Jacky Even, Charles Cornet, François Doré. To cite this version: HAL Id: hal

Size: px

Start display at page:

Download "Jacky Even, Charles Cornet, François Doré. To cite this version: HAL Id: hal"

Shanon Cook
5 years ago
Views:

Anispic and inhmgnus Culmb scning in h Thmas-Fmi appximain: Applicain uanum d-ing lay sysm and Aug laxain Jacky Evn Chals Cn Fançis é T ci his vsin: Jacky Evn Chals Cn Fançis é.

<hal-004997> HAL Id: hal-004997 hps://hal.achivs-uvs.f/hal-004997 Submid n 8 Jun 00 HAL is a muli-disciplinay pn accss achiv f h dpsi and dissminain f scinific sach dcumns hh hy a publishd n.

1 Anispic and inhmgnus Culmb scning in h Thmas-Fmi appximain: Applicain uanum d-ing lay sysm and Aug laxain Jacky Evn Chals Cn Fançis é T ci his vsin: Jacky Evn Chals Cn Fançis é. Anispic and inhmgnus Culmb scning in h Thmas-Fmi appximain: Applicain uanum d-ing lay sysm and Aug laxain. physica saus slidi (b) Wily (9) pp.05. <0.00/pssb.00644>. <hal > HAL Id: hal hps://hal.achivs-uvs.f/hal Submid n 8 Jun 00 HAL is a muli-disciplinay pn accss achiv f h dpsi and dissminain f scinific sach dcumns hh hy a publishd n. Th dcumns may cm fm aching and sach insiuins in Fanc abad fm public piva sach cns. L achiv uv pluidisciplinai HAL s dsiné au dépô à la diffusin d dcumns scinifius d nivau chch publiés u nn émanan ds éablissmns d nsignmn d chch fançais u éangs ds labais publics u pivés.

2 A mdl f anispic Culmb scning : applicain Aug laxain by and chag cais in a uanum d ing lay sysm J. Evn C. Cn and F. é LENS-UMR FOTON 608 au CNRS INSA d Rnns 0 Avnu ds Bus d Cësms CS Rnns Cdx Fanc cspnding auh : jacky.vn@insa-nns.f (J. Evn) Absac. A mdl f anispic Culmb scning by and cais simulanusly is ppsd in h Thmas-Fmi appximain. Analyical xpssins f h scnd inacin pnials and scaing maix lmns a baind. This mdl is applid h Aug laxain f cais in an InAs/InP uanum d (Q) ing lay (WL) sysm. Th influncs f h Q mphlgy and cais dnsiis n scning and Aug ffcs a sudid. - scaing is fund b h ms impan pcss dpnding spcially n Q mphlgy. A smaing ffc is assciad h ing lay avfuncin xnsin alng h gh axis. Th scnd pnial is simila a pnial scnd by cais. P.A.C.S. 7..La 7.5.Q 7.5.-m 7..j J. EEN al.

3 I. INTROUCTION Cnsidabl sach dvlpmns hav bn cnly achivd in h fild f smicnduc uanum ds (Qs). Ths nansucus may impv pfmancs f plcnic dvics as cmpad ha achivd ih smicnduc uanum lls. -4 Cun injcin fficincy and mdulain dynamics dpnd cucially n cai capu and laxain in h Qs. Th impanc f Aug pcsss has aacd much anin fm h xpimnal 5-0 and hical -8 pins f vi. Ths Aug pcsss may b assciad ih -lik cais cais in h ing lay (WL) ( vn Q 0 sas) bu ms hical analyss hav fcusd n WL sas. Th disincin bn hs yps f cais is indd alady difficul f uanum ll (QW) QW suplaic 9-. Bund sas in QW ( cais) a ui ll dfind bu h siuain is much m cmplicad f cninuum sas (-lik cais). W may als add ha h l f WL sas in h laxain pcsss is sill a usin dbad fm h xpimnal pin f vi.ths vaius scaing pcsss a influncd by cai-inducd scning f h lcnic inacins 4-9. Sm hical ks 68 us ll-knn dilcic scning funcins f h cais in h WL in d simula h Aug scaing pcsss invlving cais. Th scning f hs pcsss is hv assciad in anh k cais maining in h bai af injcin ( cais). W bliv indd ha h simulanus ls f WL sas and bulk sas shuld b xamind ihin h sam mdl. In his k psn bifly a simpl n-band mdl f h calculain f Q lcnic disc sas including h WL in a cipcal spac analysis. Th daild simulain f dilcic scning f and lcns is ppsd. Aug laxain pcsss bn h Q fis xcid and gund sas a hn dscibd. Rsuls f hs J. EEN al.

4 calculains a applid InAs/InP Qs 0-4. Finally a discussin is mad n h spciv ls f and cais. II. CALCULATION OF Q AN WL ELECTRONIC STATES Th cnsidd Q is assumd hav a uncad cylind shap. I is siuad n a WL hich is m lss simila a hin QW (figu ). Th simulain f h Q's lcnic ppis is pfmd ih a simplifid n-band ffciv mass Hamilnian h H + m cnf ( ). Oing h symmy f h pblm ( C v ) h lcnic gund sa GS and xcid sa ES hav S and P-lik symmy ppis : ψ ( ) GS ϕ GS ( ) π (Q S sa) and ψ ( ) ES ϕ ES ( ) ϑ π ± i (Q P sa). Th ϕ ( ) and ( ) GS ϕ funcins ES a dvlpd in cipcal spac n a basis f pducs f Bssl and plan avs funcins (Bssl-Fui ansfm in h adial dicin and Fui ansfm alng h axis). Th lcnic sas f h WL k Ψ ( ) discid ngy lvl is fund f ( ) ik. a dmind analyically. Only n A Ψ in h hin WL sudid in his k (figu ). In h cas f InAs/InP Qs h lcnic cnfinmn pnial is akn ual 00 m in h Q and in h WL h ducd lcnic ffciv mass 0.05 h hicknss f h WL. nm. Th dscipin f h WL is simila h n f a na QW. Th ngy f h uniu WL cnfind lcnic sa E is hn ual 6 m (h ngy is s ual 0 in h cnfinmn lay). Th xnsin f WL avfuncin ( ) Ψ alng h J. EEN al.

5 gh axis is lag f h d f 0 nm n ach sid f h WL. Th gmy f h InAs/InP Qs (hicknss h and adius R) may b cnlld duing h gh pcdu in paicula un h pical missin h lcmmunicain avlngh (λ.55µm) 0. Typical valus f hicknss and diam a.5nm and 0nm spcivly. Elcn cnfinmn is hn sng in h gh dicin han in h plan. Th pical missin ngy dpnds mainly n h hicknss h bu h ngy gap bn h gund and xcid lcnic sas E E is in a fis appximain a funcin f h adius ( GS ES E GS E 9m f h.5nm and R5nm). W mus finally add ha sval shs f ES Q+WL a fn usd in d incas h gain in pical dvics. Th spacing bn Q-WL shs is gnally chsn lag nugh (L>0nm) avid a sng cupling bn Q and WL lcnic sas bu n lag b abl sack sval Q-WL shs in h pical cnfinmn n. F InAs/InP Qs ypical valus f h spacing L a in h 0-40nm ang 0-4 (figu ). III. SCREENING BY AN CHARGE CARRIERS A. Elcnic dnsiy f sas W cnsid h simplifid appach f f. [0] hich aks in accun h simulanus psnc f cais lcalid in a QW and cais in h bai. Th al lcn dnsiy is hn calculad ih : N n L + n mkt lg πh L / ( µ E )/ m E kt ( + ) + ( E µ ) π h 0 + / kt de h m is h ffciv mass E is h uanid lvl in h WL (nly n lvl is cnsidd) µ is h lcnic Fmi lvl and L is h spacing bn Q-WL shs. I is assumd ha L is lag nugh avid h appaanc f suplaic ffcs. Th ngy 4 J. EEN al.

6 dispsins in h WL and in h bulk a suppsd b paablic. A singl lcnic Fmi lvl is dfind f h ( n ) and ( ) lcnic ppulains. I is pssibl dfin n cais mpaus bu cnsid his b bynd h scp f h psn pap. Figu -a is a psnain f h /( L* N ) n and n / N vaiains as a funcin f N f a spacing L ual 40nm. Th pcnags f cais in h WL and in h bai main sabl unil N achs a valu f abu N 7 0 cm. Th filling f lcnic sas in h WL is lss fficin f lag valus f N and n is alms ual N hn N is vy lag. Figu -b shs h vaiains f n and n as a funcin f L f a givn N 6 valu ( N 0 cm ). Whn L nds infiniy asympic valus f n and n a 0 n cm and n N. F vy small L valus suplaic ffcs a impan and his simplifid appach is n valid. I cspnds L<0nm in h InAs/InP Q sysm. F InAs/InP Qs ypical valus f h spacing L a in h 0-40nm ang. W may cnclud ha in such cass nih h filling f h WL n h n f h bai can b nglcd. Th simulanus ls f WL sas and bai sas in h scning and in h Q Aug laxain ill hn b xamind in h flling pas B. Scaing pnial scnd by cais W ill fll h classical mhd f f [4] xndd la cai ansp in suplaics 8. Th scaing pnial ( ) inducd by a cai lcalid a ("s" chag) may b baind by slving Pissn's uain : ε ( ) ( ) + ( ) [ δ ( ) + n ( )] x ind ind 5 J. EEN al.

7 h ε is h dilcic cnsan f h maial ( ) is h unscnd pnial ( ) x ind h inducd pnial and ( ) n ind is h inducd dnsiy f scning cais. W may nic ha such a calculain shuld pvid h sam sul as a Lindha-yp calculain in h lng avlngh limi 9. W uld lik pin u ha h xpssin f ( ) is unchangd by h pmuain ( ill us n h nain ( ) insad f ( ) ). In h Thmas-Fmi appximain ( ) n ind is ppinal h pnial ( ) n ind ( ) ( ) n. Th Fui ansfm f h Pissn's uain yilds µ ( ) ε ( ) + h λ and + λ n ε µ /. A paial Fui. Th paial Fui ansfm f h A i( ) ansfm is dfind by ( ) ( ) O "-scnd" and unscnd pnials a hn ual ( ) ε and x O ( ) ε ~ spcivly. W dfin h dimnsinlss pnials ( ) by ~ ( ) ( ). Th "-scnd" dimnsinlss pnial is cmpad h ε ns n figu f a fixd valu f λ. Th cuvs a) and b) psn h unscnd and "-scnd" dimnsinlss pnials spcivly. W ill s n in h nx pas ha 6 J. EEN al.

8 h pnial is scnd m fficinly hn h cnibuin f cais is akn in accun. C. Scaing pnial scnd by cais ih a dla disibuin alng h axis If scning cais a in bund sas f a WL ( QW) and if h avfuncin disibuin alng h axis is placd by a δ funcin 8 ( ) ( ) ( ) ind n n δ µ h is h in-plan cmpnn f and h psiin f h WL alng h axis. Th Pissn's uain ansfms ( ) ( ) ( ) ( ) ind ind n + δ µ ε yilding ( ) ( ) ind n µ ε. This uain is fis applid in h WL plan ( ) find ( ) µ ε ε + n O. Th classical sul 8 ( ) ( ) + λ ε ih µ ε λ n f a pu sysm is hn cvd hn h "s " chag is lcad insid h WL ( ). Th "-scnd" pnial is calculad in a scnd sp a a gnal psiin by cmbining h xpssins f ( ) x ( ) ind and ( ) : J. EEN al. 7

9 ( ) ( ) ( ) + + ind x O O λ ε Th inacin pnial ( ) ds n dpnd anym n h sl disanc bn h chag lik in h cas. Th inacin alng h axis is indd pubd by h WL a. Hv h inacing chags sill play h sam l h xpssin f h pnial bing unchangd by h pmuain. Th "-scnd" (cuv c) and unscnd dimnsinlss pnials (cuv a) a cmpad in figu f fixd valus f λ and. Th anispy inducd by h cais is claly bsvd. Th WL is lcad a h cn f h figu ( 0). Th small valu f is chsn in d sudy h influnc f h WL cls i. This migh b h cas f a chag lcad insid h Q.. Scaing pnial scnd by cais and cais ih a dla disibuin alng h axis If bh cnibuins a n cmbind flling h sps mhd usd f h cas in pa C h paial Fui ansfm f h "--scnd" pnial is : ( ) ( ) ( ) + + ind x O O λ ε W may mak ha hn h chags a n h ppsi pas f h WL ( << << ) h inacin pnial nly dpnds n. Figu -d is a psnain f his pnial. Th psnc f cais is flcd by a bn a 0 in h pnial cuv lik in h "-scnd" cas. Th ampliud is fuh ducd by h cais. Figu 4 psns h "--scnd" pnial f vaius psiins f h "s" chag alng h axis ( ). Th "-scnd" cas is cvd hn h "s" chag is lcad J. EEN al. 8

10 fa fm h psiin f h WL. In h ds h influnc f cais n scning is sng nly hn h "s" chag is lcad cls h WL. This is indd h cas f a chag lcad in h Q. Finally may pin ha h sngs scning ffc is bsvd f. Th "--scnd" pnial has a symmical pfil nly in ha cas. E. Scning pnial scnd by cais and cais ih WL avfuncin disibuin includd Th influnc f h WL avfuncin disibuin alng h axis is n akn in accun in h inducd dnsiy : h ( ) n ind ( ) Ψ ( ) Ψ ( ) ( ) d ( ) n n µ µ Ψ is h -pa f h WL avfuncin f h uanid sa. Th pblm is n m cmplica : n n ind ind ( ) + ( ) Ψ ( ) ( ) + ( ) ε µ ε µ h h pnial avagd v h WL avfuncin xnsin ( ) ( ) ( )d Ψ appas in h scnd mmb. Th pblm culd b slvd slf-cnsisnly by puing h sluin fund in pa B in ( ) a h fis sp f h cmpuain. I is simpl xnd h mhd ppsd f pu sysms ( ) is calculad in a fis sp by ingaing h Pissn's uain v and sing ( ) ual ( ) ( ) ind : x 9 J. EEN al.

11 ( ) ( ) ( ) ( ) Ψ Ψ d d n µ ε ε hn h uain is avagd v ( ) Ψ in a scnd sp yild : ( ) ( ) ( ) + g f λ ε h ( ) ( ) ( ) Ψ Ψ dd g and ( ) ( ) d f O Ψ I is n pssibl inga numically h uain v f any valu f : ( ) ( ) ( ) ( ) ( ) ~ ~ ind ind O O g d λ λ + + Ψ Ψ + Whn h WL avfuncin disibuin is simplifid h sluin his uain is knn (pa B) : ( ) + ind O ~ λ. Th sluins baind f h "--scnd" ( ) ~ aking in accun n h WL avfuncin xnsin a cmpad n figu 5 h "-scnd" pnial: ( ) O ~. Th smaing ffc assciad h WL avfuncin maks h "--scnd" pnial ih h WL avfuncin includd simila h "-scnd" pnial. In addiin h scning inducd by h cais is ducd : h ( ) g fac is small han. Figu 6 is a psnain f h dimnsinlss inducd chag dnsiy ( ) ind n ~ in h sam h cass f valus. ( ) ind n ~ is dfind by J. EEN al. 0

12 n ind A i( ) ( ) ( ) n and n ( ) n ~ ( ) ind. W hav chsn ind ind ak a na Gaussian-lik funcin pduc h dla funcin (s pa B) f h "- " inducd dnsiy hn h WL avfuncin is n includd. Th singulaiy in h inducd dnsiy is mvd by h smaing ffc assciad h lag spaial xnsin f h WL avfuncin. In ha cas h paiin f h inducd chag is n vy diffn fm h n in a pu cas. I. CARRIER RELAXATION BY AUGER PROCESSES A. Mdl Figu 7 is a schmaic psnain f h fu pssibl Aug scaing pcsss assciad h laxain f an lcn fm h ES h GS. In h - scaing pcss h mbil lcn mains cnfind in h WL alng h dicin. In h - scaing pcss h bulk lcn mains in h bai. Th h pcsss hav n bn cnsidd pviusly in h liau. In h - scaing pcss h mbil lcn is mid fm h WL h bai has h vs capu fm h bai h WL is invlvd in h - scaing pcss. Th laxain f an lcn fm h ES h GS assciad h scaing f lcns is dmind by h Fmi gldn ul : R R R ( k k ) δ ( E E ) π A d kf d ki M if P i f f i (- scaing) h 4π kf k i ( k k ) δ ( E E ) π A d k f d ki M if P i f f i h 4π 8π (- scaing) k f k i ( k k ) δ ( E E ) π A d kf d ki M if P i f f i h 4π 8π (- scaing) kf k i J. EEN al.

13 R - ( k k ) δ ( E E ) π d k f d ki M if P i f f i (- scaing) h 8π k f k i h P cnains h ppulain facs and M if is h scaing maix lmn bn iniial k i and final avvc is du h ngy cnsvain : k f lcnic sas. In h - cas a limiain n h iniial m k ( EGS EES E ) if E 0 i GS EES E (- scaing) h B. ic calculains f scaing as ih WL avfuncin disibuin includd ~ As shn in pa III-C h scnd pnial ( ) can b calculad by a simpl numical ingain v h axis. This cmpuainal sp is hv n ncssay f scaing as maix lmns divd fm h applicain f h Fmi gldn ul. F xampl in h cas f h inacin bn an lcn lcad in a QW and a Culmbic impuiy a 9 h scaing maix lmn M is ual M k ( ) k if if i f ik.. Using h suls f pa III-C i is saighfad sh ha A h k Ψ ( ) M if ( k k ) i. f i. This maix lmn can haf b avagd v h impuiy A disibuin and h ppulain f cais. Th lcnic laxain fm h Q xcid sa ES h Q gund sa GS by an Aug pcss invlving h scaing f a cai (- scaing) is an xnsin f his sul h h chagd Q plays h l f h Culmbic impuiy. I dpnds n h J. EEN al.

14 maix lmn M k ; ψ ( ) ( ) k ;ψ ( ) if (h xchang inacin is i ES nglcd). By inducing h paial Fui ansfm f h pnial : M if A d d ( kf ki ) ( ) ϕ ES ( ) J( kf ki ) f GS ϕ * GS (- scaing) Th maix lmns f Aug pcsss invlving any yp f scaing a calculad in a gnal ay : M if ( kf ki ) J( kf ki ) i(k f k i ) d d ES GS (- scaing) M if A L d d ES ( kf ki ) J( kf ki ) Ψ ( ) * ik f GS (- scaing) M if A L d d ES GS -iki ( kf ki ) J( kf ki ) Ψ ( ) (- scaing) M if A d d ( kf ki ) J( kf ki ) Ψ ( ) ES GS (- scaing) h ( ) ( ) ( ) ( )d ES GS ϕ GS ϕ ES is h avag f h pnial v h pduc ϕ ( ) ϕ ( ) GS ES. In h las cas (- scaing) his fmulain is uivaln h fis n givn abv. Th avag ingal ( ) ES GS can b xpssd using h uaniis dfind in pa III-C : ES GS n ( ) f ( ) ( ) g ( ) ES GS ES GS ε µ h g ( ES ) ( ) ( ) Ψ ( ) GS ϕ GS ϕ ES ϕ GS ϕ O and f ( ) ( ) ( ) d ES GS ES dd J. EEN al.

15 I is n pssibl sudy h smaing ffc f h avfuncin disibuin f xampl in h cas f - scaing : M if Bs * C s A ε g + λ (smaing includd) h A O B s ϕ O GS ϕ GS ( ) ϕ ES ( ) J ( kf ki ) i(k f k i ) ( ) ϕ ( ) J ( k k ) Ψ ( ) ES f i d dd d dd C s and i(kf k i ) Ψ ( ) dd M if B * C A ε + λ (smaing n includd) h B ϕ GS ( ) ϕ ES ( ) J ( kf ki ) d d C i(k f k i ) d C. Rsuls f InAs/InP Qs Figu 8 is a cmpaisn f h Q ES-GS laxain ims f h fu Aug pcsss as a funcin f h al lcn dnsiy. Th - scaing pcss is h fass n xcp f vy high dnsiis h h numb f accssibl final avvc sas f h scad lcns is ducd by filling ffcs. Th - WL bai missin is als fficin f assising h inad laxain. Finally h - capu f an lcn fm h bai h WL can b nglcd. 4 J. EEN al.

16 Figu 9 is a psnain f h ai ρ bn h - ( -) laxain ims calculad ih and ihu h ffc f h WL avfuncin includd. Th smaing ffc is m impan f h - laxain ims bu h ccin h laxain im mains small (abu 5% a high lcn dnsiis). Figu 0-a shs h vaiain f h laxain ims as a funcin f h Q adius. In h - - and - cass h incas f h adius dcass h laxain im. This is assciad a chang f h Q ES and GS avfuncins and hus a chang in h scaing maix lmns. In h - cas h ppsi vaiain is bsvd. F lag adius h ngy shif E E is small (figu 0-b). Th diffnc E GS -E W is lag han ES GS E ES and as a cnsunc E E E 0. Th numb f lcnic sas availabl GS ES f missin fm h WL h bai is limid by h cndiin m k i ( EGS EES E ). h Th ngy diffnc E E incass as h adius dcass dn h valu ES GS f R0nm h E E E GS ES. Bl R0nm all h WL sas a availabl f missin f an lcn h sas f h bai. Bl R9nm nly n Q lcnic sa is uanid and h ES-GS lcnic laxain is n dfind. Bn R9nm and R0nm h - pcss is slighly m fficin han h - pcss bcaus h numb f accssibl final avvc sas ( sas insad f sas) f h scad lcns is lag. Th hicknss h f h Q may b cnlld duing h gh pcdu 0. Figu shs h vaiain f h laxain ims as a funcin f h hicknss. Th bhaviu f h laxain ims vsus h hicknss is ppsi h n vsus h adius (figu 0) 5 J. EEN al.

17 mainly bcaus h ngy shif E E incass hn h hicknss incass. F Q ES GS hicknsss small han hnm nly n uanid lcnic sa xiss in h Q. In ms pacical cass h InAs/InP Q hicknss is cnlld duing h gh pcdu in d un h missin avlngh f h Q. Th disibuin f Aug laxain ims shuld n b vy lag. Gh sudis a pfmd ih h aim duc h Q si (mainly h adius) in d incas h GS-ES ngy spaain (uanum ffc). A small incas f h hicknss mus b usd als in d kp h missin avlngh a h sam valu (.55 µm f xampl). Fm h calculad vaiains f - Aug laxain ims as a funcin f R (figu 0-a) and h (figu ) may cnclud ha bh paams cnibu h sling dn f his - inducd cai laxain. Ou sudy shs hv ha his sling dn is paly cmpnsad by h spding up f h - cai laxain.. CONCLUSION Th ls f and lcnic sas in h scning f a Culmbic inacin a sudid. I is shn ha and cais mus b akn in accun simulanusly spcially hn a "s" chag is lcad na h QW. This is indd h cas f a cai in a Q and cls a WL. Analyical xpssins f h scnd pnials a baind in ms cass xcp in h cas h h xnsin f h bund sas alng is akn in accun. I is shn hv ha a simpl numical ingain is pssibl. F h calculain f scaing maix lmns his numical sp is n ncssay and analyical xpssins f ingals invlving h scnd pnial a givn in all h cass. Inad cai Aug laxain assisd by WL and bulk bai cais is sudid. N scaing pcsss invlving missin (-) capu (-) f cais fm h WL 6 J. EEN al.

18 h bai a analyd. I is shn hv ha in ms cass h - scaing is h pdminan pcss. Changs in h Q mphlgy n nly affc h Q pical missin ngy bu als h Aug laxain as. Th - pcss is n h sam d f magniud as h - pcss f a small Q adius. 7 J. EEN al.

19 Rfncs M. Gundmann. Bimbg and N.N. Ldnsv Quanum Hsucus (Chichs: Wily 998). L. Banyai and S.W. Kch Smicnduc Quanum s Wld Scinific Sis n Amic Mlcula and Opical Physics (Singap N Jsy Lndn Hng-Kng Wld Scinific 99) l.. M. Sugaaa Slf-Assmbld InGaAs/GaAs Quanum s Smicnducs and Smimals (Tn: Acadmic 999) l Zh. I. Alfv Quanum Wis and s sh h Way Fad (III-s Rv. 998) l. p B. Ohnsg M. Albch J. Oshin A. Fchl and Y. Aakaa Phys. Rv. B54 5 (996) 6 Z.L. Yuan E.R.A.. F J.F. Ryan.J. Mbay M.S. Sklnick and M. Hpkinsn Physica B 7 (999) 7 S. Sanguini K. Waanab T. Tan M. Wakaki N. Kguchi T. Kuda F. Minami and M. Guili Appl. Phys. L. 8 6 (00) 8 J.I. L I.K. Han N. Kguchi T. Kuda and F. Minami J. K. Phys. Sc (00) 9 K. W. Sun J. W. Chn B.C. L and A.M. Kchian Nanchnlgy 6 50 (005) 0 E.W. Bgaa J.E.M. Havk T. Man T. an Lippn R. Nöl and J.H. Wl Phys. Rv. B7 950 (005) U. Bcklmann and T. Egl Phys. Rv. B (99) M. Baskn M. Lindbg and J. Tulkki Phys. Sa. Sl. (a) (997) A.Uskv F. Adl H. Schi and Pilkhun J. Appl. Phys (997) 4 R. Fia and G. Basad Appl. Phys. L (999) 5 I.Magnusdi S. Bischff A.. Uskv and J. Mk Phys. Rv. B (00) 8 J. EEN al.

20 6 T.R. Nilsn P. Gan and F. Jahnk Phys. Rv. B69 54 (004) 7 R. Wl A. Wack and E. Schöll J. Appl. Phys (004) 8 H.H. Nilssn J. Z. Zhang and I. Galbaih Phys. Rv. B7 05 (005) 9 G. Basad Phys. Rv. Rapid Cmm. B0 547 (984) 0 H. Hidki Y. Miyak and M. Asada IEEE J. Quanum Elcn (99) G.C. C and R.A. Abam Smicnd. Sci. Tchnl. 0 (995) G.A. Baaff Phys. Rv. B (997) B.P.C. Tsu and.l. Pulfy IEEE J. Quanum Elcn. 4 8 (998) 4 F. Sn and W. E. Had Phys. Rv (967) 5 S. Mi and T. And Phys. Rv (979) 6 J.A. Bum G. Basad and C. Guillm Phys. Rv. B0 905 (984) 7 J. P. Lh and J. Singh Phys. Rv. B4 754 (990) 8 J. R. My.J. Anld C.A. Hffman and F.J. Bali Phys. Rv. B45 95 (99) 9 G. Basad Wav Mchanics Applid Smicnduc Hsucus (Pais: EP 99) 0 P. Miska C. Paanhn J. Evn N. Bu A. L C and O. has J. Phys.: Cndns. Ma 4 0 (00) C. Cn C. Labbé H. Flli N. Bu O. has J. Evn A. L C C. Paanhn C. Pla and S. Lualich Appl. Phys. L (004) P. Miska J. Evn C. Paanhn O. has A. Jibli M. Sns and X. Mai Appl. Phys. L (005) C. Cn C. Pla P. Caff J. Evn C. Labbé H. Flli A. L C and S. Lualich Phys. Rv. B (005). 4 C. Cn C. Lvallis P. Caff H. Flli C. Labbé J. Evn A. L C S. Lualich M. Hayn and.. Mschalkv Appl. Phys. L. 87 (005) 9 J. EEN al.

21 Figu capins Figu : Schmaic psnain f h Q-WL sysm. h and R a h hicknss and adius f h Q spcivly. L is h spacing bn Q-WL shs. Figu : a) aiains f n /( L* N ) (saigh lin) and n / N (dashd lin) as a funcin f N (L40nm). n /( L* N ) and n / N a calculad using h mdl f pa III-A and psn h pcnags f cais in h WL and in h bai spcivly. b) aiains f n (saigh lin) and n (dashd lin) vaiains as a funcin f h pid L f N 0 6 cm -. F L<0nm suplaic ffcs alng h axis can n b nglcd. Asympic valus f 0 0 cm - spcivly. n and n hn L nds infiniy a 0 6 cm - and 7.45 Figu : Rpsnain f h dimnsinlss pnials ( ) ~ hn h s chag is lcad a.5 nm and h WL a 0 nm in vaius cass : a) unscnd pnial (saigh lin) b) scnd pnial (dd lin) c) scnd pnial ih h WL avfuncin appximad by a dla funcin (dashd lin) and d) - scnd pnial cspnding h b) and c) cnibuins akn in accun simulanusly (dashd and dd lin). Figu 4 : Rpsnain f h dimnsinlss - scnd pnial ( ) ~ f vaius valus hn h WL avfuncin is appximad by a dla funcin alng h axis. Figu 5 : Rpsnain f h dimnsinlss pnials ( ) ~ hn h s chag is lcad a nm and h WL a 0 nm in vaius cass : a) unscnd pnial (saigh lin) b) scnd pnial (dd lin) c) - scnd pnial baind by a 0 J. EEN al.

22 numical ingain (dashd lin) and d) - scnd pnial ih h WL avfuncin appximad by a dla funcin (dashd and dd lin). ~ Figu 6 : Rpsnain f h dimnsinlss inducd chag dnsiis n ( ) ind hn h s chag is lcad a 8 nm (a) and nm (b). Th saigh lins cspnd - scnd pnial ih h WL avfuncin appximad by a dla funcin h dashd lins h scnd pnial and h dd lins h - scnd pnial baind by a numical ingain. Figu 7 : Schmaic psnain f h vaius pcsss assciad h Aug assisd laxain f a cai fm h Q xcid sa (ES) h Q gund sa (GS). Emissin fm h WL h bai is psnd by h - a. Th vs pcss is h capu fm h bai h WL (- a). Figu 8 : aiains f h laxain ims τ as a funcin f h lcn dnsiy f h - (saigh lin) - (dashd and dd lin) - (dd lin) and - (dashd lin) pcsss. F ms dnsiis h - pcss is h ms fficin n. Figu 9 : aiain f h ai ρ bn h laxain ims calculad ih and ihu h dla appximain f h WL avfuncin. Th laxain ims calculad ihu h dla appximain a sh. This ai is shn f h - (dash and dd lin) and - (saigh lin) pcsss. Figu 0 : a) aiain f h laxain ims τ as a funcin f h Q adius R f h - (saigh lin) - (dashd and dd lin) - (dd lin) and - (dashd lin) pcsss. b) aiain f h gund sa (E GS saigh lin) xcid sa (E ES dd lin) ing lay sa (E W saigh lin) ngis as a funcin f h Q adius. Th diffnc E GS -E W is pd as a dashd lin f cmpaisn ih E ES. J. EEN al.

23 Figu : aiain f h laxain ims τ as a funcin f h Q high h f h - (saigh lin) - (dashd and dd lin) - (dd lin) and - (dashd lin) pcsss. J. EEN al.

24 FIG.. Z axis h L R J. EEN al.

25 FIG. -a 4 J. EEN al.

26 FIG. -b 5 J. EEN al.

27 FIG.. 6 J. EEN al.

28 FIG J. EEN al.

29 FIG J. EEN al.

30 9 J. EEN al.

31 0 J. EEN al.

32 FIG. 6-a n ~ ( ) ind a) b) c) λ 5 λ. -07 Z 0 Z FIG. 6-b 0-05 ~ n ( ) ind - Z λ 5 λ -5 Z J. EEN al.

33 FIG E E ES E GS WL Q J. EEN al.

34 FIG.8. J. EEN al.

35 4 J. EEN al.

36 FIG. 9 5 J. EEN al.

37 FIG. 0-a 6 J. EEN al.

38 FIG. 0-b 7 J. EEN al.

39 FIG. 8 J. EEN al.

CONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT, DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS

CONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS VIMaslv SVBachuk VILapshin YuVMlnsv* EDVlkv NSC Khakv Insiu f Physics and Tchnlgy Khakv 608 Ukain *Kaain