Band alignment transition from type I to type II in GaAs / AlxGa1-x As quantum ring

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Highlights

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    Type I-type II transition of the GaAs/AlGaAs quantum ring.

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    Color map showing the shift of the point of type I-type II transition was drawn.

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    The radiative lifetime is calculated taking into account the Γ-X coupling.

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    A value of 7 meV for the coupling potential is estimated.

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    Color map showing the variation of the lifetime was drawn.

Abstract

We present a study of the electronic and optical properties of carriers in GaAs/AlxGa1-xAs quantum ring (QR) as a function of the aluminum concentration (x) in the barrier and the ring height (hM). We calculated the wavefunctions and the energies of the electrons and holes using the effective mass approximation. We found that the variation of x or hM, leads to a crossover, and consequently the mixing, of the electronic states of symmetry X and Γ. Then, a change from type I to type II of the GaAs/AlGaAs quantum ring occurs for x about 0.6 and hM about 1.3 nm. To present the point of type I-type II transition, we drew a color map that shows the shift of this point with x and hM. The radiative lifetime of the carriers is calculated in both type I and type II cases. In the latter case, we have taken into account the coupling between the confined electronic states of symmetry X and Γ. A value of 7 meV for the coupling potential is deduced from a comparison between our theoretical results and experimental ones. A color map showing the variation of the lifetime with x and hM was likewise drawn. Finally, these results can be exploited in several applications like solar cells.

Section snippets

Author contribution

Rihab Sellami: Investigation, Writing - original draft, Visualization, Afef Ben Mansour and Mohamed Souhail Kehili: Writing, Adnen Melliti: Conceptualization, Methodology, Validation, Supervision.

Theoretical model

The height of the studied GaAs/AlGaAs QR as a function of the polar coordinates is modeled by the expression proposed by Fomin et al. [18]:{h(ρ,ϕ)=h0+[hM−h0]{1−[ρ/R−1]2}{[ρ−R]/γ0}2+1,ρ≤Rh(ρ,ϕ)=h∞+hM−h∞{[ρ−R]/γ∞}2+1,ρ>RWhere R is the radius of the rim top, ho is the height at the center (i.e. r = 0), h∞ is the height away from the ring, and hM is the rim height; γ0 and γ∞ determine the inner and outer slope of the rim, respectively.

To have a QR structure similar to the AFM experimental results

Electronic energy and wavefunction

The composition in real GaAs/AlxGa1-xAs nanostructures grown by droplet epitaxy is not uniform. The Al composition (x) varies from the WL to the tip of the nanostructure [21,22]. However, to simplify the calculation, we supposed a uniform composition profile inside the QR and in the barrier.

In Fig. 2, Fig. 3, we present the hole and electron wavefunctions for different Al-concentration (x) and rim height (hM) respectively.

We notice from Fig. 2 that the hole is confined inside the QR and the

Conclusion

In this paper we studied theoretically the electronic and optical properties of carriers in a QR GaAs/AlxGa1-x As and the transition of band alignment for type I to type II. The investigation is done by calculating the wavefunctions and energies of electron and hole using the effective mass approximation with variation in Al-composition and the rim height. We showed that the localization of electrons and holes wavefunction is sensitive to the variation of x and hM.

The increase of x allows the

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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