Modeling of the Scattering Process and the Optical Photo-generation Rate of a Dye Sensitized Solar Cell: Influence of the TiO 2 Radius

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1 Amerin Journl of Nnomterils, 2016, Vol. 4, No. 3, Aville online t Siene n Eution Pulishing DOI: /jn Moeling of the Sttering Proess n the Optil Photo-genertion Rte of Dye Sensitize Solr Cell: Influene of the TiO 2 Rius E. H. O. Gueye, P. D. Tll, O. Skho, C. B. No, M. B. Gye, N. M. Niye, B. D. Ngom *, A.C. Beye Groupe e physique u Solie et Sienes es Mtériux, Fulté es Sienes et Tehniques Université Cheikh Ant Diop e Dkr (UCAD), B.P Dkr-Fnn Dkr (Sénégl) *Corresponing uthor: ngom@gmil.om Astrt We report on methoology for optil n eletril moeling of ye-sensitize solr ells (DSSCs). In orer to tke into ount the sttering proess, the optil moel is se on the etermintion of the effetive permittivity of the mixture n the sttering oeffiient using Mie n Bruggemn theories, onsiering spheril prtiles. Then, from the ritive trnsfer eqution, the optil genertion rte of ell is eue. From the presente moel, the epenene effets of the nnoprtiles size upon the extintion oeffiient n the optil genertion rte re eviene. Thus, we notie tht the extintion oeffiient ereses with the inrese of the TiO 2 nnoprtiles n vnishes when the wvelengths inreses in the visile spetrum. A signifint uniformity of the sorption for rius smller thn 10 nm is oserve, however t rius out 80 nm, we oserve nonuniformity. The simulte results se on this moel re in goo greement with the experimentl results. Keywors: ye-sensitize solr ell, mie theory, sttering prmeters Cite This Artile: E. H. O. Gueye, P. D. Tll, O. Skho, C. B. No, M. B. Gye, N. M. Niye, B. D. Ngom, n A.C. Beye, Moeling of the Sttering Proess n the Optil Photo-genertion Rte of Dye Sensitize Solr Cell: Influene of the TiO 2 Rius. Amerin Journl of Nnomterils, vol. 4, no. 3 (2016): oi: /jn Introution Dye sensitize solr ells (DSSCs) re seen s n lterntive to onventionl solr ells n hve een wiely stuie in reent yers [1,2,3]. A DSSC is mixture of nnostruture thin films, sensitizer n n eletrolyte ontining the meitor snwihe etween two eletroes: trnsprent onutive oxie s trnsprent noe n ounter eletroe s thoe, suh DSSC is epite in Figure 1. The effiieny of the ye sorption is one of the prmount prmeters tht etermine the ell performne. Aoringly, the peulir omposition of the phototive lyer, mkes it very omplite to estlish n optoeletroni moel for the DSSCs. Inee, it is ompose of mixture of three omponents (titnium ioxie (TiO 2 ), ye moleules n the eletrolyte in whih tri-ioie ions re immerge) whih oul rise homogeneity prolems. Nevertheless, vrious optil [7,8], eletril [9-18] n optoeletroni [19,20] moels hve een evelope. But, one n notie tht vrious phenomen suh s moleulr proesses for the exittion of the ye, injetion within the titnium ioxie n reomintion of hrges in the ye, nnot e simulte s it hve een one for the onventionl silion solr ells [4]. In this pper, n optil moel of ye-sensitize solr ell will e presente, putting fous on the urte esription of the optis in the phototive lyer (y pplying Bruggemn's theory, Mie's Theory n ritive trnsfer equtions). The influene of the TiO 2 rius is lso stuie. 2. Computtionl Metho Figure 1. Struture of the Dye sensitize solr ell The moel onsiere is epite in Figure 2. Thus, our stuy is essentilly limite to the phototive lyer snwihe etween the two eletroes. The phototive lyer is mixture of Titnium ioxie (TiO 2 ), ye

2 59 Amerin Journl of Nnomterils 59 (Z907), meitor n n eletrolyte I / I3. For the lultion of the effetive permittivity, we use the sme pproh s tht use in our previous pper [21]. I = ( K+ SI ) x (7) J = ( K+ SJ ). x (8) I = γki + γ(1 ζ) SI x γ(1 ζ) SJ ζsi (1 ζ) SJ J = γkj γ(1 ζ) SJ x + γ(1 ζ) SI + (1 ζ) SI + ζ xi (9) (10) Figure 2. Shemti of the ell Firstly, we lulte the sttering ross setions n sorption through the Mie theory in the se of monoisperse nnoprtile size. Our meium is ompose of three ompouns; we lulte the sttering ross setions for the nnostruture thin films (TiO 2 here) n eletrolyte / meitor. The prtile sizes of yes re low [7], therefore they o not prtiipte in the sttering proess. Then mrosopi sttering n sorption oeffiient s n k will e lulte for eh ompoun, using the following equtions. si = ns, iσ s, i (1) j = s, j s, j (2) k n σ Where i = eletrolyte/meitor or TiO 2 ; j = TiO 2 or ye or eletrolyte /meitor. The prtile ensity of the eletrolyti/ meitor will e given y the eqution: P Neletrolyte/ meitor = NTiO (3) 2 1 P The hypothesis we mking here is to onsier the TIO 2 /Dye s one prtile. Sine the iffusion of the yes prtiles is very low we onsier tht the prtile (TiO 2 /Dye) hve the sme imensions s the simple TiO 2 prtile [7]. On the other hns sine the TiO 2 prtile oesn't sor we onsier lso tht the sorption of the prtile (TiO 2 /Dye is just oming from the simple ye prtile Therefore we hve: Nye = NTiO 2 (4) With P the porosity. Then: K = kye + keletrolyte/ meitor (5) S = stio + s 2 eletrolyte/ meitor. (6) Afterwrs the mrosopi oeffiients K n S re use to lulte the ollimte flux (I n J ) n iffuse flux (I n J ). Bsilly, the pproximtion of the ritive trnsfer eqution re one using four flux [22] n the equtions re given y (equtions: 7-10). These ifferent flux re illustrte in Figure 3. In ft, the vrition of the flows in the meium with n infinitesiml vlue of the thikness x n e estlishe using the equilirium etween the sttering n the sorption energy in forwr n kwr. Figure 3. Shem of the ell with ifferent flux The ftor γ is the equivlent pth length for the iffuse flux whih rnges from 1 for ollimte light to 2 for isotropi sttere light [23]. Thus, the nlytil expression of the forwr sttering rtio (ζ) is otine from C. Rozé et l. nlysis [24]. The four flux I, I, J n J inlue in the previous equtions, (7), (8), (9) n (10) re etermine y tking into ount the following ounry onitions. At the Glss/Mixe zone: x= I = 1 r I + rj (11) I = 1 r I + rj (12) where rr, rr, rr, rr the refletive oeffiient of ollimte em, the refletive oeffiient of rition iffuse em, the refletive oeffiient of ollimte em t the k, the refletive oeffiient of rition iffuse em t k sie respetively. II n II re the inient ollimte flux n the inient iffuse flux t the interfe x=. II n e etermine y tking into ount the interferene effets t the glss/mixe zone n ir/glss interfes n is given s: I = 1 ( 1 r ) I ( r ) 0 r (13) In ft, II is equl to zero n II 0 is the inoming light. At the Mixe zone/glss: x=0 By onsiering the refletion effets t the ir/glss n the glss/mixe interfes the following onitions n e estlishe:

3 60 Amerin Journl of Nnomterils 60 Where: ( 1 2 ) r r + r J(0) = I(0) 1 rr J ( 1 2 ) i r r + r (0) = I(0) 1 rr r = r = r = r = 2 meium nir meium + nir eletrolyte eletrolyte + ir ir 2 (14) (15) (16) (17) Where n meium is etermine using ruggemn theory. Thus, the lol optil sorption rte per unit volume [8] n e estlishe using the expression elow: g = KI + KJ + γki + γkj. (18) Hene, the optil photons sorption rte is eue from g(x) [25], n is expresse s: An G ye is eue y: gx G x = (19) h λ αye Gye ( λ, x) = Gmeium ( λ, x) (20) αmeium Finlly, the optil photo-genertion rte of the DSSC is given y: Gx = G ( λ, x) η (21) ye where η eing the injetion rte of eletrons. oeffiient ereses. The reson is tht, when the rius inreses, the sorption ereses euse of the ispperne of the surfe sorption effets [8]. In Figure 5 is epite the effetive extintion oeffiient of the mixture {TiO 2 +ye (Z907)+eletrolyte+meitor} within the phototive lyer s funtion of the wvelength from nm for ifferent TiO 2 nnoprtiles rius rnging from 10 n 20 nm. Compre to the results otine in figure 4, the intensity of the extintion oeffiient presente in figure 5 ereses when the size of TiO 2 nnoprtiles inreses. Three res re ientifie: 400 nm to 450 nm, 450 nm to 600 nm n 600 nm to 800 nm. Exept the wvelength region etween 400 nm n 450 nm, where we oserve ehvior similr to tht of the meitor, the tren of the mixture is the sme for the two other regions n ompletely ifferent from the tren of the meitor. Suh oserve ehvior on {TiO 2 +ye (Z907)+eletrolyte+meitor} mixture on the first region is ue to the sorne of the meitor whih hppens only etween 400 nm n 450 nm. Figure 4. Extintion oeffiient of photo-tive lyer (mixture TiO 2 + Z907) s funtion of wvelength for ifferent rii of the TiO2 prtile 3. Results n Disussion The nlytil moel presente ove is vlite with experimentl t reporte in the literture (Cf setion D) [18]. After lulting the nlytil new expressions presente in the previous setion, numeri se oe progrm implemente y the ommeril pkge Mtl softwre is estlishe. Bsilly, numeril results re presente n isusse in this setion. Thus, the mrosopi prmeters suh s the extintion oeffiient, the four flux n the optil genertion rte of the DSSC in term of vrious phenomenologil prmeters suh s the wvelength of the inoming light, the TiO 2 nnoprtiles rius, the epth of the phototive lyer re epite The Extintion Coeffiient of the Mixture Mteril within the Phototive Lyer The Figure 4 shows the extintion oeffiient of the TiO 2 -ye (Z907) s funtion of the wvelength for ifferent TiO 2 nnoprtiles rius rnging from 10 n 20 nm. All the otine spetrums show the sme tren, however, when the rius inreses, the extintion Figure 5. Extintion oeffiient of photo-tive lyer (mixture TiO 2 + Z907+étonitrile-I - /I 3 - ) s funtion of wvelength for ifferent rii of the TiO 2 prtile 3.2. Sttering of Multiple Prtiles The vlues of the 4 flux I, J, I n J n e lulte s funtion of the epth of the ell, from the iffusion oeffiients, the mrosopi sorption, the

4 61 Amerin Journl of Nnomterils 61 forwr sttering rtio n the equivlent pth length. Figure 6 shows the flux s funtion of the ell epth. One n see tht for smll rius, I ereses slightly n muh prt of flux rehes the ege of the ell. This is ue to the smll extintion n iffusion oeffiient for smll rius. The others flux re very smll ompre to the I flux for 10 nm. This phenomenon eme ifferent with rius rnging from 20 nm to 40 nm, where I rpily ereses, while I inreses in the first hlf of the ell. Therefore the light rehing the ege of the ell is spre. J hs lso lrge vlue like I. This ue to the smll inrese in the iffusion oeffiient. For muh lrger rius (80 nm), I rpily ereses, while I inreses right t the ege efore rpily eresing too. Beuse of the high iffusion of the moleules with lrger rius, only smll prt of the flux touhes the ege of the ell Determintion of the Genertion Rte Figure 7 shows, the genertion rte of the phototive lyer epening on the epth of the mixe. In this figure, we ompre our moel n tht of Wenger et l. [19]. We n see tht our results re in the sme rnge of vlues thn those lulte y Wenger et l. [19]. Figure 7 shows the genertion rte of the phototive lyer s funtion of epth n for ifferent rius. It seems tht for low rius the sorption is firly homogeneous, s the sttering of light is low, s shown in Figure 6, the intensity of the ollimte light is lmost onstnt. More the rius inreses more sttering inreses, whih use n inrese of iffusion flux n erese of the ollimte flux. Suh ehvior mkes the mjor prt of the intensity eing sore t the ege of the ell, euse of the proess of sttering n extintion. Figure 6. Collimte flux (I, J ) n iffuse flux (I, J ), for ifferent rii of TiO 2 ( 10nm, 20nm, 40nm, - 80nm) prtile I 0=1000W m 2 Figure 7. Genertion rte of photo tive lyer s funtion of the ell epth (: omprison etween our moel n Sophie Wenger results, : for ifferent rii of TiO 2)

5 62 Amerin Journl of Nnomterils Conlusion Our moel llows us to see the influene of the nnoprtile size of TiO 2 on the effetive extintion oeffiient of the mixture. The influene of the nnoprtile size of TiO 2 on the genertion rte ws emonstrte. This stuy llowe seeing tht for the smll rius, the genertion rte is homogeneous. When rius inreses, lmost ll the light is sore t the ege of the ell. Our results re in greement with those in the literture. However, this moel shows limittions: the porosity is fixe, the nnoprtiles re not ielly spheril n sme size, n the ifferene etween the reflete oeffiient iffuse n ollimte oul e tken into ount for etter preision. Aknowlegement The uthors re grteful for the funing y the UEOMA uner the PAIS projet. Referenes [1] O Regn, B., Grätzel, M., A low-ost, high-effiieny solr ell se on ye-sensitize olloil TiO 2 films, Nture, , [2] Wng, Q., Ito, S., Grtzel, M., Fregt-Sntigo, F., Mor-Sero, I., Bisquert, J., Bessho, T., n Imi, H., Chrteristis of High Effiieny Dye-Sensitize Solr Cells, J. Phys. Chem. B 110, , [3] Mthew, S., Yell, A., Go, P., Humphry-Bker, R., Curho, B.F.E., Tvernelli, I., Rothliserger, U., Nzeeruin M.K., n Grätzel, M., Dye-sensitize solr ells with 13% effiieny hieve through the moleulr engineering of porphyrin sensitizers, Nture Chemistry 6, , [4] Green, M. A., Emery, K., Hishikw, Y., Wrt, W., n Dunlop, E. D., Solr ell effiieny tles (Version 45), Progress in photovoltis: reserh n pplitions, 23(1), 1-9, [5] Chi, Y.; Islm, A.; Wtne, Y.; Komiy, R.; Koie, N.; Hn, L., J. Appl. Phys., Prt 2, 45, L638-L640, [6] Go, F.; Wng, Y., Shi, D., Zhng, J., Wng, M. K., Jing, X. Y., Humphry-Bker, R., Wng, P., Zkeeruin, S. M., Grätzel, M., J. Am. Chem. So. 130, ,2008. [7] Ferer, J., n Luther, J., Computer simultions of light sttering n sorption in ye-sensitize solr ells. Solr Energy Mterils n Solr Cells 54 (1998) [8] Rothenerger, G., Comte, P., Grtzel, M., A ontriution to the optil esign of ye_sensitize nnorystlline solr ells, Solr Energy Mterils & Solr Cells, 58, , [9] Soeergren, S., Hgfelt, A., Olsson, J., n Linquist, S. E., Theoretil moels for the tion spetrum n the urrentvoltge hrteristis of miroporous semionutor films in photoeletrohemil ells, The Journl of Physil Chemistry, 98(21), , [10] Mtthews, D., Infelt, P., n Grätzel, M, Clultion of the photourrent-potentil hrteristi for regenertive, sensitize semionutor eletroes. Solr Energy Mterils n Solr Cells, 44(2), , [11] Ferer, J., Stngl, R., n Luther, J., An eletril moel of the ye-sensitize solr ell, Solr Energy Mterils n Solr Cells, 53(1), 29-54, [12] Usmi, A., Theoretil stuy of pplition of multiple sttering of light to ye-sensitize nnorystlline photoeletrihemil ell, Chemil Physis Letters, 277(1), , [13] Usmi, A., Theoretil stuy of hrge trnsporttion in yesensitize nnorystlline TiO 2 eletroes, Chemil physis letters, 292(1), , [14] Ferer, J., Stngl, R., n Luther, J., An eletril moel of the ye-sensitize solr ell, Solr Energy Mterils n Solr Cells, 53(1), 29-54, [15] Stngl, R., Ferer, J., & Luther, J., On the moeling of the yesensitize solr ell, Solr Energy Mterils n Solr Cells, 54(1), , [16] Usmi, A., & Ozki, H., Computer simultions of hrge trnsport in ye-sensitize nnorystlline photovolti ells, The Journl of Physil Chemistry B, 105(20), , [17] Bisquert, J., Chen, D., Hoes, G., Rühle, S., & Zn, A., Physil hemil priniples of photovolti onversion with nnoprtiulte, mesoporous ye-sensitize solr ells, The Journl of Physil Chemistry B, 108(24), , [18] Filipič, M., Bergin, M., Smole, F., & Topič, M., Anlysis of eletron reomintion in ye-sensitize solr ell, Current Applie Physis, 12(1), , [19] Wenger, S., Shmi, M., Rothenerger, G., Gentsh, A., Grtzel, M., n Shumher, J. O., Couple Optil n Eletroni Moeling of Dye-Sensitize Solr Cells for Stey-Stte Prmeter Extrtion, J. Phys. Chem. C 115, , [20] Topič, M., Čmp, A., Filipič, M., Bergin, M., Kršove, U. O., & Smole, F., Optil n eletril moelling n hrteriztion of ye-sensitize solr ells, Current Applie Physis, 10(3), S425-S430, [21] Gueye, E.H.O., Tll, P. D., No, C. B., Dioum, A., Dione, A. N., & Beye, A. C. (2016). An Optil n Eletril Moeling of Dye Sensitize Solr Cell: Influene of the Thikness of the Phototive Lyer. Amerin Journl of Moeling n Optimiztion, 4(1), [22] C. Rozé, T. Girsole, G. Gréhn, G.Goueset, B.Mheu. Four-flux moels to solve the sttering trnsfer eqution in terms of Lorenz-Mie prmeters. Optis ommunitions 194. (2001) [23] G. Kortum, Refletne Spetrosopy, Springer, Berlin, [24] B. Mheu, J. N. Letoulouzn n G. Goueset. Four-flux moels to solve the sttering trnsfer eqution in terms of Lorenz-Mie prmeters. Applie Optis Vol. 23, No. 19 (1984). [25] A. Dioum, S. Niye, E. H. O. Gueye, M. B. Gye, D. N. Fye, O. Skho, M. Fye n A. C. Beye. 3-D Moeling of ilyer heterojuntion orgni solr ell se on Copper Phthloynine n Fullerene (CuP/C60): eviene of totl exitons issoition t the onor-eptor interfe. Glol Journl of Pure n Applie Sienes, Vol 19 (2013).