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References
- 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
- Yu.A. Kruglyak, L.V. Remenyak The role of electrostatics and contacts in the «bottom – up» approach of nanoelectronics
- Yu.A. Kruglyak, T.V. Kryzhanovskaya Non-equilibrium Green’s functions method in matrix representation. 2. Model transport problems
- Kruglyak Yu.A., Kryzhanovskaya T.V. Non-Equilibrium Green’s Functions Method in Matrix Presentation. 1. Theoretical Basics
- Kruglyak Yu.A. Basics of Spintronics by «bottom – up» approach
- Kruglyak Yu.A., Kruglyak N.E. Lessons of nanoelectronics. 3. Electronic conductivity and conductivity modes by «bottom – up» approach
- Kruglyak Yu.A., Glushkov A.V. Lessons of nanoelectronics. 4. Thermoelectric phenomena in «bottom – up» approach
- Kruglyak Yu.A., Kruglyak N.E. Lessons of nanoelectronics. 1. Current generation by bottom – up approach
- Kruglyak Yu.A., Kruglyak N.E. Lessons of nanoelectronics. 2. Elastic resistor model and new Ohm’s law by bottom – up approach
- Ю.А. Кругляк, Н.Е. Кругляк Methodical Aspects in Computation of Graphene Band Structure with an Account of σ-Core. Theoretical
- Kruglyak Yu.A., Kruglyak N.E. Single-Electron Single-Molecule Field Transistor: Quantum Mechanical and Electro Dynamical Treatment with Benzene Molecule as an Example
Papers
Authors: Kruglyak Yu.A., Kryzhanovskaya T.V.
Pages: 93-104
abstract
Year: 2017
Issue: 21
Title: Non-equillibrium green’s functions method in matrix represenatation. 4. Quantum interference and dephasing
Abstract
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.
Authors: Kruglyak Yu.A., Kryzhanovskaya T.V.
Pages: 93-104
Tags: coherence; constructive interference; dephasing; destructive interference; impulse relaxation; molecular electronics; nanoelectronics; nanophysics; NEGF method; phase relaxation; pseudospin; quantum interference; spin coherence; spin transport; strong localization; weak localization; деструктивна інтерференція; деструктивна інтерференція; дефазировка; дефазировка; імпульсна релаксація; імпульсна релаксація; квантова інтерференція; квантова інтерференція; когерентність; когерентність; конструктивна інтерференція; конструктивна інтерференція; метод НРФГ; метод НРФГ; нанофизика; нанофизика; наноэлектроника; наноэлектроника; псевдоспин; псевдоспин; сильна локалізація; сильна локалізація; слабка локалізація; слабка локалізація; спинова когерентність; спинова когерентність; транспорт спинів; транспорт спинів; фазова релаксація; фазова релаксація
- 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)
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Authors: Kruglyak Yu.A., Remenyak L.V.
Pages: 105-119
abstract
Year: 2017
Issue: 21
Title: Thermoelectric coefficients in generalized electron transport model approach
Abstract
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.
Authors: Kruglyak Yu.A., Remenyak L.V.
Pages: 105-119
Tags: integrals of the Fermi - Dirac; molecular electronics; nanoelectronics; nanophysics; thermoelectric coefficients; молекулярная электроника; молекулярная электроника; нанофизика; нанофизика; наноэлектроника; наноэлектроника; термоэлектрические; термоэлектрические
- 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)
- Mark Lundstom, Jing Guo. Nanoscale Transistors: Physics, Modeling, and Simulation. Berlin: Springer, 2006.
- Kim R., Lundstrom M. S. Notes on Fermi–Dirac Inte-grals, arXiv:0811.0116. www.nanohub.org/resources/5475
- Lundstrom M., Jeong C. Near-Equilibrium Transport: Fun-damentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 2013, www.nanohub.org/resources/11763.
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- Kruglyak Yu.A., Glushkov A.V., Method of calculation of the chemical bond energies and lengths in a model of quasielectrons. Zhurnal fisicheskoy khimii ‒ Journ. of Phys. Chem., 1986, vol. 60, pp. 1259. (In Russian)
- 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)
Authors: Yu.A. Kruglyak, L.V. Remenyak
Pages: 182-194
abstract
Year: 2015
Issue: 19
Title: The role of electrostatics and contacts in the «bottom – up» approach of nanoelectronics
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.
Authors: Yu.A. Kruglyak, L.V. Remenyak
Pages: 182-194
Tags: diffusion-drift model; molecular electronics; nanoelectronics; nanophysics; role of contacts; saturation current
- 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.
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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
- Kruglyak Yu.A., Kryzhanovskaja T.V. Metod neravnovesnyh funkcij Grina v matrichnom predstavlenii. 1. Teoreticheskie osnovy [Non-equilibrium Green’s functions method in matrix presentation. 1. Theoretical basics]. – Vіsnik Odes’kogo derzh. ekologіchnogo un-tu – Vìsn. Odes. derž. ekol. unìv., 2014, no 19, pp. 175 – 192.
- Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. Hackensack, New Jersey: World Scientific Publishing Company, 2012, 474 p.; www.nanohub.org/courses/FoN2.
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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
- Кругляк Ю.О., Кругляк Н.Ю., Стріха М.В. Уроки наноелектроніки: виникнення струму, формулювання закону Ома і моди провідності в концепції «знизу – вгору» // Sensor Electronics and Microsystem Technologies. – 2012. – V. 9, N 4. – P. 5 – 29.
- Кругляк Ю.О., Кругляк Н.Ю., Стріха М.В. Уроки наноелектроніки: термоелектричні явища в концепції «знизу – вгору» // Sensor Electronics and Microsystem Technologies. – 2013. – V. 10, N 1. – P. 6 – 21.
- Кругляк Ю.О., Кругляк Н.Ю., Стріха М.В. Уроки наноелектроніки: Спінтроніка в концепції «знизу – вгору» // Sensor Electronics and Microsystem Technologies. – 2013. – V. 10, N 2. – P. 5 – 25.
- Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. – Hackensack, New Jersey: World Scientific Publishing Company. – 2012. – pp. 474; www.nanohub.org/courses/FoN1, www.nanohub.org/courses/FoN2.
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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
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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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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
- Кругляк Ю.О., Кругляк Н.Ю., Стріха М.В. Уроки наноелектроніки: виникнення струму, формулювання закону Ома і моди провідності в концепції «знизу – вгору» // Sensor Electronics and Microsystem Technologies. – 2012. – V. 3(9), N 4. – P. 5 – 29.
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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
- Mitin Vladimir V., Kochelap Viatcheslav A., Stroscio Michael A. Introduction to Nanoelectronics: Science, Nanotechnology, Engineering, and Applications. – Cambridge: Cambridge University Press. – 2012. – pp. 346.
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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.
- Sears F.W., Salinger G.L. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. – Boston: Addison-Wesley. – 1975. – pp. 331 – 336, 355 – 361.
- 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.
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
- Кругляк Ю.А., Кругляк Н.Е. Уроки наноэлектроники. 1. Причины возникновения тока в концепции «cнизу–вверх» // Вісник Одеського держ. екологічного ун-ту.- 2012, В. 14.- С. 197 – 206.
- 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.
- Mitin Vladimir V., Kochelap Viatcheslav A., Stroscio Michael A. Introduction to Nanoelectronics: Science, Nanotechnology, Engineering, and Applications. – Cambridge: Cambridge University Press. – 2012. – pp. 346.
- Мартинес-Дуарт Дж.М., Мартин-Палма Р.Дж., Агулло-Руеда Ф. Нанотехнологии для микро- и оптоэлектроники. – Москва: Техносфера. – 2007. –368 с.
- 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
- Datta Supriyo. Lessons from Nanoelectronics: A New Perspective on Transport. – Hackensack, New Jersey: World Scientific Publishing Company. – 2012. – pp. 340.
- Мартинес-Дуарт Дж.М., Мартин-Палма Р.Дж., Агулло-Руеда Ф. Нанотехнологии для микро- и оптоэлектроники. – Москва: Техносфера. – 2007. –368 с.
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Authors: Ю.А. Кругляк, Н.Е. Кругляк
Pages: 207-218
abstract
Year: 2012
Issue: 13
Title: Methodical Aspects in Computation of Graphene Band Structure with an Account of σ-Core. Theoretical
Abstract
Theoretical basis to compute graphene band structure and density of states in the simplest π–electronic approximation with derivation of the Dirac – Weyl equantions are given including results with an account for π–π–overlap and neighbours up to 3rd order. The necessity of accounting for graphene σ-core is stated. DFT/LDA, GGA and EHT-SCF approaches are shortly described. Corresponding computational observations including ab initio results are given in the next communication.
Authors: Ю.А. Кругляк, Н.Е. Кругляк
Pages: 207-218
Tags: band structure; density of states; DFT; EHT-SCF; GGA; graphene; LDA; molecular electronics; nanophysics
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Authors: Kruglyak Yu.A., Kruglyak N.E.
Pages: 201-214
abstract
Year: 2011
Issue: 12
Title: Single-Electron Single-Molecule Field Transistor: Quantum Mechanical and Electro Dynamical Treatment with Benzene Molecule as an Example
Abstract
The first-principle methods for calculating the charging molecular energies and charge stability diagram of the benzene molecule single-electron transistor under the Coulomb blockade regime were applied using the densityfunctional theory for modeling molecular properties and continuum model to describe SET environment as well as a self-consistent approach to treat the interaction between the molecule and the SET environment.
Authors: Kruglyak Yu.A., Kruglyak N.E.
Pages: 201-214
Tags: benzene; Coulomb blockade; DFT; molecular electronics; MS-SET; SET
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