Impurity center in a single quantum well in the presence of a strong magnetic field

The states and energies of an impurity electron confined within a single quantum well (QW) in the presence of a strong magnetic field directed perpendicular to the layers are derived. An analytical model in which the impurity may be positioned anywhere between the midpoint and edge of the QW is developed. The dependencies of the electron energies upon the magnitude of the magnetic field, the width of the QW, and the position of the impurity within the well are derived explicitly. Expressions for the levels of lowest energy are obtained, and have a quasi-Coulomb character, while the expressions for levels of higher energy are of the form of the size quantization levels, which form the excited subbands. Both types of levels are derived from the same original equations. The results obtained are compared with those of existing numerical calculations and specifically for the quantum numbers N=m=0. The relation between the states and the labels derived here and those obtained by others is also given. © 1996 The American Physical Society.