NONISOTHERMAL EXTENSION OF THE SCHARFETTER-GUMMEL TECHNIQUE FOR HOT-CARRIER TRANSPORT IN HETEROSTRUCTURE SIMULATIONS

The Scharfetter-Gummel technique is widely used in algorithms for the simulation of isothermal semiconductor devices. Recent interest in the modeling of ultra-small devices requires a non-isothermal analysis; i .e., a hydrodynamic model. Several non-isothermal extensions to the Sc harfetter-Gummel technique for carrier flux have been proposed for hom ostructure devices. This paper presents an extension which is suitable for the simulation of both the carrier flux and carrier energy flux e quations in heterostructure devices, with the capability of using Ferm i-Dirac statistics. Comparison with the extensions of other authors pr ovides verification of the discretization formulation developed in thi s paper. Limiting cases are discussed with suitable approximations. Ca lculated values of fluxes are presented for selected non-isothermal an d degenerate cases to highlight the need for inclusion of the Fermi-Di rac statistics in the flux formulations.