| A finite element method for semiconductor device simulation using tangential vector finite element basis functions is presented in this thesis. Tangential vector element basis functions are derived by reference to Whitney forms: the scalar variables in device equations are interpolated by using standard continuous scalar basis functions while the vector variables are interpolated by new vector basis functions in which only the tangential component of the vector is continuous. 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 are integrated exactly. We show 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 commonly used Scharfetter-Gummel method in cases of obtuse and irregular triangulations. Having established that the new method is robust, various semiconductor devices such as pn junction diode, bipolar transistor, MOS capacitor, and MOS transistor are simulated. A case study is conducted in which the reduced-field profile design for bipolar transistors is investigated by simulation. It is found that the junction electric field can be reduced with little change in the cutoff frequency by inserting a lightly doped layer. Furthermore, a phenomenon called base push-back was discovered. Base push-back may result in the falloff of high current gain and cutoff frequency. However, it reduces base resistance and emitter current crowding in power transistors. |
