Controllable resonant tunnelling through single-point potentials: A point triode

•The zero-thickness limit of three-layer heterostructures is described in terms of point interactions.•The effect of resonant tunnelling through these single-point potentials is established.•The resonant tunnelling is shown to be controlled by a gate voltage.

A zero-thickness limit of three-layer heterostructures under two bias voltages applied externally, where one of which is supposed to be a gate parameter, is studied. As a result, an effect of controllable resonant tunnelling of electrons through single-point potentials is shown to exist. Therefore the limiting structure may be termed a “point triode” and considered in the theory of point interactions as a new object. The simple limiting analytical expressions adequately describe the resonant behaviour in the transistor with realistic parameter values and thus one can conclude that the zero-range limit of multi-layer structures may be used in fabricating nanodevices. The difference between the resonant tunnelling across single-point potentials and the Fabry–Pérot interference effect is also emphasized.