(2.44) |

where denotes a weight function which can either be of scalar or vectorial type. The weight functions are usually chosen as powers of increasing order of the vector . These powers are accompanied by some appropriate scaling factors to get physically meaningful quantities. In this work moments up to the sixth order will be considered. The corresponding weight functions for the even orders read

and the weight functions for the odd orders are

where is the momentum, is the reduced PLANCK constant, is the wave vector, is the effective mass

In eqns. (2.46) to (2.51) a single
effective parabolic energy band has been assumed^{2.6}:

(2.52) |

The following derivation will be carried out only for electrons for the sake of clarity and brevity. As the derivation for holes is analogous, the results for holes will be presented without derivation. Applying the moments method to BTE the moment equations for electrons are obtained

- 2.3.2.1 Gradient Calculation
- 2.3.2.2 Macroscopic Relaxation Time Approximation
- 2.3.2.3 Isotropic Distribution Function
- 2.3.2.4 Statistical Averages