DOI: https://doi.org/10.15587/2313-8416.2015.38848

Landauer-Datta-Lundstrom conductivity model in micro- and nanoelectronics and Boltzmann transport equation

Юрій Олексійович Кругляк

Abstract


The role of the Boltzmann transport equation (BTE) in the Landauer-Datta - Lundstrom (LDL) electron and heat transport model is discussed. As the applications of the BTE there are discussed the BTE in the relaxation time approximation and the behavior of electric current in an external magnetic field as well as expression for the surface conductivity well knownintheLDLmodelisdeduced


Keywords


nanophysics; nanoelectronics; Boltzmann equation; relaxation time; surface conductivity; Hall effect; Hall mobility; Hall factor

References


Kruglyak, Yu. A., Strikha, M. V. (2014).Lessons of nanoelectronics: The role of electrostatics and contacts in “bottom – up” approach, Sensor Electronics Microsys. Tech., 11, 4–5.

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

Bol'cman, L. (1984). Izbrannye trudy. Moscow: Mir, 590.

Lundstrom, M. (2000). Fundamentals of Carrier Transport. Cambridge UK: Cambridge University Press, 415. doi: 10.1017/cbo9780511618611

Lundstrom, M., Jeong, C. (2013). Near–Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 227. Available at: www.nanohub.org/resources/11763.

Sears, F. W., Salinger, G. L. (1975). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Boston: Addison–Wesley.

Ziman, J. M. (1964). Principles of the theory of solids, Cambridge University Press, Cambridge, 468.

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

Pikulin, D. I., Hou, C.-Y., Beenakker, C. W. J. (2011). Nernst effect beyond the relaxation-time approximation. Physical Review B, 84 (3). doi: 10.1103/physrevb.84.035133

Kruglyak, Yu. A., Kruglyak, N. E., Strikha, M. V. (2013). Lessons of nanoelectronics: Thermoelectric phenomena in “bottom – up” approach, Sensor Electronics Microsys. Tech., 10, 1–6.

Lundstrom, M. (2011). Electronic Transport in Semiconductors. Available at: www.nanohub.org/resources/11872

Kruglyak, Yu. A. (2015). Thermoelectric phenomena and devices in Landauer-Datta-Lundstrom Conception. ScienceRise, 1/2 (6), 69–77. doi: 10.15587/2313-8416.2015.35891

Kruglyak, Yu. A., Strikha, M. V. (2015). Landauer-Datta-Lundstrom generalized electron transport model for micro– and nanoelectronics. Sensor Electronics Microsys. Tech., 12, 2–5.

Kruglyak, Yu. A. (2015). Accounting for scattering in Landauer – Datta – Lundstrom transport model, ScienceRise, 3/2(8), ??–??. doi: 10.15587/2313-8416.2015.38847

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

Kruglyak, Yu. A., Strikha, M. V. (2014). Lessons of nanoelectronics: Hall effect and measurement of electrochemical potentials in “bottom – up” approach. Sensor Electronics Microsys. Tech., 11 (1), 5–27.

Wolfe, C. M., Holonyak, N., Stillman, G. E. (1989). Physical Properties of Semiconductors. Prentice Hall, Englewood Cliffs, N. Jersey.

Datta Supriyo (2012). Lessons from Nanoelectronics: A New Perspective on Transport. Hackensack, New Jersey: World Scientific Publishing Company, 473. Available at: www.nanohub.org/courses/FoN1


GOST Style Citations


1. Кругляк, Ю. О. Уроки наноелектроніки: Роль електростатики й контактів у концепції "знизу – вгору" [Текст] / Ю. О. Кругляк, М. В. Стріха // Sensor Electronics Microsys. Tech. – 2014. – № 11. – С. 4–5.

2. Kruglyak, Yu. Landauer–Datta–Lundstrom Generalized Transport Model for Nanoelectronics [Text] / Yu. Kruglyak // Journal of Nanoscience. – 2015. – Vol. 2014. – P. 1–15. doi: 10.1155/2014/725420 

3. Больцман, Л. Избранные труды [Текст] / Л. Больцман. – М: Мир, 1984. – 590 с.

4. Lundstrom, M. Fundamentals of Carrier Transport [Text] / M. Lundstrom. – Cambridge UK: Cambridge University Press, 2000. – 415 p. doi: 10.1017/cbo9780511618611 

5. Lundstrom, M., Jeong C. Near–Equilibrium Transport: Fundamentals and Applications [Text] / M. Lundstrom, C. Jeong. – Hackensack, New Jersey: World Scientific Publishing Company, 2013. – 227 p. – Available at: www.nanohub.org/resources/11763

6. Sears, F. W. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics [Text] / F. W. Sears, G. L. Salinger. – Boston: Addison–Wesley, 1975.

7. Займан, Дж. Принципы теории твердого тела [Текст] / Дж. Займан. – М: Высшая школа, 1974.– 468 c.

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

9. Pikulin, D. I. Nernst effect beyong the relaxation–time approximation [Text] / D. I. Pikulin, C.-Y. Hou, C. W. J. Beenakker // Physical Review B. – 2011. – Vol. 84, Issue 3. doi: 10.1103/physrevb.84.035133 

10. Кругляк, Ю. О. Уроки наноелектроніки: Термоелектричні явища в концепції "знизу – вгору" [Текст] / Ю. О. Кругляк, Н. Ю. Кругляк, М. В. Стріха // Sensor Electronics Microsys. Tech. – 2013. – № 10. – С. 1–6.

11. Lundstrom, M. Electronic Transport in Semiconductors [Electronic resource] / M. Lundstrom. – 2011. – Available at: www.nanohub.org/resources/11872

12. Кругляк, Ю. A. Термоэлектрические явления и устройства в концепции Ландауэра-Датты-Лундстрома [Текст] / Ю. A. Кругляк // ScienceRise. – 2015. – Т. 1, № 2 (6). – C. 69–77. doi: 10.15587/2313-8416.2015.35891

13. Кругляк, Ю. О. Обобщенная модель электронного транспорта Ландауэра-Датты-Лундстрома [Текст] / Ю. О. Кругляк, М. В. Стріха // Sensor Electronics Microsys. Tech. – 2015. – № 12. – С. 2–5.

14. Кругляк, Ю. A. Учет рассеяния в транспортной модели Ландауэра-Датты-Лундстрома [Текст] / Ю. A. Кругляк // ScienceRise. – 2015. – Т. 3, № 2 (8). – С. ??–??. doi: 10.15587/2313-8416.2015.38847

15. Jeong, C. On Landauer versus Boltzman 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, Isseu 2. – P. 023707. doi: 10.1063/1.3291120 

16. Кругляк, Ю. О. Уроки наноелектроніки: Ефект Холла і вимірювання електрохімічних потенціалів у концепції "знизу – вгору" [Текст] / Ю. О. Кругляк, М. В. Стріха // Sensor Electronics Microsys. Tech. – 2014. – Т. 11, № 1. – С. 5–27.

17. Wolfe, C. M. Physical Properties of Semiconductors [Text] / C. M. Wolfe, N. Holonyak, G. E. Stillman. – Prentice Hall, Englewood Cliffs, N. Jersey, 1989.

18. Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport [Electronic resource] / Hackensack, New Jersey: World Scientific Publishing Company, 2012. – 473 p. – Available at: www.nanohub.org/courses/FoN1







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