Hetero- and low-dimensional structures. Impact of semiconductor quantum dots bandgap on reabsorption in luminescent concentrator

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1 Smconducto Pyscs, Quntum lctoncs & Optolctoncs, 8. V., N. P Hto- nd low-dmnsonl stuctus Impct of smconducto quntum dots ndgp on sopton n lumnscnt concntto A.I. Skt, A.V. Scnko, I.O. Sokolovsky, V.P. Kostylyov, M.R. Kuls Unvsty of Onto Insttut of Tcnology, Smco St. N., Osw, Onto, LH 7K4, Cnd V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn, 45, pospct Nuky, 368 Kyv, Ukn -ml:sc@sp.kv.u Astct. W v nvstgtd t nflunc of t vg dus nd ts dspson v of t smconducto quntum dots (QDs) usd n lumnscnt sol concnttos (LSCs) on sopton. To mnmz t dtmntl sopton losss n LSCs, sx smconductos usd to fct QDs wt wd ng of t ulk nd gp g v n consdd, spcfclly: CdS ( g =.4 V), CdS, ( g =.67 V), CdT ( g =.5 V), InP ( g =.7 V), InAs ( g =.355 V), nd PS ( g =.7 V). Altng nd v, w cn dtmn t optml sz fo mnml sopton. As t ws sown, dcsng t smconducto ulk nd gp fom.4 down to.4 V w cn gt suc optmum QD sz tt sopton ducs vn low t comnd xpmntl o n dtmnton of t sopton coffcnt nd lumnscnc ntnsty. Fut ducton of t gp g, owv, ncss sopton t ny vlus of nd : fo nstnc, fo PS-sd QDs of -nm dus nd dspson of %, sopton cs 54%. Kywods: potolumnscnc, quntum dots, lumnopo, sopton, sol pnls, ffcncy, concntto. do: ttps://do.og/.547/spqo..58 PACS 88.4.jm, 88.4.jp Mnuscpt cvd 7..8; vsd vson cvd 9.3.8; ccptd fo pulcton 9.3.8; pulsd onln Intoducton Cuntly, ntnsv sc fo ltntv ppocs to duc t sol ngy cost s gong. On of ts ppocs s to us lumnscnt sol concnttos (LSC). T lumnscnt sol concntto s tnspnt plt of ognc o nognc mtl tt s dopd y lumnopo, nd to t nds of wc sol clls ttcd. Among ll typs of lumnopos, t us of smconducto quntum dots (QDs) s t most ttctv vnt. QD dmt cn vy fom up to nm [, ]. QDs tnsfom od spctl ng of lgt qunt n now nd. By cngng t optcl gp, dus nd dspson v, w cn cv t good mtc twn spctl poston of t lumnscnc nd nd t potoconvt s mxmum snstvty gon. lctons nd ols n QDs cn consdd s qus-ptcls n t-dmnsonl (3D) potntl ox. Qus-ptcl s ngy s countd fom t gound potntl (poston of ol nd lcton quntum lvls countd fom t ottom of t conducton nd nd t top of t vlnc nd, spctvly). T ngy poston of quntum lvls n t QD cn clcultd usng t fomul [, 3], ϕl, n.786 n, l = g m m 4πεε * Ry, () * w g s t nd gp of ulk smconducto, Ry Rydg ngy, ε nd ε t ltv dlctc constnts fo smconducto nd ts solut vlu n vcuum, spctvly, ħ ducd Plnck s constnt, m nd m ffctv msss of t lcton nd ol, spctvly, lcton cg, nnocystl co dus, n =,, 3,... pncpl quntum nums, l =,,,... otl quntum nums, wl ϕ l, n unvsl st of nums [4], wc gvn n Tl. 8, V. Lskyov Insttut of Smconducto Pyscs, Ntonl Acdmy of Scncs of Ukn 58

2 SPQO, 8. V., N. P Tl. Vlus of t pmt φ l,n usd n q. () [4]. l/n T fst tm n q. () s t smconducto ulk ndgp g ; t scond tm dscs t ngy, l, n of quntzd lvls du to cs confnmnt n t nnocystl; t td tm dscs t ngy ducton du to ntcton of lctons nd ols. T ltt fout tm s t Rydg ngy, wc dos not dpnd on t sz of t nnoptcls nd cn usully nglctd, xcpt t css of smconductos wt low dlctc constnt. T QD sopton spctum s fomd y tnstons twn t sz-quntzd lcton nd ol lvls wt t sm quntum nums n nd l (s Fg. ). In l nnocystls, two mn mcnsms sponsl fo t od sopton nd: () t t nonzo solut tmptu t lwys s t tml odnng of t quntzd ngy lvls du to tomc vtons nd () t nnocystl sz dspson lds to t ddtonl nomognous odnng, wc s tmptu ndpndnt (Fg. ). Wn clcultng QD sopton spct, t tml ngy lvl odnng s usully nglctd, nd t only contuton fom nnocystl sz dspson tt s consdd. In ts cs, t sopton spctum cn clcultd usng t fomul [5]: α ( ) p 3 = P p 4 m π π cn ε xp V QD ( ) p w p s t poton ngy, m mss of f lcton, c spd of lgt n vcuum, n l pt of t fctv ndx of ulk smconducto, V QD volum of t quntum dot, ln wdt of t optcl tnston, P nd t mtx lmnt of momntum nd ngy wt spct to c of t -t xcton tnston. q. () ws usd n [5] to clcult t totcl dpndnc of t sopon spct of CdS QDs wt t dmt ngng fom.5 to 8 nm, cng good gmnt of t clcultd nd xpmntl sopton spct. Wn ng llumntd y sunlgt, lctons xctd fom t quntzd lvls of t vlnc nd to t cospondng quntum ngy lvls of t conducton nd. Bot lctons nd ols lx quckly (wtn pcoscond tm ntvl) fom g lvls to, () cospondng lowst lvls nd, spctvly. Tn, lctons comn wt ols s sult of t tnston fom to, mttng t lumnscnt poton. T mjoty of t scs on t nnocystls popts consd n nsml of QDs wt % sz dspson (s,.g., [6]) wt t Gussn dstuton [7] of t dus ound ts mn vlu: P =. (3) πσ ( ) σ (, ) In (3), s t mn QD dus, t stndd dvton σ cn dtmnd usng lcton mcoscopy dt. c QD mts lumnscnc potons wt ts cctstc ngy ν, t comnd msson of t st of QDs foms lumnscnt nd. T ntnsty of n lumnscnc nd nnt to QDs I PL s sum of lumnscnc ntnsts I PL ( ν, ), w s t vl dus of -t QD, mttng potons of ν ngy ( s cngd wtn t spd n t QD sz). Tfo, followng [7], t ntnsty of t lumnscnc nd of t QD st cn dscd s: n PL ( ν ) I ( ν, ) P( ) I = α,,. (4) x PL Fg.. Quntzd ngy lvls of lctons nd ols n QDs n t cs of () 3D confnd nnoptcl wt ts co sz fxd nd dsct ngy lvls,, (s t txt fo xplnton). In t cs (), t QD sz dspson s psnt wt t tml odnng of t ngy lvls ncludd. g s t ulk smconducto gp, nd N() s t cs dnsty of stts. n l A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 59

3 SPQO, 8. V., N. P T ngy dffnc twn t fst mxmum of t sopton nd nd t lumnscnc nd mxmum of QDs cn found s:.786 * ν = v.48ry, (5) 4πεε w s t vg dus of t nsml of nnoptcls. As t ws found [7], t ntnsty of lumnscnc nd, clcultd usng q. (4), coctly dscs t cospondng xpmntl dpndnc fo t nsml of InP quntum dots. Usully, st of quntum dots contns ptcls of dffnt, sttstclly dstutd szs, wc sults n ot sopton nd of lumnscnc spct, dpndnt on cctstcs of t QD nsml. In ptcul, t lumnscnc nd lfwdt ncss wt t quntum dots dspson ncs. Addtonlly, t tml smng of QDs ngy lvls sults n ncs of t sopton nd lumnscnc ndwdt. As sult of t ffct of tml wdnng t ngy lvls nd spd of quntum dots n sz, t lumnscnc nd sopton nds ovlp, dtmnng t vlu of sopton (sopton of lumnscnc quntum). T lg t spd of quntum dots, t gt t sopton vlu. Wl t ov xpssons ssntlly coctly dsc t voluton of lumnscnc nd sopton spct of t sz dspsd QDs, ty do not llow stmtng t voluton of sopton wt t dus. T pupos of ts wok s fstly to dv xpssons tt poply tk nto ccount t dstuton of nnoptcl sz nd t tml spdng t quntzd lvls on sopton. Scond nlyss of t dvd xpssons ngs undstndng t mpct of t nnoptcl sz nd t dspson of on sopton, lumnscnc nd sopton. xtctd fom t sopton nd lumnscnc spct. To nvstgt voluton of sopton wn QD dmnsons cngd, t s suffcnt to dtmn t vg QD co sz (dus o dmt). It cn don y compng known xpmntl poston of t sopton spctum mxmum fomd y lcton tnstons fom t ngy lvls nd wt t totcl on. Tfo, to xtct t vg QD dus w dvd n xpsson fo t quntum dot lgt sopton dpndnc on t poton ngy p n t fom: α ( ) p = A xp 3 ( p ) ( ) ( ) σ xp σ d, (6) H, A s t constnt, wc s QD dus, ndpndnt nd dtmnd fom nomlzton of t sopton to unty. T fst xponnt (Gussn dstuton on t ngy ) dfns t tml smng σ of t quntzd ngy lvls n t conducton nd nd of t lgt ols vlnc nd. Wn clcultng t sopton spctum fom q. (6), t s suffcntly ccutly to us σ = kt (k s t Boltzmnn constnt, nd T solut tmptu). T scond xponntl (Gussn QD sz dstuton) lts QDs dus dspson σ nd t optcl spct odnng. H, t ngy ( ) cosponds to t sopton mxmum of QD wt ts co dus. Nxt, w clcult t sp of t sopton nd fomd y t lcton tnston fom t lvl to on. T ngy spctum of lumnscnc pk poston s stmtd usng t fomul (5). W dvd t xpsson fo sp of t lumnscnc spctum, wc cn wttn s:. Asopton nd lumnscnc spct of t quntum dot co Usully, QDs wt g lumnscnc quntum yld contn co suoundd y on o mo slls of smconducto mtls nd sll of ognc mtl (Fg. ). Typclly, t co s md of now-gp smconducto, wc tnsfoms t od sol spctum nto now lumnscnc nd. T fst (nognc) sll nsus t dnglng onds pssvton t t sufc of t QD co. T nd gp of ts nognc sll s wd tn t co gp. If svl nognc slls psnt, c succssv sll dffs fom t pvous y n ncsd nd gp. T mn pupos of t mult-sll dsgn s to lgn smconducto lttc pmt, ducng dsloctons ppnc. T out ognc sll conssts of ognc molculs, dpostd on t top nognc sll, nd ts mn pupos s to pvnt gggton of QDs. Gomtc cctstcs of QDs nd t sz dspson usully dtmnd fom t lcton mcoscopy msumnts: t vg co sz cn Fg.. Scmtc psntton of t stuctu of mult-sll spcl quntum dot. Its co s composd of smconductng mtl (ts ulk ngy gp dsgnt s g ), covd y nognc sll(s) to pssvt t co sufc. T out ognc sll nsus tt QDs do not gggt. A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 6

4 SPQO, 8. V., N. P Glol Lumnscnc Intnsty (. unts) T = 98 K Glol PL c 6 A ngy (V) c 48 A c 4 A 35 A 3 A <d>=6 A xctton ngy Asonc (. unts) Fg. 3. Asopton (sold ln) nd glol PL (dottd ln) spct t 98 K fo collodl nsmls of InP QDs wt dffnt mn dmts. All QD collodl smpls w potoxctd t.48 V. (Fom t ognl Fg. n [7].) I PL ( ) p = B xp 3 ( p PL ( )) ( ) σ xp σ d, (7) w B s t constnt ndpndnt of t dus nd s dtmnd fom t nomlzton condton of t lumnscnc ntnsty I PL ( PL ) to unty, w PL ( ) s t ngy of t lumnscnc ntnsty mxmum of QD of dus. Accodng to t toy of [8], wc tts ntcton of smconducto nd stts wt potonc fld, t low ngy pt of PL spct s dtmnd y t dnsty of stts, wl t g ngy pt of t spct s dfnd y t dstuton functon. T dnsty of stts, wc contuts to fomton of t sopton spct, s muc g tn t dnsty of stts, wc contuts to fomton of lumnscnc spctum, tfo, t stndd dvton σ fo t sopton spct s lg tn tt fo t lumnscnc spct. 3. ffct of t szs of quntum dots, t dspson nd tml odnng t quntzd lvls on sopton W stmt t ffct of QD sz (nmly, ts co dus), QD sz dspson nd t tml odnng on t sopton y usng s n xmpl InP QDs. T sopton nd lumnscnc spct sown n Fg. 3. To clcult sopton, fomd s sult of t tnston of lctons fom t lvl to t lvl, nd t ntnsty of lumnscnc sultng fom tnstons of lctons fom to, w us (6) nd (7) nd tk nto ccount t dpndnc of t optcl ndgp on t QD co dus [9]. To stmt t sopton mgntud, t pocdu to follow t fstly, usng xpmntlly known ngs of t fst sopton mxmum nd t lumnscnc pk (Fg. 4), w fnd t mn dus of t quntum dot v fom q. (5). Scondly, usng qs. (6) nd (7), w clcult spct of sopton nd lumnscnc, nomlzd to unty. T ntscton of ts two cuvs s msu of sopton. It s known tt tnsmttnc msumnt o dos not xcd.4% (s, fo xmpl, []) nd fluoscnc ntnsty msumnt o (lumnscnc) dos not xcd.6% (s,.g., [, ]). Tfo, wn coosng QDs fo sol fluoscnt concnttos wt mnml sopton, w cn consd only tos smconductos, n wc t vlu of sopton s lss tn 3%. In t mjoty of scs on t ffcncy of potovoltc sol lumnscnt concnttos, t plstc PMMA plt wt QDs s usd. Snc t plstc plt s tnspnt n t wvlngt ng.4 µm, (o 3.. V), ou nlyss of t ffct of t QD dus nd ts dspson on sopton ws pfomd fo t Lumnscnc ntnsty (ν) ngy (V) Asonc (. unts) Fg. 4. Spct of QD sopton (sold ln) nd lumnscnc (dss). T lumnscnt potons, mttd wtn t ngy ng, cn sod nd t tcd cctz t sopton lumnscnt potons. T ngy spton twn t fst pk of sopton spctum nd t pk of QD lumnscnc s qul ν. T QD mn dmt s 3.5 nm. T ozontl ow ndcts t pont w t sopton nd lumnscnc spct cossng. A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 6

5 SPQO, 8. V., N. P smconducto QD co wt t optcl ndgp lyng wtn t ng. 3. V. Usng qs. (6) nd (7), w fnd dpndnc of nnoptcls sopton on t dus nd dspson (%, 5%, % nd % QDs dspson vlus consdd), nd t s sown n Fg. 5. As dstnct ftu of t totcl cuvs n Fg. 5, t psnc of t mnmum ndcts tt t optmum QD co sz mn tt mnmzs sopton cn lwys cosn. Indd, QD sz ncs ov mn ducs t ngy spton twn t pks of t sopton nd lumnscnc, tus ncsng sopton. Wn QD sz dcss low mn, t ffct of tml Ovlppng, % σ = % CdS odnng of t quntzd ngy lvls sults n t gowt of sopton. Accodng to Fg. 5, wt dcs of t QD sz dspson, t optmum mn coms smll. It s cl tt fo CdS-sd quntum dots mn s lwys ov. nm t ny vlu of t QD sz dspson. On t ot nd, n PS quntum dots vn fo t co dus of nm nd vy low QD sz dspson of %, sopton cnnot low 54%. Usng t sults fom Fg. 5 nd known smconducto ulk nd gp vlus, w plot n Fg. 6 t gp dpndnc of sopton fo svl vlus of QD co sz dspson, nmly: %, 5%, % nd %. Accodng to Fg. 6, ducton of t QD co sz Ovlppng, % InP σ = % Ovlppng, % Ovlppng, % QD sz, nm σ = % QD sz, nm CdT CdS QD sz, nm σ = % QD sz, nm A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 6 Ovlppng, % Ovlppng, % InAs QD sz, nm σ = % σ = % QD sz, nm PS Fg. 5. Dpndnc of sopton on t QD co dus fo fou vlus of t sz dspson. To pp t gps, xpmntl dpndncs of t sopton nd lumnscnc s n consdd. T followng ngy gp vlus w consdd: CdS ( g =.49 V), CdS ( g =.74 V), CdT ( g =.43 V), InP ( g =.7 V), InAs ( g =.355 V), PS ( g =.7 V).

6 SPQO, 8. V., N. P Ovlppng, % % % % % Gp, V Fg. 6. Dpndnc of sopton losss on t smconducto nd gp g fo dffnt sz dspson vlus. T d ozontl ln, clos to t x-xs, ms to comp t nomlzd xpmntl ccucy of t msud QDs spct to t sopton losss. Ovlppng, % σ = % σ = 5 % σ = % s, V Fg. 7. Dpndnc of t QD sopton on t optcl ndgp of t nnoptcl. T d ozontl ln, clos to t x xs, ms to comp t nomlzd xpmntl ccucy of t msud QDs spct to t sopton losss. T = 3 C. dspson sults n t plll sft of t sopton dpndnc on t nd gp. Consquntly, t vlu of t nd gp, t wc t sopton coms nglgl, sfts to t low ngy sd. Cunt QD tcnology offs gly omognous nnoptcls wt 5% sz dspson [8, 9]. At 5% sz dspson, sopton cn nglgl (tt s low xpmntl o), f t QD co smconducto ulk nd gp xcds.8 V. To dtmn t wdt of t sol spctum, fom wc t ncomng potons tnsfomd nto lumnscnt potons, consd t dpndnc of QDs sopton on t optcl nd gp. Fo ts, w susttut mn vlus fom Fg. 5 nto q. () nd clcult t optcl gp,, of t QD co. n l Altntvly, w cn us t gps, du to t quntum confnmnt n t nnoptcls, gvn n [9]. T sultng sopton dpndnc on t optcl ndgp of QD s sown n Fg. 7, wc dmonstts tt t slop of t sopton dpndnc dcss wt ducton of t QD sz dspson. It mns tt wt t QD sz dspson dcs, t sunlgt sopton ndwdt lso dcss. In ptcul, fo t QD cos wt 5% sz vton, t ng of sopton of sol lgt potons xtnds t g-sd sttng fom.7 V. 4. Conclusons T quntum dots sopton cctstcs v n nvstgtd consdng t dpndnc on t QD co sz, ts dspson nd t ulk nd gp of t smconducto co. It s n sown tt wt t co sz dcs t xsts t optmum QD dus tt mnmzs sopton. Dcsng o ncsng t sz of t QD co wt spct to t optml sz lwys ncss sopton. It s n found tt wt dcsng t nd gp g of t co smconducto (wl g.8 V) nd 5% sz dspson, t s possl tt sopton cn nglgly smll (tt s, low t xpmntl dtcton lmt). In contst, wn g.8 V, fut t nd gp g dcs only lds to t gowt of sopton. Fo nstnc, fo gly omognous wt only % sz dspson, PS QDs wt g =.7 V, t smllst sopton xtnds to 54%. Rfncs. Kt A. Lumnscnt Mtls nd Applctons. Jon Wly & Sons Ltd, T Atum, Soutn Gt, Ccst, Wst Sussx PO9 8SQ, nglnd.. B D., Qn L., Tsng T.-K nd Hollowy P.H. Quntum dots nd t multmodl pplctons: A vw. Mtls.. 3. P ; do:.339/m346 fl Cn P.T-K. Lumnscnt Popts of Smconducto Nnocystls. lxnd.tu.nl xt/8794.pdf. 4. Flogg S. Pctcl Quntum Mcncs. Spng Vlg, Bln Nw Yok, Jsnk J., Smt L., vn mdn J., Mulvny P., Clfno M. R-xmnton of t sz-dpndnt sopton popts of CdS quntum dots. J. Pys. Cm. C P Imn A. Modcton of Spontnous msson of Quntum Dots y Potonc Cystls. Gduton Tss, Novm 3. Complx Potonc Systms (COPS) Goup MSA + Insttut Fculty of Scnc nd Tcnology Unvsty of Twnt nscd, T Ntlnds cops. nno-cops.com/ sts / dfult / fls / mn.pdf. 7. Mcc O.I., Cong H.M., Fu H., Zung A., Spgu J.R., Mscns A., nd Nozk A.J. Szdpndnt spctoscopy of InP quntum dots. J. Pys. Cm. B P vn Roosock W. nd Sockly W. Potondtv comnton of lctons nd ols n gmnum. Pys. Rv , Issu 6. P A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 63

7 SPQO, 8. V., N. P Bskouts S., Tzs A.F. Sz-dpndnt nd gp of collodl quntum dots. J. Appl. Pys P Ruz A., Zwnkls J., Bouglux I., Buc S., ly. nd Bns P.Y. Intmcn mtology systm (Sm.) ntcompson of wvlngt scl nd potomtc scl of spctopotomty lotos CNAM-NRC-INMTRO-NIST. SIM.. Intmcn Mtology Systm (SIM.).. Plm B.J., Wntton K., Jns M. Scop of ccdtton to ISO/IC 75:5. Op- Spcon LLC 35 N 3 W Not Logn, UT ANSI-ASQ Ntonl Accdtton Bod/ACLASS; SpconScop.pdf.. Fosz K. Scop of ccdtton to ISO/IC 75:5. Molcul Dvcs, Inc. 3 Olns Dv Sunnyvl, CA documnt/so-c-75-ctfcton-fom-l.pdf Autos nd CV Skt A.I. Pofsso, P.D. n Pyscs nd Mtmtcs, Pofsso t t Unvsty of Onto, Insttut of Tcnology. T of scntfc ntsts of Pof. Skt ncluds sold stt pyscs, smconductos nd t sufcs s wll s nnomtls, nonln optcl pnomn, lctonc stuctul nd dynmcl popts of novl mtls. Unvsty of Onto Insttut of Tcnology Scnko A.V.: Pofsso, Docto of Scncs n Pyscs nd Mtmtcs, Cf Rsc t t Dptmnt of Smconducto Sufc Pyscs nd Potolctcty, V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn. T of scntfc ntsts of Pof. Scnko ncluds pyscs of smconductos nd potovoltcs dvc smulton. V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn Sokolovsky I.O.: P.D. n Pyscs nd Mtmtcs, Sno Scntst t t Dptmnt of Smconducto Sufc Pyscs nd Potolctcty, V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn. T of scntfc ntsts of D. Sokolovsky ncluds pyscs of potoconvson, nlytcl nd numcl dvc smulton. V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn Kostylyov V.P.: Docto of Scncs n Pyscs nd Mtmtcs, Hd of t Lotoy of Pyscl nd Tcncl Fundmntls of Smconducto Potongtcs, V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn. T of scntfc ntsts of D. Kostylyov ncluds potovoltc ngy convson pyscs n smconductos nd smconducto potoconvts dvlopmnt. V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn Kuls M.R.: Docto of Scncs n Pyscs nd Mtmtcs, Ldng Rsc t t Dptmnt of Optcs nd Spctoscopy, V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn. T of scntfc ntsts of D. Kuls ncluds t nvstgton of optcl nd nonln optcl popts of 3D nd D smconducto stuctus. V. Lskyov Insttut of Smconducto Pyscs, NAS of Ukn A.I. Skt, A.V. Scnko, I.O. Sokolovsky, t l. Impct of smconducto quntum dots ndgp 64