Equivalent network approach for guided electron waves obliquely incident on step discontinuities in planar heterostructures

An equivalent network approach is developed for the analysis of the guided electron wave obliquely incident on step discontinuities in planar heterostructures. Stress is placed on network representations to establish physical pictures of the quantum effects and to yield insight; in addition, a systematic: microwave network approach is employed. A coordinate transformation translates an "eigencoordinate mode" of the guided electron wave propagating at an angle to the step discontinuity into a "structure coordinate mode" propagating normally to the step discontinuity, so that the step can be viewed as a transverse discontinuity and a procedure for the normal incidence can directly be exploited; transmission line equations in the direction normal to the step discontinuity, the mode-matching procedure for the boundary-value problem, and an equivalent network for the guided electron wave obliquely incident on the step discontinuities can be obtained. Using this network, the input admittance formulation is carried out, with which one can easily derive the equations that estimate the scattering and waveguiding characteristics of the guided electron wave obliquely incident on step discontinuities. Numerical examples are presented for a three-layered electron waveguide with a stub, and it is shown that this structure operates as a channel waveguide in addition to an angle filter.