### Abstract

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 language | English |
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Pages (from-to) | 2222-2227 |

Journal | Physical Review B: Condensed Matter |

Volume | 35 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1987 |

MoE publication type | B1 Article in a scientific magazine |

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### Cite this

*Physical Review B: Condensed Matter*,

*35*(5), 2222-2227. https://doi.org/10.1103/PhysRevB.35.2222

}

*Physical Review B: Condensed Matter*, vol. 35, no. 5, pp. 2222-2227. https://doi.org/10.1103/PhysRevB.35.2222

**Generalization of the Landauer conductance formula.** / Eränen, Simo; Sinkkonen, Juha.

Research output: Contribution to journal › Article › Scientific

TY - JOUR

T1 - Generalization of the Landauer conductance formula

AU - Eränen, Simo

AU - Sinkkonen, Juha

PY - 1987

Y1 - 1987

N2 - 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.

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.

U2 - 10.1103/PhysRevB.35.2222

DO - 10.1103/PhysRevB.35.2222

M3 - Article

VL - 35

SP - 2222

EP - 2227

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 5

ER -