Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties
A simulation of quantum dot (QD) energy levels was designed to reproduce a quantum mechanical analytic method based on perturbation theory. A Schrödinger equation describing an electron–hole pair in a QD was solved, in consideration of the heterogeneity of the material parameters of the core and she...
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MDPI AG
2022-10-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/12/20/3590 |
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| author | Honyeon Lee Dongjin Kim |
| author_facet | Honyeon Lee Dongjin Kim |
| author_sort | Honyeon Lee |
| collection | DOAJ |
| description | A simulation of quantum dot (QD) energy levels was designed to reproduce a quantum mechanical analytic method based on perturbation theory. A Schrödinger equation describing an electron–hole pair in a QD was solved, in consideration of the heterogeneity of the material parameters of the core and shell. The equation was solved numerically using single-particle basis sets to obtain the eigenstates and energies. This approach reproduced an analytic solution based on perturbation theory, while the calculation was performed using a numerical method. Owing to the effectiveness of the method, QD behavior according to the core diameter and external electric field intensity could be investigated reliably and easily. A 9.2 nm diameter CdSe/ZnS QD with a 4.2 nm diameter core and 2.5 nm thick shell emitted a 530 nm green light, according to an analysis of the effects of core diameter on energy levels. A 4 nm redshift at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup></mrow></semantics></math></inline-formula> V/cm electric field intensity was found while investigating the effects of external electric field on energy levels. These values agree well with previously reported experimental results. In addition to the energy levels and light emission wavelengths, the spatial distributions of wavefunctions were obtained. This analysis method is widely applicable for studying QD characteristics with varying structure and material compositions and should aid the development of high-performance QD technologies. |
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| language | English |
| last_indexed | 2024-03-09T19:40:55Z |
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| spelling | doaj.art-e6ba732d32834b0282f9fb76438ea7b72023-11-24T01:39:45ZengMDPI AGNanomaterials2079-49912022-10-011220359010.3390/nano12203590Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission PropertiesHonyeon Lee0Dongjin Kim1Department of Electronic Materials, Devices and Equipment Engineering, Soonchunhyang University, Asan 31538, KoreaDepartment of Electronic Materials, Devices and Equipment Engineering, Soonchunhyang University, Asan 31538, KoreaA simulation of quantum dot (QD) energy levels was designed to reproduce a quantum mechanical analytic method based on perturbation theory. A Schrödinger equation describing an electron–hole pair in a QD was solved, in consideration of the heterogeneity of the material parameters of the core and shell. The equation was solved numerically using single-particle basis sets to obtain the eigenstates and energies. This approach reproduced an analytic solution based on perturbation theory, while the calculation was performed using a numerical method. Owing to the effectiveness of the method, QD behavior according to the core diameter and external electric field intensity could be investigated reliably and easily. A 9.2 nm diameter CdSe/ZnS QD with a 4.2 nm diameter core and 2.5 nm thick shell emitted a 530 nm green light, according to an analysis of the effects of core diameter on energy levels. A 4 nm redshift at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup></mrow></semantics></math></inline-formula> V/cm electric field intensity was found while investigating the effects of external electric field on energy levels. These values agree well with previously reported experimental results. In addition to the energy levels and light emission wavelengths, the spatial distributions of wavefunctions were obtained. This analysis method is widely applicable for studying QD characteristics with varying structure and material compositions and should aid the development of high-performance QD technologies.https://www.mdpi.com/2079-4991/12/20/3590quantum dotsCdSe/ZnScore diameterelectric field intensityenergy levelsperturbation |
| spellingShingle | Honyeon Lee Dongjin Kim Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties Nanomaterials quantum dots CdSe/ZnS core diameter electric field intensity energy levels perturbation |
| title | Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties |
| title_full | Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties |
| title_fullStr | Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties |
| title_full_unstemmed | Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties |
| title_short | Quantum Mechanical Analysis Based on Perturbation Theory of CdSe/ZnS Quantum-Dot Light-Emission Properties |
| title_sort | quantum mechanical analysis based on perturbation theory of cdse zns quantum dot light emission properties |
| topic | quantum dots CdSe/ZnS core diameter electric field intensity energy levels perturbation |
| url | https://www.mdpi.com/2079-4991/12/20/3590 |
| work_keys_str_mv | AT honyeonlee quantummechanicalanalysisbasedonperturbationtheoryofcdseznsquantumdotlightemissionproperties AT dongjinkim quantummechanicalanalysisbasedonperturbationtheoryofcdseznsquantumdotlightemissionproperties |