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We present a comprehensive drift-diffusion-type electroabsorption modulator (EAM) model. The model allows us to investigate both steady-state properties and to follow the sweep-out of carriers after pulsed optical excitation. Furthermore, it allows for the investigation of the influence that various design parameters have on the device properties, in particular how they affect the carrier dynamics and the corresponding field dynamics. A number of different types of results are presented. We calculate absorption spectra and steady-state field screening due to carrier pile-up at the separate-confinement heterobarriers. We then move on to look at carrier sweep-out upon short-pulse optical excitation. For a structure with one well, we analyze how the well position affects the carrier sweep-out and the absorption recovery. We calculate the field dynamics in a multiquantum-well structure and discuss how the changes in the field near each well affect the escape of carriers from that well. Finally, we look at the influence that the separate-confinement heterostructure barriers have on the carrier sweep-out.