We calculate circularly polarized luminescence emitted parallel (vertical emission) and perpendicular (edge emission) to the growth direction from a quantum well in a spin light-emitting diode (spin-LED) when either the holes or electrons are spin polarized. It is essential to account for the orbital coherence of the spin-polarized holes when they are captured in the quantum well to understand recent experiments demonstrating polarized edge emission from hole spin injection. The calculations explain many features of the circular polarizations of edge and vertically emitted luminescence for spin polarized hole injection from Mn-doped ferromagnetic semiconductors, and for spin-polarized electron injection from II-VI dilute magnetic semiconductors.
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