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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
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
Semiconductor nanocrystals
Nanocrystals are zero dimensional nanomaterials, which exhibit
strong quantum confinement in all three dimensions, and thus they
are also called “quantum dots”.
UV light
Ambient light
Size dependent optical properties!
“Particle in a Box” theory
∞
∞
The particle is restricted to the region 0 ≤ x ≤ a;
the probability that the particle is found outside
the region is zero.
0
x
j(0) = j(a) = 0
a
Free particle in a one-dimensional box
Schrödinger equation:
d2j
dx2
+
2m
[E - V(x)]j(x) = 0
ħ2
ħ = h/2p; E = total energy of the particle; V(x) = potential energy
of the particle; and j(x) = wavefunction of the particles
Free particle: the particle experience no potential energy  V(x) = 0
d2j
dx2
+
2mE
ħ2
j(x) = 0
“Particle in a Box” theory
The general solution of Schrödinger equation:
(2mE)1/2
k=
ħ
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 =
h2n2
8ma2
DE =
h2
8ma2
n = 1, 2, 3….
(nf – ni)2
=
2p(2mE)1/2
h
Quantum dots
A quantum dot is in analogy to the “particle in a box” model, where ΔE
increases with decreasing a.
DE =
h2
8ma2
(nf – ni)2
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
Synthesis of CdSe nanoparticles
Preparation of Se precursors:
1.
2.
30 mg of Se and 5 mL octadecene
3.
0.4 mL trioctylphosphine
completely dissolve the selenium
Preparation of Cd precursors:
1.
2.
a.
b.
Add 13 mg of CdO to a
25 mL round bottom
flask
add by pipet 0.6 mL
oleic acid and 10 mL
octadecene
Heat the cadmium
solution to 225 °C
http://mrsec.wisc.edu/Edetc/nanolab/CdSe/index.html
Synthesis of CdSe nanoparticles
Preparation of CdSe nanocrystals:
1.
2.
Transfer 1 mL of the room temperature Se
solution to the 225 C Cd solution and start timing
Remove approximately 1 mL samples at
10s intervals (for the first five samples)
3.
Ten samples should be removed
within 3 minutes of the initial injection
http://mrsec.wisc.edu/Edetc/nanolab/CdSe/index.html
Spectroscopy
Spectroscopic techniques all work on the principle of that, under certain conditions,
materials absorb or emit energy
Quantized energy: photon
E = hn
DE = hn = hc/l
X-axis: Frequency or wavelength
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:
i)
Within the same atom e.g. d-d or f-f
transition
ii)
To adjacent atom (charge transfer)
iii) To a delocalized energy band, conduction
band (photoconductivity)
iv) Promotion of an electron from valence band
to conduction band (bandgap in
semiconductors)
A powerful technique to study the interband electronic transition in semiconductors!
Interband absorption
Electrons are excited between the bands of a solid by making optical transition
Ef = Ei + hn
Indirect bandgap:
Direct bandgap:
• Relative position of conduction band and valence band
is not matched
hn < Eg, a(hn) = 0
hn ≥ Eg, a(hn) = (hn
–Eg)½
• The transition involve phonon to conserve momentum
Ef = Ei + hn + ħW
aindirect = (hn –Eg ± ħW)2
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
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 << tNR, hR  1 (maximum light will be emitted)
Interband luminescence
Direct bandgap materials
• Allowed transition  short lifetime (ns)
• Narrow emission line close to bandgap
• e.g. GaN, CdS, ZnS
Indirect bandgap materials
• Second order process involve
phonon
• Low emission efficiency
• e.g. Si, Ge