NANO MAT

ERIALS

THE JO

YS O

F QUANTU

M CONFIN

EMENTPhysics 355

WHERE WE’VE BEEN

symmetry bonding in solids crystal structures and diffraction band theory metals semiconductors semiconductor devices phonons magnetism superconductivity

Nanoscience would be boring if small things were just like big things.Nanoscience would be boring if small things were just like big things.Luckily they are not. Luckily they are not.

The color of gold changes with sizesThe color of gold changes with sizes

The goal of nanoscience is to The goal of nanoscience is to find and understandfind and understandhow physical properties change with size.how physical properties change with size.

graphitegraphite buckyballbuckyball nanotubenanotube

Graphite, for example, takes on interesting shapes if it is Graphite, for example, takes on interesting shapes if it is kept from becoming a big solid.kept from becoming a big solid.

Small things are different.

Why Nano

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.

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.

2 0,1,2,3,...

nq n

aN

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.

substrate

thin metal film of

thickness d

vacuum

( ) ( ) ( , )r z x y

For electrons in the thin film:

2 2

2xy

xye

kE

m

QUANTUM CONFINEMENT

( )

1,2,3...

z zik z ik z

z

z Ae Be

k d n n

2

then, 2

zk

d n

2 2 2 2 2

22 2z

ze e

k nE

m d m

Infinite well solution:

Better solution:

2 1,2,3...z I Vk d n n

QUANTUM CONFINEMENTQuantum DotsThe smallest energy for the formation of an electron-hole pair is

Semiconductor quantum dots (QDs) possess size tunable fluorescence and absorption properties.

2 2 2

min 20

1 1.8

42g

eE E

rr

SURFACES AND INTERFACES

Bloch Wave

( ) ( ) ikrk kr u r e

SURFACES AND INTERFACES

( )k( ) ( ) zk zi rk kr u r e e

k( ) ( ) i r i zk kr u r e e

Surface Localized State:

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.

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

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

insideE VMB

20E V M

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