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We present a self-consistent electric and optic model for superluminescent light-emitting diodes (SLED) using 3D finite-element method. The carrier transport is calculated by the drift-diffusion method, which is coupled with the radiative recombination obtained from the solution of Shrodinger-Poison equations self-consistently. The spontaneous emission noise is described by the fundamental theory using the Green's function method. Our model allows 2D treatment of the carrier dynamics and optical confinement on the transverse plane, along with the electronic and optical variation on the longitudinal axis. The theoretical model has been benchmarked with an InP-based edge-emitting SLED. The device has nonidentical quantum wells with broad bandwidth from 1300 to 1600 nm. The results show the importance of 3D effects and demonstrate the validity of the model.