3.5.6 Bløtekjær's Approach

In contrast to Stratton, Bløtekjær originally proposed the concept of macroscopic relaxation times introducing one relaxation time for each moment equation. The set of weight functions used in this derivation is

$$\ensuremath{X}= \left(1, \ensuremath{\ensuremath{\mathitbf{p}}}, ... ...{E}}, \ensuremath{\ensuremath{\mathcal{E}}\ensuremath{\mathitbf{p}}}\right) \,,$$ (3.79)

which gives the possibility of a direct comparison to the terms obtained throughout the derivation after Stratton. The assumptions and simplifications are listed below:

• Macroscopic relaxation time approximation
• Time derivatives are neglected in the flux equations
• Product ansatz for the kinetic energy
• Tensor-valued transport parameters are estimated by their traces
• Parabolic band-structure
• Linearized heated displaced Maxwellian distribution function as closure relation

Subsections

• 3.5.6.1 Particle Flux Equation
• 3.5.6.2 Energy Flux Equation

M. Wagner: Simulation of Thermoelectric Devices