Application of the moments method to the solution of the Boltzmann Transport equation

This research activity aims at investigating the properties and characteristics of the systems of differential equations obtained from the Boltzmann Transport Equation applying the moments method.

Part of the activity has dealt with the investigation of the closure conditions for the hydrodynamic model, obtaining a new formulation with does not resort to phenomenological relationships.

The hydrodynamic model has been generalized to include a general description of the silicon-band structure. In the same formulation the general expressions for a moment of rank $N$ have been obtained.

The coefficients of the models as, for example, the relaxation times associated to each moment, have been computed using a spatially-homogeneous solver of the spherical-harmonics expansion of the Boltzmann Transport Equation.

At the same time, the moments method has been applied to the system of equations obtained from spherical-harmonics expansion of the BTE, according to two different formulations. The obtained energy-transport models have been implemented in a two-dimensional device simulator. Thus it has been possible to compare the results of the energy-transport models with those of the spherical-harmonics expansion method and of the hydrodynamic model.


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