Finite element solution of electron waveguide discontinuities and its application to quantum field effect directional couplers

A numerical approach based on the finite element method is described for the solution of electron waveguide discontinuities with arbitrary potential and effective-mass distributions, Analytical solutions are introduced for the uniform waveguide regions, The approach is applied to a quantum field effect directional coupler with finite coupling length and longitudinal discontinuities. The effects of the longitudinal interference due to the discontinuities and of the transverse interference due to the even and odd supermodes in the coupling region are studied, The influence of the shape of the wire-tip on the transmission properties is also investigated.