Equivalent noise source for Boltzmann transport equation with relaxation‐time approximation in nondegenerate semiconductors

1993 ◽  
Vol 74 (10) ◽  
pp. 6217-6221 ◽  
Author(s):  
K. G. Moh ◽  
H. S. Min ◽  
Y. J. Park
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Noise Source ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Time Approximation ◽  
Relaxation Time Approximation

On Efficient Particle Methods for Solving the Boltzmann Transport Equation in the Relaxation-Time Approximation

2009 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou ◽  
Gregg A. Radtke ◽  
Lowell L. Baker
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Variance Reduction ◽  
Boltzmann Transport Equation ◽  
Computational Cost ◽  
Particle Methods ◽  
Boltzmann Transport ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Stochastic Particle

We present and discuss a variance-reduced stochastic particle simulation method for solving the relaxation-time model of the Boltzmann transport equation. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods. The proposed method is developed and validated in the context of dilute gases; despite this, it is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is applicable.

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.

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