Photomodulated reflectance of ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{A}\mathrm{s}$ microcavity vertical-cavity surface emitting laser structures: Monitoring higher-order quantum well transitions

In the previous paper, a line shape model was developed to describe photomodulated reflectance (PR) spectra of vertical-cavity surface emitting laser (VCSEL) structures in the vicinity of the resonance between the cavity mode and ground-state quantum well (QW) exciton, in the weak cavity exciton coupling regime. Here, this model is extended to cavity mode resonances with higher-order QW transitions, both allowed and forbidden. In addition, the model’s validity is further confirmed by demonstrating a way of obtaining “pseudo-PR” spectra of the QW ground-state and higher-order transitions. These spectra are derived by monitoring changes in PR line shape, as the cavity mode energy is tuned through the QW transitions. These spectra are virtually free of VCSEL cavity effects, and represent plots of the energy dependence of the imaginary part of the modulated QW dielectric function, $\Delta {\varepsilon }_2.$ The $\Delta {\varepsilon }_2$ spectra can be fitted using conventional excitonic PR line shapes to extract the energies and linewidths of the ground-state and higher-order QW transitions. Examples are given for two InGaAs/GaAs/AlAs VCSEL structures. The results of this technique are confirmed by comparing with those obtained in two other experimental approaches: (i) measuring sets of complete PR spectra, at different positions on the sample, of the resonances between the cavity mode and various QW excitons, and fitting these with the new line shape model; (ii) measuring the PR spectrum of the exposed QW after removal of the top Bragg stack by etching, and fitting in the conventional way. All the results are found to be in good agreement both with each other and with the ground-state and higher-order QW transition energies calculated using a three-band $\mathit{k}\cdot \mathit{p}$ model.