Coupling effects on the energy levels of a hydrogenic impurity in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As double-quantum-well structures in a magnetic field

A variational approach employing Gaussian trial wave functions has been used to calculate the binding energies of the ground (1s; m=0) and first excited (2${\mathit{p}}_{\mathrm{-}}$; m=-1) states of a hydrogenic donor associated with the first subband of a double GaAs quantum well coupled by a finite layer of ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As at the center of the two wells and sandwiched between two semi-infinite layers of ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As. The calculations have been performed for two locations of the impurity; one at the center of a well and the other at the inner edge of a well. Two different well sizes are considered. The applied magnetic field of 6.75 T is considered perpendicular to the interfaces and parallel to the axis of the growth of the double-quantum-well structure. It is found that the binding energies of the 1s and 2${\mathit{p}}_{\mathrm{-}}$ donor states depend significantly upon the barrier width, well width, and the location of the impurity. The effects are more pronounced for the narrow wells and barriers for the off-center location of the impurity.