Energy levels of ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ in graded quantum-well structures of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As under magnetic fields

Energy levels of ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ confined in graded quantum wells of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As structures under magnetic fields are investigated in detail by the variational method. Binding energies as well as the 1s→2${\mathit{p}}^{\mathrm{-}}$ transition energy for ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ in a square well calculated from the same trial wave functions are shown to be in good agreement with existing Monte Carlo calculations and with experimental data. An interesting quantum shape effect is revealed by studying the ratio of ${\mathit{D}}^{\mathrm{-}}$ transition energy to its binding energy. A detailed study of ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ states in graded quantum wells shows that (a) ${\mathit{D}}^{\mathrm{-}}$ binding energies first increase with the magnetic field and then decrease when the field increases further, (b) for a given well gradient, the singlet s-like state binding energy peaks at a much lower field strength than the triplet p-like states, producing the energy level crossing phenomenon, and (c) ${\mathit{D}}^{\mathrm{-}}$ will be dissociated into a ${\mathit{D}}^0$ and an electron when either the field or the gradient increases. © 1996 The American Physical Society.