Band offsets and transitivity of ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$${\mathrm{Al}}_{\mathit{y}}$As/InP heterostructures

${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ga}}_{\mathit{x}}$As/${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$ ${\mathrm{Al}}_{\mathit{y}}$As quantum wells (QW’s) and ${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$ ${\mathrm{Al}}_{\mathit{y}}$As layers slightly lattice mismatched to InP substrates are grown by metalorganic chemical-vapor deposition and studied by calorimetric absorption spectroscopy (CAS), photoluminescence (PL), double-crystal x-ray diffractometry (DXD), and Shubnikov–de Haas (SdH) measurements. The layer compositions and the strain are directly determined from DXD. The strain partly relaxes selection rules and forbidden transitions, which are more sensitive to the relative conduction-band discontinuities Δ${\mathit{E}}_{\mathit{c}}$/Δ${\mathit{E}}_{\mathit{g}}$ than the allowed ones, appear in the CAS spectra of the QW’s. Comparing the energies of the transitions with detailed band-structure calculations the relative conduction-band discontinuity Δ${\mathit{E}}_{\mathit{c}}$/Δ${\mathit{E}}_{\mathit{g}}$ is determined to be (72±4)% for ${\mathrm{In}}_{0.540}$ ${\mathrm{Ga}}_{0.460}$As/${\mathrm{In}}_{0.531}$ ${\mathrm{Al}}_{0.469}$As. PL spectra of the type-II heterostructure ${\mathrm{In}}_{0.489}$ ${\mathrm{Al}}_{0.511}$As/InP show apart from the band-gap emissions two spatially indirect transitions across the ${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$ ${\mathrm{Al}}_{\mathit{y}}$As/InP interface at 1.240 eV (n=1) and at 1.271 eV (n=2). The conduction-band discontinuity is determined from the energies of these transitions and SdH experiments in conjunction with self-consistent band-structure calculations for lattice-matched ${\mathrm{In}}_{0.52}$ ${\mathrm{Al}}_{0.48}$As to be Δ${\mathit{E}}_{\mathit{c}}$=252 meV or Δ${\mathit{E}}_{\mathit{c}}$=2.86Δ${\mathit{E}}_{\mathit{g}}$. From these results, the three conduction-band discontinuities ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$