Energy levels of hydrogenic impurity states in GaAs-Ga1−xAlxAs quantum well structures

Binding energies of the ground state and of four excited states of a hydrogenic impurity in quantum well structures consisting of a single slab of GaAs sandwiched between two semi-infinite slabs of Ga_1?xAl_xAs are calculated using a variational approach. The ground-state binding energy is calculated as a function of the barrier potential for a given size of the GaAs quantum well and is found to be linearly dependent on the inverse of the square root of the barrier potential except for very small potentials. The variation of the binding energies of all five states as a function of the size of the GaAs quantum well are also calculated and their behavior is discussed.