{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31300"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31300","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Computational approaches to silicon based nanostructures","abstract":"This study has three goals. First, we would like to develop computational tools that are suitable for the analysis and optimization of semiconductor device structures where quantum effects are important, as for example quantum wires and quantum dots but also ultra-narrow Metal-Oxide-Semiconductor (MOS) conduction channels at room temperature. Here, we describe these structures by the coupled system of the Schrodinger and the Poisson equation. We discuss solution strategies for both equations and outline an original iteration approach that uses a predictor-corrector procedure for solving the coupled system self-consistently. Second, we would like to apply these tools to investigate the lateral scalability limits of conduction channels in several MOS structures, at room temperature, with the goal to understand for which geometries and under which operating conditions a narrow channel approaching the quantum-wire limit can maintain reasonable isolation. We find that a good trade-off in performance and manufacturability is obtained for structures with T-shaped gate metallization. The calculations presented here also show that, depending on gate geometry and channel doping, it should be possible to operate a quasi-monomode silicon based quantum wire at room temperature. Finally, a full-band approach for the solution of Schrodinger's equation based on Fast Fourier Transforms is described. Using this simulation method, it becomes possible to solve Schrodinger's equation in the one band approximation for arbitrary band structures, putting a more complete description of high energy states and realistic temperatures within reach. Two example applications concerning non-parabolic effects in silicon quantum structures are presented, a MOS quantum capacitor and a MOS quantum cavity. Future directions for further extending this numerical method are discussed. IV","abstract_html":"This study has three goals. First, we would like to develop computational tools that are suitable for the analysis and optimization of semiconductor device structures where quantum effects are important, as for example quantum wires and quantum dots but also ultra-narrow Metal-Oxide-Semiconductor (MOS) conduction channels at room temperature. Here, we describe these structures by the coupled system of the Schrodinger and the Poisson equation. We discuss solution strategies for both equations and outline an original iteration approach that uses a predictor-corrector procedure for solving the coupled system self-consistently. Second, we would like to apply these tools to investigate the lateral scalability limits of conduction channels in several MOS structures, at room temperature, with the goal to understand for which geometries and under which operating conditions a narrow channel approaching the quantum-wire limit can maintain reasonable isolation. We find that a good trade-off in performance and manufacturability is obtained for structures with T-shaped gate metallization. The calculations presented here also show that, depending on gate geometry and channel doping, it should be possible to operate a quasi-monomode silicon based quantum wire at room temperature. Finally, a full-band approach for the solution of Schrodinger's equation based on Fast Fourier Transforms is described. Using this simulation method, it becomes possible to solve Schrodinger's equation in the one band approximation for arbitrary band structures, putting a more complete description of high energy states and realistic temperatures within reach. Two example applications concerning non-parabolic effects in silicon quantum structures are presented, a MOS quantum capacitor and a MOS quantum cavity. Future directions for further extending this numerical method are discussed. IV","abstract_has_math":false,"creators":["Trellakis, Alexandros"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Ravaioli, Umberto"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000","date_published":"2000","updated_at":"2026-07-22T22:25:30Z","subjects":["semiconductor device structures","Metal-Oxide-Semiconductor"],"languages":["en"],"rights":["©2000 Trellakis"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4340045"],"render_values":[{"text":"4340045","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/31300","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ravaioli, Umberto"]},{"key":"dc:creator","label":"Author","values":["Trellakis, Alexandros"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2000","10000-01-01","2012-05-30T21:31:30Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["semiconductor device structures","Metal-Oxide-Semiconductor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©2000 Trellakis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/31300","4340045"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This study has three goals. First, we would like to develop computational tools that are suitable for the analysis and optimization of semiconductor device structures where quantum effects are important, as for example quantum wires and quantum dots but also ultra-narrow Metal-Oxide-Semiconductor (MOS) conduction channels at room temperature. Here, we describe these structures by the coupled system of the Schrodinger and the Poisson equation. We discuss solution strategies for both equations and outline an original iteration approach that uses a predictor-corrector procedure for solving the coupled system self-consistently. Second, we would like to apply these tools to investigate the lateral scalability limits of conduction channels in several MOS structures, at room temperature, with the goal to understand for which geometries and under which operating conditions a narrow channel approaching the quantum-wire limit can maintain reasonable isolation. We find that a good trade-off in performance and manufacturability is obtained for structures with T-shaped gate metallization. The calculations presented here also show that, depending on gate geometry and channel doping, it should be possible to operate a quasi-monomode silicon based quantum wire at room temperature. Finally, a full-band approach for the solution of Schrodinger's equation based on Fast Fourier Transforms is described. Using this simulation method, it becomes possible to solve Schrodinger's equation in the one band approximation for arbitrary band structures, putting a more complete description of high energy states and realistic temperatures within reach. Two example applications concerning non-parabolic effects in silicon quantum structures are presented, a MOS quantum capacitor and a MOS quantum cavity. Future directions for further extending this numerical method are discussed. IV","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-05-30T21:31:30Z No. of bitstreams: 1 2000_trellakis.pdf: 3769352 bytes, checksum: cf9f5b40da2749b7e1d6ac8ede374229 (MD5)","Made available in DSpace on 2012-05-30T21:31:30Z (GMT). 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First, we would like to develop computational tools that are suitable for the analysis and optimization of semiconductor device structures where quantum effects are important, as for example quantum wires and quantum dots but also ultra-narrow Metal-Oxide-Semiconductor (MOS) conduction channels at room temperature. Here, we describe these structures by the coupled system of the Schrodinger and the Poisson equation. We discuss solution strategies for both equations and outline an original iteration approach that uses a predictor-corrector procedure for solving the coupled system self-consistently. Second, we would like to apply these tools to investigate the lateral scalability limits of conduction channels in several MOS structures, at room temperature, with the goal to understand for which geometries and under which operating conditions a narrow channel approaching the quantum-wire limit can maintain reasonable isolation. We find that a good trade-off in performance and manufacturability is obtained for structures with T-shaped gate metallization. The calculations presented here also show that, depending on gate geometry and channel doping, it should be possible to operate a quasi-monomode silicon based quantum wire at room temperature. Finally, a full-band approach for the solution of Schrodinger's equation based on Fast Fourier Transforms is described. Using this simulation method, it becomes possible to solve Schrodinger's equation in the one band approximation for arbitrary band structures, putting a more complete description of high energy states and realistic temperatures within reach. Two example applications concerning non-parabolic effects in silicon quantum structures are presented, a MOS quantum capacitor and a MOS quantum cavity. Future directions for further extending this numerical method are discussed. IV","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-05-30T21:31:30Z No. of bitstreams: 1 2000_trellakis.pdf: 3769352 bytes, checksum: cf9f5b40da2749b7e1d6ac8ede374229 (MD5)","Made available in DSpace on 2012-05-30T21:31:30Z (GMT). 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