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The Mean Energy and Specific Heat of the 1D Quantum Wires

Year 2020, Volume: 15 Issue: 1, 73 - 79, 31.05.2020
https://doi.org/10.29233/sdufeffd.648765

Abstract

In this study, Rashba spin-orbital interaction of one dimensional quantum wire consisting of InAs semiconductor heterostructure and the mean energy and specific heat of electrons in the direction of the magnetic field directed perpendicular to the wire axis were investigated. The partition function of the system was calculated. The mean energy of the quantum wire system and its specific heat were plotted according to the temperature and the variation of the magnetic field according to the intensity was examined. Accordingly, the mean energy of the electrons of the quantum wire increases with increasing temperature and approaches a fixed value after a certain temperature. Increasing or decreasing the intensity of the magnetic field changes the constant value of the average energy relative to the temperature. The specific heat of the electrons in the quantum wire shows the maximum peak value at low temperature, then progressively advances towards zero. The specific heat of the electrons gives different maximum peaks at different values of the magnetic field according to the temperature.

References

  • [1] H. Kroemer, “Quasi-electric and quasi-magnetic fields in non-uniform semiconductors,” RCA Review, 18, 332-342, 1957.
  • [2] H. Kroemer, “A proposed class of heterjunction injection lasers,” Proc. IEEE, 51, 1782-1783, 1963.
  • [3] H. S. Rupprecht, I. M. Woodall, G. D. Pettit,” Efficient visible electrolumınescence at 300°k from ga1‐xalxas p‐n junctions grown by liquid‐phase epitaxy,” Appl. Phys. Lett., 11, 81, 1967.
  • [4] J.I. Alferov, B.M. Andreew, M.K. Turkan, E.L. Portnoy, “Injection lasers based on heterojunctions in an AlAs-GaAs system with a low lasing threshold at room temperature,“ FTP, 3, 1328, 1969.
  • [5] I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski. “Junction lasers which operate continuously at room temperature,“Appl. Phys. Lett., 17, 109, 1970.
  • [6] H. Kroemer, “Theory of a wide-gap emmiter for transistors,” Proc. IRE, 45, 1535-1537, 1957.
  • [7] P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegman, “Toward quantum well wires: Fabrication and optical propoties,” Appl. Phys. Lett., 41, 635, 1982.
  • [8] S. Simhony, E. Kapon, T. Colas, D. M. Hwang, and N. G. Stoffel, “Vertically stacked multiple-quantum-wire semiconductor diode lasers,” Appl. Phys. Lett., 59, 2225,1991.
  • [9] E. I. Rashba and Al. L. Efros, “Orbital mechanisms of electron-spin manipulation an electric field,” Phys. Rev. Lett., 91, 126405, 2003.
  • [10] E. I. Rashba, “Properties of semiconductors with an extremum loop,” Sov. Phys. Solid. State, 2, 1109-1122, 1960.
  • [11] Y. A. Bychkov and E. I. Rashba, “Properties of a 2D electron gas with lifted spectral degeneracy,” JETP Lett., 39, 78, 1984.
  • [12] R. Winkler, Spin-Orbit Coupling Effect is Two-Dimensional Electron and Hole Systems. Berlin: Springer, 2003, ch 6.
  • [13] D. Bercioux and P. Lucignano, “Quantum transport in Rashba spin–orbit materials: a review,” Rep. Prog. Phys., 78, 106001, 2015.
  • [14] S. Debald, B. Kramer, “ Rashba effect and magnetic field in semiconductor quantum wires,” Phys. Rev., B71, 115322, 2005.
  • [15] R. Khordad, H. R. Rastegar Sadehi, “Low temperature behavior of termodynamic properties of 1D quantum wire under the Rashba spin-orbit interaction and magnetic field,” Solid State Communication, 269, 118-124, 2018.
  • [16] X. W. Zhang, J. B. Xia, “ Rashba spin-orbit coupling in InSb nanowires under transverse electric field,“ Phys. Rev., B 74, 075304, 2006.
  • [17] A. Gharati, R. Khordad, “Effects of magnetic field and spin-orbit interaction on energy levels in 1D quantum wire: analytical solution,” Optic. Quant. Electron, 44, 425, 2012.
  • [18] F. M. Gashimzade, A. M. Babayev, H. A. Gasanov, “ Thermopower of a semiconductor film with parabolic potential in a strong magnetic field,” Solid State Physics, 43, 10, 1850-1852, 2001.
  • [19] B. M. Askerov, Electron Transport Phenomena in Semiconductors. Moscow: Nauka, 1985, ch. 6.
  • [20] G. M. Fikhtengolts, Differential and integral calculus. Moscow: Nauka, 1969, 7th ed, ch 12.
  • [21] P. Graham, D. Knuth, O. Patashnik, Concrete Mathematics. Moscow: Mir, 1998, ch 2.
  • [22] M. P. Stopa, S. D. Sarma, “Parabolic-quantum-well self consistent electronic structure in a longitudinal magnetic field: Subband depopulation,” Phys. Rev. B 40 (14), 10048(R), 1989.

1D Kuantum Telin Ortalama Enerjisi ve Öz Isısı

Year 2020, Volume: 15 Issue: 1, 73 - 79, 31.05.2020
https://doi.org/10.29233/sdufeffd.648765

Abstract

Bu çalışmada InAs yarıiletken heteroyapıdan oluşan bir boyutlu kuantum telin Rashba spin-orbital etkileşimi ve tel eksenine dik yönde yönelmiş manyetik alan etkisinde elektronların ortalama enerjisi ve öz ısısı teorik olarak araştırıldı. Sistemin dağılım fonksiyonu hesaplandı. Kuantum tel sistemin ortalama enerjisi, öz ısısı sıcaklığa göre grafiği oluşturuldu ve manyetik alanın şiddetine göre değişimi incelendi. Buna göre kuantum telin elektronlarının ortalama enerjisi, sıcaklık artmakta ve belli bir sıcaklıktan sonra sabit bir değere yaklaşmaktadır. Manyetik alanın şiddetinin artması veya azalması ortalama enerjinin sıcaklığa göre sabit değerini değiştirmektedir. Kuantum teldeki elektronların öz ısısı düşük sıcaklıkta maksimum değere ulaşmakta ve artan sıcaklıkla birlikte sıfıra gitmektedir. Elektronların öz ısısı sıcaklığa göre manyetik alanın farklı değerlerinde farklı maksimum tepe noktaları vermektedir.

References

  • [1] H. Kroemer, “Quasi-electric and quasi-magnetic fields in non-uniform semiconductors,” RCA Review, 18, 332-342, 1957.
  • [2] H. Kroemer, “A proposed class of heterjunction injection lasers,” Proc. IEEE, 51, 1782-1783, 1963.
  • [3] H. S. Rupprecht, I. M. Woodall, G. D. Pettit,” Efficient visible electrolumınescence at 300°k from ga1‐xalxas p‐n junctions grown by liquid‐phase epitaxy,” Appl. Phys. Lett., 11, 81, 1967.
  • [4] J.I. Alferov, B.M. Andreew, M.K. Turkan, E.L. Portnoy, “Injection lasers based on heterojunctions in an AlAs-GaAs system with a low lasing threshold at room temperature,“ FTP, 3, 1328, 1969.
  • [5] I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski. “Junction lasers which operate continuously at room temperature,“Appl. Phys. Lett., 17, 109, 1970.
  • [6] H. Kroemer, “Theory of a wide-gap emmiter for transistors,” Proc. IRE, 45, 1535-1537, 1957.
  • [7] P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegman, “Toward quantum well wires: Fabrication and optical propoties,” Appl. Phys. Lett., 41, 635, 1982.
  • [8] S. Simhony, E. Kapon, T. Colas, D. M. Hwang, and N. G. Stoffel, “Vertically stacked multiple-quantum-wire semiconductor diode lasers,” Appl. Phys. Lett., 59, 2225,1991.
  • [9] E. I. Rashba and Al. L. Efros, “Orbital mechanisms of electron-spin manipulation an electric field,” Phys. Rev. Lett., 91, 126405, 2003.
  • [10] E. I. Rashba, “Properties of semiconductors with an extremum loop,” Sov. Phys. Solid. State, 2, 1109-1122, 1960.
  • [11] Y. A. Bychkov and E. I. Rashba, “Properties of a 2D electron gas with lifted spectral degeneracy,” JETP Lett., 39, 78, 1984.
  • [12] R. Winkler, Spin-Orbit Coupling Effect is Two-Dimensional Electron and Hole Systems. Berlin: Springer, 2003, ch 6.
  • [13] D. Bercioux and P. Lucignano, “Quantum transport in Rashba spin–orbit materials: a review,” Rep. Prog. Phys., 78, 106001, 2015.
  • [14] S. Debald, B. Kramer, “ Rashba effect and magnetic field in semiconductor quantum wires,” Phys. Rev., B71, 115322, 2005.
  • [15] R. Khordad, H. R. Rastegar Sadehi, “Low temperature behavior of termodynamic properties of 1D quantum wire under the Rashba spin-orbit interaction and magnetic field,” Solid State Communication, 269, 118-124, 2018.
  • [16] X. W. Zhang, J. B. Xia, “ Rashba spin-orbit coupling in InSb nanowires under transverse electric field,“ Phys. Rev., B 74, 075304, 2006.
  • [17] A. Gharati, R. Khordad, “Effects of magnetic field and spin-orbit interaction on energy levels in 1D quantum wire: analytical solution,” Optic. Quant. Electron, 44, 425, 2012.
  • [18] F. M. Gashimzade, A. M. Babayev, H. A. Gasanov, “ Thermopower of a semiconductor film with parabolic potential in a strong magnetic field,” Solid State Physics, 43, 10, 1850-1852, 2001.
  • [19] B. M. Askerov, Electron Transport Phenomena in Semiconductors. Moscow: Nauka, 1985, ch. 6.
  • [20] G. M. Fikhtengolts, Differential and integral calculus. Moscow: Nauka, 1969, 7th ed, ch 12.
  • [21] P. Graham, D. Knuth, O. Patashnik, Concrete Mathematics. Moscow: Mir, 1998, ch 2.
  • [22] M. P. Stopa, S. D. Sarma, “Parabolic-quantum-well self consistent electronic structure in a longitudinal magnetic field: Subband depopulation,” Phys. Rev. B 40 (14), 10048(R), 1989.
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Metrology, Applied and Industrial Physics
Journal Section Makaleler
Authors

Arif Babanlı 0000-0003-4468-999X

Vepa Sabyrov 0000-0002-3562-3086

Publication Date May 31, 2020
Published in Issue Year 2020 Volume: 15 Issue: 1

Cite

IEEE A. Babanlı and V. Sabyrov, “1D Kuantum Telin Ortalama Enerjisi ve Öz Isısı”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 15, no. 1, pp. 73–79, 2020, doi: 10.29233/sdufeffd.648765.