Modeling and Analysis of Amorphous Si /Crystalline Si Heterojunction Photovoltaic Cells

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1 Molg Alyss of Amorhous S /Crystll S Htrojuto Photoolt Clls by Frz Khlt A thss rst to th Ursty of trloo fulfllmt of th thss rqurmt for th gr of Mstr of Al S ltrl & Comutr grg trloo, Otro, C, Frz Khlt

2 I hrby lr tht I m th sol uthor of ths thss. I uthorz th Ursty of trloo to l ths thss to othr sttutos or uls for th uros of sholrly rsrh Frz Khlt I furthr uthorz th Ursty of trloo to rrou ths thss by hotooyg or by othr ms, totl or rt, t th rqust of othr sttutos or uls for th uros of sholrly rsrh. Frz Khlt

3 h Ursty of trloo rqurs th sgturs of ll rsos usg or hotooyg ths thss. Pls sg blow, g rss t.

4 Akowlgmts I woul lk to thk srly fw ol who ly mortt rol omlshg ths rsrh. Sflly I woul lk to thk Mh Frrokh Brough for hs lubl hl lb sussos through out my rsrh. hs rsrh woul t h b ossbl wthout hs hl. For lb work, I must lso thk Dr. ykumr for hs lubl hls. I woul lso lk to thk Pym Srt for hs tm t swrg my qustos. My sl thks go to Profssor Arok th Profssor Ar Szoo for thr tm rfrg ths work. Flly, I woul lk to t my srst thks to my sursor, Profssor S Soththm who g m h to ursu my stus t grut ll.

5 Abstrt Amorhous/rystll slo -S/-S htrojutos r of rtulr mort hotoolt P rgy orso s thy ro ost-fft wy for solr ll mufturg. h low tmrtur low- tur of th ross llows th us of ft, low qulty h low ost slo substrts, whh b mro by low tmrtur ssto thqus suh s lsm hyrogto tht b rt f th ross tmrturs r kt low < C. Furthr, low- rosss r lso ttrt for ft rystll slo substrts whh grlly h ty to gr wh subjt to multl hgh tmrtur ursos. I ths work, w h lo lytl mols for -S/-S htrojuto solr lls us thos mols for smulto. h rrrs trsort rombto mhsms llumt -S/-S htrojuto s h b fully stu omlt qutos for I- h b r. h -S/-S struturs wr smult for srl sg fturs th trl qutum ffy llumto I- bhour wr lyz. h sf tur of th htrojutos thr ffts o both s I- hrtrsts h b mol through umbr of ftors. h lult ths ftors trms of fft lots whh lmt th rrr flow ross th htrojuto lto rgo. Substrts wth rous surf bulk ssto lls h b osr our smultos. h slo substrts < µm ombto wth low- bulk.g. lsm hyrogto surf.g. lsm slo tr osto ssto shms l to ost fft fbrto ross wth omtt orso ffy. h lso omr our lytl smultos wth umrl smultor AMPS tht s ry grl rstl omutr smulto tool for th lyss of hyss. Our mol, o th othr h sflly trgts th -S/-S htrojuto solr lls. h htrojuto solr ll struturs wth smlr rmtrs r smult by AMPS our mol, th rsults gr ry wll. Flly, w h omr our lytl smulto rsults to rmtl rsults obt from -S/-S htrojuto solr lls fbrt our lbortory. By omrg th smult strl rsos of th to th rmtl urs w wr bl to trt umbr of rmtrs suh s og lls, bulk surf rombto rmtrs.

6 bl of Cotts Abstrt Forwor Outl of th hss Molg Alyss of Homojuto Solr Clls. Molg of Homojuto Solr Clls..... Solr Strum Absorto Cofft... Itrl Qutum ffy: Molg of.. I- Molg of. Smulto of Solr Cll Strutur... Solr Cll...8 Homojuto Solr Cll h -S/-S Htrojuto Strutur 8. Htrojuto: rgy B Strutur Htrojuto: Stt Alyss Isrtg Itrs -S lyr t th Htrojuto Stt Alyss of -S/ -S/ -S Htrostrutur Stt Alyss of -S/ -S/ -S Htrostrutur Crrr rsort Mhsms -S/-S Htrojuto. S Chrg Lmtg Currt SCLC Mult-ulg Cto msso MC hrmo msso Drt ulg hrmo msso Drft-Dffuso h -S/-S Htrojuto Itrf Rombto Currt...4

7 4 Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto 4 4. Molg th hrmo msso loty s Lmtg Ftor for Htrojuto Currt Htrojuto Currt Htrojuto Currt Molg th fft of ulg o th Itrf fft loty of Crrrs Molg th Drft-Dffuso fft loty s Lmtg Ftor for Htrojuto Currt Htrojuto Currt Htrojuto Currt....6 Htrojuto Currt Htrojuto Currt Molg th Itrf Rombto Currt -S/-S htrojuto Itrf Rombto Currt Htrojuto Itrf Rombto Currt Htrojuto otl fft lots s Lmtg Ftors Htrojuto Currt Dlomt of Alytl Mols for -S/-S Htrojuto Solr Clls ur Illumto Alytl Mol for -S/-S Htrojuto Solr Cll r Illumto Mol for th Itrl Qutum ffy Photourrt Mol for th I- Chrtrsts ur Forwr Bs Illumto Alytl Mol for -S/-S Htrojuto Solr Cll r Illumto Mol for th Itrl Qutum ffy Photourrt Mol for th I- Chrtrsts ur Forwr Bs Illumto...97

8 6 Smulto Rsults Alyss of Dlo Mols 6. Smulto Alytl of Htrojuto Solr Cll Itrl Qutum ffy I- Chrtrsts ur Illumto Smulto Alytl of Htrojuto Solr Cll Itrl Qutum ffy I- Chrtrsts ur Illumto Smulto -S/-S Htrojuto Solr Clls Usg AMPS umrl Smultor Comrso wth our Alytl Rsults AMPS Smulto of Htrojuto Solr Clls AMPS Smulto of Htrojuto Solr Clls... 7 h Htrojuto Solr Cll Fbrto Chrtrzto 6 7. h Solr Cll Fbrto h Solr Cll Chrtrzto h rmtl Rsults Coluso 6 Bblogrhy 7

9 Lst of Fgurs. Strl strbuto of th AM.5 solr strum us our mol lulto. Absorto offt of -S us our molg.... Strutur of th.4 homojuto us our molg solr ll trl qutum ffy for, s hrg rgos...5 solr ll trl qutum ffy for ffrt bk surf lots of ltros for log L solr ll trl qutum ffy for ffrt bk surf lots of ltros for short L solr ll trl qutum ffy for ffrt frot surf lots of hols for log L solr ll trl qutum ffy for ffrt frot surf lots of hols for short L....9 solr ll trl qutum ffy for ffrt ffuso lgths of bulk...4. I- grm of. I- grm of solr ll solr ll for ffrt bulk ffuso lgths rgy b grm of htrojuto for C, >, wth o hysl ott btw lyrs...9. rgy b grm of htrojuto hysl ott.... rgy b grm of htrojuto 6.4 rgy b grm of htrojuto..9. Currt sty oltg hrtrst of -S:H/ -S o msur t room tmrtur MC mol for htrojuto...6

10 . ltro trsort or th ottl brrr..7.4 fft hol lots for IAlAs/IGAs P HB s futo of mttr-bs bs B for th s of o omostol bs grg ltro flus htrojuto Hol flus htrojuto.5 4. Itrf fft loty of hols wth wthout tulg Multlt ftor to trf fft loty us to mol th rt tulg our lultos htrojuto solr ll htrojuto solr ll ll strutur us to lo th lytl mol S/-S htrojuto solr ll rgy b grm ll strutur us to lo th lytl mol S/-S htrojuto solr ll rgy b grm otl trl qutum ffy of solr ll Itrl qutum ffy of SCR, -rgo th whol solr ll fft of ffuso lgth bulk o solr ll qutum ffy solr ll trl qutum ffy of thkr, mort qulty bs rgo showg o sstty to surf ssto solr ll trl qutum ffy of thr, mort qulty bs rgo showg rs sstty to surf ssto solr ll qutum ffy of SCR for ffrt trs lyr wths otl qutum ffy of th solr ll for ffrt trs lyr wths 7

11 6.8 I- grh of solr ll for ffrt trs lyr wths I- grh of solr ll wth wr trs lyrs I- grh of solr ll for ffrt og lls 6. I- grh of solr ll for ffrt bult oltgs Itrl qutum ffy of solr ll for ffrt rgos 6. fft of ffuso lgth bulk o solr ll qutum ffy 6.4 solr ll qutum ffy hg u to hg bk surf rombto loty s solr ll qutum ffy hg u to hg frot surf rombto loty s solr ll qutum ffy of SCR for ffrt trs lyr wths otl qutum ffy of th solr ll for ffrt trs lyr wths I- grh of solr ll I- grh of solr ll for ffrt trs lyr wths.7 6. I- grh of solr ll for ffrt og lls otl trl qutum ffy of solr ll AMPS & our mol I- grh of solr ll for ffrt trs lyr wths AMPS Comrso btw AMPS our mol I- rsults of solr ll for 5m Comrso btw AMPS our mol I- rsults of solr ll for 5m wth hghr ffuso lgth bulk L µ m...

12 6.5 AMPS rsult of I- grh of solr ll for ffrt og lls AMPS otl trl qutum ffy of solr ll AMPS & our mol otl trl qutum ffy of solr ll AMPS & our mol wth hghr ffuso lgth bulk L 5µ m I- grh of solr ll for ffrt trs lyr wths AMPS Comrso btw AMPS our mol I- rsult of solr ll for 5m h strutur of htrojuto solr ll h lyout us solr ll fbrto 8 7. Blok grm of th msurg systm for qutum ffy rmtl t for trl Q our mol rsult for trl Q of solr ll Rfrt of -S, -S IO Clult totl rflt of thr lyrs solr ll. 7.7 Itrl trl qutum ffy of th fbrt solr ll Itrl qutum ffs of : mol rmt...4

13 Lst of bls. s, o FF of. s, o FF of. s, o FF of solr ll for ffrt L...6 solr ll for ffrt s...6 solr ll for ffrt s s, o FF of 6. s, o FF of 6. s, o FF of solr ll for ffrt solr ll for wr solr ll for ffrt Pross squ..7

14 Forwor Forwor S th solr ll ws t, th rystll slo hs b us ormously s lght-bsorbg smoutor fbrtg most of solr lls. It orts th hotos wth th rgy of th bg wth goo ffy. Howr, th hotos wth lowr rgy r ot bsorb thos wth hghr rgy r ru to g rgy by thrmlzto of th hotogrt rrrs []. Prstly two tys of -S r us roug th solr ll; moorystll multrystll. h moorystll s rou by slg wfrs from hgh-urty sgl rystl wfr. h so s m by swg st blok of slo frst to brs th wfrs. Slo s rt smoutor th lght bsorto s wkr rt smoutor th rt smoutor. hs rsults hgh bsorto lgth, so tht for 9% of lght bsorto, t tks oly µm of GAs rt smoutor rsus µm of S []. hrfor, th hotogrt rrrs S h to trl log wy to rh th - juto tht s so los to th frot surf. hs ms tht th morty rrrs ffuso lgth shoul b t lst tw th slo wfr thkss to h goo mout of lght bsorto. Hgh rrrs ffuso lgth ms tht th mtrl shoul b of ry hgh urty qulty. Howr, th thkr ll rqurs mor mtrls to b us fbrtg of solr ll whh uss hghr ost. h rso tht slo hs b us ormously solr ll ustry, bss th goo ffy 4% to 7%, s tht slo thology hs lry b wll lo bfor th to of th solr ll thrfor hgh qulty mtrls h b rou for th mroltro mrkt. Howr, u to th ost ssus ssot wth solr lls, th ustry hs lry strt lookg for othr mtrls s rlmt for slo. h rqurmts for th l solr ll r []: - bg btw..7 - rt b strutur - osstg of rly lbl, o-to mtrls - sy, rroubl osto thqu, sutbl for lrg r routo

15 Forwor - goo hotoolt orso ffy - log-trm stblty h ltrt solr ll struturs r: rystll th-flm slo, morhous slo, morhous slo/rystll slo htrojuto, or um sl mum tllur. Crystll th-flm slo h rystll th-flm slo s osr bus of th fwr mouts of mtrl us osqutly th lowr ost. h th-lyr slo rfrs to th slo lyrs wth th thkss of btw 5µm 5µm. Bus of ry th -S, urlyg substrt s s mhl suort for th th -S lyr. h ty of substrt tht b low qulty slo, glss, rm or grht trms th mmum tmrtur llow for th solr ll rossg. hrfor, thr b thr hgh tmrtur or low tmrtur ross for th-flm -S. hr r fw ots thology for rystll th-flm slo tht s osrto []: - Bus of th wk bsorb of th rystll, th lght trg must b us to h th hgh gr of lght trl rflto. - Rgrg th ry low thkss of th slo, th hgh surf rombto loty ru th ll ffy ry rstlly. hrfor, th frot bk surfs shoul b sst to o t. - If o-outg trmt lyrs or substrts r us, both th mttr th bs otts h to b form o th frot s. - For th solr ll formto, th lyrs r ost t ffrt tmrturs so th ul lyr tmrturs s wll s th totl thrml bugt r rul rmtrs for sussful mufturg of -S th solr lls.

16 Forwor Amorhous slo Amorhous slo s lloy of slo wth hyrog. Bus of th sorr of th tom strutur, t s qut ffrt from th rystll slo. h struturl sorr lso flus th ltro rorts of th mtrl srl wys. hs mks ffrs btw th -S -S struturs thrfor th rsrhrs f w ots stuyg th rorts of th -S suh s: b tls, lolzto sttrg, m-g stts t. Howr, morhous slo bsorbs solr rto 4 tms mor fftly th os sglrystl slo, so flm oly bout µm thk bsorb 9% of th usbl solr rgy. As mortt rsult, th ottl ost s sgftly low. h low tmrtur ross tht s us to rou -S s othr ftor tht mks t rsobl to b us solr ll ustry. Although th morhous slo bfts th low ost solr ll fbrto but th low ffy 8% obt so fr s wk ot of t. -S/-S htrojutos Combg th -S -S s htrojuto solr ll gs th oortuty to h hgh ottl of mtg th urrt ollto tgs offr by th rystll slo, whl t th sm tm, offrg low tmrtur-rossg shm th htrojuto formto, thrby og th hgh thrml bugt of - homojuto formto. Bus of ost-fft P fbrto, -S/-S htrojuto thology hs bom ry ttrt solr ll ustry. Bus th ross tht hs b us for ths fbrto s sstlly low- ross <5ºC, thr s ossblty to us rt mort qulty Slo substrts.g. rbbos whos bulk rrr lftm grs ftr hgh- thrml ursos. Furthr, th low- tur of th ross llows bulk ft ssto thqus suh s lsm hyrogto to b mlmt ror to fbrto. h tgs of ths strutur b summrz s follows []: - hgh ffy >% - ry goo surf ssto: low surf rombto loty - low rossg tmrtur - ru ost of ll thology

17 Forwor Cor um sl hs thology tht s bs o th trry omou smoutors CuIS, CuGS, CuIS thr multry lloy Cu I, G S, S ws trmly romsg t frst but th omlty of th mtrl omlts th-flm thology mlmttos. ry hgh ffs 9% h b rort for lbortory sl s. hs rsult hs b obt by ths mtrl systm by mrl otmzto of ross rmtrs. Howr, furthr hllg s to mk hgh oltg s o th bss of th trry hloyrt omous CuIS CuGS. h ffy h wth ths w rgy g mtrls s stll osrbly lowr th tht of th low g Cu I, G S []. Flly, or um sl s ot yt ommrl sgft furthr rsrh s to urst th mufturg rosss. Cmum tllur C s rly l mtrl for th-flm hotoolts bus t ombs srl tgous rorts. Although th hghst ffy tht hs b h by ths mtrl lbortory s 6% but th ommrl moul ffs hor rou 6%. It hs otl bg los to th otmum for solr rgy orso. It s lso sy to hl th-flm osto rosss. A roblm ssot wth C s th ft tht C r to mtrls lthough th omou s qut stbl hrmlss. hs mks t hr to b t by th mrkt []. I ths work w h tk u th -S/-S solr ll strutur for our rsrh. hs strutur hs hgh ottl for ost ruto fbrto s t us low qulty ft substrts whr hgh tmrtur rosss ot b l. h rto of th rsrh t Ursty of trloo s to lo thologs to h ost-fftss, ot to h hgh ffs t y ost.

18 Outl of th hss Outl of hss I htr, w h rst our lytl molg smulto rsults of homojuto solr ll. h suss smult th qutum ffy th hotourrt of th homojuto solr ll, roug th qutum ffy I- urs of th ll for ffrt qults of bulk, frot rr surf of th. I htr, w h suss th strutur of htrojutos grl rtulrly h fous o th -S/-S htrojuto strutur. h lult th qutos of th bult oltg, th wths of s hrg rgo th mout of ro oltg or - -s of th lug th trs -S lyr for both -S/-S htrojutos. I htr, w h or ffrt rrr trsort mhsms htrojutos lug SCLC, MC rft-ffuso msso ltrlly h suss th trsort mhsms tht w h hos to us our molg. I htr 4, w h mol two trsort mhsms rft-ffuso msso s two fft lots of rrrs trf fft loty rftffuso fft loty whh lmt th rrrs flow through th htrojuto. h lso lult th fft lots for th s tht trs lyr of morhous slo s srt t th htrojuto. h rt tulg hs lso b mol whl molg th thrmo msso mhsm. I htr 5, w h lo lytl mol for -S/-S htrojuto solr lls ur llumto lso ur forwr bs. h lult th qutum ffy of th lls s wll s th hotourrt lo th omlt I- urs ur forwr bs llumto, osrg th lowrg ftors of urrt rt tulg.

19 Outl of th hss I htr 6, w h suss th rsults tht w h obt by usg our lytl mol for both -S/-S htrojuto solr lls. h us AMPS softwr to smult th rsults wth th os tht w h obt form our mol. I htr 7, w h us th htrojuto solr lls h omr htrojuto lls fbrt our lbortory to lyz omr wth our lytl mol. By justg th lytl mol to ft wth th rmtl ur, w wr bl to trt mortt rmtrs for th rmtl.

20 Chtr : Molg Alyss of Homojuto Solr Clls Chtr Molg Alyss of Homojuto Solr Clls Followg th to of - juto 949, th ot of th hotoolts strt turg to rlty 954, Prso sor th rystll S solr ll []. Solr ll orts th t solr rto rgy to ltrl rgy s th most mortt logurto owr suly for stllts s hls []. owys thr s w rg of ltos for solr lls ly lf. hy rg from lultors wrstwths to solr owr rrgto systms gr-ot owr ls. I ths htr, w h mol homojuto solr ll lytlly h rt th smulto rsults. o o so, w h suss th orto of homojuto solr ll mor tls. h osr th qutum ffy th hotourrt of th homojuto solr lls sto. sto., w h us our mol to smult th solr ll, roug th qutum ffy I- urs of th ll for ffrt qults of bulk, frot rr surf of th solr ll.. Molg of Homojuto Solr Clls.. Solr Strum Absorto Cofft Solr Strum h ulr fuso su rts hug mout of rt rgy by rt of 4 r so. hs rt rgy tht s mtt s ltromgt rto th ultrolt to frr ro strl rgos. to µm s ttut by th rth tmoshr uo rhg th rth s surf. hs s bus of wtr-our bsorto th frr, ozo

21 Chtr : Molg Alyss of Homojuto Solr Clls bsorto th ultrolt, sttrg by rbor ust rosols.[] h wy whh th tmoshr ffts th sulght s msur by th r mss tht s f s follows: - Ar mss: h gr to whh th tmoshr ffts th sulght r t th rth surf. It s st of th gl btw th su th zth, msurs th tmoshr th lgth rlt to th mmum th lgth wh th su s rtly orh.[] - Ar mss.5: su t 48 9 to zth [4] rrsts stsftory rgy-wght rg for trrstrl ltos.[] Fgur. shows th solr strum owr r ut r r ut wlgth for AM.5 tht w h us our molg. h t for ths ur hs b tk from [5]. Solr Strl joul/m^.m lgth m Fg. Strl strbuto of th AM.5 solr strum us our mol lulto [5] Absorto Cofft It hotos wth rgy mor th bg rgy of th llumtg, bom bsorb gltg th rflto s thy trl through th smoutor, th lght tsty, whh s roortol to th umbr of hotos, ys otlly wth

22 Chtr : Molg Alyss of Homojuto Solr Clls st to th smoutor. h lght tsty, I, t st from th smoutor surf s g by: [] I I. whr I s th tsty of th t rto s th bsorto offt ut:/m tht s o th hoto rgy or wlgth. lso s o mtrl rorts [6]. /m Log Sl lgth m Fg. Absorto offt of -S us our molg [5] Fgur. shows th bsorto offt of rystll slo tht w h us our molg [5]. s from th fgur tht th hotos wth short wlgth r bsorb ry short st of th ll surf whl th log wlgth hotos wll h to otu trlg log th utl thy r bsorb. It s lr tht th bsorto offt hs mortt rol lultg th qutum ffy of th solr ll. hrfor, hoosg th urt t wll hl obt mor urt smulto rsults... Itrl Qutum ffy: Molg of th Solr Cll Strutur h solr ll s llumt by sulght, hoto wth rgy lss th solr ll bg os ot otrbut to th hotourrt of solr ll. Howr, hoto wth rgy grtr th solr ll bg wll rt ltro-hol r. h qutum ffy s

23 Chtr : Molg Alyss of Homojuto Solr Clls f s th rto of ltro-hol rs ollt wth rst to th umbr of t hotos: - trl qutum ffy: umbr of rrrs ollt r t hoto t h wlgth - Itrl qutum ffy: umbr of rrrs ollt r bsorb hoto t h wlgth By lultg th trl qutum ffy for rg of wlgths, o obt th totl urrt grt by lght hotourrt th whol wlgths rg. h qutum ffy s o th bsorto offt, rrrs lftm, th surf rombto loty th gomtry of th. utrl -rgo Drft utrl -rgo Dffuso Log λ Mum λ L h h Short λ h L l SCR Fg. Strutur of th homojuto us our molg Fgur. shows shmt grm of tyl solr ll. h ll s form by ry th hly o -rgo mttr wth th thkss of thk lss o -rgo bs wth th thkss of. h llumto s through -rgo wow. h s hrg 4

24 Chtr : Molg Alyss of Homojuto Solr Clls rgo SCR wth th thkss of l s rmrly to -s whh s lss o thr s ltr fl s SCR whh lts t from th fr rrrs lto rgo. L L r th ffuso lgth of th ltros hols rstly. h fgur shows tht th ltros hols grt -s -s wth ffuso lgth from th g of SCR, ffus to SCR th rft to -rgo -rgo. Most of th hotos r bsorb wth SCR or -rgo. hs s bus th -rgo s so th hly o. h hotos bsorb wth SCR wll grt ltro-hol rs HPs. hs HPs wll b swt mmtly towr th -rgos. h ltr fl s th SCR s rsosbl for swg th ltros hols towr -rgos rstly. O th ltros hols rh -rgo, thy r ollt by rombg wth th mjorty oultos. hs sro wth th -rgos s somhow ffrt. For ml, wh HP s grt -rgo, th hols ltros ths rgo r mjorty rrrs, so thy h lry b ollt by bg -rgo. O th othr h, ltros hols -rgo r morty rrrs. hrfor, thy wll ffus towr th -rgo SCR trf, whr th oulto of morty rrs r so low. As soo s th ltros hols rh ths trf, th ltr fl s SCR wll sw thm to th oost s,.. -rgo. hs ms tht th rrrs tht w shoul osr lulto of qutum ffy r: - th HPs grt SCR - ltros grt -rgo ffus to th -rgo SCR trf - hols grt -rgo ffus to th -rgo SCR trf S Chrg Rgo Qutum ffy Du to th hgh ltr fl lto rgo, ll th hoto-grt rrrs ths rgo wll b ollt. hs ms tht w ssum thr s o rombto SCR whtr s grt wll rtt formg th hotourrt of ths rgo. Usg th grto quto. ssumg tht thr s oly moohrom t lght to th surf of th, lso ssumg tht ll th hoto-grt rrrs r ollt SCR, w wrt: 5

25 Chtr : Molg Alyss of Homojuto Solr Clls SCR l q G q q[ ] q[ ]. hs ms tht SCR wll lu both hol ltro hoto-grt rrrs. -rgo Qutum ffy As suss rous stos, -rgo Fgur., th rrrs rsosbl for hotourrt r th morty rrrs,.. th ltros. S -rgo thr s o ltr fl, th ffuso urrt wll t s th m strm of rrrs two sstl rosss wll fft ths urrt: Crrr Grto Rombto. h grto rt f HPs t st from th smoutor surf s g by: [] G λ F λ λ. whr λ s th bsorto offt Fλ s th umbr of t hotos/ m /s r ut bwth. I s of o rgo, th rombto rt of rrrs wll b th rto of ss rrr otrto morty rrrs grt by lght, or th morty rrrs lftm τ : [] R.4 τ sol th qutos for sgl hoto of moohrom t lght. strt wth otuty quto for ltros -rgo rgrg th ft tht w osr th sty stt, tm ftor wll ot r our qutos: [] G R.5 q Aorg to Fgur., th boury otos r:.6 6

26 Chtr : Molg Alyss of Homojuto Solr Clls whh ms th ltros wll b swt by ltr fl s soo s thy rh th SCR borr : D s.7 tg tht th rombto rt t th bk surf must b qul to th flu of morty rrrs flowg to th surf th rombto rt of morty rrrs t th bk surf s show by th surf rombto loty, s Du to zro ltr fl ths rgo, thr wll oly b ffuso urrt []: qd.8 whr D s th rrr ffuso offt tht s ssot wth moblty: D µ. kow tht:.9 By ombg th qutos.,.4,.5,.8.9, w wll h: L. whr L s ffuso lgth of morty rrrs ltros s f by: L τ. D h grl soluto to ths so orr ffrtl quto s: L L L. D L wt to lult th ffuso urrt t : D D. By substtutg quto.. rgrg th boury otos quto.6.7, w rh th followg quto for ltro hotourrt -rgo, grt by o hoto of moohrom lght: 7

27 Chtr : Molg Alyss of Homojuto Solr Clls 8 l L L Sh L s L Cosh L s L L Sh L Cosh L s L L q τ τ τ.4 It shoul b ot tht th rsso l rflts th ft tht th lght tsty hs b ru by ths ftor wh t rhs. wll ro th sm rour to lult th hol hotourrt grt -rgo. -rgo Qutum ffy I ths s th boury otos r Fgur.:.5 s D.6 s ts th rombto rt of morty rrrs t th frot surf or th surf rombto loty h urrt for ltros t wll b: ]. [ L Sh L s L Cosh L Sh L Cosh L s L L L L q τ τ.7.. I- Molg of Solr Cll By lultg th trl qutum ffy of h rgo solr ll of Fgur., w lult th hotourrt of th. h hotourrt tht s lso ll

28 Chtr : Molg Alyss of Homojuto Solr Clls short rut urrt s obt wh thr s o l oltg o solr ll. h mgtu of hotourrt, srgrg ll th losss th ll, wth AM.5 rto, rh k of 44mA / m [7]. o lult th hotourrt, w to kow th hoto flu of sulght. hs b lult from th rgy strbuto of sulght solr strum, Fgur.4 by g th rgy ott t g wlgth by th rgy of ul hoto [8]. Suos tht w h th t of th flow of th rgy r ut r t g wlgth. h rgy of hc sgl hoto s g by: h whr C s th s of lght, h th Plk s ostt λ λ th wlgth of lght. h umbr of hotos for g rgy of sulght s obt by: [ ] [ m ][ m] whh gs th umbr of hotos r ut r t [ ][ s][ m]/[ s] h [ m ][ m] m g wlgth. By tgrtg ths strbutos or th wlgth rg for whh th ltro-hol rs b grt for g smoutor, th hotourrt wll b lult. S th t us for our work r srt umrl, th tgrl wll b rl by sgm st of λ w wll ut λ whh for our t s:. [5]. 9 h λ λ whr λ m λ 9 m. If w ly forwr bs to th solr ll, rk urrt wll flow through th rto oost to th hotourrt. hs s bus of th ft tht th rto of ltr fl SCR s from -s to -s u to th lto whl th forwr oltg s l from -s to th -s. h th rk urrt flows through th ll, t omsts th hotogrt urrt. As w wll s ltr ths htr, ths rsults th I- ur of th shftg owwr by th mout of th hotourrt. 9

29 Chtr : Molg Alyss of Homojuto Solr Clls. Smulto of Homojuto Solr Cll ow by hg th qutos.,.4.7 for qutum ffs of SCR, - -rgo, w rw th totl qutum ffy of th solr ll show Fgur.. Fgur.7 shows th trl qutum ffy grms of solr ll for, s hrg rgos. h sml ll for ths smulto hs b hos s th followg: 9 m 6 m, m µ 8 µ. s L. m L 5m, s s m s / m 7. s Qutum ffy Q -rgo Q -rgo Q SCR Q totl lgth m Fg.4 solr ll trl qutum ffy for, s hrg rgos Rgrg th sz of tht w h hos, th wths of th rgos r: rgo 5m rgo 49.4µ m SCR 59m As suss rlr, th frot rr surf rombto lots h mortt rols solr ll hotourrt. Howr, th flu of ths rmtrs o th ll ffy s o th ffuso lgths of th rrrs. For st, wh th ffuso lgth of th ltros -rgo L s omrbl to th wth of th mttr -rgo, th th bk

30 Chtr : Molg Alyss of Homojuto Solr Clls surf loty s whh b hg by ssto thqus wll ly mjor rol th solr ll hotourrt. h rso s tht ths s, th ss morty rrrs wll rh th bk surf of th bfor thy romb thrfor, th rt of thr rombto th bk surf wll ftly flu th umbr of ollt rrrs. Fgur.5 Qutum ffy L µm 49.4µm s m / s s m / s s 4 m / s s 6 m / s lgth m Fg.5 solr ll trl qutum ffy for ffrt bk surf lots of ltros for log L Howr, f th ffuso lgth of ltros s muh shortr th th mttr wth, ths ms tht th ltros wll romb bfor thy rh th bk surf osqutly, th bk surf rombto loty ot fft th ltro hotogrt urrt Fgur.6.

31 Chtr : Molg Alyss of Homojuto Solr Clls Qutum ffy L µm 49.4µm s m / s s m / s s 4 m / s s 6 m / s lgth m Fg.6 solr ll trl qutum ffy for ffrt bk surf lots of ltros for short L Qutum ffy L 5m 5m s m / s s m / s s 4 m / s s 6 m / s lgth m Fg.7 solr ll trl qutum ffy for ffrt frot surf lots of hols for log L

32 Chtr : Molg Alyss of Homojuto Solr Clls Qutum ffy L 5m 5m s m / s s m / s s 4 m / s s 6 m / s lgth m Fg.8 solr ll trl qutum ffy for ffrt frot surf lots of hols for short L Fgurs.7.8 show th qutum ffy of th ll for ffrt frot surf rombto lots s for log short ffuso lgth of hols -rgo rstly. As w s from th fgurs, for log ffuso lgths, th frot rombto loty fft th qutum ffy sgftly Fgur.7 whl s of short ffuso lgths, th qutum ffy s lmost o-sst to th frot surf rombto loty of hols Fgur.8. As w suss rlr, th ffuso lgth of morty rrrs th bulk s o th qulty of th to to th og ll. Fgur.9 shows how ths rmtr mks th totl qutum ffy of th solr ll to hg.

33 Chtr : Molg Alyss of Homojuto Solr Clls Qutum ffy µm lgth m L µm L 5µm L µm L 5µm L µm L 5µm L µm Fg.9 solr ll trl qutum ffy for ffrt ffuso lgths of bulk As t s s from th fgur, th hghr ffuso lgth of morty rrrs th bulk, whh ms th bttr qulty of th mtrl, wll ro hghr qutum ffy. 5 s Currt Dsty ma/m^ Forwr oltg o Fg. I- grm of solr ll 4

34 Chtr : Molg Alyss of Homojuto Solr Clls Usg th rour tht w suss sto.., w h lult lott th I- ur of th solr ll wth th rmtrs t. show Fgur.. hs fgur shows th short rut urrt s o rut oltg o of th solr ll. h short rut urrt, s w suss sto.., s obt wh thr s o oltg t th ll th o rut oltg s obt wh o urrt s rw from th solr ll. For Fgur. h obt: s 5. 88mA o 587. m lult th oltg urrt of th ll t th otml ortg ot, I m m, obt th k outut, m I m. h rto of k outut to th rbl I s o s ll th fll ftor FF of th ll: I m m FF.8 oi s rl I m I s by m s, rstly: FF m o m s % As w sw rlr, th qulty of th bulk rgo ffts th qutum ffy of th solr ll. Fgur. shows tht t ffts th I- ur of th s wll. Currt Dsty ma/m^ Forwr oltg L 5µm L µ m Fg. I- grm of solr ll for ffrt bulk ffuso lgths 5

35 Chtr : Molg Alyss of Homojuto Solr Clls s from th bl. tht by rsg th ffuso lgth of th ltros th bulk rgo from5 µ m to6 µ m, th short rut urrt o rut oltg rs from. m ma /.5m 54 to 5.88 m ma/.m 587, rstly. L m ma/ m s o m FF % % % % % % b. s, o FF of solr ll for ffrt L bls.. show how th short rut urrt, o rut oltg FF of solr ll hg wth th hgs of th bk surf frot surf rombto lots of th morty rrrs. s m / s,[ s ] ma/ m s o m FF % % % % b. s, o FF of solr ll for ffrt s 6

36 Chtr : Molg Alyss of Homojuto Solr Clls bl. shows tht th hg o rr surf rombto loty ffts th short rut urrt o rut oltg. It shows tht by rsg th s, th short rut urrt rss osqutly th o rut oltg rss s wll. I ft, bus th hotogrt rrrs th mttr rry out th mjor otrbuto to th hotourrt of th solr ll, y hg o ths rt wll fft th I-. s m / s,[ s ] ma/ m s o m FF % % % % b. s, o FF of solr ll for ffrt s bl. shows th fft of rsg th frot surf rombto loty o th o rut oltg short rut urrt. As w s, both o s. s rs by rsg 7

37 Chtr : h -S/-S Htrojuto Strutur Chtr h -S/-S Htrojuto Strutur I ths htr, w h suss th strutur of htrojutos grl rtulrly h fous o th -S/-S htrojuto strutur. h lult th qutos of th bult oltg, th wths of s hrg rgo th mout of ro oltg or -s of th. o r ths qutos, w h us th Posso s quto for ffrt rts of th SCR. I stos.., w h lult th bo-mto qutos for - S/-S htrojuto. As w h suss sto., solr ll ltos, ultr th trs lyr of morhous slo s trou through th juto. h rlult ll th qutos for -S/-S htrojuto s wll s for th -S/-S htrojuto stos..., rstly. h us ths qutos molg smulto of th -S/-S htrojuto solr lls t htrs. Is -S/-S htrojuto? A htrojuto s juto btw two ssmlr smoutors wth ffrt bgs. h juto s ll th soty htrojuto f two s h th sm outty t wll b soty htrojuto f th outts of two mtrls osttutg th r ffrt []. Although morhous rystll slo r ot omltly ffrt smoutors, th juto btw ths two s osr s soty htrojuto s th bg of morhous slo s ffrt from tht of th rystll slo, to to th ft tht th outty of ths two smoutors ffr. It s lso romt tht th -S/-S htrojuto b osr s brut htrojuto [9]. 8

38 Chtr : h -S/-S Htrojuto Strutur. Htrojuto: rgy B Strutur h w form htrojuto by uttg two mtrls wth ffrt bgs bs h othr, rgrg th ffr ltro ffty bg of th s, two tys of htrojutos b lu b form []: - I frst ty whh lus 8% of htrojutos, C sotuty outo b ost: sotuty l b tht r r from th followg qutos, r both. C C C X X g g C. whr X, X, r th ltro ffty th bg of mtrl, g g rstly. o k C ost, w shoul h > > C C rstly s Fgur.. hs ms tht th mtrl hs bggr bg th th mtrl. uum Ll X Φ ltro Affty Φ X ork Futo C F C g F g Bg -lyr -lyr Fg. rgy b grm of htrojuto for C, >, wth o hysl ott btw lyrs 9

39 Chtr : h -S/-S Htrojuto Strutur - I th so ty, w h: thr C or s grtr th g whh ms tht thr C or s gt: If C X X > g th < or If C X X < th > g. q b Φ X X Φ C C q P C q F Fg. rgy b grm of htrojuto hysl ott I our stuy, mtrl s morhous slo mtrl s rystll slo. hs ls us to th followg stuto: g. X 4. 5 [] g. 7 X. 8 [9] g. 6

40 Chtr : h -S/-S Htrojuto Strutur X X X X. 5 C C C < g thrfor > g C hs ms tht for -S/-S htrojuto whh s our s, both C wll h ost lus osqutly for - -S/-S htrojuto w wll h b grm lk Fgur.. As w s from th fgur, C r th ottl brrrs l outo b tht, s w wll suss ltr, fft th rrr trsort th. Htrojuto: Stt Alyss As t b s from Fgur., th htrojuto s ssum to b brut. hs s wht w h lry ssum bout th -S/-S htrojuto. hs ms tht thr s brut hg th b grm of th htrojuto t th ot of mtllurgl juto. lk to lult th bult oltg b, th oltg ro or - -s lso th wth of th lto rgo. As w kow from th - homojuto, th bult oltg s qul to th ffr btw th work futos of th - -s.., Φ Φ.It s lso qul to th oltg ro o both rgos.., hrfor, w wrt: q Φ Φ q. q b b C X C F X C F Φ Φ q q.4 q q F g F g l.5 C F l.6 P.

41 Chtr : h -S/-S Htrojuto Strutur so for bult oltg w wrt: q b X X g l l C g l b C g l.7 q q whr r th fft sts of rgy stts r ut olum for hols ltro mtrl rstly -ty mtrl mtrls rstly. r th og lls of -ty mtrl I orr to lult th lto rgo wth w h to strt wth ltr hrg quto: ρ q for < <.8 ρ q for < <.9 For < < w wrt th Posso s quto suh: for q q > for < <. ε ε < < : q q > ε ε. Although th ltr ostts for mtrl εε r ffrt but bus of th otuty of th ltr tor D, th boury oto t gs tht: D D ε ε. whh ls us to. Rgrg th rlto btw ltr fl oltg:.4 lult th oltg for ry trl:

42 Chtr : h -S/-S Htrojuto Strutur < q ε q ε q ε < < < < b <.5 From quto.5 w wrt: q q.6 ε ε q q q q.7 ε ε ε ε b q q.8 ε ε Usg quto. by substtutg.8: b q q > ε ε q q ε ε ε ε b.9 q ε ε rstly for : ε ε b. q ε ε

43 Chtr : h -S/-S Htrojuto Strutur A quk look t th lult rltos so fr hls us rogz th wy w rh th lus of b, P. From quto.7 w lult b th by substtutg t.9., wll b obt. hrfor, w lult th lus of qutos.6.7 rstly. P by usg I s of htrojuto, th roh for ll th lulto s th sm w wll f th followg qutos for th rmtrs: b g C l. q q ε ε b. q ε ε ε ε b. q ε ε q.4 ε q.5 ε b q q.6 ε ε. Isrtg Itrs -S Lyr t th Htrojuto Bus of th hrtrsts of th morhous slo, th - -S/-S htrojuto solr ll hs lowr fll ftor o rut oltg omrso to th - homojuto - S solr ll. h stus show [] tht th rombto ross th SCR whr th 4

44 Chtr : h -S/-S Htrojuto Strutur htrojuto s lot b th rso for ths oor rorts. I ft, th rombto tht hs t th -S -S trf s bus of hgh sty of m-g stts th morhous slo. h hgh sty of tr trs -S lso rss th lkg urrt u to tulg ross []. hrfor, to mro th ffy of th -S/-S htrojuto solr ll, th qulty of th htrotrf s ry rul. o surss th trf rombto, ry th trs -S lyr s srt t th -S/-S htrojuto. I orr to srt th -lyr th -S/-S htrojuto, goo ssto t th -S surf s ssry. Bus th tr sty of trs morhous slo s sgftly smllr th tht of o lyr, srtg th lyr of t rus th surf rombto s wll s th lkg urrt. hs rsults hghr o rut oltg short rut urrt. Hghr ffy s th m rso for th htrojuto solr ll fbrtors to trou th -lyr th htrojuto. Howr, g trs morhous slo lyr ffts th lto rgo wth th wy tht th bult oltg s btw SCR rgos. As w wll suss ltr, t lso ffts th trsort of th rrrs flowg through th - lyr by lmtg thr fft lots... Stt Alyss of th -S/ -S/ -S Htrostrutur h quto of bult oltg of htrojuto s smlr to of th htrojuto wthout trs lyr. For th htrojuto Fgur., w wrt: q Φ Φ q.7 b q b X C F X C F Φ Φ q q.8 q q C F g F g l.9 C F l. 5

45 Chtr : h -S/-S Htrojuto Strutur C F C q q P q C P 4 Fg. rgy b grm of htrojuto So for bult oltg w wrt: q b X X g l l C g l b C g l. q q whr r th fft sts of rgy stts r ut olum for hols ltro mtrl rstly -ty mtrl mtrls rstly. r th og lls of -ty mtrl to h th ltr fl qutos for ffrt rgos for Posso s quto, 6

46 Chtr : h -S/-S Htrojuto Strutur < ρ q < < < < 4 q < < > 4. Usg Guss lw: ε ρ < thus q ε < < < < q ε < < 4 > 4. q ε q ε < < < <.4 Boury otos g: ε ε.5 h:.6 q < < 4 ε 4 As bfor, w obt th oltg qutos: 7

47 Chtr : h -S/-S Htrojuto Strutur 8 ow w lult th oltg ros ross, rgos: q ε.8 4 q ε.9 q ε.4 b q q q ε ε ε.4 Usg w rh: b q q q ε ε ε whh gs us: ε ε ε ε ε ε b q.4 osqutly ε ε ε ε ε ε b q.4 q ε < < q q ε ε < < q q q ε ε ε 4 < <.7

48 Chtr : h -S/-S Htrojuto Strutur whr th subsrt sts for -rgo -S for, -rgo -S. hs qutos lt us lult th s hrg rgo wth o th - -s s wll s th oltg ro or, trs lyr by hg th wth of th trs lyr,... Stt Alyss of th -S/ -S/ -S Htrostrutur Fgur.4. wll rt th sm sro to lult th qutos for htrojuto X q b C Φ q q C Φ X C F q 4 Fg.4 rgy b grm of htrojuto 9

49 Chtr : h -S/-S Htrojuto Strutur q Φ Φ q.44 q b b C X C F X C F Φ Φ q q.45 q q F g F g l.46 C F l.47 so for bult oltg w wrt: qb X X g l l C g C l g b l.48 q q whr r th fft sts of rgy stts r ut olum for ltros hols mtrl rstly r th og lls of -ty mtrl -ty mtrl mtrls rstly. I orr to us th Posso s quto, w to h th ltr fl qutos: < < < q ρ < < q < < 4 > 4.49 Usg Guss lw:

50 Chtr : h -S/-S Htrojuto Strutur < q ε < < < < q ε < < 4.5 > 4 Itgrtg quto.5, w obt: q ε < < q ε < <.5 q ε 4 < < 4 Usg boury otos: ε ε.5 w h:.5 Also usg quto.5, w wll h: q ε < < q ε q < < ε.54 q ε q q < < 4 ε ε

51 Chtr : h -S/-S Htrojuto Strutur osqutly: 4 q ε.55 q ε.56 q ε.57 b q q q ε ε ε.58 Usg quto.5 by substtutg t.58, w obt: b q q q ε ε ε whh ls us to th followg: ε ε ε ε ε ε b q.59 osqutly: ε ε ε ε ε ε b q.6 hr th subsrt sts for -rgo -S for -rgo -S.

52 Chtr : Crrr rsort Mhsms -S/-S Htrojuto Chtr Crrr rsort Mhsms -S/-S Htrojuto h -S/-S htrojuto brgs w ots rrr trsort mhsm bus th thory of jto homojutos fls to out th bhour of th rrrs us by htrojuto rorts. Durg st two s, fw thors h b roos to l th trsort of rrrs htrojutos. I ths htr, w h or ths thors ltrlly h tlk bout th trsort mhsms tht w h hos to us our molg. Frst, sto., w h suss SCLC s hrg lmt urrt h tlk bout th rsos why t s ot sutbl for our s. MC mult tulg tur msso s othr trsort molg tht hs b suss ltrlly sto.. I stos..5, w h or two trsort mhsms of th rft-ffuso thrmo msso tht ly th most mortt rol rrrs trsort htrojutos. hs two mhsms l rtly wth th ffts of th ottl brrrs outo or l b o th rrrs trsort thrfor, th rsult of molg rs th I- hrtrsts of th htrojuto. Lustorm [,] hs suss th bo mto ftors htrojuto bolr trsstors h hs lso t hs work mor grl wy for gr htrojutos. Furl t. l. [4,5] h us ths smulto of -S/- S htrojuto solr ll. h lu rt tulg sto.4 whl molg th thrmo msso our mol s wll s th surf rombto urrt sto.6 t th trf of -S -S juto. h ltr boms mortt low forwr bss.. S Chrg Lmtg Currt SCLC For htrojuto btw -S -S:H, th rrr trsort mol bs o s hrg lmt urrt SCLC -S:H ws rort by Sm t l. 985 [6]. SCLC

53 Chtr : Crrr rsort Mhsms -S/-S Htrojuto orgts from hgh-ll jto of rrrs to low-o smoutor. I ths s, th sty of th jt rrrs s so hgh tht t s th mjorty rrrs sty, thus th bulk mtrl ot utrlz th jt rrrs. hs ls to s hrg rgo o-zro ltr fl th bulk rgo b bg th rgy b grm of th low-o s [7]. h hgh jto of rrrs to low o bulk rgo ours t hghl oltgs hghr th.6 rsults th rlto btw forwr bs th urrt to b o logr otl. I ths s, th I- rlto s rthr surlr: m I K. whr m s o th sty of stts -S:H bg K s o th flm thkss, tr strbuto outty [8]. Fgur. shows th urrt-oltg hrtrsts I- of -S:H/-S msur t 96 K [8]. h ltrl mol of - S:H/-S o hs b roos by Mrsl t. l. [8] s two rlll rssts o ohm th othr olr srs wth orml o.. Fg. Currt sty oltg hrtrst of -S:H/ -S o msur t room tmrtur [8] As th thory of SCLC fs, th mjor ftor tht uss SCLC to h s hgh jto of rrrs to th low-o bulk. I our s, whh s or -S/-S 4

54 Chtr : Crrr rsort Mhsms -S/-S Htrojuto htrojuto, t s ulkly to h hgh jto. hs s bus of th trs morhous lyr SCR tht s w wll suss ltr o, lmts th trsort of th rrrs by rft-ffuso fft loty ftor. Also bus of rs of ottl brrr htrojuto b l or outo, thr wll b othr lmtg ftor trf fft loty whh rts th rrrs to b hghly jt. Aothr ot tht s worth to mto s th l oltg whh ths mhsm SCLC orts tht s mor th.6. As w wll s ltr, th msso-ffuso thory ffts th urrt t hgh oltgs rs of trs lyr whh mks t ussry to lu th SCLC our mol.. Mult-ulg Ctur msso MC Mtsuur t l. [9] roos ths mol 984 to orom th roblms tht th rlr tulg mols h to f. Bfor Mtsuur, fw tulg mols h b roos lug rt tulg mult st tulg. I Mtsuur s work, rty of tulg trsort rosss hs b ssss flly th mult tulg tur-msso mol hs b ofrm by th rmts. S th lolz stts r qus-otuously strbut wth th g of -S:H stlly s wll s rgtlly, t s rsobl to t mult st tulg ross to b omt rthr th o st tulg [7]. Aorg to ths mol, hol th l b of -ty -S jums from o lolz stt to othr -S:H lot wth rgy rg of from h othr by mult tulg ross ks jumg utl th tulg rt boms smllr th th rt for hol rls from th stt to th l b of -S:H or for rombto of th hol wth ltro th outo b of -S:H. A g ot of th tulg mght b los to th g of th lto lyr of -S:H, whr th tulg rt rss u to rs of ltr fl. Fgur. shows th rrr trsort homo through mult tulg tur msso mol. [9] 5

55 Chtr : Crrr rsort Mhsms -S/-S Htrojuto Fg. MC mol for htrojuto [9] I ths mol th urrt sty flowg from -ty -S to uo -S:H s g by [9]: > B σ th A. whr A s tmrtur-t ostt, B s ostt t of l oltg tmrtur, th hol msso rt g s: σ /. th σ s th tur ross sto of ltros, th th thrml loty, th ltro sty th outo b of -S:H, σ th tur ross sto of hols F, th rgs of Frm ll trg ll of -S:H rstly [9]; th t urrt sty: [ A ], whr [9]: C F B[ σ th σ th C ].4 Although ths thory mths th rmtl t, w shoul ot tht t srbs th forwr urrt-oltg hrtrsts of morhous-rystll slo htrojuto hg thk µm uo -S:H lyr. Howr, t s ulr whthr ths mol s lso l for jutos wth hghly o ultr th -S lyrs, s us solr lls [9]. hrfor, our s tht s th molg of or -S/-S htrojuto solr ll, rgrg th 6

56 Chtr : Crrr rsort Mhsms -S/-S Htrojuto ft tht th -S lyr thkss trs or o s ot thkr th fw ts m t most, ths mol wll ot b goo ho to srb th bhour of th.. hrmo msso h two mtrls wth ffrt bgs r ut togthr to form juto, th ffr btw th bgs, whh rs s offst rgy b, uss som ffts o th trsort mhsm of rrrs. hs ks of jutos b Mtl-Smoutor, htrojuto btw two ffrt smoutors or htrojuto btw two smlr smoutors wth ffrt bgs. h thrmo thory srbs th bhour of rrrs wh thy h to ss or ottl brrr form by htrojuto. Fgur. ltro flu Brrr hght q φ F Fg. ltro trsort or th ottl brrr As w h s rous htr, th hght of brrr outo b s qul to th ffr btw outo b lls or th ltro ffty of two smoutors quto.. h rrrs ltros, for st must h mmum rgy orr to b bl to orom th brrr. hs mmum rgy quls th ottl of th brrr hght lus th Frm rgy. So for th ltro urrt ssot to th ltro flu show Fgur. w wrt: 7

57 Chtr : Crrr rsort Mhsms -S/-S Htrojuto qϕ q.5 F whr F qϕ s th mmum rgy rqur for thrmo msso or th brrr s th loty of rrrs trsort rto []. It s fou tht th urrt tht wll ss th brrr hs th form of []: * qϕ q A.6 whr φ s th brrr hght, s th forwr bs * * 4πqm k A.7 h s th Rhrso ostt for thrmo msso th rg loty of rrrs th rto of trsort or th brrr thrmo msso loty wll b [,]:.8 * π m whr * m sts for fft hol or ltro mss. hs ts tht wh thr s ottl brrr outo l b of juto, th rg loty of rrrs wll b, thrfor, s t wll b suss ltr htr four, s of hgh forwr oltg, ths loty my ly lmtg ftor rol for th trsort of th rrrs. hs loty s lso ll thrml loty of rrrs..4 Drt ulg hrmo msso I s of brut htrojuto, wh th og ll of th mttr s hgh ough to mk th sk l or outo b ry shr, th rrrs tul through th rgy sk s wll s orom t by thrmo msso. Grbrg t. l. [] h lult ths fft by th tgrto of th rg of brrr rgs lbl for tulg. h rsult s multlt ftor to th trf fft loty of th rrrs th loty tht rrrs h wh orom th ottl brrr outo or 8

58 Chtr : Crrr rsort Mhsms -S/-S Htrojuto l b tht uss t to rs fw tms osqutly mks tol rrr jto ross th htrojuto ossbl. Fgur.4 [] shows th fft of tulg o th ffrt fft lots of rrrs htrojuto bolr trsstor. s tht for th hols fft loty t th juto thrmo msso wthout wth tulg, th tulg rss t by mor th ftor of t low bs, but rss to romtly ftor of t hgh bs []. As w suss sto., MC s ot sutbl ho for our molg. O th othr h, th rt tulg srbs th bhour of th rrrs s of rrow b sk trms of ftor multl by th trf fft loty of rrrs. S w h us th trf fft loty of rrrs our molg, w h lu rt tulg our mol to smult th ss wh th tulg ours. Fg.4 fft hol lots [mttr s hrg rgo rft ffuso, thrmo msso wthout wth tulg, qus-utrl bs ffuso bs-olltor sturto loty ] for IAlAs/IGAs P HB s futo of mttr-bs bs omostol bs grg.[] B for th s of o 9

59 Chtr : Crrr rsort Mhsms -S/-S Htrojuto.5 Drft-Dffuso I to to th thrmo msso tht shoul b osr s th trsort mhsm of rrrs whl ssg or th ottl brrr, th rrrs r sttr wh flowg through th SCR htrojutos. For homojutos, t s ssum tht th rrrs urrt SCR s ostt thrfor th fft loty of rrrs wth th lto rgo s tk f. Usg ths mtho, th urrt ross th SCR s lult th trm otg th urrt sty s th SCR s srgr. Although th rmts ro tht th mol of jto for homojutos ur low-ll jto s urt, t fls to mol th sursso of jt urrt u to th b sk tht ours htrojutos []. I ft, th sttrg my st homojutos s wll but th mout of t s so smll tht t s glt. Howr, ottl brrr rgy b outo or l uss th fft of sttrg to b sgft o loty of morty rrrs tht ffus th bs. I htr four, w wll mol ths homo s fft loty of rrrs tht lmts thr trsort through th lto rgo..6 h -S/-S Htrojuto Itrf Rombto Currt h rmtl t -S/C-s htrojutos show tht th omt trsort mhsm for rrrs lowr forwr bs s trf rombto. Sog t. l. [] show tht for forwr oltgs blow., th omt outo mhsm s th rombto urrt grt by rombg th fr ltros hols ush by th forwr bs through th trs lyr th tr hols ltros th morhous/rystll trf. h tr hols ltros th -S/-S trf r lot th b tls of th -S moblty g romb by fr ltros hols. wll lult ths urrt htr four sto

60 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto Chtr 4 Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto h rs of sk rgy b of htrojutos trous tol rrr flow mhsms for rk urrt. hrmo msso ls wth rrrs flow or th ottl brrr rft-ffuso srbs th rrrs trsort wth lto rgo. h mol ths two mhsms s two fft lots of rrrs trf fft loty rft-ffuso fft loty whh lmt thr flow through th htrojuto. I stos 4. 4., w h us th thrmo msso thory lug rt tulg to mol how th trsort of th rrrs s fft whl ssg or th brrrs. Our lultos show tht th thrml loty of rrrs lys th mjor rol fg th trf fft loty. I sto 4., w h lso fou out tht th moblty th mmum ltr fl lto rgo h th mjor mts o sttrg th flow of th rrrs through th SCR. h fou tht th ottl brrr th lto rgo o ot fft th flow of hols ltros - - htrojutos rstly. Ag trs lyr of morhous slo, w h rlult th rft-ffuso fft loty for ths s. S th ottl brrr os ot hg by g th trs lyr, w o ot h to rlult th trf fft loty. Howr, troug th trs lyr ffts th rrrs flow through th lto rgo. I sto 4.4, w h lult th rombto urrt of rrrs t th -S - S trf h show tht ths urrt s lso surss wth th sm lmtg ftors tht surss th rk urrt. Flly, sto 4.5, w h rou th omlt I- qutos for htrojuto, lug th lmtg ftors s wll s th trf rombto urrt. 4

61 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto I ll bo-mto stos, w h mol both -S/-S htrojuto solr lls. As w wll suss ltr htr s, th rso s tht th fft of lmtg ftors o th s sgftly ffrt from tht of th solr lls. 4. Molg th hrmo msso loty s Lmtg Ftor for Htrojuto Currt I ths sto, w wll r th qutos for th htrojuto urrt ur th forwr oltg, srbg th rol of thrmo msso loty lmtg th urrt. 4.. Htrojuto Currt Suos tht w h htrojuto ur th forwr bs. lk to rfy how th forwr urrt woul b fft rs of two ffrt bgs. ssum tht r th oltg ros - -rgo, rstly, s w kow, th sum of ths two oltgs wll g us th bult oltg of th. I th tt of ths susso, th sursrt /or subsrt t th qulbrum stuto, A ms tht th s ur forwr bs. strt our molg wth ltro urrt htrojuto ll. Rgrg th Fgur 4., qulbrum stuto th sum of th flus of ltros t y ot shoul b zro s thr s o t urrt ths stt. h flu of rrrs t y ot b lult by multlyg th otrto of th rrrs t tht ot by th rg loty. As w h lry s, th rg loty or th ottl brrr s th thrml loty. hrfor hg th otrto of th rrrs bfor th brrr w wrt: 4

62 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto F q 4. F C q 4. Assumg th qulbrum stuto, w h: F F. hrfor, q q C whh rsults: C q q 4. F F q C q A C q q C A Fg 4. ltro flus htrojuto 4

63 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto If w ly forwr bs A to th, ssumg tht ths oltg wll ro o - - s by A A A, rstly, suh tht: 4.4 A A th th rrr flus wll o logr b qul rrr flu wll flow through th so tht: F F F, thrfor w wll h: F q C q F 4.5 F lso wrt th followg qutos btw th qulbrum stt th forwr bs stt: A A A b A 4.8 Assumg low-ll jto o th -s, w wll h: 4.9 From quto 4.5 usg 4.9, for th flu ur forwr bs w wrt: F C q q C q [ ] 4. substtutg from quto 4. : F C q [ q C q C q q ] 4. Usg qutos 4.4, , w wrt: A A A 4. hs ls us to: F C q qa [ ] 4. h: 44

64 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto 4.4 whh ms th otrto of rrrs ur forwr bs quls th qulbrum otrto lus th ss rrr otrto jt ur forwr bs. hus, w wll h: F C q qa [ ] 4.5 From quto 4.5, w s tht f th frst rsso rght h C q boms ry bg th th quto wll mostrt th orml - homojuto bhour ur forwr bs for ss rrr jto,.. qa hm 4.6 h sursrt hm ts th ft tht quto 4.6 shows th otrto of ss ltros t homojuto. hs ms tht th offt C q s rsosbl for th fft tht th ottl brrr outo b uss o ltro urrt. Cosqutly, quto 4.5 whh w wll show by sursrt ht sts for th otrto of ss ltros t htrojuto. Usg ths ftos, w rwrt 4.5 s follows: F C q hm ht [ ] 4.7 kow tht f w h th otrto of ss morty rrrs t th trf of SCR th bulk rgo, th ffuso lgth lftm of morty rrrs th bulk, w lult th urrt [4]. h ffuso lgth lftm of morty rrrs th bulk r th sm for both - htrojuto - homojuto s th -rgo s th sm mtrl. hrfor, w h: hm L q τ hm for homojuto ht L q τ ht

65 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto for htrojuto. I th quto 4.7, F sts for ltro flu htrojuto o. By multlyg or ht : F by ltro hrg q, w wll h th ltro urrt htrojuto ht qf 4. Combg qutos 4.7, 4.8, , w wrt: ht τ L C q L [ q τ hm L q τ ht τ ] L C q hm ht 4. Cosqutly: hm ht L /τ C q 4. hs shows how th urrt gts lowr rs of ottl brrr outo b. smlfy ths quto by two moftos. Frst, th rsso whh s th ffuso τ lgth by th lftm of morty rrrs, b rrst s ffuso loty L of morty rrrs th bulk rgo. I othr wors, ts how fst th τ morty rrrs wll ffus th bulk rgo. So, Lustorm fs th rsso C q s th trf fft loty of rrrs, []. th ths fto, quto 4. b rwrtt s: hm ht 4. whr: L 4.4 τ C q 4.5 From quto 4., t s s tht f s muh grtr th, thr wll b o urrt ruto omr wth th homojuto. h lu of s t of, thrfor w L 46

66 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto ot rh stmto of how bg shoul b omrso wth to gt th lmtg ftor lmt. lult tslf to s wh ths loty s lrg umbr, whh s w shoul h: C q C q >> tht ls to b smll umbr. s tht C q wll b smll umbr f C boms zro or ry smll. hs ms tht th lmtg ftor wll sh f thr s o ottl brrr outo b or C q C. It s worth to mto tht th offt shoul b tk to out f w t to stuy th trf fft loty of ltros t th trf of SCR -bulk rgo whh w o to lult th urrt. hs ms tht f w wt to mto th trf fft loty t th ottl brrr, t woul oly b rthr th C q. rt th sm roh for hols to fgur out th fft of brrr l b o hols trsort mhsm htrojuto ll. F q 4.6 q F 4.7 Assumg th qulbrum stuto: F w gt whh rsults: F q q q q 4.8 Alyg forwr bs A to th hg quto 4.7, rrr flu wll flow through th, so tht: F F F, thrfor: F q q F 4.9 F 47

67 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto Assumg low-ll jto o th -s: 4. usg quto 4.8, w wll h: F q [ q q q q ] 4. Hg lso A A A w wll h: F q hm ht [ ] 4.4 hrfor: ht τ L q L [ q τ hm L q τ ht τ ] L q hm ht 4.5 h w wrt: ht L hm /τ q 4.6 whr s th thrml loty of hols. It b s tht >> whh ls us to q L / τ q osqutly: or othr wor, th rs of brrr th ht hm l b htrojuto os ot fft th hol urrt. 48

68 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto 4.. Htrojuto Currt h mtho tht w wll us to r th trf fft loty of hols htrojuto s th sm s w for ltros htrojuto. hrfor, ths sto w wll ro to r th qutos brfly. From th Fgur 4., for th flus of hols t, w wrt: qp F 4.7 F q 4.8 Assumg th qulbrum stuto: F thrfor whh rsults: F P q qp q q 4.9 Alyg forwr bs A, th rrr flus wll o logr b qul thr wll b rrr flu suh tht: F F F thrfor: F qp q F 4.4 F Ag, by ssumg low-ll jto o th -s w wll h: 4.4 usg qutos for th hol flu ur forwr bs w wrt F q [ P q q q q P ] 4.4 thrfor F q q [ ] A

69 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto F F C q P q A P q q A C - Fg 4. Hol flus htrojuto Usg 4.44 w wll h: F q q [ ] A 4.45 s th otrto of th ss hols t htrojuto tht w show q ht by:, lso s th otrto of ss hols t A homojuto tht w show by: hm. ow w rwrt quto 4.45 s: F q hm ht [ ] 4.46 hs ls us to th followg: 5

70 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto ht τ L q L [ q τ hm L q τ ht τ ] L q hm ht 4.47 ht L hm /τ q 4.48 Mkg th sm moftos tht w h: htrojuto for quto 4., w wll ht whr hm 4.49 L 4.5 τ s th ffuso loty of hols -rgo, q 4.5 th trf fft loty of hols. It shoul b ot tht s th thrmo msso loty of hols or th ottl brrr l b. As w sw for ltro urrt htrojuto sto 4.., th lmtg ftor for hol urrt htrojuto wll sr f th brrr l b s thr smll or zro. By rtg th sm sts, w h lult th trf fft loty of ltros q htrojuto s whh s w sw for hols trf fft C P loty htrojuto sto 4.., hs bg lu whh ms tht thr s o lmtg ftor for ltro urrt ht hm htrojuto or:. 5

71 Chtr 4: Molg th Currt-oltg Chrtrsts of th -S/-S Htrojuto 4. Molg th fft of ulg o th Itrf fft loty of Crrrs As w suss rous htr, hy og ll of th mttr mks th wth of th offst th outo or l b rrow thrfor th rrrs ss through th brrr by tulg. Grbrg t. l. [] lultos show tht ths b mol by multlyg th trf fft loty of rrrs by ftor. Rtly, rsrhs [] show tht ths homo s mortt th trsort mhsm of th rrrs s t ru th lmtg ftor of ottl brrr by srl tms for low forwr bss. Itrf fft lots Log Sl o ulg th ulg Forwr oltg Fg 4. Itrf fft loty of hols wth wthout tulg [] Fgur 4. shows th t trt from Fgur.4 for hol trf fft loty wth wthout th fft of tulg. It s s tht th tulg rss th trf fft loty of rrrs by mor th ftor of t low bs, but romtly by ftor of t hgh bs. h rs of trf fft loty of rrrs ms tht th lmtg ftor of th rrrs trsort rss. I othr wors, by tulg, th rrrs f othr wy to ss through th ottl brrr l or outo b st of ssg or t by 5