Investigation of quadratic electrooptic effects and electroabsorption process in GaN/AlGaN spherical quantum dot
 Mohammad Kouhi^{1}Email author,
 Ali Vahedi^{1},
 Abolfazl Akbarzadeh^{2}Email author,
 Younes Hanifehpour^{3} and
 Sang Woo Joo^{3}Email author
DOI: 10.1186/1556276X9131
© Kouhi et al.; licensee Springer. 2014
Received: 28 November 2013
Accepted: 25 February 2014
Published: 19 March 2014
Abstract
Quadratic electrooptic effects (QEOEs) and electroabsorption (EA) process in a GaN/AlGaN spherical quantum dot are theoretically investigated. It is found that the magnitude and resonant position of thirdorder nonlinear optical susceptibility depend on the nanostructure size and aluminum mole fraction. With increase of the well width and barrier potential, quadratic electrooptic effect and electroabsorption 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.
Keywords
Quadratic electrooptic effects Thirdorder susceptibility Spherical quantum dot Relaxation timeBackground
Semiconductor quantum dots with their excellent optoelectronic properties are now mostly used for various technologies such as biological science [1–4], quantum dot lasers [5, 6], lightemitting diodes (LEDs) [7], solar cells [8], infrared and THZIR photodetectors [9–14], photovoltaic devices [15], and quantum computing [16, 17]. GaN and AlN are members of IIIV nitride family. These wide bandgap semiconductors are mostly appropriate for optoelectronic instrument fabrication.
Thirdorder nonlinear optical processes in ZnS/CdSe coreshell quantum dots are investigated in [18–20]. It is shown that the symmetry of the confinement potential breaks due to large applied external electric fields and leads to an important blueshift of the peak positions in the nonlinear optical spectrum. The effect of quantum dot size is also studied, and it is verified that large nonlinear thirdorder susceptibilities can be achieved by increasing the thickness of the nanocrystal shell.
The authors of [21, 22] studied the quadratic electrooptic effects (QEOEs) and electroabsorption (EA) process in InGaN/GaN cylinder quantum dots and CdSeZnSCdSe nanoshell structures. They have found that the position of nonlinear susceptibility peak and its amplitude may be tuned by changing the nanostructure configuration. The obtained susceptibilities in these works are around ${10}^{17}\frac{{\mathit{m}}^{2}}{{\mathit{v}}^{2}}$ and 10^{15} esu, respectively.
In reference [23], selffocusing effects in wurtzite InGaN/GaN quantum dots are studied. The results of this paper show that the quantum dot size has an immense effect on the nonlinear optical properties of wurtzite InGaN/GaN quantum dots. Also, with decrease of the quantum dot size, the selffocusing effect increases.
In a recent paper [24], we have shown that with the control of GaN/AlGaN spherical quantum dot parameters, different behaviors are obtained. For example, with the increase of well width, thirdorder susceptibility decreases. The aim of this study is to investigate our proposed GaN/AlGaN quantum dot nanostructure from quadratic electrooptic effect and electroabsorption process points of view. In this paper, we study thirdorder nonlinear susceptibility of GaN/AlGaN semiconductor quantum dot based on the effective mass approximation. The numerical results have shown that in the proposed structure, the thirdorder nonlinear susceptibilities near 2 to 5 orders of magnitudes are increased.
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 order to calculate R_{ nℓ }(r), the two E < V_{01} and E > V_{01} cases must be considered. With change of variables and some mathematical rearranging, the following spherical Bessel functions in both cases are obtained:
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 electrooptic effect and electroabsorption 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 N = 1 × 10^{24} m^{3}, electrostatic constant is ϵ = (0.3x + 10.4)ϵ_{o}[30, 31], and typical relaxation constants are ℏΓ = 0.27556 and 2.7556 meV which correspond to 15 and 1.5ps relaxation times, respectively.
Conclusions
In this paper, we have introduced spherical centered defect quantum dot (SCDQD) based on GaN composite nanoparticle to manage electrooptical properties. We have presented that the variation of system parameters can be tuned by the magnitude and wavelength of quadratic electrooptic effects and electroabsorption 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 $\left(7.218\times {10}^{12}{\scriptscriptstyle \frac{{\mathit{m}}^{2}}{{\mathit{V}}^{2}}}\phantom{\rule{0.37em}{0ex}}\mathrm{to}1.062\times {10}^{12}{\scriptscriptstyle \frac{{\mathit{m}}^{2}}{{\mathit{V}}^{2}}}\right)$ and blueshifted (59.76 to 37.29 μm). With decreasing dot potential, the thirdorder susceptibility is increased $\left(2.444\times {10}^{12}\frac{{\mathit{m}}^{2}}{{\mathit{v}}^{2}}\phantom{\rule{0.5em}{0ex}}\mathrm{to}\phantom{\rule{0.5em}{0ex}}7.218\times {10}^{12}\frac{{\mathit{m}}^{2}}{{\mathit{v}}^{2}}\right)$ and red shifted (45.25 to 59.76 μm). The effect of relaxation constant (ħ Γ) which is verified by the peak of the thirdorder susceptibility is decreased by the increasing relaxation rate. These behaviors can be related to the quantum confinement effect and inverse impact of relaxation constant.
Abbreviations
 EA:

electroabsorption
 FWHM:

fullwidth at half maximum
 LEDs:

lightemitting diodes
 QEOEs:

quadratic electrooptic effects
 SCDQD:

spherical centered defect quantum dot
Declarations
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 20110014246 of the National Research Foundation of Korea.
Authors’ Affiliations
References
 Valizadeh A, Mikaeili H, Farkhani MSM, Zarghami N, Kouhi M, Akbarzadeh A, Davaran S: Quantum dots: synthesis, bioapplications, and toxicity. Nanoscale Res Lett 2012, 7: 480. 10.1186/1556276X7480View Article
 Absalan H, SalmanOgli A, Rostami R: Simulation of a broadband nanobiosensor based on an onionlike quantum dot quantum well structure. Quantum Electron 2013, 43(7):674–678. 10.1070/QE2013v043n07ABEH014990View Article
 Bruchez MJ, Moronne M, Gin P, Weiss S, Alivisatos AP: Semiconductor nanocrystals as fluorescent biological labels. Science 1998, 281(5385):2013–2016.View Article
 Deb P, Bhattacharyya A, Ghosh SK, Ray R, Lahiri A: Excellent biocompatibility of semiconductor quantum dots encased in multifunctional poly (Nisopropylacrylamide) nanoreservoirs and nuclear specific labeling of growing neurons. Appl Phys Lett 2011, 98(10):103702–103703. 10.1063/1.3562036View Article
 Li SG, Gong Q, Cao CF, Wang XZ, Yan JY, Wang Y, Wang HL: The developments of InPbased quantum dot lasers. Infrared Phys Technol 2013, 60: 216–224.View Article
 Weng WC, Frank J: On the physics of semiconductor quantum dots for applications in lasers and quantum optics. Prog Quant Electron 2013, 37(3):109–184. 10.1016/j.pquantelec.2013.04.001View Article
 Brault J, Damilano B, Kahouli A, Chenot S, Leroux M, Vinter B, Massies J: Ultraviolet GaN/Al_{0.5}Ga_{0.5}N quantum dot based light emitting diodes. J Cryst Growth 2013, 363: 282–286.View Article
 Nozik AJ: Quantum dot solar cells. Phys E 2002, 14: 115–120. 10.1016/S13869477(02)003740View Article
 Su X, Chakrabarti S, Bhattacharya P, Ariyawansa G, Perera AGU: A resonant tunneling quantumdot infrared photodetector. IEEE J Quantum Electron 2005, 41: 974–979.View Article
 Su XH, Yang J, Bhattacharya P, Ariyawansa G, Perera AG: Terahertz detection with tunneling quantum dot intersublevel photodetector. Appl Phys Lett 2006, 89: 031117–1031117–3.
 Huang G, Yang J, Bhattacharya P, Ariyawansa G, Perera AG: A multicolor quantum dot intersublevel detector with photoresponse in the terahertz range. Appl Phys Lett 2008, 92: 011117–1011117–3.
 Kochman B, StiffRoberts AD, Chakrabarti S, Phillips JD, Krishna S, Singh J, Bhattacharya P: Absorption, carrier lifetime, and gain in InAs–GaAs quantumdot infrared photodetectors. IEEE J Quantum Electron 2003, 39: 459–467. 10.1109/JQE.2002.808169View Article
 Rasooli Saghai H, Sadoogi N, Rostami A, Baghban H: Ultrahigh detectivity room temperature THZ IR photodetector based on resonant tunneling spherical centered defect quantum dot (RTSCDQD). Opt Commun 2009, 282: 3499–3508. 10.1016/j.optcom.2009.05.064View Article
 Asadpour SH, Golsanamlou Z, Rahimpour Soleimani H: Infrared and terahertz signal detection in a quantum dot nanostructure. Phys E 2013, 54: 45–52.View Article
 McDonald SA, Konstantatos G, Zhang S, Cyr PW, Klem EJD, Levina L, Sargent EH: Solutionprocessed PbS quantum dot infrared photodetectors and photovoltaics. Nat Mater 2005, 4: 138–142. 10.1038/nmat1299View Article
 Loss D, DiVincenzo DP: Quantum computation with quantum dots. Phys Rev A 1998, 57: 120–126. 10.1103/PhysRevA.57.120View Article
 Bose R, Johnson HT: Coulomb interaction energy in optical and quantum computing applications of selfassembled quantum dots. Microelectron Eng 2004, 75(1):43–53. 10.1016/j.mee.2003.11.008View Article
 Cristea M, Niculescu EC: Hydrogenic impurity states in CdSe/ZnS and ZnS/CdSe coreshell nanodots with dielectric mismatch. Eur Phys J B 2012, 85: 191.View Article
 Niculescu EC, Cristea M: Impurity states and photoionization cross section in CdSe/ZnS core–shell nanodots with dielectric confinement. J Lumin 2013, 135: 120–127.View Article
 Cristea M, Radu A, Niculescu EC: Electric field effect on the thirdorder nonlinear optical susceptibility in inverted core–shell nanodots with dielectric confinement. J Lumin 2013, 143: 592–599.View Article
 Wang C, Xiong G: Quadratic electrooptic effects and electroabsorption process in InGaN/GaN cylinder quantum dots. Microelectron J 2006, 37: 847–850. 10.1016/j.mejo.2006.03.007View Article
 Bahari A, RahimiMoghadam F: Quadratic electrooptic effect and electroabsorption process in CdSe–ZnS–CdSe structure. Phys E 2012, 44(4):782–785. 10.1016/j.physe.2011.11.028View Article
 Kaviani H, Asgari A: Investigation of selffocusing effects in wurtzite InGaN/GaN quantum dots. Optik 2013, 124(8):734–739. 10.1016/j.ijleo.2012.01.012View Article
 Vahedi A, Kouhi M, Rostami A: Third order susceptibility enhancement using GaN based composite nanoparticle. Optik 2013, 124(9):6669–6675.View Article
 Schooss D, Mews A, Eychmuller A, Weller H: Quantumdot quantum well CdS/HgS/CdS: theory and experiment. Phys Rev B 1994, 49: 17072–17078. 10.1103/PhysRevB.49.17072View Article
 Wang LW, Williamson AJ, Zunger A, Jiang H, Singh J: Compression of the K.P. and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots. Appl Phys Lett 2000, 76: 339–342. 10.1063/1.125747View Article
 Ngo CY, Yoon SF, Fan WJ, Chua SC: Effects of size and shape on electronic states of quantum dots. Phys Rev B 2006, 74: 245331.View Article
 Fang Y, Xiao M, Yao D: Quantum size dependent optical nutation in CdSe/ZnS/CdSe quantum dot quantum well. Phys E 2010, 42: 2178–2183. 10.1016/j.physe.2010.03.036View Article
 Griffiths DJ: Introduction to Quantum Mechanics. Boston: AddisonWesley; 2004.
 Asgari A, Kalafi M, Faraone L: The effects of GaN capping layer thickness on twodimensional electron mobility in GaN/AlGaN/GaN heterostructures. Phys E 2005, 25: 431–437. 10.1016/j.physe.2004.07.002View Article
 Liu J, Bai Y, Xiong G: Studies of the secondorder nonlinear optical susceptibilities of GaN/AlGaN quantum well. Phys E 2004, 23: 70–74. 10.1016/j.physe.2004.01.004View Article
 Boyd RW: Nonlinear Optics. New York: Academic; 1992.
 Shen YR: The Principles of Nonlinear Optics. New York: Wiley; 2003.
 Zhang X, Xiong G, Feng X: Well widthdependent thirdorder optical nonlinearities of a ZnS/CdSe cylindrical quantum dot quantum well. Phys E 2006, 33: 120–124. 10.1016/j.physe.2005.11.017View Article
 Takagahara T: Excitonic optical nonlinearity and exciton dynamics in semiconductor quantum dots. Phys Rev B 1987, 36: 9293–9296. 10.1103/PhysRevB.36.9293View Article
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.