Size dependence of the polarizability and Haynes rule for an exciton bound to an ionized donor in a single spherical quantum dot

Abstract

We study the effect of an external electric field on an exciton bound to an ionized donor (D þ , X) confined in a spherical quantum dot using a perturbative-variational method where the wave function and energy are developed in series of powers of the electric field strength. After testing this new approach in the determination of the band gap for some semiconductor materials, we generalize it to the case of (D þ , X) in the presence of the electric field and for several materials ZnO, PbSe, and InAs, with significant values of the mass ratio. Three interesting results can be deduced: First, we show that the present method allows to determine the ground state energy in the presence of a weak electric field in a simple way (E ¼ E 0 À af 2) using the energy without electric field E 0 and the polarizability a. The second point is that our theoretical predictions show that the polarizability of (D þ , X) varies proportionally to R 3.5 and follows an ordering a D 0 < a X < a ðD þ ;XÞ. The last point to highlight is that the Haynes rule remains valid even in the presence of a weak electric field.

Adjustment of Terahertz Properties Assigned to the First Lowest Transition of (D+, X) Excitonic Complex in a Single Spherical Quantum Dot Using Temperature and Pressure

“…In glass matrix or in other medium with large band gap, the confinement relative to a SSQD can be described by [12][13][14] :…”

“…Thus, it admits two possible paths for its formation or even for its dissociation (D + , X) → D + + X or (D + , X) → D 0 + h. Stébé et al [11] have discussed its stability in spherical quantum dots and demonstrated that the first process is more stable. In the last few years, we have developed many theoretical studies concerning the identification of the spectral lines of this complex using an electric field and comparing the Stark shift [12]. More recently, the effects of the magnetic field and host dielectric environment on the (D + , X) binding energy has been analysed [13].…”

Polarizability of Exciton in Surface Quantum Well

“…19 Feddi et al have determined the effect of electric field on polarizability of an exciton bound to an ionised donor in a spherical quantum dot by perturbative-variational method. 20 Investigations on surface quantum wells (SQW) composed of a quantum well with infinite barrier on one side and finite barrier on another side, are of special interest due to the asymmetric nature that leads to: (1) the presence of localised resonant states above the finite single quantum barrier; and (2) the formation of image charges for electron and hole at the single infinite barrier/well interface with large dielectric constant mismatch, unlike the symmetrical quantum wells, where the image charge formation is at both interfaces. 21 In our previous work, we have estimated the exciton binding energy in SQW formed by vacuum/GaAs/Ga x Al 1-x As considering with and without the image charge potentials for isotropic and anisotropic masses.…”