In this paper, we have performed a theoretical study on nonlinear optical rectification (OR) and second harmonic generation (SHG) for three-level dome-shaped InAs/GaAs quantum dots (QDs) in the presence of wetting layer (WL). We used the compact density matrix framework and effective mass approximation to investigate the second order nonlinear phenomena on InAs/GaAs QD. It is demonstrated that second harmonic generation (SHG), optical rectification (OR), and their mutual absorption and refractive index changes are quite sensitive to the size of QDs. The size variations have profound irregular behavior owing to distribution of envelope function on WL and QD simultaneously. Moreover it is found that ?nm is a critical radius where the regular variation takes place. It is shown that size variation causes blue shift until Critical radius ( ?nm) and after that, increasing the QD size lead to redshift in second order phenomena. 1. Introduction In the last few years the nonlinear optical properties of intersubband transitions in semiconducting materials have attracted remarkable attention due to the potential application in electronics and optoelectronics devices [1–13]. Among the semiconductor materials, zero-dimensional quantum dots (QDs) are very interesting; tunable features of QDs are one of the main reasons for this increasing performance of semiconductor QDs. The rapid advances in nanotechnology techniques such as molecular beam epitaxy (MBE) [14, 15], metal-organic chemical vapor deposition [16], and Stranski-Krastanov (S-K) [17] methods have made it possible to prepare different shape and geometry of QDs [14–18]. In QDs the carriers are confined by the confinement potential, named as quantum confinement effect in all spatial directions. Confinement provides the quantization of electronic energy levels based on the size of the dots; confinement leads to significant optical nonlinearities [11, 18]. Photons with proper energy can cause the intersublevel transitions involving large electric dipole moments [19, 20]. Among the nonlinear optical properties, the second-order nonlinear optical property plays a crucial role because it is the simplest and the lowest-order nonlinear effect; moreover, its magnitude is usually stronger than the other optical nonlinearities [21]. The second order nonlinear optical interaction of two incident fields with optical media leads to some phenomena’s like Second harmonic generation (SHG) and optical rectification (OR). To the best of our knowledge the early work on OR is dated back to 1962 by Xie and Bass et al. [21, 22] as
References
[1]
C. Bose, C. Chakraborty, and C. K. Sarkar, “Electric field induced shifts of electronic energy levels in spherical quantum dot,” Solid-State Electronics, vol. 41, no. 9, pp. 1383–1385, 1997.
[2]
L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots, Springer, Berlin, Germany, 1998.
[3]
A. M. Elabsy, “Effect of temperature on the binding energy of a confined impurity to a spherical semiconductor quantum dot,” Physica Scripta, vol. 59, no. 4, pp. 328–330, 1999.
[4]
C. Bose, “Perturbation calculation of impurity states in spherical quantum dots with parabolic confinement,” Physica E, vol. 4, no. 3, pp. 180–184, 1999.
[5]
V. L. Nguyen, M. T. Nguyen, and T. D. Nguyen, “Magnetic field effects on the binding energy of hydrogen impurities in quantum dots with parabolic confinements,” Physica B, vol. 292, no. 1-2, pp. 153–159, 2000.
[6]
A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic, optical, luminescence and related properties of low dimensional systems,” Advances in Physics, vol. 50, no. 1, pp. 1–208, 2001.
[7]
E. C. Niculescu, “Energy spectra of donors in spherical quantum dots with parabolic confinement,” Czechoslovak Journal of Physics, vol. 51, no. 11, pp. 1205–1213, 2001.
[8]
Y. Masumoto and T. Takagahara, Semiconductor Quantum Dots, Springer, Berlin, Germany, 2002.
[9]
S. Sahoo, Y. C. Lin, and Y. K. Ho, “Quantum-confined hydrogenic impurity in a spherical quantum dot under the influence of parallel electric and magnetic fields,” Physica E, vol. 40, no. 10, pp. 3107–3114, 2008.
[10]
I. Karabulut, H. ?afak, and M. Tomak, “Excitonic effects on the nonlinear optical properties of small quantum dots,” Journal of Physics D, vol. 41, no. 15, Article ID 155104, 2008.
[11]
L. He and W. Xie, “Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot,” Superlattices and Microstructures, vol. 47, no. 2, pp. 266–273, 2010.
[12]
S. J. Liang and W. F. Xie, “The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot,” The European Physical Journal B, vol. 81, no. 1, pp. 79–84, 2011.
[13]
W. Xie and Q. Xie, “Electric field effects of hydrogenic impurity states in a disc-like quantum dot,” Physica B, vol. 404, no. 12-13, pp. 1625–1628, 2009.
[14]
K. Nishi, T. Kageyama, M. Yamaguchi et al., “Molecular beam epitaxial growths of high-optical-gain InAs quantum dots on GaAs for long-wavelength emission,” Journal of Crystal Growth, vol. 378, pp. 459–462, 2013.
[15]
T. Sugaya, R. Oshima, K. Matsubara, and S. Niki, “In(Ga)As quantum dots on InGaP layers grown by solid-source molecular beam epitaxy,” Journal of Crystal Growth, vol. 378, pp. 430–434, 2013.
[16]
T. Li, Q. Wang, X. Guo et al., “The saturation density property of (B)InAs/GaAs quantum dots grown by metal-organic chemical vapor deposition,” Physica E, vol. 44, no. 7-8, pp. 1146–1151, 2012.
[17]
C. Himwas, R. Songmuang, L. S. Dang et al., “Thermal stability of the deep ultraviolet emission from AlGaN/AlN Stranski-Krastanov quantum dots,” Applied Physics Letters, vol. 101, no. 24, Article ID 241914, 2012.
[18]
H. Hassanabadi, G. Liu, and L. Lu, “Nonlinear optical rectification and the second-harmonic generation in semi-parabolic and semi-inverse squared quantum wells,” Solid State Communications, vol. 152, no. 18, pp. 1761–1766, 2012.
[19]
M. Barati, G. Rezaei, and M. R. K. Vahdani, “Binding energy of a hydrogenic donor impurity in an ellipsoidal finite-potential quantum dot,” Physica Status Solidi B, vol. 244, no. 7, pp. 2605–2610, 2007.
[20]
K. J. Kuhn, G. U. Lyengar, and S. Yee, “Free carrier induced changes in the absorption and refractive index for intersubband optical transitions in AlxGa1-xAs/GaAs/AlxGa1-xAs quantum wells,” Journal of Applied Physics, vol. 70, article 5010, 1991.
[21]
W. Xie, “The nonlinear optical rectification of a confined exciton in a quantum dot,” Journal of Luminescence, vol. 131, no. 5, pp. 943–946, 2011.
[22]
M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Physical Review Letters, vol. 9, no. 11, pp. 446–448, 1962.
[23]
P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Physical Review Letters, vol. 7, no. 4, pp. 118–119, 1961.
[24]
R. W. Boyd, Nonlinear Optics, Elsevier, 3rd edition, 2008.
[25]
S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, “Optical rectification at semiconductor surfaces,” Physical Review Letters, vol. 68, no. 1, pp. 102–105, 1992.
[26]
K.-X. Guo and S.-W. Gu, “Nonlinear optical rectification in parabolic quantum wells with an applied electric field,” Physical Review B, vol. 47, no. 24, pp. 16322–16325, 1993.
[27]
O. A. Aktsipetrov, P. V. Elyutin, A. A. Nikulin, and E. A. Ostrovskaya, “Size effects in optical second-harmonic generation by metallic nanocrystals and semiconductor quantum dots: the role of quantum chaotic dynamics,” Physical Review B, vol. 51, no. 24, pp. 17591–17599, 1995.
[28]
Z.-H. Zhang, K.-X. Guo, B. Chen, R.-Z. Wang, and M.-W. Kang, “Nonlinear optical rectification in cubical quantum dots,” Physica B, vol. 404, no. 16, pp. 2332–2335, 2009.
[29]
W. Xie, “Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot,” Physica B, vol. 404, no. 21, pp. 4142–4145, 2009.
[30]
C. M. Duque, M. E. Mora-Ramos, and C. A. Duque, “Hydrostatic pressure and electric field effects and nonlinear optical rectification of confined excitons in spherical quantum dots,” Superlattices and Microstructures, vol. 49, no. 3, pp. 264–268, 2011.
[31]
S. Baskoutas, E. Paspalakis, and A. F. Terzis, “Effects of excitons in nonlinear optical rectification in semiparabolic quantum dots,” Physical Review B, vol. 74, no. 15, Article ID 153306, 2006.
[32]
C. M. Duque, M. E. Mora-Ramos, and C. A. Duque, “Effects of hydrostatic pressure and electric field on the nonlinear optical rectification of strongly confined electronhole pairs in GaAs quantum dots,” Physica E, vol. 43, no. 4, pp. 1002–1006, 2011.
[33]
T. Chen, W. Xie, and S. Liang, “The nonlinear optical rectification of an ellipsoidal quantum dot with impurity in the presence of an electric field,” Physica E, vol. 44, no. 4, pp. 786–790, 2012.
[34]
B. Vaseghi, G. Rezaei, V. Azizi, and S. M. Azami, “Spin-orbit interaction effects on the optical rectification of a cubic quantum dot,” Physica E, vol. 44, no. 7-8, pp. 1241–1243, 2012.
[35]
L. Bouza?ene, R. B. Mahrsia, M. Baira, L. Sfaxi, and H. Maaref, “Hydrostatic pressure and temperature effects on nonlinear optical rectification in a lens shape InAs/GaAs quantum dot,” Journal of Luminescence, vol. 135, pp. 271–275, 2013.
[36]
G. Liu, K. Guo, Q. Wua, and J. H. Wub, “Polaron effects on the optical rectification and the second harmonic generation in cylindrical quantum dots with magnetic field,” Superlattices and Microstructures, vol. 53, pp. 173–183, 2013.
[37]
T. Brunhes, P. Boucaud, S. Sauvage et al., “Midinfrared second-harmonic generation in p-type InAs/GaAs self-assembled quantum dots,” Applied Physics Letters, vol. 75, no. 6, pp. 835–837, 1999.
[38]
A. Liu and G. W. Bryant, “Near-field second-harmonic generation of semiconductor quantum dots,” Physical Review B, vol. 59, no. 3, pp. 2245–2253, 1999.
[39]
T. Brunhesa, P. Boucauda, S. Sauvagea et al., “Second-harmonic generation in InAs/GaAs self-assembled quantum dots,” Physica E, vol. 7, pp. 155–158, 2000.
[40]
T. Brunhesa, P. Boucauda, S. Sauvagea et al., “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Physical Review B, vol. 61, no. 8, pp. 5562–5570, 2000.
[41]
T. Brunhesa, P. Boucauda, S. Sauvagea et al., “Second-harmonic generation resonant with s-p transition in InAs/GaAs self-assembled quantum dots,” Physical Review B, vol. 63, no. 11, Article ID 113312, 4 pages, 2001.
[42]
B. Li, K.-X. Guo, C.-J. Zhang, and Y.-B. Zheng, “The second-harmonic generation in parabolic quantum dots in the presence of electric and magnetic fields,” Physics Letters A, vol. 367, no. 6, pp. 493–497, 2007.
[43]
S. Shao, K.-X. Guo, Z.-H. Zhang, N. Li, and C. Peng, “Studies on the second-harmonic generations in cubical quantum dots with applied electric field,” Physica B, vol. 406, no. 3, pp. 393–396, 2011.
[44]
M. Sabaeian and A. Khaledi-Nasab, “Size-dependent intersubband optical properties of dome-shaped InAs/GaAs quantum dots with wetting layer,” Applied Optics, vol. 51, no. 18, pp. 4176–4185, 2012.
[45]
C. Sun, P. Lu, Z. Yu, H. Cao, and L. Zhang, “Wetting layers effect on InAs/GaAs quantum dots,” Physica B, vol. 407, no. 22, pp. 4440–4445, 2012.
[46]
T. Konishi and S. Tsukamoto, “Spatial point analysis of quantum dot nucleation sites on InAs wetting layer,” Surface Science, vol. 605, no. 5-6, pp. L1–L5, 2011.
[47]
F. Adler, M. Geiger, A. Bauknecht et al., “Optical transitions and carrier relaxation in self assembled InAs/GaAs quantum dots,” Journal of Applied Physics, vol. 80, no. 7, pp. 4019–4026, 1996.
[48]
O. Stier, M. Grundmann, D. Bimberg et al., “Electronic and optical properties of strained quantum dots modeled by 8-band k·p theory,” Physical Review B, vol. 59, no. 8, pp. 5688–5701, 1999.
[49]
Y. Li, O. Voskoboynikov, C. P. Lee, and S. M. Sze, “Computer simulation of electron energy levels for different shape InAs/GaAs semiconductor quantum dots,” Computer Physics Communications, vol. 141, no. 1, pp. 66–72, 2001.
[50]
R. V. N. Melnik and M. Willatzen, “Modelling coupled motion of electrons in quantum dots with wetting layers,” in Proceedings of the International Conference on Modeling and Simulation of Microsystems (MSM '02), pp. 506–509, San Juan, Puerto Rico, USA, April 2002.
[51]
R. Oshima, N. Kurihara, H. Shigekawa, and Y. Okada, “Electronic states of self-organized InGaAs quantum dots on GaAs (3 1 1) B studied by conductive scanning probe microscope,” Physica E, vol. 21, no. 2-4, pp. 414–418, 2004.
[52]
R. V. N. Melnik and K. N. Zotsenko, “Finite element analysis of coupled electronic states in quantum dot nanostructures,” Modelling and Simulation in Materials Science and Engineering, vol. 12, no. 3, pp. 465–477, 2004.
[53]
F. Zhang, L. Zhang, Y.-X. Wang, and R. Claus, “Enhanced absorption and electro-optic Pockels effect of electrostatically self-assembled CdSe quantum dots,” Applied Optics, vol. 44, no. 19, pp. 3969–3976, 2005.
[54]
A. D. Seddik and I. Zorkani, “Optical properties of a magneto-donor in a quantum dot,” Physica E, vol. 28, no. 4, pp. 339–346, 2005.
[55]
X.-F. Yang, X.-S. Chen, W. Lu, and Y. Fu, “Effects of shape and strain distribution of quantum dots on optical transition in the quantum dot infrared photodetectors,” Nanoscale Research Letters, vol. 3, no. 12, pp. 534–539, 2008.
[56]
A. Rostami, H. R. Saghai, N. Sadoogi, and H. B. A. Nejad, “Proposal for ultra-high performance infrared quantum dot,” Optics Express, vol. 16, no. 4, pp. 2752–2763, 2008.
[57]
C.-H. Liu and B.-R. Xu, “Theoretical study of the optical absorption and refraction index change in a cylindrical quantum dot,” Physics Letters A, vol. 372, no. 6, pp. 888–892, 2008.
[58]
M. R. K. Vahdani and G. Rezaei, “Intersubband optical absorption coefficients and refractive index changes in a parabolic cylinder quantum dot,” Physics Letters A, vol. 374, no. 4, pp. 637–643, 2010.
[59]
W. Xie, “Laser radiation effects on optical absorptions and refractive index in a quantum dot,” Optics Communications, vol. 283, no. 19, pp. 3703–3706, 2010.
[60]
G. Rezaei, Z. Mousazadeh, and B. Vaseghi, “Nonlinear optical properties of a two-dimensional elliptic quantum dot,” Physica E, vol. 42, no. 5, pp. 1477–1481, 2010.
[61]
L. Lu and W. Xie, “Impurity and exciton effects on the nonlinear optical properties of a disc-like quantum dot under a magnetic field,” Superlattices and Microstructures, vol. 50, no. 1, pp. 40–49, 2011.
[62]
W. Xie, “A study of nonlinear optical properties of a negative donor quantum dot,” Optics Communications, vol. 284, no. 19, pp. 4756–4760, 2011.
[63]
S. Liang and W. Xie, “Effects of the hydrostatic pressure and temperature on optical properties of a hydrogenic impurity in the disc-shaped quantum dot,” Physica B, vol. 406, no. 11, pp. 2224–2230, 2011.
[64]
R. V. N. Melnik and K. N. Zotsenko, “Finite element analysis of coupled electronic states in quantum dot nanostructures,” Modelling and Simulation in Materials Science and Engineering, vol. 12, no. 3, pp. 465–477, 2004.
[65]
T. Walther, A. G. Cullis, D. J. Norris, and M. Hopkinson, “Nature of the Stranski-Krastanow transition during epitaxy of InGaAs on GaAs,” Physical Review Letters, vol. 86, no. 11, pp. 2381–2384, 2001.
[66]
J. J. Coleman, J. D. Young, and A. Garg, “Semiconductor quantum dot lasers: a tutorial,” Journal of Lightwave Technology, vol. 29, no. 4, Article ID 5664751, pp. 499–510, 2011.
[67]
P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Applications of quantum dots in optical fiber luminescent oxygen sensors,” Applied Optics, vol. 45, no. 16, pp. 3760–3767, 2006.
[68]
A. Luque, A. Marti, E. Antolin, and P. Garcia-Linares, “Intraband absorption for normal illumination in quantum dot intermediate band solar cells,” Solar Energy Materials & Solar Cells, vol. 94, no. 12, pp. 2032–2035, 2010.
[69]
Y.-K. Ee, H. Zhao, R. A. Arif, M. Jamil, and N. Tansu, “Self-assembled InGaN quantum dots on GaN emitting at 520?nm grown by metalorganic vapor-phase epitaxy,” Journal of Crystal Growth, vol. 310, no. 7-9, pp. 2320–2325, 2008.