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Recursive Tight-Binding Green’s Function Method: Application to Ballistic and Dissipative Transport in Semiconductor Nanostructures

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thesis on green function

  • Fernando Sols 5  

Part of the book series: NATO ASI Series ((NSSB,volume 342))

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The purpose of this chapter is to present a specific numerical application of Green’s functions in tight-binding structures. The numerical technique is conventionally called the recursive Green’s function method. It was first introduced by ( 1981 ) to study electron transport in disordered systems and, since then, it has been widely used by many authors as a practical tool to simulate quantum transport in a variety of structures. The Green’s function must be defined in a tight-binding structure, which means that the space must be discretized in sites that represent either real atoms with strongly localized orbitals, or fictitious sites that fill the space with a sufficiently high density. The use of tight-binding Green’s functions (TBGF’s) has some practical advantages. For example, hard-wall boundary conditions are simply simulated by the absence of sites. Impurities are conveniently included by introducing sites with unequal diagonal energy. In particular, diagonal disorder may be introduced by making the site energy a random variable. It is also useful for describing transport in geometries with hard-wall boundaries defined by straight segments and right angles (or angles whose tangent is the ratio of low integers). Among its possible shortcomings, we may mention that the recursive TBGF method is not particularly suited to study transport in structures defined by geometrical parameters one may want to vary continously, such as the angle between two wires or the length of a given segment. For this type of purposes, a wave-function matching method ( Schult et al., 1989 ) may be more advantageous [see, for example, ( 1990 ) for a study of electron transport through a circular bend linking two leads with an arbitrary angle]. Within a recursive TBGF scheme, these difficulties can be overcome in principle by introducing a sufficiently dense grid, but the computational cost may easily become prohibitive.

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Baranger, H. U., DiVincenzo, D. P., Jalabert, R. A., and Stone, A. D., 1991, Phys. Rev. B 44:10367.

Article   Google Scholar  

Büttiker, M. 1986, Phys. Rev. Lett. 57:1761.

Article   ADS   Google Scholar  

Caldeira, A. O., and Leggett, A. J., 1983, Ann. Phys. (N.Y.) 149:374.

Ferry, D. K., and Grubin, H. L., 1994, Solid State Physics , to be published.

Google Scholar  

Fisher, D. S., and Lee, P. A., 1981, Phys. Rev. B 23:6851.

Article   MathSciNet   ADS   Google Scholar  

MacKinnon, A., 1985, Z. Phys. B 59:385.

Meir, Y., and Wingreen, N.S., 1992, Phys. Rev. Lett. 68:2512

Pevzner, V., Sols, F., and Hess, K., 1991, in “Granular Nanoelectronics”, J. R. Barker, D. K. Ferry, and C. Jacoboni, eds., Plenum, New York.

Schult, R. L., Ravennati, D. G., and Wyld, H. W., 1989, Phys. Rev. B 39:5476.

Sols, F., Macucci, M., Ravaioli, U., and Hess, K., 1989, J. Appl. Phys. 66:3892.

Sols, F., and Macucci, M., 1990, Phys.Rev. B 41:11887.

Sols, F., 1992, Ann. Phys. (N.Y.) 214:386.

Sols, F., 1993, in: “Phonons in semiconductor nanostructures”, J. P. Leburton, J. Pascual, and C. M. Sotomayor-Torres, eds., Kluwer, Norwall, CT.

Stone, A. D., and Szafer, A., 1988, IBM J. Res. Develop . 32:384.

Thouless, D. J., and Kirkpatrick, S., 1981, J. Phys. C 14:235.

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Departamento de Física de la Materia Condensada, C-XII, Universidad Autónoma de Madrid, Cantoblanco, E-28049, Madrid, Spain

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Arizona State University, Tempe, Arizona, USA

David K. Ferry

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University of Modena, Modena, Italy

Carlo Jacoboni

Technical University of Denmark, Lyngby, Denmark

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Sols, F. (1995). Recursive Tight-Binding Green’s Function Method: Application to Ballistic and Dissipative Transport in Semiconductor Nanostructures. In: Ferry, D.K., Grubin, H.L., Jacoboni, C., Jauho, AP. (eds) Quantum Transport in Ultrasmall Devices. NATO ASI Series, vol 342. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1967-6_16

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