Influence of position dependent effective mass on donor binding energy in square and V-shaped quantum wells in the presence of a magnetic field

In this paper we have calculated variationally the ground state binding energy of a hydrogenic donor impurity in square quantum well and V-shaped quantum well as a function of the well width in the presence of magnetic fields with both constant and position dependent effective mass. The wave function of electrons confined to donor impurity within the quantum well is considered as the two dimensional and three dimensional trial wave functions. It has been found that by increasing the well width, the binding energy decreases smoothly to bulk values while its steepness is sharper in square quantum well in comparison with V-shaped quantum well. Increasing the magnetic field leads to the enhancement of binding energy. At higher magnetic fields, by increasing the well width, binding energy tends to a constant value. The effect of position dependent effective mass on the enhancement of binding energy is more evident in comparison with constant effective mass one.