Lower Lying States of Hydrogenic Impurity in A Multi-Layer Quantum Dot

Cheng-Ying Hsieh

《Chinese Journal of Physics》 38卷3期 (2000/06) Pp. 478-490

並列摘要

The lower lying states of a hydrogenic impurity, located at the center of a multi-layer quantum dot (MLQD), are calculated within the framework of the effective-mass theory. Our MLQD consists of a spherical core (e.g. GaAs) coated by a spherical shell (e.g., Ga1-xAlxAs) and then embedded in a bulk material (e.g., Ga1-yAlyAs). The eigenfunctions are expressed in terms of Whittaker functions and Coulomb wave functions. The ground state and lower-lying-excited state energies of a hydrogenic impurity are calculated as functions of the dot radius and potential barrier strength of the MLQD. It is found that the state energies of the hydrogenic impurity in the MLQD approach to the corresponding limit Ry/n2 of a 3-D free hydrogen atom as the core radius is increased to infinity, where n is the principle quantum number and Ry is the Rydberg constant. As the radius becomes zero, the state energies of the hydrogenic impurity are found to depend on the energy difference between the barrier heights V2 and V3.