Theory of reduced threshold current density in GaAs/AlGaAs quantum well lasers

Abstract

It has recently been demonstrated that (111) GaAs/AlGaAs quantum well lasers can have a lower threshold current density than equivalent (001) lasers. We have used the envelope function method to calculate the hole confinement energies and valence subband dispersion energies of (111) and (001) quantum wells of varying width. We find that the differences in threvalence subband dispersion can account fully for the measured differences in threshold current densities. The heavy-hole mass is significantly larger along (111) than along the conventional (001) growth direction. This increases the number of heavy-hole confined states for a given well width. Away from the zone centre, the subband dispersion in the well plane shows less mixing between heavy- and light-hole bands than for (001) growth and, in thin wells, the highest subband has a low in-plane effective mass over a greater energy range, resulting in a reduced density of states at the valence band maximum. Laser gain calculations show that this enhanced light-hole behaviour can explain the reduction in threshold current density of (111) lasers compared to equivalent (001) lasers, in good agreement with experimental observation. We also calculate optical matrix elements for TE and TM modes and find that in thin (111) lasers, an improved selection of TE over TM modes is possible, due mainly to the different subband orderings in the two growth directions. This leads to the elimination in (111) lasers of the TM jump of the laser mode observed in some (001) lasers and its replacement by a TE jump, in agreement with experimental observations.