EFECTUL%20CONFINARII%20CUANTICE%20ASUPRA%20STRUCTURII%20ENERGETICE%20A%20SISTEMELOR%20CU%20DIMENSIONALITATE%20REDUSA

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EFECTUL CONFINARII CUANTICE ASUPRA STRUCTURII
ENERGETICE A SISTEMELOR CU DIMENSIONALITATE
REDUSA

• Magdalena Lidia Ciurea
• National Institute of Materials Physics,
  Bucharest-Magurele

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CONTENT 1. INTRODUCTION 2. 2D SYSTEMS 3. 1D
SYSTEMS 4. 0D SYSTEMS 5. CONCLUSIONS
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1. INTRODUCTION
Low dimensional system (LDS) ? nanometric size on
at least one direction.
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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

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2. 2D SYSTEMS

• Plane nanolayers
• Hamiltonian splitting (exact)
• parallel part Bloch-type ? 2D band structure
• perpendicular part infinite rectangular
  quantum
• well (IRQW) ? QC levels

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T 0 K ? en(kx, ky) Ev EQC0 ? By
convention, EQC0 0.
QC levels located in the band gap!
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• Application quantum well solar cells (QWSC)
• Matrix element of electric dipole interaction
  Hamiltonian

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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-th non-null zero of cylindrical Bessel
function Jl(x)
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T 0 K ? en(kz) Ev EQC0 ? ? EQC0 0.
QC levels located in the band gap!
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Valence band particle reservoir ? excitation
transitions start from the fundamental level ?
activation energy ratio
Thermal transition ? ?e minimum Electrical
transition (eU gtgt kBT) ? ?l 0 Optical
transition ? ?l 1.
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Thermal excitation
Electrical excitation
Optical transition
?E min
?l 0
?l 1
E
E
E
l 0
l 1
l 2
l 2
l 2
l 1
l 1
l 0
l 0
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Application nc-PS

• I T characteristics ? ?l 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 e d 2 ? df 3.31 0.03 nm LCAO e
d a, a 1.02 ? df 3.40 0.03 nm.
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Application nc-PS

• I ? characteristics ? ?l 1.

No. 1 2 3 4 F 5 6 7 8
? (nm) 504 574 629 717 761 827 873 932 1025
E (eV) 2.46 2.16 1.97 1.73 1.63 1.50 1.42 1.33 1.21
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QC transitions identified in nc-PS
nc-PS No. Eexp (eV) Transition
PT spectral maxima 1 2.46 (2, 1) ? (3, 2)
PT spectral maxima 2 2.16 (0, 0) ? (2, 1)
PT spectral maxima 3 1.97 (1, 1) ? (3, 0)
PT spectral maxima 4 1.74 (0, 2) ? (2, 1)
PT spectral maxima 5 1.50 (0, 2) ? (1, 3)
PT spectral maxima 6 1.42
PT spectral maxima 7 1.33 (0, 1) ? (2, 0)
PT spectral maxima 8 1.21 (0, 1) ? (1, 2)
PL 1 1.89 (1, 1) ? (2, 2) (1, 1) ? (3, 0)
TDDC 1 0.55 (0, 0) ? (1, 0)
TDDC 2 1.50 (0, 0) ? (2, 0)
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4. 0D SYSTEMS

• Spherical nanodots quantum dots
• d 5 nm ? no more bands ? groups of energy
  levels quasibands

xp,l p-th non-null zero of spherical Bessel
function jl(x)
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T 0 K ? e(0) Ev EQC0 ? ? EQC0 0.
l orbital quantum number.
QC levels located in the quasiband gap!
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EMA e d 2 LCAO e d a, a 1.39
? m m0e for quantum dots
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No more proper VB no more particle reservoir ?
excitation transitions from the last occupied
level to the next one ? selection rules
?
Thermal transition ? ?e minimum Electrical
transition (eU gtgt kBT) ? ?l 0 Optical
transition ? ?l 1.
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Thermal excitation
Electrical excitation
Optical transition
?E minim
?l 0
?l 1
E
E
E
l 0
l 1
l 2
l 2
l 2
l 1
l 1
l 0
l 0
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• Application Si SiO2

PL spectrogram ? ?l 1
I T characteristics ? ?l 0
No. 1 2 3 4
? (nm) 415 436 571 479
E (eV) 2.99 2.85 2.71 2.59
E1 0.22 0.02 eV E2 0.32 0.02 eV E3 0.44
0.02 eV
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QC transitions identified in Si SiO2
Si SiO2 No. Eexp (eV) Transition
PL (d 4,92 nm) 1 2,99 (1, 2) ? (6, 1)
PL (d 4,92 nm) 2 2,85 (0, 1) ? (5, 2)
PL (d 4,92 nm) 3 2,71 (1, 1) ? (6, 0)
PL (d 4,92 nm) 4 2,59 (1, 1) ? (5, 2)
TDDC (d 5,28 nm) 1 0,22 (0, 1) ? (1, 1)
TDDC (d 5,28 nm) 2 0,32 (1, 1) ? (2, 1)
TDDC (d 5,28 nm) 3 0,44 (2, 1) ? (3, 1)
sr lt 3
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5. CONCLUSIONS
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THANK YOU FOR YOUR ATTENTION!