Semiconductor quantum wells as electron wave slab waveguides

A quantum well in a semiconductor can act as a slab waveguide for electron waves in a manner analogous to the way a layered dielectric can act as a slab waveguide for electromagnetic waves (e.g., as commonly employed in integrated optics). In this work, the case of a general electron asymmetric slab waveguide (a quantum well comprised of three materials each with a different potential energy and a different effective mass) is analyzed and the conditions for electron waveguiding are quantified. Electron waveguide modes exist for electron energies in the well and for electron energies above one or both of the potential energy barriers. Furthermore, due to dispersion, each electron waveguide mode has an upper‐energy cutoff as well as a lower‐energy cutoff. This is in contrast to electromagnetic guided modes which typically have only lower‐energy (low‐frequency) cutoffs. At the upper‐energy cutoff the electron wave is refracted into the substrate and/or cover. An example quantum well waveguide consisting of Ga_0.80 Al_0.20 As (substrate), GaAs (film), Ga_0.55 Al_0.45 As (cover) is analyzed. This structure is a single‐mode electron waveguide for GaAs thicknesses of from 5 (1.413 nm) to 26 monolayers (7.349 nm).