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EFECTUL CONFINARII CUANTICE ASUPRA STRUCTURII ENERGETICE A SISTEMELOR CU DIMENSIONALITATE REDUSA

NATIONAL INSTITUTE OF MATERIALS PHYSICS BUCHAREST-MAGURELE. EFECTUL CONFINARII CUANTICE ASUPRA STRUCTURII ENERGETICE A SISTEMELOR CU DIMENSIONALITATE REDUSA. Magdalena Lidia Ciurea National Institute of Materials Physics, Bucharest-Magurele. CONTENT: 1. INTRODUCTION 2. 2D SYSTEMS

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EFECTUL CONFINARII CUANTICE ASUPRA STRUCTURII ENERGETICE A SISTEMELOR CU DIMENSIONALITATE REDUSA

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  1. NATIONAL INSTITUTE OF MATERIALS PHYSICS BUCHAREST-MAGURELE EFECTUL CONFINARII CUANTICE ASUPRA STRUCTURII ENERGETICE A SISTEMELOR CU DIMENSIONALITATE REDUSA Magdalena Lidia Ciurea National Institute of Materials Physics, Bucharest-Magurele

  2. CONTENT: 1. INTRODUCTION 2. 2D SYSTEMS 3. 1D SYSTEMS 4. 0D SYSTEMS 5. CONCLUSIONS

  3. Ratio between the number of atoms located at the surface/interface and the total number of atoms: δ – system dimensionality; a – interatomic distance; d – (minimum) LDS size; a ≈ 0.25 nm  d0 = 3 nm, d1 = 2 nm, d2 = 1 nm. 1. INTRODUCTION Low dimensional system (LDS)  nanometric size on at leastone direction.

  4. Surface/interface  potential barrier  wall of a quantum well  quantum confinement (QC) • QC – ZERO ORDER EFFECT • nature of the material – first order effect • infinite quantum well = first approximation • Shape of the quantum well  ratios between energies of consecutive levels  choice of the shape rectangular quantum well = good approximation

  5. 2. 2D SYSTEMS • Plane nanolayers • Hamiltonian splitting (exact): • parallel part – Bloch-type  2D band structure; • perpendicular part – infinite rectangular quantum well (IRQW)  QC levels

  6. T = 0 K  εn(kx, ky) = Ev; EQC0 = ? By convention,EQC0 ≡ 0. QC levels located in the band gap!

  7. pi = 1 internal quantum efficiency: • Application: quantum well solar cells (QWSC) • Matrix element of electric dipole interaction Hamiltonian:

  8. 3. 1D SYSTEMS • Cylindrical nanowires • Hamiltonian splitting (approximate): • longitudinal part – Bloch-type  1D band structure; • transversal part – infinite rectangular quantum well (IRQW)  QC levels xp,l–p-thnon-null zero of cylindrical Bessel functionJl(x)

  9. l – orbital quantum number. T = 0 K  εn(kz) = Ev; EQC0 = ? EQC0 ≡ 0. QC levels located in the band gap!

  10. Valence band = particle reservoir  excitation transitions start from the fundamental level activation energy ratio Thermal transition  Δε = minimum; Electrical transition (eU >> kBT)  Δl= 0; Optical transition  Δl= ± 1.

  11. Thermal excitation Electrical excitation Optical transition ΔE = min Δl = 0 Δl = ± 1 E E E l = 0 l = 1 l = 2 l = 0 l = 1 l = 2 l = 0 l = 1 l = 2

  12. a b E1 = ε1,0, E2 = ε2,0; ds = 3.22 ± 0.05 nm.  Application: nc-PS • I – Tcharacteristics Δl = 0. b – stabilized sample; activation energies: E1 = 0.55 ± 0.05 eV, E2 = 1.50 ± 0.30 eV; E2/E1 = 2.727 a – fresh sample; activation energy: E1 = 0.52 ± 0.03 eV EMA:ε ~d– 2 df= 3.31 ± 0.03 nm; LCAO:ε ~ d– α, α = 1.02  df = 3.40 ± 0.03 nm.

  13. 5 6 2 1 V 20 V 7 1 3 8 1 4 F 5 7 2 3 Application: nc-PS • I – λcharacteristics Δl = ± 1.

  14. , |σr| ≤ 5 %. QC transitions identified in nc-PS:

  15. 4. 0D SYSTEMS • Spherical nanodots – quantum dots • d≤ 5 nm no more bands  groups of energy levels = quasibands xp,l–p-thnon-null zero of spherical Bessel functionjl(x)

  16. T = 0 K  ε(0) = Ev; EQC0 = ? EQC0 ≡ 0. l – orbital quantum number. QC levels located in the quasiband gap!

  17. EMA:ε ~d – 2 LCAO:ε ~ d–α, α = 1.39 m*≈ m0efor quantum dots

  18. No more proper VB = no more particle reservoir  excitation transitions: from the last occupied level to the next one  selection rules  Thermal transition  Δε = minimum; Electrical transition (eU >> kBT)  Δl= 0; Optical transition  Δl= ± 1.

  19. Thermal excitation Electrical excitation Optical transition ΔE = minim Δl = 0 Δl = ± 1 E E E l = 0 l = 1 l = 2 l = 0 l = 1 l = 2 l = 0 l = 1 l = 2

  20. 3 2 4 64 % nc-Si 1 • Application: Si – SiO2 I – TcharacteristicsΔl = 0 PL spectrogram Δl = ± 1 E1 = 0.22 ± 0.02 eV E2 = 0.32 ± 0.02 eV E3 = 0.44 ± 0.02 eV

  21. QC transitions identified in Si – SiO2 |σr| < 3 %

  22. Allmost ALL the energies measured in electrical transport, phototransport and photoluminescence  transitions between QC levels. Different quantum selection rules different energy levels. • Differences between model and experiment due to: • size distribution; • shape distribution; • finite depth of the quantum well. 5. CONCLUSIONS

  23. THANK YOU FOR YOUR ATTENTION!

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