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Landauer equation in three-dimensional amorphous materials

Godoy1

  • 1Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Mexico, 04510, Distrito Federal, Mexico.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
Summary

We calculated a 3D Landauer equation for electron transport in amorphous materials. The transmission coefficient in three dimensions closely resembles the 1D case, offering insights into electron diffusion.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Transport Phenomena

Background:

  • Understanding electron transport in amorphous materials is crucial for device applications.
  • The Landauer equation typically describes 1D transport, limiting its applicability to complex systems.
  • Incoherent electron diffusion in disordered materials presents unique challenges.

Purpose of the Study:

  • To develop a three-dimensional (3D) Landauer equation for incoherent electron transport.
  • To investigate electron diffusion in amorphous material slabs.
  • To analyze the multiple-scattering transmission coefficient in relation to the diffusion coefficient.

Main Methods:

  • Utilized the Boltzmann transport equation.
  • Applied the P1 approximation for calculating the multiple-scattering transmission coefficient.

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  • Modeled electron transport in a 3D slab of amorphous material.

    • Main Results:

    • Derived a 3D version of the Landauer equation for incoherent electron diffusion.
    • Found the 3D transmission coefficient to be numerically similar to the 1D case.
    • Established the validity of the results for thick slabs far from boundaries.

    Conclusions:

    • The 3D Landauer equation provides a framework for understanding electron transport in amorphous materials.
    • Electron transmission in 3D disordered systems exhibits similarities to 1D transport.
    • The findings are applicable to systems with thicknesses significantly larger than the mean free path.