The drift-diffusion and energy-transport equations of Chaps. 5 and 6 are derived from the Boltzmann equation by considering the moments\( n = \int_B F\frac{\mathrm{d} k}{4\pi^3}, \quad ne = \int_B F E(k)\frac{\mathrm{d}k}{4\pi^3},\)where F is the distribution function. We have already indicated in Sect. 2.4 that this strategy can be generalized. In this chapter, we detail the derivation of a hierarchy of diffusive moment models.
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Jüngel, A. (2009). Diffusive Higher-Order Moment Equations. In: Transport Equations for Semiconductors. Lecture Notes in Physics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89526-8_8
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