Conduction-band and valence-band structures in strained ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/InP quantum wells on (001) InP substrates

We study conduction-band and valence-band structures in strained ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/InP quantum wells on (001) InP substrates using the k⋅p perturbation approach and magneto-optical absorption measurements. We evaluate the band offset between ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As and InP using the tight-binding model. We derive a formula for calculating conduction-band dispersion both in biaxially strained bulk layers and quantum wells from the first-order k⋅p perturbation. We use our formula to show that the electron effective mass of strained ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As and strained ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/InP quantum wells are anisotropic, and that the masses depend significantly on the strain and well width. We evaluate magneto-optical absorption spectra of multiple quantum wells with compositions, x, from 0.34 to 0.58, corresponding to about ±1% in-plane strain, and with well widths from 6 to 14 nm. We analyze the diamagnetic shifts of exciton resonances based on the effective-mass equations taking both conduction- and valence-band nonparabolic dispersion into account. We obtain in-plane electron, hole, and reduced effective masses of excitons and Luttinger-Kohn effective-mass parameters for valence bands as a function of composition.