Yat Li

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CHEM 146_Experiment 6 A Visual Demonstration
of Particle in a Box theory Multicolor CdSe
Quantum Dots
Yat Li Department of Chemistry
Biochemistry University of California, Santa Cruz
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Objective
In this laboratory experiment, we will learn

1. The principle of interband transition and quantum
   confinement effect in zero dimensional quantum
   dots
2. Synthesis of CdSe nanocrystals
3. Absorption and Emission properties of CdSe
   nanocrystals

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Semiconductor nanocrystals
Nanocrystals are zero dimensional nanomaterials,
which exhibit strong quantum confinement in all
three dimensions, and thus they are also called
quantum dots.
Size dependent optical properties!
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Particle in a Box theory
Schrödinger equation

E - V(x)j(x)
0
h h/2p E total energy of the particle V(x)
potential energy of the particle and j(x)
wavefunction of the particles
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Particle in a Box theory
The general solution of Schrödinger equation
j(x) A cos kx B sin kx
when j(0) 0
cos (0) 1 sin (0) 0
? A 0
when j(a) 0
j(a) B sin ka 0

• B 0 (rejected) or ka np n 1, 2, 3.

Substitute k np/a back to equation for k
En
n 1, 2, 3.
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Quantum dots
A quantum dot is in analogy to the particle in a
box model, where ?E increases with decreasing a.
CdSe has a Bohr exciton radius of 56 Å, so for
nanocrystals smaller than 112 Å in diameter the
electron and hole cannot achieve their desired
distance and become particles trapped in a box.
Free exciton
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Synthesis of CdSe nanoparticles
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Synthesis of CdSe nanoparticles
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Spectroscopy
Spectroscopic techniques all work on the
principle of that, under certain conditions,
materials absorb or emit energy
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UV-vis Spectroscopy

• Transitions in the electronic energy levels of
  the bonds of a molecule and results in excitation
  of electrons from ground state to excited state
• Energy changes 104 to 105 cm-1 or 100 to 1000
  kJ mol-1

Four types of transitions

1. Within the same atom e.g. d-d or f-f transition
2. To adjacent atom (charge transfer)
3. To a delocalized energy band, conduction band
   (photoconductivity)
4. Promotion of an electron from valence band to
   conduction band (bandgap in semiconductors)

A powerful technique to study the interband
electronic transition in semiconductors!
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Interband absorption
Electrons are excited between the bands of a
solid by making optical transition
Ef Ei hn
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Beer-Lambert law
log(I0/I) ecl e A/cl
e extinction coefficient I0 incident
radiation c concentration I transmitted
radiation l path length A absorbance
e value determine transition is allowed or
forbidden
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Luminescence
Spontaneous emission when electron in excited
states drop down to a lower level by radiative
emission
Spontaneous emission rate
tR A-1
Non-radiative emission

• Electron in excited states will relax rapidly to
  lowest level in the excited band
• Sharp emission peak

If tR ltlt tNR, hR ? 1 (maximum light will be
emitted)
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Interband luminescence
Direct bandgap materials
Indirect bandgap materials

• Second order process involve phonon
• Low emission efficiency
• e.g. Si, Ge

• Allowed transition ? short lifetime (ns)
• Narrow emission line close to bandgap
• e.g. GaN, CdS, ZnS