Tangential vector finite elements for semiconductor device simulation

The authors present a finite element method for semiconductor device simulation using tangential vector finite element basis functions. Tangential vector basis functions are derived by reference to Whitney forms. In the new formulation, current is approximated by a quadratic polynomial, rather than as a constant within the element as has been done previously; the tangential components of a vector along the mesh edges are expressed in a consistent manner with the other variables, and the weak form of the device equations is integrated exactly. It is shown that this weak form is closely related to the Voronoi cell method and that an artificial diffusion constant may be used to stabilize the solutions. Numerical studies show that the new method is superior to the Scharfetter-Gummel algorithm in cases of obtuse and irregular triangulations