Two-dimensional tensor temperature extension of the hydrodynamic model and its applications

The fundamental assumption that is made in most hydrodynamic simulation programs is the scalar nature of the temperature. In this paper we examine this assumption and present a model that takes into account the full tensorial nature of the temperature. The results show good agreement with 1-D Monte Carlo calculations for a ballistic diode and reproduce some of the qualitative features of 2-D Monte Carlo results for MOSFETs. In terms of terminal currents, 2-D tensor temperature simulation of BJTs shows only small differences when compared with results from scalar temperature formulation. For MOSFETs the differences are up to 15%. Internal distribution of temperature in MOSFETs shows some interesting properties that cannot be reproduced by the scalar temperature hydrodynamic model. The details of the physical models and transport coefficients used are also described.