Photoluminescence of Single-Walled Carbon Nanotubes:
The Role of Stokes Shift and Impurity Levels
Jinglin Mu,1Yuchen Ma,1,*Huabing Yin,1Chengbu Liu,1,†and Michael Rohlfing2
1School of Chemistry and Chemical Engineering,Shandong University,Jinan250100,People’s Republic of China 2Institut fu¨r Festko¨rpertheorie,Universita¨t Mu¨nster,48149Mu¨nster,Germany (Received9March2013;revid manuscript received28July2013;published25September2013)
Recent experiments have indicated that dopants and defects can trigger new redshifted photolumines-cence(PL)peaks below the E11peak in single-walled carbon nanotubes(SWCNTs).To understand the origin of the new PL peaks,we study theoretically the excited-state properties of SWCNTs with some typical dopants and defects by ab initio many-body perturbation theory.Our calculations demonstrate that the Stokes shift in doped centers can be as large as170meV,which is much larger than that of intact SWCNTs and must be taken into account.Wefind dipole-allowed transitions from localized midgap and shallow impurity levels,which can give ri to pronounced PL peaks.Dark excitons,on the other hand, em to have oscillator strengths that are too small to account for the new PL peaks.
DOI:10.1103/PhysRevLett.111.137401PACS numbers:78.67.Ch,71.55.Ài,78.20.Bh
Single-walled carbon nanotubes(SWCNTs)exhibit remarkable optical properties and have promising applica-tions in optoelectronics,biological imaging and nsing. Such applications require a high photoluminescence(PL) quantum yield at certain wavelengths.A perfect SWCNT has a prominent PL peak given by the E11exciton. However,PL spectra of pristine SWCNTs often also have weak emission sidebands below E11,which have been attributed to localized exciton states[1–5].
The physical mechanism of such localized excitons is still under debate.One common interpretation would be that they originate from the brightening(or activation)of intrinsic dark states[4–7],i.e.,of excitons that should be dipole forbidden due to lection rules within a perfect SWCNT.For example,adsorbed hydrogen was thought to brighten the dark triplet excitons and thus reduce the PL quantum yield at E11[7].This assignment had been bad on the comparison between the measured energies of the peaks and the calculated energies of dark excitons in some perfect SWCNTs viafirst-principles methods[8]. However,this kind of assignment is debatable with respect to two important issues:(i)until now there has been no evidence that the oscillator strengths of the activated dark excitons are high enough to dominate the new PL peaks, and(ii)the Stokes shifts of the new PL peaks are much larger than tho obrved in perfect SWCNTs($4meV) [9].Here we define the Stok
es shift of an optical transition as the energy difference between absorption and emission.
A completely different interpretation of the localized-exciton sidebands considers localized midgap and shallow states from chemical modifications[1,10]or from defects [2].In oxygen-doped SWCNTs,for example,the PL at E11 can been quenched and a strong near-infrared peak domi-nates the emission spectrum[10].There have been some attempts to investigate the influence of dopants and defects.Bad on quantum chemical calculations by a miempirical method,Ghost et al.attributed the new redshifted emission peaks in O-doped SWCNTs to a split-ting of previously degenerate bands[10],but this cannot explain their experimental obrvation that no photoab-sorption takes place at the emission energy.
In order to resolve the above-mentioned issues and con-troversies,we investigate in this Letter the absorption and luminescence of SWCNTs with dopants and defects within ab initio electronic-structure theory.We consider doping with oxygen and hydrogen,as well as single vacancy and Stone-Wales defects that are typical for SWCNTs.We show that in all cas the locally disturbed symmetry of the SWCNT leads to dipole-allowed excitons that are derived from either the E11state of the pristine SWCNT or from localized impurity states.Furthermore,the reduced sym-metry caus strong Stokes shifts that are1order of magni-tude larger than in pristine SWCNTs.Ourfindings suppor
t the interpretation that the sidebands obrved experimen-tally result from such local states.The contributions from dark excitons to the PL,on the other hand,are small.
For the determination of the optical spectra we employ state-of-the-art many-body perturbation theory,in particu-lar the GW method and the Bethe-Salpeter equation (GWþBSE)[11–13].The GWþBSE method has become a standard approach to the optical spectra of materials of different dimensions,including SWCNTs [8,14,15].Different from most GWþBSE studies,which mostly focus on the spectrum of the ground-state geometry, we also consider the change of the geometric structure when an exciton is formed.Here we evaluate the equilib-rium structures of the optically excited states by con-strained density functional theory(CDFT),finally allowing for the determination of the Stokes shift of the exciton.The combination of CDFT and GWþBSE offers a highly reliable approach for predicting emission energies [16,17]from the equilibrium geometry of the excited state.
All DFT and CDFT calculations are carried out with the SIESTA code[18]within the Perdew-Burke-Ernzerhof generalized-gradient approximation.Bad on this,the GWþBSE calculations are done with a Gaussian-orbital bad code[12,13].All calculations are performed for a(8, 0)SWCNT with a supercell of17.1A˚length,containing four primitive unit ,128atoms).
As a starting point,Fig.1shows the band structure and optical absorption spectrum of a perfect(8,0)SWCNT. Two pronounced peaks(E11and E22)are found at1.53and 1.79eV excitation energies,which are in good agreement with previous GWþBSE results[15]and experiments (1.60and1.88eV for E11and E22,respectively)[9].The exciton binding energies are about1eV,1order of magni-tude larger than tho in bulk miconductors with similar band gaps.This strong excitonic effect aris from the one-dimensional nature of the(8,0)SWCNT[15].We focus on the E11state for the rest of the Letter.We optimize the excited-state geometry of E11within CDFT andfind a Stokes shift of about20meV,which agrees with experi-ments[9,19].The E11exciton is compod from band-to-band transitions between the HOMO band and the LUMOþ3band[as indicated in Fig.1(a)].Since both bands are double degenerate(as a result of the rotational symmetry of the tube),four singlet excitons are formed between ,the dipole-allowed E11state and three dark states:two degenerate states(C)and one single state (D)at excitation energies of 1.56eV and 1.50eV, respectively[indicated as open triangle and open circle in Fig.2(b)].
The electronic structure changes dramatically when ada-toms are involved.For example,an oxygen atom breaks a C-C bond of the SWCNT and forms a C-O-C link as shown in Fig.2(a)[10].The oxygen atom splits the HOMO and LUMOþ3bands into nondegenerate bands(HÀ=Hþand L3À=L3þ,r
espectively),as shown in the band structure [Fig.2(a)].Note that the oxygen atom does not cau any extra impurity energy levels.Orbital analysis of the states demonstrates that the2p orbitals of the oxygen atom mix with the orbitals of the SWCNT.Becau of the oxygen atom,the four original HOMO!LUMOþ3excitons of the pristine tube change drastically.Instead of only one dipole-allowed state(E11),two dipole-allowed states(A1 and A2)are found at1.45eVand1.62eVexcitation energy. The states are mostly formed from band-to-band transi-tions between Hþand L3À(A1)and HÀand L3þ(A2), respectively,both of which are dipole-allowed.In addition, the transitions Hþ!L3þand HÀ!L3À,respectively, cau two additional dipole-forbidden excitons(C1and C2).In the pristine tube,the band degeneracies(E HÀ¼E Hþ,E L3À¼E L3þ)would allow the linear combination of
A1and A2into the dipole-allowed E11state and the dipole-forbidden dark state(D).We therefore conclude that oxy-gen doping changes the lection rules of the excitons, turning dipole-forbidden excitons into dipole-allowed ones,as a conquence of breaking the rotational symme-try of the tube.Note that the excitons A1and A2are still delocalized along the tube[e the spatial distribution of A1in Fig.2(d)],similar to the E11exciton[15
]
.
FIG.1.(a)GW band structure and(b)absorption spectrum for
the(8,0)SWCNT.Optically allowed transitions are indicated by
arrows in
(a).
FIG.2(color online).(a)GW band structure,(c)optical ab-
sorption and emission spectra for the O-doped(8,0)SWCNT of
the configuration shown in the int of(a).The C-O bond lengths
are1.39A˚.The distance between the two C atoms bonded to O is
2.15A˚.Optically allowed transitions are illustrated by arrows.
(b)Exciton energies for the pristine(open symbols)and O-doped
(filled symbols)(8,0)SWCNTs.E11,A1and A2are bright
excitons.C,D,C1,and C2are dark excitons.(d)Real-space
distribution of the exciton A1,where the electron(hole)is
reprented in red or medium gray(blue or dark gray).
The splitting between A1and A2(here:about170meV) should scale with the oxygen concentration,which is 1=128in our study.In the experiments of Ref.[10],the
oxygen concentration is about1=2000,so we expect a splitting of about10meV,only,which would be very difficult to identify.In fact,only a small broadening of the E11absorption peak was measured[10].
The most important effect of oxygen,besides lifting the lection rules,is an enhanced coupling between exciton and structure near the symmetry-breaking adatom. The structural relaxation in the excited state A1leads to a Stokes shift of0.15eV,with the photoemission peak [labeled AÃ1in Fig.2(c)]at1.30eV.The energy difference to the E11state of the pristine tube(which obrves a Stokes shift of0.02eV only,e above,leading to photo-emission at1.51eV)amounts to0.21eV.In fact,PL experiments show emission lines106–214meV below E11[10],in full accordance with ourfindings. Photoabsorption,on the other hand,does not occur at this new emission energy[10],supporting our obrvation of a large Stokes shift.
Structural relaxation in the state A2could result in a similar emission peak AÃ2[not shown in Fig.2(c)]. However,according to Kasha’s rule[20],excitons with higher energies will nonradiatively decay into the lowest excited state with the aid of phonons,especially for the ca here where the energies of A1and A2are so clo to
each other.Therefore the emission peak AÃ2may not appear in experiment.
Another typical doping material is hydrogen,which tends to adsorb in form of pairs on the outside of the SWCNT[21][e Fig.3(c)for the optimized structure]. Concomitantly,localized impurity states[labeled state1 and state2in Fig.3(a)]appear near the frontier orbitals. Differently from the oxygen-doped ca,state1is spatially localized[e Fig.3(b)].The optical absorption spectrum [Fig.3(c)]is characterized by two peaks,A and B.While B can again be identified as a HOMO!LUMOþ3transi-tion(similar to the E11exciton),the A state at1.27eV absorption energy originates from the transition between state1and state2.Since state1is a localized state,the A exciton is localized at the H defect site,as well,which is distinctly different from the ca of oxygen defects.Again, structural relaxation in the A exciton state leads to a strong Stokes shift of0.17eV and a photoemission peak at 1.10eV,far below the original E11absorption or emission peaks.In O-doped and H-doped SWCNTs,the exciton radii for the states A1and A are still much larger than the C-C bond length,so the exciton-lattice coupling is not too strong.The structural relaxations are not localized at the dopants,but are distributed over a large area with atom displacements of less than0.01A˚.Nonetheless,the large number of affected atoms significantly shifts the initial (final)state of the optical transition up(down)and thus reduces the energy gap between them,causing the Stokes shift.Note that the exciton binding energies are hardly affected.
In a recent experiment on H-doped(9,8)SWCNT,a PL peak appeared about50meV below the E11peak[7].A GWþBSE calculation for that system is beyond our
computational capabilities,but some comparison can be achieved from the DFT band structure of a H-doped(14,0) SWCNT[which has a diameter similar to a(9,8)tube]. From the location of the H-derived bands,state1and state2,relative to the HOMO and LUMO bands(from which the E11exciton is formed in the ca of a(14,0) SWCNT),we estimate that the A absorption peak should be0.11eV above E11.After including a Stokes shift of again0.17eV,PL from AÃshould occur0.06eV below E11 and0.04eV below the Stokes-shifted EÃ11PL peak. This would indicate that the measured PL peak originates from a defect-induced localized,Stokes-shifted spin-singlet exciton.This would be in contrast to the interpre-tation of Nagatsu et al.,who attributed their new PL peak in H-doped SWCNTs to a spin-triplet,dark exciton [7].However,Konabe and Watanabe discuss in their fol-lowing work[22]that the oscillator strength of triplet excitons would be negligible,even when the carbon-to-hydrogen ratio is100,and could not cau the strong A peak.We thus conclude that triplet excitons cannot be responsible for the new PL peak,which in fact originates from defect-associated electronic levels and a strong Stokes
shift.
FIG.3(color online).(a)GW band structure,(c)optical ab-sorption and emission spectra for the H-doped(8,0)SWCNT of the configuration shown in the int of(c).The C-H bond lengths are1.11A˚.The C-C bonds nearest to H are elongated by about 0.12A˚.Optically allowed transitions are illustrated by arrows. Impurity states are illustrated by ellips.(b)Charge distribution for the two impurity states.
Defects of the SWCNTs may also occur intrinsically,
either from preparation or from being damaged.Inten
puld excitation[6],for example,caus new PL peaks
about0.1–0.2eV below E11that were attributed to the
activation of optically dark excitons[6].However,we
believe that the oscillator strengths of such activated states
may be quite small.We argue instead that the new peaks
may equally well result from new electronic states of the
damaged SWCNTs.Two prominent intrinsic defects are
given by single vacancies(SVs)and by Stone-Wales(SW)
defects.We have investigated the optical spectra of both
defect types,both for a(8,0)SWCNT and for a(6,4)
SWCNT[as was ud in the experiments of[6],with152
atoms in a18.6A˚long unit cell].Ourfindings for the
lowest-energy dipole-allowed transitions are summarized
in Table I.
Wefind that the SV and SW defects still exhibit a mi-
conducting band structure.Some localized electron states
exist near the conduction band minimum and the valence
band maximum.In both cas,the optical spectrum starts
with spatially localized excitations below the E11transition
(e Table I),similar to the adatom-related spectra.The
Stokes shifts of the SV and SW spectra,however,are much
smaller($0:02eV,only),comparable with tho of the E11state of the pristine SWCNT.We believe that the defect-induced states may be responsible for the new PL
peaks found experimentally.This holds in particular for the
SW defect,which leads to excited states0.16eV below E11,consistent with the experimental obrvation.
In summary,we have investigated the origin of satellite
PL peaks below E11in SWCNTs induced by defects and
dopants obrved in recent experiments.We argue that the
contribution from dark excitons,which have been empha-
sized before,may be insignificant.Instead,wefind local-
ized impurity levels and corresponding optical transitions
near or below the E11excitation energy of the pristine tube,with dipole oscillator strengths that are much larger than tho of dark excitons.In the ca of vacancies,the ont of the spectrum is in the infrared.Furthermore,the strong Stokes shifts of adatom-related states lead to redshifted PL peaks that dominate the spectrum.From our results we conclude that the photoluminescence of imperfect SWCNTs would be determined by defect levels.We believe that our interpretation should also hold for other defects and for other kinds of ,TiO2or ZnO, and that defect states might be of general significance for thefields of optoelectronics,nsing,etc.
This work was supported by the National Natural Science Foundation of China(Grants No.21173130and No.91127014),the Natural Science Foundation of Shandong Province(No.BS2012CL022),and Open Fund of State Key Laboratory of Information Photonics and
Optical Communications(Beijing University of Posts and Telecommunications).Computational resources have been provided by the National Supercomputing Centers in Jinan and Tianjin(TH-1A
system).
*myc@
†cbliu@
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ð8;0Þþ2H 1.27 1.100.17 (14,0)E110.92(Exp:0.96a)ÁÁÁÁÁÁð14;0Þþ2H 1.03b0.86bÁÁÁð8;0ÞþSV0.970.950.02ð8;0ÞþSW 1.35 1.330.02 (6,4)E11 1.41(Exp:1.42a)ÁÁÁÁÁÁð6;4ÞþSV0.79ÁÁÁÁÁÁ
c)ÁÁÁ
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