Abstract
In this chapter MEP is applied to close the moment equations for electrons in silicon semiconductors. In our model we consider the electrons distributed in the six X-valleys assumed as equivalent. The approximation given by Kane will be used as dispersion relation.
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Notes
- 1.
Indeed, we have written \(\boldsymbol {\lambda } = \delta \overline {\boldsymbol {\lambda }}\) and \( \boldsymbol {\lambda }^{W} = \delta \overline {\boldsymbol {\lambda }}^{W} \) and expanded around δ = 0. Once the expansion has been obtained, we the original variables have been restored.
- 2.
Round brackets mean symmetrization, e.g. A (ij) = 1∕2(A ij + A ji).
- 3.
The electron Fermi quasi-level is defined up to an additive constant. We assume that \(N_C \exp \big ( q \frac {V + \varphi _n}{K_B T_n} \big ) \) is equal to the intrinsic concentration n i.
- 4.
In the parabolic approximation \(\frac {3}{2 \lambda ^W} = W\). In the case of the Kane dispersion relation it can be used as a reasonable approximation.
- 5.
We recall that a summation must be intended with respect to repeated dummy indices.
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Camiola, V.D., Mascali, G., Romano, V. (2020). Application of MEP to Silicon. In: Charge Transport in Low Dimensional Semiconductor Structures. Mathematics in Industry(), vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-35993-5_4
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