Electric field effect on the energy of an off-centre donor in quantum crystallites

The quantum size, impurity position and electric field effects on the energy of a shallow donor placed anywhere in a GaAs spherical quantum crystallite embedded in Ga(1-x)AI(x)As matrix are studied theoretically in the framework of the effective mass approximation. The impurity is supposed on the z-axis. The conduction band offset between the crystallite and the matrix is assumed to be finite. The ground state energy and the spatial extension of the unperturbed hydrogenic donor are determined by Ritz's variational method. It appears that for a fixed size of the crystallite, the energy and the spatial extension increase monotonically when the impurity is displaced from the centre to the surface of the crystallite. The influence of a uniform electric field F is analysed. It is found that for a donor placed at the centre of the crystallite, the energy level is shifted to low energies. However for an off-centre donor the energy level shift depends on the angle between F and z.