Single-wall carbon nanotubes

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1 CARBON NANOTUBS Nnotus r idl systms for studying th trnsport of lctrons in on dimnsion, nd hv commrcil potntil s nnoscl wirs, trnsistors nd snsors Singl-wll cron nnotus Pul L Mcun 1 Curling up with nnotu SOLID-STAT dvics in which lctrons r confind to twodimnsionl plns hv providd som of th most xciting scintific nd tchnologicl rkthroughs of th lst 50 yrs. From mtl-oxid-silicon fild ffct trnsistors to highmoility gllium-rsnid htrostructurs, ths dvics hv plyd ky rol in th microlctronics rvolution nd r criticl componnts in wid rry of products from computrs to compct-disk plyrs. From mor prochil prspctiv, th study of lctrons in two-dimnsionl systms hs lso n rsponsil for two Nol prizs in physics to Klus von Klitzing in 1985 nd to Rort Lughlin, Horst Störmr nd Dnil Tsui in This is tstimony to th sic s wll s pplid intrst of such dvics (s Hilum nd Strn in furthr rding). Howvr, 1-D systms r lso proving to vry xciting. For mny yrs, studis of qusi 1-D systms, such s conducting polymrs, hv providd fscinting insight into th ntur of lctronic instilitis in on dimnsion. In ddition, 1-D dvics such s lctron wvguids in which lctrons propgt through nrrow chnnl of mtril hv n crtd. xprimnts on ths dvics hv shown, for xmpl, tht th conductnc of llistic 1-D systms in which lctrons trvl th lngth of th chnnl without ing scttrd is quntizd in units of 2 /h, whr is th chrg on th lctron nd h is th Plnck constnt. Ths systms, howvr, hv n limitd y th fct tht thy r inhrntly complx nd/or difficult to mk. Wht hs n lcking is th prfct modl systm for xploring ondimnsionl trnsport 1-D conductor tht is chp nd sy to mk, cn individully mnipultd nd msurd, nd hs littl structurl disordr. Singl-wll cron nnotus fit this ill rmrkly wll. Ths thin, hollow cylindrs of cron wr discovrd in 1993 y groups ld y Sumio Iijim t th NC Fundmntl Rsrch Lortory in Tsuku, Jpn, nd y Donld Bthun t IBM s Almdn Rsrch Cntr in Cliforni nd wr first mss-producd in 1995 y Rick Smlly s group t Ric Univrsity in Txs. Sinc thn, this nw typ of 1-D conductor hs n th focus of mzingly intns study. Hr I will dscri just smll prt of tht ctivity: th crtion of tiny nnolctronic dvics in which nnotus r th ctiv lmnt. As w will s, som nnotus r smiconductors. Thy cn thrfor usd to construct dvics tht r ondimnsionl nlogus of mtl-oxid-silicon fild ffct trnsistors, in which th lctrons mov long th surfc of thin two-dimnsionl lyr. Othr nnotus, in contrst, r nrly prfct mtllic conductors, nd r nw lortory for studying th motion of lctrons in on dimnsion. Both smiconducting- nd mtllic-nnotu dvics r likly to hv significnt tchnologicl pplictions. lctronic structur of nnotus Th rmrkl lctricl proprtis of singl-wll cron nnotus stm from th unusul lctronic structur of grphn th 2-D mtril from which thy r md. P HYSICS W ORLD J UN c Frmi nrgy Frmi nrgy x F F k x y k x mtllic smiconducting () Th lttic structur of grphn th two-dimnsionl mtril tht is rolld up to form nnotu. Th lttic is md up of honycom of cron toms. () Th nrgy of th conducting stts in grphn s function of th wvvctor, k, of th lctrons. Th mtril dos not conduct, xcpt long crtin, spcil dirctions whr cons of stts xist. (c) If th grphn is rolld up round th y xis, th nnotu is mtl (uppr figur), ut if it is rolld up round th x xis, th nnotu is smiconductor (lowr figur). Th nd structur of th nnotu is thn givn y on-dimnsionl slics through th two-dimnsionl nd structur shown in (). Th prmittd wvvctors r quntizd long th xis of th tu. k y x y y x

2 CARBON NANOTUBS 2 Msuring th conductnc of nnotus 1µm To find out how nnotus conduct lctricity, w c hv to ttch lctrods to thm. lctron-m drin lithogrphy is normlly usd to frict th sourc lctrods, which r thn connctd to ithr singl tu or undl of tus. () An tomic forc microscop (AFM) img of singl nnotu dvic md y rsrchrs t th Dlft Institut of Tchnology. Th nnotu is th tiny rd lin running gt from th ottom cntr to th top lft. () An AFM img of nnotu cross, md in my l t th Univrsity of Cliforni t Brkly. Th two nnotus r th grn lins tht join th lctrods. In oth css, th dvics r frictd on n conducting sustrt covrd with n insulting oxid lyr. (c) Th sustrt cts s gt to llow th chrg dnsity of th nnotu to vrid. Grphn is simply singl tomic lyr of grphit, th mtril tht mks up pncil ld. Grphn hs two-dimnsionl honycom structur, md up of sp 2 -ondd cron toms (figur 1). Its conducting proprtis r dtrmind y th ntur of th lctronic stts nr th Frmi nrgy, F, which is th nrgy of th highst occupid lctronic stt t zro tmprtur. Th nrgy of th lctronic stts s function of thir wvvctor, k, nr F is shown in figur 1(). This nd structur, which is dtrmind y th wy in which lctrons scttr from th toms in th crystl lttic, is quit unusul. It is not lik tht of mtl, which hs mny stts tht frly propgt through th crystl t F. Nor is th nd structur lik tht of smiconductor, which hs n nrgy gp with no lctronic stts nr F du to th ckscttring of lctrons from th lttic. Th nd structur of grphn is instd somwhr in twn ths xtrms. In most dirctions, lctrons moving t th Frmi nrgy r ckscttrd y toms in th lttic, which givs th mtril n nrgy nd gp lik tht of smiconductor. Howvr, in othr dirctions, th lctrons tht scttr from diffrnt toms in th lttic intrfr dstructivly, which supprsss th ckscttring nd lds to mtllic hviour. This supprssion only hppns in th y dirction nd in othr dirctions tht r 60 o,120 o,180 o nd 240 o from y (figur 1). Grphn is thrfor clld smimtl, sinc it is mtllic in ths spcil dirctions nd smiconducting in th othrs. Looking mor closly t figur 1(), th nd structur of th low-nrgy stts ppr to sris of cons. At low nrgis, grphn rsmls two-dimnsionl world popultd y msslss frmions. To mk 1-D conductor from this 2-D world, w follow th ld of string thorists nd curl up on of th xtr dimnsions 1µm to form tu (figur 1c). Th rsulting priodic oundry conditions on th wvfunction quntizs k n, th componnt of k prpndiculr to th xis of th tu: in th simplst cs, k n =2πn/C, whr C is th circumfrnc of th tu nd n is n intgr. Th componnt of k long th lngth of th tu, mnwhil, rmins continuous vril. If th tu xis is chosn to point in th y dirction, th nrgy s function of k (i.. th nd structur) is slic through th cntr of th con. Th tu thn cts s 1-D mtl with Frmi vlocity tht is similr to most mtls. Howvr, if th tu xis points in diffrnt dirctions, such s long th x xis, thn th nd structur hs diffrnt conic sction. This typiclly rsults in smiconducting 1-D nd structur, with n nrgy gp twn th filld hol stts nd th mpty lctron stts. Th ottom lin is tht nnotu cn ithr mtl or smiconductor, dpnding on how th tu is rolld up. This rmrkl thorticl prdiction hs n vrifid using numr of msurmnt tchniqus. Prhps th most dirct ws crrid out y Cs Dkkr s group t th Dlft Univrsity of Tchnology in th Nthrlnds nd y Chrls Lir s group t Hrvrd Univrsity in th US. Th Dlft nd Hrvrd rsrchrs usd scnning tunnlling microscopy to dtrmin th tomic structur of prticulr tu out of th mny typs of tu tht r producd whn smpl is grown for proing its lctronic proprtis with th microscop. Thir msurmnts confirmd th rltionship twn th structur of nnotu nd its lctronic proprtis s outlind ov. Nnotus: how thy conduct Bfor w cn msur th conducting proprtis of nnotu, w hv to wir up th tu y ttching mtllic lctrods to it. Th lctrods, which cn connctd to ithr singl tu or undl of up to svrl hundrd tus, r usully md using lctron-m lithogrphy. Th tus cn ttchd to th lctrods in numr of diffrnt wys. On wy is to mk th lctrods nd thn drop th tus onto thm (figur 2). Anothr is to dposit th tus on sustrt, loct thm with scnning lctron microscop or tomic forc microscop, nd thn ttch lds to th tus using lithogrphy (figur 2). Mor dvncd tchniqus r lso ing dvlopd to mk dvic friction mor rproducil nd controlld. Ths includ th possiility of growing th tus twn lctrods (s th rticl y Di on pg 43), or y ttching th tus to th surfc in controlll fshion using ithr lctrosttic or chmicl forcs. Th sourc nd drin lctrods so nmd in nlogy to stndrd smiconducting dvics llow th conducting proprtis of th nnotu to msurd. In ddition, third trminl clld gt is oftn usd (figur 2c). Th gt nd th tu ct lik th two plts of cpcitor, which mns tht th gt cn usd to lctrostticlly induc 32 P HYSICS W ORLD J UN 2000

3 crrirs onto th tu. A ngtiv is on th gt inducs positiv chrgs onto th tu, nd positiv is inducs ngtiv chrgs. Whn th conductnc of th tu is msurd s function of th gt voltg (nd hnc s function of th chrg pr unit lngth of th tu), two typs of hviour r osrvd, corrsponding to mtl nd smiconducting tus. Individul mtllic singl-wlld nnotus wr first studid in 1997 y Dkkr s group t Dlft nd y th uthor s group t th Univrsity of Cliforni t Brkly, oth in conjunction with Smlly s group t Ric. Smiconducting hviour ws thn rportd y th Dlft group in Sinc thn, mny groups hv md nd msurd th proprtis of similr dvics. Indd, most mjor univrsitis nd industril lortoris, such s IBM, now hv t lst on group studying ths mtrils for vrity of lctronic pplictions. Although th dt prsntd in this rticl r tkn ntirly from th Brkly group ld y Alx Zttl, Stvn Loui, Mrvin Cohn nd m, thy should viwd s rprsnttiv of th fild. In most css, similr rsults hv lso n otind y othr rsrchrs. Nnotu trnsistors Smiconducting nnotus cn work s trnsistors. Th tu cn turnd on i.. md to conduct y pplying ngtiv is to th gt, nd turnd off with positiv is (figur 3). A ngtiv is inducs hols on th tu nd mks it conduct. Positiv iss, on th othr hnd, dplt th hols nd dcrs th conductnc. Indd, th rsistnc of th off stt cn mor thn million tims grtr thn th on stt. This hviour is nlogous to tht of p-typ mtl-oxid-silicon fild ffct trnsistor (MOSFT), xcpt tht th nnotu rplcs silicon s th mtril tht hosts th chrg crrirs. But why is th tu p-typ? Aftr ll, on might xpct n isoltd smiconducting nnotu to n intrinsic smiconductor in othr words, th only xcss lctrons would thos crtd y thrml fluctutions lon. Howvr, it is now livd tht th mtl lctrods s wll s chmicl spcis dsord on th tu dop th tu to p-typ. In othr words, thy rmov lctrons from th tu, lving th rmining moil hols rsponsil for conduction. Indd, rcnt xprimnts y Hongji Di s group t Stnford Univrsity nd y th group t Brkly show tht chnging tu s chmicl nvironmnt cn chng th lvl of doping, significntly chnging th voltg t which th dvic turns on. Mor drmticlly, tus cn vn dopd n-typ y xposing th tu to lmnts such s potssium tht dont lctrons to th tu. Th smiconducting dvic of th typ shown in figur 3 is, in mny wys, truly rmrkl. First, it is only on nnomtr wid. Whil much work hs n don to crt ultrsmll smiconducting dvics from ulk smiconductors, such dvics hv lwys n plgud y surfc stts lctronic stts tht ris whn thr-dimnsionl crystl is intrruptd y surfc. Ths surfc stts gnrlly dgrd th oprting proprtis of th dvic, nd controlling thm is on of th ky tchnologicl chllngs to dvic minituriztion. Nnotus solv th surfc-stt prolm in n lgnt fshion. First, thy r inhrntly two-dimnsionl mtrils, so th prolm of 3-D lttic mting surfc dos not xist. Scond, thy void th prolm of CARBON NANOTUBS 3 Nnotus s trnsistors conductnc ( 2 /h) hol nrgy c sourc 0 5 gt voltg (V) smiconducting singl-wlld nnotu drin () Th conductnc of smiconducting cron nnotu s function of gt voltg. Th tu cn turnd on y pplying ngtiv voltg, nd turnd off with positiv voltg. Th dvic turns on t ngtiv voltgs cus hols r ddd to th tu. () Th potntil profil sn y ths hols du to disordr in th structur of th nnotu nd imprfct contcts twn th lctrods nd th tu. Th hols must hop through th rrirs in this profil if th nnotu is to conduct. (c) Th tip of scnning pro microscop cn usd to mp th rrirs to conduction. Th horizontl lin indicts th loction of th nnotu nd th vrticl lins indict th contct oundris. Th conductnc of th tu is msurd s th positivly isd tip is scnnd ovr th smpl. Th right spots r whr th tip dcrsd th conductnc, with grtr intnsity corrsponding to grtr chng in th conductnc. dgs cus cylindr hs no dgs! Looking mor closly t th conductnc of smiconducting nnotus, w s tht initilly it riss linrly s th gt voltg is rducd, conducting ttr s mor nd mor hols r ddd from th lctrod to th nnotu. Th conductnc is limitd only y ny rrirs tht th hols s s thy trvrs th tu. Ths rrirs my cusd y structurl dfcts in th tu, y toms dsord on th tu, or y loclizd chrgs nr th tu. Th hols thrfor s sris of pks nd vllys in th potntil lndscp, through which thy must hop if th tu is to conduct (figur 3). Th rsistnc of th tu will domintd y th highst rrirs in th tu. Rcnt xprimnts y th Brkly nd Dlft groups confirm this simpl pictur. Th rsrchrs usd th tip of scnning pro microscop to idntify th mjor scttring sits, thus nling mp of th rrirs to conduction to producd (figur 3c). At lowr gt voltgs, th conductnc vntully stops incrsing nd coms constnt, cus th contct rsistnc twn th mtllic lctrods nd th tu cn quit high. Unfortuntly, this contct rsistnc cn vry y svrl ordrs of mgnitud twn dvics, proly du 0.75 µm P HYSICS W ORLD J UN

4 CARBON NANOTUBS 4 Nnotus s mtls conductnc ( 2 /h) to mundn issus such s surfc clnlinss. To improv th consistncy of nnotu trnsistors, mny groups r thrfor trying to improv th qulity of ths contcts y dvloping nw clning nd nnling procdurs with som significnt succss. Ths tiny MOSFT-lik dvics will proly just th first in host of nw smiconducting-dvic structurs sd on cron nnotus. Othr dvics, such s nnotu p njunction diods nd ipolr trnsistors, hv n discussd thorticlly nd r likly to rlizd soon. Nnotus s on-dimnsionl mtls In drmtic contrst to smiconducting nnotus, th conductnc of som othr nnotus nr room tmprtur is not noticly ffctd y th ddition of fw crrirs. This hviour is typicl of mtls, which hv lrg numr of crrirs nd hv conducting proprtis tht r not significntly ffctd y th ddition of fw mor crrirs. Th conductnc of ths mtllic nnotus is lso much lrgr thn th smiconducting-nnotu dvics, s xpctd. Indd, numr of groups hv md tus with conductncs tht r twn 25% nd 50% of th vlu of 4 2 /h tht hs n prdictd for prfctly conducting llistic nnotus. This rsult indicts tht lctrons cn trvl for distncs of svrl microns down tu for thy r scttrd. Svrl msurmnts support this conclusion, including thos crrid out y our group using scnning pro microscopy. Ths msurmnts lso show tht th contct rsistnc twn th tu nd th lctrods cn sustntil, just s it is with smiconducting tus. Furthr vidnc for th nr-prfct ntur of ths tus coms from th wy thy hv t low tmprturs. Th conductnc is osrvd to oscillt s function of gt voltg (figur 4). Ths Coulom oscilltions occur ch tim n dditionl lctron is ddd to th nnotu. In ssnc, th tu cts lik long ox for lctrons, oftn clld quntum dot (s Kouwnhovn nd Mrcus in furthr rding). Th K 129 K 40 K 16 K 8 K 1.3 K conductnc ( 2 /h) gt voltg (V) Th conductnc of mtllic nnotu t six diffrnt tmprturs s function of gt voltg. At low tmprturs th conductnc oscillts s individul lctrons r ddd to th tu. This indicts tht th nnotu cts lik long nd nrrow quntum dot, with lctronic stts tht xtnd ovr th ntir lngth of th tu. Th vrg conductnc of th tus slowly dcrss s th tmprtur is lowrd (s insrt). Th functionl form is consistnt with th powr-lw hviour prdictd for tunnlling into Luttingr liquid tmprtur (K) 5 lctrons in on dimnsion Frmi liquid Luttingr liquid () An lctron tunnlling from mtl lctrod into Frmi liquid lvs othr lctrons in th Frmi s rltivly undisturd. () An lctron finds it lss sy, howvr, to tunnl into Luttingr liquid, cus collctiv xcittions in th lctron liquid must xcitd. Clcultions show tht th Luttingr liquid hs tunnlling conductnc tht dcrss in proportion to ( F ) α whr is th nrgy of th lctron, F is th Frmi nrgy nd α is powr. Th xcss nrgy of th tunnlling prticl is providd y ithr n pplid tmprtur or voltg. lctronic nd mgntic proprtis of ths nnotu quntum dots rvl grt dl out th hviour of lctrons in nnotus. For xmpl, th fct tht th oscilltions r quit rgulr nd priodic indicts tht th lctronic stts r xtndd long th ntir lngth of th tu. If, howvr, thr ws significnt scttring in th tu, th stts would com loclizd nd th Coulom oscilltions would lss rgulr. Nnotu quntum dots tht r s long s 10 µm hv n found to xhiit ths wll-ordrd oscilltions, gin indicting tht th mn fr pth cn vry long. Th xprimnts dscrid ov indict tht lctrons cn trvl for long distncs in nnotus without ing ckscttrd. This is in striking contrst to th hviour osrvd in trditionl mtls lik coppr, in which scttring lngths from lttic virtions r typiclly only svrl nnomtrs t room tmprtur. Th min rson for this rmrkl diffrnc is tht n lctron in 1-D systm (lik nnotu) cn only scttr y compltly rvrsing its dirction, whrs lctrons in 2-D or 3-D mtril cn scttr y simply chnging dirction through tiny ngl. Phonons long-wvlngth lttic virtions tht scttr lctrons in oth 2-D nd 3-D mtrils t room tmprtur do not hv nough momntum to rvrs th dirction of spding lctron in 1-D nnotu. Thy thrfor do not influnc its conductnc, t lst not t low voltgs. Rcnt xprimnts y Dkkr s group t Dlft hv shown tht t high voltgs (grtr thn 0.15 V), lctrons cn mit high-momntum phonons tht cn scttr lctrons in 1-D nnotus. This lds to drmtic rduction in th conductnc t high voltgs, cusing th currnt to sturt t out 25 micromps for singl nnotu. Still, this is rmrkly mcroscopic currnt to crrid y such nnoscopic systm! Th fct tht mtllic nnotu cts lik nr-prfct 1-D conductor t low voltgs mks it n idl systm to tst som ids out lctrons in on dimnsion tht hv n round for hlf cntury. Strting in th 1950s, sris of pprs y Sin-Itiro Tomong, Joquin Luttingr nd ltr Duncn Hldn md it clr tht 1-D lctron systm should hv vry diffrntly from its 2-D nd 3-D countrprts whn th rpulsiv Coulom intrctions twn nighouring lctrons r tkn into ccount. Undr ordinry conditions, 2-D or 3-D mtllic conductor hvs s Frmi liquid, vn whn th lctrons intrct with ch othr vi th Coulom forc. Th lctrons in such mtrils fill th low-nrgy stts up to th Frmi nrgy, crting wht F P HYSICS W ORLD J UN 2000

5 6 Nnotus s rctifirs V c V hol nrgy mtl tu smiconducting tu loction of mtl tu V = is known s Frmi s of lctrons. Th low-nrgy xcittions (or qusiprticls ) of this systm ct lmost lik compltly fr lctrons, moving ntirly indpndntly of on nothr. In othr words, n xcitd stt looks vry much lik singl xtr lctron ov th Frmi s. In 1-D systms, on th othr hnd, th low-nrgy xcittions r collctiv xcittions of th ntir lctron systm. Th lctrons mov in concrt, rthr thn s indpndnt prticls of Frmi liquid. This systm is rfrrd to s Tomong Luttingr liquid (or, mor simply, Luttingr liquid) to mphsiz its diffrnc from th stndrd Frmiliquid hviour of 2-D nd 3-D mtls. On wy to tst this prdiction is to s if n lctron cn tunnl into th systm from th outsid world for xmpl from mtllic contct. If th low-nrgy xcittions r simpl qusiprticls, thn n lctron will hv no difficulty tunnlling into th systm (figur 5). Th tunnlling conductnc would not xpctd to chng with tmprtur or is voltg. If, on th othr hnd, th low-nrgy xcittions r collctiv in ntur, th othr lctrons in th tu must mov in concrt with th tunnlling lctron to mk room for it. Th lctron must litrlly mk splsh whn it jumps into th Luttingr liquid (figur 5). If th nrgy,, of th tunnlling lctron is much highr thn th Frmi nrgy, F, thn this splsh is not prolm. As th lctron tunnls in with lss nd lss xcss nrgy, howvr, it hs lss nd lss nrgy to push th othr lctrons out of th wy. Clcultions show tht th Luttingr liquid hs tunnlling conductnc tht dcrss in proportion to ( F ) α, whr α is prticulr powr. Th vlu of α dpnds on th strngth of th Coulom intrction twn th lctrons. It lso dpnds on whthr th lctron tunnls into th middl of tu, th nd of tu, or twn th nds of two tus. I currnt (na) 0 rvrs is forwrd is voltg (mv) rvrs is forwrd is () A mtllic nnotu crossing ovr smiconducting nnotu crts rctifir. () In othr words, positiv voltg cuss currnt to flow in on dirction, whil ngtiv voltg stops th currnt flow ltogthr. Th mtllic tu loclly dplts th lctrons in th undrlying smiconducting tu, crting rrir, th hight of which is fixd y th potntil pplid to th mtllic tu. (c) A positiv voltg pplid to th smiconducting tu givs th hols th ncssry nrgy to ovrcom th potntil rrir, whrs ngtiv is dos not (d). d V loction of mtl tu CARBON NANOTUBS Thorists hv n l to stimt ths powrs firly ccurtly for nnotus, rsulting in vry spcific prdictions tht xprimntlists cn tst. Our group t Brkly tstd ths prdictions y msuring th tunnlling conductnc into nnotu from mtllic lctrod s function of th tmprtur nd is. In this cs, th poor contcts workd to our dvntg, srving s th tunnl rrirs twn th tu nd th lctrod. Th vrg conductnc dcrss slowly s function of tmprtur (figur 4). Th rltionship is dscrid y powr lw tht grs wll with thory. Th group hs lso msurd th powrs for lctrons tunnlling into th middl nd nds of tu, whil our collgus t Dlft hv don th sm for lctrons tunnlling from th nd of on nnotu into th nd of nothr. All of ths rsults gr wll with th thorticl prdictions. Ths xprimnts clrly dmonstrt tht intrcting 1-D mtls hv vry diffrntly to 2-D nd 3-D mtls. This is prhps not so surprising to us trffic nlogy, cr cr intrctions r much mor importnt on on-ln highwy thn thy r in 2-D prking lot, whr cr cn mov mor-or-lss indpndntly of th othr crs. Wht is surprising, howvr, is how long it took for ths prdictions wr tstd in dtil. Whil prvious msurmnts of othr systms hd shown vidnc for Luttingr hviour, nnotus rprsnt prhps th clrst nd most strightforwrd rliztion of Luttingr-liquid physics to dt. Nw dvics nd gomtris Whil th ov xprimnts dmonstrt tht mny of th sic proprtis of singl-wll cron nnotus r now undrstood, thr is n lmost limitlss numr of nw gomtris nd topics witing to xplord nd ll mnnr of nw structurs to crtd. Indd, rsrchrs r dvloping host of nw tchniqus tht crtivly comin lithogrphy, chmistry nd nnoscl mnipultion, for xmpl y growing tus on prfrictd structurs or y pushing thm round with th tips of tomic forc microscops. It is quit rmrkl how fr th fild hs com sinc th first msurmnts wr md in 1997 nd this progrss shows no sign of slowing. For xmpl, nw dvics cn crtd y th intrsction of two nnotus, such s mtllic tu crossing ovr smiconducting tu (figur 6). Th mtllic tu loclly dplts th hols in th undrlying p-typ smiconducting tu. This mns tht n lctron trvrsing th smiconducting tu must ovrcom th rrir crtd y this mtl tu. Bising on nd of th smiconducting tu rltiv to th mtl tu lds to rctifying hviour. In othr words, th rrir is ovrcom in on is dirction, ut not in th othr. This structur is just on of mny possiilitis for nnotu dvics witing to xplord. Mnwhil, Phdon Avouris nd co-workrs t IBM s T J P HYSICS W ORLD J UN

6 CARBON NANOTUBS Wtson Rsrch Cntr in Nw York hv md nnotu coils, in which n individul tu loops ck on itslf to form ring-lik structur. Such coils might usd s tiny solnoids to crt mgntic filds or to study quntum intrfrnc phnomn. Suprconducting contcts hv lso n ttchd to nnotus y svrl groups to study th hviour of suprconductors connctd y 1-D conductor. Nnotus lso offr grt promis s th ctiv lmnts in nno-lctromchnicl systms. Thir rmrkl mchnicl nd lctronic proprtis mk thm xcllnt cndidts for pplictions such s high-frquncy oscilltors nd filtrs. Mny groups hv now crtd dvics in which th sustrt nth th nnotu is rmovd, lving th nnotu suspndd in fr spc twn th two contcts. Th tu is thrfor fr to virt lik guitr string, nd rsrchrs r strting to invstigt th intrctions twn th mchnicl nd lctronic dgrs of frdom (s rticl y Di on pg 43). Th futur lis in tus Singl-nnotu dvics hv com long wy, ut how fr thy will go is nyon s guss. Clrly, thy will prt of th scintific lndscp for yrs to com s modl systm for studying physics t th nnomtr scl. Mny commrcil pplictions hv lso n proposd, from molculr lctronics to snsing. Whthr ths will pn out is mor difficult to ssss (s rticl y d Hr nd Mrtl on pg 49). If ths rl-world pplictions of nnotus r to succd, w must find wys of succssfully intgrting thm into xisting microlctronic products nd tchniqus. But if w mng to dvlop th tchnology to frict nnotus of prticulr typ, lngth nd dimtr in controlld fshion nd to incorport th tus into lithogrphic circuits t prticulr plcs with fficincis pproching 100% thn th sky is, indd, th limit. Whil this is chllnging gol, thr ppr to no fundmntl rrirs to chiving it. A propr mrrig of physics, chmistry nd lctricl nginring my up to th tsk. lctronics my gin to go th wy of iology nd us th cron tom s its ckon. Furthr rding C Bouronnis nd D Jérom 1998 On-dimnsionl conductors Physics World Sptmr pp41 45 C Dkkr 1999 Cron nnotus s molculr quntum wirs Physics Tody My pp22 28 M Drsslhus t l Cron nnotus Physics World Jnury p33 T W son (d) 1997 Cron Nnotus: Prprtion nd Proprtis (CRC Prss, Princton, NJ) M Hilum nd A Strn 2000 Frctionl quntum Hll ffcts Physics World Mrch pp37 43 L Kouwnhovn nd C Mrcus 1998 Quntum dots Physics World Jun p35 Th Nnotu Sit Pul Mcun is in th Mtrils Scinc Division, Lwrnc Brkly Ntionl Lortory, 1 Cyclotron Rod, Milstop 19A-0563, CA 94720, USA, nd in th Dprtmnt of Physics, Univrsity of Cliforni t Brkly, Brkly, CA 94720, USA, -mil mcun@socrts.rkly.du 36 P HYSICS W ORLD J UN 2000

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

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