scholarly journals Monte Carlo Analysis of Anisotropy in the Transport Relaxation Times for the Hydrodynamic Model

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 161-165 ◽  
Author(s):  
Rossella Brunetti ◽  
Maria Cristina Vecchi ◽  
Massimo Rudan
Keyword(s):  
Monte Carlo ◽  
Band Structure ◽  
Hydrodynamic Model ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Monte Carlo Analysis ◽  
Collision Term ◽  
Monte Carlo Code ◽  
Boltzmann Transport ◽  
Transport Relaxation

This paper investigates the anisotropy properties of the relaxation times used in the hydrodynamic model. To this purpose a calculation of the collision term of the Boltzmann Transport Equation is performed by means of a Monte Carlo code accounting for the proper band structure and scattering features. Numerical results for electrons in silicon are shown at 77 and 300 K for E ║ <100> and E ║ <111>.

scholarly journals Spherical Harmonic Modeling of a 0.05 μm Base BJT: A Comparison with Monte Carlo and Asymptotic Analysis

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 147-151 ◽  
Author(s):  
C.-H. Chang ◽  
C.-K. Lin ◽  
N. Goldsman ◽  
I. D. Mayergoyz
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Band Structure ◽  
Asymptotic Analysis ◽  
Energy Distribution ◽  
Transport Equation ◽  
Spherical Harmonic ◽  
Boltzmann Transport Equation ◽  
System Of Equations ◽  
Boltzmann Transport

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.

scholarly journals A New Concept for Solving the Boltzmann Transport Equation in Ultra-fast Transient Situations

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 217-222
Author(s):  
Ming-C. Cheng
Keyword(s):  
Distribution Function ◽  
Equilibrium Distribution ◽  
Electron Distribution Function ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Equilibrium Distribution Function ◽  
Boltzmann Transport ◽  
Hydrodynamic Parameters ◽  
Lower Conduction Band ◽  
Rapid Changes

A concept based on relaxation of the hydrodynamic parameters is introduced to arrive at a computational model for the extreme non-equilibrium distribution function of carriers in multi-valley bandstructure. The relaxation times are taken to describe the evolution scale of the distribution function. The developed model is able to account for transport phenomena at the momentum relaxation scale. The model, together with the Monte Carlo simulation, is applied to obtain the electron distribution function in each valley of the lower conduction band in GaAs, and to study the evolution of the distribution function in GaAs subjected to rapid changes in field.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Thermal Transport ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

Collision Term in the Boltzmann Transport Equation

1960 ◽  
Vol 28 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Edward A. Desloge ◽  
Steven W. Matthysse
Keyword(s):  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Collision Term ◽  
Boltzmann Transport
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