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References
- Kruglyak Yu. А., Kostritskаya L. S. Thermoelectric phenomena and devices in the generalized model of electron transport
- Kruglyak Yu. A., Shtefan N. Z. Heat transfer by phonons in the generalized transport model
- Kruglyak Yu.A., Kryzhanovskaya T.V. Non-equillibrium green’s functions method in matrix represenatation. 4. Quantum interference and dephasing
- Kruglyak Yu.A., Remenyak L.V. Thermoelectric coefficients in generalized electron transport model approach
Papers
In the tutorial review article intended for researchers, university lecturers and students the thermoelectric Seebeck and Peltier phenomena are considered in the framework of a generalized transport model due to R. Landauer, S. Datta, and M. Lundstrom of modern nanoelectronics within the “bottom – up” approach. The Wiedemann – Franz law and Lorenz numbers as well as the four transport coefficients (specific resistivity, Seebeck and Peltier coefficients, and electronic thermal conductivity) are also qualitatively discussed. Referring to a 3D resistor in the diffusion regime the thermoelectric cooler and energy power generator are analyzed with an account of only electrons as real current carriers as well as with artificial but useful electron/hole conception. Coefficient of performance, power factor and figure of merit for thermoelectric devices are introduced and defined. How transport coefficients depend on the properties of electrotermics are also discussed. Qualitative dependence of the Seebeck coefficient and electronic conductivity from the position of the Fermi level relative to the bottom of the conduction band is demonstrated. Maximization of the power factor near the bottom of the conduction band is shown. As the Fermi level approaches to the bottom of the conduction band and then moves up, the Seebeck coefficient decreases. At the same time, the electronic conductivity increases due to the appearance of an increasing number of conductivity modes. Their product is the power factor, which is maximal in the vicinity of the bottom of the conduction band. The position of the maximum for a specific electrotermics is dependent on the band structure of the conductor and the physics of its scattering centers. It is shown why in practice we try by doping the semiconductor to shift the Fermi level closer to the bottom of the conduction band.
- Kruglyak Yu. S. Nanosystems, Nanomaterials, Nanotechnologies, 2013, vol. 11, no. 3, pp. 519 – 549. (In Russian)
- Kruglyak Yu. S. Nanosystems, Nanomaterials, Nanotechnologies, 2013 vol. 11, pp. 655 – 677. (In Russian)
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- Lundstrom M., Jeong. Near-Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 2013. http://www.nanohub.org/resources/11763). (In Russian).
On the basis of Landauer – Datta – Lundstrom transport model the generalized model of heat transfer by phonons is formulated. Similarly to the Fermi window for electron conductivity the concept of the Fermi window for phonon conductivity is introduced and used to obtain the general expression for the lattice thermal conductivity with the quantum of thermoconductance appearing at the very beginning. There are emphasized the similarity and differences in the construction of the theory of electron conductivity and the theory of heat conduction. There are discussed the thermal conductivity of the conductors, the physical sense of proportionality between the thermal conductivity and specific heat capacity at constant volume, the relationship between the transmission coefficient and the mean-free-path, the calculation of the number of phonon modes and density of phonon states, the Debye model of heat conductivity and scattering of phonons, the temperature dependence of the lattice thermal conductivity, the difference between the lattice thermal conductivity and electron conduction, and quantization of thermal conductivity.
In the present review it is emphasized that the concepts used to describe the electron transport can be successfully transferred to the phonon transport. And in both cases the Landauer approach, generalized subsequently by Datta and Lundstrom, allows a quantitative description of transport processes in conductors of any dimension and in all modes of transport from diffusive to ballistic. Lattice thermal conductivity and electronic conductivity are described very similar as far as the shape of corresponding equations. There are, however, two significant differences related to the physics of electron and phonon processes which are also emphasized in the review.
- Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. Hackensack, New Jersey: World Sci-entific Publishing Company, 2012, 473 p. www.nanohub.org/courses/FoN1.
- Lundstrom Mark, Jeong Changwook. Near-Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 2013, 227 p. www.nanohub.org/resources/11763.
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- Kruglyak Yu. A. Nanoelektronika «znyzu – vverkh» [Nanoelectronics “bottom-up”]. Odessa: TES, 2015.
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The following topics are discussed in the frame of the «bottom – up» approach of modern nanoelectronics: a super-brief but hopefully self-containing introduction to the Hamiltonian matrix whose eigenvalues tell us the allowed energy levels in the channel. However, the Hamiltonian describes an isolated channel and we can not talk about the steady-state resistance of an isolated chan-nel without bringing in the contacts and the battery connected across it. Non-equilibrium Green’s functions method in matrix presentation was initially formulated and applied to model transport problems for 1D and 2D conductors using a nearest neighbor orthogonal tight-binding model in the frame of the «bottom – up» approach of modern nanoelectronics. General method to account for electric contacts in Schrödinger equation to solve electron quantum transport problems is given. There are also discussed the elastic and spin dephasing modeling, account for non-coherent processes using Buttiker probe, 1D conductor with two and more scatterers, quantum interference, strong and weak localization, potential drop across scatterers, quantum oscillations in NEGF method without dephasing and with its account under phase and impulse relaxation regimes, destructive and constructive interference effects, four-component description of spin transport with account for dephasing and ending with discussion of quantum nature of classics including spin coherence and pseudo-spin formalism.
- Kruglyak Yu. A. Nanoelectronics “bottom – up”: Non-equilibrium Green function method, model transport prob-lems and quantum interference. Science-Rise, 2015, vol. 9, no. 2 (14), pp. 41–72. (In Russian)
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- Golizadeh-Mojarad R., Datta S. Non-equilibrium Green’s function based model for dephasing in quantum transport. Phys. Rev. B., 2007, vol. 75, no. 8, pp. 081301/1–4.
- Kruglyak Yu. О., Strіkha M. V. Hall effect and measurement of electrochemical potentials within «bottom – up» approach. Sensor Electronics Microsys. Tech., 2014, vol. 11, no. 1, pp. 5–27. (In Ukrainian)
- Datta Supriyo. Lessons from Nanoelectronics: A New Per-spective on Transport. Hackensack, New Jersey: World Sci-entific Publishing Company, 2012. 473 р.
- Kruglyak Yu. O., Kruglyak N. E., Strіkha M. V. Lessons of Nanoelectronics. Spintronics in «Bottom – Up» Approach. Sensor Electronics Microsys. Tech., 2013, vol. 10, no. 2, pp. 5–35. (In Ukrainian)
- Kruglyak Yu. О., Strіkha M. V. Lessons of nanoelectronics: spin transport and quantum spin Hall effect by «bottom – up» approach. Sensor Electronics Microsys. Tech., 2014, vol. 11, no. 2, pp. 5–22. (In Ukrainian)
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- Kruglyak Yu. A. Graphene in the Landauer – Datta – Lund-strom Transport Model. ScienceRise, 2015, vol. 2, no. 2 (7), pp. 93–106. (In Russian)
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- Glushkov A. V., Kruglyak Yu. A. Quasiparticle Lagrange method in theory of atoms and ions. In: Aktual’nye problemy spektroskopii [Actual Problems of Spectroscopy]. Moscow: AS USSR, 1985, p. 291. (In Russian)
- Kruglyak Yu. A., Glushkov A. V. Method of calculation of the chemical bond energies and lengths in a model of qua-sielectrons. Zhurnal fizicheskoy khimii ‒ Journ. of Phys. Chem., 1986, vol. 60, p. 1259. (In Russian)
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General issues of electronic conductivity and the causes for the current flow, role of electro-chemical potentials, Fermi functions, and Fermi window for conduction are discussed, as well as there given detailed description of the Landauer elastic resistor model, different transport regimes from ballistic to diffusion and in between, conductivity modes, and transmission coefficient in the frame of the «bottom – up» approach of modern nanoelectronics. Generalized model of electron transport in the linear response regime developed by R. Landauer, S. Datta, and M. Lundstrom with application to the resistors of any dimension, any size and arbitrary dispersion working in ballistic, quasi-ballistic or diffusion regime is summerized.
In summary, the Landauer equation for the conductivity describes the electron transport in the conductor from the very general positions. The conductivity is proportional to the fundamental constants q and h, which determine the quantum of conductance, associated with contacts. The conductivity depends on the number of modes of conductance and transmission coefficient, representing the probability that an electron with energy E injected by one contact to reach another contact. Conductivity we finally find by integrating the contributions from all modes of conduction. The equations valid for 1D, 2D and 3D conductors for ballistic nanoreactors as well as for massive conductors.
- Kruglyak Yu.O., Kruglyak N.E., Strikha M.V. Lessons of Nanoelectronics: Current generation, Ohm’s Law Formulation and Conduction modes in «Bottom – Up» Approach. Sensor Electronics Microsys. Tech, 2012, vol. 9, no. 4, pp. 5-29 (In Ukrainian)
- Kruglyak Yu. O., Strikha M. V. Generalized model of elec-tron transport in micro- and nanoelectronics. Sensor Elec-tronics Microsys. Tech. 2015, vol. 12, no 3. pp. 4–27. (In Ukrainian)
- Kruglyak Yu.O., Strikha M.V. Thermoelectric phenomena and devices in the Kgeneralized model of electron transport.Sensor Electronics Microsys. Tech. 2015, vol. 12, no. 4. pp. 5–18. (In Ukrainian)
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- Kruglyak Yu.A., Kvakush V.S., Dyadyusha G.G., Khil’chenko V. I. Metody vychisleniya v kvantovoy khimii [Methods of calculations in quantum chemistry]. Kiev: Nauk. Dumka, 1967.
- Glushkov A.V., Kruglyak Yu.A. Quasiparticle Lagrange method in theory of atoms and ions. V kn.: Aktual’nye problemy spektroskopii [In bk: Actual Problems of Spectroscopy]. Moscow: AS USSR, 1985, p. 291. (In Russian)
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- Glushkov A.V. Relativistic and correlation effects in spectra of atomic systems. Odessa: Astroprint, 2006.
- Glushkov A.V., Khetselius O.Y., Svinarenko A. A. Prepe-litsa G. P. Energy approach to atoms in a laser field and quantum dynamics with laser pulses of different shape . In: Coherence and Ultrashort Pulse Laser Emission. Intech, 2010, p. 159. (Ed.: Dr. F. J. Duarte)