In this paper, we present a theoretical study of the effects of light trapping and carrier recombination in thin-film crystalline silicon (c-Si) solar cells. We develop a new electro-optical model which is based on the analytic solution of drift-diffusion equations. We explore the effects of different thickness and material qualities on the energy conversion efficiency of the device. The results clearly point out that c-Si absorbers with a thickness between 10 and 80 microns are very attractive for future high efficiency applications. We find that in this range of thickness, thin-film devices can be more efficient than those based on bulk wafers. The requirements in terms of bulk and surface quality that ensure this result are quantified by our model. This analytic framework can be applied as a valid tool in understanding experimental and numerical results for c-Si solar cells with rough interfaces or other isotropic optical structures for light trapping.