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A self-consistent numerical Poisson-Schrodinger-drift-diffusion solver is described for simulation of multiple-quantum-well (MQW) AlxGa1-xAs-GaAs solar cells. The rates of escape, capture, and recombination of photoexcited carriers in quantum wells embedded in the intrinsic region of a p-i-n device are self-consistently incorporated in the model. The performance of the device for various quantum-well configurations is investigated and the device characteristics are related to the dynamics of capture, escape, absorption, and recombination of carriers in the quantum wells. Our results show that the incorporation of MQWs in the intrinsic region of a p-i-n solar cell can improve the conversion efficiency of non-optimal devices, if the device is designed based on careful consideration of the behavior of the photoexcited carriers in the quantum wells. Specifically, we found out that an Al0.1Ga0.9As-GaAs cell with multiple quantum wells of 150 Å is more efficient than an identical single bandgap Al0.1Ga0.9As cell with no quantum wells, but less efficient than a single bandgap GaAs cell without such quantum wells.