Magnetic field dependence of electrical transport properties in acceptor doped bismuth

Transcription

1 IOSR Journl of Appld Physcs (IOSR-JAP) -ISS: Volum 7, Issu Vr. III (Mr. - Apr. 5), PP -6 Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth Kjl Krshn Dy Dprtmnt of Physcs, Bnwrll Bhlot Collg, Asnsol P.O.Ushgrm, Dst.Burdwn Pn Cod-7333, Wst Bngl, Ind Abstrct: Msurmnts wr md on th ll coffcnt nd trnsvrs mgntorsstnc of bsmuth lloys contnng smll mount of gllum nd ndum s functons of mgntc fld t dffrnt constnt tmprturs. Chng of sgn of th ll coffcnt wth mgntc fld s obsrvd t low tmprtur. Chng of sgn of th ll coffcnt wth rs n tmprtur s common phnomnon n cs of ccptor dopd smconductor. But rvrsl of sgn n th ll coffcnt wth mgntc fld s not tht commonly obsrvd. Vlus of th mgntorsstnc nd ll coffcnt strongly vry wth mgntc fld strngth. Th mgntorsstnc dos not oby th qudrtc dpndnc on mgntc fld strngth. Th obsrvd rsults my b consqunc of th prtculr bnd structur whch llows th prsnc of dffrnt nds chrg crrrs wth hgh nd strongly nsotropc moblts. Kywords: bsmuth, lctrcl trnsport, ll coffcnt, mgntorsstnc, smmtl I. Introducton Bsmuth hs smll vlnc nd conducton bnd ovrlp, thr smll L pont lctron rm pocts, nd T pont hol rm poct, whch gvs n qul (smll) numbr of both chrg spcs t th rm lvl.[] L nd T rfr to symmtry ponts n th rducd Brlloun on of bsmuth. Bsmuth s smmtl whch plys n mportnt rol n sold-stt physcs. Th lctrcl trnsport proprts of bsmuth nd ts lloys hv bn subjct of ntrst du to th ovrlp. Bsmuth hs n xtrmly smll rm surfc. So ths mtrl provds th rmrbl possblty to obsrv strong ffcts nducd by th prsnc of xtrnl flds,.., mgntc fld nd tmprtur, vn f ths xtrnl forcs r of modrt mpltud. Invstgtons on th proprts of lloys of bsmuth r mportnt bcus vrous dvcs r bng dvlopd by usng lloys of bsmuth. [,3] Svrl bsmuth-contnng oxds hv bn found to b hgh-t C suprconductng mtrl.[4,5] Bsmuth-ntmony lloys hv pplctons n pltr coolng moduls nd n nfrrd dtctors. xtnsv nvstgtons of th trnsport proprts of bsmuth dopd wth mpurts l ld, tn, tllurum, ntmony tc hv bn md.[6-9] In th lst fw yrs, srs of xprmnts hs onc gn drwn th ttnton of th communty to lmntl bsmuth nd chllngd our undrstndng of ths mtrl. w xprmnts clrly ndctd tht th quston of trnsport n bsmuth ws stll not undrstood. [] In fct, smlr qustons stll xstd for th stndrd rsstvty s wll. [] A mtrl of much long trm ntrst wth mny ntrstng proprts bsmuth hs rcntly bn found to host vrty of xotc lctronc phnomn, ncludng phs trnstons t hgh fld. Thr hs bn xtnsv ntrst n th trnsport proprts of bsmuth bcus of ts unusul bhvor tht s xhbtd du to th low dnsty nd vry hgh moblts of crrrs. Bsmuth bhvs l mtl though not strctly mtllc. Its bhvor s n btwn mtl nd smconductor. Both th hols nd lctrons r found to b rsponsbl for th trnsport proprts. Th bnd structur of pur bsmuth my b consdrd to consst of pr of lght mss bnds (L C for lctrons nd L V for hols) t sx symmtrclly rltd postons n -spc (sx hlf llpsod) nd hvy mss hol bnd (T V ) t two postons n -spc (two hlf llpsod). Ths sx hlf llpsods for ch of th lctrons nd lght hols n th Brlloun on my b consdrd s thr whol llpsods cntrd t L-pont nd two hlf llpsods for th hvy hols s on whol llpsod cntrd t T-pont. Th nrgy spctrum of bsmuth hs bn nvstgtd n lrg numbr of xprmntl nd thortcl pprs. [-4] owvr, rght up to th prsnt tm modls dscrbng th spctrum of crrrs t th ponts L nd T n th rducd Brlloun on, s wll s crtn mportnt prmtrs of th spctrum hv not bn gvn unqu vlus, owng to th complxty of th bnd structur of bsmuth nd th strong nsotropy of ts proprts. At ccptor mpurty concntrtons blow. t.% th lttc prmtrs of bsmuth do not vry mrdly [3] nd th ffct of th ccptors s pprntly only to m th lctron nd hol concntrtons unqul nd to chng th lctron nd hol moblts. Addtonl complctons r cusd by th nsotropc ntur of th rlxton tm, [5] th strongly non-prbolc ntur of th dsprson lw for crrrs t th L-xtrm. [6, 7] Th purpos of ths wor s to r-xmn th trnsport proprts of dopd smmtl. W prsnt hr th rsults of th mgntc fld vrton of th ll coffcnt nd mgntorsstnc study of gllum nd ndum dopd bsmuth sngl crystl. DOI:.979/ Pg

2 R xy (cm3 /coulomb) Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth II. xprmnts And Rsults Sngl crystls of bsmuth (B) dopd wth gllum (G) nd ndum (In) wr prprd by th vrtcl Brdgmn tchnqu usng modfd Brdgmn furnc. Th prcntgs of dopng of th studd smpls, s dtrmnd by DX Anlytcl Systm (ISIS Ln, Oxford Instrumnts, U.K.) r shown n Tbl I. Th thn nd smll portons wr cut nd thn ground nto rctngulr shps of dmnson cm.3cm.cm for msurmnts. Tbl I. Prprd smpls nd thr prcntgs of mpurty. lloys smpl numbr wghtd tomc % B-In S.5 B-G S. Th crystllogrphc xs r usully rfrrd to s th bnry, th bsctrx, nd th trgonl or c-xs, prtnng to th x-, y-, nd -xs rspctvly. Th currnt ws ppld n th drcton prpndculr to th trgonl xs nd mgntc fld ws ppld prlll to th trgonl xs. gurs nd show th mgntc fld vrton of th ll coffcnt ( R ) nd trnsvrs mgntorsstnc ) / of th smpls. xy ( Th vlus of th mgntorsstnc nd ll coffcnt strongly vry wth th mgntc fld strngth. ll coffcnt s found to b ngtv nd t pprochs to th postv vlu wth th ncrs of mgntc fld. A chng of sgn of R xy wth mgntc fld s obsrvd t thr low tmprturs for th smpl S. Th mgntorsstnc dos not show strctly qudrtc dpndnc on mgntc fld strngth K K 37 K 69 K 8 K 3 K (G) ( - )/ K 37 K 69 K 96 K 35 K 6 K 3 K (G) () (b) g. Mgntc fld dpndnc of th () ll coffcnt nd (b) trnsvrs mgntorsstnc of. t% gllum dopd bsmuth t dffrnt constnt tmprturs ndctd n th fgurs. DOI:.979/ Pg

3 R xy (cm3 /coulomb) Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth K 34 K 45 K 98 K 5 K 99 K (G) (G) () (b) g. Mgntc fld dpndnc of th () ll coffcnt nd (b) trnsvrs mgntorsstnc of.5 t% ndum dopd bsmuth t dffrnt constnt tmprturs ndctd n th fgurs. DOI:.979/ Pg ( - )/ K K 34 K 7 K 88 K 5 K 7 K III. Thortcl Consdrton Bsmuth s pntvlnt nd from th two toms n th unt cll tn vlnc lctrons orgnt. Thy would fll whol numbr of bnds f slght bnd ovrlp dd not occur. Du to ths ovrlp fw lctrons r ccumultd n th nxt-hghr bnd, lvng n qul numbr of hols n nrly flld bnd. Both ths lctrons nd hols ct s fr crrrs. Bsd on nfrrd trnsmsson xprmnts [8], Lx [9] proposd n llpsodl-non-prbolc modl for th rm surfc of bsmuth whch hs bn found to wor qut wll n xplnng physcl proprts. On xs of ch lctron llpsod s prlll to crystllogrphc xs (bnry xs hvng or x), th othr two xs of ch llpsod r tltd wth rspct to th othr crystllogrphc xs (trgonl xs hvng 3 or nd bsctrx xs hvng or y). Accordng to th rlton of nrgy vrsus wv-vctor proposd by Lx, th lctron llpsods cn b dscrbd s ( ) ( ) ( ) ( ) x y 33 3 y g m whr s th lctron rm nrgy, g s th bnd gp btwn th two lght mss bnds(l C nd L V ), nd () j s th componnt of rcprocl lctron mss tnsor () n unt of (/m o ); m o bng th fr lctron mss. Ths s nown s th Lx or llpsodl-non-prbolc modl. Th thr lght hol llpsods r lso of th sm form s th thr lctron llpsods. Th rm surfc of hvy hols s dscrbd by on st of llpsod wth ts xs of rvoluton prlll to th trgonl xs. Th llpsod of rvoluton for hvy hol s of th form h x y 33 m (h) whr h s th hvy hol rm nrgy nd j s th componnt of rcprocl hvy hol ffctv mss tnsor (h). gur 3 shows schmtc dgrm of nrgy bnds n bsmuth showng projcton of nrgy bnds L C, T V nd L V on two-dmnsonl pln. C s th lowrmost vlbl nrgy lvl n th L C bnd nd nd (h) V r th upprmost vlbl nrgy lvls n th T V nd L V bnds rspctvly. As bsmuth hs suffcnt numbr of lctrons to fll th bnd T V, w gt rm lvl n th rgon of ovrlp du to th dstrbuton of lctrons mong th nrgy stts of T V nd L C n tht rgon. L V nd L C bnds wll gv rs to lght mss hols nd lctrons rspctvly s fr crrrs nd th T V bnd to hvy mss hols. Gllum nd ndum r lmnts of group III nd so thy ct s ccptor mpurty to bsmuth. Accptor mpurty ts (h) V

4 Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth lctrons from both th ovrlppng bnds, thrby ncrsng th numbr of hols nd dcrsng th numbr of lctrons. Th rm lvl thn movs to lowr nrgy to poston. L C T V (h) V C (h) V L V g. 3 Schmtc dgrm of th lctron nd hol bnds. or lctrons nd lght hols w us Lx modl or llpsodl-non-prbolc bnd. If nd rprsnt th dnsts of hols nd lctrons n th two bnds T V nd L C t T=K, w thn hv V Ch V d nd / dfl 4 (h ) 3 whr / 3/ ( ) 8 3 Ch m 3 m nd / () 3 C f L m m C h h g m (h) s th ffctv mss tnsor of hvy hols n T V bnd nd nd m () s tht for lctrons t th bottom of th L C bnd. Th dnsts of th crrrs n bnds T V nd L C n th mpur smpl wll bcom V / Ch V d nd If b th dnsty of ccptor mpurty cntrs ddd thn b whr nd b r th frctons of ccptor cntrs tng wy lctrons from th bnds T V nd L C rspctvly nd r thrfor proportonl to th dnsty of stts n T V nd L C ; (>b nd +b=). Th totl dnsty of mpurts ddd wll b mp nd If th concntrton of mpurty s ncrsd th mpurty wll t mor lctrons from th bnds nd for suffcnt prcntg of mpurty th rm lvl movng to th lowr nrgy, my ntr nto th rgon of L V bnd. As rsult, thr wll b crtd mor hols n T V nd L V bnds nd L C bnd wll b dvod of lctron. Th bov xprssons rlt th concntrton of mpurts nd th numbr of fr crrrs wth th consqunt shft of th rm lvl. Th thortcl thr bnd modl for pur s wll s dopd bsmuth prdcts th ll coffcnt nd th trnsvrs mgntorsstvty wth th mgntc fld long -xs s A A R xy A A nd A A whr th followng trms hv bn tn s A nd A n th bov xprssons, ( h) { h} { h} ( h) ( h) C C { } { } d df d L A d d 3/ DOI:.979/ Pg

5 nt prlll spn prlll spn nt prlll spn prlll spn nt prlll spn prlll spn Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth ( h) ( h) ( h) ( h) s th (sotropc) moblty of hvy hols n th xy-pln, nd r th lctron moblts tn for ch lctron llpsod n th xy-pln nd nd ( h) ( h) A r thos for lght hols rspctvly. ( h) ( h) () (h) nd r th vrg moblts of lctrons nd lght hols n th xy-pln rspctvly. Th rsstvty n th bsnc of mgntc fld s thn gvn by ( h) Th trnsvrs mgntorsstnc s thn gvn by ( h) 3. ffct of Mgntc ld Lt us now s wht hppns to th lctrons n mtls whn mgntc fld s ppld. or smplcty, w consdr th stuton t T=K. or th sm rson, th lctrons wth spn prlll nd ntprlll to th drcton of mgntc fld () r shown n g.4 n two groups so tht ll th stts blow th rm lvl r occupd nd thos bov r mpty. If mgntc fld s ppld, thr wll b n unstbl stuton du to th shft n nrgy of lctrons n th two hlvs (s g.4b) nd numbr of lctrons wth ntprlll spn wll ntr th group of prlll ons. In qulbrum both hlvs r gn flld to th sm lvl s shown n g.4c. In qulbrum t, th dnsty of stts n th rght hlf (prlll spn) s grtr thn tht n th lft hlf (ntprlll spn) nd t s xpctd tht, >. Ths mns tht th rm nrgy s lowrd by th pplcton of mgntc fld by n mount -. r nd r such tht + = B. If B <<, t s vdnt tht th shft - wll hv no sgnfcnt ffct. In th cs of mtls whl fndng th spn prmgntsm of fr lctrons ths dffrnc s nvr consdrd bcus thr fw V nd for ordnry flds G, B -4 V. In th prsnt cs of bsmuth, th rm surfc s smll - V. [] So th smll chng n th rm nrgy du to th pplcton of th mgntc fld wll cus smll chng n th dstrbuton of fr crrrs. Snc thr r two ovrlppng bnds, ths smll chng n th dstrbuton of fr crrrs wll cus n unqul chng n th dstrbuton of hols nd lctrons n dopd bsmuth bcus th dnsty of stts of th two bnds bov th rm surfc r dffrnt. Ths chng wll of cours not b bl to produc ny sgnfcnt chng n th proprts whr th contrbuton of crrrs r ddtv. But t my produc sgnfcnt ffct n thos proprts whr th contrbuton from hols nd lctrons oppos ch othr. If th rm nrgy s lowrd, thr wll b gn n th numbr of hols ovr lctrons. Snc, th gn n hols wll ncrs wth mng R xy postv wth ncrsng fld. B B + = B () (b) (c) g. 4 () =, (b) unstbl stuton n prsnc of, (c) qulbrum poston n prsnc of. DOI:.979/ Pg

6 Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth 3. ffct of Tmprtur Whn smll mount of ccptor mpurty s ddd, th rm lvl my l wthn th ovrlp rgon. As th tmprtur rss, lctrons from T V wll go to th vcnt stts n L C, thrby ncrsng th numbr of fr lctrons n L C nd th sm numbr of hols wll b crtd n th bnd T V. rom L V, xctd lctrons wll go to both T V nd L C. lctrons, thos go to th vcnt stts n T V, dcrs th numbr of hols n T V nd thos go to L C, ncrs th numbr of fr lctrons. Also th totl numbr of lctrons xctd from L V wll gv rs th sm numbr of hols n L V. umbr of lctrons n th L C bnd grows fstr wth tmprtur thn th hols. Th dnsty of lctrons xctd from on bnd to nothr cn b clcultd s functon of tmprtur usng th rm-drc dstrbuton functon f(), l ths, d g f d g ; dnsty of stts t nrgy Th two mportnt fctors rsponsbl for th tmprtur vrton of moblty r phonons nd ond mpurty toms. Any rbtrry crrr moblty, whn scttrng mchnsm occurs ndpndntly, s dtrmnd by mp lt whr mp rprsnts scttrng du to mpurty ons nd lt rprsnts scttrng du to phonons. Whn th concntrton of ond donors or ccptors s hgh, th chrg crrrs suffr Ruthrford scttrng du to th prsnc of such ons. Th scttrng of lctrons t low tmprturs s domntd by ond mpurty toms wth pproxmt powr lw, T 3/ 3/ nd t hgh tmprturs lttc scttrng ( T ) bcoms mor promnnt. xprmntl obsrvtons howvr r not lwys n prcs ccord wth ths formul. IV. Concluson In th prsnt smpls lctrons r prsnt s mnorty crrr. Snc R xy s ngtv t low mgntc flds, t s concludd from th bov xprsson of R xy tht th lctron moblts xcd th hol moblts. It s clr tht th crrr proprts r rprsntd by mny prmtrs, v. th dnsts of fr crrrs nd th strongly nsotropc moblts. If th nrgy bnd structur shown n g.3 s corrct for th dlut bsmuth lloys, th lctrons whch r thrmlly xctd nto th conducton bnd cn contrbut to th conducton phnomn. Th msss of th lctron nd lght hol chng wth th poston of th rm lvl ccordng to th bult-n-proprty of th Lx llpsodl-non-prbolc bnd modl. Th ffctv mss nd th rlxton tm dtrmn th moblty of th crrr. Th dnsty of lctrons n L C s suffcnt t low tmprtur nd th moblts of lctrons r much grtr thn thos of hols. Thn t s possbl tht th ffctv contrbuton of lctrons towrds th ll coffcnt s grtr thn tht of hols, whch ms th ll coffcnt ngtv. Th numbr of lctrons n th L C bnd grows fstr wth tmprtur thn th hols. It s xpctd tht th rto of th dnsty of lghtr hols to tht of hvr hols chngs s th crrr dstrbuton dvts from complt dgnrcy wth th ncrs n tmprtur. Th ncrss n th concntrton of thr typs of crrrs to grt xtnt dcrs th mgntuds of th ll coffcnt nd mgntorsstnc. Zro fld rsstvty shows th tmprtur dpndnc of pproxmtly T. [] Ths rsult ndcts th domntng contrbuton of phonon scttrng ovr th ond mpurty scttrng. So th ffct of phonon scttrng mght lso b thr n th hghr tmprtur lmts. or closd rm surfc wth qul numbr of hols nd lctrons, th mgntorsstnc vrs s nd for unqul numbr of lctrons nd hols, t sturts t hgh fld lmt. [] In th prsnt cs t vrs s n whr th vlus of n r n th rng.3<n<.5 for gllum dopd nd.5<n<.5 for ndum dopd smpl. Wth ncrsng tmprtur t pprochs n pproxmtly qudrtc dpndnc on fld strngth. At vry low tmprtur t my sturt n th hgh fld lmt. [] Th rsults hr pont to th vrton of th concntrton of thr dffrnt typs of crrrs. Th obsrvd bhvours r ccountd for qulttvly n trms lctronc bnd structur nd th chng of crrr concntrton wth dffrncs n thr msss (moblty) nd th scttrng mchnsm wth tmprtur. Rfrncs []. J. M. oothovn vn Goor, Donors nd Accptors n Bsmuth, Phlps Rs. Rp.(Suppl.), o.4, 97. []. M. Inou,. Ur nd. Yg, Surfc Scnc, 86, 979, [3]. A. V. Butno, V. Sndomrsy, Y. Schlsngr, Dm. Shvrts, nd V. A. Sool, J. Appl. Phys., 8 (3), 997, DOI:.979/ Pg

7 Mgntc fld dpndnc of lctrcl trnsport proprts n ccptor dopd bsmuth [4]. L. Prr, D. Morn, J. Schnc, J. C. Toldno, J. Prmot, C. Dgut,. Gls, J. trllrd nd. Svry, Sold Stt Commun., 69 (5), 989, [5]. A. Md, T. Yb, S. Tbysh, M. s nd K. Uchmour, Phys. Rv. B, 4, 99, [6]. A. Msu, T. C. Chu, M. S. Drsslhus, nd J. rmns, Phys. Rv. B, 5, 98, [7]. O. S. s-sd nd. D. Mrchnt, J. Lss-Common Mt.,, 984, [8]. J. rmns nd O. P. nsn, J. Phys. C, 6, 983, [9]. rtmn R. (969), Phys. Rv., 8, 969, []. C. Uhr nd W. P. Prtt Jr., J. Phys., 8, 978, []. W. Kr, R. rrmnn, nd. upt, Phys. Sttus Sold (b), 9, 98, []. M.. Cohn, Phys. Rv.,, 96, [3]. S. Goln, Phys. Rv., 66, 968, [4]. A. A. Abrosov, J. Low Tmp. Phys., 8, 97, [5]. R.. Zttr, Phys. Rv., 7, 96, [6]. J. L. Mlgrng, Phys. Sttus Sold, 35, 969, [7].. B. Brndt, Kh. Dttmnn, nd Y. G. Ponomrv,. Tvrd. Tl (Lnngrd) 3, 97, [SOY. Phys. Sold Stt, 3, 97, [8]. W. S. Boyl nd A. D. Brlsford, Phys. Rv.,, 96, [9]. R.. Brown, J. G. Mvrods, nd B. Lx, Phys. Rv., 9, 963, []. B. Abls nd S. Mboom, Phys. Rv.,, 956, []. K. K. Dy, Th Intrntonl Journl of Scnc nd Tchnoldg, 3 (), 5, []. I. M. Lfsht, M. I. Abl, M. I. Kgnov, Sov. Phys. JTP, 4, 957, DOI:.979/ Pg