Calculation of threshold current density in 633-nm AlGaInP/GaInP strained quantum well lasers

Using a 6 x 6 Luttinger-Kohn Hamiltonian1 considering the SO band effects, we calculated valence bands in (Alo~7Ga0~3~0~51n0~5P/GaxInl-xP QWs with Ga compositions (x) of 0.46 to 0.57, corresponding to strains ranging from 0.40% compressive to 0.43% tensile. We varied the well width until the bandgap energy equaled 1.96 eV, or 633 nm. For comparison, we also calculated the valence bands using a 4 x 4 Hamiltonian without SO band effects. Under tensile strain, the topmost band is light-hole (LH) like, but is coup!ed with the SO band. We found that this coupling widens the k-vector dispersion of the topmost band, and increeases the in-plane effective mass. Under compressive strain, the effective mass is smaller, due to less mixing of the topmost heavy hole band with both the LH band and the SO band. To obtain the relationship between modal gain Gln and current density J, we calculated the optical gain and. radiative lifetime from the valence band described above, assuming a parabolic conduction band. We found that structures under tensile strain have a larger transparent current density Ju and a larger differential gain than those under compressive strain. Those properties observed in structures under tensile strain result from the small spinorbit splitting in GaInP, because a large effective mass causes a large Jt, and a large differential gain. Therefore, the Gm curve for compressive strain crosses that for tensile. Comparing 0.40% compressive with 0.43% tensile strain, Gm for compressive is larger than that for tensile below Gm of 25 cm-l, while the opposite is true above 25 cm-l. As a result, we found that, for lasers with low threshold gain such as those with high-reflectivity optical coatings, compressive strain is effective in reducing Jth. In contrast, tensile strain is more effective in lasers with high threshold gain such as those with a saturatable absorber. These SO band effects have not been seen in GaInAsP long-wavelength strained QW lasers with a large spin-orbit splitting2.