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CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra of
Nano-particles
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Conduction
band
Energy
gap
Electron energy
Electron energy band structure in semiconductor
-
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 = 1.829 eV @ room temperature
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Conduction
band
Energy
gap
Electron energy
Electron energy band structure in semiconductor
+
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Conduction
band
Energy
gap
Electron energy
Electron energy band structure in semiconductor
+
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Electron energy band structure in semiconductor


F  ma

a

F
Why the effective charge
of the hole is positive?
Lack of mass
Lack of charge
m is negative!
negative mass
negative charge
Instructor: Dr. Aleksey I. Filin
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra of
Nano-particles
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Low dimensional structures
3D
2D
1D
y
y
y
z
x
Bulk: motion is
not confined at all
z
x
Quantum well:
motion is not
confined in 2
dimensions
y
z
x
Quantum wire:
motion is not
confined in 1
dimensions
0D
z
x
Quantum Dot:
motion is
confined in all
dimensions
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Energy
Wavefunction of Electron in Quantum Well
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Introduction
Energy
Wavefunction of Electron in Quantum Well
Energy level shifts towards higher energy for smaller size
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
Absorbance
(in diagram form)
Bulk
Single QD in theory
0
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
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)
Absorbance
(in diagram form)
Average
size
Bigger
size
Smaller
size
Each sample contains
mostly the particles of
certain average size.
There is also some
amount of particles of
bigger and smaller sizes.
0
Absorption lines are
broadened due to
particles size
distribution:
Eg
Photon energy
Absorption lines
have near-Gaussian
shape due to nearGaussian particles
size distribution
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
Absorbance
(in diagram form)
0
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Absorption Spectra
Absorbance
(in diagram form)
1hr
2hrs
4hrs
0.5hrs
0
Photon energy
Samples were heat treated @7000C 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
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
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Measurements
Spectrophotometer measures
absorbance vs. wavelength
Absorbance
Absorbance
Theory works with absorbance
vs. photon energy
0
0
Wavelength
Photon energy
Lowest exciton state
To transfer wavelength
into energy, use the formula:
1240
E[eV ] 
[nm]
Instructor: Dr. Aleksey I. Filin
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Gaussian
Parabola
y
Gaussian + Parabola
y
y
+
=
x
x
x
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Absorbance
Parabola (result of your fit)
Gaussian + Parabola
(your experimental curve)
Gaussian
0
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
Absorption Spectra of
Nano-particles
CHEM 4396 (W237)
Physical Chemistry Laboratory
Fall 2009
Data Analysis
Energy can be calculated using formula E[eV]=1240/[nm]
In theory, dependence of the shift of lowest exciton absorption state Ex on
nanoparticle radius r can be approximately expressed as:
Ex = Eg + 0.038[eV]+ 2.4[eV*nm2]/r2
(After Ekimov et al, J. Opt. Soc. Am. B10, January 1993)
Energy gap of bulk CdSe is Eg = 1.829 eV
So, you know the Ex for the particle, you can calculate the particle size as:
r[nm] 
2.4[eV  nm 2 ]
E x [eV ]  E g [eV ]  0.038eV
Instructor: Dr. Aleksey I. Filin
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