Stark shift of binding energy for on and off-center donor impurities in quantum rings under the influence of charged rods electric fields

In the present work, we study the stark shift of binding energy for a Hydrogenic donor impurity confined within a circular quantum ring composed from three different semiconducting heterostructures AlxGa1-xN/GaN, InxGa1-xN/GaN, Ga1-xAlxAs/GaAs under the electric fields along different directions. We supplied a position-dependent electric field by using a charged rod of radius 'a' and charge density lambda. By placing the charged rod and donor impurity in different positions, we have studied the changes in the on and off-center donor binding energies, system energy levels, probability densities, average position of the electron, and the probability finding electron inside the quantum ring. We describe the redshift and blueshift of the donor impurity binding energy when different parameters change.