Wave Mechanical Analysis of Quantum Dots Materials for Solar Cells Application

Transcription

1 Iteratioal Trasatios i Applied Siees Jauar-Marh 04, Volume 6 No, pp ISSN-(Pritig) , (Olie) AACS. ( All right reserved. Wave Mehaial Aalsis of Quatum Dots Materials f Solar Cells Appliatio Reeta, N.D.Kaushika ad V.P.Sigh, D.J.(P.G.) College, Baraut (Baghpat) U.P. Istitute of Tehologial Eduatio ad Researh, SOA Uiversit, Bhuveshwar, Orissa, Idia ABSTRACT Spatial ofiemet of eletros i semiodut aostrutures leads to remarkable hages i their quatum states. Quatum dots are quasi ero dimesioal sstems whih are pratial realiatio of the familiar oept of partile i a bo. The quatum dot solar ell oept is proposed as a sheme f ireased solar ell effiie. These are alterative of ovetioal tadem approahes to higher oversio effiie. I this paper, a wave mehaial the of phsial proess of Q-dot i ao media is preseted ad iremet i the oversio effiie of Q-dot solar ells is disussed. The the is based o the osideratio of partile i a bo. The problem is solved with Shrodiger wave equatio uder boudar oditio of bo. INTRODUCTION Maimum oversio effiie f a solar ell was alulated b Shokle ad Queissar i 96 [] to be about %. Several shemes f eeedig S-Q limit have bee proposed like multi jutio ells, thermo photovoltai ells [], hot arrier ells [-5]. Oe approah to irease the limitig oversio effiie is to use the hot arriers befe their relaatio at their bad edges via phoo emissio []. Oe wa f ehaig oversio effiie b usig hot arriers is to etrat the hot arriers from the photo overter befe the ool [4,5] ad the other wa requires the hot arriers to produe a seod me eletro-hole pair through impat ioiatio [6,7]. I

2 Wave Mehaial Aalsis of Quatum Dots Materials f Solar Cells Appliatio 56 this wa, oversio effiie of solar ells a be irease b otrollig relaatio damis of photo geerated arriers. I reet ears, it has bee see that the relaatio damis ma be affeted b quatum ofiemet i semi odut (Quatum well, Quatum dots)[]. F quatum dots, the eletro-hole pairs eist as eitos. Whe the eletros ad holes i semi odut are ofied b potetial barrier to regios of spae that are smaller tha omparable to their de-broglie wave legth to the Bohr radius of eitos i bulk semi odut, the hot arriers oolig rates redued ad the rate of impat ioiatio beome equal with the rate of oolig. ero dimesioal quatum ofiemet that is quatum dots ame i earl 980s. Fabriatio of quatum dots proeeds through a series of maskig ad ethig steps as show i Fig. Fig () (). Iitial quatum well o a substrate, ad overed b a resist (). First, a eletro beam sas the surfae of a semiodut otaiig a buried laer of quatum-well material shielded b template (). Resist is removed where the beam has draw a patter. (4). A metal laer (mask) is deposited o the resultig surfae (5). ad the a solvet removes the remaiig resist, leavig mask ol where the eletro beam eposed the resist. (6). Reative ios eth awa the uwated quatum well material eept where it is proteted b mask. (7).fial Q-dot o substrate after removal of ethig mask.

3 57 Reeta, N.D.Kaushika & V.P.Sigh A eletro i a quatum dot is ostraied to have a quatum wave futio that fits evel withi its bders. A eletro whih is elosed iside a Q-dot is osidered as a partile i a retagle bo havig edges a,b ad i legth (Fig ). The potetial futio V(,,)is havig a ostat value of ero i the regios give as follows: V(,,) = 0, 0<<a, V(,,) = 0, 0<<b, ad V(,,) = 0, 0<<. The potetial outside the bo is ifiite. The Shrödiger time idepedet wave equatio f a partile iside the bo ma be put as follows: m E 0.() It is possible to separate Eq.() b makig the followig substitutios :,, ( ) ( ) ( ).() Differetiatig Eq.() with respet to, ad separatel b keepig the remaiig two fats as ostat, we obtai,,.(a) O substitutig Eq.(a) i Eq.(), we obtai me. O dividig the above equatio b, we obtai

4 Wave Mehaial Aalsis of Quatum Dots Materials f Solar Cells Appliatio 58 me.() F the give eerg of the partile, the term 8 me/ h is ostat ad eah term o the left side is a futio of oe variable ol. If we allow ol oe of these ( ) to var at a time ad keep the other two ostats (sa we var keepig ad ostat), the sum of the three terms is still equal to the ostat o the right had side. This meas that eah of the three terms o the left is itself a ostat ad is idepedet of the other variables, preset i it. Let us represet the ostats f the three terms as, ad. These have a mius sig beause the term o the right side of equatio has mius sig. This gives three differetial equatios. me.(4) d d 0.(5) ad from Eq.(4), we have me.(6) d d 0.(7) Agai from Eq.(6), we have

5 59 Reeta, N.D.Kaushika & V.P.Sigh me.(8) d d 0.(9) O substitutig Eqs.(5),(7) ad (9), we obtai me.(0) The solutios of Eqs.(5),(7) ad (9) are as :.() A os B si.() A os B si A os B si.() I the above equatios, A, A ad Aare ostats; B, B ad B are also ostats. It is possible to obtai the values of these ostats b applig the boudar oditios. As vaishes at the surfaes of ifiite potetial, it meas that =0 whe, a b If these boudar oditios are applied, the we have A A A 0. Also, B 0 si a 0, i.e., a B 0 si b 0, i.e., b a b

6 Wave Mehaial Aalsis of Quatum Dots Materials f Solar Cells Appliatio 60 B 0 si 0, i.e., b Hee B si.(4) a where represets a iteger ( =,, ). Also, B si.(5) b =,, ad B si.(6), =,,, k si si a b si.(7) I the above equatio, k is termed as maliatio ostat. It is possible to obtai the value of k b usig the malied oditio, i.e. k.(8) ab,, si si ab a b si.(9) From Eq.(0), we have me.(9a)

7 6 Reeta, N.D.Kaushika & V.P.Sigh a b me.(9b) E m a b.(9) E h 8m a b.(0) But if we osider a bo that is ubial i shape suh that a=b=, eerg a be epressed b h E.() 8ma From Eq.(0) ad (), the eerg of the quatum dots are depedet o their sie due to the quatum ofiemet effets, whih domiate below the ritial sie. Carrier ofiemet i a Q- dot quaties their eerg spetrum ito a series of disrete levels. The Q-dot solar ell is based o the priiple that, b suitable hoie of various sies of Q-dots, the absptio a take plae at the differet quatum eerg levels ad therefe redues the thermaliatio losses. There are three differet Q-dot solar ell ofiguratios:) Photo eletrodes omposed of Q-dot arras: a Q- dot arra used as a photo eletrode f a photo eletro hemial as the i-regio of a p-i- photovoltai ell ) Q-dot sesitied ao rstallie TiO solar ell. ) Q-dots dispersed i gai semiodut polmer matries, proposed b Noik. I Q-dot solar ells, the absptio edge ad spetral harateristis a be moited b the sie of Q-dots ad therefe photourret ad voltage a be idividuall optimied, while the output voltage is still primaril determied b wider bad gap bulk material. A pratial Q-dot solar ell based o a p-i- ell struture whih iludes multi quatum-dot laers i the itrisi regio of the struture to ehae the photo urret. The self-gaied IAs/Gas sstem a over a rage of bad gaps that is of partiular imptae f solar ells [8].

8 Wave Mehaial Aalsis of Quatum Dots Materials f Solar Cells Appliatio 6 CONCLUSION Quatum dots (QD) able to irease the effiie of toda s tpial silio photovoltai ells. Silio ells a reate oe eito per high-eerg photo, with high kieti eerg arriers losig their eerg as heat. Quatum dots of PbSe (Eg=0.8 ev) produe as ma as three eitos from oe high eerg photo of su-light [9]. The geeratio of me tha oe eito b a sigle photo is alled multiple eito geeratio (MEG) arrier multipliatio. This meas that ever QD i the sample produes three eletro-hole pairs/photo. Further wk will preset the theetial traspt model f a pratial p-i- QD solar ell built o the basis of the self-gaiatio. We will stud the advatages of the use of QDs i the ative regio f photo absptio i the whole-wavelegth part of the spetrum. Referees [] W.Shokle ad H.J.Queisser, J. Appl. Phs. (96) 50. [] M.A.Gree, Third Geeratio Photovoltai (Bridge Priter, Sde) 00. [] A.J.Noik, Au. Rev. Phs. Chem. 5 (00) 9. [4] R.T.Ross ad A.J.Noik, J.Appl. Phs. 5 (98) 8. [5] D.S.Boudreau, F.Williams, ad A.J.Noik, J.Appl. Phs. 5 (980) 58. [6] P.T.Ladsberg, H.Nussbaumer, ad G.Willeke, J.Appl. Phs. 74 (99) 45. [7] S.Kolodiski, J.H.Werer, T.Witthe, ad H.J.Queisser, Appl. Phs. Lett.6 (99) 405. [8] D.Bimberg.M.Grudma ad N.Ledetsov, Quatum Dot Hetero-strutures (Wile, New k, 999). [9] R.D.Shaller ad V.I.Kilmov. High-effiie arrier multipliatio i PbSe astals: impliatios f solar eerg oversio PRL 9, 8660 (004).