efectul confinarii cuantice asupra structurii energetice a sistemelor cu dimensionalitate redusa...
TRANSCRIPT
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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
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.
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.
daNNS 32
,5.0 NNS
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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 effectinfinite quantum well = first approximation
Shape of the quantum well ratios between energies of consecutive levels choice of the shaperectangular quantum well = good approximation
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2. 2D SYSTEMS
Plane nanolayersHamiltonian splitting (exact): parallel part – Bloch-type 2D band structure; perpendicular part – infinite rectangular quantum well (IRQW) QC levels
.0,2
, 22
222
pp
dmkk yxn
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T = 0 K εn(kx, ky) = Ev; EQC0 = ? By convention, EQC0 ≡ 0.
QC levels located in the band gap!
.,
122
,
1
22
22
2
222
pyxs
n
yxn
kk
pdmdm
kk
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Application: quantum well solar cells (QWSC)
Matrix element of electric dipole interaction Hamiltonian:
0sinsin2
0
t
iffi dz
d
zp
d
zprEe
dH
12; pppEEppEE ifif
pi = 1 internal quantum efficiency: 42
22
20
2
2
14
sin4096
p
ip
c
e
r
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3. 1D SYSTEMS
Cylindrical nanowiresHamiltonian 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)
2,2
221 2
lpt
zn xdm
k
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T = 0 K εn(kz) = Ev; EQC0 = ? EQC0 ≡ 0.
QC levels located in the band gap!
,
22
,1
20,1
2,2
222
0,12
221
lpzs
n
lptt
zn
k
xxdm
xdm
k
l – orbital quantum number.
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Valence band = particle reservoir excitation transitions start from the fundamental level activation energy ratio
20,1
2',1'
20,1
2'',1''
xx
xxR
lp
lpnw
Thermal transition Δε = minimum;Electrical transition (eU >> kBT) Δl = 0;Optical transition Δl = ± 1.
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E E
Thermal excitation
Electrical excitation
Optical transition
E
ΔE = min Δl = 0 Δl = ± 1
l = 0
l = 1
l = 2
l = 2
l = 2l = 1
l = 1
l = 0
l = 0
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Application: nc-PS
a b
a – fresh sample; activation energy: E1 = 0.52 ± 0.03 eV
b – stabilized sample; activation energies:E1 = 0.55 ± 0.05 eV, E2 = 1.50 ± 0.30 eV;
E2/E1 = 2.727
E1 = ε1,0, E2 = ε2,0;ds = 3.22 ± 0.05 nm.
I – T characteristics Δl = 0.
EMA: ε ~ d – 2 df = 3.31 ± 0.03 nm;LCAO: ε ~ d – α, α = 1.02 df = 3.40 ± 0.03 nm.
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Application: nc-PS I – λ characteristics Δl = ± 1.
No. 1 2 3 4 F 5 6 7 8
λ (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
1
2
34
5 6
78
1
23
F5
7
1 V 20 V
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nc-PS No. Eexp (eV) Transition
PTspectral maxima
1 2.46 (2, 1) (3, 2)
2 2.16 (0, 0) (2, 1)
3 1.97 (1, 1) (3, 0)
4 1.74 (0, 2) (2, 1)
5 1.50 (0, 2) (1, 3)
6 1.42 –
7 1.33 (0, 1) (2, 0)
8 1.21 (0, 1) (1, 2)
PL 1 1.89(1, 1) (2, 2)(1, 1) (3, 0)
TDDC1 0.55 (0, 0) (1, 0)
2 1.50 (0, 0) (2, 0)
QC transitions identified in nc-PS:
1exp theorr EE , |σr| ≤ 5 %.
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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)
2,2
220 2
lpxdm
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T = 0 K ε(0) = Ev; EQC0 = ? EQC0 ≡ 0.
QC levels located in the quasiband gap!
l – orbital quantum number.
lpVlp Exxdm
xdm
,12
0,12
,2
222
0,12
220 22
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EMA: ε ~ d – 2
LCAO: ε ~ d – α, α = 1.39
m* ≈ m0e for quantum dots
mmd
amm e0
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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 Δε = minimum;Electrical transition (eU >> kBT) Δl = 0;Optical transition Δl = ± 1.
21,
21','
21','
21'',''
plpl
plplqd
xx
xxR
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E E E
Thermal excitation
Electrical excitation
Optical transitionΔE = minim Δl = 0 Δl = ± 1
l = 0
l = 1
l = 2
l = 2
l = 2l = 1
l = 1
l = 0
l = 0
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Application: Si – SiO2
1
2 34 64 % nc-Si
No. 1 2 3 4
λ (nm) 415 436 571 479
E (eV) 2.99 2.85 2.71 2.59
PL spectrogram Δl = ± 1I – T characteristics Δl = 0
E1 = 0.22 ± 0.02 eVE2 = 0.32 ± 0.02 eVE3 = 0.44 ± 0.02 eV
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Si – SiO2 No. Eexp (eV) Transition
PL(d = 4,92 nm)
1 2,99 (1, 2) → (6, 1)
2 2,85 (0, 1) → (5, 2)
3 2,71 (1, 1) → (6, 0)
4 2,59 (1, 1) → (5, 2)
TDDC(d = 5,28 nm)
1 0,22 (0, 1) (1, 1)
2 0,32 (1, 1) (2, 1)
3 0,44 (2, 1) (3, 1)
QC transitions identified in Si – SiO2
|σr| < 3 %
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5. CONCLUSIONS
Differences between model and experiment due to: size distribution; shape distribution; finite depth of the quantum well.
Allmost ALL the energies measured in electrical transport, phototransport and photoluminescence transitions between QC levels.
Different quantum selection rules different energy levels.
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THANK YOU FOR YOUR ATTENTION!