Impurities in a quantum dot: A comparative study

The donor binding energies and density of impurity states of a hydrogenic impurity in a quantum dot are presented within the effective-mass approximation following a variational procedure. The emphasis is placed on the dependence of the binding energy on the volume of the dot and on the impurity position. We show that the results for the donor binding energy in the quantum dot goes to the exact limits of a square-cross-sectional quantum-well wire and a quantum well when appropriate limits are considered. Comparing the donor binding energies for cubic and spherical quantum dots, we found that the values are very close provided the dots have similar volumes.