Effect of temperature on non-linear optical properties of InGaAs/GaAs single quantum dot

Transcription

1 Indian Jounal of Pu & Applid Pysics Vol. 44, Fuay 6, pp ffct of tmpatu on non-lina optical poptis of InGaAs/GaAs singl quantum dot M K afna, P Sn & P K Sn Dpatmnt of Applid Pysics, S G S Institut of Tcnology & Scinc, 3, Pak Road, Indo 45 3 mail: patima_sn@otmail.com Rcivd 5 May 5; visd 3 Novm 5; accptd 5 Dcm 5 asd upon t smi-classical dnsity matix appoac, a dtaild totical invstigation as n mad to analyz t ffct of tmpatu on non-lina optical poptis of InGaAs/GaAs singl quantum dot (QD. T tmpatu ffcts av n incopoatd via tmpatu dpndnt (i dpasing mcanism, (ii gap ngy (iii population dnsity. T smiconducto QD as n cosn to small noug suc tat t confinmnt ffct dominats ov t Coulomic contiution. Dtaild numical stimats of t non-lina faction asoption poptis av n mad. Rdsifts of t non-lina faction asoption paks as wll as duction in t inducd polaization a found to occu wit incasing tmpatu. T psnt analysis fut vals tat t non-lina gain ducs at ig tmpatu. Kywods: Smiconducto quantum dot, Tmpatu dpndnt non-lina asoption, xciton, ixciton, Tid-od suscptiility. IPC Cod: 8 3/ 1 Intoduction T zo dimnsional stuctus a finding applications in advancd optlctonic dvics suc as lass 1, dtctos optical mmoy lmnts 3 as ty pov advantagous in tms of low tsold cunt dnsitis, ig gain ig quantum fficincis 1,4. T poptis of t nanostuctus, in paticula quantum dots (QDs can modifid in a contolld mann y canging ti siz sap. T ducd dimnsions of QD causs incasd spatial ovlap twn lcton ols. As a sult, along wit xcitons, ixcitons a also fomd. Tus in t dtmination of optical poptis of smiconducto QDs, ixciton also play an impotant ol. T ngy spaation of t xcitonic ixcitonic lvls is tmpatu snsitiv nc t dvic ngining quis a full undsting of t tmpatu dpndnc of t potoluminscnc spcta (PL in t QDs. xtnsiv studis 5-8 av ing caid out to discuss t ffct of tmpatu on t potoluminscnc poptis of quantum dot. Jiang t al. 9 Mazu 8 av potd a d sift in t PL pak in InGaAs/GaAs QDs wit incasing tmpatu. T d sift in an odd aay of quantum dot is suggstd to occu du to t latal vtical tansf of xcitations. Tmal quncing of potoluminscnc in QDs can attiutd to t tmal activation of cag cais fom confind wll into ai followd y an ffctiv nonadiativ comination 7-9. T unusual tmpatu aviou lik duction in linwidt wit incasing tmpatu as wll as fast dsift in ngy implis intsting intactions in dot systms suc a tmionic mission cai population among QDs. In cnt yas, ig spatial solution tcniqus av n usd to isolat singl QD stuctu allowing t masumnt of linwidt, Stak-sift, ixcitonic ngy lvls tc. Most of ts studis a asd on PL as a po. In t psnt pap, w av studid t ffct of tmpatu on t PL spcta of a singl QD. Totical Fomulations Smiclassical dnsity matix appoac as n mployd to analyz t ffct of tmpatu on t optical poptis of smiconducto QDs. W consid singl smiconducto quantum dot of spical sap in a stong confinmnt gim. It is appopiat to dsci t optical poptis of t quantum dot y taking into account t xcitonic ixcitonic ngy lvls. T optical tansitions occu twn t cystal gound stat o> to xciton stat > as wll as xciton > to t ixciton stat >. T

2 AFNA t al.: FFCT OF TMPRATUR ON OPTICAL PROPRTIS OF QUANTUM DOT 153 xciton ngy lvl in tis confinmnt gim is dfind as 1 : 3.57 ff κ a nl g.48 ; R m R R ω ω (1 ff αt ω g ω g (. ( T β ff In q. (1, ω g is t ulk cystal gap ngy at tmpatu T (Rf. 11; m R a ffctiv ducd mass xciton Rydg ngy, spctivly wil α β a Vasni paamts. T scond tm on t R.H.S. of q. (1 psnts t confinmnt ngy. κ nl is t n t oot of t l t od ssl function wit n l cosponding to t 1s, 1p 1d lvls of t lctons ols, spctivly. T tid tm psnts t Coulomic intaction ngy of lcton-ol pais w a R a t ulk xciton o adius quantum dot adius, spctivly. T Coulom xcang foc twn xciton pais gnats ixciton nc t ixciton ngy is sligtly small tan t ngy of two xcitons dfind as: ω ω. ( T ixciton inding ngy is dpndnt on t quantum dot siz can calculatd y using t following xpssion 1 a 1/ R[1.8( a / R.4] R. H, a ing t ol o adius. T unptud Hamiltonian can dfind as, ω o H o ω. (3 ω T intaction of QD wit t lctomagntic 1 iωt adiation ( t ( o c. c is considd to dipol typ. T intaction Hamiltonian is psntd y H I ˆ μo. * ˆ μ. ˆ μ. ˆ μ. *, (4 w t lctic fild is takn to paalll to t tansition dipol momnt opatos μˆ ij, wic is latd to t tansition momntum p as 13 μ ij j p i. (5 moωij H, m o is t lcton st mass, ωij is t tansition ngy. In t psnt calculation, w av incopoatd t losss occuing du to ot adiativ non-adiativ dcay pocsss. T omognous oadning at low tmpatu is potd in t ang of 5 μ V, in In x Ga 1-x As QD is attiutd to pu dpasing 14. Ts laxation pocsss a incopoatd via H as: H γ o γ (6 γ T laxation paamts a stongly tmpatu dpndnt a givn y γ γ at xp ( a / kt 1 ( / k T 1 (7a γ γ 11 a1t. (7 xp a H, a, γ, γ 11, a, a 1 a takn fom t xpimntal osvation of oi Co-Woks T QD-adiation intaction is psntd y t Scoding s quation of motion d i 1 [ H, ] { H, }, (8 dt wit dnsity matix takn as oo o o. (9 o T dnsity matix quations a xpd fo vaious ods of t dnsity matix lmnts (1 ( (3..., w t zo t od tmpatu dpndnt dnsity distiution function of cystal gound, xciton ixciton stats a dfind as

3 154 INDIAN J PUR & APPL PHYS, VOL 44, FRUARY 6, (1a 1 ff { ω ( / } ω g κnl mr kt xp(, (1 ω xp( { }. k T (1c H, k T is t tmal ngy. Vaious ods of t dnsity matix lmnts a calculatd y using qs (4-(1 as Ω( (1 Ω ( Ω(, Ω ( (11 A ( C, (1 D (3 ( Ω( C A Ω ( Ω( A C ΩD ( Ω( C Ω ( Ω( C ΩD A wit 4Ω 1 1 (, ω 4 ΩΩ ( (, ω o ( C ( Ω ω iγ 1 1 (, Ω D 4Ω Ω ω ( ( 4Ω 1 1 ( ω iγ, w, ij ω ± ωij iγ ij is t damping incopoatd dtuning paamt wit suffixs 1 cosponding to (iv ( iv signs, spctivly. Also Ωij μ ijε o / is t Rai fquncy. T damping constant psntd y γ ij cosponds to t pas laxation tms of xciton ixciton, spctivly. T total inducd polaization (1 ( (3 P P P P... ; as n otaind. T vaious ods of t inducd polaization a otaind a: P (1 ± μ ( μ ( ( ω ω iγ ( ω ω ω iγ, (14 ( P, (15 P 16 μ ( ( ω iγ 4 3 (3 3 ωω (. iγ( ωω iγ 3 8( μ ( μ ( 3 ( ω ωω ωω γ γγ ω( ω iγ( ω ω iγ ( ω ω ω iγ i( ωγ ωγ ωγ γ ω ωω ( iγ( ωω iγ ( ω ω ω iγ

4 AFNA t al.: FFCT OF TMPRATUR ON OPTICAL PROPRTIS OF QUANTUM DOT μ μ ( 3 ( ω ωω γγ γ ωω ωω ( iγ( ωω iγ( ω ω ω iγ i(ωγ ωγ γ ω ωω ( γ ( ω ω γ ( ω ω ω γ i i i μ. ( ( ω iγ 3 ( ω iγ( ω iγ( ω ω ω iγ (16 In otaining qs (14-15, t off sonant tm ij as n nglctd quation (14 distinctly yilds t fist od-inducd polaization P (1. T fist t scond tm cospond to t o> > > > tansitions via fist t scond tm, spctivly. At low tmpatus w t xciton population lvls a mpty, t > > tansitions will asnt. Fo a symmtic quantum dot, as givn y q. (15 t scond-od polaization tm vaniss. In alistic situation, t asymmty in t quantum dots du to ti sap siz is always psnt w av not givn du attntion to t asymmty popty of t QD. T tid-od inducd polaization as psntd y q. (16 compiss of t contiutions fom ot o> > > > tansitions. Also t tid-od inducd polaization can dictly latd to t tid-od non-lina optical suscptiility via t wll-known (3 (3 lation χ P. T fist tm in ε q. (16 psnts t tid-od optical nonlinaity aising du to o> > tansitions only dpnds stongly on t sonanc of incidnt poton ngy wit t xcitonic ngy. T scond tid tms av ti oigins in t contiutions fom ot t xcitonic o> > ixcitonic > > tansitions. 3 Rsults Discussion T numical analysis to xamin t tmpatu dpndnc of tid-od non-lina optical suscptiility in a smiconducto QD sujctd to a cw cont adiation is psntd. W av cosn InGaAs/GaAs QD duly iadiatd y a cw Ti: Sappi las. T matial paamts slctd fo t psnt analysis a 16 ω g 1.3 V, m.5 m, m.384 m wit m ing t f lcton mass quantum dot diamt 15 nm. In od to calculat t xciton (γ ixciton (γ dpasing tims, w us q. (7 wit t numical valus of t vaious paamts fom t xpimntal osvations of oi t al. 14,15 as a 16 mv, γ.67 μ V, γ 11 μ V, a. μ V/K, a 1.37 μ V/K 1.1 mv fo spcific valus of t tmpatu T. W av slctd t input fild stngt 1 7 Vm -1 in t psnt computation. In Fig. 1, t total inducd polaization as a function of t pump poton ngy at 5, 1, 15 K as n plottd. Fom Fig. 1, it can sn tat two distinct paks appa at 5 K. Ts paks cospond to t xciton ixciton ngis (ixciton pak ing at low ngy. Wit incas in tmpatu, t tmal oadning also incass suc tat t ixciton pak coms almost insignificant. Tis is quit ovious du to t wll-known fact tat ixcitonic ffct plays impotant ol only at vy low tmpatus. T pak positions of t inducd polaization fut vals tat t incasing tmpatu causs significant dsift in t pak valu of t polaization. T duction in ot xciton ixciton ngis wit incasing tmpatu is claly manifstd fom t sam figu, suc d sift in t PL pak was also potd y Jiang 9 Mazu 8 indpndntly. W av calculatd t non-lina asoption cfficint α fom t non-lina polaization y (3 dfining it as α k Im P ; k ing ε t wav vcto of t pump poton. In Fig., α as Fig. 1 Caactistic tmpatu dpndnc of t total inducd polaization in In x Ga 1-x As/GaAs singl quantum dot

5 156 INDIAN J PUR & APPL PHYS, VOL 44, FRUARY 6 of non-lina faction incass at low tmpatus. 4 Conclusion T ffct of tmpatu on non-lina optical poptis gain in an InGaAs/GaAs singl quantum dot is studid. It is found tat t ixcitons play an impotant ol only at low tmpatu. Moov, t lowing of tmpatu nancs ot non-lina faction asoption poptis of t singl quantum dot. Fig. Caactistic tmpatu dpndnc of t non-lina asoption cfficint in In x Ga 1-x As/GaAs singl quantum dot Fig. 3 Caactistic tmpatu dpndnc of t non-lina faction cfficint in In x Ga 1-x As/GaAs singl quantum dot a function of pump poton ngy as n plottd at 14, K. A ngativ valu of na t sonanc ngy manifsts t occunc of nonlina gain. Fom Fig., a d, sift in sonanc ngy wit incasing tmpatu can noticd. T magnitud of t non-lina gain is also found to dcas wit incas in tmpatu. Fut, t ffct of tmpatu on non-lina faction (nonlina factiv indx n is xamind is found to dictly popotional to t al pat of t tidod non-lina optical suscptiility. In Fig. 3, n as n plottd as function of t pump poton ngy at 14, K. It can claly osvd tat n coms significant only na t sonanc fquncy. Fom Fig. 3, w find tat apat fom dsift in sonanc fquncy, t magnitud Acknowldgmnt On of t autos (MK is gatful to All India Council fo Tcnical ducation Nw Dli, fo t awad of National Doctoal Fllowsip. T financial assistanc fom Dpatmnt of Scinc Tcnology, Govnmnt of India is also gatfully acknowldgd. Rfncs 1 Aakawa Y & Sakaki H, Appl Pys Ltt, 4 ( Pan D & Tow, lcton Ltt, 34 ( Tamamua K, Sugiyama Y, Nakata Y, Muto S & Yokoyama N, Jpn J Appl Pys, 34 (1995 L img D, Kistt D, Ldntsov N N, Alfov Z I, Kop'v P S & Ustinov V M, I J Sl Top Quantum lcon, 3 ( Lonad D, Fafad S, Pond K, Zang Y H, Mz J L & Ptoff P M, J Vac Sci Tcnol, 1 ( Luysv D I, Gonzalz-oo P P, Maga (J, Ptitpz, Lascala N (J & asmaji P, Appl Pys Ltt, 68 ( Hu Z Y, Lu Z D, Yang X P, Yuan Z L, Zng Z, Xu J Z, Wang W K G Y, Wang J & Cang L L, Pys Rv, 54 ( Mazu Yu I, Ma W Q, Wang X, Wang Z M, Salamo G J, Xiao M, Misima T D & Jonson M, Appl Pys Ltt, 83 ( Jiang W H, Y X L, Xu, Xu H Z, Ding D, Liang J & ang Z G, J Appl Pys, 88 ( Twoga P F, Knyon J A & Pitt C W, J Appl Pys, 83 ( O Donnll K P & Cn X, Appl Pys Ltt, 58 ( anyai L, Hu Y Z & Koc S W, Pys Rv, 38 ( Takagaaa T, Pys Rv, 39 ( oi P, Langin W, Scnid S, Woggon U, Sllin R L, Ouyang D & img D, Pys Stat Sol (, 38 ( oi P, Langin W, Scnid S, Woggon U, Sllin R L, Ouyang D & img D, Pys Rv Ltt, 87 ( Kazi Z I, gawa T, Jimo T & Umno M, Jpn J Appl Pys, 39 ( 386.