Excitons in semiconductor quantum discs

Abstract

The ground-state binding energy of the exciton in a finite-potential quantum disc setting is calculated variationally to study the change in dimensionality of the exciton within the limiting cases of the quantum well, wire, and dot, as well as the intermediate regime between these limiting geometries. Quantitative comparisons have been made with previous calculations using different trial wavefunctions to show the superiority of the present trial wavefunction in the quantum disc setting and to further illustrate the behaviour of the exciton in the quantum dot limit. Using the binding energy obtained from the present calculations, we further calculated the virial theorem number for the exciton in various confinement geometries, to disprove the recent claim of the existence of universal-constant virial theorem numbers for the quantum wells and wires. Also, the dimensionality parameter of the fractional-dimensionality model for confined excitons in the various confinement geometries has been calculated to facilitate discussion of its applicability to these structures, including the quantum dot limit.

Investigations on optical transitions in InAs/InP quantum dash structures

“…It is worthwhile to mention that the excitonic effect is ignored in our theoretical model for the computation of transition energies. Several studies on QD structures (Koh et al 2001;Heitz et al 2000) reported the excitonic binding energy in the range 10-20 meV. Hence, the energy Fig.…”

Lateral electric field effects on quantum size confinement in cylindrical quantum dot under parabolic potential

“…In this work, we are using the approximation of separating the time independent Schrödinger equation into in-plane part and z-direction part depending on the potential separation approximation [24].…”

“…The form of the wave function given in Eq. (13) satisfies not only the strong interaction region requirements (such as in a very narrow QDs), but also yields the correct hydrogenic form in the bulk limit (weak interaction region), where both the in-plane and the z-axis electron motions are strongly coupled [6,24]. The ground-state energy of D 0 is given by…”

Exciton in wurtzite GaN/AlxGa1−xN coupled quantum dots

“…(5) gives lower exciton energies (E ex ), and in variational sense implies that wave function Eq. (5) is a better trial wave function to describe the motion of the exciton [28]. Fig.…”