### Abstract

We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach, the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two- and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the "squeezed limit" as a δ- and a δ'-potential and referred to as a "point" transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a "resonance set" is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a δ-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values.

Original language | English |
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Article number | 87 |

Journal | Frontiers in Physics |

Volume | 7 |

Issue number | JUN |

DOIs | |

Publication status | Published - 2019 |

### Keywords

- Controllable potentials
- Heterostructures
- One-dimensional quantum systems
- Point interactions
- Resonant tunneling
- Transmission

### ASJC Scopus subject areas

- Biophysics
- Materials Science (miscellaneous)
- Mathematical Physics
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*Frontiers in Physics*,

*7*(JUN), [87]. https://doi.org/10.3389/fphy.2019.00087