Influence of a squeezed prewell on tunneling properties and bound states in heterostructures

A resonant tunneling effect of an extremely thin potential well on the transmission of charged particles through a planar heterostructure with an arbitrary potential profile is investigated in a squeezing limit as the well width tends to zero. In this limit, the transmission probability through the structure is shown to be blocked for all the parameter values of the well, except a resonance set of Lebesgue measure zero. The peak-to-valley ratio is shown to increase crucially with the squeezing of the well: the thinner is its thickness, the resonant peaks become sharper and localized at isolated points. Contrary, a discrete spectrum of the heterostructure (if any) does exist both on the resonance set and beyond it, however, the squeezing scenario here turns out to be quite interesting and sophisticated.