WHERE WE’VE BEEN
symmetry  bonding in solids  crystal structures and diffraction 
band theory  metals  semiconductors  semiconductor devices 
phonons  magnetism  superconductivity
Why Nano
Small things are different.
Nanoscience would be boring if small things were just like big things.
Luckily they are not.
The color of gold changes with sizes
Graphite, for example, takes on interesting shapes if it is kept from becoming
a big solid.
graphite
buckyball
nanotube
The goal of nanoscience is to find and understand
how physical properties change with size.
LET’S LOOK AT THREE ASPECTS OF THE NANOSCALE
1. Number of possible vibrational states, or electronic states,
is greatly reduced.
2. Small structures have a large ratio of surface area to
volume than macroscopic objects.
3. Ferromagnetism is different on the nanoscale than in the
bulk.
QUANTUM CONFINEMENT
In our previous work on phonons,
we calculated phonon spectra for
essentially a near infinite network
of atoms. In reality, these
systems are finite. We solve this
problem by having periodic
boundary conditions.
q
n 2
aN
n  0,1,2,3,...
Numerical (symbols) and analytical (lines)
phonon dispersion curves in the first Brillouin
zone of a monoatomic atomic chain with
N = 16, m = 1, a = 1, and k = 1.
QUANTUM CONFINEMENT
When the number of atoms is relatively small, the number of allowed states is
reduced. Instead of having a quasi-continuum, we have a set of discrete states.
These states are separated by significant energy amounts – this is the essence of
quantum confinement.
vacuum
thin metal
film of
thickness
d
substrate
For electrons in the thin film:
(r )  (z )( x, y )
2
Exy 
2
k xy
2me
QUANTUM CONFINEMENT
Infinite well solution:
(z)  Ae
k zd  n
kz 
ikz z
 ikz z
 Be
n  1,2,3...
2
k z2  2n 2 2
Ez 

2me 2d 2me
2

then, 2d  n
Better solution:
2kzd  I  V  n
n  1,2,3...
QUANTUM CONFINEMENT
Quantum Dots
The smallest energy for the formation of an electron-hole pair is

1 1.8e
 Eg 

2
4 0  r
2 r
2
Emin
2
2
Semiconductor quantum dots (QDs) possess size tunable
fluorescence and absorption properties.
SURFACES AND INTERFACES
Bloch Wave
 k (r )  uk (r )e ikr
SURFACES AND INTERFACES
In bulk ferromagnetic materials, the energy required to flip
one magnetic moment is on the order of the exchange
energy, kBTCurie.
ik r ( k ) z
This
(
r
)

u
(
r
)
e
e
is truek for nano-particles
as well.
k
z
Surface Localized State:
 k (r )  uk (r )e
ik r
e
i z
MAGNETISM ON THE NANOSCALE
In bulk ferromagnetic materials, the energy required to flip
one magnetic moment is on the order of the exchange
energy, kBTCurie.
This is true for nano-particles as well.
Iron Nanoparticles
BLOCH WALLS
The drawing shows a ferromagnetic material containing a 180o
domain wall (center). On the left, the magnetic moments are
aligned downward. The hypothetical wall structure is shown if
the spins reverse direction over Na atomic distances
In real materials, N: 40 to 104. The thickness is typically 0.5 m.
MAGNETISM ON THE NANOSCALE
Assuming no external field, the energy required to rotate the
entire magnetic moment of a small particle is
E  VMBinside
Unfortunately, we do not know Binside. But, it turns out that it
is dependent on the shape of the particle and its order of
magnitude is µ0M, so we make the approximation that
E  V 0M 2
MAGNETIC PROPERTIES OF IRON NANOPARTICLES
coercivity is the magnetic-field strength necessary to demagnetize a
ferromagnetic material that is magnetized to saturation. It is measured in
A/m, or traditionally in Oersted. 1 Oe = 79.578 A/m