Dimensionality and potential-shape effects on ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ ground states in quantum dots

The binding energies ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^0$) and ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^{\mathrm{-}}$) of neutral and negative donor (${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$) centers in quantum dots (QD’s) with different dimensionality and potential shape have been obtained by a variational approach with a trial function, which consists of the exact solutions of ${\mathit{D}}^0$-like ground states in the dots, includes the electron-correlation effect, and approaches the Chandrasekhar-type trial function at zero barrier height. The dimensionality and potential-shape effects of QD’s on ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^0$) and ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^{\mathrm{-}}$) have been studied in detail. It has been found that the electron-correlation effect on ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^{\mathrm{-}}$) depends on the dimensionality and decreases with increasing confinement. The ratio σ of ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^{\mathrm{-}}$) to ${\mathit{E}}_{\mathit{B}}$(${\mathit{D}}^0$) approaches a constant value in the limit of strong confinement. It has been shown that the ratio σ and the electron-correlation effect are strongly dependent on the dimensionality of QD’s and weakly dependent on the potential shape. Using the value of the σ obtained, calculated results of different quantum-well structures can be checked and compared with others.