Crystal orientation dependence of many-body optical gain in wurtzite GaN/AlGaN quantum-well lasers

Crystal orientation effects on the optical gain of wurtzite GaN/AlGaN quantum-well (QW) lasers with a spontaneous and piezoelectric polarization are investigated by the non-Markovian gain model with many-body effects. These results are compared with those of the flat-band (FB) model which neglects the spontaneous and piezoelectric polarization. The constant energy contour of the general crystal orientation shows twofold symmetry. The matrix elements near the band-edge (k = 0) increase rapidly with increasing crystal orientation due to the decrease of the internal field with the crystal orientation. It is found that the Coulomb enhancement effect is the most dominant in the case of the (0001)-oriented QW (θ = 0°) and decreases with increasing crystal orientation angle (θ) measured from the (0001) axis. This is mainly attributed to the fact that the effective mass gradually decreases with increasing crystal angle. The FB model shows that the optical gain gradually decreases with increasing crystal angle. On the other hand, the SC model shows that the optical gain increases with increasing crystal angle and reaches a maximum near θ = 60°. This can be explained by the decrease of the Coulomb enhancement effect and the increase of the matrix elements with increasing crystal angle.