Effective Medium Analysis of Plasmonic Silver Nanoparticle Films
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Effective Medium Analysis of Plasmonic Silver Nanoparticle Films Rudi Santbergen1, Jeroen Sap1, Tristan Temple1,2, Serge Solntsev1, Arno HM Smets1, René van Swaaij1 and Miro Zeman1 1
Delft University of Technology, Photovoltaic Materials and Devices laboratory/DIMES, P.O. Box 5053, 2600 GB Delft, the Netherlands 2 Southampton University, Electronics and Computer Science, Highfield, Southampton SO17 1BJ, UK ABSTRACT Films of silver nanoparticles have optical properties that are useful for applications such as plasmonic light trapping in solar cells. We illustrate experimentally and by means of simulations how the particle shape affects the optical properties. In addition we show that these nanoparticle films can be represented by an effective medium layer with an almost identical reflectance and transmittance. The Bergman effective medium theory that we used provides a link between the nanoparticle shape and the optical properties. This insight can be used for the optical analysis of nanoparticle films and for further optimization of plasmonic solar cells. INTRODUCTION Solar cells have an absorber layer where photons are absorbed and charge carriers are generated. To reduce solar cell cost and to enhance the extraction of the charge carriers, there is an ongoing trend to reduce the thickness of this absorber layer. Light trapping techniques, aimed at maximizing the absorption of light in a thin absorber layer, are therefore becoming increasingly important for obtaining a high conversion efficiency. State-of-the-art solar cells employ rough surfaces introduced by surface textured substrates to scatter incident light in combination with a back reflector. It has been suggested that plasmons can play an important role in light trapping [1]. For example, localized surface plasmons excited on metal nanoparticles can be used to scatter light and to enhance absorption in the near field. Numerical simulations are a valuable tool for optimizing solar cell design. Optical simulations are required to study the light-trapping effects of embedded silver nanoparticles. Electrodynamic models that solve Maxwell’s equations rigorously are accurate but computationally expensive. Most simulations presented in literature are therefore limited to a single nanoparticle [2] or, if periodic boundary conditions are used, to a periodic array of identical nanoparticles [3-5]. The most commonly used nanoparticle fabrication technique results in a random array of particles of various shapes and sizes [6-11]. Modeling such a vast collection of particles rigorously is still out of reach of modern computers. In this paper we explore a simplification of the problem. We demonstrate the possibility of modeling films of nanoparticles as an effective medium. The goal is then to find a dielectric function (or refractive index) of the effective medium that results in the same macroscopic optical properties as the film of nanoparticles. We show that Bergman’s effective medium theory
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is very suitable for this task. In addition we illustrate how this t
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