Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of parameters from the LBIC image by least-squares formulation. Numerical examples are presented to illustrate the success of identifying parameters such as junction depth, diffusion length, and equilibrium potential of an abrupt p-n junction diode from its LBIC image. The differentiability of the image with respect to the parameters also is established.