1. Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra of Nano-particles
Instructor: Dr. Aleksey I. Filin

2. - Introduction Electron energy band structure in semiconductor
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Electron energy band structure in semiconductor
Conduction
band
Electron energy
Energy
gap
Forbidden
band -
Valence
band
Eph>Eg
If the photon energy is higher than the energy gap the electron can be excited
We work with CdSe nanostructures (quantum dots)
Energy gap of bulk CdSe is Eg = room temperature
Instructor: Dr. Aleksey I. Filin

3. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Electron energy band structure in semiconductor
Conduction
band -
Electron energy
Energy
gap
Forbidden
band +
Valence
band
Electron being excited left in the valence band positively charged quasi-particle known as the electronic hole, or the hole.
Positively charged hole interacts with negatively charged electron by Coulomb interaction.
Instructor: Dr. Aleksey I. Filin

4. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Electron energy band structure in semiconductor
Conduction
band -
Electron energy
Energy
gap
Forbidden
band +
Valence
band
Exciton: Large and strongly interactive particles formed when an electron, excited by a photon into the conduction band of a semiconductor, binds with the positively charged hole it left behind in the valence band.
Exciton Bohr radius is the smallest possible orbit for the electron, that with the lowest energy, is most likely to be found at a distance from the hole
Instructor: Dr. Aleksey I. Filin

5. m is negative! Introduction
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Electron energy band structure in semiconductor
m is negative!
Why the effective charge
of the hole is positive?
Lack of mass negative mass
Lack of charge negative charge
Instructor: Dr. Aleksey I. Filin

6. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
A Quantum Dot is:
A crystal of semiconductor compound (eg. CdSe, PbS) with a diameter on the order of the compound's Exciton Bohr Radius
Or:
A nanostructure that confines the motion of Excitons in all three spatial directions
Exciton is an atomic-like quasi-particle, so, its energy spectrum is similar to that for Hydrogen atom
Instructor: Dr. Aleksey I. Filin

7. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Low dimensional structures 3D 2D 1D x y z x y z x y z x y z 0D
Bulk: motion is
not confined at all
Quantum well:
motion is not confined in 2 dimensions
Quantum wire:
motion is not confined in 1 dimensions
Quantum Dot:
motion is confined in all dimensions
Instructor: Dr. Aleksey I. Filin

8. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Wavefunction of Electron in Quantum Well
Energy
WF of electron in QW can contain only integer number of half wavelength
-> Energy spectrum of electron in QW is discrete
Instructor: Dr. Aleksey I. Filin

9. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Wavefunction of Electron in Quantum Well
Energy
Energy level shifts towards higher energy for smaller size
Instructor: Dr. Aleksey I. Filin

10. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
(in diagram form)
Bulk
Absorbance
Single QD in theory Eg
Photon energy
Lowest exciton state
Energy spectrum of exciton in QD is discrete (or quantized) (similar to spectrum of electron in QW)
Instructor: Dr. Aleksey I. Filin

11. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
(in diagram form)
Position of lowest exciton state (as well as other states) depends on particle size: energy level shifts towards higher energy for smaller size (similar to electron in quantum well)
Each sample contains mostly the particles of certain average size. There is also some amount of particles of bigger and smaller sizes.
Average
size
Absorbance
Smaller
size
Bigger
size Eg
Photon energy
Absorption lines have near-Gaussian shape due to near-Gaussian particles size distribution
Absorption lines are broadened due to particles size distribution:
Instructor: Dr. Aleksey I. Filin

12. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
(in diagram form)
Absorbance Eg
Photon energy
Lowest exciton state
For each sample, the lowest exciton state position is defined by average particle size
Instructor: Dr. Aleksey I. Filin

13. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
(in diagram form)
Absorbance
1hr
2hrs
4hrs
0.5hrs
Photon energy
Samples were heat for different times (0.5, 1, 2 and 4 hrs). Average particle size increases with increasing of heat treatment time. Absorption peak position shifts towards lower energy with average particle size increasing.
Instructor: Dr. Aleksey I. Filin

14. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Typical absorption spectra of CdSe nanoparticles
Real experimental lines are broadened due to particles size distribution
Instructor: Dr. Aleksey I. Filin

15. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Our goals:
investigate the absorption spectra of nanoparticles (QDs) embedded in glass;
define the lowest exciton absorption peak position for each sample;
analyze the data and calculate an average particle size for each sample.
Instructor: Dr. Aleksey I. Filin

16. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Measurements
Spectrophotometer measures absorbance vs. wavelength
Theory works with absorbance vs. photon energy
Absorbance
Absorbance
Wavelength
Photon energy
Lowest exciton state
To transfer wavelength
into energy, use the formula:
Instructor: Dr. Aleksey I. Filin

17. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Gaussian
Parabola
Gaussian + Parabola x y x y x y + =
Maximum of (Gaussian + Parabola) curve is shifted in comparison with that for the Gaussian curve. To find the correct position of Gaussian we have to subtract the background from the summary curve
Instructor: Dr. Aleksey I. Filin

18. Data Analysis Parabola (result of your fit) Absorbance
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Parabola (result of your fit)
Gaussian + Parabola
(your experimental curve)
Absorbance
Gaussian
Wavelength
Pick 2 points on the left and 2 points on the right shoulders of the peak
Fit this 4 points with parabola
Subtract the parabola from the experimental curve
You get the unshifted position of the lowest exciton absorption peak
Find the wavelength, corresponding to the maximum position
Calculate the energy, corresponding to this wavelength
Instructor: Dr. Aleksey I. Filin

19. Physical Chemistry Laboratory
Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Energy can be calculated using formula E[eV]=1240/l[nm]
In theory, dependence of the shift of lowest exciton absorption state Ex on nanoparticle radius r can be approximately expressed as:
Ex = Eg [eV]+ 2.4[eV*nm2]/r2
(After Ekimov et al, J. Opt. Soc. Am. B10, January 1993)
Energy gap of bulk CdSe is Eg = eV
So, you know the Ex for the particle, you can calculate the particle size as:
Instructor: Dr. Aleksey I. Filin

20. Absorption Spectra of Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Summary
We measure the absorption spectra of CdSe nanoparticles in glass
We define the energy of lowest exciton absorption peak position
We estimate the average size of the nanoparticles in each sample
Instructor: Dr. Aleksey I. Filin