A theoretical study of the threshold current of quantum well lasers

The work described in this thesis is a theoretical investigation of the effects of band structure, strain, pressure, and growth orientation on the performance of semiconductor quantum well lasers. The effect of degenerate light- and heavy-hole bands on the carrier and current density and the differential gain are studied and compared with the non-degenerate case in semiconductor quantum well (QW) lasers. It is demonstrated that the presence of two degenerate bands at the valence band maximum will always lead to an increased threshold radiative current density compared to the case where only one band is significantly populated. When the two valence bands are separated by an energy E5, the current density decreases rapidly with increasing E5, with greater reductions being achieved for a given tensile than compressive strain. The effect of the second subband becomes less important with increasing E5, and the radiative current density reverts to that of the one valence band case, demonstrating the importance of maximising the subband energy separation to optimise laser characteristics. We investigate different formulations of the envelope function method and show that the accuracy of the calculated zone-centre confinement energies can be simply predicted by plotting the equivalent bulk band structure using the various formulations. We show how coupling to the conduction and spin-split-off bands can decrease the light-hole zone-centre energies and lead to significant differences in the calculated subband dispersion, with the effects being most pronounced for systems having a narrow band gap and small spin-orbit splitting energy. Since the loss mechanisms in a semiconductor laser are often strongly wavelength dependent and hydrostatic pressure can vary the band gap, the pressure dependence of the threshold current can then provide a clear picture of the dominant loss mechanisms in a given laser structure. The pressure dependence of the optical confinement factor, band structure, transparency and threshold carrier density, and the combined effect of these on both radiative- and non-radiative current contributions have been evaluated for lasers operating at a range of wavelengths. We investigate in particular the predicted pressure dependence of several Auger processes in long wavelength (1.5mum) lasers. It is found that the rate of decrease of phonon-assisted Auger recombination with pressure is close to that observed experimentally, implying that phonon-assisted Auger is the dominant loss mechanism. It is shown that although the transparency carrier density increases with pressure in all laser structures, the threshold carrier density, nth, can decrease in long wavelength single quantum well (SQW) lasers due to the pressure dependent parameters. The decrease of nth in the long wavelength SQW case results in a quicker decrease in the threshold current of a SQW laser compared to that of a multiple quantum well (MQW) laser, in agreement with experimental measurements. The optical properties of quantum well structures can also change with crystal orientation, and, therefore, the substrate orientation is an additional parameter which can be used in engineering the band structure. The effects of orientation on critical thickness and material parameters are reviewed for (001) and (111) oriented strained InGaAs QWs grown on GaAs substrates and their consequences for laser emission wavelength are investigated. Calculations are presented which show that a significant fraction of the piezoelectric field remains unscreened at laser threshold in (111) lasers, which, together with decreased HH1-HH2 separation, adversely affect the laser threshold characteristics in comparison to (001) oriented strained lasers.