An Efficient Approach to Include Full-Band Effects in Deterministic Boltzmann Equation Solver Based on High-Order Spherical Harmonics Expansion

2011 ◽  
Vol 58 (5) ◽  
pp. 1287-1294 ◽  
Author(s):  
Seonghoon Jin ◽  
Sung-Min Hong ◽  
Christoph Jungemann
Keyword(s):  
Boltzmann Equation ◽  
Spherical Harmonics ◽  
High Order ◽  
Efficient Approach ◽  
Full Band ◽  
Spherical Harmonics Expansion

Boundary conditions for spherical harmonics expansion of Boltzmann equation

1992 ◽  
Vol 28 (11) ◽  
pp. 995-996 ◽  
Author(s):  
D. Schroeder ◽  
D. Ventura ◽  
A. Gnudi ◽  
G. Baccarani
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Spherical Harmonics ◽  
Spherical Harmonics Expansion

scholarly journals Temperature Dependence of the Electron and Hole Scattering Mechanisms in Silicon Analyzed through a Full-Band, Spherical-Harmonics Solution of the BTE

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 361-365 ◽  
Author(s):  
Susanna Reggiani ◽  
Maria Cristina Vecchi ◽  
Massimo Rudan
Keyword(s):  
Temperature Dependence ◽  
Spherical Harmonics ◽  
Hole Mobility ◽  
Scattering Mechanisms ◽  
Mobility Data ◽  
Number Of Factors ◽  
Wide Range ◽  
Full Band ◽  
Spherical Harmonics Expansion ◽  
Full Band Structure

By adopting the solution method for the BTE based on the spherical-harmonics expansion (SHE) [1], and using the full-band structure for both the electron and valence band of silicon [2], the temperature dependence of a number of scattering mechanisms has been modeled and implemented into the code HARM performing the SHE solution. Comparisons with the experimental mobility data show agreement over a wide range of temperatures. The analysis points out a number of factors from which the difficulties encountered in earlier investigations seemingly originate, particularly in the case of hole mobility.

AN INFINITE SYSTEM OF DIFFUSION EQUATIONS ARISING IN TRANSPORT THEORY: THE COUPLED SPHERICAL HARMONICS EXPANSION MODEL

2001 ◽  
Vol 11 (05) ◽  
pp. 903-932 ◽  
Author(s):  
PIERRE DEGOND
Keyword(s):  
Boltzmann Equation ◽  
Diffusion Model ◽  
Spherical Harmonics ◽  
Transport Theory ◽  
Weak Sense ◽  
Uniqueness Result ◽  
Diffusion Operator ◽  
The Boltzmann Equation ◽  
Free Case ◽  
Spherical Harmonics Expansion

In this paper, we derive a diffusion model of "SHE" type from a diffusion approximation of the Boltzmann equation. SHE (or Spherical Harmonics Expansion) models consist of a diffusion equation in the position-energy space. In the present model, the diffusion operator couples the various energy levels, while they stay uncoupled in the standard SHE model, at least in the force-free case. This new model is expected to give a better description of particle transport when inelastic collisions are important. The duality structure of the diffusion operator is underlined. A uniqueness result for the diffusion model is shown. A rigorous proof that the solutions of the Boltzmann equation converge (in a weak sense) towards those of the SHE model is developed in the force-free case.

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