Landauer-Datta-Lundstrom Generalized Transport Model for Nanoelectronics

The Landauer-Datta-Lundstrom electron transport model is briefly summarized. If a band structure is given, the number of conduction modes can be evaluated and if a model for a mean-free-path for backscattering can be established, then the near-equilibrium thermoelectric transport coefficients can be calculated using the final expressions listed below for 1D, 2D, and 3D resistors in ballistic, quasiballistic, and diffusive linear response regimes when there are differences in both voltage and temperature across the device. The final expressions of thermoelectric transport coefficients through the Fermi-Dirac integrals are collected for 1D, 2D, and 3D semiconductors with parabolic band structure and for 2D graphene linear dispersion in ballistic and diffusive regimes with the power law scattering. 1. Introduction The objectives of this short review is to give a condensed summary of Landauer-Datta-Lundstrom (LDL) electron transport model [1–5] which works at the nanoscale as well as at the macroscale for 1D, 2D, and 3D resistors in ballistic, quasiballistic, and diffusive linear response regimes when there are differences in both voltage and temperature across the device. Appendices list final expressions of thermoelectric transport coefficients through the Fermi-Dirac integrals for 1D, 2D, and 3D semiconductors with parabolic band structure and for 2D graphene linear dispersion in ballistic and diffusive regimes with the power law scattering. 2. Generalized Model for Current The generalized model for current can be written in two equivalent forms: where “broadening” relates to transit time for electrons to cross the resistor channel: density of states with the spin degeneracy factor is included; is the integer number of modes of conductivity at energy ; the transmission where is the mean-free-path for backscattering and is the length of the conductor; Fermi function is indexed with the resistor contact numbers 1 and 2; is the Fermi energy which as well as temperature may be different at both contacts. Equation (3) can be derived with relatively few assumptions and it is valid not only in the ballistic and diffusion limits, but in between as well: The LDL transport model can be used to describe all three regimes. It is now clearly established that the resistance of a ballistic conductor can be written in the form where is fundamental Klitzing constant and number of modes represents the number of effective parallel channels available for conduction. This result is now fairly well known, but the common belief is that it applies only to short resistors and