Electron transfer between regions of quasi-two-dimensional and three-dimensional dynamics in semiconductor microstructures

A theoretical study is carried out on the transfer of electrons at the edge of a microstructure, where electrons may cross between a region of quasi-two-dimensional dynamics and a ``contact region'' of three-dimensional dynamics. Working in the one-electron, effective-mass approximation, a formal solution is found for a model having a general profile for the confining potential in the two-dimensional region. The general form of the threshold behavior is found for ejection probabilites and injection cross sections. Numerical results are obtained for the case of a parabolic confining potential.