The Response of the Hydrodynamic Model to Heat Conduction, Mobility, and Relaxation Expressions

We study simulations of then+-n-n+ diode, by means of higher moment models, derived from the Boltzmann equation. We emply such realistic assumptions as energy dependent mobility functions, with doping dependent low field mobility. It is known that a critical role is played in the hydrodynamic model by the heat conduction term. When the standard choice of the Wiedemann-Franz law is made for the conductivity, and constant low field mobility values are used, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime has in the past been achieved by empirical modification of this law. In this paper, we consider the effect of representing the heat flux by the sum of two terms. It is found that the effect is negligible with respect to overshoot in comparison to that achieved by employing a doping dependent low field mobility. We also compare the hydrodynamic model to recently introduced energy transport models. Finally, in low temperature regimes, we study the dependence of shock formation on the momentum relaxation time representations and on the heat conduction term. The algorithms employed for both models are the essentially nonoscillatory (ENO) shock capturing algorithms.

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