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We proposed a discrete scattering model for a 1D electron–optical phonon scattering operator

Discrete Kernel Preserving Model for 1D Electron---Optical Phonon Scattering

J. Sci. Comput., no. 2 (2015): 317-335

Cited: 1|Views11
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Abstract

We investigate the discretization of of an electron---optical phonon scattering using a finite volume method. The discretization is conservative in mass and is essentially based on an energy point of view. This results in a discrete scattering system with elegant mathematical features, which are fully clarified. Precisely the discrete sca...More

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Introduction
  • As the development of the miniature technology, low-dimensional semiconductor devices such as nanowires and nanotubes have drowned interest of more and more researchers [9].
  • It has been pointed out in [3,5] that as the channel length is as short as 50nm, the relaxation time approximation of electron scattering fails.
Highlights
  • As the development of the miniature technology, low-dimensional semiconductor devices such as nanowires and nanotubes have drowned interest of more and more researchers [9]
  • We propose a finite volume method to discretize an electron– optical phonon scattering integral, where the grid is symmetric in velocity purposely
  • We prove that the algebraic multiplicity of eigenvalue λ = 0 of M is equal to the number of the strongly connected components of a directed graph, which depends only on the energy grids used in the finite volume discretization
  • We proposed a discrete scattering model for a 1D electron–optical phonon scattering operator
  • Criteria have been given to judge whether a discrete scattering matrix is irreducible from the grid partition
Results
  • As electrons are scattered from one state to another by absorbing or emitting an optical phonon with energy p, uniform energy grids with E = p/n, n ∈ N + is often considered.
  • When n > 1, n ∈ N, the scattering matrix M derived from a uniform energy grid is reducible because there exist Ei = (i −1) E, i = 1, .
Conclusion
  • The authors proposed a discrete scattering model for a 1D electron–optical phonon scattering operator.
  • For an irreducible scattering matrix, the eigenvalue λ = 0 is proved to be semisimple and the real part of all the other eigenvalues are negative.
  • Criteria have been given to judge whether a discrete scattering matrix is irreducible from the grid partition.
  • This provided further understanding to the discretization of the scattering operator
Funding
  • This research was supported in part by the National Basic Research Program of China (2011CB309704) and NSFC (91230107, 11325102)
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