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Some basic concepts related to variable band-gap absorbing semiconductors in solar cell structures such as the associated quasi-electric field will be discussed. The effects of this quasi-electric field upon the minority carrier drift-diffusion length and the back surface recombination velocity will cause a larger generated carrier collection with the corresponding increase of the illumination current density. It will also be shown that an additional improvement of the open-circuit voltage is possible when the band-gap is reduced within the space charge region so that the dark saturation current density is reduced there. Our estimation is that in the case of a solar cell where the band-gap reduces from 1.35 eV to 1.15 eV, at the space charge region (of the order of 0.2 mum), an increase of the open-circuit voltage by around 65-70 mV will be observed with respect to the single gap absorbing material case. A similar (increasing) band-gap variation in the bulk of the material will cause an increase of the drift-diffusion length of minority carriers by a factor of 4 with respect to a single band-gap material. Therefore, based on these physical concepts, two possible structures with variable band-gap CIGS layers are proposed in order to have higher efficiencies than for cells without any band-gap grading.