Nanomaterials for Photovoltaics (v11) 10. Bulk-Heterojunction Solar Cells

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1 1 10. Bulk-Heteojuctio Sola Cells Naostuctued sola cells We ca imagie a spectum of aostuctue sola cells agig fom a ogaic, bulk heteojuctio type just discussed to a iogaic, 3-D ogaized type. Example: CuSCN/TiO DSH example of a dye-sesitized sola cell is sho belo [B. O Rega ad F. Lezma, J. Phys. Chem. B 108, 434 (004)]. The image is a SEM coss sectio.

2 The cell as sythesized by Spay pyolysis/spi coatig of TiO, folloed by icopoatio of Ru-535 dye. CuSCN solutio icopoated ito ad above film. The cell oks by absoptio of light by dye, ith electo ijectio ito the CB of the TiO. The dye is egeeated by captue of electos fom the VB of CuSCN. This type of cell has bee called a "itepeetatig etok heteojuctio". The J-V chaacteistics ae sho belo Example: TiO/PbS QDs Quatum dots ca also povide cotol of badgap ad bad offsets useful fo heteojuctios sola cells [P. Hoye ad R. Koekamo, ppl. Phys. Lett. 66, 349 (1995)]. Naostuctued sola cells Coside a aostuctued, bulk heteojuctio device:

3 3 Bulk heteojuctio (I) We ca idealize the stuctue as peiodic, vetical colums of the to mateials. Igoig bad bedig, the bad diagam is detemied by the bad offsets ad bad gaps. 1, EC, Eg Eg E g1, EV Eg Bulk heteojuctio (II) Let's say a peiod of the supelattice is D1. ssume a uifom chage desity i each egio qn1 1 x, 0 x qn, 0 x The electic field satisfies d x dx We have the bouday coditio 1 x0 x0

4 4 Bulk heteojuctio (III) ssume the to egios have equal thickess. The i egio 1 ( 1 x 0 ) x qn1 qn1 1 x dx x x 1 hile i egio ( 0 x ) 1 1 x qn qn x 0 dx 0 x x0 qn qn qn x x Notice that 0 at both x 1 ad x

5 5 Bulk heteojuctio (IV) The potetial i egio 1 ( 1 x 0 ) is qn qn qn V x x dx x dx x dx x 1 1 x x xx 1 1 x 0 0 qn1 1 1 x 1 I egio ( 0 x ) qn qn V x x dx x dx x 0 qn x x x x Notice that V 0 at both x0, D, D,.... qn x, x qn, 0 x x qn, 1 0 x 1 x V qn x, 0 x Flatbad sola-cell model The voltage dop acoss oe peiod is 1 qn qn1 1 q N1 1 N V V V 1 1 We impose chage eutality o each supelattice peiod So N11 N

6 6 N 1 D, N1 N The N1 N N 1 D q 1 1 D V 1N1 N 1 1 N1 N Notice that if 1, the q 1 D V 1 1 N1 N hich is the sam as a p/h homojuctio ith D. If 1 D, the N1 N N ad qnd 1 1 V 3 1 Flatbad sola-cell model (II) The voltage dop acoss a sigle SL peiod iceases as D. Fo a aoscale SL, this emais small (less tha kt q. This small voltage vaiatio (bad bedig) idicates that the flatbad appoximatio is valid i the aoscale egime.

7 7 Flatbad sola-cell model (III) Flatbad sola-cell model (IV) Withi the flatbad appoximatio, e ca detemie the chage desity i each egio. The quasi-femi levels E ad E ill be oughly costat ove the legth of a peiod. The caie cocetatios i F egio 1 ae F p EF E kt EF Ei kt Ei kt 1 e e e F i F E E p kt E E p kt Ei kt 1 e e e p Those i egio ae EF Ei kt EF Ei kt Ei kt i e i e e i F i F E E p kt E E p kt Ei kt i e i e e p We defie a itisic caie cocetatio Ni i ad a heteojuctio caie cocetatio Nh Ni coshei kt Some othe abbeviatios ae useful E E kt F i e, x The poduct gives y E F e i E p kt x y lso EF F e E p kt z, EF EF kt qv kt p z xy e e e Ei kt These allo us to ite

8 8 ad x p y 1, 1 i y i x, p Flatbad sola-cell model (V) ssume accepto dopig oly o side 1 ad doo dopig oly o side. The N N p, N N p D If e have full ioizatio of dopats ( N N, N N ), the D D N1 N 1 p1, N ND p Let's assume 1, so chage eutality ( N1 N N ) gives N p N p This becomes 1 1 D i i i x y N N Notice y z z x, so 1 D i i i x z N N z x z Flatbad sola-cell model (VI) fe moe defiitios ae useful. Defie 1 D u i, We have v N N i, ad D x z u v x x z It is useful to ite e x z. The uvsih uvcosh z The pefactos ca be paameteized as uv Rcosh, uv Rsih So, atah u v R u v u v uv u v Usig the idetity coshsih sihcosh sih, e have uv sih z

9 asih v u atah 1 uv z v u This allos us to ite x ze e Flatbad sola-cell model (VII) We have so 1 asih uv z 1 e exp asih uv z lso so vu e tah 0 vu e e e v 1 0 v v 0 e e 0 l u u u We aive at a geeal esult v x z exp asih : u uv z ll othe quatities ca be detemied oce x is foud. Flatbad sola-cell examples Badgap diffeeces ad bad offsets ofte exceed kt. ssume 1 ad 1 i i The 1, so 1 Nh Ni N i lso, this assues i ad Notice that i so u i ad v v u We also have i

10 10 uv N i h uv i i hich fives i 1 The uv N N h i x z exp asih i Nh z Flatbad sola-cell examples: case 1 (o dopig) (I) With o dopig ( N N 0 ), e ca say that 0 ad asih 0 0, so a d x v e qv kt z u ad i The i egio 1 y z x qv kt e i x ad qv kt 1 e Nh I egio p y N qv kt 1 h e x N ad p qv kt i h e y i i qv kt e Nh Flatbad sola-cell examples: case 1 (o dopig) (II) We ca say that Nh N ad. Thus Nh N, i h h so 1 p1 p N 1 1 ppaetly, p1 p1 N e qv kt h, N p N h qv kt e N N N h The chage desity iss qv kt 1 e qn x h qv kt e, 0 x qv kt e, 0 q Nh x Flatbad sola-cell examples: case (asymmetic dopig) (I) Coside the case ND N Nh. Let's say ND N qv kt e 1 uv z Nh This implies small quasi-femi-level splittig, i.e.

11 11 kt V l N N q D N h Let's say ND N, so 0. The so 1 sih1 e e uv z 1 e e uv z No e have ad x z v u uv z u x u z z u y x Flatbad sola-cell examples: case (asymmetic dopig) (II) No ad z u p1, Nh qv kt e ND N N N D 1 u i N N N 1 D h N D N i z u p i qv kt e ND N ND N Theefoe N1 N 1 p1 N ad N ND p ND ND N We see that N1 N N The chage desity is the N, i u i ND N i N D N qn, x0 x q N, 0 x With small quasi-femi level splittig, the chage desity is geeally equal to the dopig level i the moe lightly doped side.

12 1 Flatbad sola-cell model: p/+ (I) Coside a bulk heteojuctio ith N ND. We have N x e i O the p side p D Ei kt Ei kt i Ei kt 1 e e N x ND N N xe e N Ei kt D Ei kt 1 i O the side e Ei kt i x ND The moe lightly doped side detemies the chage desity, so N N p1 1 N. the quasi-femi level slope is small, so e have N ioized acceptos o the p-side ad N fee holes o the + side. Flatbad sola-cell model: p/+ (II) The sola cell opeates i the o-equilibium coditio qv E E E E F -side Fp p-side F Fp

13 13 We oly eed to coside electos o the -side ad holes o the p-side. Coside photogeeatio. O the -side, the photogeeated caie desity is g ND, so ND. O the p side, pg G p, so p p. No 1 g ad p g E 1 F 1 e i E p kt i EF D e E i kt N i The voltage may be much lage tha the built-i potetial diffeece e calculated. pg ND qv kt l E i Ni Notice that holes ae the mioity caie o the p-side fo the p/+ juctio. Flatbad sola-cell model: p/+ (III) Let's compae this to a bulk, p/ homojuctio, fo hich ou model gave photo OC l J qv kt J 1 0 J photo qgl Lp D Dp J0 qi L N Lp N D I the p/+ case: ND N, L Lp, J photo qg L, ad So J D 0 qi L N Jphoto GL N N J0 D No g i i N g qvoc kt l i I this case, electo geeatio o the p-side domiates. Naostuctued sola cell: equivalet cicuit equivalet cicuit fo a aostuctued sola cell is sho belo.

14 14 The diode chaacteistics aise fom itefacial ecombiatio May small subcells coected i paallel. Vetical chage pecolatio/hoppig epeseted by seies esistos. Chage sepaatio may ivolve excito dissociatio