Effective absorption coefficient for graded band-gap semiconductors and the expected photocurrent density in solar cells

A simple model for the generation of carriers by photons incident on a (linearly) decreasing band-gap material, such as has been described in recent CIGS solar cells, is developed. The model can be generalized for different cases such as increasing band-gap grading or for having a more complex band-gap profile.The model developed for direct band semiconductors such as CIGS or AlGaAs allows us to define an effective absorption coefficient, so that the ideal photocurrent density can be calculated in a similar manner as for solar cells with non-graded band-gap materials.We show that this model gives completely different results as those expected from intuitive approaches for calculating this ideal photocurrent density. We also show that grading of the band-gap of the absorbing material in solar cells makes the photocurrent less sensitive to the total band-gap change, in such a way that the design of the band-gap variation can be more flexible in order to have other advantages such as higher built-in voltage or higher back surface field in the device structure.