Nanoelectronics «bottom – up»: non-equillibrium Green’s functions method, model transport problems and quantum interference
DOI:
https://doi.org/10.15587/2313-8416.2015.48827Keywords:
nanoelectronics, quantum transport, quantum interference, dephasing, NEGF, coherence, spin transportAbstract
Non-equilibrium Green’s functions (NEGF) method in matrix form is presented and applied to model transport problems for 1D and 2D conductors using Huckel approximation in the «bottom – up» approach of modern nanoelectronics. General method to account for electric contacts in Schrödinger equation is given. Elastic and spin dephasing modeling and account for non-coherent processes are also discussed
References
Krugljak, Ju. O., N. Krugljak, Ju., Striha, M. V. (2012). Lessons of nanoelectronics: current generation, Ohm’s law formulation and conduction modes in «bottom–up» approach. Sensor Electronics and Мicrosystem Technologies, 9 (4), 5–29.
Krugljak, Ju. A. (2015). Nanoelectronics «bottom – up»: current generation, generalized ohm’s law, elastic resistors, conductivity modes, thermoelectricity. ScienceRise, 7/2 (12), 76–100. doi: 10.15587/2313-8416.2015.45700
Krugljak, Ju. A. (2015). The «bottom – up» nanoelectronics: elements of spintronics and magnetronics. ScienceRise, 8/2 (13), 51–68. doi: 10.15587/2313-8416.2015.47792
Datta, S. (2012). Lessons from Nanoelectronics. Hackensack, New Jersey: World Scientific Publishing Company, 492. Available at: https://nanohub.org/courses/FoN1 doi: 10.1142/8029
Datta, S., Narlikar, A. V., Fu, Y. Y. (2012). Nanoelectronic devices: A unified view. The Oxford Handbook on Nanoscience and Nanotechnology: Frontiers and Advances. Oxford University Press, 1 (1), 26.
Datta, S. (2005). Quantum Transport: Atom to Transistor, 404. doi: 10.1017/cbo9781139164313
Datta, S. (2008). Nanodevices and Maxwell’s Demon. Lecture Notes in Nanoscale Science and Technology, 2, 59–81. doi: 10.1007/978-0-387-73048-6_7
Caroli, C., Combescot, R., Nozieres, P., Saint-James, D. (1972). A direct calculation of the tunnelling current: IV. Electron-phonon interaction effects. Journal of Physics C: Solid State Physics, 5 (1), 21–42. doi: 10.1088/0022-3719/5/1/006
Kubo, R. (1957). Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. Journal of the Physical Society of Japan, 12 (6), 570–586. doi: 10.1143/jpsj.12.570
Sears, F. W., Salinger, G. L. (1975). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Boston: Addison-Wesley, 331–336, 355–361.
Martin, P. C., Schwinger, J. (1959). Theory of Many-Particle Systems. I. Physical Review, 115 (6), 1342–1373. doi: 10.1103/physrev.115.1342
Kadanoff, L. P., Baym, G. (1962). Quantum Statistical Mechanics. New York: W. A. Benjamin, 203.
Keldysh, L. V. Diagram Technique for Non-Equilibrium Processes [Text] / L. V. Keldysh // JETP. – 1965. – Vol. 20, Issue 4. – P. 1018–1026.
Landauer, R. (1957). Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction. IBM Journal of Research and Development, 1 (3), 223–231. doi: 10.1147/rd.13.0223
Landauer, R. (1970). Electrical resistance of disordered one-dimensional lattices. Philosophical Magazine, 21 (172), 863–867. doi: 10.1080/14786437008238472
Landauer, R. (1996). Spatial variation of currents and fields due to localized scatterers in metallic conduction (and comment). Journal of Mathematical Physics, 37 (10), 5259. doi: 10.1063/1.531590
Datta, S. (1989). Steady-state quantum kinetic equation. Physical Review B, 40 (8), 5830–5833. doi: 10.1103/physrevb.40.5830
Datta, S. (1990). A simple kinetic equation for steady-state quantum transport. Journal of Physics: Condensed Matter, 2 (40), 8023–8052. doi: 10.1088/0953-8984/2/40/004
Meir, Y., Wingreen, N. S. (1992). Landauer formula for the current through an interacting electron region. Physical Review Letters, 68 (16), 2512–2515. doi: 10.1103/physrevlett.68.2512
Datta, S. (2001). Electronic Transport in Mesoscopic Systems. Cambridge: Cambridge University Press, 377.
Smit, R. H. M., Noat, Y., Untiedt, C., Lang, N. D., van Hemert, M. C., van Ruitenbeek, J. M. (2002). Measurement of the conductance of a hydrogen molecule. Nature, 419 (6910), 906–909. doi: 10.1038/nature01103
Buttiker, M. (1988). Symmetry of electrical conduction. IBM Journal of Research and Development, 32 (3), 317–334. doi: 10.1147/rd.323.0317
Anderson, P. W. (1958). Absence of Diffusion in Certain Random Lattices. Physical Review, 109 (5), 1492–1505. doi: 10.1103/physrev.109.1492
Anderson, P. W. (1981). New method for scaling theory of localization. II. Multichannel theory of a “wire” and possible extension to higher dimensionality. Physical Review B, 23 (10), 4828–4836. doi: 10.1103/physrevb.23.4828
Krugljak, Ju. A. (1967). Metody vychislenij v kvantovoj himii. Raschet π-jelektronnoj struktury molekul prostymi metodami molekuljarnyh orbitalej. Kyiv: Naukova dumka, 161.
Kruglyak, Y. A., Ukrainsky, I. I. (1970). Study of the electronic structure of alternant radicals by theDODS method. International Journal of Quantum Chemistry, 4 (1), 57–72. doi: 10.1002/qua.560040106
Kruglyak, Yu. A. (2015). Quantum-chemical studies of quasi-one-dimensional electron systems. 1. Polyenes. ScienceRise, 5/2 (10), 69–105. doi: 10.15587/2313-8416.2015.42643
Kventsel, G. F., Kruglyak, Y. A. (1968). Local electronic states in long polyene chains. Theoretica Chimica Acta, 12 (1), 1–17. doi: 10.1007/bf00527002
Striha, M. V. (2010). Fizyka grafenu : stan i perspektyvy. Sensor Electronics and Microsystem Technologies, 1 (7(3)), 5–13.
Krugljak, Ju. A. (2015). Graphene in Landauer-Datta-Lundstrom transport model. ScienceRise, 2/2 (7), 93–106. doi: 10.15587/2313-8416.2015.36332
Kruglyak, Y. A., Dyadyusha, G. G. (1968). Torsion barriers of end-groups in cumulenes. Theoretica Chimica Acta, 10 (1), 23–32. doi: 10.1007/bf00529040
Kruglyak, Y. A., Dyadyusha, G. G. (1968). Torsion barriers of end-groups in cumulenes. Theoretica Chimica Acta, 12 (1), 18–28. doi: 10.1007/bf00527003
Kruglyak, Yu. A. (2015) Quantum-chemical studies of quasi-one-dimensional electron systems. 2. Cumulenes and origin of the forbidden zone. ScienceRise, 6/2 (11), 122–148. doi: 10.15587/2313-8416.2015.44540
Van Wees, B. J., van Houten, H., Beenakker, C. W. J., Williamson, J. G., Kouwenhoven, L. P., van der Marel, D., Foxon, C. T. (1988). Quantized conductance of point contacts in a two-dimensional electron gas. Physical Review Letters, 60 (9), 848–850. doi: 10.1103/physrevlett.60.848
Wharam, D. A., Thornton, T. J., Newbury, R., Pepper, M., Ahmed, H., Frost, J. E. F. et. al. (1988). One-dimensional transport and the quantisation of the ballistic resistance. Journal of Physics C: Solid State Physics, 21 (8), L209–L214. doi: 10.1088/0022-3719/21/8/002
Golizadeh-Mojarad, R., Zainuddin, A. N. M., Klimeck, G., Datta, S. (2008). Atomistic non-equilibrium Green’s function simulations of Graphene nano-ribbons in the quantum hall regime. Journal of Computational Electronics, 7 (3), 407–410. doi: 10.1007/s10825-008-0190-x
Berger, C., Zhimin, S., Xuebin, L., Xiaosong, W., Brown, N., Naud, C. et. al. (2006). Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science, 312 (5777), 1191–1196. doi: 10.1126/science.1125925
Fujita, M., Wakabayashi, K., Nakada, K., Kusakabe, K. (1996). Peculiar Localized State at Zigzag Graphite Edge. Journal of the Physical Society of Japan, 65 (7), 1920–1923. doi: 10.1143/jpsj.65.1920
Nakada, K., Fujita, M., Dresselhaus, G., Dresselhaus, M. S. (1996). Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Physical Review B, 54 (24), 17954–17961. doi: 10.1103/physrevb.54.17954
Brey, L., Fertig, H. A. (2006). Electronic states of graphene nanoribbons studied with the Dirac equation. Physical Review B, 73 (23), 235411. doi: 10.1103/physrevb.73.235411
Wakabayashi, K., Takane, Y., Yamamoto, M., Sigrist, M. (2009). Electronic transport properties of graphene nanoribbons. New Journal of Physics, 11 (9), 095016. doi: 10.1088/1367-2630/11/9/095016
Koch, M., Ample, F., Joachim, C., Grill, L. (2012). Voltage-dependent conductance of a single graphene nanoribbon. Nature Nanotechnology, 7 (11), 713–717. doi: 10.1038/nnano.2012.169
Buttiker, M. (1986). Four-Terminal Phase-Coherent Conductance. Physical Review Letters, 57 (14), 1761–1764. doi: 10.1103/physrevlett.57.1761
Golizadeh-Mojarad, R., Datta, S. (2007). Nonequilibrium Green’s function based models for dephasing in quantum transport. Physical Review B, 75 (8), 081301(R). doi: 10.1103/physrevb.75.081301
Krugljak, Ju. O., Striha, M. V. (2013). Uroky nanoelektroniky : Efekt Hola i vymirjuvannja elektrohimichnyh potencialiv v koncepcii' «znyzu – vgoru». Sensor Electronics Microsystem Technologies,10 (4), 5–22.
Krugljak, Ju. O., Striha, M. V. (2014). Uroky nanoelektroniky : Transport spiniv v modeli NRFG i kvantovyj spinovyj efekt Hola v koncepcii' «znyzu – vgoru». Sensor Electronics Microsystem Technologies, 11 (1), 5–27.
Weber, B., Mahapatra, S., Ryu, H., Lee, S., Fuhrer, A., Reusch, T. C. G. et. al. (2012). Ohm’s Law Survives to the Atomic Scale, 335 (6064), 64–67. doi: 10.1126/science.1214319
Zurek, W. H. (2003). Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75 (3), 715–775. doi: 10.1103/revmodphys.75.715
nanoHUB-U: Fundamentals of Nanoelectronics, Part 2: Quantum Models. Available at: https://nanohub.org/courses/FoN2
PurdueX. Free online courses from Purdue University. Available at: https://www.edx.org/school/purduex
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