Quantum confined Stark effects of single dopant in polarized hemispherical quantum dot: Two-dimensional finite difference approach and Ritz-Hassé variation method

Eigenvalues equation of hydrogen-like off-center single donor impurity confined in polarized homogeneous hemispherical quantum dot deposited on a wetting layer, capped by insulated matrix and submitted to external uniform electric field is solved in the framework of the effective mass approximation. An infinitely deep potential is used to describe effects of quantum confinement due to conduction band offsets at surfaces where quantum dot and surrounding materials meet. Single donor ground state total and binding energies in presence of electric field are determined via two-dimensional finite difference approach and Ritz-Hassé variation principle. For the latter method, attractive coulomb correlation between electron and ionized single donor is taken into account in the expression of trial wave function. It appears that off-center single dopant binding energy, spatial extension and radial probability density are strongly dependent on hemisphere radius and single dopant position inside quantum dot. Influence of a uniform electric field is also investigated. It shows that Stark effect appears even for very small size dots and that single dopant energy shift is more significant when the single donor is near hemispherical surface. •We solve Poisson equation in the case of Hemispherical Quantum Dot deposited on a wetting layer, capped by insulating matrix and submitted to electrostatic field.•We derive, for the first time, authentic analytic expressions for scalar electrostatic potential inside and outside, polarization vector inside and electrostatic field vector inside and outside.•We investigate Stark effect on an off-center single dopant confined in polarized HQD using finite difference approach and Ritz-Hassé variation principle.•We show that position and electrostatic field strength have important effects on single dopant energy and radial probability density.