bottom – up | Bulletin of Odessa State Environmental University

Non-equilibrium Green’s functions method in matrix representation. 2. Model transport problems

Authors: Yu.A. Kruglyak, T.V. Kryzhanovskaya

Pages: 201-209

abstract

Year: 2015

Issue: 19

Title: Non-equilibrium Green’s functions method in matrix representation. 2. Model transport problems

Abstract

Non-equilibrium Green’s functions method is applied to model transport problems for 1D and 2D uniform conductors using the nearest neighbor orthogonal tight-binding approximation in the frame of the «bottom – up» approach of modern nanoelectronics.
First of all we discuss the construction of the contact matrices of self-energies. The basic idea is that infinitely long conductor described by the Hamiltonian [H] is replaced by a conductor of the finite length described by the matrix [H + Σ1 + Σ2] with the open boundary conditions at the ends meaning “good” contacts, which do not create the reflected streams at its ends. Further we discuss 1D ballistic conductor, a 1D conductor with a single scattering center, then 2D conductor is modeling and explanation is given to the steplike dependence of the transmission coefficients over the energy, and finally there is given the representation of 2D/3D conductor in the form of parallel 1D conductors, which is not only physically correct but also extremely useful in interpreting experimental data.
In summary the physical adequacy of the Huckel approach is stated in the framework of the method of nonequilibrium Green’s functions.

Authors: Yu.A. Kruglyak, T.V. Kryzhanovskaya

Pages: 201-209

Tags: 1D conductor; 2D conductor; bottom – up; conductor modeling; molecular electronics; nanoelectronics; nanophysics; NEGF method; quantum transport

bibliography

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Non-Equilibrium Green’s Functions Method in Matrix Presentation. 1. Theoretical Basics

Authors: Kruglyak Yu.A., Kryzhanovskaya T.V.

Pages: 175-192

abstract

Year: 2014

Issue: 18

Title: Non-Equilibrium Green’s Functions Method in Matrix Presentation. 1. Theoretical Basics

Abstract

Non-equilibrium Green’s functions method in matrix presentation is given with application to transport of electrons in quantum regime.

Authors: Kruglyak Yu.A., Kryzhanovskaya T.V.

Pages: 175-192

Tags: bottom – up; molecular electronics; multiple-level resistor; nanoelectronics; nanophysics; NEGF method; one-level resistor

bibliography

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Basics of Spintronics by «bottom – up» approach

Authors: Kruglyak Yu.A.

Pages: 168-195

abstract

Year: 2013

Issue: 16

Title: Basics of Spintronics by «bottom – up» approach

Abstract

Basic topics of spintronics such as spin valve, interface resistance due to mode mismatch, spin potentials, non-local spin voltage, spin moment and its transport, Landau – Lifshitz – Gilbert equation, and explanation on its basis why a magnet has an “easy axis”, nanomagnet dynamics by spin current, polarizers and analyzers of spin current, diffusion equation for ballistic transport and current in terms of non-equllibrium potentials are discussed in the frame of the «bottom – up» approach of modern nanoelectronics.

Authors: Kruglyak Yu.A.

Pages: 168-195

Tags: analyzer; ballistic transport; bottom – up; diffusion equation; magnetization; molecular electronics; nanoelectronics; nanophysics; polarizer; spin current; spin moment; spin potential; spin transport; spin valve; spintronics

bibliography

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Lessons of nanoelectronics. 3. Electronic conductivity and conductivity modes by «bottom – up» approach

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 213-222

abstract

Year: 2013

Issue: 15

Title: Lessons of nanoelectronics. 3. Electronic conductivity and conductivity modes by «bottom – up» approach

Abstract

General questions of electronic conductivity, conductivity modes, n- and p-type conductors and graphene are discussed in the frame of the «bottom – up» approach of modern nanoelectronics

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 213-222

Tags: bottom – up; conductivity modes; electronic conductivity; graphene; molecular electronics; n-type conductor; nanoelectronics; p-type conductor

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Lessons of nanoelectronics. 4. Thermoelectric phenomena in «bottom – up» approach

Authors: Kruglyak Yu.A., Glushkov A.V.

Pages: 223-238

abstract

Year: 2013

Issue: 15

Title: Lessons of nanoelectronics. 4. Thermoelectric phenomena in «bottom – up» approach

Abstract

Thermoelectric phenomena of Seebeck and Peltier, quality indicators and thermoelectric optimization, ballistic and diffusive phonon heat current are discussed in the frame of the «bottom – up» approach of modern nanoelectronics.

Authors: Kruglyak Yu.A., Glushkov A.V.

Pages: 223-238

Tags: bottom – up; molecular electronics; nanoelectronics; nanophysics; Peltier; Seebeck; thermal conductivity; thermoelectric phenomena; thermoelectric. phonon current

bibliography

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Lessons of nanoelectronics. 1. Current generation by bottom – up approach

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 197-206

abstract

Year: 2012

Issue: 14

Title: Lessons of nanoelectronics. 1. Current generation by bottom – up approach

Abstract

Current generation with the use of electrochemical potentials and Fermi functions is discussed in the frame of the bottom – up approach of modern theoretical and applied nanoelectronics.

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 197-206

Tags: bottom – up; electric current; electrochemical potential; Fermi function; molecular electronics; nanoelectronics

bibliography

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Datta Supriyo. Electronic Transport in Mesoscopic Systems.- Cambridge: Cambridge University Press. – 2001. – pp. 377.
Datta Supriyo. Quantum Transport: Atom to Transistor. – Cambridge: Cambridge University Press. – 2005. – pp. 404.
www.nanohub.org/topics/ElectronicsFromTheBottomUp
Landauer Rolf. Spatial variation of currents and fields due to localized scatterers in metallic conduction // IBM J. Res. Dev. – 1957. – V. 1, N 3. – P. 223 – 231.
Landauer Rolf. Electrical resistance of disordered onedimensional lattices // Philos. Mag. – 1970. – V. 21. – P. 863 – 867.
Landauer Rolf. Spatial variation of currents and fields due to localized scatterers in metallic conduction // J. Math. Phys. – 1996. – V. 37, N 10. – P. 5259.
Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. – Hackensack, New Jersey: World Scientific Publishing Company. – 2012. – pp. 340.
Ашкрофт Н., Мермин Н. Физика твердого тела, том 1. – М: Мир. – 1979. – 400 с.
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Kubo R. Statistical-Mechanical Theory of Irreversible Processes.I. General Theory and Simple Applications to Magnetic and Conduction Problems // J.Phys.Soc. Japan. – 1957. – V. 12. – P. 570 – 586.

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Lessons of nanoelectronics. 2. Elastic resistor model and new Ohm’s law by bottom – up approach

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 207-216

abstract

Year: 2012

Issue: 14

Title: Lessons of nanoelectronics. 2. Elastic resistor model and new Ohm’s law by bottom – up approach

Abstract

Elastic resistor model, ballistic and diffusion transport and new formulation of the Ohm’s law are discussed in the frame of the bottom – up approach of modern nanoelectronics.

Authors: Kruglyak Yu.A., Kruglyak N.E.

Pages: 207-216

Tags: bottom – up; conductivity modes; elastic resistor; electric current; molecular electronics; nanoelectronics; Ohm’s law

bibliography

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References

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