efectul confinarii cuantice asupra structurii energetice a sistemelor cu dimensionalitate redusa l.
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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

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

slide2

CONTENT:

1. INTRODUCTION

2. 2D SYSTEMS

3. 1D SYSTEMS

4. 0D SYSTEMS

5. CONCLUSIONS

slide3

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.

slide4

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

slide5

2. 2D SYSTEMS

  • Plane nanolayers
  • Hamiltonian splitting (exact):
  • parallel part – Bloch-type  2D band structure;
  • perpendicular part – infinite rectangular quantum

well (IRQW)  QC levels

slide6

T = 0 K  εn(kx, ky) = Ev; EQC0 = ? By convention,EQC0 ≡ 0.

QC levels located in the band gap!

slide7

pi = 1 internal quantum efficiency:

  • Application: quantum well solar cells (QWSC)
  • Matrix element of electric dipole interaction Hamiltonian:
slide8

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)

slide9

l – orbital quantum number.

T = 0 K  εn(kz) = Ev; EQC0 = ? EQC0 ≡ 0.

QC levels located in the band gap!

slide10

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.

slide11

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

slide12

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.

slide13

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.
slide14

, |σr| ≤ 5 %.

QC transitions identified in nc-PS:

slide15

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)

slide16

T = 0 K  ε(0) = Ev; EQC0 = ? EQC0 ≡ 0.

l – orbital quantum number.

QC levels located in the quasiband gap!

slide17

EMA:ε ~d – 2

LCAO:ε ~ d–α, α = 1.39

m*≈ m0efor quantum dots

slide18

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.

slide19

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

slide20

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

slide22

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