On the soft wall guiding potentials in realistic quantum waveguides

A transfer matrix method is presented for the study of electron conduction in a quantum waveguide with soft wall lateral confinement. By transforming the two-dimensional Schrodinger equation into a set of second order ordinary differential equations, the total transfer matrix is obtained and the scattering probability amplitudes are calculated. The proposed method is applied to the evaluation of the electron transmission in two types of cavity structure with finite-height square-well confinement. The results obtained by our method, which are found to be in excellent agreement with those from another transfer matrix method, suggest that the infinite square-well potential is a good approximation to finite-height square-well confinement for electrons propagating in the ground transverse mode, but softening of the walls has an obvious effect on the electron transmission and mode-mixing for propagating in the excited transverse mode. (C) 1996 American Institute of Physics.