Magneto-optical absorption spectrum of a ${\mathit{D}}^{\mathrm{-}}$ ion in a GaAs-${\mathrm{Ga}}_{0.75}$${\mathrm{Al}}_{0.25}$As quantum well

The magneto-optical absorption spectrum of a ${\mathit{D}}^{\mathrm{-}}$ ion in a GaAs-${\mathrm{Ga}}_{0.75}$ ${\mathrm{Al}}_{0.25}$As quantum well is calculated. We used the variational method based on a two-orbital picture of a ${\mathit{D}}^{\mathrm{-}}$ ion, in which each wave function is represented by a linear combination of anisotropic Gaussian orbitals. The calculated magnetic-field dependence of the binding energy of a ${\mathit{D}}^{\mathrm{-}}$ ion agrees qualitatively with the experimental result. In a magnetic field perpendicular to the well interface, the energies of the one-electron excited states of a ${\mathit{D}}^{\mathrm{-}}$ ion are completely quantized, and broadening is essential for the calculation of the line shape of the magneto-optical absorption spectrum. We considered two types of broadening effect, lifetime broadening and inhomogeneous broadening. Only the lifetime broadening effect reproduces fairly well the observed line shape of the magneto-photoconductivity spectrum. The assumed value of the lifetime is consistent with the measured Hall mobility.