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In this study, we have obtained the exact solutions of the Schr\"{o}dingerequation for a multi-layered quantum antidot (MLQAD) within the effective massapproximation and dielectric continuum model for the spherical symmetry. TheMLQAD is nano-structured semiconductor system that consists of a spherical core(e.g. $Ga_{1-x}Al_{x}As $) and a coated spherical shell (e.g. $Ga_{1-y}Al_{y}As$) as the whole anti-dot is embedded inside a bulk material (e.g. $GaAs $). Thedependence of the electron energy spectrum and its radial probability densityon nano-system radius are studied. The numeric calculations and analysis ofoscillator strength of intersubband quantum transition from the ground stateinto two first allowed excited states at the varying radius, for both thefinite and infinite confining potential (CP) as well as constant shellthickness, are performed. It is shown that, in particular, the binding energyand the oscillator strength of the hydrogenic impurity of a MLQAD behavedifferently from that of a single-layered quantum antidot (SLQAD). For a MLQADwith finite core and shell CPs, the state energies and the oscillator strengthsof the impurity are found to be dependent on the shell thickness. At the largecore radius and very small shell thickness, our results are closer torespective values for a SLQAD that previously reported.

Oscillator strengths of the intersubband electronic transitions in the multi-layered nano-antidots with hydrogenic impurity