1. Quantum Dots in Photonic Structures
Lecture 8: Semiconducotor Quantum dots
Jan Suffczyński
cqd.eecs.northwestern.edu
Wednesdays, 17.00, SDT
Projekt Fizyka Plus nr POKL /11 współfinansowany przez Unię Europejską ze środków Europejskiego
Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

2. Ordering in self-organized
Plan for today
Reminder 2.
Excitons in semiconductor quantum dots 3.
Ordering in self-organized
Quantum Dot system

3. Holes
Consider an insulator (or semiconductor) with a few electrons excited from the valence band into the conduction band
“Deficiency” of negative charge can be treated as a positive charge
Negative curvature of the band  negative hole effective mass

4. Semiconductor Quantum Well

5. Semiconductor Quantum Well

6. Semiconductor Quantum Well
Confinement
potential

7. Quantum Confinement in Nanostructures
1 Direction: Quantum well (thin film)
Two-dimensional excitons
2 Directions: Quantum wire
One-dimensional excitons
3 Directions: Quantum dot
Zero-dimensional excitons
Each confinement direction converts a continuous k in a discrete quantum number n. kx ky nz kx nz ny ny nz nx

8. Density of states Structure Degree of Confinement Bulk Material 0D
Quantum Well 1D 1
Quantum Wire 2D
Quantum Dot 3D
d(E)

9. Confined levels in Quantum Wells
Energy of confined levels
GaAs/AlGaAs Quantum Well
Decrease of the level energy when width of the Quantum Well decreased
R. Dingle,
Festkorperprobleme’1975

10. Confined levels in Quantum Dots
Photoluminescence of
GaAs/GaAlAs Quantum Dots
QD as an artificial atom
B. Piętka et al.

11. QD types and fabrication methods
Goal: to engineer potential energy barriers to confine electrons in 3 dimensions
Basic types/methods
Colloidal chemistry
Electrostatic
Lithography
Epitaxy
Fluctuation
Self-organized
Patterned growth
- „Defect” QDs

12. Photoluminescence spectra of GaN template on sapphire
GaN grown on direction, CEA Valbonne
An evidence for narrow, discrete emission lines!

13. „Defect” type quantum dots

14. „Defect” type quantum dots
HRTEM, S. Kret, IF PAN

15. Cubic GaN vs wurtzite GaN
Structure
Zinc blende
Wurtzite
Lattice constant at 300 K
0.450 nm
a0 = nm c0 = nm
Energy Gap at ~0 K
3.30 eV Ramirez-Flores et al.,1994, Ploog et al., 1995
3.50 eV Dingle et al., 1971 Monemar 1974
Energy of emission (~ eV) agrees resonably with an expectation for cubic GaN inclusions in wurtzite GaN

16. Self-organized Semiconductor QDs
Number of atoms ~
C. H. Li et al,
APL’2005

17. Epitaxy: Self-Organized Growth
Lattice-mismatch induced
island growth
Self-organized QDs through epitaxial growth strains
Stranski-Krastanov growth mode (use MBE, MOCVD)
Islands formed on wetting layer due to lattice mismatch (size ~10s nm)
Disadvantage: size and shape fluctuations, strain,
Control island initiation
Induce local strain, grow on dislocation, vary growth conditions, combine with patterning

18. Semiconductor Quantum Dot
Klimeck et al.

19. QD confined electron wavefunctions
Klimeck et al.

20. InGaAs self-assembled QDs
Calculated confined eh-pair energies
for InAs assuming pyramidal shape
Grundmann, Bimberg et al., TU Berlin

21. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
GaAs:Si substrate
F. Tinjod et al., APL (2003)

22. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
ZnTe buffer 1000 nm
GaAs:Si substrate
F. Tinjod et al., APL (2003)

23. CdTe QDs qrowth – amorfous Te method
ZnTe buffer 1000 nm
GaAs:Si substrate
CdTe layer
F. Tinjod et al., APL (2003)

24. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
amorphous Te
ZnTe buffer 1000 nm
GaAs:Si substrate
CdTe layer
F. Tinjod et al., APL (2003)

25. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
amorphous Te
QDs
ZnTe buffer 1000 nm
GaAs:Si substrate
F. Tinjod et al., APL (2003)

26. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
QDs
ZnTe buffer 1000 nm
GaAs:Si substrate
F. Tinjod et al., APL (2003)

27. CdTe QDs qrowth – amorfous Te deposition method
J. Kobak et al.
ZnTe cap 100 nm
ZnTe buffer 1000 nm
GaAs:Si substrate
F. Tinjod et al., APL (2003)

28. Control of CdTe/ZnTe QD density with the temperature of CdTe deposition
PL intensity
µPL
6 K
0 – 2 QDs
15 – 30 QDs
30 – 60 QDs
300 – 600 QDs
3 ML
Czas nakładania stały różna temperatura nakładania
80 – 160 QDs
500 – 1000 QDs
Photon Energy (meV)
J. Kobak et al., arXiv: (2012)

29. Control of CdTe/ZnTe QD density with the thickness of CdTe layer
PL intensity
T=334 oC
µPL
6 K
1 ML
10 – 20 QDs
2 ML
100 – 200 QDs
3 ML
300 – 600 QDs
4 ML
500 – 1000 QDs
Photon Energy (meV)
J. Kobak et al., arXiv: (2012)

30. Control of CdTe/ZnTe QD density with the thickness of CdTe layer

31. Epitaxy: Patterned Growth
Growth on patterned substrates
Grow QDs in pyramid-shaped recesses
Recesses formed by selective ion etching
Disadvantage: density of QDs limited by mask pattern
T. Fukui et al. GaAs tetrahedral quantum dot structures fabricated using selective area metal organic chemical vapor deposition. Appl. Phys. Lett. May, 1991

32. Excitons in Semiconductor Quantum Dots

33. Exciton formation
The absorption of photon by an interband transition in a semiconductor or insulator creates an electron in the conduction band and hole in the valence band. Eg

34. Exciton formation
This oppositely charged particles attract each other though Coulomb interaction, and there may be the probability of the formation of neutral electron-hole pair called an Exciton.

35. Exciton formation Wannier-Mott excitons Frenkel exciton
A striking resemblance with the hydrogen atom is already evident at first sight; the role of the proton is played here by the hole. If we regard the electron and hole as point charges characterized by their charge and effective masses (the so-called effective mass approximation), we can apply a modified Bohr model of the hydrogen atom. We shall see that this illustrative approximation can explain the majority of the principal features observed in the optical spectra of Wannier excitons in semiconductors

36. Exciton – Bohr model Wannier-Mott excitons
Moddified Bohr model of the hydrogen atom applies
reduced mass
binding energy
dielectric constant

37. Exciton binding Energy
Ry(H) = 13.6 eV
Binding Energy of electron
in Hydrogen atom
Exciton compared to hydrogen atom:
larger ratio of the effective masses
electron and hole are in medium with dielectric constant ranging between 10-30,
 Smaller exciton binding energy
Unlike the pair of a light electron and a very heavy proton, the exciton is composed of two light quasi-particles with comparable masses me mh which entails a lower stability of the exciton in comparison with the hydrogen atom
For stability of Excitons binding energy must be higher than ∼ kBT

38. Exciton Bohr Diameter - bulk
The same size dot of different material may
not assure quantum confinement

39. Oscillator strength of the exciton recombination confined in QD
J. Hours, P. Senellart, E. Peter, A. Cavanna, and J. Bloch, PHYSICAL REVIEW B (R)2005

40. Oscillator strength of the exciton recombination confined in QD

41. How to observe excitons in Semiconductor Quantum Dots?

42. Spectroscopy of individual Quantum Dots
Towards detector
Laser beam
Microscope objective
Sample with QDs

43. Experimental setup
Laser beam

44. Spatial resolution <1m)
Microscope objective
Spatial resolution <1m)
J. Jasny and J. Sepioł, Chem. Phys. Lett. 273,

45. QD exciton emission QDs ensamble emission
Individual QD emission spectrum

46. Excitonic transitions in a quantum dot
Exciton (X) X X:

47. Excitonic transitions in a quantum dot
Biexciton (XX)
XX
XX:

48. Excitonic transitions in a quantum dot
Charged exciton (X+ or X-)
CX
CX:

49. X Xdark X Neutral exciton X Formed by: heavy hole and electron
Jz = ±3/2
Jz = ±1/2
4 possible spin states of X
Xdark X
Jz = -1
Jz = +1
Jz = -2
Jz = +2

50. Fine structure of neutral exciton
( + )/ 2 X
δ1~0.1meV
( – )/ 2 X
Anisotropic exchange
δ0~1meV
Isotropic exchange
( + )/ 2
δ2 ≈0
Xdark
( – )/ 2

51. QD anisotropy
AES
Energy ~ XX
AES V H
AES X V H
empty dot

52. Fine structure of neutral exciton
Anisotropic exchange splitting:
AES = 182  6eV

53. Excitonic states in magnetic field
B = 0 - +
B > 0, B||z
~gXBB XX H V X
AES H V
empty dot

54. Evolution of -PL spectrum in magnetic field

55. Is dark exciton emission possible?
T. Smoleński et al.
Spin flip to bright state due to fonon absorption? δ0
fonon
Decay of X
Double exponential decay of X
log(PL) X
Spin flip induced decay of Xdark
At low temperatures small probability
~ exp(-δ0/kT)
of spin flip due to phonon absorption
Time

56. However, emission of Xdark possible at magnetic field!
T. Smoleński et al. B
Magnetic field in the plane of the sample induces mixing of bright and dark excitonic states 2X X- X+
Xdark X

57. Identification of excitonic transitions
PL intensity vs excitation power
measurement of anisotropic exchange splitting
+ correlation measurements

58. Ordering in self-organized
Quantum Dot system

59. Coupled Quantum Dots
G. J. Beirne et al., Phys. Rev. Lett. 96, (2006)
B.D.Gerardot et al., Phys. Rev. Lett. 95, (2005)

60. Spontaneous ordering in self-organized
Quantum Dot system
orientation
shape
size
distribution

61. Spontaneous ordering in self-organized
Quantum Dot system
P. Wojnar, IF PAN