CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Conduction
band
Energy
gap
Electron energy
Electron energy band structure in semiconductor
-
Forbidden
band
Valence
band
Eph<Eg
Eg = 
insulator
Eg ~ Etermal
semiconductor
Eg = 0
conductor
If the photon energy is lower than the energy gap the
electron can not be excited
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Conduction
band
Energy
gap
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.
Electron energy
Electron energy band structure in semiconductor
+
Forbidden
band
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Conduction
band
Energy
gap
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.
Electron energy
Electron energy band structure in semiconductor
Forbidden
band
Valence
band
+
Hydrogen atom: An atom of the
chemical element hydrogen. The
electrically neutral atom contains a single
positively-charged proton and a single
negatively-charged electron bound to the
nucleus by the Coulomb force.
The exciton is a woking model of the Hidrogen atom!
Why the effective charge of the hole is positive?
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Electron energy band structure in semiconductor
Why the effective charge
of the hole is positive?
a


F  ma
F
F is pointed in
opposed direction
with respect to a
m is negative!
Lack of mass
Lack of charge
negative mass
negative charge
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
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
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Energy
Wavefunction of Electron in Quantum Well
Energy level shifts towards higher energy for smaller size
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Introduction
Wavefunction of Electron in Parabolic 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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Typical absorption spectra of CdSe nanoparticles
Our simple
simulation
Real experimental lines are broadened due to particles size distribution
(After Ekimov et al, J. Opt. Soc. Am. B10, January 1993)
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Spring 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
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)
So, you know the Ex for the particle, you can calculate the particle size as:
r[nm] 
2.4[eV  nm 2 ]
Ex [eV ]  Eg [eV ]  0.038eV
Energy gap of bulk CdSe is Eg = 1.829 eV
@ room temperature
Instructor: Dr. Aleksey I. Filin
CHEM 3398
Physical Chemistry Laboratory
Fall 2013
Absorption Spectra of
Nano-particles
Conclusion
• Measure the absorption spectra of CdSe nanoparticles in glass
• Define the energy of first absorption peak position
• Estimate the size of the nanoparticles using a formula which
\ you are provided with
Instructor: Dr. Aleksey I. Filin
Personal page: http://astro.temple.edu/~filin/
E-mail: filin@temple.edu
Office location: Barton Hall, A230