Many-body effects, space-charge potential, and valence-band mixing on the optical gain in quantum-well structures

The subband energy and gain in quantum wells are calculated with the local-density approximation, including valence-band mixing. The effects of the space-charge potential and the exchange-correlation potential are considered self-consistently. The space-charge potential is estimated to be as large as 45 meV for a 5-nm-thick ${\mathrm{Ga}}_{0.5}$${\mathrm{In}}_{0.5}$P/(${\mathrm{Al}}_{0.4}$${\mathrm{Ga}}_{0.6}$${)}_{0.5}$${\mathrm{In}}_{0.5}$P single quantum well with a carrier density of 4×${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ at room temperature. It is shown that the exchange-correlation potential compensates the space-charge potential for holes to some extent in the present system. Comparison between the Hartree approximation (neglecting the exchange-correlation potential) and the full calculation shows the necessity of both the space-charge potential and the exchange-correlation potential to obtain accurate subband energies and optical gain. Some of the previous calculations on the many-body effects in quantum wells have not considered the space-charge potential. Thus, they are valid only for systems with weak space-charge potentials, for example, GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells. © 1996 The American Physical Society.