Recombination on Locally Processed Wafer Surfaces

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1 Vailable olie at Eergy Procedia 27 (2012 ) SilicoPV: April 2011, Freiburg, Germay Recombiatio o Locally Processed Wafer Surfaces P. Sait-Cast *, J. Nekarda, M. Hofma, S. Kuehhold, R. Preu Frauhofer Istitute for Solar Eergy systems, Heidehofstrasse 2, Freiburg 79110, Germay Abstract This paper is revisitig the problem of recombiatio o locally processed area (cotacts, local dopig ), based o the cocept of poit recombiatio rate (p ). The ewly itroduced ective poit recombiatio rate (p ) ca be easily determied from the ective surface recombiatio velocity. It also allows predictios ad comparisos i most of the practical cases. Further aalysis allows the separatio of the ifluece of p from the oe of the trasport of the carrier i a trasparet way. Due to its simplicity, trasparecy ad accuracy, the model proposed here is believed to be more suitable to recet local processig techology tha the existig aalytical models Published by by Elsevier Ltd. Ltd. Selectio ad ad peer-review uder uder resposibility of the of scietific the scietific committee of the committee SilicoPV of 2012 the SilicoPV coferece Ope coferece access uder CC BY-NC-ND licese. Keywords: local process; recombiatio; aalytical model 1. Itroductio More ad more processes are developed for low cost maufacturig of advaced solar cells (icludig ivated emitter ad rear cells (PERC)). They are used as a cost-ective alterative to photolithography which requires may process steps. I order to desigate the surfaces where these processes are applied, we use the ame of locally processed area (). A accurate modelig ad characterizatio of has two mai applicatios: the predictio of the recombiatio o processed surfaces ad the compariso of several methods or processes. The models used i recet literature are based o the work of Fischer[1]. This led to a pair of iterdepedet parameters: the cotact radius (a) ad the local surface recombiatio velocity (S), these parameters are usually obtaied by fittig. The problem is that usually, a small variatio of a iduces a large variatio of the local surface recombiatio velocity. This pair of parameters is therefore ustable, * Correspodig author. Tel.: ; fax: address: pierre.sait-cast@ise.frauhofer.de Published by Elsevier Ltd. Selectio ad peer-review uder resposibility of the scietific committee of the SilicoPV 2012 coferece. Ope access uder CC BY-NC-ND licese. doi: /j.egypro

2 260 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) ad ot well suited for a compariso of differet processes. I additio, this model is ofte used eve though oe defied boudary coditio (emitter o the frot) is ot fulfilled. 2. Cocept of poit recombiatio rate 2.1. Local surface recombiatio I most of the models, the is cosidered as a homogeeous area, which has a defied geometry (poit, square, lie) ad a surface recombiatio velocity (SRV). I priciple, the geometrical parameters are idepedet from the SRV. Therefore, the geometrical parameters ca be chaged without chagig the local SRV. This type of model is very relevat to photolithography, however it is ot the case with low cost local processig. (a) (b) (c) 100 μm Fig. 1. Microscope images of locally processed wafer surfaces: (a) laser chemical process (LCP), (b) ablated dielectric with local Al back surface field (Al-BSF), (c) laser-fired cotact (LFC) o evaporated Al (these images were copied form (a) [2], (b) [3] ad (c) [4]). I Fig. 1, a selectio of locally processed silico areas realized by differet idustrially relevat methods is preseted. O these images, the processes are lookig ihomogeeous ad they have probably a very ihomogeeous local surface recombiatio velocity. Additioally for most of these processes, the SRV is ot idepedet from the geometry of the. I Fig. 1 (b) the local Al-BSF formed is very differet depedig o the opeed area, i other words the SRV will be differet for differet cotact sizes. It is also the case for laser processes where chagig the beam shape, the special pulse overlappig or the fluece i order to chage shape of the, result automatically i a chage of the SRV. Therefore, curret models, based o a homogeeous SRV ad the impedace of the SRV from the geometrical parameter, are ot adapted to processed with the idustrially relevat techologies curretly uder developmet. We thik that the cocept of poit recombiatio rate (p ) ad lie recombiatio rate are more adapted to. The p correspods to the itegral of the surface recombiatio velocity o the, x, y x y p S, ds, (1) where is the average excess carrier desity o the, Δ is the local excess carrier desity ad S is the local surface recombiatio velocity. Lookig at this defiitio, we could thik that the poit recombiatio rate will be determied by itegratio of the local S, which would be very fastidious ad would require the use of micro-

3 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) photolumiescece[5]. Istead, we use macroscopic data to determie p, we will cocetrate o the statistical behavior of the over large area with may, j = q N p, (2) where j is the recombiatio curret desity o the ad N is the surface desity. For lie the same defiitio ca be used The model I order to write mathematically the behavior of the rear of the solar cell, we use the variables listed i Table 1. Table 1. List of variables for the aalytical model Variable Uit Parameter a cm Radius of a or half lie width f Area fractio of j A cm -2 Recombiatio curret desity o the j A cm -2 Effective recombiatio curret desity o the rear j A cm -2 Recombiatio curret desity o the ivatio N cm -2 Surface desity of cm -3 Average excess carrier desity o the cm -3 Average excess carrier desity o the ivatio p cm 3 s -1 Poit recombiatio rate o the R diff A -1 cm -1 Diffusio resistace betwee the ivatio ad the r diff s cm -2 Normalized diffusio resistace S cm s -1 Effective surface recombiatio velocity S cm s -1 Surface recombiatio velocity o the ivatio W cm Wafer thickess For most of practical cases, the iduces high recombiatio rates. For this reaso, the fractio of the is reduced to its miimum. Therefore, f << 1 ca usually be cosidered. I additio, we have a higher recombiatio rate o the area compared with the ivated area therefore we have > >. By defiitio of S [6], j qs 1 f f, j qs. (4) j ca be also writte as the additio of the recombiatio curret desities, f j q f S qn p j 1 j, j 1, j qs qn p. (5)

4 262 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) By combiig Eq. 4 ad 5, we obtai, S N p S. (6) I order to switch from a system with a ihomogeeous recombiatio curret like i the real solar cell to the model with homogeeous recombiatio curret j, a part of the recombiatio curret eeds to be trasferred from the area to the ivated area, see Fig. 2. Recombiatio curret o the rear (a.u.) Passivatio Local recombiatio curret Effective recombiatio curret Positio rear (a.u.) Passivatio Fig. 2. Schematic of the recombiatio curret profiles over the surface for real ad for the model with a ective recombiatio curret The curret desity, which eeds to be trasferred, correspods to the differece betwee the local recombiatio curret ad the ective recombiatio curret. As the diffusio is a liear trasport drive by the gradiet of carrier desity, a diffusio resistace (R diff ) ca be derived i order to describe the trasfer of curret betwee the ad the ivatio. It follows that a Ohm s law liks the carrier desity differeces betwee the ivatio ad the ad the curret desity that eed to be trasferred, j f j f Rdiff 1 1, qr S S, (7) diff which ca be used to fid the ratio /, diff 1 qr S S. (8) Fially, S ca be obtaied by combiig the Eqs. 6 ad 7, S N p S (9) 1 qrdiff N p

5 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) As this demostratio is very geeral, Eq. 9 ca be used for poit or lie shaped. It ca be oticed that the differece S - S depeds o three variables p, N ad R diff. p. The poit recombiatio rate depeds o the process, N the desity of ad the diffusio resistace R diff, which deped o the diffusio coiciet ad o the geometry of the. The diffusio resistace is more difficult to obtai tha N. However, it ca be calculated for basic cotact geometry Determiatio of the diffusio resistace 10 1 Fractio of 1% (a) W >> a (c) Normalized diffusio resistace q x R diff x N x a x D /p -- r diff x D /p r diff x D /p ~ Samples w/. emitter Samples w/o emitter Fractio of 1% r diff x D /p ~ 1.38 (b) W >> a -40% (d) -63% Normalized half width - a / W Area fractio of [%] Fig. 3. Normalized diffusio resistace as a fuctio of the ormalized cotact width, for poit (a) ad lie (b) shaped. Normalized diffusio resistace as a fuctio of the fractio of, for poit (c) ad lie (d) shaped, whe W >> a. The diffusio resistace is the key of the balace betwee the recombiatio o the ad o the ivatio. It ca be observe as a parameter represetig how easy it is for a carrier to diffuse from oe regio to the other. Whe the diffusio betwee two regios is easy, they will have very similar carrier cocetratio eve if the recombiatio rates o these regios are very differet. However if the diffusio betwee to regios is difficult, the they will behave idepedetly from each other. The lateral diffusio of the miority carrier is iflueced by the presece of a emitter o the surface opposig the. Ideed, i the emitter, there is a high cocetratio of the carriers that are i miority i the bulk. Therefore, their lateral trasport is eased by a emitter, ad for a emitter without sheet resistace (perfect emitter), the cocetratio of miority carriers is costat at the juctio. However whe there is o emitter, it is the curret desity that will be costat, as the carriers are homogeeously geerated. This defied two cases for the boudary coditios for the surface opposig the : Perfect emitter with a homogeeous carrier desity, No emitter with a homogeeous curret desity.

6 264 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) I order to simplify the calculatio, the boudary coditio o the ad o the ivated regio is homogeeous recombiatio curret desity. Eve if this simplificatio could seem to be rough, it is usually a relatively accurate compromise [7]. Applyig these boudary coditios, the diffusio resistace ca be simply calculated by solvig Laplace equatios usig the Fourier trasformed method. I order to simplify the graphic represetatio of the results, the ormalized diffusio resistace (r diff = q R diff N a) is itroduced. I Fig. 3, the ormalized diffusio resistaces for lie (a) ad poit (b) shaped are give i the cases of a perfect emitter ad o emitter. Ay real emitter will be betwee these two cases. Whe the width of the cotact is very small compared to the wafer thickess (W >> a) the ormalized diffusio resistace teds to a costat value. This value is the same for ay type of emitter; however, it slightly chages with the coverage. I Fig. 3 (c) ad (d), r diff is give as a fuctio of the emitter coverage for W >> a. For a variatio of two orders of magitude of the fractio r diff shows a chage of 40% ad 63% for the poit ad lie shaped cotact, respectively. Therefore for a arrow rage of fractio r diff is cosidered as costat. The diffusio legth has also a ifluece o R diff, if the diffusio legth is lower tha the distace betwee the, R diff decreases. 3. Determiatio of the poit recombiatio rate 3.1. Effective poit recombiatio rate For the extractio of the ective poit recombiatio rate (p ), several types of samples might be used. The samples ca have a emitter o the opposite side to the, it might have o emitter, or it ca also be processed symmetrically. The sample used should be a well-ivated wafer with a high bulk lifetime. We recommed a measuremet of the ective carrier lifetime i order to extract S. The ective poit recombiatio rate is simply defied by, S p N S. (9) For the calculatio of p we recommed to have a variatio i the desity of cotacts. Effective surface recombiatio velocity (10 3 cm/s) LFC 1 ( li. fit) LFC 2 ( li. fit) P = 1.5 cm 3 /s P = 0.6 cm 3 /s desity (10 3 cm -2 ) Fig. 4. Effective surface recombiatio velocity as a fuctio of the desity (N ), for two differet LFC processes.

7 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) I Fig. 4, the liear relatio betwee S ad p ca be observed for two differet LFC processes. p ca be calculated by a simple liear regressio. For most of the practical cases, kowig p is usually sufficiet withi the approximatio W >> a (see ext sectio). It ca be used for the compariso of differet processes ad to predict S Advaced aalysis Whe the wafer thickess is much higher tha the radius of the (W >> a), tha the ormalized diffusio resistace r diff is costat to the variatio of the wafer thickess, ad it becomes almost idepedet from the desity of (see Fig. 3). Therefore, we have p 1 p 1 r a diff (11) where r diff is cosidered as costat. Effective poit recombiatio velocity - p (cm 3 /s) 10 3 p = f (p, a) 10 2 p = f (ifiity, a) for p-si 1-10.cm D ~ 30 cm 2 /s 10 1 LFC LFC p = ifiity Poits radius - a (cm) Poit recombiatio velocity - p (cm 3 /s) Fig. 5. Effective poit recombiatio rate as a fuctio of the cotact radius for several P, with r diff = s cm -2. I Fig. 5, the poit recombiatio rate is plotted as a fuctio of the estimated radius for several p. The two poits from the LFC processes preseted i Fig. 4 are also plotted. The radius is a approximated radius observed with a microscope. These poits are very close to asymptote (p ifiite), we ca therefore coclude that i the experimet performed here the recombiatios were maily limited by the diffusio resistace, ad it is ot possible to determie p with precisio. However, a recombiatio radius cosiderig p to be ifiite ca be obtaied, with 100 μm for LFC1 ad 40 μm for LFC2. I the other case, whe the experimetal poits are very far from the asymptote, the the p value is very close to the measured p. However, i this case, the radius of recombiatio would ot be determied precisely. This method of aalysis allows to evaluate which iformatio is cotaied i the measuremet ad to extract it.

8 266 P. Sait-Cast et al. / Eergy Procedia 27 ( 2012 ) Summary The model developed here is very geeral ad allows to treat poit ad lie shaped, for samples with or without emitter. Additioally the recombiatios o the are allowed to be ihomogeeous which is much more represetative to the reality of. The mathematical expressio of the model was purified i order to simplify the access to the model. Clear ad trasparet methods were developed for the measuremet ad the aalysis of the recombiatio properties. This method allows the separatio of the ifluece of recombiatio rate with the oe of the trasport. Refereces [1] B. Fischer, Dissertatio, Physics, Uiversität Kostaz, Kostaz, [2] A. Fell, D. Kray, T. Wütherich, M. R., G.P. Willeke, S.W. Gluz, Proc. 23rd EU PVSEC, Valecia, Spai, 2008, p [3] F.S. Grasso, L. Gautero, J. Retsch, R. Preu, R. Lazafame, Proc. 5th WCPEC, Valecia, Spai, 2010, p [4] J.-F. Nekarda, M. Hörteis, F. Lottspeich, A. Wolf, R. Preu, 25th EU PVSEC, Valecia, Spai, 2010, p [5] P. Gudel, M.C. Schubert, W. Warta, physica status solidi (a) 207/2 (2010) 436. [6] P. Sait-Cast, M. Rudiger, A. Wolf, M. Hofma, J. Retsch, R. Preu, Joural of Applied Physics 108/1 (2010) [7] P. Sait-Cast, Ph.D. Thesis, Costace Uiversity, p 50 (to be published)