Feifar, A.

Feitknecht, L.

Meier, J.

Poruba, A.

Shah, A.

Springer, J.

Vanecek, M.

Wyrsch, N.

Infoscience - École polytechnique fédérale de Lausanne

NANOTEXTURED THIN FILM SILICON SOLAR CELLS: OPTICAL MODELJ. Springer, A. Poruba, A. Fejfar and M. Vanecek*Institute of Physics, Academy of Sciences of the Czech Republic,Cukrovarnicka 10, Prague 6, CZ-16253 Czech Republic* corresponding author, phone ++420 2 20318540, fax ++420 2 3123184, e-mail  vanecek@fzu.czL. Feitknecht, N. Wyrsch, J. Meier and A. ShahInstitute of Microtechnology, Neuchatel University,Rue A. L. Breguet 2, CH-2000 Neuchatel, SwitzerlandABSTRACT: Light trapping scheme based on nanotextured surfaces/interfaces of thin film silicon solar cells(amorphous, microcrystalline) deposited on textured ZnO is modeled with the help of Monte Carlo method taking intoaccount the effects of light coherence. Spectral response and short circuit current density are computed as a function ofnanoroughness, angular distribution of scattered light, thickness and optical constants of all layers of single or multi-junction solar cells. Simultaneously, optical constants of each layer have been measured. Finally, model results arecompared with experimentally determined spectral response of microcrystalline single-junction silicon solar cells.Keywords: Si-Films – 1: Modeling – 2: Texturization - 31. INTRODUCTIONEfficient light trapping is of great importance for thinfilm silicon solar cells. Recently, a new light trappingscheme based on nanotextured surfaces/interfaces havebeen introduced [1], which differs from the usualmicrotextured (textured on the micrometer scale) thicksilicon wafers. Internal reflection in a material with a highindex of refraction (silicon) and a nanotextured interface(with a random roughness on the scale of tens ofnanometers) can lead to complete diffuse reflection of light[2]. The optical path of weakly absorbed light is thereforegreatly enhanced.To calculate an absorption enhancement and thespectral response of nanotextured solar cells geometricaloptics cannot be used; therefore, usual ray tracing programscannot be applied. On the other hand, a rigorous treatmentusing Maxwell electromagnetic theory (being availableonly for a periodically repeating surface features) is verycomplicated and time-consuming [3]. Hence, we havedeveloped a simple Monte Carlo model based on scalarscattering theory, which takes into account the part of lightscattered at each interface/surface as well as the coherentpart of the non-scattered light in each layer. Eitheridealized Lambertian distribution of the scattered light ordirectly measured scattering distribution function isincluded in our model. Using this method, spectralresponse (SR) of a single-junction or multi-junction cellscan be easily calculated, in a few minutes on a personalcomputer.Furthermore, we have measured all optical parametersof each layer of the cells investigated. This is especiallyimportant for new materials, as for microcrystalline silicon,or for doped layers where the optical absorption coefficientand the refractive index depend on the doping level. Ourmodel, thus, has no free parameter, since all input data aredetermined experimentally. We should stress that ourmodel is quite general, not limited to thin film silicon solarcells.2. MODELING APPROACHWe use the Monte Carlo method for modeling ofquantum efficiency (QE) of single-junction or multi-junction solar cell. With an increasing computing power ofrecent PC’s the Monte Carlo method represents an optimalapproach to this task. A scheme of the computer program isbased on tracing of 20 000 photons for each wavelength.First of all, coherent contribution of the multilayer structureis calculated using wave theory taking into account thescattering losses. Then ray tracing of scattered photons iscalculated up to the final absorption in any layer of thesolar cell or photon loss due to the reflection into air. Thisenables us to analyze the origin of all optical losses. Weconsider just the photons absorbed in the intrinsic layer ofp-i-n or n-i-p single-junction solar cells as contributing tothe photogeneration of free electrons and holes. Finally, theshort circuit current is obtained by multiplying SR with theAM 1.5 spectrum, 100 mW/cm2.In the optical model we use the followingapproximations in order to describe the influence of therough surfaces/interfaces and the bulk light scattering: thescalar scattering theory [4], the effective mediaapproximation (EMA) [5] and the isotropic bulk scattering[5]. Wave theory enables to treat light coherently in thinmultilayer structures of solar cells, for tracing of scatteredphotons geometrical optics is applied. We useexperimentally determined optical constants of allmaterials (exceptions are mentioned in the text) andexperimentally determined typical angular distribution ofscattered light at rough surface.3. DETERMINATION OF OPTICAL CONSTANTSMicrocrystalline hydrogenated silicon (µc-Si:H) oralternatively amorphous hydrogenated silicon (a-Si:H) areused as active layers of thin-film solar cells. Opticalconstants of these layers can be found in the differentenergy ranges using elipsometry, standard transmittanceand reflectance (T/R) spectroscopy, PhotothermalDeflection Spectroscopy (PDS) and/or ConstantPhotocurrent Method (CPM). Although effects of lightscattering at rough interfaces are of great importance forachieving high solar cell efficiency, they remarkablycomplicate the evaluation of all optical parameters.Recently, we have developed procedures how to eliminatesuch effects from measured T/R, CPM and PDS data[6,7,8]. Fig.1 and 2 show typical data of the spectraldependencies of the absorption coefficient α(E) and theindex of refraction n(E) of both amorphous andmicrocrystalline solar grade materials. It is well known thatthe bandgap of amorphous silicon depends on thetechnology and particular deposition conditions. Here wepresent the data of a-Si:H prepared by standard PECVD(GD) and α(E) and n(E) of microcrystalline silicon grownusing the VHF GD technique [9]. One can observe verylow defect-connected optical absorption below 1 eV, astypical for a device grade material. Although this part ofcurves is not usually applied during the modeling(wavelength range from 375 to 1200 nm) it reflects thequality (mainly the defect concentration) of thin films.1 2 310-1100101102103104105106 µc-Si:H (VHF GD) a-Si:H (GD)  c-Si (M.A.Green)Absorption coefficient (cm-1 )Photon energy (eV)1500 1000 500Wavelength (nm)Fig. 1 Measured and evaluated spectral dependencies of theabsorption coefficient of microcrystalline silicon (µc-Si:H)and amorphous hydrogenated silicon (a-Si:H); α(E) ofcrystalline silicon is shown for the comparison [10].It is obvious that the absorption coefficient of dopedmaterial differ mainly in the low energy range due to theenhanced defect concentration and because of free carrierabsorption. At the present stage of our model we fix theabsorption coefficient at a constant value of around300 cm-1 here. The effects of bandgap shift with doping aretaken into account in our modeling, simply by changing thedoped layer thickness.1 2 33456 µc-Si:H (VHF GD) a-Si:H (GD) c-Si (M.A.Green)Index of refraction (-)Photon energy (eV)1500 1000 500Wavelength (nm)Fig. 2 Measured and evaluated spectral dependencies of therefractive index of microcrystalline silicon (µc-Si:H) andamorphous silicon (a-Si:H); n(E) of crystalline silicon isshown for the comparison [10].Optical data (α(E) and n(E)) of transparent conductiveoxide (TCO) (in our case doped or undoped ZnO ) wereobtained using T/R spectroscopy and PDS measurements[6,7,8]. Surface roughness of TCO was determined fromT/R measurement and checked by AFM. Finally, theoptical properties of silver are calculated from data alreadypublished [5]. Hence, in the present stage of our model we use theexperimental values of optical constant just for undopedmicrocrystalline and amorphous silicon and for undoped ordoped ZnO.4. MODEL RESULTS AND DISCUSSIONMicrocrystalline silicon single-junction n-i-p solar cellstructure is shown in Fig. 3.ZnOM icrocrystalline silicon n-i-p solar cellZnOSilver back reflectorIncident photon flux   Fig. 3 Sketch of n-i-p thin film solar cell.Model output has been compared to experimentallymeasured spectral response (presented as the externalquantum efficiency) of fully microcrystalline silicon n-i-psolar cells (with thickness around 2 microns). In our modelwe assume that all electrons and holes generated in theintrinsic layer of n-i-p are collected. In a particular cellwith SR shown in Fig. 4 this case happens at reverse biasof −3 V. Details of solar cell deposition are presented inRef. 11.400 500 600 700 800 900 10000.00.20.40.60.81.0Sample L300899Gbias:   0.00 V   0.30 V  -1.00 V  -3.00 VQEWavelength (nm)3 2.5 2 1.5Photon energy (eV)Fig. 4 Quantum efficiency (QE) of the single micro-crystalline silicon solar cell measured with the differentbias voltage.Fig. 5 compares the experimental QE curve (−3V bias)with our model. Very good agreement can be seen, evenfor all residual interference effects.400 500 600 700 800 900 10000.00.20.40.60.81.0Isc (380-1200nm) = 25.01 mA/cm2QE, A, RWavelength (nm) experimental QE model QElosses: reflectance into air front ZnO (C) (1.41µm) p+ (20nm) n+ (25nm) back ZnO (A) (0.3µm) Ag 3 2.5 2 1.5Photon energy (eV)Fig.  5 Measured and modeled quantum efficiency (QE) ofthe microcrystalline silicon n-i-p solar cell. Optical losses(A) at each layer and reflection (R) of light into the air arealso shown.Fig. 5 allows to analyze where the photons of eachwavelength are lost. Reflection losses, absorption in frontor back ZnO (they differ in thickness and doping level), insilver backreflector and in p+ and n+ layers is directly seenin Fig. 5.In Fig. 6 we have compared the scattering properties ofour experimental 2 microns thin microcrystalline Si n-i-psolar cell [11] with the ultimate scattering properties ofideal Lambertian diffuser. We have plotted Isc as a functionof cell thickness. We can see that ideal Lambertian diffuserused just as the backreflector gives the best results.1 2 3 42022242628303234cell L300899I SC (mA/cm2 )Intrinsic layer thickness (µm) similar scattering as L300889 cellIdeal cosine distribution and 100% scattering at all interfaces 100% scattering at backreflectorFig. 6 Comparison of model results of short circuit currentIsc  for a different cell thickness and scattering properties.QE model data of amorphous / microcrystalline silicontandem cell (so-called micromorph cell) are plotted inFig. 7. Our modeling can be used not only for analysis ofoptical losses, but also for an optimal current matchingbetween the top amorphous and bottom microcrystallinecell with the surface roughness of each interface used as aparameter.400 600 800 1000 12000.00.20.40.60.81.0Absorptance in intrinsic layer           a-Si:H (330 nm)           µc-Si:H (1.9µm)           sum11.87 mA/cm211.84 mA/cm2Wavelength (nm)Quantum efficiency3 2.5 2 1.5Photon energy (eV)Fig. 7 Model data for quantum efficiency of tandemamorphous / microcrystalline silicon n-i-p n-i-p solar cell.5. CONCLUSIONSOur optical model of solar cell gives the ultimateperformance of nanotextured thin film solar cell in terms ofmaximum achievable short circuit current, for a giventhickness of all layers and the light scattering parameters oflayers and interfaces. It enables us to analyze and identifythe losses due to each parameter. Model gives the resultswithin a few minutes on standard PC. Precise knowledge ofoptical constants and detailed study of scattering propertiesis needed in a long wavelength region, where an efficientlight trapping is absolutely necessary for the efficient thin-film-silicon solar cells.REFERENCES[1] A. Poruba, Z. Remes, J. Fric, M. Vanecek, J. Meier, P.Torres, N. Beck, N. Wyrsch and A. Shah, Proc. 14thEuropean Photovoltaic Solar Energy Conference,Barcelona 1997, p. 2105[2]  A. Poruba, Z. Remes, J. Springer, M. Vanecek, A.Fejfar, J. Kocka, J. Meier, P. Torres and A. Shah, Proc. 2ndWCPSEC, Vienna 1998, p. 781[3] B.L. Sopori, J. Madjdpour, W. Chen, Proc. 2ndWCPSEC, Vienna 1998, p. 156[4] P. Beckman, A. Spizzichno, The Scattering ofElectromagnetic Waves from Rough Surfaces, (PergamonPress, Oxford 1963), chapter 5[5] Handbook of Optics, 2nd ed., edited by M. Bass(McGraw-Hill, New York, 1995).[6]  M. Vanecek, A. Poruba, Z. Remes, N. Beck, M.Nesladek, J. Non-Crystal. Solids 227-230 (1998) 967[7] A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M.  			ﬀﬁﬂﬃ !#"$&%(''	J.Appl.Phys. (July 2000), in print[8]  A. Poruba, A. Fejfar, O. Salyk, M. )*+ ,-./*+0/1234,.*5 J.Non-Cryst.Solids (2000), in print[9]  J. Meier, S. Dubail, J. Cuperus, U. Kroll, R. Platz, P.Torres, J.A. Anna Selvan, P. Pernet, N. Beck, N. PellatonVaucher, Ch. Hof, D. Fischer, H. Kepner and A. Shah, J.Non-Crystal. Solids 227-230 (1998) 1250[10]  M. A. Green, High efficiency silicon solar cells,(Trans Tech SA, 1987)[11] L. Feitknecht, O. Kluth, Y. Ziegler, X. Niquille, P.Torres, J. Meier, N. Wyrsch, and A. Shah, this ConferenceKEYWORD LISTKeywords:Si-Films – 1Modeling – 2Texturization - 3

Nanotextured Thin Film Silicon Solar Cells: Optical Model

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Nanotextured Thin Film Silicon Solar Cells: Optical Model

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