Angular optical behavior of photonic-crystal-based dye-sensitized solar cells

Theoretical modeling of the incidence angle dependence is important for the performance evaluation of solar cells especially when they employ structural photonics that enhance their aesthetics for building-integrated photovoltaic applications. We present an optical model based on transfer matrix method, which is tailored for the analysis of the angular optical characteristics of dye-sensitized solar cells (DSSC) that incorporate a porous one-dimensional photonic-crystal (1DPC) back reflector. We provide complete mathematical description of the angular optics and electromagnetic energetics of DSSC, including solutions that avoid numerical instabilities in the case of thick, strongly light-absorbing layers. The model showed excellent quantitative agreement with angle-dependent spectral transmittance measurements recorded from complete DSSCs, allowing detailed analysis of the light harvesting enhancement by the dye provided by back-reflection of light from the 1DPC. Determining the ratio of the device transmittance measured with and without a 1DPC is proposed as a simple and practical way o determine the internal reflectance of the 1DPC embedded in the device structure. The reported model provides an accurate description of the coherent angular optics of DSSCs, applicable for situations where light scattering in the device structure can be neglected.