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 Boltzmannequation. We emply such realistic assumptions as energy dependent mobility functions, with doping dependentlow field mobility. It is known that a critical role is played in the hydrodynamic model by the heat conductionterm. When the standard choice of the Wiedemann-Franz law is made for the conductivity, and constant low fieldmobility values are used, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regimehas in the past been achieved by empirical modification of this law. In this paper, we consider the effect ofrepresenting the heat flux by the sum of two terms. It is found that the effect is negligible with respect toovershoot in comparison to that achieved by employing a doping dependent low field mobility. We also comparethe hydrodynamic model to recently introduced energy transport models. Finally, in low temperature regimes, westudy the dependence of shock formation on the momentum relaxation time representations and on the heatconduction term. The algorithms employed for both models are the essentially nonoscillatory (ENO) shockcapturing algorithms