Statistical Mechanical Modelling and Termodynamical Properties of Single Electron Quantum Dot with Gaussian Confinement
Abstract
In this study, statistical
mechanical modelling and termodynamical properties of a GaAs quantum dot with
Gaussian confinement have been investigated. The Hamiltonian of a particle
under magnetic field was solved in polar coordinates, energy eigenvalues and eigenfunctions
have been obtained. The total energy of the system was found by using the Fock
Darwin states and the first order Perturbation theory. Therefore, the behavior
of the thermodynamical quantities of the system such as, free energy, entropy,
average energy and heat capacity were investigated as a function of temperature,
magnetic field, quantum dot size and Gaussian potential depth by using the
partition function obtained by using canonical ensemble approach.
References
- Adamowski, J., Sobkowicz, M., Szafran, B. ve Bednarek, S., “Electron pair in a Gaussian confining potential”, Phys. Rev. B, 62, 4234-4240, 2000.
- Johnson, N.F., “Quantum dots: few-body, low-dimensional systems”, J. Phys. Condens. Matter, 7, 965-971, 1995.
- Woggon, U., “Optical Properties of Semiconductor Quantum Dots”, Springer, 230s, 1997.
- Jacak, L., Hawrylak, P. ve Wojs, A., “Quantum Dots”, Springer, 176 s, Germany, 1998.
- Bimberg, D., Grundmann, M. ve Ledentsov, N.N., “Quantum Dot Hetero-structures”, Wiley, 338s, Germany, 1998.
- Chatterjee, A., “1/N expansion for Gaussian potential”, J. Phys. A., 18, 2403-2422, 1985.
- Maksym, P.A. ve Chakraborty, T., “Quantum dots in a magnetic field: Role of electron-electron interactions”, Phys. Rev. Lett., 65, 108-122, 1990.
- Oh, J.H., Chang, K.J., Ihm, G. ve Lee, S., “Electronic structure of three-dimensional quantum dots in tilted magnetic fields”, J. Phys. Rev. B, 50, 15397-15410, 1994.
- Lee, S.J., Chang, J.H., Won. K.T., ve Souma, S., “Transitions of density of states and heat capacity in spherical quantum structure formed by a thin barrier”, Physica E, 40, 2198-2215, 2008.
- Gornik, E., Lassnig, R., Strasser, G., Steormer, H.L., Gossard, A. C. ve Wiegmann, W., “Specific Heat of Two-Dimensional Electrons in GaAs-GaAlAs Multilayers”, Phys. Rev. Lett., 54, 1820-1832, 1985.
Gaussyen Potansiyel İle Sınırlandırılmış Tek Elektronlu Kuantum Noktanın İstatistiksel Mekaniksel Modellenmesi ve Termodinamik Özellikleri
Abstract
Bu
çalışmada, Gaussyen potansiyel ile sınırlandırılmış GaAs kuantum noktanın
istatistiksel mekaniksel modellenmesi ve termodinamik özellikleri
araştırılmıştır. Manyetik alan içerisindeki parçacığın kutupsal
koordinatlardaki Hamiltoniyeni çözülmüş, enerji özdeğer ve özdurumları
bulunmuştur. Fock Darwin durumları olan bu öz durumlar kullanılarak pertürbasyon
teorisi yardımıyla sistemin toplam enerjisi elde edilmiştir. Böylelikle kanonik
topluluk yaklaşımı ile elde edilen partisyon fonksiyonundan; serbest enerji,
entropi, ortalama enerji ve ısı kapasitesi gibi termodinamik niceliklerin
değişimleri, sıcaklık, manyetik alan, Gaussyen potansiyelin erimi ve Gaussyen
potansiyelin derinliği gibi parametrelere bağlı olarak incelenmiştir.
References
- Adamowski, J., Sobkowicz, M., Szafran, B. ve Bednarek, S., “Electron pair in a Gaussian confining potential”, Phys. Rev. B, 62, 4234-4240, 2000.
- Johnson, N.F., “Quantum dots: few-body, low-dimensional systems”, J. Phys. Condens. Matter, 7, 965-971, 1995.
- Woggon, U., “Optical Properties of Semiconductor Quantum Dots”, Springer, 230s, 1997.
- Jacak, L., Hawrylak, P. ve Wojs, A., “Quantum Dots”, Springer, 176 s, Germany, 1998.
- Bimberg, D., Grundmann, M. ve Ledentsov, N.N., “Quantum Dot Hetero-structures”, Wiley, 338s, Germany, 1998.
- Chatterjee, A., “1/N expansion for Gaussian potential”, J. Phys. A., 18, 2403-2422, 1985.
- Maksym, P.A. ve Chakraborty, T., “Quantum dots in a magnetic field: Role of electron-electron interactions”, Phys. Rev. Lett., 65, 108-122, 1990.
- Oh, J.H., Chang, K.J., Ihm, G. ve Lee, S., “Electronic structure of three-dimensional quantum dots in tilted magnetic fields”, J. Phys. Rev. B, 50, 15397-15410, 1994.
- Lee, S.J., Chang, J.H., Won. K.T., ve Souma, S., “Transitions of density of states and heat capacity in spherical quantum structure formed by a thin barrier”, Physica E, 40, 2198-2215, 2008.
- Gornik, E., Lassnig, R., Strasser, G., Steormer, H.L., Gossard, A. C. ve Wiegmann, W., “Specific Heat of Two-Dimensional Electrons in GaAs-GaAlAs Multilayers”, Phys. Rev. Lett., 54, 1820-1832, 1985.
Details
| Subjects | Engineering |
|---|---|
| Journal Section | Fizik |
| Authors | |
| Publication Date | July 28, 2017 |
| Published in Issue | Year 2017 Volume: 6 Issue: 1 |
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