The cell-centered Finite-Volume self-consistent approach for heterostructures: 1D electron gas at the Si-SiO2 interface
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866915236109352960 |
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| author | Mosallanejad, Vahid Li, Haiou Cao, Gang Chiu, Kuei-Lin Dou, Wenjie Guo, Guo-ping |
| author_facet | Mosallanejad, Vahid Li, Haiou Cao, Gang Chiu, Kuei-Lin Dou, Wenjie Guo, Guo-ping |
| contents | Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below $4.2~K$) is a challenging task, which mostly lies in the discontinuities in material properties (e.g., effective-mass, electron affinity, dielectric constant). In this article, we develop a novel self-consistent approach based on cell-centered Finite-Volume discretization of the Sturm-Liouville form of the effective-mass Schr{ö}dinger equation and generalized Poisson's equation (FV-SP). We apply this approach to simulate the one-dimensional electron gas (1DEG) formed at the Si-SiO$_2$ interface via a top gate. We find excellent self-consistent convergence from high to extremely low (as low as $50~mK$) temperatures. We further examine the solidity of FV-SP method by changing external variables such as the electrochemical potential and the accumulative top gate voltage. Our approach allows for counting electron-electron interactions. Our results demonstrate that FV-SP approach is a powerful tool to solve effective-mass Hamiltonians. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_15375 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The cell-centered Finite-Volume self-consistent approach for heterostructures: 1D electron gas at the Si-SiO2 interface Mosallanejad, Vahid Li, Haiou Cao, Gang Chiu, Kuei-Lin Dou, Wenjie Guo, Guo-ping Mesoscale and Nanoscale Physics Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below $4.2~K$) is a challenging task, which mostly lies in the discontinuities in material properties (e.g., effective-mass, electron affinity, dielectric constant). In this article, we develop a novel self-consistent approach based on cell-centered Finite-Volume discretization of the Sturm-Liouville form of the effective-mass Schr{ö}dinger equation and generalized Poisson's equation (FV-SP). We apply this approach to simulate the one-dimensional electron gas (1DEG) formed at the Si-SiO$_2$ interface via a top gate. We find excellent self-consistent convergence from high to extremely low (as low as $50~mK$) temperatures. We further examine the solidity of FV-SP method by changing external variables such as the electrochemical potential and the accumulative top gate voltage. Our approach allows for counting electron-electron interactions. Our results demonstrate that FV-SP approach is a powerful tool to solve effective-mass Hamiltonians. |
| title | The cell-centered Finite-Volume self-consistent approach for heterostructures: 1D electron gas at the Si-SiO2 interface |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2112.15375 |