Generalization of the Landauer conductance formula

Simo Eränen, Juha Sinkkonen

Research output: Contribution to journalArticleScientific

6 Citations (Scopus)

Abstract

We study the electrical current transport in conductor-insulator-conductor structures, where the charge carriers are assumed to traverse the insulating layer by tunneling.
The current flow in the conductor contacts is treated by solving self-consistently the Poisson equation and the relaxation time form of the Boltzmann equation for an inhomogeneous electron system. The tunneling is taken into account by the appropriate boundary conditions for the electronic distribution functions in the two contacts. It is shown that the tunneling current density consists of two contributions, the first of which is a direct generalization of the celebrated Landauer conductance formula into the nonlinear voltage regime.
The second contribution or the correction term originates from the screening of the electrical potential across the insulating layer and from the matching of the distribution functions on the opposite sides of the barrier. In the linear voltage regime for well-conducting contacts the tunneling current density is given by the ordinary Landauer result, but for semiconducting contacts the second contribution may become comparable to the first one.
Moreover, it is shown that in the correction term the matching of the distribution functions is always negligible when compared to the screening effect. Finally, the limits of validity of our results are discussed.
Original languageEnglish
Pages (from-to)2222-2227
JournalPhysical Review B: Condensed Matter
Volume35
Issue number5
DOIs
Publication statusPublished - 1987
MoE publication typeB1 Article in a scientific magazine

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Distribution functions
conductors
distribution functions
Screening
Current density
screening
Boltzmann equation
Poisson equation
Electric potential
current density
Charge carriers
Relaxation time
electric potential
Boundary conditions
charge carriers
Electrons
relaxation time
insulators
boundary conditions
conduction

Cite this

Eränen, Simo ; Sinkkonen, Juha. / Generalization of the Landauer conductance formula. In: Physical Review B: Condensed Matter. 1987 ; Vol. 35, No. 5. pp. 2222-2227.
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Generalization of the Landauer conductance formula. / Eränen, Simo; Sinkkonen, Juha.

In: Physical Review B: Condensed Matter, Vol. 35, No. 5, 1987, p. 2222-2227.

Research output: Contribution to journalArticleScientific

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T1 - Generalization of the Landauer conductance formula

AU - Eränen, Simo

AU - Sinkkonen, Juha

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AB - We study the electrical current transport in conductor-insulator-conductor structures, where the charge carriers are assumed to traverse the insulating layer by tunneling. The current flow in the conductor contacts is treated by solving self-consistently the Poisson equation and the relaxation time form of the Boltzmann equation for an inhomogeneous electron system. The tunneling is taken into account by the appropriate boundary conditions for the electronic distribution functions in the two contacts. It is shown that the tunneling current density consists of two contributions, the first of which is a direct generalization of the celebrated Landauer conductance formula into the nonlinear voltage regime. The second contribution or the correction term originates from the screening of the electrical potential across the insulating layer and from the matching of the distribution functions on the opposite sides of the barrier. In the linear voltage regime for well-conducting contacts the tunneling current density is given by the ordinary Landauer result, but for semiconducting contacts the second contribution may become comparable to the first one. Moreover, it is shown that in the correction term the matching of the distribution functions is always negligible when compared to the screening effect. Finally, the limits of validity of our results are discussed.

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