Light Trapping Gratings for Solar Cells: An Analytical Approach to Find the Best Periods

Grating-based light trapping for solar cells has been investigated since 1989, when Kiess and Morf [1] proposed that concept. Over the years, various grating designs have been explored theoretically and experimentally. Different grating types were investigated, such as linear, crossed and hexagonal gratings. The periods of the investigated gratings typically are in the range between 300 nm and a few micrometers. While for small periods, only a few diffraction orders propagate in the semiconductor at very high angles with respect to the surface normal, gratings with larger periods excite a higher number of orders with a large variety of propagation angles. Gratings could improve the solar cell performance only in a few cases. One example is a III-V//Si triple junction solar cell developed at Fraunhofer ISE [2], in which a crossed grating with 1 µm period contributed to achieve the record efficiency of 35.9%. Although many researchers have investigated gratings for light trapping and have performed various optimizations, the results do not converge to a clear picture. For the optimization, basically two aspects need to be considered: (1) the path length enhancement due to the propagation angle and (2) the escape probability that is connected to the number of diffraction orders which are either trapped or within the escape cone. In this contribution, we present an analytical approach, which takes single path-length enhancement, escape probability, the divergence of solar radiation and the reciprocity of diffraction efficiencies into account. The basic principles of the approach are strongly related to works by Yablonovich [3], Green [4] and Mellor [5]. Based on rather simple assumptions concerning the distribution of the diffraction efficiencies, we show that for crossed and hexagonal gratings there are sweet spots in the period range leading to excellent light trapping, resulting in enhanced near infrared absorptance and photocurrent. One advantage of such a basic model is that fundamental interrelations of the grating parameters can be understood very well.