Ordering parameter and band-offset determination for ordered ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}/({\mathrm{Al}}_{0.66}{\mathrm{Ga}}_{0.34}{)}_y{\mathrm{In}}_{1-y}\mathrm{P}$ quantum wells

Low-temperature (1.8 K) optical reflectivity measurements have been carried out to identify the principal interband transition energies in ordered ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}/({\mathrm{Al}}_{0.66}{\mathrm{Ga}}_{0.34}{)}_y{\mathrm{In}}_{1-y}\mathrm{P}$ 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 $\left[\Delta E_g\right(\eta \left)\right]$ and valence-band splitting $\left[{\Delta }_{111}^O\right(\eta \left)\right]$ 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 $\Delta E_g\mathrm{}\left(1\right)\mathrm{}$ values available in the literature, two combinations $\Delta E_g\mathrm{}\left(1\right)/{\Delta }_{111}^O\mathrm{}\left(1\right)\mathrm{}$ 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 $\Delta E_g\mathrm{}\left(1\right)\mathrm{}$ 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 $Q_c\sim \mathrm{0.58.}$ (iv) Ordering causes an increase in $Q_c,$ and for lattice-matched and compressively strained QW’s $Q_c$ falls in a range of $0.58-0.72$ as $\eta$ 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.