{"id":{"repo_id":"tu-berlin","oai_identifier":"oai:depositonce.tu-berlin.de:11303/22681"},"canonical_url":"https://search.dev.ndltd.org/etd/tu-berlin/oai:depositonce.tu-berlin.de:11303/22681","repository":{"repo_id":"tu-berlin","name":"Technische Universität Berlin","base_url":"https://api-depositonce.tu-berlin.de/server/oai/request"},"display":{"title":"Assessing electronic transport in solid materials via the fluctuation-dissipation theorem","abstract":"For the first-principles evaluation of electronic heat and charge transport coefficients, the Kubo-Greenwood formalism represents an appealing alternative to perturbative approaches, since it naturally incorporates all orders of anharmonic and vibronic effects. In practice, however, Kubo-Greenwood calculations often come with prohibitive computational costs, since crystalline materials typically require both dense reciprocal-space 𝐤-grids for the electronic degrees of freedom and large real-space supercells for the vibrational ones. This is especially challenging for the charge transport coefficient of intrinsic semiconductors with dispersive electronic structures, because the free carriers are very localised in 𝐤-space, which demands an extremely fine 𝐤-grid. In this work, we implement and investigate the application of the Fourier interpolation that can facilitate access to the extremely fine 𝐤-grids necessary to establish convergence. This enables the use of very dense 𝐤-grids for the evaluation of the Kubo-Greenwood formula, while 𝐤-grids used during the self-consistency cycle must only be dense enough to converge the total energy, which can typically be accomplished with substantially coarser 𝐤-grids. As demonstrated for silicon, this enables us to achieve 𝐤-grid convergence of the electrical conductivity spectrum with reduced computational resources. In other words, we can obtain 𝐤-grid convergence for systems, for which this was impossible before. This constitutes an important step towards affordable, fully anharmonic predictions of electronic heat and charge transport coefficients for all crystalline materials.","abstract_html":"For the first-principles evaluation of electronic heat and charge transport coefficients, the Kubo-Greenwood formalism represents an appealing alternative to perturbative approaches, since it naturally incorporates all orders of anharmonic and vibronic effects. In practice, however, Kubo-Greenwood calculations often come with prohibitive computational costs, since crystalline materials typically require both dense reciprocal-space 𝐤-grids for the electronic degrees of freedom and large real-space supercells for the vibrational ones. This is especially challenging for the charge transport coefficient of intrinsic semiconductors with dispersive electronic structures, because the free carriers are very localised in 𝐤-space, which demands an extremely fine 𝐤-grid. In this work, we implement and investigate the application of the Fourier interpolation that can facilitate access to the extremely fine 𝐤-grids necessary to establish convergence. This enables the use of very dense 𝐤-grids for the evaluation of the Kubo-Greenwood formula, while 𝐤-grids used during the self-consistency cycle must only be dense enough to converge the total energy, which can typically be accomplished with substantially coarser 𝐤-grids. As demonstrated for silicon, this enables us to achieve 𝐤-grid convergence of the electrical conductivity spectrum with reduced computational resources. In other words, we can obtain 𝐤-grid convergence for systems, for which this was impossible before. This constitutes an important step towards affordable, fully anharmonic predictions of electronic heat and charge transport coefficients for all crystalline materials.","abstract_has_math":false,"creators":["Fiebig, Florian"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024","date_published":"2024","updated_at":"2026-07-27T21:28:29Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by-nc-sa/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.14279/depositonce-21491"],"render_values":[{"text":"https://doi.org/10.14279/depositonce-21491","href":"https://doi.org/10.14279/depositonce-21491","code":true}]}]},"links":{"outbound_url":"https://depositonce.tu-berlin.de/handle/11303/22681","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Fiebig, Florian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-10-16T07:22:39Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-10-16T07:22:39Z"]},{"key":"dc:date.issued","label":"Date","values":["2024"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by-nc-sa/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://depositonce.tu-berlin.de/handle/11303/22681","https://doi.org/10.14279/depositonce-21491"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For the first-principles evaluation of electronic heat and charge transport coefficients, the Kubo-Greenwood formalism represents an appealing alternative to perturbative approaches, since it naturally incorporates all orders of anharmonic and vibronic effects. In practice, however, Kubo-Greenwood calculations often come with prohibitive computational costs, since crystalline materials typically require both dense reciprocal-space 𝐤-grids for the electronic degrees of freedom and large real-space supercells for the vibrational ones. This is especially challenging for the charge transport coefficient of intrinsic semiconductors with dispersive electronic structures, because the free carriers are very localised in 𝐤-space, which demands an extremely fine 𝐤-grid. In this work, we implement and investigate the application of the Fourier interpolation that can facilitate access to the extremely fine 𝐤-grids necessary to establish convergence. This enables the use of very dense 𝐤-grids for the evaluation of the Kubo-Greenwood formula, while 𝐤-grids used during the self-consistency cycle must only be dense enough to converge the total energy, which can typically be accomplished with substantially coarser 𝐤-grids. As demonstrated for silicon, this enables us to achieve 𝐤-grid convergence of the electrical conductivity spectrum with reduced computational resources. In other words, we can obtain 𝐤-grid convergence for systems, for which this was impossible before. This constitutes an important step towards affordable, fully anharmonic predictions of electronic heat and charge transport coefficients for all crystalline materials.","Zur Bestimmung der elektronischen Wärme- und Ladungstransportkoeffizienten stellt der Kubo- Greenwood-Formalismus eine reizvolle Alternative zu störungstheoretischen Methoden dar, weil er auf natürliche Weise alle Ordnungen von Anharmonizitäten berücksichtigt. Die Kubo-Greenwood- Rechenkosten sind allerdings oft so hoch, dass die Durchführung der Berechnung unmöglich ist, weil kristalline Materialien gleichzeitig ein dichtes, reziprokes Gitter zum Erfassen der elektronischen Freiheitsgrade und eine große Realraum-Superzelle für die phononischen Freiheitsgrade benötigen. Eine besondere Herausforderung stellt die elektrische Leitfähigkeit von intrinsischen Halbleitern mit dispersiven Elektronenstrukturen dar, weil die freien Ladungsträger im reziproken 𝐤-Raum extrem lokalisiert sind, sodass ein sehr feines 𝐤-Gitter erforderlich ist. In dieser Arbeit implementieren und untersuchen wir die Anwendung der Fourier-Interpolation, um entsprechend feine 𝐤-Gitter zugänglich zu machen. So wird zur Auswertung der Kubo-Greenwood- Formel ein sehr feines 𝐤-Gitter mithilfe der Fourier-Interpolation berechnet, während in der Selbstkonsistenz-Schleife ein 𝐤-Gitter verwendet werden kann, das lediglich dicht genug ist, um die Gesamtenergie zu konvergieren, was typischerweise mit deutlich gröberen 𝐤-Gittern erreicht werden kann. Wie wir für den prototypischen Halbleiter Silizium in dieser Arbeit gezeigt haben, können wir dadurch das elektrische Leitfähigkeitsspektrum in Bezug auf das 𝐤-Gitter mit Rechenkapazitäten konvergieren, mit denen dies zuvor unmöglich war. Damit ist ein wichtiger Schritt auf dem Weg zu bezahlbaren, elektronischen Wärme- und Ladungstransportkoeffizienten gemacht, die elegant alle Ordnungen von Anharmonizitäten berücksichtigen."]},{"key":"dc:title","label":"Title","values":["Assessing electronic transport in solid materials via the fluctuation-dissipation theorem"]}]}],"canonical_facts":{"dc:creator":["Fiebig, Florian"],"dc:date.accessioned":["2024-10-16T07:22:39Z"],"dc:date.available":["2024-10-16T07:22:39Z"],"dc:date.issued":["2024"],"dc:description.abstract":["For the first-principles evaluation of electronic heat and charge transport coefficients, the Kubo-Greenwood formalism represents an appealing alternative to perturbative approaches, since it naturally incorporates all orders of anharmonic and vibronic effects. In practice, however, Kubo-Greenwood calculations often come with prohibitive computational costs, since crystalline materials typically require both dense reciprocal-space 𝐤-grids for the electronic degrees of freedom and large real-space supercells for the vibrational ones. This is especially challenging for the charge transport coefficient of intrinsic semiconductors with dispersive electronic structures, because the free carriers are very localised in 𝐤-space, which demands an extremely fine 𝐤-grid. In this work, we implement and investigate the application of the Fourier interpolation that can facilitate access to the extremely fine 𝐤-grids necessary to establish convergence. This enables the use of very dense 𝐤-grids for the evaluation of the Kubo-Greenwood formula, while 𝐤-grids used during the self-consistency cycle must only be dense enough to converge the total energy, which can typically be accomplished with substantially coarser 𝐤-grids. As demonstrated for silicon, this enables us to achieve 𝐤-grid convergence of the electrical conductivity spectrum with reduced computational resources. In other words, we can obtain 𝐤-grid convergence for systems, for which this was impossible before. This constitutes an important step towards affordable, fully anharmonic predictions of electronic heat and charge transport coefficients for all crystalline materials.","Zur Bestimmung der elektronischen Wärme- und Ladungstransportkoeffizienten stellt der Kubo- Greenwood-Formalismus eine reizvolle Alternative zu störungstheoretischen Methoden dar, weil er auf natürliche Weise alle Ordnungen von Anharmonizitäten berücksichtigt. Die Kubo-Greenwood- Rechenkosten sind allerdings oft so hoch, dass die Durchführung der Berechnung unmöglich ist, weil kristalline Materialien gleichzeitig ein dichtes, reziprokes Gitter zum Erfassen der elektronischen Freiheitsgrade und eine große Realraum-Superzelle für die phononischen Freiheitsgrade benötigen. Eine besondere Herausforderung stellt die elektrische Leitfähigkeit von intrinsischen Halbleitern mit dispersiven Elektronenstrukturen dar, weil die freien Ladungsträger im reziproken 𝐤-Raum extrem lokalisiert sind, sodass ein sehr feines 𝐤-Gitter erforderlich ist. In dieser Arbeit implementieren und untersuchen wir die Anwendung der Fourier-Interpolation, um entsprechend feine 𝐤-Gitter zugänglich zu machen. So wird zur Auswertung der Kubo-Greenwood- Formel ein sehr feines 𝐤-Gitter mithilfe der Fourier-Interpolation berechnet, während in der Selbstkonsistenz-Schleife ein 𝐤-Gitter verwendet werden kann, das lediglich dicht genug ist, um die Gesamtenergie zu konvergieren, was typischerweise mit deutlich gröberen 𝐤-Gittern erreicht werden kann. Wie wir für den prototypischen Halbleiter Silizium in dieser Arbeit gezeigt haben, können wir dadurch das elektrische Leitfähigkeitsspektrum in Bezug auf das 𝐤-Gitter mit Rechenkapazitäten konvergieren, mit denen dies zuvor unmöglich war. Damit ist ein wichtiger Schritt auf dem Weg zu bezahlbaren, elektronischen Wärme- und Ladungstransportkoeffizienten gemacht, die elegant alle Ordnungen von Anharmonizitäten berücksichtigen."],"dc:identifier.uri":["https://depositonce.tu-berlin.de/handle/11303/22681","https://doi.org/10.14279/depositonce-21491"],"dc:language.iso":["en"],"dc:rights.uri":["https://creativecommons.org/licenses/by-nc-sa/4.0/"],"dc:title":["Assessing electronic transport in solid materials via the fluctuation-dissipation theorem"],"dc:type":["Master Thesis"]},"updated_at":"2026-07-27T21:28:29Z"}