DOI: https://doi.org/10.15587/2313-8416.2014.30728

Обобщенная модель транспорта электронов и тепла Ландауэра-Датты-Лундстрома в микро- и наноэлектронике

Юрий Алексеевич Кругляк

Аннотация


Излагается обобщенная модель транспорта электронов, развитая Р. Ландауэром, С. Даттой и М. Лундстромом,  вплоть до вычисления проводимости резисторов любой размерности, любого масштаба и произвольной дисперсии, работающих в баллистическом, квази-баллистическом или диффузионном режиме линейного отклика как вблизи 0º K, так и при высоких температурах. Обсуждаются и поныне широко используемое понятие подвижности, а также диссипация тепла и падение напряжения в баллистических резисторах.


Ключевые слова


нанофизика; наноэлектроника; транспорт электронов; линейный отклик; диссипация тепла; баллистический резистор

Полный текст:

PDF

Литература


Landauer, R. (1957).Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM Journal of Research and Development, 1 (3), 223–231. doi: 10.1147/rd.13.0223

Landauer, R. (1970). Electrical resistance of disordered one dimensional lattices. Philosophical Magazine, 21 (172), 863–867. doi: 10.1080/14786437008238472

Landauer, R. (1996). Spatial variation of currents and fields due to localized scatterers in metallic conduction. Journal of Mathematical Physics, 37 (10), 5259. doi: 10.1063/1.531590

Datta, S. (2012). Lessons from Nanoelectronics: A New Perspective on Transport. Hackensack, New Jersey: World Scientific Publishing Company. Available at: www.nanohub.org/courses/FoN1

Datta, S. (2001). Electronic Transport in Mesoscopic Systems. Cambridge: Cambridge University Press.

Datta, S. (2005). Quantum Transport: Atom to Transistor. Cambridge: Cambridge University Press.

Lundstrom, M., Jeong, C. (2013). Near-Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company. Available at: www.nanohub.org/resources/11763

Lundstrom, M. Nanoscales Transistors. Available at: www.nanohub.org/courses/NT

Pierret, R. F. (1996). Semiconductor Device Fundamentals. Reading, MA: Addison–Wesley.

Jeong, C., Kim, R., Luisier, M., Datta, S., Lundstrom, M. (2010). On Landauer versus Boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients. Journal of Applied Physics, 107 (2), 023707. doi: 10.1063/1.3291120

Berg, H. C. (1993). Random walks in biology. Princeton: Princeton University Press.

van Wees, B. J., van Houten, H., Beenakker, C. W. J., Williamson, J. G., Kouwenhoven, L. P., van der Marel, D., Foxon, C. T. (1988)Quantized conductance of point contacts in a two-dimensional electron gas. Physical Review Letters, 60 (9), 848–850. doi: 10.1103/physrevlett.60.848

Holcomb, D. F. (1999). Quantum Electrical Transport in samples of limited dimensions. American Journal of Physics, 67 (4), 278. doi: 10.1119/1.19251

Cvijovic, D. (2009). Fermi-Dirac and Bose-Einstein functions of negative integer order. Theoretical and Mathematical Physics, 161 (3), 1663–1668. doi: 10.1007/s11232-009-0153-9

Dingle, R. (1957). The Fermi-Dirac Integrals. Appl. Scientific Res., 6 (1), 225.

Kim, R., Lundstrom, M. S. Notes on Fermi-Dirac Integrals. Available at: www.nanohub.org/resources/5475

Lundstrom, M. (2000). Fundamentals of Carrier Transport, 2nd Ed. Cambridge: Cambridge Univ. Press, 440

Peter, Yu., Manuel, C. (2010). Fundamentals of Semiconductors. Physics and Materials Properties. Berlin: Springer, 775

Shur, M. S. (2002). Low Ballistic Mobility in GaAs HEMTs, IEEE Electron Device Letters, 23 (9), 511–513. doi: 10.1109/led.2002.802679

Wang, J., Lundstrom, M. (2003). Ballistic Transport in High Electron Mobility Transistors. IEEE Transactions on Electron Devices, 50 (7), 1604–1609. doi: 10.1109/ted.2003.814980

Ashcroft, N. W., Mermin, N. D. (1979). Solid State Physics. Philadelphia: Suanders College, 458

Yao, Z., Kane, C. L., Dekker, C. (2000). High-Field Electrical Transport in Single-Wall Carbon Nanotubes. Physical Review Letters. 84 (13), 2941–2944. doi: 10.1103/physrevlett.84.2941

Kruglyak, Yu. (2014). Landauer – Datta – Lundstrom Generalized Transport Model for Nanoelectronics, Journal of Nanoscience, 2014, 1–15. doi: 10.1155/2014/725420

Kruglyak, Yu. A. (2014). A Generalized Landauer – Datta – Lundstrom Electron Transport Model. Russian Journal of Physical Chemistry A, 88 (11), 1826–1836. doi: 10.1134/s0036024414110119

Kruglyak, Yu. A. (2013). The Generalized Landauer – Datta – Lunstrom Electron Transport Model. Nanosystems, Nanomaterials, Nanotechnologies, 12 (2), 415.

Kruglyak, Yu. A. (2013).From Ballistic Conductivity to Diffusional in the Landauer-Datta-Lunstrom Transport Model, Nanosystems, Nanomaterials, Nanotechnologies, 11 (4), 655–677.


Пристатейная библиография ГОСТ


1. Landauer, R. Spatial variation of currents and fields due to localized scatterers in metallic conduction [Text] / R. Landauer // IBM Journal of Research and Development. – 1957. – Vol. 1, Issue 3. – P. 223–231. doi: 10.1147/rd.13.0223 

2. Landauer, R. Electrical resistance of disordered one dimensional lattices [Text] / R. Landauer // Philosophical Magazine. – 1970. – Vol. 21, Issue 172. – P. 863–867. doi: 10.1080/14786437008238472 

3. Landauer, R. Spatial variation of currents and fields due to localized scatterers in metallic conduction [Text] / R. Landauer // Journal of Mathematical Physics. – 1996. – Vol. 37, Issue 10. – P. 5259. doi: 10.1063/1.531590 

4. Datta, S. Lessons from Nanoelectronics: A New Perspective on Transport [Electronic resource] / S. Datta. – Hackensack, New Jersey: World Scientific Publishing Company, 2012. – Available at: www.nanohub.org/courses/FoN1

5. Datta, S. Electronic Transport in Mesoscopic Systems [Text] / S. Datta. – Cambridge: Cambridge University Press, 2001.

6. Datta, S. Quantum Transport: Atom to Transistor [Text] / S. Datta. – Cambridge: Cambridge University Press, 2005.

7. Lundstrom, M. Near-Equilibrium Transport: Fundamentals and Applications [Electronic resource] / M. Lundstrom, C .Jeong. – Hackensack, New Jersey: World Scientific Publishing Company, 2013. – Available at: www.nanohub.org/resources/11763

8. Lundstrom, M. Nanoscales Transistors [Electronic resource] / M. Lundstrom. – Available at: www.nanohub.org/courses/NT

9. Pierret, R. F. Semiconductor Device Fundamentals [Text] / R. F. Pierret. – Reading, MA: Addison–Wesley, 1996.

10. Jeong, C. On Landauer versus Boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients [Text] / C. Jeong, R. Kim, M. Luisier, S. Datta, M. Lundstrom // Journal of Applied Physics. – 2010. – Vol. 107, Issue 2. – P. 023707. doi: 10.1063/1.3291120 

11. Berg, H. C. Random walks in biology [Text] / H. C. Berg. – Princeton: Princeton University Press, 1993.

12. van Wees, B. J. Quantized conductance of point contacts in a two-dimensional electron gas [Text] / B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, C. T. Foxon // Physical Review Letters. – 1988. – Vol. 60, Issue 9. – P. 848–850. doi: 10.1103/physrevlett.60.848 

13. Holcomb, D. F. Quantum Electrical Transport in samples of limited dimensions [Text] / D. F. Holcomb // American Journal of Physics. – 1999. – Vol. 67, Issue 4. – P. 278. doi: 10.1119/1.19251 

14. Cvijovic, D. Fermi-Dirac and Bose-Einstein functions of negative integer order [Text] / D. Cvijovic // Theoretical and Mathematical Physics. – 2009. – Vol. 161, Issue 3. – P. 1663–1668. doi: 10.1007/s11232-009-0153-9 

15. Dingle, R. The Fermi-Dirac Integrals [Text] / R. Dingle // Appl. Scientific Res. – 1957. – Vol. 6, Issue 1. – P. 225.

16. Kim, R. Notes on Fermi-Dirac Integrals [Electronic resource] / R. Kim, M. S. Lundstrom. – Available at: www.nanohub.org/resources/5475

17. Lundstrom, M. Fundamentals of Carrier Transport, 2nd Ed. [Text] / M. Lundstrom. – Cambridge: Cambridge Univ. Press, 2000. – 400 p.

18. Peter, Yu. Fundamentals of Semiconductors. Physics and Materials Properties [Text] / Yu. Peter, C. Manuel. – Berlin: Springer, 2010. – 775 p.

19. Shur, M. S. Low Ballistic Mobility in GaAs HEMTs [Text] / M. S. Shur // IEEE Electron Device Letters. – 2002. – Vol. 23, Issue 9. – P. 511–513. doi: 10.1109/led.2002.802679 

20. Wang, J. Ballistic Transport in High Electron Mobility Transistors [Text] / J. Wang, M. Lundstrom // IEEE Transactions on Electron Devices. – 2003. – Vol. 50, Issue 7. – P. 1604–1609. doi: 10.1109/ted.2003.814980 

21. Ашкрофт, Н. Физика твердого тела [Текст] / Н. Ашкрофт, Н. Мермин. – М: Мир, 1979. – 458 с.

22. Yao, Z. High-Field Electrical Transport in Single-Wall Carbon Nanotubes [Text] / Z. Yao, C. L. Kane, C. Dekker // Physical Review Letters. – 2000. – Vol. 84, Issue 13. – P. 2941–2944. doi: 10.1103/physrevlett.84.2941 

23. Kruglyak, Yu. Landauer-Datta-Lundstrom Generalized Transport Model for Nanoelectronics [Text] / Yu. Kruglyak // Journal of Nanoscience. – 2014. – Vol. 2014. – P. 1–15. doi: 10.1155/2014/725420 

24. Kruglyak, Yu. A. A Generalized Landauer-Datta-Lundstrom Electron Transport Model [Text] / Yu. A. Kruglyak // Russian Journal of Physical Chemistry A. – 2014. – Vol. 88, Issue 11. – P. 1826–1836. doi: 10.1134/s0036024414110119 

25. Кругляк, Ю. А. Обобщенная модель электронного транспорта Ландауэра-Датты-Лундстрома [Текст] / Ю. А. Кругляк // Nanosystems, Nanomaterials, Nanotechnologies. – 2013. – Т. 11, № 3. – С. 519–549.

26. Кругляк, Ю. А. От баллистической проводимости к диффузионной в транспортной модели Ландауэра-Датты-Лундстрома [Текст] / Ю. А. Кругляк // Nanosystems, Nanomaterials, Nanotechnologies. – 2013. – Т. 11, № 4. – С. 655–677.






Copyright (c) 2014 Юрий Алексеевич Кругляк

Creative Commons License
Эта работа лицензирована Creative Commons Attribution 4.0 International License.

ISSN 2313-8416 (Online), ISSN 2313-6286 (Print)