A full consistent discretization scheme of the improved carrier density, momentum‐ and energy‐conservation equations is presented. The carrier heat flux as well as the convection and recombination terms are considered. The convection terms are averaged and then the differential constitutive relations of the current density and the energy flux are solved. The proposed discretization scheme generalizes the Scharfetter‐Gummel (S‐G) difference approximation to the generalized hydrodynamic model (HDM). On the basis of this scheme the hydrodynamic equations (HDE's) are solved for both electrons and holes. The transport of hot carriers in the p‐i‐n diode is investigated over a large scale of biasing values. The electric field distribution is not severely purturbed by the hot electron effects up to the medium biasing range. However, the minority carrier distribution is significantly affected by the carrier temperature‐gradients near the space‐charge‐regions. The minority carriers that are diffused to the edge of depleted regions are heated and if the carrier temperature gradient is sufficiently strong they diffuse back to the neutral cold region rather than to be captured by the electric field as known from the standard DDM theory.
Hamza, M., Morel, H. and Chante, J.P. (1991), "SIMULATION OF BIPOLAR TRANSPORT IN SEMICONDUCTOR P‐N JUNCTIONS USING THE GENERALIZED HYDRODYNAMIC EQUATIONS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 10 No. 4, pp. 289-299. https://doi.org/10.1108/eb051706
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