Lower-lying states of hydrogenic impurity in lens-shaped and semi-lens-shaped quantum dots

Abstract

The lower-lying states of a hydrogenic impurity, located at the centre of an infinite barrier lens-shaped quantum dot (LSQD), are calculated analytically in parabolic rotational coordinates. The solutions are obtained directly using the Frobenius method and by transforming the separated differential equations into the Whittaker equation. Results are given for both symmetric and asymmetric LSQDs. It is found that the energy states of the system are positive for a very small LSQD and decrease as the size of the dot increases. They become negative as the size increases, and approach the energy states of a free hydrogen atom. Also symmetric and antisymmetric eigenfunctions have been constructed for a hydrogenic impurity in a symmetric LSQD. Antisymmetric eigenfunctions can be used as eigenfunctions of a hydrogenic impurity located at the surface of a semi-LSQD.

Optical Absorption and Electroabsorption Related to Electronic and Single Dopant Transitions in Holey Elliptical GaAs Quantum Dots

“…So much attention on QDs is due to their outstanding electronic and optical properties, related to quantum size effects . This means that atomic‐like discrete energy levels arise, instead of energy bands like in bulk crystals . In spite of this similarity with “real atoms,” the application of external fields on QD generates important changes on quantum states, contrary to what happens in atoms.…”

“…[11] This means that atomic-like discrete energy levels arise, instead of energy bands like in bulk crystals. [12][13][14][15][16][17] In spite of this similarity with "real atoms," the application of external fields on QD generates important changes on quantum states, contrary to what happens in atoms. For instance, Zhou and Lorke [3] mention that in order to reach for a perturbation on quantum states and energy spectrum of hydrogen atoms with the use of a magnetic field it is necessary to apply an intensity which is five times larger than the needed for QDs.…”

Effects of external fields, the hydrostatic pressure and temperature on the electronic Raman scattering of a hydrogenic impurity in a two-dimensional parabolic quantum dot

“…Due to the aforementioned properties, studies on the electronic and optical properties of QDs with different shapes and various confinement potentials have attained considerable attention in the past few decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].…”

Polarizabilities of Impurity Doped Quantum Dots Under Pulsed Field: Role of Multiplicative White Noise

“…The change originates from the interplay between the intrinsic dot confinement potential and the introduced dopant potential. Such a change in the dot properties has led to a number of prominent investigations on doped QD [1][2][3][4][5][6][7][8][9]. In the context of optoelectronic applications, impurity-induced modulation of linear and nonlinear optical properties is highly important in photodetectors and in several high-speed electro-optical devices [10].…”