Department of Physics, College of Science, Tabriz Branch, Islamic Azad University, Tabriz 5157944533, Iran

Department of Medical Nanotechnology, Faculty of Advanced Medical Science, Tabriz University of Medical Sciences, Tabriz 5154853431, Iran

School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, South Korea

Abstract

Quadratic electro-optic effects (QEOEs) and electro-absorption (EA) process in a GaN/AlGaN spherical quantum dot are theoretically investigated. It is found that the magnitude and resonant position of third-order nonlinear optical susceptibility depend on the nanostructure size and aluminum mole fraction. With increase of the well width and barrier potential, quadratic electro-optic effect and electro-absorption process nonlinear susceptibilities are decreased and blueshifted. The results show that the DC Kerr effect in this case is much larger than that in the bulk case. Finally, it is observed that QEOEs and EA susceptibilities decrease and broaden with the decrease of relaxation time.

Background

Semiconductor quantum dots with their excellent optoelectronic properties are now mostly used for various technologies such as biological science

Third-order nonlinear optical processes in ZnS/CdSe core-shell quantum dots are investigated in

The authors of ^{-15} esu, respectively.

In reference

In a recent paper

The organization of this paper is as follows. In the 'Methods’ section, the theoretical model and background are described. The 'Results and discussion’ section is devoted to the numerical results and discussion. Summarization of numerical results is given in the last section.

Methods

In this section, theoretical model and mathematical background of the third-order nonlinear properties of a new GaN/AlGaN quantum dot nanostructure are presented. The geometry of a spherical centered defect quantum dot and potential distribution of this nanostructure are shown in Figure

Structure of the spherical quantum dot and related potential distribution

**Structure of the spherical quantum dot and related potential distribution.**

In this paper, the potential in the core region is supposed to be zero, and the potential difference between two materials is constant

where _{
i
}
^{∗} and _{
i
}(

and

where _{e}, and _{c}(_{g}(_{g}(0)] is the conduction band offset _{
x
}Ga_{1 - x
}N is _{g}(

where _{
ℓm
}(_{
nℓ
}(

In order to calculate _{
nℓ
}(_{01} and _{01} cases must be considered. With change of variables and some mathematical rearranging, the following spherical Bessel functions in both cases are obtained:

Case 1: _{01}.

where

Case 2: _{01}.

where

For the whole determination of eigenenergies and constants that appeared in the wave function, _{
nℓ
}(

After determining the eigenvalues and wave functions, the third-order susceptibility for two energy levels, ground and first excited states, the model should be described _{1} and _{2} appears in Equation 11:

where _{fg} = 〈_{f}|_{g}〉 indicates the dipole transition matrix element, _{o} = (_{f} - _{g})/_{1} = 0, _{2} = -^{(3)}(-^{(3)}(-

These nonlinear susceptibilities are important characteristics for photoemission or detection applications of quantum dots.

Results and discussion

In this section, numerical results including the quadratic electro-optic effect and electro-absorption process nonlinear susceptibilities of the proposed spherical quantum dot are explained. In our calculations, some of the material parameters are taken as follows. The number density of carriers is ^{24} m^{-3}, electrostatic constant is _{o}

The quadratic electro-optic effect and electro-absorption process susceptibilities as functions of pump photon wavelength at 15-ps relaxation time are illustrated in Figure

Quadratic electro-optic effect and electro-absorption process susceptibilities versus pump photon wavelength

**Quadratic electro-optic effect and electro-absorption process susceptibilities versus pump photon wavelength.** For 15-ps relaxation time, _{01} = 0.062 eV. **(a)**_{02} = 0.423 eV. **(b)**_{02} = 0.268 eV. **(c)** V_{02} = 0.127 eV.

The third-order susceptibility of GaN/AlGaN quantum dot versus pump photon wavelength with different barrier potentials as parameter is shown in Figure

Third-order susceptibility of GaN/AlGaN quantum dot versus pump photon wavelength

**Third-order susceptibility of GaN/AlGaN quantum dot versus pump photon wavelength.** With different barrier potentials and defect sizes for 15-ps relaxation time.

Same as Figure

Quadratic electro-optic effect and electro-absorption process susceptibilities versus pump photon wavelength

**Quadratic electro-optic effect and electro-absorption process susceptibilities versus pump photon wavelength.** For 1.5-ps relaxation time, _{01} = 0.062 eV. **(a)**_{02} = 0.423 eV. **(b)**_{02} = 0.268 eV. **(c)**_{02} = 0.127 eV.

In Figure

Third-order susceptibility versus pump photon wavelength

**Third-order susceptibility versus pump photon wavelength.** With different barrier potentials and defect sizes for 1.5-ps relaxation time (black

The effect of relaxation constant (

Peak of third-order susceptibility as a function of relaxation constant

**Peak of third-order susceptibility as a function of relaxation constant.**

Conclusions

In this paper, we have introduced spherical centered defect quantum dot (SCDQD) based on GaN composite nanoparticle to manage electro-optical properties. We have presented that the variation of system parameters can be tuned by the magnitude and wavelength of quadratic electro-optic effects and electro-absorption susceptibilities. For instance, the results show an increase of well width from 15 to 30 Å; the peaks of the both QEOEs and EA susceptibilities are decreased

Abbreviations

EA: electro-absorption; FWHM: full-width at half maximum; LEDs: light-emitting diodes; QEOEs: quadratic electro-optic effects; SCDQD: spherical centered defect quantum dot

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

MK conceived of the study and participated in its design and coordination. AV assisted in the numerical calculations. AA and YH participated in the sequence alignment and drafted the manuscript. SWJ supervised the whole study. All authors read and approved the final manuscript.

Acknowledgements

The authors thank the Department of Physics, Tabriz Branch, Islamic Azad University, and the Department of Medical Nanotechnology, Faculty of Advanced Medical Science of Tabriz University for all the supports provided. This work is funded by the Grant 2011-0014246 of the National Research Foundation of Korea.