Effect of a finite-width barrier on binding energy in modulation-doped quantum-well structures

The ground bound state of hydrogenic impurity in a double quantum well consisting of alternate layers of ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As and GaAs is investigated. The dependence of the binding energy on the impurity position in the barrier, on the barrier heights of the quantum well, and on the thickness of the wells and the barrier is calculated. The results of the present calculation in the single well limit agree with previous results and have much simpler formula expressions. The condition under which the impurity and the electron are separated from each other in the ground state is given.