Ordering parameter and band-offset determination for ordered Ga x In 1 − x P / ( Al 0.66 Ga 0.34 ) y In 1 − y P quantum wells

Low-temperature (1.8 K) optical reflectivity measurements have been carried out to identify the principal interband transition energies in ordered ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P}/({\mathrm{Al}}_{0.66}{\mathrm{Ga}}_{0.34}{)}_{y}{\mathrm{In}}_{1\ensuremath{-}y}\mathrm{P}$ quantum well (QW) samples. To account for ordering effects on the band offset and optical transition energy, a theoretical model has been constructed by incorporating the CuPt-type ordering effects of band-gap reduction $[\ensuremath{\Delta}{E}_{g}(\ensuremath{\eta})]$ and valence-band splitting $[{\ensuremath{\Delta}}_{111}^{O}(\ensuremath{\eta})]$ into the model-solid theory. Fitting of the observed transition energies to the calculations indicates that the model can reasonably describe the band-to-band transitions in the ordered QW's. Conclusions are reached that show that (i) ordering parameters in the QW's can be estimated with the first band-to-band transition energy. (ii) Among the $\ensuremath{\Delta}{E}_{g}(1)$ values available in the literature, two combinations $\ensuremath{\Delta}{E}_{g}(1)/{\ensuremath{\Delta}}_{111}^{O}(1)$ of -0.43 eV/0.16 eV and -0.471 eV/0.20 eV lead to good descriptions of the lattice-matched QW's. For the compressively strained samples, however, a smaller absolute value of $\ensuremath{\Delta}{E}_{g}(1)$ is favorable. Compressive strain tends to weaken the ordering effects. (iii) For a disordered and lattice-matched/compressively strained QW, the conduction-band-offset ratio has a nearly constant value of ${Q}_{c}\ensuremath{\sim}0.58.$ (iv) Ordering causes an increase in ${Q}_{c},$ and for lattice-matched and compressively strained QW's ${Q}_{c}$ falls in a range of $0.58\ensuremath{-}0.72$ as $\ensuremath{\eta}$ changes from 0 through 1. The influence is checked by using different values of the valence- and conduction-band deformation potentials in the calculations. A comparison of ${Q}_{c}$ is also made with previously reported values.