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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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finite volume methodeigenspaceseigenvaluessemiconductor device simulationelectron---phonon scattering integral operator

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)

Reference

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Author

Ruo Li (李若)

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Tiao Lu (卢朓)

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Wenqi Yao

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