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### Absorption Spectra of Nano-particles

Physical Chemistry Laboratory

Fall 2009

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

Conduction

band

Forbidden

band

Electron energy

Energy

gap

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

Electron energy band structure in semiconductor

Conduction

band

Forbidden

band

Electron energy

Energy

gap

+

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

Electron energy band structure in semiconductor

Conduction

band

Forbidden

band

Electron energy

Energy

gap

+

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

Lack of charge negative charge

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?

Instructor: Dr. Aleksey I. Filin

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

y

y

y

z

z

z

z

x

x

x

x

Absorption Spectra of Nano-particles

CHEM 4396 (W237)

Physical Chemistry Laboratory

Fall 2009

Introduction

Low dimensional structures

2D

3D

1D

0D

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

Bulk: motion is

not confined at all

Instructor: Dr. Aleksey I. Filin

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

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

Absorption Spectra of Nano-particles

CHEM 4396 (W237)

Physical Chemistry Laboratory

Fall 2009

Absorption Spectra

(in diagram form)

Bulk

Absorbance

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

(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

Smaller

size

Absorbance

Bigger

size

0

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

Absorption Spectra of Nano-particles

CHEM 4396 (W237)

Physical Chemistry Laboratory

Fall 2009

Absorption Spectra

(in diagram form)

Absorbance

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

(in diagram form)

Absorbance

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

Theory works with absorbance vs. photon energy

Absorbance

Absorbance

0

0

0

0

Wavelength

Photon energy

Lowest exciton state

To transfer wavelength

into energy, use the formula:

Instructor: Dr. Aleksey I. Filin

y

y

x

x

x

Absorption Spectra of Nano-particles

CHEM 4396 (W237)

Physical Chemistry Laboratory

Fall 2009

Data Analysis

Gaussian

Parabola

Gaussian + Parabola

+

=

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

Parabola (result of your fit)

Gaussian + Parabola

(your experimental curve)

Absorbance

Gaussian

0

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/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 + 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:

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

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