Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

2004 ◽  
Vol 69 (9) ◽  
Author(s):  
A. J. H. McGaughey ◽  
M. Kaviany
Keyword(s):  
Thermal Conductivity ◽  
Relaxation Time ◽  
Boltzmann Transport Equation ◽  
Single Mode ◽  
Boltzmann Transport ◽  
Phonon Thermal Conductivity ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Thermal Conductivity Model ◽  
Quantitative Validation

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.

scholarly journals Calculations of the thermal conductivity of Si1-xGex films with nonuniform composition

2018 ◽  
Vol 19 (1) ◽  
pp. 48-52
Author(s):  
V. V. Kuryliuk ◽  
O. M. Krit
Keyword(s):  
Thermal Conductivity ◽  
Relaxation Time ◽  
Boltzmann Equation ◽  
Temperature Interval ◽  
Thermoelectric Properties ◽  
Bulk Material ◽  
Nonuniform Distribution ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Available Information

SiGe films have attracted much attention recently due to experimental demonstrations of improved thermoelectric properties over those of the corresponding bulk material. However, despite this increasing attention, available information on the thermoelectric properties of Si1-xGex films is quite limited, especially for nonuniform composition in wide temperature interval. In this paper we have used the Boltzmann equation under the relaxation-time approximation to calculate the thermal conductivity of Si1-xGex films with nonuniform composition. It is confirmed that SiGe films with nonuniform composition has significantly lower thermal conductivity than its uniform counterpart. This suggests that an improvement in thermoelectric properties is possible by using the SiGe films with nonuniform distribution of germanium.

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