Phys. Status Solidi B 247, Nos. 11–12, 3006–3009 (2010) / DOI 10.1002/pssb.201000622 p s sb

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basic solid state physics

Temperature dependent band gap

behavior and excitons in metallic carbon nanotubes

Patrick May*, Hagen Telg, Christian Thomsen, and Janina Maultzsch

Institut fur Festkorperphysik, Technische Universitat Berlin, Hardenbergstraße 36, 10623 Berlin, Germany

Received 4 July 2010, revised 30 July 2010, accepted 5 August 2010

Published online 8 October 2010

Keywords metallic carbon nanotubes, excitons

* Corresponding author: e-mail pmay@physik.tu-berlin.de

Resonant Raman spectroscopy is used to investigate the

temperature dependence of the optical transitions of metallic

and semiconducting nanotubes. While the semiconducting

nanotubes show an approximately linear temperature depend-

ence as known for bulk semiconductors, the metallic nanotubes

show a different temperature dependent behavior with a non-

monotonic dependence of the transition energy on the temper-

ature. This result can be attributed to dissociation of bound

electron–hole pairs (excitons), leading to a quasi band-to-band

transition.

First optical transitionEM11 of metallic nanotubes and sketch of a

metallic (13,1) tube.

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1 Introduction The temperature dependence of theband gap EgðTÞ has been investigated for years in classicalbulk semiconductors. It is one of the characteristic features ofsemiconductors [1]. EgðTÞ dependences show a lineardecrease at sufficiently high temperatures, whereas it isnonlinear at temperatures near 0 K [2]. Carbon nanotubes canbe either metallic or semiconducting [3]. These 1-D systemstherefore belong to a new class of semiconductors showing amore complex behavior owing to their chirality and diameterdependence [4]. The behavior of the temperature depen-dence of the electronic band is important for a variety ofapplications such as field electron transistors or opticalemission devices [5]. Assignments of the nanotube chiralindex (n,m) are often done by a comparison of experimentaldetermined transition energies with theoretical predictions,which calculate the optical band-gap at zero temperature.One technique to obtain the optical transition energy (Eii) isresonant Raman spectroscopy, due to a resonant enhance-ment of the transition. The optical transitions are dominated

by excitons with large binding energies of several hundredmeV for semiconducting tubes [6–8]. Even in metallicnanotubes excitons exist, because the screening of electronsis less effective in comparison to bulk metals. There has beentheoretical studies predicting binding energies in the range of50 to 100 meV for metallic tubes depending on the diameter[9–12]. Experimental evidence of excitons in metallic tubeswas first shown by Wang et al. [13] by performing absorptionspectroscopy on individual metallic tubes. While absorptionspectroscopy is considerably difficult to measure onindividual tubes, resonant Raman spectroscopy can beapplied to ensembles with many different chiral indices toobtain information on specific chiral indices (n,m).

In this work we present a temperature dependentresonant Raman study for both semiconducting and metallicnanotubes. We show the optical transition energy as afunction of the temperature for one selected tube of each typeand present a comparison of these results with theoreticalpredictions of the band gap. Furthermore we derive a lower

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IðE

Phys. Status Solidi B 247, Nos. 11–12 (2010) 3007

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limit of the exciton binding energy of the metallic (13,1)tube.

2 Experimental The sample was fabricated by chemi-cal vapor deposition (CVD). This method leads to a forest-like structure of metallic and semiconducting nanotubes withdifferent chiral indices in a diameter range between 0:5 and2:0 nm. The Raman measurements of the radial breathingmode (RBM) were performed at different temperaturesvarying from 300 K up to 870 K in a commerciallyobtainable heating stage in Argon gas environment. Dyelasers were used as excitation source in the range of 1:8 to2:25 eV to access the first transition of the metallic (EM

11) andthe second transition of the semiconducting (EM

22Þ branch.The laser power was kept below 500 W to avoid laserinduced heating of the sample [14]. The Raman signal wasdetected in backscattering geometry using a Dilor-XY triplemonochromator system attached with a nitrogen-cooledCCD to acquire the Raman spectra. Furthermore eachRaman spectrum was calibrated with respect to the spectrallines of Ne. The intensity was normalized in considerationof the non-resonant response of CaF2 which is around321 cm�1 [15].

3 Results and discussion Figure 1 displays thenormalized intensity of the resonant RBM response as aninterpolated contour plot for seven different wavelengths andthree temperatures. There is no observable shift in the Ramanfrequency within the accuracy of the experiment. However,there is downshift of the RBMs around 210 cm�1 inexcitation energy till 570 K followed by a slightly upshiftat 770 K. The area around 250 cm�1 shows a shift throughoutthe entire temperature region. Following the proceduredescribed in Ref. [16] the area around 210 cm�1 can beassigned to metallic, while the area around 250 cm�1 can beassigned to semiconducting nanotubes. In the further

Figure 1 (online color at: www.pss-b.com) Contour plot of the RBtemperatures. The intensities in each plot are normalized to the strongesof the strongest peak in each region. The region of the left bar is assignedto the semiconducting nanotubes. The contour plots were obtained bybetween 2:01 and 2:16 eV.

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analysis we picked the strongest RBM response of eacharea. The metallic can be assigned to the (13,1) tube and thesemiconducting to the (11,1) tube. The optical transitionenergies Eii are then derived by fitting the resonance profileswith [17]

Mst peato than i

lÞ ¼ Mc

�hvRBM

� �2

� 1

ðEl�Eii�iG=2Þ�1

ðEl��hvRBM�Eii�iG=2Þ

��������2

;

where M contains all matrix elements and c summarizes allremaining factors. El corresponds to the laser energy, whileEii is the energy of the i-th allowed optical transition. G is thelifetime-broadening of the intermediate electronic states.

The resulting dependence ofEiiðTÞ is displayed in Fig. 2.The semiconducting (11,1) tube shows an approximatelylinear behavior as predicted by theory for the band gapdependence. A linear fit of the temperature behavior of thesemiconducting (11,1) tube results in a shift of approxi-mately �6:4� 10�5 eV K�1. This is in very good agreementwith theoretical predictions for the band gap of Capaz et al.[4]. The temperature dependence of the band gap can beexplained by the fact that the increase of temperature leads toan enhanced number of atomic vibrations, larger interatomicdistances and therefore to a dilatation of the lattice [2, 18].The behavior of the metallic (13,1) tube is different from thesemiconducting tube: first, the optical transition energy (Eii)decreases similar to the semiconducting tube, but from acertain temperature, Eii tends to increase (blueshift). Afterthis increase, the EiiðTÞ dependence decreases again.The linear shift of the metallic tube with a value of �9:4�10�5 eV K�1 is within the range of experimental results ofEii

and theoretical predictions of the band gap Eg [19]. Theupshift of the metallic tube can be explained in terms of

(RBMs) as a function of excitation energy for three differentk. The black bars indicate the maximum of the excitation energye metallic nanotubes, while the region of the right bar is assignednterpolation of seven different excitation energies in the range

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3008 P. May et al.: Excitons in carbon nanotubesp

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Figure 2 (online color at: www.pss-b.com) Temperature depend-ence of the optical transition (dEii=dT) for both the semiconductingð11; 1Þ (black squares) and the metallic ð13; 1Þ tube (red dots). Thesolid lines are linear fits to the data; the dashed line is a guide tothe eye.

excitons dissociated into free electron–hole pairs at tem-peratures related to the corresponding binding energy. Hencewe obtain a binding energy of around 50 meV. Figure 3shows a sketch of the Raman process, which comparesexcitonic transitions (�300 K) with quasi band-to-bandtransitions (�600 K). At room temperature, the incominglight excites a bound electron–hole pair (exciton). At hightemperatures the excitons are dissociated into free electron–hole pairs. This leads to a larger optical transition energy.After the dissociation the optical transition energy decreases

|0>T~ 300K |0>T~ 600K

Egap

Eexc

Figure 3 (online color at: www.pss-b.com) Sketch of the Ramanprocess for excitonic (300 K) and quasi band-to-band transitions athigher temperatures (� 600 K).

� 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

again. The decrease tends to have a shift rate similar to thedecrease before the dissociation. This can be explained asfollows: at room temperature optical transition in carbonnanotubes differ from the single particle energies due to bandgap renormalization [20] and excitonic effects [7, 6, 13].However, the band gap renormalization and excitonic effectsrather depend on the dielectric environment than tempera-ture [19, 21]. Therefore single particle energies are thedetermining factor in the behavior of EiiðTÞ. Thus we candirectly compare the temperature dependent shift ofDEiiðTÞ/DT and DEgðTÞ/DT . All things considered thesmall shifts of EiiðTÞ do not strongly affect assignments ofnanotubes to specific ðn;mÞ.

4 Conclusions We used resonant Raman spec-troscopy to determine the dependence of the measured Eii

in comparison to theoretical Eg calculations of a semicon-ducting and a metallic nanotube as a function of temperature.Our results show the importance of excitonic effects inoptical transitions of metallic single-walled carbon nano-tubes. When investigating optical transition at higher thanroom temperature, which are related to the exciton bindingenergy, the optical response of free electron–hole pairsshould be taken into account, i.e. band-to-band transitions.Furthermore we were also able to determine a minimummeasure of the exciton binding energy of the metallic (13,1)tube, which is around 50 meV.

Acknowledgements We acknowledge support from theDFG under grant no. MA 4079/3-1. HT acknowledges fundingfrom the European union (Technotubes; CP-IP 228579-1). J. M. andC. T. acknowledge support from the Cluster of Excellence UnifyingConcepts in Catalysis coordinated by the Technische UniversitatBerlin and funded by the Deutsche Forschungsgemeinschaft.

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