Abstract
This chapter opens with a presentation of the classical Drude theory of electrical conduction and a theory proposed by Landauer. Based on the assumption that electrical conduction can be modeled as transfer of electrons between two electron reservoirs, the Landauer theory proves to describe particularly well the electrical resistance in nanoscale conductors, i.e., in nanostructures. Surprisingly, this theory implies that the conductance (and resistance) of a nanostructure is independent of its material and temperature, and only depends on the dimensions of the sample, changing in a stepwise manner with a step of h/2e2 representing the conductance quantum. The quantization of electrical and thermal conductance in nanostructures has been verified experimentally. Conductance quantization in nanostructures is used in the analysis of large-scale integration circuits, as required by the currently used 14 nm technology and future technologies.
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References
N. Agrait, G. Rubio, S. Vieira, Plastic deformation of nanometer-scale gold connective necks. Phys. Rev. Lett. 74, 3995–3998 (1995)
N.W. Ashcroft, N.D. Mermin, Solid State Physics (Hartcourt College Publisher, Orlando, 1976)
J.L. Costa-Krämer et al., Nanowire formation in macroscopic metallic contacts: quantum mechanical conductance tapping a table top. Surf. Sci. 342, L1144–L1149 (1995)
M.P. Das, F. Geen, Landauer formula without Landauer’s assumptions. J. Phys. Condens. Matter 14, L687 (2003)
T.S. Fisher, Thermal Energy at the Nanoscale (World Scientific, New Jersey-London, 2014)
J.K. Gimzewski, R. Möller, Transition from the tunneling regime to point contact studied using STM. Phys. Rev. B 36, 1284–1287 (1987)
A. Greiner, L. Reggiani, T. Kuhn, L. Varani, Thermal conductivity and lorenz number for onedimensional ballistic transport. Phys. Rev. Lett. 78, 1114–1117 (1997)
K. Hansen et al., Quantized conductance in relays. Phys. Rev. B 56, 2208–2220 (1997)
H. Ibach, H. Lüth, Solid-State Physics. An Introduction to Principles of Materials Science (Springer, Heidelberg, 1995)
A. Kamenec, W. Kohn, Landauer conductance without two chemical potentials. Phys. Rev. B 63, 155304 (2001)
R. Landauer, Spatial variation of currents and fields due to localized scatters in metallic conduction. IBM J. Res. Dev. 1, 223–231 (1957)
R. Landauer, Conductance determined by transmission: probes and quantised constriction resistance. J. Phys. Condens. Matter 1, 8099–8110 (1989)
C.J. Muller et al., Qunatization effects in the conductance of metallic contacts at room temperature. Phys. Rev. B 53, 1022–1025 (1996)
W. Nawrocki, M. Wawrzyniak, J. Pajakowski, Transient states in electrical circuits with a nanowire. J. Nanosci. Nanotechnol. 9, 1350–1353 (2009)
F. Ott, J. Lunney, Quantum conduction: a step-by-step guide. Europhys. News 29, 13–15 (1998)
L.G.C. Rego, G. Kirczenow, Qunatized thermal conductance of dielectric quantum wire. Phys. Rev. Lett. 81, 232–235 (1998)
K. Schwab, E.A. Henriksen, J.M. Worlock, M.L. Roukes, Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000)
Y.V. Sharvin, A possible method for studying Fermi surface. J. Exper. Theoret. Phys. 21, 655–656 (1965)
P. Středa, Quantised thermopower of a channel in the ballistic regime. J. Phys. Condens. Matter 1, 1025–1028 (1989)
The International Technology Roadmap for Semiconductors. Internet site (2013)
van Wees et al., Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848–850 (1988)
B.J. van Wees et al., Quantum ballistic and adiabatic electron transport studied with quantum point contacts. Phys. Rev. B 43, 12431–12453 (1991)
M. Wawrzyniak, Measurements of electric nanocontacts (in Polish). Serie: Dissertations, Publishing House of Poznan University of Technology (2012)
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Nawrocki, W. (2019). Quantization of Electrical and Thermal Conductance in Nanostructures. In: Introduction to Quantum Metrology. Springer, Cham. https://doi.org/10.1007/978-3-030-19677-6_7
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DOI: https://doi.org/10.1007/978-3-030-19677-6_7
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