A consistent nonisothermal extension of the Scharfetter—Gummel stable difference approximation

Computer simulation is becoming an increasingly important aspect of device analysis and design, and it is well known that stability of the associated numerical solution procedures is enhanced by use of the Scharfetter-Gummel (SG) approximation. Accurate transport models utilizing carrier temperature as a crucial parameter are emerging, however the SG expression is valid only for isothermal analyses. In this letter, a consistent nonisothermal extension of the SG stable difference approximation is presented. Simplifications of the new expression are shown to agree with previous results.