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

Abstract

In this study, we have obtained the exact solutions of the Schrödinger equation for a multi-layered quantum antidot (MLQAD) within the effective mass approximation and dielectric continuum model for the spherical symmetry. The MLQAD 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). The dependence of the electron energy spectrum and its radial probability density on nano-system radius are studied. The numeric calculations and analysis of oscillator strength of intersubband quantum transition from the ground state into two first allowed excited states at the varying radius, for both the finite and infinite confining potential (CP) as well as constant shell thickness, are performed. It is shown that, in particular, the binding energy and the oscillator strength of the hydrogenic impurity of a MLQAD behave differently from that of a single-layered quantum antidot (SLQAD). For a MLQAD with finite core and shell CPs, the state energies and the oscillator strengths of the impurity are found to be dependent on the shell thickness. At the large core radius and very small shell thickness, our results are closer to respective values for a SLQAD that previously reported.

Linear and nonlinear optical properties of multi-layered spherical nano-systems with donor impurity in the center

“…where i = 2, 1 and 0 are corresponding to r < a, a ≤ r ≤ b and r > b respectively. Just as we can see in [7], we can solve this equation as follows. Using the following definitions…”

“…and the change of variable as W (ξ i ) = ξ i R (i) (r), then the above Schrödinger equation can be rewritten as following Whittaker equation (7) The general solution to this equation is the Whittaker functions [29]…”

“…The most known spherical nano-systems are single-layered quantum dots (QDs), multi-layered QDs and quantum anti-dots (QADs). Such systems lead to foundation of discrete and not degenerate energy levels like atoms [1,2,3,4,5,6,7]. The amount of energy is dependent on the material, the shape, the size, the confinement potential and the surrounding matrix of QDs.…”

Impurity photoionization cross-section and intersubband optical absorption coefficient in multilayer spherical quantum dots

“…For the case of a central impurity, this problem is solved by using exact solutions of the Schrödinger equation based on Mathieu and Whittaker functions, degenerate hypergeometric or Coulomb wave functions [33][34][35][36][37]. Their numerical calculation is more complicated than the Bessel functions, but using an orthonormal basis on Coulomb WFs decreases the size of the matrix required for diagonalization when studying the effect of electric or magnetic field on the impurity states in MSQD.…”

Refractive index changes of multi-layered spherical nanostructures with donor impurity

“…These confined structures, have atomic-like discrete energy levels (subbands) and particular optical properties. Recently, investigations of the physical properties of some new nanostructures such as the multi-layered quantum dots (MLQDs) and anti-dots (MLQADs) have attracted the attention of researchers [7,8,9]. These newfound spherical nano-systems can be created by synthesizing different semiconductor materials.…”