Limiting acceptance angle to maximize efficiency in solar cells

Within a detailed balance formalism, the open circuit voltage of a solar cell can be found by taking the band gap energy and accounting for the losses associated with various sources of entropy increase. Often, the largest of these energy losses is due to the entropy associated with spontaneous emission. This entropy increase occurs because non-concentrating solar cells generally emit into 2π steradian, while the solid angle subtended by the sun is only 6.85x10 steradian. Thus, for direct normal irradiance, non-concentrating solar cells with emission and acceptance angle limited to a narrow range around the sun could see significant enhancements in open circuit voltage and efficiency. With the high degree of light trapping we expect given the narrow acceptance angle and the ray optics brightness theorem, the optimal cell thickness will result in a discrete modal structure for most materials. Thus, limiting the acceptance and emission angle can be thought of as coupling to only a subset of radiating modes, or, alternatively, as altering the modal structure such that some radiating modes become bound modes. We have shown the correspondence between the ray optics picture and the modal picture, by deriving the ray optics results for light trapping under angular restrictions using a modal formulation. Using this modal formulation we can predict the light trapping and efficiencies for various thin structures under angular restriction. We will discuss these predicted efficiencies and various options for implementing broadband and angle-specific couplers.