Quantum size effect on discrete states of a hydrogenic impurity in a core/ shell nanowire

The hydrogenic impurity states in a core/shell nanowire is studied by a variational method combined with a finite-difference algorithm. The quantum size effect on the wavefunction localization and energy levels at the ground state and lowing-excited eigenstates are analyzed by changing the core radius or shell composition. The transition from discrete states (confined) to extended states (continuum) will occur if changing the core radius or shell composition to a certain critical value. The ground-state binding energy of the hydrogenic impurity in the core/shell nanowire shows different variation trends with radius and composition.