The magnetic field dependence of shallow donor impurity states in GaAs/GaAlAs multi-quantum wells: a non-variational approach

We present a novel approach to the calculation of shallow impurity states in single- and multi-quantum-well systems. The Schrodinger equation is directly integrated numerically using an iterative technique. Thus, by avoiding a variational ansatz for the wave function and including a proper treatment of the coupling between the wells, the whole range from low to high magnetic fields as well as from the two-dimensional to the three-dimensional limit is treated on the same level. For the case of a single quantum well we discuss the dependence of the binding energies on the magnetic field as well as on the position of the impurity. For the case of a multi-quantum-well system we analyse the influence of the barrier width on the energies and the localization of the wave functions and we show that for barriers thicker than about 10 nm a single-well analysis is sufficient. A comparison with experimental results shows good agreement.