İki Elektronlu Kuantum Nokta Yapılarda Elektrik Alan Etkisinin Pertürbasyon Yöntemiyle İncelenmesi

Yıl 2016, Cilt: 42 Sayı: 1, 64 - 76, 01.06.2016

Ahmet Türker Bekir Çakır Ayhan Özmen Yusuf Yakar

Öz

Bu çalışmada iki elektronlu kuantum nokta yapının dış elektrik alan etkisi altında elektronik özellikleri Pertürbasyon yöntemiyle incelendi. Hesaplamalarda helyum benzeri safsızlığa sahip olan iki elektronlu kuantum nokta yapı ele alındı ve sonsuz derinlikli küresel simetrik sınırlayıcı potansiyel göz önüne alındı. Sistemin dalga fonksiyonları tek elektron spin orbitallerinden oluşan Slater determinantı ile tanımlandı. Tek elektron spin orbitalleri ise Slater Tipi Orbitallerin(STO) lineer bileşimleri olarak kuruldu. Kuantum Genetik Algoritma(KGA) tekniği ile Schrödinger denkleminin olası çözümleri olan dalga fonksiyonları belirlendi ve bu dalga fonksiyonları kullanılarak iki elektronlu kuantum noktayapının taban ve bazı uyarılmış durumların enerjilerinin beklenen değerleri Hartree-Fock-Roothaan Metodu(HFR) ile hesaplandı. İki elektronlu kuantum nokta yapının dış elektrik alan etkisinde iken bu enerji seviyelerine gelen katkı pertürbasyon yöntemiyle hesaplandı.

Anahtar Kelimeler

Hartree-Fock Roothaan Metod, Kuantum nokta yapı, Kuantum Genetik Algoritm Hartree-Fock Roothaan Metod, Kuantum nokta yapı, Kuantum Genetik Algoritma

Investigation of the Electric Field Effect by Perturbation Method in Two Electron Quantum Dot

Öz

In this study electronic properties two-electron quantum dots under an external electric field were investigated by using Perturbation method. In calculation we used helium-like quantum dot with two electron confined with infinite spherically symmetric potential. The wave function of the system is defined by a Slater determinant constructed single-electron spin orbitals. The single electron spin orbitals were created as linear combinations of Slater type orbitals (STO). The wave functions which are the possible solutions of the Schrödinger equation were determined by using Quantum Genetic Algorithm (QGA). The energy eigenvalues of ground and excited states quantum dot with two electron were calculated using Hartree-Fock-Roothoon Method (HFR). The contributions came from the external electric field on these states of two electron quantum dot were calculated using Perturbation method.

Anahtar Kelimeler

Hartree-Fock Roothaan Method, Quantum dot, Quantum Genetik Algorithm, Perturbation Method, Slater Type orbital

Kaynakça

• Arfken G (1985). Mathematical Methods for Physics, Third Edition, Academic Press Inc, Orlando.
• Chang K, Xia JB (1998). The effects of electric field on the electronic structure of a semiconductor quantum dot, Journal of Applied Physics 84(3), 1454.
• Çakır B, Özmen A, Atav U, Yüksel H, Yakar Y (2007). Investigation of electronic structure of a Quantum Dot using Slater-Type Orbitals and Quantum Genetic Algorithm, International Journal of Modern Physics C 18(1), 61–72.
• Çakır B, Özmen A, Atav U, Yüksel H, Yakar Y (2008). Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree-Fock-Roothaan method, International Journal of Modern Physics C 19(4), 599–609.
• Çakır B, Yakar Y, Özmen A (2013). Calculation of oscillator strength and the effects of electric field on energy states, static and dynamic polarizabilities of the confined hydrogen atom, Optics Communications 311, 222–228.
• Çakır B, Yakar Y, Özmen A (2015). Linear and nonlinear optical absorption coefficients of two-electron spherical quantum dot with parabolic potential, Physica B: Condensed Matter 458, 138–143.
• Dane C, Akbas H, Minez S, Guleroglu A (2008). Electric field effect in a GaAs/AlAs spherical quantum dot, Physica E-Low-Dimensional Systems & Nanostructures 41(2), 278–281.
• Dujardin FA, Oukerroum E, Feddi JBB, J. Martínez-Pastor, Zazi M (2012). Effect of a lateral electric field on an off-center single dopant confined in a thin quantum disk, Journal of Applied Physics 111(3), 034317.
• Duque CA, Kasapoglu E, Sakiroglu S, Sari H, Sokmen I (2011). Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field, Applied Surface Science 257(6), 2313–2319.
• Fry PW, Finley JJ, Wilson LR, Lemaître A, Mowbray DJS, MS, Hopkinson M, Hill G, Clark JC (2000). Electric-field-dependent carrier capture and escape in self-assembled InAs/GaAs quantum dots, Applied Physics Letters 77(26), 43–44.
• Håkanson U, Håkanson H, Johansson MKJ, Samuelson L, Pistol ME (2003). Electric field effects in single semiconductor quantum dots observed by scanning tunneling luminescence, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 21(6), 23–44.
• He L, Xie W (2010). Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot, Superlattices and Microstructures 47(2), 266–273.
• Huangfu YF, Yan ZW (2008). Bound polaron in a spherical quantum dot under an electric field, Physica E-Low-Dimensional Systems & Nanostructures 40(9), 2982–2987.
• Jiang L, Wang H, Wu H, Gong Q, Feng S (2009). External electric field effect on the hydrogenic donor impurity in zinc-blende GaN/AlGaN cylindrical quantum dot, Journal of Applied Physics 105(5), 053710.
• Karabulut I, Duque CA (2011). Nonlinear optical rectification and optical absorption in GaAs-Ga1-xAlxAs double quantum wells under applied electric and magnetic fields, Physica E-Low-Dimensional Systems & Nanostructures 43(7), 1405–1410.
• Karabulut I, Baskoutas S (2008). Linear and nonlinear optical absorption coefficients and refractive index changes in spherical quantum dots: Effects of impurities, electric field, size, and optical intensity, Journal of Applied Physics 103(7), 073512.
• Kırak M, Altınok Y, Yılmaz S (2013). The effects of the hydrostatic pressure and temperature on binding energy and optical properties of a donor impurity in a spherical quantum dot under external electric field, Journal of Luminescence 136, 415–421.
• Kırak M, Yılmaz S, Şahin M, Gençaslan M (2011). The electric field effects on the binding energies and the nonlinear optical properties of a donor impurity in a spherical quantum dot, Journal of Applied Physics 109(9), 094309.
• Kırak M, Yılmaz S, Temizer U (2013). Nonlinear optical rectification and oscillator strength in a spherical quantum dot with parabolic confinement in the presence of the electric field, Journal of Nanoelectronics and Optoelectronics 8(2), 165–169.
• Lin SW, Song AM, Peaker AR, Caldas Ml, Studart N (2010). Electric-field dependence of electron emission from InAs∕GaAs quantum dots, 291–292.
• Özmen A, Çakır B, Yakar Y (2013). Electronic structure and relativistic terms of one-electron spherical quantum dot, Journal of Luminescence 137, 259–268.
• Rezaei G, Vaseghi B, Ebrahimi J (2011). External electric field effects on the electronic and hydrogenic impurity states in ellipsoidal and semi-ellipsoidal quantum dots, Superlattices and Microstructures 49(6), 591–598.
• Rezaei G, Vaseghi B, Sadri M (2011). External electric field effect on the optical rectification coefficient of an exciton in a spherical parabolic quantum dot, Physica B-Condensed Matter 406(24), 4596–4599.
• Ribeiro FJ, Latgé A, Pacheco M, Barticevic Z (1997). Quantum dots under electric and magnetic fields: Impurity-related electronic properties, Journal of Applied Physics 82(1), 270.
• Sadeghi E (2011a). Electric field and impurity effects on optical property of a three- dimensional quantum dot: A combinational potential scheme, Superlattices and Microstructures 50(4), 331–339.
• Sadeghi E (2011b). Linear and nonlinear optical absorption coefficients in an asymmetric graded ridge quantum wire, Superlattices and Microstructures 49(1), 91–98.
• Sahin M, Tomak M (2005a). Electronic structure of a many-electron spherical quantum dot with an impurity, Physical Review B 72(12).
• Sahin M, Tomak M (2005b). The self-consistent calculation of a spherical quantum dot: A quantum genetic algorithm study, Physica E-Low-Dimensional Systems & Nanostructures 28(3), 247–256.
• Vázquez GJ, del Castillo‐Mussot M, Mendoza CI, Spector HN (2004). Spherical quantum dot under an electric field, Physica Status Solidi (C) 1(S1), S54–S57.
• Vinolin A, Peter AJ (2014). Optical rectification in a strained GaAs0.9P0.1/GaAs0.6P0.4 quantum dot: Simultaneous effects of electric and magnetic fields, AIP Conference Proceedings, 1496–1497.
• Xia C, Zeng Z, Wei S (2010a). Electron and impurity states in GaN/AlGaN coupled quantum dots: Effects of electric field and hydrostatic pressure, Journal of Applied Physics 108(5), 054307.
• Xia C, Zeng Z, Wei S (2010b). Shallow-donor impurity in zinc-blende InGaN/GaN asymmetric coupled quantum dots: Effect of electric field, Journal of Applied Physics 107(5), 054305.
• Yakar Y, Cakir B, Ozmen A (2010a). Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential, Optics Communications 283(9), 1795–1800.
• Yakar Y, Cakir B, Ozmen A (2010b). Linear and nonlinear optical properties in spherical quantum dots, Communications in Theoretical Physics 53(6), 1185–1189.
• Yakar Y, Çakır B, Özmen A (2010c). Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential, Optics Communications 283(9), 1795–1800.
• Yakar Y, Çakır B, Özmen A (2011). Computation of ionization and various excited state energies ofhelium and helium-like quantum dots, International Journal of Quantum Chemistry 111(15), 4139–4149.
• Yakar Y, Çakır B, Özmen A (2013). Computation of relativistic terms in a spherical quantum dot, Journal of Luminescence 134, 778–783.
• Yakar Y, Çakır B, Özmen A (2015a). Electronic structure of two-electron quantum dot with parabolic potential, Philosophical Magazine 95(3), 311–325.
• Yakar Y, Çakır B, Özmen A (2015b). Linear and nonlinear absorption coefficients of spherical two-electron quantum dot, Computer Physics Communications 188, 88–93.
• Yeşilgül U, Ungan F, Kasapoğlu E, Sarı H, Sökmen I (2011). The linear and nonlinear intersubband optical absorption coefficients and refractive index changes in a V- shaped quantum well under the applied electric and magnetic fields, Superlattices and Microstructures 50(4), 400–410.