A mixed finite element method for the stationary semiconductor continuity equations

We discuss a finite element approximation of the semiconductor continuity equations based on quadrilateral and hexahedral space discretizations. This method can be regarded as an extension to higher dimensions of the well‐known one‐dimensional Scharfetter‐Gummel scheme. The existence, uniqueness and error estimates of the solution is discussed. Using a lumping technique we get a linear system similar to that obtained from the conventional box‐scheme. We also discuss the evaluation of the approximate terminal currents, which are shown to be convergent and conservative.