Energy Level Calculations in Diluted Magnetic Semiconductor Core Shell Quantum Dots

Transcription

1 Cloud Publications Intrnational Journal of Advancd Physics 03, Volum, Issu, pp. 4-8, Articl ID Sci- Rsarch Articl Opn Accss Enrgy Lvl Calculations in Dilutd Magntic Smiconductor Cor Shll Quantum Dots Bashir Mohi Ud Din Bhat and Pratima Sn Dpartmnt of Physics, Govt. Dgr Collg Boys, Baramulla, Jammu and Kashmir, India Dpartmnt of Physics, DAVV, Indor, Madhya Pradsh, India Corrspondnc should b addrssd to Bashir Mohi Ud Din Bhat, bhatbashirphy@gmail.com Publication Dat: 9 Sptmbr 03 Articl Link: Copyright 03 Bashir Mohi Ud Din Bhat and Pratima Sn. This is an opn accss articl distributd undr th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original work is proprly citd. Abstract From th prsnt xprimnt, it is clar that in small magntic fild, th nrgis of spin up lctron stat incrass with incrasing magntic filds and dcrass for spin-down lctron stats with incrasing magntic filds. At small magntic fild, th nrgis ar dtrmind by th xchang intraction trm for both spin up and spin down lctron stats. At larg magntic fild, th xchang trm approachs to a constant and th nrgis ar dtrmind mainly by th magntic confinmnt trm that is th Zman trm. Th analysis mad in this rsarch can b usful for prdicting tunnling of lctrons and hols from cor to shll and can hav applications in calculating th spin polarizd currnt from th CSQDs. Kywords Smiconductor, Junction Smiconductors, Quantum Dots. Introduction Magntic smiconductors ar smiconductor matrials that xhibit both frromagntism and usful smiconductor proprtis. Magntic smiconductors would also allow control of quantum spin stat (up or down). Furdyna J.K., (988) for th first tim rviwd th physical proprtis of dilutd magntic smiconductors (DMS) of th typ A II -xmnxb VI. Dilutd magntic smiconductors (DMSs), i.. smiconducting crystals whos lattic is mad up in part of substitutional magntic ions (.g. Cd - xmn x T, Hg -x F x S, Zn -x Co x S) (Samarth t al., 990). A wid class of smiconducting matrials is availabl, which ar charactrizd by th random substitution of a fraction of th original atoms by magntic atoms. Such matrials ar trmd commonly as smimagntic smiconductors (SMSC) or dilutd magntic smiconductors (DMS) (Balkanski and Wallis, 000). Th most common SMSC ar II-VI compounds (lik CdT, ZnS, CdS, CdS, tc.), with transition mtal ions (.g. Mn, F or Co) substituting thir original cations. Thr ar also matrials basd on IV-VI (.g. PbT, SnT) and rcntly III-V (.g. GaAs, InSb) crystals. In som cass, th rar arth lmnts (.g. Eu, Gd, Er) ar also usd as magntic atoms in SMSC. Ths mixd crystals (smiconductor alloys) ar thought to considr as containing two intracting subsystms. Th first of ths is th systm of dlocalizd

2 IJAPhy An Opn Accss Journal conduction and valnc band lctrons (Kyrychnko and Kossut, 000). Th scond is th random, dilutd systm of localizd magntic momnts associatd with th magntic atoms. Th fact that both th structur and th lctronic proprtis of th host crystals ar wll known mans that thy ar prfct for studying th basic mchanisms of th magntic intractions coupling th spins of th band carrirs and th localizd spins of magntic ions. Th coupling btwn th localisd momnts rsults in th xistnc of diffrnt magntic phass (such as paramagnts, spin glasss and antifrromagnts). Th mangans-basd SMSC (i.. with Mn as th magntic cations) has providd a good undrstanding of th bhavior of ths smiconductors. Th first of wid gap SMSC to b studid was CdMnT. Th xtrmly larg Zman splittings of th lctronic bands, and th giant Faraday rotation obsrvd hav bn ascribd to th xchang intraction btwn th s, p band lctrons and th d lctrons associatd with th Mn ions. A quantum dot (QD) is a nanoscal structur (Goronkin t al., 999) consisting of on or mor smiconducting matrials in which th motion of fundamntal charg carrirs is confind in all spatial dimnsions (Nicolas, 006). Nanocrystals of group II-VI smiconductor quantum dots in which lctron and hols ar thr dimnsionally confind within th xciton Bohr radius of matrial ar charactrizd by th optical proprtis such as broad absorption and sharp mission bands.. Matrials and Mthods Th xprimnt was carrid as pr th standard mthod of Luttingr (995). Undr sphrical approximation th luttingr paramtrs for ZnS ar as 3. 94,. 00,and 3. 5, th luttingr paramtrs for ZnS ar. 77, 0. 3 and ; Land g-factor for lctron, g.5 and for hol g. 6 ; fitting paramtrs So and To ar 0.4 and 3.6 rspctivly; ffctiv mass of lctron o. 7 h * m and th Luttingr paramtr kappa Rsults and Discussion Th fram work so far has th gnrality intact and is applicabl to all magntic dopd II-VI smiconductor cor shll quantum dots (CSQDs). Th prsnt rsults hav bn applid to a spcific CSQDs of which cor is mad of Mn dopd ZnS and shll is ZnS. For numrical stimation, w hav chosn Mn ions as th transition mtal ions for doping and hav accountd for th s-d and p-d xchang intraction. W considrd vry small DMS CSQDs in th strong confinmnt rgim with both magntic fild and gomtrical confinmnts influncing th optical proprtis of th CSQDs. Mor or lss similar obsrvations hav bn rportd by Brgqvist t al., (004). Th authors dmonstratd that th magntic proprtis of dilutd magntic smiconductors ar dominatd by short rangd intratomic xchang intractions that hav a strong dirctional dpndnc. In prsnt xprimnt, th radius of th cor of 9 CSQDs is takn to b.5x0 m which is smallr than th xciton Bohr radius 5.x0-9 m. Th magntic fild was assumd to b applid along z-dirction such that a symmtric magntic confinmnt occurs in x-y plan. Th lctron and hol nrgis ar givn by: 9 Ac E = g BB Ax 4 3 m V c Intrnational Journal of Advancd Physics 5

3 Elctron Enrgis (mv) IJAPhy An Opn Accss Journal 3hB E 3 hh B x m0a 4m0 Th matrial paramtrs usd in th calculation ar th conduction and valnc band offst which ar 0.58v and 0.03v rspctivly. Kyrychnko and Kossut (000) prsntd a thortical study of th valnc-band stats in dilutd magntic smiconductor quantum wir structurs. As a consqunc of confinmnt in two dirctions, th hol stats in a quantum wir ar known to b mixturs of havy- and light-hol componnts. Du to a strong p-d xchang intraction in dilutd magntic smiconductors, th rlativ contribution of ths componnts is strongly affctd by an xtrnal magntic fild, which lnds complt support to our findings. Luttingr paramtrs undr sphrical approximation ar takn as 3.94,.00 and.5 for ZnS whil for ZnS th sam Luttingr paramtrs ar.77, 0.3 and 0.6. Land g-factor for lctron g. 5 and for hol g. 6, fitting paramtrs So and To b 0.4 and 3.6 h rspctivly. Effctiv mass of lctron m 0. 7 and th Luttingr paramtr Using ths paramtrs in quations and abov, th lctron nrgy as function of magntic fild hav bn plottd in Figur for concntration (0., 0., 0.3) at tmpratur T=0k. 6 4 a + con. 0. b + con. 0. c + con. 0.3 a - con. 0. b - con. 0. c - con Magntic Fild (T) Figur : Elctron Enrgy as Function of Magntic Fild Th curvs a,, b c ar plottd for th dopant concntration 0., 0. and 0.3 rspctivly. Th supr scripts rprsnt th lctron spin up and spin down stats. From th Figur, it is clar that at small magntic fild, th nrgis of spin up lctron stats incrass with incrasing magntic filds and dcrass for spin-down lctron stats with incrasing magntic filds. At small magntic fild, th nrgis ar dtrmind by th xchang intraction trm for both spin up and spin down lctron stats. At larg magntic fild, th xchang trm approachs to a constant and th nrgis ar dtrmind mainly by th magntic confinmnt trm that is th Zman trm. Th rason for this is that at larg magntic filds, th dopd Mn ions ar alignd compltly. This furthr rvals that th Zman splitting of lctron dominats ovr th xchang splitting. Thrfor, w find cross ovr point of both spin up and spin down stats whr th xchang trm and th Zman trm compnsat. Intrnational Journal of Advancd Physics 6

4 Hol Enrgis (mv) IJAPhy An Opn Accss Journal Anothr intrsting obsrvation from Figur is th occurrnc of chang of th sign of th splitting nrgy. Th chang in th sign splitting ariss du to th fact that th xchang splitting opposs th Zman splitting and thir ordrs of magnitud ar sam for th lctrons. Also th splitting nrgis incras linarly with low filds, dpnding on doping concntration and shows non linar bhavior at modst filds. Th rason is that th low xtrnal magntic fild partially aligns th Mn spins, and at highr filds all th Mn spins ar alignd compltly. As th ffctiv mangans concntration incrass, th Zman splitting nrgis ar gtting largr. In carrying out lctron nrgy calculations, w incorporatd s-d xchang intraction. In ordr to xamin th ffct of magntic impurity doping on hol nrgis, p-d xchang intraction is incorporatd. Using th physical paramtrs dfind for ZnS/ZnS CSQDs, w hav obtaind th variation in hol nrgis as a function of magntic fild at T=50k for 0, 0, 30 prcnt impurity concntration. Figur xhibits hol nrgy variations as a function of magntic fild in arbitrary scal Magntic Fild (T) d + con con. 0. f + con. 0.3 d - con con. 0. f - con. 0.3 Figur : Hol Enrgy as a Function of Magntic Fild Th curvs d,, f ar plottd for th dopant concntration 0., 0. and 0.3 rspctivly. Th supr scripts rprsnt th hol spin up and spin down stats. Th bhavior of th nrgis of th hol stats shown in Figur is much mor complicatd as thy dcras rapidly with incrasing magntic fild and cross ovr at crtain valu of magntic fild whr th Zman splitting is compnsatd by th xchang splitting. Th xchang splitting can b ascribd to th p-d xchang intraction. Th splitting undr N0 S z x such circumstancs is approximatly 6Bx. If w considr an quivalnt 6 magnitud of Zman splitting for hols, thn th intrinsic magntic fild which can gnrat B m such amount of Zman splitting can b found to b x 0. Sinc B x is dirctly proportional to th dopant concntration, th magnitud of th intrinsic magntic fild can b sn to incras with th incrasing Mn dopant concntration. Figur also indicats that th xchang splitting of hol dominats ovr th Zman splitting which is rvrs in cas of lctrons. Intrnational Journal of Advancd Physics 7

5 IJAPhy An Opn Accss Journal Th hol stats ar mor complicatd than th lctron stats, bcaus th wav function of th hol stat consists of componnts of diffrnt J and l valus and thy mix with ach othr du to th contribution of th off- diagonal trms in th hol Hamiltonian. Th xchang intraction trm and th Zman trm caus splitting of th nrgis of ths componnts at small magntic fild. At larg magntic fild, th hol nrgy incrass slightly du to th magntic confinmnt, but is diffrnt for diffrnt stats that hav diffrnt orbital momntum ( l ). Also from Figur, th nrgy lvls du to spin up and spin down hol stats cross with ach othr. This is bcaus th magntic fild du to xchang and th fild du to magntic confinmnt ar applid simultanously to ZnS/ZnS CSQDs. 5. Conclusion Conclusivly, w calculatd lctron and hol nrgis in CSQDs in which th cor is a dilutd magntic smiconductor by taking into account th s-d and p-d xchang intractions. Th hol nrgis hav bn calculatd using th Luttingr Hamiltonian. For this purpos, it was assumd that th lctrons and hols ar confind within th cor of th quantum dot. Th confinmnt nrgy bing qual to th conduction and valnc band offsts. In DMS th spin of lctrons and hols is liftd du to s-d and p-d xchang intractions rspctivly. By using Luttingr Hamiltonian it was found that th Luttingr paramtrs modify du to xchang intractions in th prsnc of magntic fild. Th analytical rsults ar applicabl to th ntir II-VI smiconductor CSQDs. Th numrical analysis has bn carrid out for ZnS/ZnS CSQDs with cor bing dopd by Mn ions. It was obsrvd that th xchang splitting compnsats th Zman splitting. Th analysis mad in this rsarch can b usful for prdicting tunnling of lctrons and hols from cor to shll and can hav applications in calculating th spin polarizd currnt from th CSQDs. Rfrncs Balkanski M., t al., 000: Smiconductor Physics and Applications, Oxford Univrsity Prss, Unitd Kingdom. Brgqvist L., t al. Magntic Prcolation in Dilutd Magntic Smiconductors. Phys. Rv. Ltt (3) Furdyna J.K. Dilutd Magntic Smiconductors. Journal of Applid Physics (4) Kyrychnko F.V., t al. Valnc-Band Stats in Dilutd Magntic Smiconductor Quantum Wirs. Physics Rv. B (7) Luttingr J.M., t al. Motion of Elctrons and Hols in Prturbd Priodic Filds. Phys Rv ; 869. Nicolas Mokhoff, 006: MIT Spinoff Dmos Quantum Dot Display Tchnology. EE Tims. Samarth N., t al. Dilutd Magntic Smiconductors. Procdings of th IEEE (6) z Intrnational Journal of Advancd Physics 8