Investigation of Ground State of Hydrogenlike Quantum Dot Structure with Quantum Genetic Algorithm

Abstract

In this study, the electronic structure of the ground states of a quantum dot structure with spherical well was investigated. The ground state energy depending on dot radius and stoichiometric ratio was calculated for GaAs/AlxGa1-x As quantum structure including hydrogenlike impurity on center. Wave function was constructed in terms of Slater type basis functions and it was obtained by using Quantum Genetic Algorithm (KGA) method and the ground state energy was calculated by Hartree-Fock-Roothaan (HFR) method.

Keywords

• Kuantum Genethic Algorithm, finite potential well, quantum dot structure

Hidrojen Tipi Kuantum Nokta Yapının Taban Durumunun Kuantum Genetik Algoritma Yöntemiyle İncelenmesi

Abstract

Bu çalışmada sonlu küresel kuyudaki kuantum nokta yapısının taban durum elektronik özellikleri incelendi. Merkezinde hidrojen benzeri safsızlık olan GaAs/Alx Ga1-x As kuantum nokta yapısının farklı kuantum nokta yarıçapları için taban durum enerjileri nokta yarıçapına ve katkılanma oranına bağlı olarak hesaplandı. Slater tipi baz fonksiyonları cinsinden oluşturulan dalga fonksiyonu Kuantum Genetik Algotirma (KGA) yöntemi kullanılarak elde edildi ve Hartree-Fock-Roothaan (HFR) yöntemi ile taban durumu enerjisi hesaplandı.

Keywords

• Kuantum Genetik Algoritma, sonlu potansiyel kuyu, küresel kuantum nokta yapı.

References

1. 1. Ryzhii, V., The theory of quantum-dot infrared phototransistors, Semiconductor Science and Technology, 11, 759-765, 1996.
2. 2. Levine, I. N.,Quantum Chemistry, Prentice-Hall, Inc., New Jersey, 2000.
3. 3. Maksym, P.A., Chakrabotry, t., Quantum dots in a magnetic field: role of electron-electron interactions, American Physical Society, 65, 108-111, 1990.
4. 4. Kouwenhoven, L., Marcus, C., Quantum dots, PhysicsWorld, 11, 35-39, 1998.
5. 5. Holland, J. H., Adaptation in Natural and Artifical Systems, University of Michigan, Ann Arbor, MI, 1975.
6. 6. Chaudhury, P. And Bhattacharyya, S. P., Numerical solutions of the Schrödinger equation directly or perturbatively by a genetic algorithm: test cases, Chemical Physics Letters, 296, 51-60, 1998.
7. 7. Grigorenko, I., Garcia, M. E., An evolutionary algorithm to calculate the ground state of a quantum systems, Physica A, 284, 131-139, 2000.
8. 8. Şahin, M., Tomak, M., Self-consistent calculation of semiconductor heterojunctions using quantum genetic algorithm, International Journal of Modern Physics B, 16, 3883-3893, 2002.

9. 9. Şafak, H., Şahin, M., Gülveren, B., Tomak, M., Efficiency of genetic algorithm and determination of ground state energy of impurity in a spherical quantum dot, International Journal of Modern Physics C, 14, 775-784, 2003.
10. 10. Coley, D. A., An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific Publishing Co. Pte. Ltd., Singapore, 2001.
11. 11. Yakar, Y., Özmen, A., Atav, Ü., Evaluation of two-center one- and two-electron integral over Slater type orbitals, Chinese Journal of Chemistry, 24, 603-608, 2006.
12. 12. Adachi, S., GaAs and Relati Materials, World Scientific, Singapore, 1994.
13. 13. Çakır, B., Özmen,A., Atav, Ü., Yüksel,H. And Yakar, Y., Investigation of Electronic structure of a spherical quantum dot using a Slater-Type orbitals and quantum genetic algorithm, International Journal of Modern Physics C, Vol.18, No 1, 61-72, 2007.
14. 14. Çakır, B., Özmen, A., Atav, Ü., Yüksel, H. And Yakar, Y., Calculation of Electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree-FockRoothaan Method, International Journal of Modern Physics C, Vol.19, No 4, 599-609, 2008.
15. 15. Marin, J. L., Cruz, S. A., On the use of direct variational methods to study confined quantum systems, American Journal of Physics, 59: 931-935, 1991.
16. 16. Marin, J. L., Cruz, S. A, Enclosed quantum systems:use of direct variatinal method, Jornal Physics B: At. Mol.Opt. Phys., 24:2899-2907., 1991.
17. 17. Varshni, Y. P., Binding energy of a screened donor in a spherical quantum dot with a parabolic potential, Superlattices and microstructures, 29: 233-238, 2001.