1. Quantum Dots: Confinement and Applications
John Sinclair
Solid State II
Dr. Dagotto
Spring 2009

2. Outline Confinement Applications What do we mean?
Small dot or Quantum Dot?
Experimental Evidence
Applications
Lasers
Biology

3. Recent History and Motivation
Advances in imaging techniques all us to image things at the angstrom level
Scanning Tunneling Electron Microscopes
Atomic Force Microscopy
Scanning Transmission Electron Microscopes
AFM Image InAs
SEM Image of graphene

4. Quantum Confinement 3-D 2-D or Quantum Wells 1-D or Quantum Wires
All carriers act as free carriers in all three directions
2-D or Quantum Wells
The carriers act as free carriers in a plane
First observed in semiconductor systems
1-D or Quantum Wires
The carriers are free to move down the direction of the wire
0-D or Quantum Dots
Systems in which carriers are confined in all directions (no free carriers)

5. Confinement Continued
So what if a material is confined in one direction?
As the material becomes confined its Density of States changes
In the confined direction you can think of the carriers as particles in boxes

6. What is the relevant length scale?
Optical Excitations
Optical excitations should require the band gap
In semiconductors excitations exist just below the band gap
The Exciton
These excitations are bound hole electron pairs
Below the band gap due to binding energy
Hydrogen like quasi particle
Hydrogen like energy states
Effective Bohr Diameter

7. Exciton Bohr Diameter Material Dependent Parameter
The same size dot of different materials may not both be quantum dots
The Bohr Diameter determines the type of confinement
3-10 time Bohr Diameter: Weak Confinement
ΔE ~ 1/M*
M* effective mass of exciton
Smaller than 3 Bohr Diameter: Strong Confinement
ΔE ~ 1/μ*
μ* effective mass of hole and electron

8. Exciton Bohr Diameter

9. Experimental Observation of Confinement
Just imaging a small dot is not enough to say it is confined
Optical data allows insight into confinement
Optical Absorption
Raman Vibration Spectroscopy
Photoluminescence Spectroscopy

10. Optical Absorption
Optical Absorption is a technique that allows one to directly probe the band gap
The band gap edge of a material should be blue shifted if the material is confined
Bukowski et al. present the optical absorption of Ge quantum dots in a SiO2 matrix.
As the dot decreases in size there is a systematic shift of the band gap edge toward shorter wavelengths

11. The Blue Shift
The amount of Blue Shift is a material dependent property
It is largest for Ge, but Why?
The amount of blue shift scales with the concavity of the band gap
Particularly the portion of the band that is important as confinement sets in and the DOS changes

12. Band Gap Comparison Band gap comparison of Ge and CdTe
Must greater concavity of Ge translates to larger blue shift

13. Raman Vibrational Spectroscopy
Raman vibrational spectroscopy probes the vibrational modes of a sample using a laser
As the nanocrystal becomes more confined the peak will broaden and shrink
Here we see a peak shift toward the laser line
Various Ge dots of different sizes on an Alumina film

14. Direction of Raman Shift
Here we see the same broadening and shrinking of the Raman Peak
We see a peak shift away from the laser line
No systematic shift of the Raman line
Shifts toward the laser line are due to confinement
Shifts away from the line are due to lattice tension due to film miss-match
Ge dots in a SiO2 matrix

15. Photoluminescence Spectroscopy
Photoluminescence spectroscopy is a technique to probe the quantum levels of quantum dots
Here we see dots of various size in a quantum well
(a) is quantum well spectrum
(d) is smallest particles 80 nm

16. Promise from Photoluminescence
Photoluminescence spectrum of a 3-layer stack of InP quantum dots
Very narrow absorption should allow for production of great lasers
At present QD lasers only out perform other solid state lasers at low temperatures (below room temperature)
Problems arise due to high threshold currents at high temperature
Some QD lasers do not even lase at room temperature

17. A Brief Look at Biological Applications
Attaching ligand molecules and receptors to surface of quantum dots can create new functional form of joined dots
Patterned substrates can cause QDs to form intricate patterns
QDs can be used as cellular structure tags with attachment of appropriate ligands

18. References
Tracie J. Bukowski, Critical Reviews in Solid State and Materials. Sciences (2002)
D. L. Huaker, G. Park and D. G. Deppe, Applied Physics. Journal (1998)
S. Hoogland, V. Sukhovatkin, Optics Express. (2006)
Teresa Pellegrino, Stefan Kudera and W. J. Parak. small (2005)
N. N. Ledentsov, et al., Quantum dot heterostructures: fabrication, properties, lasers. Semiconductors (1998)