Donor states in a multi-layered quantum dot

Abstract

The ground and excited state energies of a hydrogenic impurity located at the centre of a multi-layered quantum dot (MLQD) are calculated in the framework of the effective-mass approximation. The MLQD consists of a spherical core (e.g. GaAs) and a coated spherical shell (e.g. Ga 1−x Al x As). The whole dot is then embedded inside a bulk material (e.g. Ga 1−y Al y As). We solve the Schrödinger equation exactly. The eigenfunctions of the impurity are expressed in terms of Whittaker function and Coulomb wavefunction. The state energies are expressed in terms of the shell thickness, core radius, total dot radius and the potential heights. Our calculation shows that, as the dot radius approaches infinity, the state energies of an impurity located at the centre of a multi-layered or a single-layered QD approach −1/n 2 Ry, where n is the principal quantum number, Ry = µe 4 /2ε 2h2 , µ and ε are the electronic effective mass and the dielectric constant of GaAs material. Thus it behaves like a three-dimensional free hydrogen atom. For very small dot radius, however, the state energy of the hydrogenic impurity of a MLQD behaves very differently from that of a single-layered QD. For a multi-layered QD with finite shell and bulk potential barrier heights, the state energies of the impurity are found to be dependent on the difference of the shell potential (V 2) and the bulk potential (V 3).

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

“…In the case of MLQD, the Eq. (5) has been solved in detail by Hsieh et al in [6], so we do not directly solve this equation and we shortly review their results for three different regions as follows (i=0) Inside the core of system (r < a) with V 0 = 0, the positive energy bound states are possible for an electron that is confined inside the core dot; therefore, solutions of the Schrödinger equation can be studied in three energy states [6]…”

Binding Energy of D0 and D− Impurity Centers in CdTe/ZnTe Spherical Quantum Dot

“…The validity of the effective mass approximation for the conduction band is assumed. Difference of the electron effective masses [16][17][18][19] and dielectric constants 20 between the QD region and the surrounding medium are considered.…”

Binding Energy of the Hydrogenic Impurity in CdTe/ZnTe Spherical Quantum Dot

“…The validity of the effective mass approximation is assumed. Difference of the electron effective masses [6][7][8][9] and dielectric constants [10] between the QD region and the surrounding medium are considered.…”