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Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices

John R Barker, Antonio Martinez, Antonio Martinez Muniz Orcid Logo

Journal of Physics: Condensed Matter, Volume: 30, Issue: 13, Start page: 134002

Swansea University Author: Antonio Martinez Muniz Orcid Logo

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DOI (Published version): 10.1088/1361-648X/aaaf98

Abstract

Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent co...

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Published in: Journal of Physics: Condensed Matter
ISSN: 0953-8984 1361-648X
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39351
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spelling 2021-06-01T09:51:23.4323395 v2 39351 2018-04-09 Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices cd433784251add853672979313f838ec 0000-0001-8131-7242 Antonio Martinez Muniz Antonio Martinez Muniz true false 2018-04-09 EEEG Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent computation for advanced device modeling. The underlying semi-classical model for the self-energy has been established and validated during recent years and depends on a slight modification of the macroscopic static dielectric constants for individual homogeneous dielectric regions. The model has been validated for point charges as close as one interatomic spacing to a sharp interface. A brief introduction to image charge methodology is followed by a discussion and demonstration of the traditional failure of the methodology to derive the electrostatic potential at arbitrary distances from a source charge. However, the self-energy involves the local limit of the difference between the electrostatic Green functions for the full dielectric heterostructure and the homogeneous equivalent. It is shown that high convergence may be achieved for the image charge method for this local limit. A simple re-normalisation technique is introduced to reduce the number of image terms to a minimum. A number of progressively complex 3D models are evaluated analytically and compared with high precision numerical computations. Accuracies of 1% are demonstrated. Introducing a simple technique for modeling the transition of the self-energy between disparate dielectric structures we generate an analytical model that describes the self-energy as a function of position within the source, drain and gated channel of a silicon wrap round gate field effect transistor on a scale of a few nanometers cross-section. At such scales the self-energies become large (typically up to ~100 meV) close to the interfaces as well as along the channel. The screening of a gated structure is shown to reduce the self-energy relative to un-gated nanowires. Journal Article Journal of Physics: Condensed Matter 30 13 134002 0953-8984 1361-648X 5 3 2018 2018-03-05 10.1088/1361-648X/aaaf98 http://eprints.gla.ac.uk/157919/ COLLEGE NANME Electronic and Electrical Engineering COLLEGE CODE EEEG Swansea University 2021-06-01T09:51:23.4323395 2018-04-09T12:53:42.3884656 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Electronic and Electrical Engineering John R Barker 1 Antonio Martinez 2 Antonio Martinez Muniz 0000-0001-8131-7242 3 0039351-16052018084211.pdf barker2018.pdf 2018-05-16T08:42:11.7770000 Output 3128841 application/pdf Accepted Manuscript true 2019-02-15T00:00:00.0000000 true eng
title Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
spellingShingle Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
Antonio Martinez Muniz
title_short Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
title_full Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
title_fullStr Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
title_full_unstemmed Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
title_sort Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices
author_id_str_mv cd433784251add853672979313f838ec
author_id_fullname_str_mv cd433784251add853672979313f838ec_***_Antonio Martinez Muniz
author Antonio Martinez Muniz
author2 John R Barker
Antonio Martinez
Antonio Martinez Muniz
format Journal article
container_title Journal of Physics: Condensed Matter
container_volume 30
container_issue 13
container_start_page 134002
publishDate 2018
institution Swansea University
issn 0953-8984
1361-648X
doi_str_mv 10.1088/1361-648X/aaaf98
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Electronic and Electrical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Electronic and Electrical Engineering
url http://eprints.gla.ac.uk/157919/
document_store_str 1
active_str 0
description Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent computation for advanced device modeling. The underlying semi-classical model for the self-energy has been established and validated during recent years and depends on a slight modification of the macroscopic static dielectric constants for individual homogeneous dielectric regions. The model has been validated for point charges as close as one interatomic spacing to a sharp interface. A brief introduction to image charge methodology is followed by a discussion and demonstration of the traditional failure of the methodology to derive the electrostatic potential at arbitrary distances from a source charge. However, the self-energy involves the local limit of the difference between the electrostatic Green functions for the full dielectric heterostructure and the homogeneous equivalent. It is shown that high convergence may be achieved for the image charge method for this local limit. A simple re-normalisation technique is introduced to reduce the number of image terms to a minimum. A number of progressively complex 3D models are evaluated analytically and compared with high precision numerical computations. Accuracies of 1% are demonstrated. Introducing a simple technique for modeling the transition of the self-energy between disparate dielectric structures we generate an analytical model that describes the self-energy as a function of position within the source, drain and gated channel of a silicon wrap round gate field effect transistor on a scale of a few nanometers cross-section. At such scales the self-energies become large (typically up to ~100 meV) close to the interfaces as well as along the channel. The screening of a gated structure is shown to reduce the self-energy relative to un-gated nanowires.
published_date 2018-03-05T03:49:57Z
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score 11.035634

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