Impurity states in a spherical GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum dot: Effects of the spatial variation of dielectric screening

We calculate the binding energies of shallow donors and acceptors in a spherical GaAs-${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As quantum dot for both a finite barrier and an infinitely high barrier using the variational approach, including the spatial variation of dielectric screening. The results show that when the spatial variation of dielectric screening is considered, the impurity binding energies increase noticeably, especially when the radius of the quantum dot is small. The results also show that the effects of spatial variation of dielectric screening on acceptors are larger than those on donors. The dielectric mismatch in this structure is also discussed.