Solar cells based on CdTe have reached a maximum efficiency of 16.5%, which has remained almost unchanged for a long time. Physical reasons for this fact have been given by different authors, but not much advance has been achieved in this regard for about 15 years. Therefore, new concepts have to be developed for a further increase of the efficiency of this kind of solar cells. One of the possibilities is to use a graded band-gap absorbing semiconductor causing an associated quasi-electric field. The effects of this quasi-electric field upon the minority carrier drift-diffusion length and the back surface recombination velocity may induce a larger carrier collection at the junction with the corresponding increase of the illumination current density. Therefore, based on these concepts, the author has recently proposed structures based on CdZnTe with a variable Zn content profile. In this work, an analytical model is developed for taking into account the quasi-electric field, the carrier back surface recombination velocity and the "graded" absorption in a solar cell using a variable band-gap semiconductor in the base. The conditions to be satisfied in order to have a real improvement of the illumination current density are discussed, in particular for a graded CdZnTe solar cell. (C) 2011 Elsevier B.V. All rights reserved.