DOI: https://doi.org/10.15587/2313-8416.2015.38847

Accounting for scattering in the Landauer-Datta-Lundstrom transport model

Юрій Олексійович Кругляк

Abstract


Scattering of carriers in the LDL transport model during the changes of the scattering times in the collision processes is considered qualitatively. The basic relationship between the transmission coefficient T and the average mean free path  is derived for 1D conductor. As an example, the experimental data for Si MOSFET are analyzed with the use of various models of reliability.


Keywords


nanophysics; nanoelectronics; electron scattering; phonon scattering; transmission coefficient; mean free path; diffusion coefficient; mobility; Si MOSFET

References


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

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

Kruglyak, Yu. A. (2013). The Generalized Landauer – Datta – Lunstrom Electron Transport Model. Nanosystems, Nanomaterials, Nanotechnologies, 11 (3), 519–549. Erratum: ibid, (2014). 12 (2), 415.

Kruglyak, Yu. A. Heat transfer by phonons in Landauer-Datta-Lunstrom transport model, ScienceRise. – 2015. – Т. 2, № 2 (7). – С. 81–93. doi: 10.15587/2313-8416.2015.36332

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

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

Dirac, P. A. M. (1927). The Quantum Theory of the Emission and Absorption of Radiation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 114 (767), 243–265. doi: 10.1098/rspa.1927.0039

Fermi, E. (1950). Nuclear Physics. University of Chicago Press.

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

Shockley, W. (1962). Diffusion and Drift of Minority Carriers in Semiconductors for Comparable Capture and Scattering Mean Free Paths. Physical Review, 125 (5), 1570–1576. doi: 10.1103/physrev.125.1570

Jeong, C., Antoniadis, D. A., Lundstrom, M. S. (2009). On Backscattering and Mobility in Nanoscale Silicon MOSFETs. IEEE Transactions on Electron Devices, 56 (11), 2762–2769. doi: 10.1109/ted.2009.2030844

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

Lundstrom, M. (2008). ECE 612: Nanoscale Transistors. Lecture 4. Polysilicon Gates. QM Effects. Available at: www.nanohub.org/resourses/5364

Taur, Y., Ning, T. (2009). Fundamentals of Modern VLSI Devices, 2nd Ed., Cambridge univ. Press, Cambridge, UK.

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

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


GOST Style Citations


1. 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

2. Lundstrom, M. Near-Equilibrium Transport: Fundamentals and Applications [Electronic resource] / M. Lundstrom, J. Changwook. – Hackensack, New Jersey: World Scientific Publishing Company, 2013. – 227 p. – Available at: www.nanohub.org/resources/11763

3. Kruglyak, Yu. A. Обобщенная модель электронного транспорта Ландауэра-Датты-Лундстрома [Текст] / Yu. A. Kruglyak // Nanosystems, Nanomaterials, Nanotechnologies. – 2013. – Vol. 11, Issue 3. – P. 519–549. Erratum: ibid, 2014. – Vol. 12, Issue 2. – P. 415.

4. Кругляк, Ю. А. Перенос тепла фононами в транспортной модели Ландауэра-Датты-Лундстрома [Текст] / Ю. А. Кругляк // ScienceRise. – 2015. – Т. 2, № 2 (7). – С. 81–93. doi: 10.15587/2313-8416.2015.36332

5. 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 

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

7. Lundstrom, M. Fundamentals of Carrier Transport, 2nd Ed. [Text] / M. Lundstrom. – Cambridge: Cambridge Univ. Press, 2000. – 418 p. doi: 10.1017/cbo9780511618611 

8. Dirac, P. A. M. The Quantum Theory of Emission and Absorption of Radiation [Text] / P. A. M. Dirac // Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. – 1927. – Vol. 114, Issue 767. – P. 243–265. doi: 10.1098/rspa.1927.0039 

9. Fermi, E. Nuclear Physics [Text] / E. Fermi. – University of Chicago Press, 1950

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. 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.

12. Shockley, W. Diffusion and Drift of Minority Carriers in Semiconductors for Comparable Capture and Scattering Mean Free Paths [Text] / W. Shockley // Physical Review. – 1962. – Vol. 125, Issue 5. – P. 1570–1576. doi: 10.1103/physrev.125.1570 

13. Jeong, C. On backscattering and mobility in nanoscale silicon MOSFETs [Text] / C. Jeong, D. A. Antoniadis, M. S. Lundstrom // IEEE Trans. Electron Dev. – 2009. – Vol. 56, Issue 11. – P. 2762–2769. doi: 10.1109/ted.2009.2030844 

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

15. Lundstrom, M. ECE 612: Nanoscale Transistors. Lecture 4 [Electronic resource] / M. Lundstrom. – Polysilicon Gates/QM Effects, 2008. – Available at: www.nanohub.org/resourses/5364

16. Taur, Y. Fundamentals of Modern VLSI Devices, 2nd Ed. [Text] / Y. Taur, T. Ning. – Cambridge univ. Press, Cambridge, UK, 2009.

17. 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

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







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