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Quantitative Analysis of Optical Spectrafrom Individual Single-Wall CarbonNanotubes

Axel Hagen and Tobias Hertel*

Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft,

Faradayweg 4-6, D-14195 Berlin, Germany

Received November 28, 2002

ABSTRACT

We discuss how tight-binding band-structure calculations with a chirality- and diameter-dependent nearest-neighbor hopping integral may be

used to relate well resolved features in the UV-VIS-NIR spectra of individual single-wall carbon nanotubes (SWNTs) to electronic excitations

in specific tube types. The assignment of (n,m) indices to interband transitions in specific tube types can support a quantitative analysis ofabsorption spectra which may eventually be used for rapid screening and optimization of sample composition during SWNT synthesis.

Since the discovery of single-wall carbon nanotubes (SWNTs)in 1993,1 their unique structure and properties have sparkedthe interest and imagination of researchers worldwide. Theatomic lattice of SWNTs is frequently visualized by rollingup a narrow slice from a 2-dimensional graphene sheet to aseamless cylinder of typically about one nm in diameter.2

Their structure is then uniquely defined by the so called chiralvector Ch ) na1 + ma2, which connects crystalographicallyequivalent points of the graphene lattice that are folded back

onto one another in the wrapping process. Here, a1 and a2are the graphene lattice unit vectors and n and m are integers.One of the most striking features of SWNTs is that theirelectronic properties depend crucially on their structure andthus on (n,m) indices, where tubes with (n - m) ) 0, 3, 6,9,... are predicted to be metallic while the remainder areexpected to be semiconducting. However, both types of tubesare generally found in synthesized SWNT material and,consequently, research efforts have been directed towardbetter control over the SWNTs structural properties. Suchoptimization requires efficient and reliable screening toolsfor quantitative determination of the sample composition.

Here we discuss how absorption spectroscopy from theultraviolet to the near infrared region (UV-VIS-NIR) can beused to obtain quantitative information on the compositionof SWNT ensembles. We show that highly resolved spectralfeatures in mixed samples of individual SWNTs can beassigned to transitions in specific tube types.

UV-VIS-NIR spectra were obtained from tubes synthe-sized by the high pressure CO decomposition technique(HiPCO-material).3,4 For illustrative purposes we here also

report on spectra previously recorded for material obtainedby the pulsed laser vaporization technique (PLV-material).5

Purified PLV material has been purchased by tubes@rice,and HiPCO material is available from CNI Houston. Bothsynthesis techniques yield SWNTs that are agglomerated inquasi-crystalline SWNT ropes of a few to tens of nanometersin diameter. Individual tubes of the PLV and HiPCO materialsupposedly have a mean diameter of 1.2 nm and 0.8-1.0nm, respectively.3,5-7 Individual SWNTs were isolated from

HiPCO raw material in micelles by the technique describedin ref 8. At wavelengths below 1350 nm, the well-resolvedspectrum from micelles in H2O was extended by results frommeasurements in D2O.

The optical density of a PLV film, sprayed on a quartzsubstrate, is shown together with the spectrum of colloidalgraphite in aqueous solution in Figure 1a. Three broadfeatures labeled A, B, and C in the absorption spectrum canbe discriminated from the continuously rising backgroundof the PLV spectrum. These features can be attributed tosymmetric interband transitions between the first and secondsubbands of the semiconducting (A and B) and the second

subband of the metallic species in these samples (C), asindicated in Figure 1b. Background corrected spectra allowto distinguish some fine structure in the form of small andreproducibly measurable wiggles. These wiggles can tenta-tively be attributed to transitions between subbands ofdifferent tube types. Each one of the A, B, and C featuresthus likely consists of several such transitions and will bereferred to as A-, B-, and C-absorption cluster. Previousattempts to obtain quantitative information from these spectrawere mostly aimed at a determination of the mean SWNT* Corresponding author. E-mail: hertel@fhi-berlin.mpg.de.

NANO

LETTERS

2003Vol. 3, No. 3

383-388

10.1021/nl020237o CCC: $25.00 2003 American Chemical SocietyPublished on Web 01/29/2003

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diameter or tried to detect a propensity of tube concentrationstowards either armchair (m ) n) or zigzag (m ) 0) tubetypes.9-12

Spectra from HiPCO material, shown in Figure 1c, exhibitmore structure due to the smaller average tube diameter ofabout 1.0 nm and may thus convey a higher degree of

structural information. In particular, the spectra from indi-vidual, micelle-encased SWNTs exhibit an extraordinary richfine structure. The small width common to all features atenergies below 1.4 eV of25 meV suggests that these aredue to excitation across the first band gap of semiconductingtubes. Interestingly, these spectra closely resemble those fromthe raw HiPCO material if broadened by about 80 meVand shifted by 50 meV to smaller energies (see dashed curvein Figure 1c). Note that this shift is nearly constant up to2.0 eV, beyond which it appears to increase slightly. Theonly striking differences between the broadened micelle and

the HiPCO rope spectra are found at intermediate energiesbetween about 2.0 eV and 2.9 eV. The good overallagreement of the two spectra, however, suggests that thediameter distribution of the micelle-encased tubes is verysimilar to that of the raw HiPCO material reported, forexample, in refs 6 and 7.

The small shift observed between absorption features ofthe HiPCO rope and micelle material can arise due to anumber of factors. Screening of excited carriers or electron-

hole pairs, for example, will depend on the material sur-rounding a tube. Alternatively, one may have to considerthe hydrostatic pressure on tubes induced by interfacialenergies, which is enhanced at small tube diameters and isestimated to reach values as high as 100 MPa. The resultingstrain may change the electronic structure of individual tubes,on the average by increasing gap energies. Regardless ofthe nature of such a shift, it is important to keep in mindthat the measured gap energies may in fact be slightlydisplaced with respect to those of isolated tubes free fromperturbation by the environment.

In the following we will use the well-resolved featuresfrom individual tubes in the A-cluster range to attempt an

identification of the corresponding transitions and tube types.We begin by discussing the band-structure used for thecomputation of optical properties.

The periodic boundary conditions imposed on the nanotubewavefunctions by wrapping a graphene sheet to a seamlesscylinder lead to a set of one dimensional dispersion relationsE

((k) that are obtained from the valence- and conductionbands, Eg2D

( of two dimensional graphene in the usualmanner by zone-folding:2

with

Here, T is the length of the nanotubes unit cell, k themomentum along its axis, and the subband index. Ndenotes the number of hexagons of the graphene honeycomblattice that lie within the nanotubes unit cell. K1 and K2 areunit wave vectors pointing along the circumferential directionand along the nanotube axis, respectively.

The only adjustable parameter within the tight-binding(TB) graphene band-structure commonly used in eq 1 is thenearest-neighbor hopping integral 0. Reported values for0 range from 2.4 eV up to about 3.0 eV.13 Scanningtunneling spectroscopy on individual SWNTs yields valuesbetween 2.45 and 2.7 eV,14,15 while those from an analysisof optical experiments range from 2.65 to 3.0 eV (see, forexample, refs 11 and 12). Resonant Raman spectra aregenerally analyzed using a hopping integral around 3.0 eV.13

Unfortunately, the dependence of0 on tube diameter andchirality is frequently overlooked but will be accounted for

Figure 1. UV-VIS-NIR spectra from different SWNT sampletypes. (a) Spectrum of PLV rope material shown for comparisontogether with the spectrum of colloidal graphite (offset for clarity).(b) A, B, and C features can be attributed to symmetric transitionsbetween the lowest subbands in semiconducting (A, B) and metallic

(C) tubes. (c) Comparison of background-corrected spectra fromHiPCO rope material with that of individual tubes in micelles. Thenumerically broadened spectrum from individual tubes (dashed line)reveals a 50 meV blue shift with respect to the rope spectrum. Thediameter distribution in the lower panel is thus characteristic ofboth materials and was obtained from refs 6 (histogram) and 7 (solidline).

E((k) ) Eg2D

( (kK2

|K2|+K1) (1)

(-

T< k