Abstract
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.
Highlights
We study simulations of the n +-n-n + diode, by means of higher moment models, derived from the Boltzmann equation
An issue of continuing debate in the literature is the role of heat conduction in the hydrodynamic model
The original goal of this work was to detail the effect of this use of the heat flux in the hydrodynamic model, with particular attention paid to alteration of the spurious velocity overshoot at the right junction
Summary
N previous work, we have demonstrated the robustness of an algorithm (ENO" Essentially NonOscillatory) designed for conservation systems admitting steep fronts and possible shock like behavior. The algorithm captures steady states by explicit time stepping and identification of characteristic directions It is an apt choice for the simulation of the hydrodynamic model for semiconductors over a wide range of parameters. The original goal of this work was to detail the effect of this use of the heat flux in the hydrodynamic model, with particular attention paid to alteration of the spurious velocity overshoot at the right junction. These are precisely the expressions employed in Monte-Carlo simulations. For example, the finding of [13] that the Wiedemann-Franz law overstates the (signed) flux in significant portions of the device This is perhaps the principal reason for making use of the modified heat flux.
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