Electrically driven thermal light emission from individual single-walled carbon nanotubes

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1 Eletrilly riven therml light emission from iniviul single-wlle ron nnotues DAVID MANN,Y.K.KATO, ANIKA KINKHABWALA,ERICPOP,,JIENCAO,XINRANWANG, LI ZHANG,QIANWANG,JINGGUO AND HONGJIE DAI * Deprtment of Chemistry n Lortory for Avne Mterils, Stnfor University, Stnfor, Cliforni 94, USA Intel Corportion, Snt Clr, Mission College Boulevr, Cliforni 94, USA Deprtment of Eletril n Computer Engineering, University of Flori, Ginesville, Flori 6, USA *e-mil: hi@stnfor.eu LETTERS Pulishe online: Jnury 7; oi:.8/nnno.6.69 Light emission from nnostrutures exhiits rih quntum effets n hs ro pplitions. Single-wlle ron nnotues (SWNTs) re one-imensionl metls or semionutors in whih lrge numers of eletroni sttes in nrrow energy rnges, known s vn Hove singulrities, n le to strong spetrl trnsitions,. Photoluminesene n eletroluminesene involving intern trnsitions n exitons hve een oserve in semionuting SWNTs 9, ut re not expete in metlli tues owing to non-ritive relxtions. Here, we show tht, uner low is voltges, suspene qusi-metlli SWNT (QM-SWNT) emits light owing to Joule heting, isplying strong peks in the visile n infrre, orresponing to intern trnsitions. This is result of therml light emission in one-imensionl system, in strk ontrst with fetureless lkoy-like emission oserve in lrge unles of SWNTs or multiwlle nnotues. This llows for proing of the eletroni temperture n non-equilirium hot optil phonons in Joule-hete QM-SWNTs. We investigte eletrilly riven therml light emission of iniviul QM-SWNTs in oth the visile n infrre (wvelength l ¼, nm; see experimentl etils in Supplementry Informtion), in wier spetrl winow thn previously explore for eletroluminesene of nnotues. We frite suspene n non-suspene SWNT (imeter 4 nm) evies with tue length L mm (Fig., insets), s esrie previously. QM-SWNTs were ientifie s those exhiiting wek soure rin urrent (I s ) epenene (ue to smll ngps of tens of mev (refs 4,6) on gtevoltge (V gs ) with I s (mx)/i s (min), (t is V s ¼ mv), ross the V gs rnge (Fig. ). On sustrte, QM-SWNTs show urrent sturtion ner ma t high is, ut suspene ones exhiit negtive ifferentil onutne (tht is, reue urrents t higher ises) n muh lower mximum urrent, ma (Fig. ) ue to Joule heting n eletron sttering y hot optil phonons use y slow het issiption in the suspene SWNTs. We oserve light emission from suspene QM-SWNTs (in the on stte uner high negtive V gs, with the evie kept in Ar) eginning t low V s, with pronoune peks in the spetr (Figs,, ). We mesure the visile emission hrteristis of the suspene n on-sustrte setions of severl QM-SWNTs (Fig. ) n oserve tht the onset of etetle visile light for suspene QM-SWNT evies egn s low s V s ¼.9 V (lwys in the negtive ifferentil onutne region in I s V s s in Fig. ), ut the visile emission for on-sustrte SWNTs ws not mesurle until V s. V. For severl long ( mm) suspene QM-SWNTs, we sptilly resolve light emission n foun tht the lotion of the rightest spot ws lwys ner the entre (Fig. ) n remine sttionry t vrious V s n V gs. We investigte light emission from ten suspene (ll in Ar) QM-SWNTs (Fig. ). All QM-SWNTs exhiite spetrl peks n the pek positions vrie (Fig.,). In SWNTs, eletroni trnsitions etween the vn Hove singulrities re ipole-llowe (enote s E nn trnsitions) 7. We ttriute the oserve peks to optil emission (highly polrize long the tue xis; Fig. inset) from E (infrre) n E (visile or ner infrre) trnsitions (Fig. ) of QM-SWNTs. Lorentzin fitting is use to etermine the pek lotions of E n E. We fin resonle greement with simple tight-ining preite E n E vlues 8 ( : rtio) (Fig. ) for QM-SWNTs with.8 4 nm ( ws mesure y tomi fore mirosopy over the on-sustrte portion of the nnotues). To unerstn the light emission in QM-SWNTs, we note tht the negtive ifferentil onutne in the I s V s of suspene QM-SWNTs is initive of signifint self-heting n eletron sttering y hot optil phonons. The slow ey n long lifetimes of optil phonons in suspene SWNTs le to high non-equilirium optil phonon popultion n temperture (T op ), using signifint eletron heting (T e T op ) well ove the temperture of the SWNT lttie,9. Anlysis of the negtive ifferentil onutne region of the I s V s urve of mm suspene QM-SWNT y the hot phonon moel,9 les to n estimte T e T op, K t V s. V. This heting gives rise to therml istriution of eletrons n holes with ppreile popultions t the vn Hove singulrities in QM- SWNTs (Fig. ). These rriers n then ritively reomine to nture nnotehnology VOL JANUARY 7

2 4 V s = mv S SWNT Gte D V gs = V Sustrte I s (na) I s (µa) Suspene V gs (V ) V s (V ) V s =.4 V Suspene V s = 7 V S D Distne (µm) Trenh Soure Sustrte S. Drin Figure Visile therml light emission of qusi-metlli SWNTs., Current versus gte voltge I s V gs urve for -mm-long suspene QM-SWNT evie shemtilly shown in the inset (S, soure; D, rin)., Current versus is I s V s hrteristis of the SWNT in (showing negtive ifferene onutne), together with those of the non-suspene portion of the sme tue., Visile emission spetr for the suspene n non-suspene portion of the QM-SWNT reore t low n high is V s, respetively (V s ¼.4 V, I s ¼ ma; V s ¼ 7V,I s ¼ ma). The inset shows snning eletron mirosopy imge (sle r is mm) of the evie with suspene n on-sustrte SWNT portions riging eletroes., Visile onfol imge of -mm suspene QM-SWNT t V s ¼.9 V (I ma) ollete y silion vlnhe photoetetor superimpose on rk-fiel optil imge (the rightest horizontl lines mrk the ege of the eletroes). The strongest light emission is seen t the entre of the suspene tue (pproximte lotion tre y the she line). Right pnel: g line ut (totl photon ounts) long the tue length. The resolution of this mesurement is nerly iffrtion limite ( mm). proue E n E emission peks, thus prouing istint spetrl fetures rther thn fetureless lkoy spetrum. Note tht exitons my ply role in metlli n QM-SWNTs, ut the effet shoul e smller in our se thn in semionuting SWNTs owing to lrge 4 nm QM-SWNTs use with low exiton ining energies reltive to the high T e involve. The effet is iffiult to isern from our spetr with ro peks use y signifint heting. This therml light emission moel is onsistent with the oserve emission photon energy exeeing the is-voltge injetion energy ev s (emission well ove ev s ¼.4 ev is seen in Fig. ). It is lso onsistent with the rsti ifferene in light emission etween the suspene n on-sustrte portions of SWNT (Fig. ), euse self-heting of the ltter is muh lower owing to effiient therml issiption n optil phonons relxing into the sustrte,. In ft, in mient ir without the protetion of Ar flow, our suspene SWNTs rek own t sustine ises V s. V (see Supplementry Informtion, Fig. S) s result of oxition s their lttie temperture pprohes 8 K (ref. ). The therml light emission moel is lso onsistent with the ft tht light emission is rightest t the entre of the suspene QM-SWNTs (Fig. ) where proli temperture profile peks. This iffers from previous sptilly resolve eletroluminesene in semionuting-swnts in whih 4 emission ws oserve t the suspene trenh ege ttriute to impt exittion n exiton reomintion 7, n the moile emission spot seen s result of mipolr rrier injetion. We rrie out theoretil moelling (see Methos setion) to fit the experimentl spetr (Fig. & ) n extrt eletron tempertures y spetr fitting in the visile region, n the results were lose to the optil phonon temperture (T e T op ) erive from the hot phonon moel (Fig., left xis),9. Note tht our moel is minly use to fit the exponentil emission til in the visile for extrting eletron temperture n is not intene to preisely fit the pek positions. Severl fetures in our spetr re not well unerstoo. First, E : E :.7 hs een oserve for semionuting- SWNTs y photoluminesene experiments,4. In our se of QM-SWNT therml light emission, in whih we o not onsier exitoni effets, we expet E : E :, ut evitions from this rtio were oserve (Fig. ). One possile use is signifint heting effet on the nnotue struture n in turn eletroni struture. Some of our QM-SWNTs exhiite unexpline peks (for exmple, in the re urve of Fig. ) etween E n E. Possile explntions for this inlue phonon-ssiste trnsitions, inter-n trnsitions (suh s E, for whih theoretil work hs suggeste perpeniulr polriztion n intensity up to / / ofe nn trnsitions ), nture nnotehnology VOL JANUARY 7

3 ,7,4,, 7 6 E E E.L. (.u.) 9 Angle (eg) E E E (ev) E (ev) Figure Therml light emission of suspene metlli SWNTs with E n E peks., Light emission spetr (sle for reility) in the infrre for three inepenent -mm-long QM-SWNTs (re, green n lue) t V gs ¼ V n V s ¼.4,. n. V, respetively (I s ¼ 6.,.,.9 ma)., Corresponing light emission spetr for the three tues in in the visile t V gs ¼ V n V s ¼.,.,. V (I s ¼ 6., 4.78,.7 ma), respetively. In the inset, the symols re mesure photon ounts for emission polrize t vrious ngles reltive to the tue xis. The soli line is os fit., Illustrtion of the therml light emission mehnism in (n,m) ¼ (4,) QM-SWNT (with nm,e.8 ev, E.6 ev s for the tue in n with re urves). The urve on the lue region orrespons to the eletron popultion t vrious energies lulte y multiplying the ensity-of-sttes (lk line) n the Fermi Dir istriution (re line) t T e, K. The finite popultions t the first n seon vn Hove singulrities re responsile for E n E optil emission n epen on T e n energy exponentilly., E versus E pek lotions from ten suspene QM-SWNT evies etermine from their visile n infrre spetr. The re line orrespons to E ¼ E from the simple tight-ining pproximtion. The peks were etermine using Lorentzin urve fit. As result, some of the evies showing symmetri peks h some offset ue to n imperfet fit. n perhps emission from sttes ue to efets long the reltively long tues. These possiilities require further investigtion. We lulte the effet of trigonl wrping 6 on our spetr n foun the effet to e inonsequentil in this imeter rnge (.8 4 nm), given the reth of the mesure emission peks (. mev). For the SWNT in Fig. we nlyse the pek with (fullwith hlf mximum s of mev) s funtion of is y fitting severl spetr (V s ¼.7. V). As V s n thus T e inrese, the emission pek is expete to wien from inrese therml n lifetime roening effets. Inee, we oserve hnge in pek with over the is rnge (Fig. ). The pprent pek withs orrespon to effetive totl lifetimes of t TOT 4 fs, inluing ll sttering mehnisms (Fig., left xis). By using the lulte T op (n the orresponing Bose Einstein optil phonon ouption numer) from the hot phonon moel,9, we etermine n eletron phonon sttering lifetime t e op of 8 fs (Fig., right xis), out % greter thn t TOT. This suggests tht only portion of t TOT is ue to eletron phonon sttering, with itionl roening likely ue to other mehnisms, suh s eletron eletron sttering. Finlly, we rrie out light emission mesurements of QM- SWNTs s funtion of is V s n gte-voltge V gs (Fig. 4). At fixe is V s, the infrre light emission g (own to.7 ev) uner vrious V gs sle exponentilly with urrent or power (P ¼ I s V s ) (Fig. 4), s inreses in the ltter use higher T e. Current moultion y V gs (Fig. 4; lso Fig. ) ws ue to the existene of smll ngps (of the orer of tens of mev) in the QM-SWNTs 6. By simultneously mesuring light emission g n power P versus V s n V gs (Fig. 4 n, respetively), we oserve tht the exponentil epenene of g on P hel ross the entire V gs n V s two-imensionl spe. Figure 4 hs striking similrities to the t presente previously 7. Although Chen et l. ttriute this to impt exittion n reomintion of free rriers n exitons 7, we rule out impt exittion s the use of light emission in our evies owing to the oservtion of photons of greter energy thn the pplie fiel (E photon. ev s ) (Fig., re urve, n Fig. ). Aitionlly, we o not expet ppreile light emission from impt exittion s result of non-ritive relxtion of exite rriers in QM-SWNTs. We hve lso mesure light emission of suspene semionuting SWNTs n foun nture nnotehnology VOL JANUARY 7

4 , 8 6 Experiment,, I s (µa) 4 Theory T e (K) ,8,, Experiment 8 7 Theory τ TOT (fs) 6 τ OP (fs) Energy (ev ) Figure Therml light emission spetr of.9-mm-long suspene QM-SWNT ompre with theory., The top pnel shows visile spetr of.9-mmlong suspene QM-SWNT t two ises V s ¼. V (lue) n. V (re). The lower pnel shows spetr lulte for nm SWNT with E.8 ev n E.6 ev using eqution () (see Methos). Severl nm SWNTs, suh s (4,) n (8,6), hve similr E n E, mking it not possile to uniquely etermine (n,m )., Left xis: Eletron temperture T e (T op ) versus is (lue line) erive y fitting I s V s t (symols in inset) using the hot phonon moel,9. Blue squres re T e extrte from fitting visile therml light emission spetr (see Methos) in for the two ises. Right xis: Mesure g versus is in the infrre region (re symols) n ompute g (re line) se on T e erive from the I s V s moel,9., Therml light emission spetr in the infrre region for the SWNT t V s ¼.7 (lk),.8 (green),. (lue) n. V (re) (top pnel). The lower pnel shows spetr lulte using eqution () n T e t orresponing ises from. Note tht more preise theoretil tretment shoul inlue ny exiton effets in our 4 nm QM-SWNTs. The exiton ining energies for lrge-imeter QM-SWNTs re unknown, ut shoul e smller thn the 8 mev theoretilly expete for. nm QM-SWNT 7. The effet my use shift in the emission pek positions, ut the shift will e smll ompre to the lrge therml light emission pek with ( mev)., Left xis: estimte hot-eletron lifetime (t TOT ) t vrious ises. Right xis: lulte eletron optil phonon sttering time t vrious ises t orresponing tempertures otine from I s V s nlysis. tht therml effets lso our in semionuting tues (see Supplementry Informtion, Fig. S). The t suggest tht therml heting my ply role in other eletroluminesene mesurements of semionuting SWNTs 9 where similr or higher powers thn those reporte here re issipte in the evies. Our mesurement revels the high-temperture optoeletroni properties of qusi-metlli SWNTs. By exploiting SWNTs of speifi imeters, one n proue therml light emission peke t esire wvelength, from the visile to the infrre, whih is useful in optoeletronis for teleommunitions in the.. mm rnge. Although therml light emission of ulk mterils hs een extensively stuie, our result, reveling rsti 6 spetr peks for SWNTs, unerlines the importne of exmining eletroni heting n emission in novel nnomterils. METHODS EXPERIMENTAL DETAILS Frition of evies, methos for ensuring single tues, light emission spetr n sptilly resolve emission n eletril mesurements re esrie in the Supplementry Informtion. THEORETICAL MODELLING OF THERMAL LIGHT EMISSION SPECTRA OF QM-SWNTs We use the tight-ining pproximtion to lulte the pproximte joint ensity of sttes D J (E) ¼ D(E/)/ (where E is the trnsition energy n D is the ensity of sttes) 8 for SWNT of ertin imeter, n nture nnotehnology VOL JANUARY 7

5 . I s (µa). V s =. V 4 6 P (µw) P (µw) Figure 4 Therml light emission of suspene QM-SWNTs exhiits exponentil epenene on power issiption in the evies., Totl power issiption P( ¼ I s V s )versusv gs for typil QM-SWNT evie t V s ¼ V (lk line, left xis in liner sle) n orresponing emission (totl photon ount in log sle) versus V gs in the infrre (re line, right xis). The eletril ontt resistne is lwys n orer of mgnitue less thn the suspene SWNT resistne t high is. Power issiption ue to ontt resistne ws not exlue from P., I s mp (olour sle r on top) t vrious V s n V gs, showing the evolution of I s V s versus V gs., Therml light emission (g) mp (top: olour sle in log) in the infrre region t vrious V s n V gs., Power issiption mp P (top: olour sle r in liner sle) lulte y P ¼ I s V s from t vrious V s n V gs. The lose resemlne etween the therml light emission mp in the log sle n power issiption mp in the liner sle strongly suggests tht light emission sles exponentilly with power n supports the therml light emission moel. introue roening of the D J y onvolving it with funtion B (either gussin or Lorentzin) 8 D B J ðeþ ¼ ð þ E D J ðe ÞBðE E ; sþ; where s is the roening with (ue to the finite lifetime of rriers sttere y phonons n other mehnisms) n is use s fitting prmeter. It is importnt to note tht D J oes not inlue the metlli eletroni n, euse the ipole trnsition mtrix element is zero for tht n 9.Asn pproximtion (without inluing exiton effets for the lrge-imeter QM- SWNTs use in the urrent work), we lulte the emission spetrum y SðEÞ ¼ n h io tðeþ D J ðeþf ½E C ðkþ F n Š f E V ðkþ F p ; ðþ where S(E) is the photon ount (light intensity), E ¼ E C (k)e V (k) is the emitte photon energy, D J (E) is the joint ensity-of-sttes, f (E) is the Fermi Dir istriution t high T e (resulting from self-heting) n /t(e) is the trnsition proility. E C (k) ¼E V (k) if the mile of the ngp is efine s the energy zero, euse the onution n vlene ns of SWNTs re symmetri, n we ssume tht the eletron n hole qusi-fermi levels F n F p uner ll experimentl gte voltges euse the nnotue is qusi-metlli n the gte effiieny ftor is smll (.; refs ). (Fermi level moultion y gte voltges only les to vrition of,% in the prout of the eletron n hole Fermi Dir popultion terms in eqution ().) The emission rte /t (E) ¼ p/é(q/m p CV A) (/D ph (E)) epens on the momentum mtrix element p CV, the mgnitue of the vetor potentil A, n the photon ensity of sttes D ph (E), n we ssume tht it is energy-inepenent for simpliity. For three-imensionl isotropi (lkoy) photons, D ph / v (E ¼ hv), n /t(e) p CV vr CV v, where the ipole mtrix element r CV ¼ p CV /(im v) n i is the imginry unit. In qusi one-imensionl SWNT, the momentum mtrix element p CV slightly ereses with energy 9. The energy epenene of the emission spetrum in eqution () is then ominte y the Fermi Dir istriution terms in n exponentil mnner. From. ev to. ev in the visile rnge in whih our moel fitting is rrie out for eletron temperture extrtion, /t(e) is ompute using p CV v vries y ftor of,, ut the prout of the Fermi Dir istriution terms vries y more thn 4 orers of mgnitue t T e ¼, K. Using our moel with gussin roening, we otine exellent fitting of the experimentl visile spetr (Fig. ) n were le to extrt T e t vrious V s (squre symols in Fig. ). The emission spetrum in the visile essentilly exhiits n exponentil ey (e E=kBTe ue to the Fermi Dir nture nnotehnology VOL JANUARY 7 7

6 istriutions in eqution ()) into the high-energy en, with superimposing hump t.6 ev orresponing to the E trnsition (Fig. ). Thus the visile spetrum of suspene QM-SWNTs llows for n experimentl etermintion of T e (T op ) for iniviul SWNTs uner Joule heting t vrious V s. Uner higher V s, suspene SWNT exhiits more Joule heting n higher T e (Fig., left xis), n thus n exponentil inrese in light emission (see isepenent spetr in Fig., n Fig., right xis). Importntly, we foun tht the extrte T e (squres in Fig. ) from the emission spetr gree well with those otine (Fig., lue line) y fitting I s V s urves (Fig. inset) using the hot phonon moel,9. The emission spetr of suspene QM-SWNTs in the lower energy infrre regime were ominte y the E pek (Figs n ). This supports our ssumption for the moel where the trnsitions within the metlli n re forien 9, euse otherwise n exponentilly inresing emission woul exist on the lower energy sie of the E pek. It is interesting tht therml light emission spetr provie insights into the mgnitues of the optil trnsition mtrix elements, ut the lk of n exponentil slope uses iffiulty in extrting T e y spetrl nlysis in the infrre region. Inste, y using the lulte tempertures from the I s V s fits, Lorentzin roening, n llowing only the with s to vry (fter fixing the other prmeters y fitting one spetrum), we moelle the infrre spetr with exellent greement with experiment for the SWNT in Fig.. This greement suggests tht ontrsting SWNT emission spetr in the infrre region with lkoy is not suffiient to exlue the possiility of therml emission, s rrie out in reent work 8. The totl photon ounts g in the infrre (Fig., re line) n e estimte s g (T e ) Ae E=kBTe t vrious V s (n in turn vrious T e ) with E.8 ev E (photon energy of the pek in Fig. ), in greement with the mesure results (Fig., re symols). Reeive 4 August 6; epte Novemer 6; pulishe Jnury 7. Referenes. Dresselhus, M. & Di, H. 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Competing finnil interests The uthors elre tht they hve no ompeting finnil interests. Reprints n permission informtion is ville online t 8 nture nnotehnology VOL JANUARY 7