Hong Lin

Jérôme Lagoute

Vincent Repain

Cyril Chacon

Yann Girard

Jean-Sébastien Lauret

Raul Arenal

François Ducastelle

Sylvie Rousset

Annick Loiseau

Coupled study by TEM/EELS and STM/STS of electronic properties of C-and CN x -nanotubes

Keywords: Carbon nanotubes, STM/STS, EELS Mots-clés : Nanotubes de carbone, STM/STS, EELS

Carbon nanotubes are the focus of considerable research efforts due to their fascinating physical properties. They provide an excellent model system for the study of one dimensional materials and molecular electronics. The chirality of nanotubes can lead to very different electronic behaviours, either metallic or semiconducting. Their electronic spectrum consists of a series of Van Hove singularities defining a bandgap for semiconducting tubes and molecular orbitals at the corresponding energies. A promising way to tune the nanotubes electronic properties for future applications is to use doping by heteroatoms. Here we report on experimental investigation of the role of many-body interactions in nanotube bandgaps, the visualization in direct space of the molecular orbitals of nanotubes and the properties of nitrogen doped nanotubes using scanning tunneling microscopy and transmission electron microscopy as well as electron energy loss spectroscopy.

Résumé Etude couplée par TEM/EELS et STM/STS des propriétés structurales et électroniques des nanotubes C et CN x

Les nanotubes de carbone sont l'objet d'importants efforts de recherche en raison de leurs fascinantes propriétés physiques. Ils constituent un système modèle particulièrement intéressant pour l'étude fondamentale de matériaux à une dimension et pour l'électronique moléculaire. En fonction de leur chiralité, les nanotubes peuvent adopter un comportement électronique soit semiconducteur soit métallique. Leur spectre électronique est dominé par une série de singularités de Van Hove qui définit la bande interdite des tubes semiconducteurs et les orbitales moléculaires situées à ces énergies. Pour contrôler et moduler les propriétés électroniques des nanotubes, une voie prometteuse est d'utiliser le dopage par des hétéroatomes. Les travaux présentés ici portent sur l'étude expérimentale de l'influence des interactions à N corps sur la valeur de la bande interdite des tubes semiconducteurs, la visualisation dans l'espace direct des orbitales moléculaires des nanotubes et les propriétés des nanotubes dopés par l'azote en utilisant des mesures de microscopie tunnel, microscopie électronique à balayage et spectroscopie de perte d'énergie des électrons.

Introduction

Carbon nanotubes (CNTs) have attracted considerable interest for their unique electronic properties due to their one dimensional character [START_REF] Saito | Physical Properties of Carbon Nanotubes[END_REF][START_REF] Loiseau | Understanding carbon nanotubes[END_REF]. A nanotube consists in a single graphene layer rolled up into a hollow cylinder. The many possibilities to roll up this sheet lead to different chiralities for the CNTs. Depending on this chirality, the Email addresses: hong.lin@univ-lyon1.fr (Hong Lin), jerome.lagoute@univ-paris-diderot.fr (Jérôme Lagoute) Preprint submitted to Comptes rendus -Physique October 11, 2011 resulting CNTs can be either metallic or semiconducting. This special link between atomic structure and electronic properties makes the CNTs fascinating candidates for molecular electronics. A promising way to further tune and control the electronic structure of CNTs is to dope them with foreign atoms. Direct doping during the synthesis opens a promising route for potential applications, such as field emission, gas sensor and negative differential resistance (NDR) devices [START_REF] Terrones | New direction in nanotube science[END_REF][START_REF] Ewels | Nitrogen Doping in Carbon Nanotubes[END_REF][START_REF] Ayala | The physical and chemical properties of heteronanotubes[END_REF][START_REF] Ayala | The doping of carbon nanotubes with nitrogen and their potential applications[END_REF][START_REF] Arenal | Boron-nitride and boron-carbonitride nanotubes: synthesis, characterization and theory[END_REF]. In this context, multiwall nanotubes containing nitrogen dopants (CN x -MWNTs) have been successfully produced by different groups [START_REF] Terrones | N-doping and coalescence of carbon nanotubes: synthesis and electronic properties[END_REF][START_REF] Glerup | Synthesis of multi-walled carbon nanotubes and nano-fibres using the aerosol method with metal-ions as the catalyst precursors[END_REF]. However, the as-grown CN x -MWNTs usually have a bamboolike structure involving a high density of defects, which complicates the investigation of nitrogen configurations and nitrogen-induced effects. Compared to MWNTs, single-wall nanotubes (SWNTs) are better candidates, but only a few studies on the synthesis of nitrogen-doped SWNTs (CN x -SWNTs) have been reported [START_REF] Glerup | Synthesis of N-doped SWNT using the arc-discharge procedure[END_REF][START_REF] Ayala | Effects of the reaction atmosphere composition on the synthesis of single and multiwalled nitrogen-doped nanotubes[END_REF][START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. In these studies, chemical characterization, such as electron energy loss spectroscopy (EELS) [START_REF] Glerup | Synthesis of N-doped SWNT using the arc-discharge procedure[END_REF][START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF] or X-ray photoelectron spectroscopy (XPS) [START_REF] Ayala | Effects of the reaction atmosphere composition on the synthesis of single and multiwalled nitrogen-doped nanotubes[END_REF], has been employed to analyze the C-N bonding environment, as done before on CN x materials, films or multi-wall nanotubes [START_REF] Ewels | Nitrogen Doping in Carbon Nanotubes[END_REF][START_REF] Ayala | The physical and chemical properties of heteronanotubes[END_REF]. These studies on CN x -SWNTs diverge, to some extent, in their interpretation of C-N bonding. An efficient approach providing more than chemical information is needed to understand nitrogen incorporation and doping impact on the atomic and electronic structure of nanotubes. Scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are powerful tools to measure local electronic properties of SWNTs and correlate them with their atomic structure [START_REF] Wilder | Electronic structure of atomically resolved carbon nanotubes[END_REF][START_REF] Odom | Atomic structure and electronic properties of single-walled carbon nanotubes[END_REF]. Theoretical calculations [START_REF] Krasheninnikov | Theoretical STM Images of Carbon Nanotubes with Atomic Vacancies: A Systematic Tight-Binding Study[END_REF][START_REF] Meunier | Scanning tunneling microscopy and spectroscopy of topological defects in carbon nanotubes[END_REF][START_REF] Orlikowski | Theoretical STM signatures and transport properties of native defects in carbon nanotubes[END_REF] have shown that a single defect (vacancy, pentagon, adatom) can manifest itself as a perturbation in the carbon network in STM images and as a modification of the local density of states (LDOS) in STS measurements. Thus STM/STS measurements can reveal the atomic structure and the DOS change of nanotube-based hetero-junctions [START_REF] Ouyang | Atomically Resolved Single-Walled Carbon Nanotube Intramolecular Junctions[END_REF][START_REF] Kim | Direct Observation of Localized Defect States in Semiconductor Nanotube Junctions[END_REF][START_REF] Ishigami | Identifying Defects in Nanoscale Materials[END_REF], plasma-sputtered nanotubes [START_REF] Buchs | Scanning tunneling microscopy investigations of hydrogen plasma-induced electron scattering centers on single-walled carbon nanotubes[END_REF] and other nanotube based systems. Czerw et al [START_REF] Czerw | Identification of electron donor states in N-doped carbon nanotubes[END_REF] have reported STM/STS studies on CN x -MWNTs. However, studies concerning CN x -SWNTs are still scarce.

In the case of pristine nanotubes, the pioneering experiments of local tunneling spectroscopy on SWNTs have been interpreted within a tight-binding single particle model [START_REF] Hamada | New one-dimensional conductors: Graphitic microtubules[END_REF][START_REF] Mintmire | Are fullerene tubules metallic?[END_REF][START_REF] Saito | Electronic structure of graphene tubules based on C60[END_REF] neglecting many-body effects. The same model was also able to reproduce optical measurements. However it has been shown that excitons have a major contribution to the optical transitions [START_REF] Ando | Excitons in Carbon Nanotubes[END_REF][START_REF] Kane | Ratio Problem in Single Carbon Nanotube Fluorescence Spectroscopy[END_REF][START_REF] Dresselhaus | Exciton Photophysics of Carbon Nanotubes[END_REF][START_REF] Ando | Theory of Electronic States in Carbon Nanotubes[END_REF]. As a consequence, the similar values of the gap of SWNTs measured either by STM -not expected to be sensitive to the excitons -or optical absorption became unclear and it is necessary to revisit the STS study of SWNTs.

In this context, we studied by STS the electronic bandgaps of pure C-SWNTs and solved this apparent controversy using a model where many-body effects are screened by the image charge induced in the metallic substrate. In order to provide a complete picture of the electronic structure of nanotubes as can be measured at the atomic scale by STM, we also investigated the wavefunctions associated to the Van Hove singularities (VHSs) which can be regarded as nanotube molecular orbitals. These orbitals play a major role in controlling the electronic bandstructure of carbon nanotubes upon doping or functionalization [START_REF] Strano | Electronic Structure Control of Single-Walled Carbon Nanotube Functionalization[END_REF]. The modification of the electronic structure of CNTs by nitrogen doping has also been studied [START_REF] Lin | Combined STM/STS, TEM/EELS investigation of CNx-SWNTs[END_REF] by coupling morphology analysis by TEM, chemical characterization by EELS and STM/STS measurements.

Experimental

Different sorts of nanotubes were used in the present study. Using the home-made reactor at ONERA [START_REF] Cochon | A continuous wave CO2 laser reactor for nanotubes synthesis[END_REF], pure carbon SWNTs were synthesized in the arc discharge configuration whereas the nitrogen doped nanotubes were synthesized in the laser vaporization configuration described elsewhere [START_REF] Lin | Combined STM/STS, TEM/EELS investigation of CNx-SWNTs[END_REF]. The synthesis products were ultrasonically dispersed in absolute ethanol for 15 min and deposited on grids for TEM studies (Philips CM20, 200 kV) of the morphology and of the diameter of nanotubes. Several tens of pure carbon nanotubes were statistically analyzed. Using a Gaussian fit, we obtained a statistical distribution of tube diameter centred on 1.4 nm with a full-width at halfmaximum of 0.2 nm. A third type of tubes was synthesized in a vertical flow aerosol reactor [START_REF] Susi | High quality SWCNT synthesis in the presence of NH3 using a vertical flow aerosol reactor[END_REF]. EELS experiments have been carried out in a dedicated scanning TEM (STEM) VG-HB501 (100 KV). We used a sligthly defocussed probe of a few nm in diameter, with a convergence angle of 15 mrad and a collection angle of 24 mrad. Particular attention has been devoted to contamination and damage during acquisition. STM measurements at room temperature were performed using an Omicron Nanotechnology c variable temperature STM. STM/STS measurements were performed using an Omicron Nanotechnology c low temperature (5K) STM operating under UHV conditions (less than 10 -10 mbar). Arc and laser nanotubes were deposited from a dispersion in alcohol after sonication onto a singlecrystalline Au (111) surface previously cleaned under UHV condition by repeated cycles of ion argon sputtering and annealing at 800 K. The samples were dried in air and introduced into the UHV system. CVD nanotubes were deposited in situ onto commercial gold on glass surface previously flashed by butane flame in air. Before STM/STS measurements, the samples were outgassed for 2 hours to remove residual molecules. All measurements were performed with tungsten tips.

Electronic bandgap of CNTs on a Au(111) surface

Bandgap distribution in a bundle of nanotubes

After dispersion and deposition on the Au(111) substrate, most of the nanotubes remain arranged in bundles, allowing us to measure bandgaps of single nanotubes, either directly in contact with the metallic substrate, or separated from the metal by neighboring nanotubes. In Fig. 1(a), we present the topographic image of a bundle on the Au(111) substrate. The nanotubes are intertwined in the bundle. The differential conductance image at 20 mV (Fig. 1(b)) depicting the distribution of the local densities of states permits us to distinguish clearly the metallic from the semiconducting tubes in the bundle. Its color scale corresponds to the level of the LDOS at 20 mV and reveals the presence of semiconducting tubes in the bundle, that appear dark whereas the metallic tubes appear with a color code closer to that of the gold substrate.

This conductance image can be further understood by looking at the dI/dV spectra plotted in Fig. 1(c). On the gold substrate, the differential conductance has a constant non-zero value, as expected (black dashed curve). On the nanotubes, the spectra are dominated by VHSs. On the metallic tube, the conductance (blue dotted spectrum) between the two first singularities is close to that of the substrate, except around the Fermi level where it displays a local minimum. This pseudo-gap [START_REF] Ouyang | Energy Gaps in "Metallic" Single-Walled Carbon Nanotubes[END_REF] can be induced by a curvature effect [START_REF] Kleiner | Curvature, hybridization, and STM images of carbon nanotubes[END_REF] or to intertube interactions [START_REF] Delaney | Broken symmetry and pseudogaps in ropes of carbon nanotubes[END_REF]. Two spectra of semi-conducting tubes are also shown in Fig. 1(c). The spectrum of tube 1 (green curve) exhibits a strong asymmetry with respect to the Fermi level, which can be attributed to charge transfer from the substrate [START_REF] Wilder | Electronic structure of atomically resolved carbon nanotubes[END_REF][START_REF] Odom | Atomic structure and electronic properties of single-walled carbon nanotubes[END_REF][START_REF] Venema | Atomic structure of carbon nanotubes from scanning tunneling microscopy[END_REF] . The energy separation between the first two singularities on each side of the Fermi level is denoted E s 11 for semiconducting tubes and E M 11 for metallic tubes, respectively. One can measure these values at the point of maximum slope in the peak [START_REF] Venema | Spatially resolved scanning tunneling spectroscopy on single-walled carbon nanotubes[END_REF] . In this way, E s 11 is found to be equal to 0.70 eV (green spectrum) for tube 1 directly contacting the substrate and to 0.91 eV for tube 2 (red spectrum) at the top of the bundle. The renormalization of the electronic gap of a molecule due to substrate-induced charging effects in STS measurement has been already studied both theoretically and experimentally [START_REF] Hesper | Strongly reduced band gap in a correlated insulator in close proximity to a metal[END_REF][START_REF] Lu | Charge transfer and screening in individual C60 molecules on metal substrates: A scanning tunneling spectroscopy and theoretical study[END_REF][START_REF] Sau | Electronic Energy Levels of Weakly Coupled Nanostructures: C[sub 60]-Metal Interfaces[END_REF]. The screening effect due to the image charge in the metal was found to account for the decrease of the electronic gap of the molecules deposited on the substrate. For the nanotubes, when they are in contact with a metallic substrate, this effect should also be considered. Here the measured E S 11 value of tube 1 is indeed smaller than for tube 2 and the difference cannot be explained by the distribution in tube diameters [START_REF] Lin | Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy[END_REF]. This suggests that the tube-substrate distance would probably have an impact on the E S 11 value measured by STS.

Bandgap reduction due to screening by the metallic substrate

In order to verify the relation between the tube-substrate separation and the measured bandgap, we have also studied the pure carbon SWNTs synthesized by CVD. The histogram of the measured E S 11 values (see Fig. 2) shows a clear right shift of E S 11 measured on the top of bundles (red) with respect to those measured on the tubes contacting the substrate (blue), in good agreement with the results obtained on the arc samples.

The present observation can be explained as follows (see the scheme in Fig. 3). According to the literature, the intrinsic gap of semiconducting tubes is the sum of the single-particle gap and of the self-energy induced by the manybody effect [START_REF] Wang | The Optical Resonances in Carbon Nanotubes Arise from Excitons[END_REF][START_REF] Dukovic | Structural Dependence of Excitonic Optical Transitions and Band-Gap Energies in Carbon Nanotubes[END_REF]. In STS measurements, the screening effect can be understood from an image charge model, where the E S 11 transition of a nanotube adsorbed on a metal corresponds to the gap of the free nanotube (including electronelectron interactions) reduced by the screening energy resulting from the image charge in the metal Ce 2 /(2h a ), where h a is the tube-substrate distance [START_REF] Lin | Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy[END_REF]. For the tubes contacting the substrate (h a = h 1 ), the many-body effect is practically compensated by the substrate-induced screening, which reduces significantly the gap and approaches the single-particle gap value. As h a increases (h a = h 2 ), the screening effect decreases and leads to larger experimental STS values. The limit h a → ∞, allows us then to estimate the unscreened gap of nanotubes. Experimentally, the major role played by many-body effects has been first demonstrated by optical measurements [START_REF] Wang | The Optical Resonances in Carbon Nanotubes Arise from Excitons[END_REF][START_REF] Dukovic | Structural Dependence of Excitonic Optical Transitions and Band-Gap Energies in Carbon Nanotubes[END_REF]. The electron-hole interaction confined in the quasi one dimension system leads to important excitonic effect in the optical absorption. At first glance, the STM experiments are not supposed to be sensitive to such an electron-hole interaction [START_REF] Kane | Ratio Problem in Single Carbon Nanotube Fluorescence Spectroscopy[END_REF]. Therefore, it is instructive to compare the STS measurement with optical absorption experiments. The inset in Fig. 3 shows the optical absorption spectrum measured on the same patch of arc nanotubes. The energy difference (∆E) between the optical transition and the asymptotic values E ∞ ii by STS is then expected to correspond to the exciton binding energy. In this way, we obtain ∆E s 11 ∼ 0.4 eV, close to the value determined in previous optical measurements [START_REF] Dukovic | Structural Dependence of Excitonic Optical Transitions and Band-Gap Energies in Carbon Nanotubes[END_REF].

The molecular orbitals of carbon nanotubes

In the context of controlling the electronic band structure of carbon nanotubes using doping or functionalization, the molecular orbitals of SWNTs play a major role, since they are fully involved in the transport properties and the chemical reactivity of SWNTs [START_REF] Strano | Electronic Structure Control of Single-Walled Carbon Nanotube Functionalization[END_REF]. It has been predicted that, in defect-free semiconducting tubes, the electronic states would exhibit broken symmetry [START_REF] Kane | Broken symmetries in scanning tunneling images of carbon nanotubes[END_REF][START_REF] Meunier | Tight-Binding Computation of the STM Image of Carbon Nanotubes[END_REF][START_REF] Meunier | Scanning tunneling microscopy and spectroscopy of topological defects in carbon nanotubes[END_REF][START_REF] Lambin | Computation of STM images of carbon nanotubes[END_REF]. Local conductance measurement of SWNTs using atomically resolved STS allows us to investigate such an asymmetry at VHSs.

Semiconducting tube: 3p+1

In Fig. 4(a-d), we present the differential conductance images (dI/dV maps) in color scale of a semiconducting tube at the energies of the VHSs. The hexagonal lattice is determined on the topographic image [START_REF] Lin | Imaging the symmetry breaking of molecular orbitals in single-wall carbon nanotubes[END_REF] and superimposed in the images to indicate the position of carbon atoms. The significant deformation of the lattice is mostly due to the drift occurring during the long acquisition time as well as distorsions induced by the curvature of the nanotube. These conductance images show a strong anisotropy of density of states which is energy-dependent. More precisely, for the images at VHS+1 and VHS-2, one third of the C-C bonds are highlighted while the other C-C bonds are more intense at VHS-1 and VHS+2. The four images can be summarized into two different patterns sketched in Fig. 4(e,f). The superimposition of these two types of images, such as VHS±1, restitutes a full sixfold symmetry. In Fig. 4(g), we plot the differential conductance profiles along an hexagon. Starting from the atom labeled 1 in Fig. 4(f), the VHS+1 profile in the clockwise direction of the hexagon displays two maxima corresponding to higher DOS and four minima indicating lower DOS. The maxima/minima of VHS+1 are exactly at the same position as the minima/maxima of VHS-1. The conductance profile at VHS-1 has the mirror symmetry with respect to the profile at VHS+1, demonstrating clearly the complementary nature of these two patterns.

Semiconducting tube: 3p-1

Similar patterns with broken symmetry were systematically observed on the defect-free nanotubes. Fig. 5 shows the dI/dV maps of a second type of semiconducting tube. At VHS+1 and VHS-2, two thirds of the C-C bonds have a maximum of LDOS. The most inclined bond with respect to the axial orientation has maxima of electron density at VHS-1 and VHS+2, presenting an opposite behavior to that of the previous example. As will be shown in the following, this behavior is the signature of (n,m) tubes with nm = 3p -1 wheras the example shown in the previous section is typical of a nm = 3p + 1 tube.

Tight binding analysis

In the literature, interference patterns have been observed in STM topographic images close to defects such as chemical impurities, cap ends or in finite length nanotubes [START_REF] Clauss | Electron backscattering on single-wall carbon nanotubes observed by scanning tunneling microscopy[END_REF][START_REF] Furuhashi | Chiral Vector Determination of Carbon Nanotubes by Observation of Interference Patterns Near the End Cap[END_REF][START_REF] Venema | Imaging Electron Wave Functions of Quantized Energy Levels in Carbon Nanotubes[END_REF]. Differential conductance images have also been obtained in a finite length tube using local differential conductance spectroscopy [START_REF] Lemay | Two-dimensional imaging of electronic wavefunctions in carbon nanotubes[END_REF]. These observations have been explained qualitatively by interference effects between the Bloch waves [START_REF] Kane | Broken symmetries in scanning tunneling images of carbon nanotubes[END_REF][START_REF] Rubio | Electronic States in a Finite Carbon Nanotube: A One-Dimensional Quantum Box[END_REF][START_REF] Furuhashi | Chiral Vector Determination of Carbon Nanotubes by Observation of Interference Patterns Near the End Cap[END_REF]. In contrast, our results of dI/dV maps were performed far from the extremity of the tube and were observed systematically. Our observations are consistent with the prediction that the electronic states would display broken symmetry effect [START_REF] Meunier | Tight-Binding Computation of the STM Image of Carbon Nanotubes[END_REF][START_REF] Clauss | Electron backscattering on single-wall carbon nanotubes observed by scanning tunneling microscopy[END_REF][START_REF] Kane | Broken symmetries in scanning tunneling images of carbon nanotubes[END_REF][START_REF] Lambin | Computation of STM images of carbon nanotubes[END_REF][START_REF] Meunier | Scanning tunnelling microscopy of carbon nanotubes[END_REF].

A chemist approach in real space [START_REF] Lin | Imaging the symmetry breaking of molecular orbitals in single-wall carbon nanotubes[END_REF] appears to be very fruitful also as we show now. We follow the classical zone-folding theory based on a π tight binding description of the graphene band structure. The rolling up of the graphene sheet implies that the allowed k vectors belong to the so-called cutting lines parallel to the tube axis, separated by 2π/L, where L = πd is the length of the chiral vector and d is the diameter of the tube. If (n,m) are the coordinates of the chiral vector, the position of the cutting lines with respect to the K points depends on the value of nm modulo 3. In the case of metallic tubes, nm = 3p and some cutting lines are going through the K points. In the case of semiconducting tubes, nm = 3p ± 1, and the nearest line is at a distance 2π/3L on the left (resp. right) hand side of K point when nm = 3p + 1 (resp. 3p -1). This depends on the specific choice of the K point (see Fig. 6(a)), but the final result of our analysis will not. Close to the K point, the linearity of the dispersion relation of graphene implies that the energy E is proportional to | k -K|. For a nm = 3p + 1 tube, as indicated in Fig. 6(a), the k vector of its LUMO state corresponds to k = K + q, where q = q 0 , q 0 is defined as a vector of length 2π/3L pointing along the direction of the chiral vector in the negative direction. On the other side of the K point, the k = K + q = K -2 q 0 vector corresponds to the second singularity. The Bloch eigenstates of a singularity have only a double trivial degeneracy ± k, -k being close to a K ′ point of the Brillouin zone.

Since there are two atoms per unit cell in the graphene structure, the eigenstates | ψ k are built from two independent Bloch states | k 1 and | k 2 :

|

ψ k = C 1 | k 1 + C 2 | k 2 . (1)
These two Bloch states | k 1(2) are linear combinations of atomic state | n at site n in the two sublattices. Relation between ω, q and chiral angle θ. ω is the angle between the q vector and the x axis and is related to the chiral angle θ. θ is defined as the smallest angle between a 1 vector and chiral vector C h and 0 ≤ θ ≤ π/6. For the LUMO state of a nm = 3p + 1 tube, q = q 0 , q 0 being a vector of length 2π/3L pointing along the direction of the chiral vector in the negative direction, the corresponding ω = θ + 5π 6 . (c) Illustration of the angle θ α = ωπ 6 -K. τ α for the LUMO state of the tubes of nm = 3p + 1 type, α = 1, 2, 3. θ α = θ, θ + 2π/3 and θ -2π/3, respectively. Thus, θ α represents the angle between the vector τ α and the tube axis T .

| k 1(2) = n ∈1(2) e i k. n | n . (2)
Dropping for simplicity the k indices, the wavefunctions in real space ψ( r) can be written as:

ψ( r) = r | ψ = C 1 n∈1 e i k. n φ( r -n) + C 2 n∈2 e i k. n φ( r -n) = C 1 ψ 1 + C 2 ψ 2 , (3)
where φ( rn) is the π atomic orbital centered on site n. 1 We can now calculate the electronic density ρ

( r) = |ψ| 2 , ρ( r) = |C 1 | 2 |ψ 1 | 2 + |C 2 | 2 |ψ 2 | 2 + C 1 C * 2 ψ 1 ψ * 2 + C * 1 C 2 ψ * 1 ψ 2 . (4)
This development involves an expansion in products of the atomic wavefunctions at different sites. For |ψ 1(2) | 2 :

|ψ 1(2) | 2 = n, m∈1(2) e i k.( n-m) φ( r -n) φ( r -m). ( 5
)
In the first neighbor approximation, the overlap function φ( rn) φ( rm) can be neglected when n m, because first neighbour sites belong to different sublattices and the above terms reduce to the superposition of atomic densities:

|ψ 1(2) | 2 = n∈1(2) φ 2 ( r -n). ( 6
)
In the same approximation, the cross term is given by:

ψ 1 ψ * 2 = n∈1, m∈2 e i k.( n-m) φ( r -n) φ( r -m) , (7)
where n and m are first neighbors. Close to the K point, the ratio C 1 /C 2 is given by: 2

C 1 /C 2 = sgn(E)e i(ω-π 6 ) . (8)
1. Here we consider only the π states. 2. In the tight binding model, the Hamiltonian H( k) has only off-diagonal non-vanishing matrix elements:

H( k) 11 = H( k) 22 = 0 and H( k) 12 = H * ( k) 21 .
The eigenvalues of energy is given by E = ±γ 0 |Γ( k)| = ±γ 0 |e i k. τ 1 + e i k. τ 2 + e i k. τ 3 |, where γ 0 is thet transfer integral between first neighbors. τ 1 , τ 2 and τ 3 are the vectors joining one atom to its three first neighbors, as indicated in Fig. 6. Close to a K point, k = K + q and Γ( K) = 0. Thus, by developing Γ( k) ito first order in q, Γ( k) = -3acc 2 qe i(ω-π 6 ) , where a cc is the C-C nearest neighbor distance, q is the module of q, ω is the angle between q and the x axis, see Fig. 6(a). The energy E = ± 3accγ 0 2 q depends only on the modulus of q. Since Hψ = Eψ, EC 1 = -γ 0 Γ( k)C 2 , the ratio C 1 /C 2 is then directly obtained.

where sgn(E)= ± 1 depends on the sign of E and ω is the angle between q and the x axis. This implies that the ratio C 1 /C 2 just introduces a phase factor related to the direction of the q vector, i.e. finally to the chiral angle θ, as indicated in Fig. 6(b). The chiral angle θ here is precisely defined as the smallest angle between the a 1 lattice vector and the chiral vector C h , so that 0 ≤ θ ≤ π/6. Since|C 1 | 2 = |C 2 | 2 we can normalize the density in Eq. ( 4) by fixing these quantities equal to unity. Finally, combining Equations. ( 6), ( 7) and ( 4), we obtain the expression of the local density of states n( r, E), which is the quantity measured in STS. n( r, E) can be written as:

n( r, E) = n(E) × ρ( r) ≃ n(E) × { n∈1+2 φ 2 ( r -n) + [sgn(E) n∈1, m∈2 e i[ k.( n-m)+ω-π 6 ] φ( r -n)φ( r -m) + complex conjugate]} = n(E) × {ρ at ( r) + ρ int ( r)} , (9)
where n(E) is the density of states, ρ at ( r) is the superposition of electron atomic densities and ρ int ( r) is the interference centered on the C-C bonds.

The breaking of the sixfold symmetry is caused by the second term ρ int ( r). Its intensity is proportional to the nearest neighbor overlap. Then, mn is one of the τ α vectors between first neighbors shown in Fig. 6(b,c). Keeping only the terms of lowest order, we can also replace k by K, and the interference term ρ int ( r) can be written as:

ρ int ( r) = 2φ( r)φ( r -τ α ) × sgn(E) cos θ α , (10)
where θ α = ωπ 6 -K. τ α . From Eq. ( 10), we see that the electronic density of the interference term is determined by the factor sgn(E) cos θ α . To discuss the value of cos θ α , let us first consider the LUMO state of a nm = 3p + 1 tube. As mentioned above, the corresponding vector q = q 0 , points along the negative direction of the chiral vector C h , so that ω = θ + 5π 6 (see Fig. 6(b)). When τ α = τ 1 , τ 2 , τ 3 , K. τ α is equal to 2π/3, 0 and 4π/3 respectively and the corresponding values of θ α = ωπ 6 -K. τ α are equal to θ, θ + 2π/3 and θ -2π/3. As shown in Fig. 6(c), these angles are equal to the angles between the tube axis T and the C-C bonds τ 1,2,3 . We have cos θ 1 > 0, cos θ 2,3 < 0. Switching to the LUMO+1 case, the q vector should take the value -2 q 0 . This leads to a shift of π in ω with respect to the LUMO state and inverts the sign of cos θ α . Considering both the sign of E and cos θ α , there are four possibilities, as listed in table. 1. Depending on the sign of sgn(E) cos θ 1 , basically two types of images are then expected:

HOMO-1 HOMO LUMO LUMO+1 E - - + + q -2 q 0 q 0 q 0 -2 q 0 cos θ 1 - + + - cos θ 2 + - - + cos θ 3 + - - + sgn(E) cos θ 1 + - + - sgn(E) cos θ 2 - + - + sgn(E) cos θ 3 - + - + Image Type I II I II
Table 1: Sign of the phase factor sgn(E) cos θ α of the interference term ρ int ( r) for nm = 3p + 1 tubes and the resulting interference image type.

Image of Type I: sgn(E) cos θ 1 > 0. As schematically illustrated in Fig. 4(e), the electron density above the C-C bonds pointing close to the tube axis ( τ 1 ) is reinforced, all the more when θ is small, i.e. close to a zig-zag orientation (cos θ ≃ 1).

Image of Type II: sgn(E) cos θ 1 < 0. In this case, when the chiral angle θ is close to zig-zag orientation (θ ≃ 0, cos θ 2,3 ≃ -1/2), the images present stripe reinforcements on the bonds perpendicular to the axis ( τ 2,3 ), as indicated in Fig. 4(f). The images of type I and type II are complementary and the superposition of both types reconstitutes the six-fold symmetry of the graphene network. As θ increases, ωπ 6 -K. τ 3 → 0 and the density on the corresponding bonds ( τ 3 in Fig. 6(b,c)) gradually vanishes and the density concentrates principally on the bonds τ 2 .

To summarize, for the tubes such that nm = 3p + 1, the LUMO and HUMO contributions are of type I and type II, respectively, presenting complementary natures, because the corresponding sign(E) values are opposite. When going from the first VHS to the neighboring second VHS (same sign of E), the q vectors are along opposite directions, implying a shift of π in the phase factor ω, which inverts the sign of cos θ α . Therefore, the singular contribution at the second VHSs is also complementary of those of the first ones.

Considering now the other family of semiconducting tubes, where nm = 3p -1, the q vector of the LUMO state should be replaced byq 0 , giving rise to a phase shift of π with respect to the nm = 3p + 1 tubes. Thus, the LUMO state presents the image type II. By analogy with the analysis in table. 1, their HOMO-1, HOMO, LUMO and LUMO+1 states correspond to the images of type II, I, II and I, respectively, and are complementary to those of the nm = 3p + 1 tubes. These results agree perfectly with those obtained by Kane and Mele [START_REF] Kane | Broken symmetries in scanning tunneling images of carbon nanotubes[END_REF].

Turning back to experimental data, in Fig. 4(a-d) (see section 4.1), we have observed exactly only two types of interference images as predicted by the tight-binding model. The axially oriented C-C bond has maximum electron density at VHS+1 and minimum density at VHS-1. This implies that the investigated tube belongs to the family 3p + 1. As for the tube shown in Fig. 5 (see section 4.2), its conductance images at VHS-1 and VHS+1 exhibit the interference pattern of Type I and Type II, respectively. According to our tight binding model, it belongs to the family 3p -1.

Nitrogen doped single-walled carbon nanotubes

After having attained a deep understanding of the electronic properties of pure carbon nanotubes, we now study nitrogen incorporation and its doping impact on the atomic and electronic structure of nanotubes.

Structural and chemical characterization of CN x -SNWTs by TEM/EELS

Fig. 7(a) displays a TEM image of as-grown products dispersed in solution. We observe a random network of single-walled nanotubes, which are assembled into bundles. These bundles contain a number of tubes varying from a few units to a few tens. The tubes are well-crystallized, and very few defects are observed. Local chemical characterization of as-grown nanotubes has been previously carried out using spatially-resolved electron energy loss spectroscopy (SREELS) of bundles of SWNTs and individual nanotubes [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. This analysis revealed a mean nitrogen content about 1.7 atom %. Fig. 7(b) shows a representative example of the EELS spectrum recorded of those NTs. This EELS spectrum corresponds to the sum of six EEL spectra acquired on the bundle of NTs shown in the bright field image (acquisition conditions are described elsewhere [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]; the acquisition time was two seconds for each spectrum). From the shape of the C-K edge it can be deduced that the nanotubes consist of a typical graphitic network with sp 2 -type bonding and that the tubes are very well graphitized [START_REF] Ayala | The doping of carbon nanotubes with nitrogen and their potential applications[END_REF][START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. The inset of Fig. 7(b) shows the N-K edge. Two features can be observed at ∼ 398 and ∼ 402 eV, respectively. They could be attributed to the π states of the pyridine-like and graphitic-like configuration, respectively [START_REF] Ayala | The doping of carbon nanotubes with nitrogen and their potential applications[END_REF][START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. As a matter of fact, we observed a predominance of pyridine-like nitrogen configuration [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF].

Structural and electronic characterization of CN x -SNWTs by STM/STS

Following this chemical analysis, STM measurements of CN x -SWNTs have revealed the presence of defects with different characteristics. Fig. 8(a) displays a tube containing multiple defects. Two types of perturbation of carbon network, appearing as a local protrusion, can be readily distinguished. The rectangle indicates the first defect with large spatial extension (5∼6 nm), comprising axially oriented spots with a 0.44 nm periodicity, as indicated by the black dots in the magnified image of Fig. 8(b). Similar defect has been previously observed in our CN x -SWNTs and reported in [START_REF] Lin | Combined STM/STS, TEM/EELS investigation of CNx-SWNTs[END_REF]. We will present later on a detailed study on this kind of defect by combining STS spectroscopic data.

The second defect is indicated by the square in Fig. 8(a) and a magnified image in Fig. 8(c). It appears as a local protrusion with a series of "ridges" aligned along its axial direction. Compared to the first defect, its spatial extension is much smaller, ∼1 nm. It is worth mentioning that such a signature has also been observed several times in our CN x -SWNTs. Even if the exact configuration of this defect is not known, we can exclude some cases. We first consider topological defects. The signature of a vacancy is predicted to be a bright hillock structure [START_REF] Krasheninnikov | Theoretical STM Images of Carbon Nanotubes with Atomic Vacancies: A Systematic Tight-Binding Study[END_REF][START_REF] Krasheninnikov | Predicted scanning tunneling microscopy images of carbon nanotubes with atomic vacancies[END_REF] and it has few in common with the present observation. The present signature is more similar to the presence of a pentagon in the graphitic network which is a ring protrusion [START_REF] Meunier | Tight-Binding Computation of the STM Image of Carbon Nanotubes[END_REF] or a Stone-Wales defect exhibiting a combination of double rings protrusion with ridge-like structure [START_REF] Meunier | Scanning tunneling microscopy and spectroscopy of topological defects in carbon nanotubes[END_REF]. According to DFT calculations [56], the signature of a single graphitic nitrogen is a triangular bright spot cluster weakly sensitive to STM bias, which seems to exclude the possibility of a single nitrogen atom in a substitutional site. The observation of two different defect signatures in the same tube also indicates that these two signatures should correspond to different atomic structures.

Fig. 9(a) shows the image of a nanotube measured at 1.0 V. The defect is localized in the middle of the image (zone D). The difference in height between the defect and the other part of the tube is very small, which is different from the local protrusions presented above. It is worth noting that, next to the defect site, the STM image exhibits an interference pattern over long distance with a √ 3a × √ 3a periodicity (a is the graphene lattice constant). This pattern can be interpreted in terms of electronic interference originating from large momentum scattering of the electron wave functions at the defect site between two nonequivalent K points, which leads to a modulation in the electron density [START_REF] Kane | Broken symmetries in scanning tunneling images of carbon nanotubes[END_REF][START_REF] Clauss | Electron backscattering on single-wall carbon nanotubes observed by scanning tunneling microscopy[END_REF]. Similar patterns have been experimentally obtained in the vicinity of tube end caps [START_REF] Furuhashi | Chiral Vector Determination of Carbon Nanotubes by Observation of Interference Patterns Near the End Cap[END_REF], of defects created by hydrogen electron [START_REF] Buchs | Creation of paired electron states in the gap of semiconducting carbon nanotubes by correlated hydrogen adsorption[END_REF] and STM tip-induced defects [START_REF] Berthe | Reversible Defect Engineering of Single-Walled Carbon Nanotubes Using Scanning Tunneling Microscopy[END_REF]. In an oversimplified description, such an interference pattern is a fingerprint of the presence of a localized defect, which can act as an electron scatterer. In our observation, since the amplitude of the DOS oscillation decreases with the distance, the mixture of various electron states leads to a continuous change in the imaging pattern [START_REF] Furuhashi | Chiral Vector Determination of Carbon Nanotubes by Observation of Interference Patterns Near the End Cap[END_REF]. Upon increasing the bias voltage up to 1.3 V, the perturbation area (zone D) fades out, and the tube presents a uniform interference pattern over a distance of 10 nm, consisting of bright spots and wavy lines. Such long range interference patterns have been frequently observed, suggesting the existence of a several localized defects in our CN x -SWNTs.

In order to have a deeper understanding of the defects observed in our CN x -SWNTs, a spectroscopic study has been undertaken at low temperature. Fig. 10(a) displays an atomically resolved STM image of a nanotube with a protrusion with a spatial extension about 6 nm, similar to the first defect reported above. In Fig. 10(b), we plot the color map of differential conductance spectra as a function of the bias voltage and the position along the tube, which is oriented vertically. Starting from the defect-free zone at the bottom of the image, the tube exhibits a typical electronic structure of a defect-free semiconducting tube. In Fig. 10(c), a typical STS of this defect-free zone (black curve) exhibits the two first VHSs, giving an electronic gap about 1.2 V. When the tip approaches the protrusion zone, two new states appear inside the electronic gap at around -0.37 V and 0.24 V, respectively (dashed curve in Fig. 10(c)). Referring to the literature, paired states near the Fermi level have been attributed to the presence of vacancy-adatom complex [START_REF] Kim | Deep levels in the band gap of the carbon nanotube with vacancy-related defects[END_REF] or any two close point defects [START_REF] Buchs | Creation of paired electron states in the gap of semiconducting carbon nanotubes by correlated hydrogen adsorption[END_REF]. Assuming that this defect is due to the presence of nitrogen, there are several possibilities based on the understanding of paired states : 1) the presence of several nitrogen atoms; 2) the combination of nitrogen with vacancy. This observation is in line with the results presented above where the defects observed cannot be explained by a simple substitution of a nitrogen atom in the carbon lattice, but most likely by a complex structure.

Nitrogen configuration in CN x -SWNTs

The C-N bonding in nitrogen doped CNTs has been studied in previous works by Glerup et al. [START_REF] Glerup | Synthesis of N-doped SWNT using the arc-discharge procedure[END_REF] and Ayala et al. [START_REF] Ayala | Tailoring N-doped single and double wall carbon nanotubes from a nondiluted carbon/nitrogen feedstock[END_REF] who found that the nitrogen is incorporated in the walls with both graphitic and pyridine-like forms. In contrast to these analysis, our EELS results suggest that the pyridine-like configuration is preferentially stabilized in SWNT, with respect to the graphitic one [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. Some recent theoretical studies concerning the formation energy of pyridinic and graphitic configurations have proved the possibility of having only pyridinic configurations under some conditions: on the basis of first-principles total energy calculations, Min et al. [START_REF] Min | Unusual transport characteristics of nitrogen-doped singlewalled carbon nanotubes[END_REF] showed that the pyridine-like nitrogen configuration is indeed energetically favored as compared to graphitic configuration when two hydrogen atoms are attached to passivate the broken carbon bond. Yang et al. [START_REF] Yang | The Nature of Graphite-and Pyridinelike Nitrogen Configurations in Carbon Nitride Nanotubes: Dependence on Diameter and Helicity[END_REF] showed that pyridine-like nitrogen becomes more favorable than graphite-like nitrogen as the diameter decreases and as the chiral angle increases, in agreement with [START_REF] Li | sub x] nanotubes with pyridinelike structures: p-type semiconductors and Li storage materials[END_REF]. It is also worth noting that Ayala et al. [START_REF] Ayala | Tailoring N-doped single and double wall carbon nanotubes from a nondiluted carbon/nitrogen feedstock[END_REF] have reported that pyridine-like configuration occurs at higher synthesis temperature while the graphitic substitution configuration fades away. At the highest temperature achieved in their synthesis (950 • ), they showed a predominance of pyridine-like configuration. These results support our EELS findings.

Turning back to STM data, the protrusion with small extension observed in our CN x -SWNTs cannot be due to the presence of a single graphitic nitrogen, whose signature is predicted to be a triangular bright cluster. In addition, if the large protrusion in our sample observed by STM/STS is indeed caused by nitrogen, its electronic structure is also consistent with a non-graphitic nitrogen configuration. It is generally believed that the graphitic nitrogen gives rise to a donor state [START_REF] Nevidomskyy | Chemically Active Substitutional Nitrogen Impurity in Carbon Nanotubes[END_REF][START_REF] Choi | Defects, Quasibound States, and Quantum Conductance in Metallic Carbon Nanotubes[END_REF], while we observed a double peak structure within the gap. All these results imply that the graphitic nitrogen is not the dominant one in our CN x -SWNTs, which is in line with EELS analysis [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. Therefore, although a chemical characterization cannot be unambiguously performed from the STM/STS data, we can conclude that, if nitrogen atoms are at the origin of the defects observed, the dominant configuration is probably not a single simple substitution.

In order to have a general idea of defect distribution and defect content in our CN x -SWNTs, we have performed a statistical study of the atomically resolved STM images. Defects have been detected in ∼ 1/3 of the investigated zones (each is ∼ 20 nm). Assuming that all the defects observed by STM measurements are due to the presence of nitrogen, the frequency of their detection in STM images is at first sight hardly compatible with the N concentration determined from EELS, which revealed an average nitrogen concentration of ∼1.7 at% [START_REF] Lin | Nitrogen Configuration in Individual CNx-SWNTs Synthesized by Laser Vaporization Technique[END_REF]. If the distribution of nitrogen atoms on the tube surface is homogenous, according to EELS data, we should be able to observe a defect associated with the presence of nitrogen every 4 nm (this estimation takes into account the fact that N atoms can be randomly distributed along the tube circumference and that only the upper side of tube can be detected by the STM tip). This apparent discrepancy between EELS and STM data can be explained by a heterogenous N distribution, in which case we should find some areas rich in N atoms. This leads to the question of the nature of N configurations when embedded in the graphitic network. As discussed above, nitrogen atoms are incorporated in SWNTs as complex defects, involving several nitrogen atoms. Thus, a smaller frequency of defect detection can be expected, as it is the case of our STM measurement. This also agrees with the inhomogeneous distribution of nitrogen at the surface of tubes found in the EELS analysis. Indeed, as shown in Fig. 8, we observe a long range unperturbed zone (∼ 20 nm), but highly perturbed zones in some areas of the tubes.

Summarizing our results, STM data reveal the presence of different defects in our CN x -SWNTs. These defects could be most likely made of complex structures involving one or more nitrogen and defects such as vacancies or 5/7 rings. STM and EELS results indicate that the nitrogen atoms are not regularly dispersed along the tubes. Based on this understanding, we would expect that the structure of nitrogen rich defects might vary from one defect to another, randomly dispersed along the tube.

Conclusion

In this study, we have discussed the structural and electronic properties of pristine and CN x single-walled nanotubes by combining TEM/EELS and STM/STS analyses. Firstly, we have evidenced the role of many-body effects played in STS and the role of the metal substrate which screens these interactions via the image charge. The comparison between STS and optical absorption measurement has allowed us to estimate the exciton binding energy of the semiconducting tubes. Secondly, we have performed a complete experimental investigation of the molecular orbitals associated with Van Hove singularities in pure semiconducting SWNTs. Using a simple tight-binding model, we have analyzed the symmetry of wavefunctions in SNWTs and demonstrated that the molecular orbitals of nanotubes at the Van Hove singularities display only complementary behaviours. Finally, based on the analysis by TEM/EELS and STM/STS, we have tentatively proposed a model for our CN x -SWNTs: the insertion of nitrogen atoms should be associated with different structural defects, such as vacancies or pentagons and/or heptagons and the clusters of these structures disperse randomly along the tubes.

Figure 1 :

 1 Figure 1: (Color online) STM/STS of a bundle of tubes on the substrate. (a) Topographic image. U bias = 1 V, I set point = 0.4 nA. (b) Differential conductance images at 20 mV. The images are 40x40 nm 2 . The color scale corresponds to the level of DOS. At 20 mV, the semiconducting tubes have zero DOS and turn out to be darker compared to the substrate and the metallic tubes. (c) Representative dI/dV spectra taken at locations indicated by markers blue, red, green and black in image (a).

Figure 2 :

 2 Figure 2: (Color online) Histogram of E S 11 measured on the CVD sample. Blue bars: values measured on the tubes contacting the metallic substrate, Magenta bars: values measured on top of the bundles.

Figure 3 :

 3 Figure 3: (Color online) Schematic illustration for the E S 11 transition in different situations. The inset shows optical absorption measured on our arc nanotube sample.

Figure 4 :

 4 Figure 4: (Color online) Differential conductance image of the semiconducting tube at (a) VHS-2 = -0.778 V; (b) VHS-1 = -0.374V; (c) VHS+1 = 0.374 V; (d) VHS+2 = 0.778 V. The white arrow indicates the axial direction of the tube and the honeycomb lattice of the tube is drawn by blue lines. (e, f) Schematic illustration of the two wave patterns. (g) Differential conductance profiles at VHS±1 along the hexagon indicated by the blacks dots in figure (f). The starting point is the atom labeled 1 and we followed the clockwise direction. The dashed lines indicate the position of the atoms.

Figure 5 :

 5 Figure 5: (Color online) Differential conductance images of the semiconducting tube 2 at (a) -0.640 V; (b) -0.302 V; (c) 0.447 V and (d) 0.809 V. (e, f) Schematic illustration of the imaging patterns. The tube axis is oriented in the horizontal direction.

Figure 6 :

 6 Figure 6: (Color online) (a) Brillouin zone of the hexagonal graphene lattice (left) with a zoom close to the K point showing the cutting lines parallel to the tube axis in the case of semiconducting tube with nm = 3p + 1 (right). (b) Relation between ω, q and chiral angle θ. ω is the angle between the q vector and the x axis and is related to the chiral angle θ. θ is defined as the smallest angle between a 1 vector and chiral vector C h and 0 ≤ θ ≤ π/6. For the LUMO state of a nm = 3p + 1 tube, q = q 0 , q 0 being a vector of length 2π/3L pointing along the direction of the chiral vector in the negative direction, the corresponding ω = θ + 5π 6 . (c) Illustration of the angle θ α = ωπ 6 -K. τ α for the LUMO state of the tubes of nm = 3p + 1 type, α = 1, 2, 3. θ α = θ, θ + 2π/3 and θ -2π/3, respectively. Thus, θ α represents the angle between the vector τ α and the tube axis T .

Figure 7 :

 7 Figure 7: (Color online) (a)TEM image of dispersed CN x -SWNTs. (b) Sum of 6 EEL spectra recorded on the bundle of CN x -SWNTs displayed in the inset (marked with an arrow). Inset: N-K edge spectrum obtained after background substraction (see the text).

Figure 8 :

 8 Figure 8: (Color online) (a)STM image of a SWNT containing multiple defects. V= 0.5 V, I = 200 pA, scale bar: 3 nm. The rectangle and square indicate two types of defects. (b) Magnified image of a defect with large spatial extension. The distance between black dots is equal to 0.44 nm. (c) Magnified image of a defect with small spatial extension.

Figure 9 :

 9 Figure 9: (Color online) STM images of a defective SWNT at 1.0 V (a) and 1.3 V (b). I = 200 pA. A defect is localized in the D zone. Next to the defect site, an interference pattern can be observed.

Figure 10 :

 10 Figure 10: (Color online) The evolution of the electronic structure on the defective nanotube. (a) STM image of a defective tube with a local protrusion at the upper part of the tube. V = 1.1 V, I = 1 nA (b) Color map of the differential conductance as a function of the bias voltage and of the position along the defective tube in image (a). (c) Typical STS in the defect-free zone (black curve) and on the protrusion (red dashed curve).

Acknowledgments

This study has been supported by the European Contract STREP "BCN" Nanotubes 30007654-OTP25763, by a grant of CNano IdF "SAMBA" and by the ANR project "CEDONA" of the PNANO programme (ANR-07-NANO-007_02). We gratefully acknowledge Luc Henrard, Patrick Hermet and Bin Zheng for fruitful discussions.


Y Wang

P D Townsend
email: pdtownsend@googlemail.com

Indications of bulk property changes from surface ion implantation

Keywords: insulators, ion implantation, luminescence, optical properties, radiation effects implantation effects thermoluminescence, ZnO: Cu, ZnO: Tb, nanoparticles, phase transitions PACS Thermoluminescence 78.60.Kn Phase transitions 64.70.K-Radiation effects in solids 61.80.-x

Indications of bulk property changes from surface ion implantation

Ion implantation is a highly successful and ubiquitous tool for the production of semiconductor components [START_REF] Yu | Fundamentals of semiconductors[END_REF][START_REF]Ion implantation in semiconductors[END_REF]. Additionally there is an extensive literature in many fields for surface modification of other types of material. There are examples ranging widely from optical waveguide and photonic structures in insulators [START_REF] Townsend | [END_REF], to surface hardening and catalytic effects with metals [START_REF] Dearnaley | [END_REF]5], to controlled production of nanoparticles [6]. In all such instances the primary objective has been to induce controllable and desirable changes in the surface of the host materials. Consequently the property changes that are measured focus on surface layers, and to a large extent the possibility that deeper features exist are mostly ignored. However, effects which extend a few microns beyond the implant have been noted, and these are mostly ascribed to the result of induced stress, or exciton and charge trapping. These effects are clearly important as any such distortions or changes of the original lattice will also occur laterally within the surface implant zone in patterned implant devices. By contrast, there has been negligible consideration, or experimental investigation, of the possibility of changes in bulk responses resulting from near surface ion implantation.

Potential materials that could demonstrate long range effects

Implantation in semiconductors requires small ion doses to achieve control of electrical conductivity, but with increasing ion implant concentrations several other effects develop. A primary factor is radiation damage, in which the structure is perturbed from the original crystalline or amorphous atomic arrangement, and this is accompanied by sputtering of atoms from the surface. Consequently the density of the layer is altered, and there are changes in composition both from preferential sputtering, and the injection of impurity ions. The chemical changes can result in new compounds, precipitates or inclusions [START_REF] Townsend | [END_REF]6]. All these factors will allow local variations in the atomic packing density, the possibility for relaxations into alternative phases and an overall stress gradient relative to the interior of unimplanted material.

Depending on the intensity of the stress gradient, implant temperature and subsequent annealing treatments, there is scope for further relaxation and inter-diffusion between ions in the implant and/or into the substrate regions. All such changes are familiar, but are either discussed as of minor importance, or considered as being limited to depths of, at most, a few microns beyond the implant zone. Hence damage, amorphisation or crystalline phase changes, of either the host or nanoparticle inclusions, are still considered as being relevant to a depth defined approximately by the primary ion range.

With insulating materials there are further possible factors as ionisation can cause changes in valence and bond linkages [START_REF] Hayes | Defects and defect processes in non-metallic solids[END_REF][START_REF] Agullo-Lopez | Point defects in Materials[END_REF][START_REF] Kelly | Crystallography and crystal defects[END_REF]. Similarly, secondary electron ejection will cause locally intense electric fields across the insulating implanted layer.

Each of these features will be sensitive to the original stoichiometry and initial degree of perfection in the host material. Potentially, the interface between the implanted and substrate regions can act as a nucleation plane from which relaxations and crystalline transformations can be initiated. Indeed, in annealing of amorphised silicon, the wavefront of crystalline regrowth moves rapidly from the interface through the amorphous implant. However, in many materials there is the potential for such seeding of relaxations and phase change to run from the implant zone into the bulk substrate. Obvious candidate materials for such long range lattice relaxations are crystals which intrinsically have a variety of metastable phases and/or are structurally sensitive to variations in stoichiometry, impurities or intrinsic defects. One assumes that bulk changes are most likely to be initially triggered in the highly stressed zone immediately adjacent to the implant region, and then this modified front propagates throughout the crystal. Equally, there may be relaxations driven by electric fields which develop during implantation of insulators.

There are many materials that match these criteria for potential instability. For example in electro-optics and photonics a key material is lithium niobate [START_REF]Properties of lithium niobate[END_REF]. It is of value precisely because the lattice is not totally stable, but can be easily deformed by pressure or electric fields. Consequently, it is extremely sensitive in terms of electro optic properties both as the result of dopants, and because it does not grow as a perfect stoichiometric material. Because of the commercial importance of LiNbO 3 there has been nearly 50 years of intense effort associated with the crystal growth. Nevertheless, even "stoichiometric" LiNbO 3 still has lithium deficiency and a significant vacancy concentration, and the proton exchanged variants have a plethora of phase modifications as a function of temperature and hydrogen doping level.

Lithium niobate is of further relevance here as one can reverse the direction of poling (i.e. the sequence of the ABCABC… structure formed by the Li, Nb and structural vacancy) either by heating and applying an electric field across the crystal, For materials which have had less commercial investment in crystal growth, such as strontium titanate, silicon carbide, bismuth germanate or zinc oxide there are many conflicting reports of property differences, and even the presence of different crystal phases, which are all sensitive to supplier, impurities and growth conditions. Similar variations and sensitivity to the production are seen in coating layers that are deposited on a substrate (as used for optical applications). This process inevitably means they are non-stoichiometric, stressed, and with a high defect density. Further, thin film coatings are invariably structurally distorted at the interface with the substrate. Ion implantation into all such insulating materials could initiate structural relaxations. The implication is that, rather than being a rare event, the possibility of bulk relaxations induced by surface implants could be quite widespread. The dearth of relevant literature may be an indication of failure to seek such events, rather than a lack of examples.

Techniques to discriminate between surface and bulk property changes

For insulating materials extremely sensitive measurement techniques include luminescence and Raman studies since they respond to changes in lattice parameters and local defect environments. In order to record changes within an implanted surface region the luminescence excitation can be depth limited to separate the modified and bulk regions. Photoluminescence (PL) may be excited with band gap light so that the signals are generated in a near surface layer. Similarly, by varying the electron energy, there is some control over the probe depth of cathodoluminescence (CL). Neither method is a perfect match to the ion implanted volume since both absorption of band gap photons, and electron energy deposition, are strongly depth dependent. Further, depending on ionisation, charge and exciton diffusion, the luminescence can originate at some distance way from the excitation site (typically much less than a micron).

Even with such caveats it is simple to record spectral and lifetime changes of the luminescence within ion implanted surfaces of insulators. Data are then interpreted in terms of new localised defect sites, changes in lattice parameters, precipitates and inclusions.

To monitor the luminescence properties of the substrate, without contributions from the implant zone, is more difficult. In principle one may record PL and CL from the non-implanted surface of the crystal. Alternatively it is possible to record bulk luminescence signals during, or after, excitation with X-rays (RL -radioluminescence or X-ray induced thermoluminescence, (TL)). This is the approach used in the present work for very low penetration of surface implants (a few hundred nanometres) relative to the bulk material (millimetres). Since the implants only directly damage around ~0.01% of the material one assumes that the RL responses are still totally dominated by the bulk signals. Therefore if one records any significant changes in signal then these are related to bulk modifications caused by surface implants. range of insulating materials as part of a Sussex based programme to optically detect relaxations and phase changes. Of particular relevance is that data with SrTiO 3 clearly evidenced that surface implants could induce crystalline phase transitions throughout the bulk substrate [START_REF] Yang | [END_REF][12][13].

Experimental details

Nominally pure ZnO crystals were obtained from the Shanghai Institute of Optics and Fine Mechanic in China and the Juelich laboratory in Germany. Spectrally resolved thermoluminescence (TL) data were collected with a sensitive thermoluminescence system over the temperature range from 25 to 280 K. The details of this TL spectrometer have been reported before [14]. The signals are corrected for the wavelength dependent sensitivity of the detection system. One key feature of the data collection is that the spectra are taken with a wavelength multiplexed system, which cleanly identifies if different emission bands occur at different temperatures. A 6K/min heating rate was selected to minimize temperature gradients across the samples. Excitation for the TL was with X-rays and all samples were irradiated at 25 K and the radiation dose was 5 Gy.

Samples were ion beam implanted with either Cu or Tb ions using a high ion beam current implanter in Juelich in Germany. The samples were implanted with 400kev ion energy with different doses (from 1.0x10 16 to 2.5x10 16 ions/cm 2 for Cu ions, and from 2x10 16 to 2x10 17 ions/cm 2 for Tb ions). One Cu sample implanted, with a dose of 1×10 16 ions/cm 2 , and a Tb sample with a dose of 2×10 17 ions/cm 2 were Deleted: 3-5 Deleted: 19 As mentioned, to minimise distortion of the bulk TL signals in implanted samples the implanted face was on the heater block. This avoids absorption of light from the bulk of the crystal within the implant layer. This geometry implies that luminescence signals from the bulk material resulting from the X-ray irradiation should be observable under all circumstances.

The initial assumption would normally be that the bulk TL signal is unaffected by the surface implant and so this will be a constant signal in all samples (both original and implanted). New TL signals may well be generated by the ion implants and reconstruction of the implant ZnO layer and these will exist as additional features.

Experimentally they may be difficult to detect relative to the bulk TL signals since the implant represents merely ~10 -4 of the volume of the total sample, particularly as for our samples there were relatively clear signals from the bulk region.

Results and comments

Initial material

The initial TL measurements contrasted the differences and similarities of samples from the Chinese and German suppliers. An overall isometric view of the TL in terms of spectra and intensity during the TL heating are shown in figure 1. Figure 1a shows isometric data for a German ZnO sample. The contour map, These results indicate that, although there are minor differences in the emission spectra and TL from material between the two sources, the overall response pattern is similar in both cases. This suggests that the signals originate primarily from intrinsic type luminescence sites of the ZnO. nm have been replaced with a feature at slightly longer wavelengths of ~730nm. On more careful inspection one notes that for the higher temperature peaks the orange and red features occur at different temperatures, with the 550 nm emission preceding the 730 nm glow peak by ~15 degrees.

Effects of ion implantation

Post implant annealing One sample, which had received a smaller ion dose of 1×10 16 ions/cm 2 of copper was annealed at 1,000 o C to test if the changes in TL response were sustained after annealing. The isometric data are shown in figure 6 and spectrally resolved TL plots are presented in figure 7a and 7b are for orange and red emission.

Signals for the original unimplanted ZnO are included for comparison.

Whilst there are now signals at the lower temperatures after the annealing treatment, the form of the glow curves and the position of the emission bands are significantly different from the original data. Annealing has added new complexity to the signals, rather than just regenerating the pre-implant data. Annealing has however retained a strong red emission peak, even though it has moved in TL temperature.

Discussion

The showing different TL response to the X-ray excitation.

Whilst these data satisfy our original objective of demonstrating very long range effects in an insulator as the result of surface implants, the results do not reveal the mechanism for the change, nor the precise changes which have occurred. The discussion of the mechanisms and modifications which occur must therefore be very speculative. Nevertheless, the detection of such changes has significant implications for consideration of ion implantation in many types of material. This is not the first demonstration of such effects as we have conducted quite detailed studies of luminescence signals from strontium titanate [START_REF]Properties of lithium niobate[END_REF][START_REF] Yang | [END_REF][12][13]. The SrTiO 3 case was perhaps less surprising as it is known to be structurally very sensitive to impurities and growth conditions, and the relevant literature has many anomalies and conflicts as to how many low temperature phase transition, or relaxations, can occur.

Therefore the interpretation for SrTiO 3 was that stress generated from the implant layer was sufficient to induce phase changes. Further, there were discontinuities in the temperature dependence of the luminescence signals, which are characteristic For ZnO it is less obvious if there have been any phase changes as there are no discontinuities in the luminescence signals with temperature. This does not exclude the possibility that the lattice parameter has not been modified, or that stress or electric field derived from the implant zone have not introduced asymmetry into the lattice structure. Volume and distortion changes in the lattice will of course modify the intrinsic (and impurity) luminescence sites and will shift the glow peak temperatures.

Such TL peak shifts as a function of lattice distortion have already been reported in several other insulating materials.

ZnO was chosen for this experiment as it is unlikely to be fully stoichiometric [15] and it is known from the higher temperature studies that it can relax under high pressure and even undergo phase transitions, deform readily and is sensitive to impurities [16][17][START_REF] Chen | Formatted: Font: 12 pt Formatted: Font: 12 pt Formatted: Font: 12 pt Formatted: Font: 12 pt Deleted: Deleted[END_REF]. The normal material is a hexagonal (wurtzite) structure but cubic variants have been formed. For non-stoichiometric or impure material, lattice perfection is suspect. Interestingly, it has been claimed that ZnO can form the richest family of nanostructures [START_REF] Zhong Lin | [END_REF]. The excellent non-linear and piezo-or electro-optic properties also imply structure with the potential to readily distort. Similarly the measurement of photoluminescence or cathodoluminescence has generated a literature where the emission spectra are extremely varied both in terms of peak position, substructure, and different relative intensities of the nominal green and red emission bands. Variations are invariably a key indicator that the materials are non-

Deleted: 18

Deleted: 20-22 Deleted: 9

Deleted: Such In terms of luminescence efficiency and the types of defect which contribute to the TL signals it is essential to note that the older models of highly localized defects are inappropriate (e.g. as reviewed in [20]). Instead one must recognize that luminescence efficiency is strongly influenced by many neighbouring shells of lattice ions. The more sensitive experiments and calculations suggest that "point" defects can influence many thousands of neighbouring ion sites. Thus distortions of the local symmetry, for example by a uniaxial stress induced from the implant surface, relaxations of the basic lattice spacing, or even, in an extreme case conversion to a new crystalline phase, would all change the emission site properties. This would be reflected by changes in emission spectra and shifts in the glow peak temperatures, as seen here for ZnO. The parallel experiments with SrTiO 3 identified that, at least in that lattice, the ion implantation stress can induce phase transitions. Equally clear is that in many materials long range effects exist from phase changes of nanoparticle inclusions. In each situation there are changes in luminescence efficiency and emission spectra. The use of luminescence to detect such phase transitions and relaxations has recently been reviewed [21,22].

The temperatures at which glow peaks occur are similar to the critical temperatures at which ESR defects anneal or convert into different species. In particular the lowest temperature signals match to charge release of holes as have been reported, and the V O + decays into a V O with an activation energy of ~0.3eV, [27,28] corresponding to TL activation energy of the 150K type features.

In terms of spectra the emission bands noted during the TL measurements are broadly consistent with luminescence bands discussed elsewhere for ZnO and which are generally ascribed to intrinsic defects. Nevertheless the literature, although extensive (e.g. [15,[START_REF] Zhong Lin | [END_REF][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]) is not totally satisfactory, as a large fraction of the studies which mention luminescence relate to thin film or particulate size ZnO, or material which is doped. The films and small particle work is thus biased by problems of non-stoichiometry and the importance of surfaces and grain boundaries. Both green and yellow emission bands are cited with varying models based on intrinsic, or intrinsic plus impurity, sites. The features seen here near 590 nm might fit to the "yellow" emission bands but there are obviously a number of component features.

There have been studies of copper doping in ZnO [29] which activates green emission near 510 nm. For our copper implanted samples recorded there is no obvious enhancement of emission in that range. Indeed since the copper would be confined to the tiny implant surface zone any such X-ray stimulated TL signals would be very small compared with those from the bulk material. One also notes that the spectra from Cu and Tb implants were very similar, so it is lattice damage that is important for this data. Indications of bulk property changes from surface ion implantation Y Wang (1) , B Yang (2) , N Can (3) and P D Townsend

  irradiation (which generates a space charge field).

  Experimentally the luminescence signals are viewed from the non-implanted face to avoid any optical absorption within the implant layer.Detection of such bulk changes from surface implants has been addressed for a

  air at 1,000 o C for one hour. The post implant annealing was primarily intended to remove intrinsic implantation damage. However, within the implant layer such anneals are complicated as copper migration may well occur and, depending on the rate of cooling, copper nanoparticles may form within the layer.

  figure 1b, emphasises that the emission bands differ between the two temperature

Figure 4

 4 offers examples of TL performance from ion implanted ZnO. Figure4ais a TL plot of a sample implanted with Cu to a dose of 2.5x 10 16 ions/cm 2 and figure4bshows the effect from using a dose of 2.0 x 10 16 ions/cm 2 of Tb ions. Visually the two images are very similar but the more detailed TL plots for the two main emission band regions show some slight differences in terms of the relative heights of the bands. Figure5ais for the Cu data and figure5bis for the Tb implant. Despite small differences between Cu and Tb samples it is clear that neither that taken for unimplanted samples (as in figure1a). In particular the low temperature signals have been completely suppressed, and the red signals seen near 140K have become very intense. The original red bands near 700

  transitions, and indeed they occurred at temperatures which matched critical points discussed in the strontium titanate literature.

  or contain a variety of defect clusters and/or impurities. Such situations therefore have the potential for the crystal to distort and relax into alternative stable zones under stress or electric fields.

Formatted

  [23][24][25][26][27]. Signals in the region of 150 K have been linked to annealing of oxygen vacancy (V O ) centres. All three charge states of V O ,

Figure 1

 1 Figure 1 Low temperature thermoluminescence from ZnO after X-ray irradiation at 25 K for a heating rate of 6 K/minute. (a) an isometric view and (b) a contour map which emphasizes that different spectral regions peak in intensity at different temperatures.

Figure 2

 2 Figure 2 Comparisons of 40 K TL emission spectra from samples from different suppliers.

Figure 3

 3 Figure 3 Wavelength resolved ZnO TL curves for the orange and red emission regions. (3a) is for a Chinese sample and (3b) for one from Germany.

Figure 4

 4 Figure 4 The isometric view of the TL emission after the surface had been implanted with high doses of (a) Cu and (b) Tb ions.

Figure 5

 5 Figure 5 Examples of wavelength resolved TL for implanted samples, (a) after Cu implantation and (b) after Tb implants.

Figure 6

 6 Figure6The glow curve of a copper implanted annealed ZnO sample.

Figure 7

 7 Figure 7 Spectrally resolved TL for (a) orange and (b) red emission of ZnO for three stages of treatment. The plots include TL of an original crystal, data for a Cu implanted sample, and the TL patterns seen after a Cu implanted sample had been annealed.

  Figures

  objective of this experiment was to consider if high dose surface implants, luminescence signals of ZnO crystals. The advantages of the x-ray excited low temperature TL is that the measurement does not introduce any thermal heating after the implantation and, since the implant volume is only ~10 -4 of the sample volume, the bulk signals should be retained. New TL features from within the implant volume may exist, but such signals may be overshadowed by the bulk signals. The reality is that the surface implants have totally modified the bulk signals, as is seen by comparing figures 1 and 4. This is extremely clear evidence that the bulk ZnO is

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	11

  The experimental data strongly indicate that ion implantation with Cu or Tb into ZnO can result in changes in the luminescence responses of the bulk material.Mechanisms for the bulk changes are speculatively linked to stress or electric fields generated by the surface implants which modify the bulk structure. This is not the first example of such an effect and it may be indicative that many other non-stoichiometric or metastable crystalline structures undergo similar long range relaxations and/or phase changes as the result of surface treatments. The dearth of a relevant literature probably reflects a lack of investigations, rather than a rarity of such effects. Whilst luminescence measurements do not offer models of the defect sites they do at least reveal a number of participating defects and also clearly demonstrate the more subtle changes from the original lattice.

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