{{{ #!html
}}} [[Image(/site/media/images/negf.gif, class=align-left nolink)]] The non-equilibrium Greens function (NEGF) formalism provides a powerful conceptual and computational framework for treating quantum transport in nanodevices. It goes beyond the Landauer approach for ballistic, non-interacting electronics to include inelastic scattering and strong correlation effects at an atomistic level. Learn more about the NEGF approach from the resources available on this site, listed below. {{{ #!html
}}} ==== Tutorial Papers ==== * S. Datta, "Nanoscale Device Simulation: The Green's Function Method," [http://dx.doi.org/10.1006/spmi.2000.0920 Superlattices and Microstructures, ''28'', 253-278 (2000)]. * S. Datta, "Non-Equilibrium Green's Function (NEGF) Formalism: An elementary Introduction," ''Proceedings of the International Electron Devices Meeting (IEDM),'' [http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=1175935 IEEE Press (2002)]. [http://cobweb.ecn.purdue.edu/~datta/negf1.htm (preprint)][[span(-, style=color:red)]] * S. Datta, "Electrical resistance: an atomic view," [http://www.iop.org/EJ/abstract/0957-4484/15/7/051 ''Nanotechnology,'' '''15''', S433-S451 (2004)]. [/resources/1919/ (preprint)] * M. P. Anantram, M. S. Lundstrom and D. E. Nikonov, "Modeling of Nanoscasle Devices," [http://arxiv.org/abs/cond-mat/0610247v2 http://arxiv.org/abs/cond-mat/0610247v2 (2007)]. [/resources/1902/ (preprint)][[Span(-, style=color:red)]] * M. Paulsson, "Non Equilibrium Green's Functions for Dummies: Introduction to the One Particle NEGF equations," [http://arxiv.org/abs/cond-mat/0210519 arXiv.org cond-mat/0610247 (2002)]. [/resources/1932/ (preprint)][[Span(-, style=color:red)]] * E. Polizzi, and S. Datta, "Multidimensional Nanoscale device modeling: the Finite Element Method applied to the Non-Equilibrium Green's Function formalism," [http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=1231709 ''IEEE-NANO 2003. Third IEEE Conference on Nanotechnology,'' '''2''', 40-43 (2003)]. [/resources/1935/ (preprint)][[Span(-, style=color:red)]] * A. P. Jauho, "Introduction to the Keldysh nonequilibrium Green function technique," [/resources/1877 (online copy)][[Span(-, style=color:red)]] ==== Online Seminars ==== * Datta: [[Resource(2039)]] (4 part lecture) * Datta: [[Resource(385)]] * Klimeck: [[Resource(178)]] * Klimeck: [[Resource(165)]] * Lundstrom: [[Resource(934)]] ==== Simulators ==== * [[Resource(rtdnegf)]]:Compute charge and current through a resonant tunneling diode and multi-barrier heterostructures in a single band effective mass approximation. * [[Resource(nanomos)]]: 2-D simulator for thin body (< 5 nm), fully depleted, double-gated n-MOSFETs. * [[Resource(nanowire)]]: Simulate electron transport in 3D through nanowires in the effective mass approximation subject to 3D Poisson solution * [[Resource(2704)]]: 3D Simulator for Silicon Nanowire Field Effect Transistors with Multiple Gates ==== Research Publications ==== '''''NEGF simulation of semiconductor devices at the tight binding or Huckel level:''''' * Gerhard Klimeck, Roger K. Lake, R. Chris Bowen, William R. Frensley and Ted Moise,, "Quantum Device Simulation with a Generalized Tunneling Formula," [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000067000017002539000001&idtype=cvips&gifs=yes ''Appl. Phys. Lett.,'' '''67''', 2539, 1995]. * R. C. Bowen, G. Klimeck, R. Lake, W. R. Frensley and T. Moise,, "Quantitative Resonant Tunneling Diode Simulation," [http://link.aip.org/link/?JAPIAU/81/3207/1 ''J. Appl. Phys.,'' '''81''', 3207, 1997]. * R. Lake, G. Klimeck, R. C. Bowen and D. Jovanovic, "Single and multiband modeling of quantum electron transport through layered semiconductor devices," [http://link.aip.org/link/?JAPIAU/81/7845/1 ''J. Appl. Phys.,'' '''81''', 7845, 1997]. * J. Guo, S. Datta, M.S. Lundstrom and M.P. Anantram, "Towards Multiscale Modeling of Carbon Nanotube Transistors," [http://arxiv.org/abs/cond-mat/0312551 ''International J. on Multiscale Computational Engineering,'' special issue on multiscale methods for emerging technologies, ed. N. Aluru, '''2''', 257-276, 2004]. [/resources/1818/ (preprint)] ''(a treatment of carbon nanotube transistors by a pz orbital, tight-binding method)''[[Span(-, style=color:red)]] * M. Paulsson, F. Zahid, and S. Datta, "Resistance of a Molecule," chapter in ''Handbook of Nanotechnology,'' ed. S. Lyshevski, [http://www.crcpress.com/shopping_cart/products/product_detail.asp?sku=1200CRC Press, 2002, ISBN: 0-849312000]. [/resources/123 (preprint)] ''(Huckel approach for molecules)''[[Span(-, style=color:red)]] * F. Zahid, M. Paulsson, and S. Datta, "Electrical Conduction in Molecules," chapter in ''Advanced Semiconductors and Organic Nano-Techniques,'' ed. H. Morkoc, [http://www.elsevier.com/wps/product/cws_home/680682 Academic Press, 2003, ISBN: 0-12-507060-8]. [/resources/124 (preprint)] ''(Huckel approach for molecules)''[[Span(-, style=color:red)]] '''''NEGF simulation of nanoscale transistor at the effective mass level:''''' * Z. Ren, R. Venugopal, S. Goasguen, S. Datta and M. S. Lundstrom, "nanoMOS 2.5: A Two-Dimensional Simulator for Quantum Transport in Double-Gate MOSFETs," [http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=1224493 ''IEEE Trans. Electron. Dev.,'' special issue on Nanoelectronics, '''50''', 1914-1925, 2003]. [/resources/1875 (preprint)][[Span(-, style=color:red)]] * R. Venugopal, Z. Ren, S. Datta, and M. S. Lundstrom, "Simulating Quantum Transport in Nanoscale Transistors: Real versus Mode-Space Approach," [http://link.aip.org/link/?JAPIAU/92/3730/1 ''J. Appl. Phys.,'' '''92''', 3730-3739, 2002]. [/resources/1835 (preprint)][[Span(-, style=color:red)]] * R. Venugopal, S. Goasguen, S. Datta, and M. S. Lundstrom, "A Quantum Mechanical Analysis of Channel Access, Geometry and Series Resistance in Nanoscale Transistors," [http://jap.aip.org/jap/top.jsp?vol=95&pg=292 ''J. Appl. Phys.,'' '''95''', 292-305, 2004]. [/resources/1900/ (preprint)][[Span(-, style=color:red)]] * J. Wang, E. Polizzi, and M. S. Lundstrom, "A Three-Dimensional Quantum Simulation of Silicon Nanowire Transistors with the Effective Mass Approximation," [http://link.aip.org/link/?JAPIAU/96/2192/1 ''J. Appl. Phys.,'' '''96''', 2192, 2004]. [/resources/1926/ (preprint)][[Span(-, style=color:red)]] '''''NEGF simulation at the ab initio level''''' * P.S. Damle, A.W. Ghosh, and S. Datta, "Nanoscale Device Modeling," chapter I in ''Molecular Nanoelectronics,'' ed. M. Reed and T. Lee, [http://www.aspbs.com/molecularnano.htmlAmerican Scientific Publishers, 2003, ISBN: 1-58883-006-3]. * P.S. Damle, A.W. Ghosh, and S. Datta, "First-principles Analysis of Molecular Conduction Using Quantum Chemistry Software," [http://dx.doi.org/10.1016/S0301-0104(02)00496-2 ''Chem. Phys.,'' '''281''', 171-188, 2002]. * P.S. Damle, A.W. Ghosh, and S. Datta, "Unified Description of Molecular Conduction: From Molecules to Metallic Wires," [http://link.aps.org/abstract/PRB/v64/e201403 ''Phys. Rev. B,'' '''64''', Rapid Communication, 201403-1-201403-4, 2001]. '''''NEGF in Phonon Transport''''' * N. Mingo and Y. Liu, "Phonon Transport in Amorphous-Coated Nanowires: an Atomistic Green Function Approach," [http://link.aps.org/abstract/PRB/v68/e245406 ''Phys. Rev. B,'' '''70''', 249901, 2004]. ==== Related Ph.D. Theses ==== * Roger Lake, "Application of the Keldysh Formalism to Quantum Device Modeling and Analysis", Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI9301332/ Purdue University, 1992]. [/resources/3833/ (online copy)][[Span(-, style=color:red)]] * Gerhard Klimeck, "Electron-Phonon and Electron-Electron Interactions in Quantum Transport" Purdue University, 1994. [/resources/3831/ (online copy)][[Span(-, style=color:red)]] * Zhibin Ren, "Nanoscale MOSFETs: Physics, Simulation, and Design," Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI3075713/ Purdue University, December 2001]. [/resources/1917/ (online copy)][[Span(-, style=color:red)]] * Prashant Damle, "Nanoscale Device Modeling: From MOSFETs to Molecules," Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI3108335/ Purdue University, May 2003.]. [/resources/1816/">(online copy)][[Span(-, style=color:red)]] * Ramesh Venugopal, "Modeling Quantum Transport in Nanoscale Transistors," Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI3113884/ Purdue University, August 2003]. [/resources/1930/">(online copy)][[Span(-, style=color:red)]] * Jing Guo, "Carbon Nanotube Electronics: Modeling and Physics," Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI3154636/ Purdue University, August 2004]. [/resources/1928/">(online copy)][[Span(-, style=color:red)]] * Jing Wang, "Device Physics and Simulation of Silicon Nanowire Transistors," Ph.D. Thesis, [http://docs.lib.purdue.edu/dissertations/AAI3185687/ Purdue University, August 2005]. [/resources/1833/ (online copy)][[Span(-, style=color:red)]] * M. Luisier, "Quantum Transport for Nanostructures," (2005) [/resources/1792 (preliminary technical report)][[Span(-, style=color:red)]] ==== Online Classes ==== * Datta: [[Resource(1490)]] * Datta: [[Resource(626)]] ==== Downloads ==== * Datta: [[Resource(103)]] * Koswatta/Nikonov: [[Resources(1989)]] (Matlab) * Nikonov: Scripts for "[[Resource(1983)]]" * [[Resource(110)]] ==== Standard References ==== Most device simulation is based on models that neglect interactions or at best treat them to first order, for which simple treatments are adequate. But here are a few standard references and review articles on the NEGF formalism all of which are based on the use of advanced concepts like the “Keldysh contour”, which are needed for a systematic treatment of higher order interactions. '''''Infinite homogeneous media:''''' * Martin, P. C. and Schwinger, J., "Theory of many-particle systems," [http://link.aps.org/doi/10.1103/PhysRev.115.1342 ''Phys. Rev.'' '''115''', 1342, 1959]. * Kadanoff, L. P. and Baym, G., ''Quantum Statistical Mechanics,'' Frontiers in Physics Lecture Note Series, WA Benjamin, New York, 1962, now published by [http://www.perseusbooksgroup.com/westview/book_toc.jsp?isbn=020141046X Perseus Books, ISBN: 020141046X] * Keldysh, L. V., "Diagram technique for non-equilibrium processes," Sov. Phys. JETP, 20, 1018, 1965. * Danielewicz, P., "Quantum theory of non-equilibrium processes," Ann. Phys., 152, 239, 1984. * Rammer, J. and Smith, H., "Quantum field-theoretical methods in transport theory of metals," [http://link.aps.org/doi/10.1103/RevModPhys.58.323 ''Rev. Mod. Phys.,'' '''58''', 323, 1986]. * Mahan, G. D., "Quantum transport equation for electric and magnetic fields," [http://dx.doi.org/10.1016/0370-1573(87)90004-4 ''Phys. Rep,'' '''145''', 251, 1987]. * Khan, F. S., Davies, J. H. and Wilkins, J. W., "Quantum transport equations for high electric fields," [http://link.aps.org/doi/10.1103/PhysRevB.36.2578 ''Phys. Rev. B,'' '''36''', 2578, 1987]. '''''Finite structures:''''' Many authors have applied the NEGF formalism to problems involving finite structures. * E.V. Anda and F. Flore, "The role of inelastic scattering in resonant tunneling heterostructures," [http://www.iop.org/EJ/abstract/0953-8984/3/46/010 ''J. Phys. Cond. Matt.,'' '''3''', 9087, 1991]. * C. Caroli, R. Combescot, P. Nozieres and D. Saint-James, "A direct calculation of the tunneling current: IV. Electron-phonon interaction effects," [http://www.iop.org/EJ/abstract/0022-3719/5/1/006 ''J. Phys. C: Solid State Physics,'' '''5''', 21, 1972]. * Y. Meir and N.S. Wingreen, "Landauer Formula for the Current through an Interaction Electron Region," [http://link.aps.org/abstract/PRL/v68/p2512 ''Phys. Rev. Lett.,'' '''68''', 2512, 1992]. * S. Datta, "A simple kinetic equation for steady-state quantum transport," [http://www.iop.org/EJ/abstract/0953-8984/2/40/004 ''J. Phys. Cond. Matt.,'' '''2''', 8023, 1990]. * A.P. Jauho, N.S. Wingreen and Y. Meir, "Time-dependent transport in interacting and non-interacting resonant tunneling systems," [http://link.aps.org/doi/10.1103/PhysRevB.50.5528 ''Phys. Rev. B,'' '''50''', 5528, 1994]. * H. Haug and A.P. Jauho, ''Quantum Kinetics in Transport and Optics of Semiconductors,'' Springer, Berlin, 1996, ISBN: 3540616020 ==== Additional nanoHUB Resources ==== * [/resources/?tag=negf Search for all NEGF related content]