View in EDS

Ballistic electron transport described by a fourth-order Schrödinger equation.

Saved in:
Bibliographic Details
Title: Ballistic electron transport described by a fourth-order Schrödinger equation.
Authors: Aliffi, Giulia Elena1 (AUTHOR) giuliaelena.aliffi@phd.unict.it, Nastasi, Giovanni2 (AUTHOR) giovanni.nastasi@unikore.it, Romano, Vittorio1 (AUTHOR) vittorio.romano@unict.it
Source: Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Aug2025, Vol. 76 Issue 4, p1-21. 21p.
Subjects: Resonant tunneling, Ballistic conduction, Tunnel diodes, Dispersion relations, Loans
Abstract: A fourth-order Schrödinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple effective mass approximation. Similarly to the standard (second order) Schrödinger equation, the problem is reduced to a finite spatial domain with appropriate transparent boundary conditions to simulate charge transport in a quantum coupler (Lent and Kirkner in J Appl Phys 67:6353, 1990; Ben Abdallah et al. in ZAMP 48:135–155, 1997; Ben Abdallah in J. Math. Phys. 41:4241–4261, 2000), where an active region representing an electron device is coupled to leads which take the role of reservoirs. Some analytical properties are investigated, and a generalized formula for the current is obtained. Numerical results show the main features of the solutions of the new model. In particular, an effect of interference appears due to a richer wave structure than that arising for the second-order Schrödinger equation in the effective mass approximation. [ABSTRACT FROM AUTHOR]
Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:A fourth-order Schrödinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple effective mass approximation. Similarly to the standard (second order) Schrödinger equation, the problem is reduced to a finite spatial domain with appropriate transparent boundary conditions to simulate charge transport in a quantum coupler (Lent and Kirkner in J Appl Phys 67:6353, 1990; Ben Abdallah et al. in ZAMP 48:135–155, 1997; Ben Abdallah in J. Math. Phys. 41:4241–4261, 2000), where an active region representing an electron device is coupled to leads which take the role of reservoirs. Some analytical properties are investigated, and a generalized formula for the current is obtained. Numerical results show the main features of the solutions of the new model. In particular, an effect of interference appears due to a richer wave structure than that arising for the second-order Schrödinger equation in the effective mass approximation. [ABSTRACT FROM AUTHOR]
ISSN:00442275
DOI:10.1007/s00033-025-02535-5