Optical Simulation of Arbitrary Thin Film Solar Cells with Rough Interfaces Thomas Lanz a ,† , B. Perucco b , D. Rezzonico b , Felix M ¨ uller b , N. A. Reinke a , R. H ¨ ausermann a , B. Ruhstaller a ,b a Zurich University of Applied Sciences, Institute of Computational Physics, Wildbachstrasse 21, 8401 Winterthur, Switzerland, b Fluxim AG, 8835 Feusisberg, Switzerland, www.fluxim.com † lanz@zhaw.ch FLUXiM 1. Abstract I N thin-film solar cells optical scattering effects at rough layer interfaces are exploited to enhance the light absorp- tion and make it possible to construct thin cells with inor- ganic materials such as a-Si or μc-Si [5]. SETFOS [2] is an optical and electrical device simulator, that is widely used in the OLED and OPV community. To perform an optical simulation of an arbitrary combination of inorganic or or- ganic layers of any thickness, it is necessary to be able to treat light propagation both as coherent or incoherent. We have therefore extended the optical model of SETFOS for the treatment of mixed systems of incoherent/coherent layers. We have broadened the scope of the simulator by including scattering effects at rough layer interfaces. Aluminium n a-Si p a-Si i a-Si ITO Glass Figure 1: Amporphous silicon p-i-n solar cell used for the calculations. The following layout was used in the simulations, as illus- trated in Figure 1: Glass (1 mm), ITO (200 nm), p a-Si (5 nm), i a-Si (600 nm), n a-Si (50 nm), Al (500 nm). 2. Incoherence T HE ability of the incident light to interfere within the structure is expressed using the coherence length. Co- herence within the structure can be reduced due to reflec- tions at rough interfaces or in passing through bulk layers. 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength nm Absorbance l  2000 um l  500 um l  500 nm l  5 nm Figure 2: Calculated absorbance for the a-Si solar cell de- scribed in the text. Reducing the coherence length of the incident light reduces the interference fringes. The label gives the coherence length that was used for the calcula- tions. 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength nm Absorbance Total iaSi Al Figure 3: Calculated normalized layer absorbances for the a-Si solar cell. The glass is treated as incoherent. The coherent calculation (Figures 2 and 3) reveals strong interference fringes in the absorption for wavelengths be- tween 500 and 1000 nm. They can be attributed to internal reflections in the a-Si layer. 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength nm Absorbance Total iaSi Al ITO paSi Figure 4: Calculated normalized layer absorbances for the a-Si solar cell. The glass and the intrinsic a-Si layer are treated as incoherent. 3. Effective Media Approximation T HE effect of a rough interface can be approximated us- ing a gradient in the effective refractive index. One in- troduces interlayers between layers with a rough interface which effectively reduces the reflectance of the interface [3]. 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength nm Layer Absorbance i aSi P  20  P  50  P  0  P  80  Figure 5: Calculated layer absorbance for the intrinsic a-Si layer. The label states the volume fraction that determines the effective refractive index of the n a-Si layer. 100 % cor- responds to pure a-Si and 0 % to pure Aluminium. In Figure 5 the n a-Si layer is used as an EMA layer and its complex refractive index is determined with linear interpo- lation between the indices of a-Si and Aluminium: ˜ n EMA = P · ˜ n a -Si + (1 - P ) · ˜ n Al . 4. Modified Fresnel Coefficients 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength nm Absorbance Σ 20 nm Σ 40 nm Σ 0 nm Σ 100 nm Figure 6: Calculated total unpolarized absorbance (A = 1 - R - T ) for the a-Si solar cell for increasing back contact (a-Si / Al interface) roughness. T O account for the scattering effects we have extended the transfer-matrix formalism [4] to reproduce partial co- herence. This is achieved by modifying the Fresnel coeffi- cients in the transfer-matrix formalism using the root-mean- square roughness σ [1]. Figure 6 illustrates the effect of interface roughness at the a-Si / ITO interface. The in- terference fringes disappear for increasing interface rough- ness. For wavelengths shorter than 500 nm the absorption is not affected as they are almost completely absorbed in the Glass, ITO and p a-Si layers, as illustrated in Figure 4. The presented method can so far not track and quantify the scattered light that leads to higher total absorbance in real cells. The three methods are compared in Figure 7, where the calculated localized generation in the ITO, a-Si and Alu- minium layer is shown. ITO p i n aSi Al 1.0002  10 6 1.0004  10 6 1.0006  10 6 1.0008  10 6 10 16 10 17 10 18 10 19 10 20 Position nm Generation m 2 nm 1 s 1  EMA 80 l  1 um l  50 nm Σ 40 nm Figure 7: The computed generation in the ITO, a-Si and Aluminium layer. For both short coherence length (l = 50 nm ) and surface roughness (σ = 40 nm ) no inter- ference fringes are visible in the a-Si layer. To demonstrate the use of incoherence in a tandem structure, we calculate in Figure 8 the localized ab- sorbance in an a-Si based tandem cell, composed of two a-Si subcells (i1 and i2). The glass, ITO and the intrinsic cell i2 (a-Si) are treated as incoherent. 300 400 500 600 700 800 1000 1200 1400 1600 1800 Wavelength nm Absolute Position nm i2 i1 silver electrode Figure 8: Localized absorbance (a.u.) in an a-Si based tandem solar cell, layout taken from [5]. 5. Conclusion T HREE distinct simulation approaches are presented to model the optical scattering effects: Effective Media Ap- proximation, incoherence and modified Fresnel coefficients in the Transfer-Matrix-Formalism for partial coherence. We assess and illustrate these methods using single-junction and tandem a-Si-based solar cells by calculating key fig- ures such as the spectral layer absorbance and the local- ized generation. References [1] C. L. Mitsas and D. I. Siapkas. Applied Optics, 34:1678– 1683, April 1995. [2] SETFOS. Semiconducting thin film optics simulator, Fluxim AG, Switzerland. [3]J. Springer, A. Poruba, and M. Vanecek. Journal of Ap- plied Physics, 96:5329–5337, Nov. 2004. [4]P. Yeh. Wiley, New York, 1988. [5]M. Zeman, J. A. Willemen, L. L. A. Vosteen, G. Tao, and J. W. Metselaar. Solar Energy Materials and Solar Cells, 46(2):81 – 99, 1997. We acknowledge the Swiss Federal Office of Energy and Swiss Electric Research for funding the thinPV CCEM project (http://thinpv.empa.ch/). 4th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, Germany Session Reference Number: 3BV.4.57