Non-isothermal extension of the Scharfetter-Gummel technique for hot carrier transport in heterostructure simulations

Points out that the Scharfetter-Gummel technique is widely used in algorithms for the simulation of isothermal semiconductor devices. Recent interest in the modeling of ultrasmall devices requires a nonisothermal analysis, i.e., a hydrodynamic model. Several nonisothermal extensions to the Scharfetter-Gummel technique for carrier flux have been proposed for homostructure devices. An extension is presented which is suitable for the simulation of both the carrier flux and carrier energy flux equations in heterostructure devices, with the capability of using Fermi-Dirac statistics. Comparison with the extensions of other authors provides verification of the discretization formulation developed here. Limiting cases are discussed with suitable approximations. Calculated values of fluxes are presented for selected nonisothermal and degenerate cases to highlight the need for inclusion of the Fermi-Dirac statistics in the flux formulations