Ground state transition energies of electron and hole in biased In_xGa_1–xN/GaN quantum dots

Abstract

We are interested in our study of the III-V nitrides to the In x Ga 1-x N/GaN quantum dots, where x = 17.5 % denotes the indium concentration. The adopted model to describe these III-V nitride quantum dots is that of In x Ga 1-x N truncated cones of radius r c lying on wetting layer, both buried into GaN matrix. This model is consistent with recent experimental works. We examine the internal electric field and radius r c of the quantum dots effects on the ground state transition energies of the electron and the hole. Our results are in sound agreement with recent experimental data.1 Introduction III-V nitride semiconductors have been investigated very extensively in the last decade. GaN is a direct and wide band-gap semiconductor and when alloyed with InN and AlN, a spectrum from visible to ultraviolet can be covered. III-V nitride nanostructures are strongly polar crystal as compared to GaAs-based compounds, and thus shown a piezoelectric effect. Macroscopic polarization, both in intrinsic and piezoelectric nature, is unusually strong in III-V nitride, and the built in electric fields in the layers of nitride-based nanostructures, stemming from polarization changes at heterointerfaces. The strong built in electric field of the order of few MV/cm is oriented along the growth direction and has opposite sign inside and outside the quantum dots (QDs) [1,2]. This is considerably stronger than in GaAs-based nanostructures because the piezoelectric constants in nitrides are orders of magnitude greater than in other III-V compounds. Our main goal is to examine how the electric field and the QDs basis radius r c affect the ground state transition energies of the electron and the hole. We are essentially interested to In x Ga 1-x N/GaN III-V nanostructures QDs.The paper is organized in the following way. In Section 2, we present the model and our numerical approach. In Section 3, the electron and the hole energy levels have been calculated. This is followed in Section 4 by the presentation of how basis radius of the QDs and the applied electric field affect the electron-hole ground state transition energies. Finally, in Section 5 we summarize the main conclusions.

Excitonic complexes correlation energies in individual biased InAs/GaAs and InGaN/GaN quantum dots

“…In particular, in their recent work based on the self-consistent Hartree method, Winkelnkemper et al found a dominant influence of the built-in electric field causing a spatial separation of the bound electron and hole in nitride QD [5]. The main conclusion one can make from the above discussion about the radius effect in nitride QDs is that the internal electric field induces a localization effect more important than that found in the InAs case [28,29]. This strong localization implies the rigidity of the bound states toward perturbation, such as Coulomb effects.…”

“…This strong localization implies the rigidity of the bound states toward perturbation, such as Coulombic effects. The two lower lying electron bound levels are spaced in the QDs by more than 100 meV and 80 meV for InAs and InGaN, respectively [28,29]. This should play an important role in studying the energy relaxation rates.…”

“…The Hamiltonian describing a single particle (electron or hole) in the effective mass approximation is given by [25][26][27][28][29]…”

“…We find that the first two confined levels energy difference is varied by 2% and 50% in InAs/GaAs and InGaN/GaN, respectively for 100 kV cm −1 variation of the electric field. The electric field effect on the relative position of energy levels is therefore more important in nitride compounds than in arsenide ones [28,29].…”

“…QDs for optoelectronics must be able to accommodate at least two types of carriers, electrons and holes. The single particle energies as well as the neutral X, negatively X − and positively X + charged excitons and biexciton energies depend heavily on the geometry of the QDs [27][28][29].…”