Quantum size effects in the fermi energy and electronic density of states in a finite square well thin film model |
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| Affiliation: | 1. Institute for Nanoscale Technology, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia;2. Australian Institute for Bioengineering and Nanotechnology, University of Queensland, QLD 4072, Australia;3. Centre for Advanced Imaging, University of Queensland, QLD 4072, Australia;4. Institute for Nanocale Technology, Sydney, Australia;5. Plasma Nanoscience Laboratories, CSIRO Manufacturing Flagship, PO Box 218, Lindfield, NSW 2070, Australia;6. Institute for Future Environments and School of Chemistry, Physics, and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD 4000, Australia;1. Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia;2. Department of Physics, Donbass State Engineering Academy, Shcadinova 72, 84313 Kramatorsk, Ukraine;3. Centro de Investigación en Ciencias, Instituto de Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos, Mexico;1. College of Information and Communication Engineering, Sungkyunkwan University, Gyeong-do 16419, Suwon 440-746, Republic of Korea;2. Department of Electrical and Computer Engineering, Sungkyunkwan University, Gyeong-do 16419, Suwon 440-746, Republic of Korea;1. Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, People''s Republic of China;2. College of Information Science and Engineering, Fujian University of Technology, Fuzhou 350118, People''s Republic of China |
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| Abstract: | The dependence of the Fermi energy, EF, and the electronic density of states, ρ(E), of thin metallic films (Lz ≲ 50 Å) on film thickness, electron density, and potential well depth, is systematically investigated in a free-electron, finite square well model. Two size-dependent effects are observed: (1) oscillations in EF and ρ(E) due to the size-quantization of the energy levels, and (2) changes in the mean values of these quantities, averaged over several oscillation periods, relative to their bulk values. The mean value of EF is increased relative to its bulk value by as much as 5%–10% for physically reasonable well depths and typical metallic electron densities. For the special case in which the top energy level in the well is occupied, the mean value of EF is equal to its bulk value. The mean value ofρ(EF) can be either greater than or less than its bulk value, depending on the well depth. In contrast to the small amplitude oscillations in EF, the oscillations in ρ(EF) may have an amplitude as large as 25% of the mean value for sufficiently thin films. Accurate analytic expressions for the thickness dependence of the Fermi energy and density of states are derived. |
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