Towards a generalized framework for the analysis of solar cell performance based on the principle of detailed balance

The principle of detailed balance forms the basis of the present thesis. It states that all microscopic processes in thermodynamic equilibrium are equal to their respective counter processes. For solar cells in thermodynamic equilibrium, for example, as many photons get absorbed by the cell as are emitted. Shockley and Queisser used this principle to determine a theoretical conversion efficiency limit for a solar cell with a given band gap energy, using additionally the assumption that all photons with energies higher than the band gap energy are absorbed and that there is zero absorption below the band gap energy. This so-called step-function in absorption is one of the idealizations of the model as no material shows this kind of sharp absorption edge. There are different conventions on how to quantify the band gap energy, each of which is preferentially used in different solar cell technology communities. This band gap energy, for instance, is used to quantify losses that occur in the solar cell with respect to the ideal solar cell after Shockley and Queisser. This thesis introduces a procedure based on the theory of Shockley and Queisser to determine the band gap energy that is applicable to all technologies. It is derived from a mathematical definition of a distribution of band gap energies that is calculated solely from the external quantum efficiency of the solar cell. This so-called Shockley-Queisser band gap energy is then used to quantify voltage loss mechanisms with respect to the ideal case. Because the Shockley-Queisser band gap energy is not determined from internal material properties, it allows for the comparison of these loss mechanisms consistently throughout all solar cell technologies.In contrast, to determine the efficiency potential of theoretical materials generated via first-principle calculations it is necessary to deduce external solar cell parameters such as the short-circuit current from internal material properties such as the complex refractive index. The state-of-the-art model by Yu and Zunger used to determine efficiency limits from computationally or experimentally derived absorption spectra, however, is not compatible with the principle of detailed balance. In the present thesis it is shown that the refractive index must be taken into account in order to achieve compatibility with the principle of detailed balance. A consistent model is described and a selection metric for computational high-throughput materials screening is developed. This selection metric is then applied to a variety of materials. The efficiency potential is shown to differ from the state-of-the-art model by up to \SI{20}{\percent}.After looking at the solar cell solely from the outside and establishing a model that connects internal and external parameters, the final topic in the thesis is dedicated to modelling the organic solar cell exclusively by internal means. Due to the low dielectric constants typical of organic materials, the generated electron-hole pairs are found as strongly bound excitons. To efficiently split these excitons an additional state is needed, namely the charge transfer state. Based on the principle of detailed balance a 0-dimensional rate model is described that accounts for this extra electronic state. It is shown that for this model both the superposition of electro and photoluminescence and the opto-electronic reciprocity theorem by Rau hold under non-saturation conditions. The occupation of the charge transfer state as well as the collection efficiency are thoroughly discussed for the transfer rate models according to both the Miller-Abrahams and Marcus theory