Experiment 5
SPECTROSCOPIC CHARACTERIZATION OF CADMIUM SELENIDE
NANOCRYSTALS
By Gordana Dukovic, Robert Onorato, and Alex Pines
Revised by Mark Babin, Mark Creelman, and Rich Saykally
Introduction
Nanotechnology is quickly becoming a household word as nanoscale materials find
applications in diverse areas, from conversion of light into electricity in solar cells to visualization
of cancer cells. As their name implies, nanoscale materials are broadly defined as materials whose
individual crystals have dimensions in the nanometer range. What makes these materials extremely
interesting from a scientific point of view is the fact that their electronic structure changes
depending not only on their chemical composition, but also their size and shape. To illustrate this
principle, you will analyze the absorption spectra of cadmium sulfide (CdSe) solutions to
determine how their electronic transition energies differ based on the size of the nanocrystals in
solution.
The electron microscopy image in Figure 1 shows a CdSe
nanocrystal with the planes of individual Cd atoms clearly
resolved. Nanocrystals can contain anywhere from tens to tens
of thousands of atoms. In this size regime, they can be thought
of as very large molecules or very small semiconductor
materials. The electronic structure of semiconductors can be
described by two bands: the valence (occupied) band and
conduction (unoccupied) band, which are separated by an
energy gap (the band gap). Figure 2 illustrates how the
semiconductor bands develop from atomic and molecular
orbitals. As the number of atoms in a species increases from
molecules (with a few atoms) to crystals (with tens of
thousands or more atoms), the number of electronic orbitals in
Figure 1. High-resolution
these materials increase; these orbitals become so closely
transmission electron
microscopy (TEM) image of a spaced in energy that they are essentially continuous and are
thus referred to as bands. These large crystals are referred to as
CdSe nanocrystal. Adapted
bulk semiconductors. The electronic structure of nanocrystals
from Ref. 1.
fits somewhere between the molecular orbitals shown in Figure
2d and the bands shown in Figure 2e.
Figure 2. Diagram showing how the energy levels change as the number of atoms n
increases. (a) atomic orbital, n = 1; (b) molecular orbitals, n = 2; (c) molecular orbitals, n =
4; (d) molecular orbitals, n = 13; (e) bands, n ∼ 6 × 1023. Adapted from Ref 2.
Next, we consider what happens when a semiconductor absorbs a photon and an electron is
promoted from the valence band to the conduction band. Not only can the electron move inside
the crystal, but the positive charge it leaves behind, the “hole,” can also move, in the sense that
other electrons in the crystal can move to that positive site, leaving another positive charge behind,
and so on. The electron-hole pair is termed an exciton. The electron and the hole interact in a way
that is very similar to the way the negatively charged electron and the positively charged nucleus
interact in a hydrogen atom. Just as the electron in the hydrogen atom can be found with high
probability within a certain region of space (the atomic orbital), the electron in the semiconductor
has a certain spatial extent. In bulk CdSe, the spatial extent of the electron is approximately 5 nm.
When the size of the CdSe crystal is smaller than 5 nm, the electron is confined, i.e. forced into a
space smaller than its natural extent, thereby raising the energy and leading to a difference in
transition energies between bulk and nanoscale semiconductors.
A simple way to think about a confined electron is by applying the model of a particle in a onedimensional box, for which the energies are given by
𝐸 =
(1)
where L is the length of the box, n is the quantum number, and me is the mass an electron. As the
length of the box decreases, the energies and associated transition energies and frequencies
increase. An extension of the particle in a one-dimensional box to a particle in a three-dimensional
spherical box more accurately describes the confinement of a particle in a real container (with a
non-zero volume) for which the energies are given by
(2)
𝐸 =
where D is the diameter of the spherical box.
A more accurate description of the lowest transition energy (i.e., band gap) in
semiconductor nanocrystals is obtained by treating it as a correction to the band gap in the bulk
semiconductor. The corresponding energy is well described by the following form of the Brus
equation:
𝐸
= 𝐸
+
∗
+
∗
ℎ
−
.
(3)
Here D is the nanocrystal diameter, 𝑚𝑒∗ and 𝑚ℎ∗ are the effective masses of the electron and the
hole, e is the elementary unit of charge, 𝜖0 is the permittivity of a vacuum, and ε is the permittivity
of the material of interest relative to that of a vacuum (see the post-lab questions for definitions
and values of these constants). The effective masses express the extent of the interaction of the
electrons and holes with the crystal, and therefore have different values in different materials. Note
the similarity between the second term in the Brus equation and the expression for a particle in a
three-dimensional spherical box, Equation 2 (for n = 1). This term describes the shift to higher
transition energies to the extent that the electron and/or hole are confined to a smaller “box” than
their spatial extent in the bulk. The third term in Equation 3 describes the electrostatic attraction
between the negatively charged electron and the positively charged hole.
Absorbance Spectroscopy
To measure the energy of these transitions (that of the band gap), we will perform
absorbance spectroscopy on these materials. When an atom or molecule absorbs a single photon,
an electron makes a transition to a higher energy orbital. Which orbital this electron ends up in
depends on a number of factors, but most important is the energy of the light – if the energy of the
photon absorbed matches the energy difference between two orbitals, the electron will
preferentially transition between those two (see Figure 3 below).
Figure 3. Diagram outlining the absorption of light by molecules. (a) Three possible
absorptions from one molecular orbital to three different orbitals. (b) Cartoon displaying
the light spectrum before and after passing through the sample outlined in (a). At bottom,
an absorbance spectrum displaying the three wavelengths absorbed corresponding to the
three transitions outlined in (a).
As energy must be conserved, if a photon has energy that does not match the energy difference
between two states, it cannot be absorbed. Thus, if we measure how much light is absorbed at each
wavelength, some wavelengths will have much more light absorbed than others – these
wavelengths correspond to the energies of transitions. You will learn more about the technical
details of this method in coming labs. For this lab, you will practice analyzing absorbance data.
Post-lab Questions
1. Using the absorbance data provided in the accompanying Excel sheet, generate a series of
professional-looking absorbance spectra for the CdSe nanocrystal solutions. Indicate the
wavelength (in nm) at which maximum absorbance occurs for each spectrum.
2. Calculate the size of the CdSe nanocrystals in each solution using the particle in a one-
dimensional box model (Eq. 1), the particle in a three-dimensional spherical box model (Eq. 2),
and the Brus equation (Eq. 3). Pay special attention to units. For the Brus equation calculation,
be sure to show enough work that it is clear how you arrived at your answer. You will need
these constants:
h = 6.626 × 10-34 J s
me = 9.1 × 10-31 kg
me* =1.73 x 10-31 kg
mh* = 7.29 x 10 −31 kg
e = 1.602 × 10-19 C
ε = 5.7 (unitless)
εo = 8.854 × 10-12 C2 (J m)-1
𝐸
= 2.788 × 10-19 J
3. There exists an empirical formula for determining the size of certain nanoparticles based on
collecting both the absorption spectra and a TEM image of the nanoparticles (see reference 3).
For CdSe, the equation to determine the diameter (D) of these nanocrystals in nanometers is
D = (1.6122 x 10-9)  4 - (2.6575 x 10-6)  3 + (1.6242 x 10-3)  2 - (0.4277)  + 41.57
where  is the location of the peak of your absorption spectrum in nanometers. Use this equation
to determine the size of your nanocrystals.
4. Describe the differences between the four models you have used to calculate particle size.
Which method do you believe gives you the most accurate size of the nanocrystals and why?
5. CdSe nanocrystals are rarely “bare” – they often are coated with molecules (ligands) on the
exterior that allow for these particles to be solvated. Most often, this shell of molecules does
not alter the energetics of the quantum dot (i.e. the molecular orbital picture in Figure 2 is
unchanged by the existence of these). If we were to somehow change this coating with
something that allowed electrons to delocalize into this ligand shell, how would that impact the
absorbance spectrum?
6. Hit the library or the web and look for a scientific paper on nanocrystals. You can choose a paper
describing a synthesis, characterization method or application. Write a short summary of your
chosen topic ~300 words (consider looking in ACS journals or in the publication list of Berkeley
groups that do nanoparticle research, for example Paul Alivisatos and Peidong Yang).
References
[1] C. Ricolleau, L. Audinet, M. Gandais, T. Gacoin, J. P. Boilot, Journal of Crystal Growth
1999, 203, 486.
[2] K. Winkelmann, T. Noviello, S. Brooks, Journal of Chemical Education 2007, 84, 709.
[3] W. W. Yu, L. Qu, W. Guo, X. Peng, Chemistry of Materials 2003, 15, 2854.