The common assumptions for closure of the first three moment equations with non-parabolic band structure have led to many inconsistencies associated with the electron temperature, effective mass and heat flux. The assumptions are involved in the heat flux based on the Fourier law and in the electron temperature determined from the average kinetic and drift energies. The inconsistencies resulting from these assumptions are studied and illustrated for electrons in silicon with a non-parabolic energy band. A simple alternative by means of which to avoid the inconsistent assumptions and to truncate the hierarchy of the hydrodynamic equations with non-parabolic band structure is proposed. Instead of using the Fourier-law heat flux to close the hydrodynamic equations, the energy flux is separated into fluxes carried by average and random velocities. The proposed model and a Fourier-law-based hydrodynamic model, together with the Monte Carlo method, are applied to a silicon sub-micrometre - n - diode with a non-parabolic band at various applied voltages. Effects on electron transport in the sub-micrometre device resulting from the assumptions of the Fourier-law heat flux and the electron temperature determined from the average kinetic and drift energies are investigated.

Two hydrodynamic models for a non-parabolic band structure are proposed in order to obtain closed sets of the first four moment equations derived from the Boltzmann transport equation. Instead of using the Fourier-law heat flux to determine the energy flux and to close the first three moment equations as applied to the conventional hydrodynamic model, the energy flux is solved directly from the third-order moment equation. The physical quantities introduced in the third-order moment equation are expressed in terms of the lower-order moments and the average parameters associated with the random velocity. To close the third-order moment equation, the average parameters related to the random velocity are assumed to be energy dependent. Transport results for a submicrometre silicon -n- diode obtained from the proposed four-moment hydrodynamic models, compared with those from Monte Carlo simulations and from three-moment hydrodynamic models, are studied in detail.