**Authors: **Yu.A. Kruglyak, L.V. Remenyak

**Year: **2015

**Issue: **19

**Pages: **182-194

**Abstract**

The theory of electrical conduction is developed in the framework of the “bottom – up” approach without invoking the concept of an external electric field generated by a potential difference applied to the conductor. Within the concept of «bottom – up» approach of modern nanoelectronics the diffusion-drift model of a current on the basis of the Boltzmann transport equation is described. There are also discussed the role of the external electric field beyond the linear response regime, field-effect transistor and saturation current, the role of conductor charging, the point and extended models of a conductor, the role of contacts, the model of p-n junctions, the generation of a current in a conductor with asymmetric contacts.

In summary, we conclude, that when a band structure is given, number of modes can be evaluated and, if a model for the mean-free-pass for backscattering can be chosen, then the near-equilibrium transport coefficients can be evaluated. Next, the new generalized Ohm’s law was formulated and used which provides a quite different view of resistivity in terms of the number of modes per unit area and the mean-free-path. Finally, the transport model given is equally well applied either to nanoresistors or as well to micro- and macroconductors made of any kind of materials.

**Tags: **diffusion-drift model; molecular electronics; nanoelectronics; nanophysics; role of contacts; saturation current

**Bibliography**

- Kruglyak Yu.A., Kruglyak N.E., Strikha M.V. Uroky nanoelektroniky. vynyknennya strumu, formulyuvannya zakonu Oma i mody providnosti v kontseptsiyi «znyzu – vhoru» [Lessons of Nanoelectronics: Current generation, Ohm’s Law Formulation and Conduction modes in «Bottom – Up» Ap-proach]. Sensor Electronics Microsys. Tech., 2012, vol.9, no.4, pp. 5-30.
- Kruglyak Yu.A., Kruglyak N.E., Strikha M.V. Uroky nanoelektroniky. Spintronika v kontseptsiyi «znyzu – vhoru» [Lessons of Nanoelectronics: Spintronics in «Bottom – Up» Approach]. Sensor Electronics Microsys. Tech., 2013, vol.10, no.2. pp. 5-37.
- Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. – Hackensack, New Jersey: World Scientific Publishing Company, 2012, pp. 473; www.nanohub.org/courses/FoN1.
- Einstein A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Physikб, 1905, vol.322, no.8, pp. 549-560.
- Lindsay Stuart. Introduction to Nanoscience. – Oxford, Eng-land: Oxford University Press, 2009, 472 p.
- Ashcroft N.W., Mermin N.D. Fyzyka tverdoho tela, toma 1 y 2 [Solid State Physics]. Moscow, Mir, 1979.
- Kruglyak Yu.A., Kruglyak N.E., Strikha M.V. Uroky nanoelektroniky. Efekt Khola i vymiryuvannya elektrokhimichnykh potentsialiv v kontseptsiyi «znyzu – vhoru» [Lessons of Nanoelectronics: The Hall Effect and Measurement of Electrochemical Potentials by «Bottom – Up» Approach]. Sensor Electronics Microsys. Tech., 2014, vol.11, no.1, pp. 5-27.
- Sears F.W., Salinger G.L. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Boston: Addison-Wesley, 1975.
- Kruglyak Yu.A., Hrafen v transportnoy modely Landauэra – Dattы – Lundstroma [Graphene in the Landauer – Datta – Lundstrom Transport Model]. ScienceRise, 2015, Т.2: no.2(7), pp. 93-106.
- Kruglyak Yu.A., Kruglyak N.E. Metodicheskie aspekty rascheta zonnoy struktury grafena s uchetom σ–ostova. Teoreticheskie osnovy [Methodical Aspects in Computation of Graphene Band Structure with an Account of ?-Core. Theoretical Basis]. Visnyk Odes’koho derzhavnoho ekolohichnoho universytetu – Vìsn. Odes. derž. ekol. unìv., 2012, vol.13, pp. 207-218.
- Rabiu M., Mensah S.Y., Abukari S.S. General Scattering Mechanism and Transport in Graphene. Graphene, 2013, vol.2, no.1, pp. 49-54.
- Bode N., Mariani E., von Oppen F. Transport properties of graphene functionalized with molecular switches. J. Phys.: Condens. Matter, 2012, vol.24. pp. 394017/1-10.
- Dong H.M., Xu W., Peeters F.M. High-field transport properties of graphene. J. Appl. Phys, 2011, vol.110, pp. 063704/1-6.
- Chauhan J., Guo Jing. Inelastic Phonon Scattering in Graphene FETs. IEEE Trans. Electron Dev, 2011,vol.58, no.11, pp. 3997-4003.
- Peres N.M.R. The transport properties of graphene. An introduction. Rev. Mod. Phys., 2010, vol.82, no.3, pp. 2673-2700.
- Barreiro A., Lazzeri M., Moser J., Mauri F., Bachtold A. Transport properties of graphene in the high-current limit. Phys. Rev. Lett., 2009, vol.103, pp. 076601/1- 4.
- Ludwig Boltzmann. Izbrannye trudy [Selected Works]. Moscow: Mir, 1984, 590 p.
- Salahuddin S., Lundstrom M., Datta S. Transport Effects on Signal Propagation in Quantum Wires. IEEE Trans. Electron Dev., 2005, vol.52, no.8, pp. 1734-1742.
- Kruglyak Yu.A., Kruglyak N.E., Strikha M.V. Uroky nanoelektroniky: Termoelektrychni yavyshcha v kontseptsiyi «znyzu – vhoru» [Lessons of Nanoelectronics: Thermoelectric Phenomena in «Bottom – Up» Approach]. Sensor Electronics Microsys. Tech, 2013, vol.10, no.1, pp. 6-21.
- Rahman A., Guo Jing, Datta S., Lundstrom M. Theory of Ballistic Nanotransistors. IEEE Trans. Electron Dev., 2003, vol.50, no.9, pp. 1853-1864.
- Pierret Robert F. Semiconductor Device Fundamentals. – Reading. MA: Addison–Wesley, 1996, 791 p.