Ballistic electron transport described by a fourth-order Schrödinger equation
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arXiv
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| Natura: | Preprint |
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2025
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| author | Aliffi, Giulia Elena Nastasi, Giovanni Romano, Vittorio |
| author_facet | Aliffi, Giulia Elena Nastasi, Giovanni Romano, Vittorio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_01401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ballistic electron transport described by a fourth-order Schrödinger equation Aliffi, Giulia Elena Nastasi, Giovanni Romano, Vittorio Mathematical Physics Mesoscale and Nanoscale Physics 81Q05, 35J10, 34L40 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. |
| title | Ballistic electron transport described by a fourth-order Schrödinger equation |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics 81Q05, 35J10, 34L40 |
| url | https://arxiv.org/abs/2503.01401 |