In this paper we introduce the three-dimensional formulation of the OPTOS formalism, a matrix-based method that allows for the efficient simulation of non-coherent light propagation and absorption in thick textured sheets. As application examples, we calculate the absorptance of solar cells featuring textures on front and rear side with different feature sizes operating in different optical regimes. A discretization of polar and azimuth angle enables a three-dimensional description of systems with arbitrary surface textures. We present redistribution matrices for 3D surface textures, including pyramidal textures, binary crossed gratings and a Lambertian scatterer. The results of the OPTOS simulations for silicon sheets with different combinations of these surfaces are in accordance with both optical measurements and results based on established simulation methods like ray tracing. Using OPTOS, we show that the integration of a diffractive grating at the rear side of a silicon solar cell featuring a pyramidal front side results in absorption close to the Yablonovitch Limit enhancing the photocurrent density by 0.6 mA/cm² for a 200 µm thick cell.

In this paper, we introduce a simulation formalism for determining the Optical Properties of Textured Optical Sheets (OPTOS). Our matrix-based method allows for the computationally-efficient calculation of non-coherent light propagation and absorption in thick textured sheets, especially solar cells, featuring different textures on front and rear side that may operate in different optical regimes. Within the simulated system, the angular power distribution is represented by a vector. This light distribution is modified by interaction with the surfaces of the textured sheets, which are described by redistribution matrices. These matrices can be calculated for each individual surface texture with the most appropriate technique. Depending on the feature size of the texture, for example, either ray- or wave-optical methods can be used. The comparison of the simulated absorption in a sheet of silicon for a variety of surface textures, both with the results from other simulation techniques and experimentally measured data, shows very good agreement. To demonstrate the versatility of this newly-developed approach, the absorption in silicon sheets with a large-scale structure (V-grooves) at the front side and a small-scale structure (diffraction grating) at the rear side is calculated. Moreover, with minimal computational effort, a thickness parameter variation is performed.

The OPTOS formalism is a matrix-based approach to determine the optical properties of textured optical sheets. It is extended within this work to enable the modelling of systems with an arbitrary number of textured, plane-parallel interfaces. A matrix-based system description is derived that accounts for the optical reflection and transmission interaction between all textured interfaces. Using OPTOS, we calculate reflectance and absorptance of complete photovoltaic module stacks, which consist of encapsulated silicon solar cells featuring textures that operate in different optical regimes. As exemplary systems, solar cells with and without module encapsulation are shown to exhibit a considerable absorptance gain if the random pyramid front side texture is combined with a diffractive rear side grating. A variation of the sunlight's angle of incidence reveals that the grating gain is almost not affected for incoming polar angles up to 60°. Considering as well the good agreement with alternative simulation techniques, OPTOS is demonstrated to be a versatile and efficient method for the optical analysis of photovoltaic modules.

Molds are used to dictate their shape to other materials in embossing or filling processes. In optics fabrication especially, the exact surface slope of the polymer replica is of high relevance. The quality control of molds is challenging: non-invasive, optical metrologies struggle with shiny surfaces that minimize the scattering of light. In addition, the inspection of complex shaped molds with a stepped optical surface can be difficult. In response, the authors show a backward ray-tracing approach combined with fringe-reflection technique to determine the slopes of a Fresnel-shaped mold surface with topography features in the magnitude order of a quarter millimeter. The error is kept small by stitching together several measurements with different sample rotations.

Abstract.A network model for multi-junction solar cells has been combined with ray tracing and finite element simulations of a Fresnel lens in order to interpret experimentally derived measurement results. This combined model reveals a good agreement between simulation and measurement for advanced four-junction solar cells under a Fresnel lens when the cell-to-lens distance was varied. Thus, the effect of fill factor drop caused by distributed series resistance losses due to chromatic aberration is well described by this model. Eventually, this model is used to calculate I-V characteristics of a four-junction cell, as well as of a upright metamorphic and lattice-matched triple-junction solar cell under the illumination profile of a Fresnel lens. A significant fill factor drop at distinct cell-to-lens distances was found for all three investigated solar cell types. In this work we discuss how this fill factor drop can be avoided. It is shown that already a halving of the sheet resistance within one of the lateral conduction layer in the solar cell increases the module efficiency significantly.