Exact solutions for hydrogenic impurity states in quantum dots

According to the hydrogenic-effective-mass theory and assumed finite barrier height for a confining potential, the analytical solutions and quantum energy-level structure for a hydrogenic impurity located at the center of a spherical quantum dot (SQD) are obtained. The calculated results reveal that because of the spatial confinement of the quantum dots, the energy, quantum numbers and radius of the SQD must satisfy a certain relation which arises from the boundary conditions. Given a barrier height or energy, the relation allows for the existence of bound states only for some discrete values of the radius of the SQD. On the other hand, for a fixed radius the energies of the bound states are discrete.