Optical gain of InGaP and cubic GaN quantum-well lasers with very strong spin-orbit coupling

In this article, we study the effects of strong spin-orbit (SO) split-off band coupling on the valence-band structure and the optical gain of 70 Å strained InGaP-In(AlGa)P quantum-well lasers and a 100 Å cubic GaN quantum well using the 6x6 Luttinger-Kohn model. We first calculate the optical gain of InGaP quantum wells by comparing the 6x6 and 4X4 Luttinger-Kohn models. In the case of InGaP-In(AlGa)P quantum wells which have a SO split-off energy of 0.1 eV, the peak gain of the strained quantum well is overestimated in the low carrier injection region and is underestimated in the high injection, in the 4X4 model. On the other hand, the peak gain of an unstrained quantum well is overestimated in the 4X4 model over the wide range of carrier densities. Second, we obtain the Luttinger valence-band parameters γ₁, γ₂, and γ₃ for a cubic phase of GaN using a semiempirical five level k·p model. Calculated valence-subband structures show that the subbands originated from the "light hole" and the "SO" are strongly coupled even at the zone center because of the very narrow SO split-off energy. It is expected that a very narrow separation (10 meV) between the SO band and the heavy- and light-hole bands causes two undesirable effects on the lasing of the GaN quantum well: (1) the TE and the TM polarizations have comparable magnitudes over the wide range of carrier densities and (2) the SO band will be easily occupied by the injected holes which in turn reduces the injection efficiency or increases the lasing threshold. Band-structure engineering is proposed to reduce the hole and the electron masses and to increase the SO band separation in order to reduce the lasing threshold.