means of a spatially resolved EELS. The experimental impact parameter dependence of the surface plasmon peak was successfully described. Further analysis of the experimental results on carbon onions [ 111 and carbon and boron nitride nanotubes [12] within dielectric framework will be reported elsewhere L.H. is grateful to Ph. Lambin, P. Rudolf, A. Lucas and F. Malengreau for fruitful discussion. L.H. benefit financial support of the NAMITECH (Nanotubes for Microstructure TECHnology) European TMR research network (ERBFMRX-CT96-0067 (DG12 - MIHT))
Radial +
Anti-symmetric
I
d
Fig 1 a) Dispersion curves of the resonance energy of the plasmon excitation of an isotropic dielectric shell as a function of 1(1-p). The inset shows the dispersion curves of a dielectric film with respect to Qd (see text) b) Schematic representation of the excitation modes of a spherical shell and a dielectric film A striking feature of experimental spectra is the shift of the 17eV peak as a function of the impact parameter. We can see in fig 2b that theoretical simulation reported this effect. It is explained by the change of the relative contribution of the multipolar terms in the total loss function with the impact parameter. Indeed, a grazing electron excites high multipolar modes where an electron passing far from the particle is mainly described by a
References [l] H.W. Kroto et al. Nature 318 (1985) 163 [2] S. Iijima. Nature 354 (1991) 56 [3] D. Ugarte. Nature 359 (1992) 707 [4] MS. Dresselhaus, G. Dresselhaus, P.C. Eklund. ‘Science of fullerenes and carbon nanotubes’. Academic Press. 1996 [5] L. Henrard et al. Ap.J. 406 (1993) 92 ; Ap.J. 487 (1997) 719 [6] L. Henrard. Ph. Thesis (University of Namur) ; A.A. Lucas, L. Henrard, Ph. Lambin Phys. Rev. B 49 (1994) 2888 ; L. Henrard et al. Full. Sci. & Tech. 4 (1996) 131 ; J.Phys. B 29 (1996) 5127 ; Synthetic Metals 77 (1996) 27 [7] Th. Cabioch et al. Europhys. Lett. 38 (1997) 471 [8] T. Stockli et al. Phys. Rev. B 57 (1998) 15599 [9] B.T. Draine. Princeton Observatory Report. 1987 [lo] P. Moreau et al. Phys. Rev. B 56 (1997) 6774 [ 1 l] L. Henrard et al. Submitted [ 121 0. Stephan, L. Henrard, C. Colliex. In preparation [ 131 E. Sandre and F. Cyrot-ackman in ‘Le carbone dans tous ses Ctats’. Ed. by P. Bernier, S. Lefrant. Gordon and Breach editors. Amsterdan (1998)
ELECTRON
SyntheticMetals 103(1999) 2502-2503
ENERGY
LOSS
STUDY
OF PLASMON NETWORK
EXCITATIONS
IN CURVED
CARlBON
L. Henrard”, 0. Stephanb,C. Colliexb ‘Groupe de Dynamique des Phases Condensees. Universitt de Monpellier II. Place E. Bataillon CC026 34095 Montpellier, France Taboratoire de Physique du solide. B8t 5 10. UniversitB de Paris&d. 91405 Orsay, France
Abstract In the present contribution, we focus on the plasmon excitations of curved carbon sp2 bonded materials : onion-like fullerenes and nanotubes. Experimental spatially resolved transmission Electron Energy Loss Spectroscopy (EELS)-data are analysed within a dielectric approach where the anisotropy of particles is fully treated. Combination of-theoretical simulation and experimental results allows the differentiation of tangential radial (12.8 eV) and tangential (16-19 eV) surface plasmon and of volume (23-27 eV) plasmons. A shift of the surface plasmon resonance energy with the electron impact parameter is attributed to a change of relative contributions of multipolar modes.
For several years and following fullerene discovery [ 11, carbon multishell compounds (onion-like fullerenes and carbon nanotubes) brought attention of material scientists. Carbon nanotubes were first observed in the soot resulting from an electrically produced arc between carbon electrodes [2] and carbon spherical multishell onions were first observed by electron bombardment of carbon soot in electron microscope [3]. These findings put the question of the relative stability of, thermodynamically most stable, graphite and diamond and the dangling bonds free new forms of carbon cited above. Even if carbon nanotubes are now well known for their potential application (electron emitters, i-dimension quantum conductors, ...)[4] and onion-like fullerenes have been proposed as carriers for interstellar dust extinction [S], the role of the special ‘curved anisotropy’ in electronic structure and polarisability is also of fundamental interest [ 131. Here we report an energy electron loss (EELS) study of dielectric response of onion-like fullerene and we stress the effect of the anisotropy on collective excitations of dielectric shells. Details of the model we used for the simulation of plasmon excitation cross section (both optical and for EELS) were presented elsewhere [6]. There are based on a semi-analytical resolution of Maxwell equations for dielectric shells formed with anisotropic material described by a dielectric tensor diagonal in spherical coordinates and boundary conditions matching. Dielectric functions of graphite are used throughout this paper. high Experimental spatial resolution EELS measurement in the low-loss region were performed on onion-like fullerenes produced by carbon ions implatation into silver polycrystalline substrate 171. Collections of
spectra were acquired using a 100 KV STEM VG -FIB 501 equipped with a field emission gun tind a parallel detector providing a 0.7 eV energy resolution, The 0.5 nm probe was scanned point to point across the nanoobject. In the first figure, we used a losntzian model for the dielectric tensor [6] so that excitations modes dearly show UP* In fig. 1, we would emphasised the analogy between the two modes of dielectric shells (called tangential and radial) and the symmetric and anti-symmetric modes of a selfsupported dielectric film (see fig. lb for a schematic representation of these modes). If we look at a film as a dielectric shell of infinite radius, we can make the following analogy :
lJRtiQ;R-rwd;l(l-p)eQd In fig la, we show the resonance energy of the plasmon excitation modes with respect to 1 (I-p) where 1 is the multipolar order of the excitation (I=I for dipolar modes, 1=2 for quadrupolar modes, ...) and p is the r/R ratto with r and R the inner and outer radius of the dielectric shell, respectively. The inset of fig. la display the dispersion relation of the excitation energy of a film with Qd where Q is the transfer momentum and d the thickness of the film . We have shown [S] that this two modes structure is no more valid for anisotropic shells. In this case, a multi-mode spectrum is obtained with maxima corresponding to resonance in both in plane and out of plane component of the dielectric tensor, We call former excitations ta@entiirl modes and the latter radial modes. Fig 2a presents experimental spatially resolve&EELS spectra acquired for different impact parameters. The two upper curves are obtained for an electron beam penetrating
0379~67791996 - seefront matter0 1999 Elsevier ScienceS.A. All rights reserved. PII: SO379-6779(98)01072-S
L. Henrard
et al. 1 Synthetic
the carbon shells. Volume plasmon modes are then mainly observed at 28 eV and 25 eV depending on the orientation of the carbon layers regarding the electron beams [8]. The other three curves are for external electrons and then only surface long range plasmons are excited. Comparison with theoretical simulation based on ref [6] (fig 2b) leads to the following assignment of the peaks : e-n* collective excitation is found at 12.8 eV (The simulated spectra show this radial resonance at 14.2 eV. This small disagreement is due to the chosen input dielectric function 191). It corresponds to radial (out of plane) excitation. The large resonance around 17 eV is attributed to a tangential excitation of the surface o-o*plasmon.
Metals
103 (1999)
2503
25024503
dipolar field. The dispersion of the resonance energy with respect to I can be seen in fig la. For a planar surface, this effect of the dispersion on the impact parameter dependence of the resonance energy can only be described by a relativistic theory [IO]
Energy CC”)
Enqy (cV)
Fig. 2 : Experimental (a) and theoretical (b) EELS loss probabilities of a carbon onion for various impact parameter.
Tangential +
Symmetric
In conclusion, we have compared the plasmon excitation of a dielectric film and of a dielectric shell and the crucial role of anisotropy for the interpretation of the experimental analysis of the onion polarisability by means of a spatially resolved EELS. The experimental impact parameter dependence of the surface plasmon peak was successfully described. Further analysis of the experimental results on carbon onions [ 111 and carbon and boron nitride nanotubes [12] within dielectric framework will be reported elsewhere L.H. is grateful to Ph. Lambin, P. Rudolf, A. Lucas and F. Malengreau for fruitful discussion. L.H. benefit financial support of the NAMITECH (Nanotubes for Microstructure TECHnology) European TMR research network (ERBFMRX-CT96-0067 (DG12 - MIHT))
Radial +
Anti-symmetric
I
d
Fig 1 a) Dispersion curves of the resonance energy of the plasmon excitation of an isotropic dielectric shell as a function of 1(1-p). The inset shows the dispersion curves of a dielectric film with respect to Qd (see text) b) Schematic representation of the excitation modes of a spherical shell and a dielectric film A striking feature of experimental spectra is the shift of the 17eV peak as a function of the impact parameter. We can see in fig 2b that theoretical simulation reported this effect. It is explained by the change of the relative contribution of the multipolar terms in the total loss function with the impact parameter. Indeed, a grazing electron excites high multipolar modes where an electron passing far from the particle is mainly described by a
References [l] H.W. Kroto et al. Nature 318 (1985) 163 [2] S. Iijima. Nature 354 (1991) 56 [3] D. Ugarte. Nature 359 (1992) 707 [4] MS. Dresselhaus, G. Dresselhaus, P.C. Eklund. ‘Science of fullerenes and carbon nanotubes’. Academic Press. 1996 [5] L. Henrard et al. Ap.J. 406 (1993) 92 ; Ap.J. 487 (1997) 719 [6] L. Henrard. Ph. Thesis (University of Namur) ; A.A. Lucas, L. Henrard, Ph. Lambin Phys. Rev. B 49 (1994) 2888 ; L. Henrard et al. Full. Sci. & Tech. 4 (1996) 131 ; J.Phys. B 29 (1996) 5127 ; Synthetic Metals 77 (1996) 27 [7] Th. Cabioch et al. Europhys. Lett. 38 (1997) 471 [8] T. Stockli et al. Phys. Rev. B 57 (1998) 15599 [9] B.T. Draine. Princeton Observatory Report. 1987 [lo] P. Moreau et al. Phys. Rev. B 56 (1997) 6774 [ 1 l] L. Henrard et al. Submitted [ 121 0. Stephan, L. Henrard, C. Colliex. In preparation [ 131 E. Sandre and F. Cyrot-ackman in ‘Le carbone dans tous ses Ctats’. Ed. by P. Bernier, S. Lefrant. Gordon and Breach editors. Amsterdan (1998)