NPTEL_Optical properties of Nanomaterials.pdf_20251015_174048_0000.pdf

This is about optical properties of nanomatrials

1. OPTICAL PROPERTIES of
Nanomaterials
Semester VI

2. Many of the optical properties are closely related to the electrical and electronic
properties ofthematerial. But as we shall see other factors also come into the
pict ure when dealing with optical properties.
When one is talking about optical properties, one is usually referring to the
interactionofelectromagnetic radiation with matter. The simple picture one can
star t with is by considering a 'ray' of an electromagnetic wave of a single
frequency entering a medium from vacuum. This ray could be reflected,
transmitted (refracted) or absorbed.
The reflection could be specularor diffuse.
Optical Properties

3. From a more fundamental perspective, there are only two possibilities (of interaction of a
medium with electromagnetic radiation):
(i)s cattering &
(ii) absorption

If one co
absorbed while the other frequencies could be scattered.
nsiders a wider spectrum of frequencies, then some part of the spectrum could be

4. Electronic transitions
Rotational transitions
Vibrational transitions

Absorption essentially involves activating some process in the material to take it to an
excited state (from the ground state).
The se processes are: (i) electronic, (ii) vibrational and (iii) rotational excitations
Further part of the absorbed energy could be re-emitted.
If the absorbed energy is dissipated as heat, this is called dissipative absorption.
Mechanisms
for absorption
Atomic orbitals
Molecular orbitals
Band

5. When an electromagnetic wave impinges on an atom (or a material containing an atomic
spec
which emits radiation of the same frequencyin all directions. This is the proc
scattering. Similar to absorption, scattering is also
There are two possible ways in which transmission can take place:
ies), the electron cloud is set into oscillation. This situation is like adipole oscillator,
ess of
frequency dependent.
(i) i
f the medium is sparse, the ray (wave) could just pass through the particles of the
medium (like in vacuum), which essentially means there is no interaction;
(ii)but the more common mechanism for 'denser media' is 'forward scattering'(i.e. what
we call a
s transmission in common usage is actually forward scattering).
When a wave is being transmitted form one medium (say vacuum) toanother, its
freq
uency remains constant, but its velocity decreases(the wave being slow er in the
medium). The ratio of the velocities c/vmediumis called the r
efractive index (n):
Where, is permittivity of the medium and is the permeability of the medium. The subscript
'0' refer to these values in vacuum. KEis the relative permittivity (dielectric constant) and KM
is the relative permeability of the medium.
n
c
v
KEKM

0 0



KE
KM


0


0



6. Usually KMis close to unity. KEis a function of the frequency of the electromagnetic
wav
e and leads to the phenomenon of dispersion (e.g. dispersion of white light by a prism
into 'VIBGYOR' colours).
Physically, the origin of the dependence of 'n' on frequency is due to three factors:
(i) o
rientational polarization
(ii) electronic polarization
(iii) ionic polarization
(iv) space charge.

7. 
Usually the refractive index (n) is greater than one (n>1), but under certain
circ
umstances it can be less than one (n<1) or even be negative (n<0).
n<1implies that light is traveling faster than
s peed of light which is in 'a p parent'
con
tradict ion to the theory of Relativity.
In cases where n<1, the velocity which one needs to consider (instead of the 'phase
velocit
y') is the 'group v el ocity (vg)' (or in still other cases the 'signal velocity' (vs)), which
will be less than 'c'. [i.e. causality will not be violated!].

In negative refractive index materials (or typically structures) the refracted beam (in the
med
ium) will be on the other side of the normal.

8. A special kind of scattering of importance to materials science is diffraction. Diffraction is
nothing but 'coherent reinforced scattering' and comes into playin periodic and
qua siperiodic structures. The incoming 'coherent beam' (assumed monochromatic for
now) energy is redistributed in space as 'transmitted' and diffracted beams. The
transmitted beam in this case is a forward diffracted beam. If there are an array of scatters
(1D) with spacing 'a', a schematic of dominant regimes of the three possible outcomes
which can take place.
Though in our discussions here we have considered EMwaves, phenomena such as
scattering and diffraction are true for all kinds of waves. Young's double slit experiment
perf ormed in a ripple tank (with water as the medium) is a go od example of scattering and
interference, which does not involve EMradiation.

9. Prism
Blue sky
Oil films on water, CD,
Butterfly wing
Colourcan arise from various mechanisms as outlined below.
Origin of Colour
Origin of colour Scattering
Dispersion
Interference
Absorption/emission
Reflection/Transmission

Atomic electronic transitions can give rise to colour: yellow colourof sodium in flame test
3p
3s
2.105 eV
2.103 eV
589.6 nm
589.1 nm

10. Plasmons(akin to phonons for lattice vibrations) are collective oscillation s of free electrons.
Bulk plasmons
Incoming visible electromagnetic radiation sets up plasmon oscillations and hence is
absorbed (bulk metals are opaque in the visible region).
are longitudinal oscillations of electrons gas w.r.t. the ion cores.
Interaction of electromagnetic radiation with metals: Absorptionin metals

11. Three (two, sub-divided into three) frequency regimes can be identified for interaction of
EMradiation with metals.

AuPt
2.181.243.57
Al Ag
2.18


15P(10 /s)
1) Low frequency range ( < 1) →beam penetrates the metal for a short distance (skin
depth) below the surface. (for Cu at = 107

/s, = 100 ) →absorbed(& reflected)

2) High frequency range ( >> 1→visibl
e and ultra violet range)
a) < →reflection

Ne2

P

P

*
a) > →metal becomes a non-absorbing transparentdielectric
Latticem

P
•→tim e b etw een two consecutive collisions.~ 1014 s.
•1/~ probability of an electron suffering a collision/unit time
• P →plasma frequency
•N →electron density










12. 
character to their bond and exhibit absorption and reflection in the
Ionic crystals show strong absorption and reflection in the IRregion
(due to interaction of light with optical phonons).
Co mpound semiconductors(GaAs, GaPetc.) have a partial ionic
IR.
If energy of the incoming photon is greater than the band gap then
the photon can be absorbed. h> Eg 0= Eg/his known as the
abso rption edge.


As the wave vector of a photon in the optic al reg ion is very small
(only constant momentum transfers are allowed across the bandgap)
→v ertical transitions in k-space are allowed (valence to conduction
band).
As the bandgapin semiconductors is ~ 1eV the fundamental edge
occurs in the IR.

In indirect bandgapsemiconductors both photon and phononneeds
to be absorbed (the phonon energy ~ 0.05eVand can be ignored and
hen ce it can be thought o f as contributing only momentum to the
electron).

Optical properties of semiconductors

13. 



The
transport energy without transporting electric charge(excited state can travel through
latti ce without transfer of charge). [The free exciton(Mott-Wannier)can move in the crystal.
Exciton trapped by an impurity is a bound exciton(has a h igher binding energy than free

Exciton is a bound state of an electron and hole. The binding is due to electrostatic
(Coulomb) attraction →the exciton has lower energythan the unbound electron + hole.
This brings the energy levels closer to the conduction band (and the Bohr radius
increases)

Itisan electrically neutral quasiparticlethat exists in insulators and semiconductors.
exciton can be considered as an element ary excitation in materials which can
exciton)].

The effective reduced mass of exciton ():

*
m

the free electron mass me)
e
Exciton
*
exciton
m*m*
h

e
m*em*h
For GaAs:
(this is muchsmaller than
0.059
exciton


m*e→effective mass of electron
m*h→effective mass of hole

14. g exciton
h E E

Small ~ 0.01 eV






Photon absorption by a semiconductor can lead to the formation of an exciton.
The
exciton binding energy for most semiconductors is in the range of few to few 10s of
(milli-electron volts) [Eexciton(GaAs)= 4.6 meV, Eexciton(CdS)= 28 meV] .
meV
For compa
rison:
the binding energy of Hatom is 13.6 eVand
2
kTa t room temperature is 40 meV.
nthesmallvalueofE

Give ex→an exciton can be dissociated by thermal energy at RT.
Theexciton spectrum has a sharp line, just below the fundamental edge →usually
observed at low temperature wher e thermal energy is lower than the binding energy.

15. GaAs
CdSe
CdS
28
Exciton
energy (meV)
4.6
Exciton
radius (nm)
~11.8
~5
~3 (2.4)
The exciton diameter can be calculated as:
Band-Gap
energy (eV)
1.43
1.74
2.58
If the dimension of the crystal ~ of the exciton diameter (or less)
→confinement effects become prominent.

rB→Bohr radius in the absence of exciton
→dielectric constant of the medium
→di
0
electric constant of free space
me→mass of free electron
m*e→effective mass of electron
m*h→effective mass of hole







e[1

*
h)]
rExciton
Bohr
r
Bm
(m*e/m
*
0me

Exciton radius has
nanoscale dimensions
Small ~ 0.01 eV
rExciton
Bohr
h2
e2

0
Hydrogen atom ground state: 13.6 eV

16. Optical Properties of Nanomaterials

17. Bulk metal samples absorb electromagnetic radiation (say visibleregion). Thin films of
met
als may partially transmit, just because there is insufficient materia l to absorb the
radiation. Au films few 10s of nmthick become partially transparent.
Apart from ‘insufficient material’effec
ts, there are important phenomena which come into
play
in nanomaterials.

These include: dominance of surface plasmons, quantum confinement effects, etc.
E.g.
(hig
in semiconductor quantum dotsoptical absorption and emission shift to the blue
her energies) as the size of the dots de creases.

The size reduction is more prominent in the case of semiconductorsas compared to metals
(i.e.
quantum size confinement effects become more important in metals at smaller sizes
than semiconductor crystals).
We have already seen that at very small sizes metal nanoparticles can develop a bandgap
(can
become a semiconductor or insulator).
Size effect on optical properties

18. On decreasing the size the electron gets confined to the particle (confinement effects)
leading to:
(i)i ncrease in bandgapenergyand
(ii)band levels get quantized(discrete).

Surface states (trap states), which lie in the bandgapbecome important →alter the optical
properties of nanocrystals.

Theenergy level spacing increases with decreasing dimension
→QunatumSize Confinement Effect
Semiconductor nanoparticles & films

19. 





R E→this dominates over
The effective bandgapof particle of radius R:
R E
Eeffective
g
→effective band gap energy of particle of radius R
Eg() →bulk bandgap
→dielectric constant (bulk)
m→m
e

ass of free electron
m*e→effective mass of electron
m*h→effective mass of hole
(Coulombicattraction term)
2
2
( )
2
1
m*e
1
m*h
1.8

effective
g
E R E
R
e2
R
2


g()






effective
g
effective
g

 effective
g
R E

20. J. Nayaket al., PhysicaE 24 (2004) 227–233
GaAsnanocrystalline thin film (nano-GaAs)
deposited on ITO substrate

In nano-GaAs(with size range 7-15 nm) a broad excitonic peak at 526.0 nm(2.36 eV) is
seen
eV)] due to the QSE. →energy gap of the nano-GaAshas been blue shifted by 0.93 eV[bulk band gap (1.43
Enhancement of absorbance over the range of wavelengthsseen →enhanced oscillator
stren gth (dimensionless quantity to express the strength of the tr ansition).
The excitonic peak is broad due to the size distribution of crystallites.

21. Absorption spectra of PbSenanocryatals
With reducing size of the particle the density of states becomesmore quantized and the band
gap shifts to higher energies (shorter wavelengths) →the absorption spectrum shows a blue
shift

22. In photoluminescence material is excited by EMradiation, followed by relaxation to
ground state by emission of photons.

When the semiconductor relaxes to the ground state by recombination of electron and
hole, a photon is emitted.

If the photon energy lies in the range 1.8 -3.1 eVthe radiation will be in the visible range
→luminescence.

By changing the sizeof the nanoparticles the frequency of emission can be tailored.
As the size of the nanopar
ticles decrease →‘blue shift’in frequencies.
Photoluminescence

23. The luminescent properties are a characteristic of the core.
The
shell leads to an enhancement of the luminescent properties of the core (the
inescence of nanoparticles are well defined with narrow spectral ranges, which depend
lum
on particle size).
Deposition of a semiconductor with a larger bandgapthan that of the coretypically results
in ‘l uminescence enhancement’due to the suppression of r adiationlessrecomb ination
mediated by surface states.

E.g. CdScoated with MoS4, ZnSecoated with CdSe, CdSecoated with CdS.
Ban
markers.
dgapstunable in the near-IR, which can be useful as IRbiological luminescen t

Properties of core-shell nanostructures: semiconductor on semiconductor

24. ZnS CdSe
Fluorescence emission of (CdSe)ZnScore-
shell quantum dots.

Fluorescence from core-shell quantum dots
Dabbousiet al., J. Phys. Chem. B 1997, 101, 9463-9475

25. Gold nan oparticles were used as a pigment of ruby-colored stained glass dating back to
the 17th century.1-10 nmsized particles give rise to this colour.
Thin film ofAu(~100
nm or les s) will transmit blue-violet light.
The
colourof me talli c nanoparticles depends on size in the nanoscale regime.
k Au is ‘gold en’yellow colour. Nanoparticles of gold (colloidal) can have red, purple
lue colour.
Bul
or b
The colourdepends on the size (& shape) of the particle and the dielectric properties of
the medium.

Surface plasmonsare excited by incident electromagnetic radiation.

Surface plasmons have lower energythan bulk plasmons which quantize the (or plasma).
MF
the particl
In particles with shape anisotropy (e.g. cylinders) more than one type of plasmon
Pof Au, Ag ~50 nm for particles sm aller than this there will be no scattering within
e and all the interactions will be with the surface.
abso
rption peak may be observed.
Colourof metallic nanoparticles

26. •For the sphere(d~15nm) only the Transverse plasmon peakis observed ( ~ 520nm).
•If th
e radius of the s phere is doubled (d~30nm), the transverse pl asmon absorption peak
will only shift slightly →this is
is strongly affected by size in the nanoscale
.
•For the
•For the long
are observed.
er cylinder the longitudinal plasmon peak s hifts to longer w avelengths.
•Many applications has been envisaged due to large enhancement of surface electric field.
unlikesemiconductornanoparticleswheretheabsorbance
cylinderboththe surface andlongitudinalplasmonpeaks

27. After: S. J. Oldenburg, R. D. Averitt, S. L. Westcott, N. J. Halas, Chem. Phys. Lett. 288, 243 (1998)


In Au shells coated on SiO2cores the plasmon band depends on the core radius and on the
core
to shell ratio.
Increasing core to shell ratio red-shifts the plasmon resonance band(figure below).
Properties of core-shell nanostructures: metal on dielectric

28. Metamaterials(with negative refractive index)



Metam




Negative index m etamaterials(negative index materials) are man made structures where
therefractive index has a negative value(typically over some frequency range).
So far this has not been discover ed in natural materials.

aterialshave been made with negative effective permittivity and permeability.
Acrystal with Mag
netic Split Ring Resonator (SRR) as the motif can be used for the
construction of a negative refractive index material.
When the SRRscale is of the order of ~200nm→negative refractive index can be
obtained in the mid-infrared range (100 THz)

( )()
 
+ Refraction
n 
( )( ) Refraction
n
n
 




29. End of Course

30. SiO2shell on various cores have been studied. E.g. Au@SiO2.
e shell nanowireshave also been prepared. E.g. Ni@TiO2.
Cor

Au@
SiO2: Nanosized gold colloids show a very intense surface plasmon absorption band
in the visible (around 520 nm). The exact position of this plasmon band is extremely
sens itive both t o particle size and shape and to the optical andelectronic properties of the
medium surrounding the particles. Silica does not exchange charge with the Au particles
and hence can be considered inert.
As the shell thickness is increased, there is an increase in theintensity of the plasmon
absorption band, as well as a red shift in the position of the absorption maximum (due to
the increase in the local refractive index around the particles). At l arger shell thicknesses,
scattering becomes significant, resulting in a strong increase in the absorbance at shorter
wavelengths. This effect promotes a blue shift of the surface plasmon band and a
weakening in the apparent intensity of the plasmon band. Eventually at shell thicknesses
above 80 nm, the scattering almost completely masks the surface plasmon band.
Properties of core-shell nanostructures: dielectric or semiconductor on metal
Au core, SiO2shell.
Constant core diameter,
increasing shell
diameter.
Core shell nanowire

31. The shell usually stabilizes the core (also in colloidal form).
The core gives rise to the relevant properties.
Fe@Aunanoparticles show superparamagnetic behaviour.
Fe@Ndshows low coercivities.
Examples: Au@Ag, Au@Pb, Au@Sn, Ag@In.
Met
al nanoparticles display very interesting optical and electronic properties.
se arise due to the collective oscillation of conduction electrons, when interacting with
The
an electromagnetic radiation (of certain frequency).

Surface plasmon resonance frequency is the relevant property.
For
mation of core-shell structures alters the property of the pure metal.
: Pure Au has an plasmon absorption frequency of ~518nm
E.g.
Silver coating blue shifts and broadens the absorption peak. Thepeaks shifts to 400nm for
suff iciently thick Ag shells.
Coated magnetic nanoparticles
Properties of core-shell nanostructures: metal on metal

33. When an electromagnetic wave impinges on an atom (or a material containing an atomic
spec
which emits radiation of the same frequencyin all directions. This is the proc
scattering. Similar to absorption, scattering is also
There are two possible ways in which transmission can take place:
ies), the electron cloud is set into oscillation. This situation is like adipole oscillator,
ess of
frequency dependent.
(i) i
f the medium is sparse, the ray (wave) could just pass through the particles of the
medium (like in vacuum), which essentially means there is no interaction;
(ii)but the more common mechanism for 'denser media' is 'forward scattering'(i.e. what
we call a
s transmission in common usage is actually forward scattering).
When a wave is being transmitted form one medium (say vacuum) toanother, its
freq
uency remains constant, but its velocity decreases(the wave being slow er in the
medium). The ratio of the velocities c/vmediumis called the r
efractive index (n):

B = 0(H + M)
E
P
eE
Where, is permittivity of the medium and is the permeability of the medium. The subscript
'0' refer to these values in vacuum. KEis the relative permittivity (dielectric constant) and KM
is the relative permeability of the medium.
n
c
v
KEKM

0 0



K
KM


0


0


D
(EP)


B
H
M
H

34. exciton
E
me
n2
eV
13.6 /
(/)20















Eexciton→exciton binding energy
→dielectric constant of the medium

dielect
0→ ric constant of free space
me→m ass of free electron
m* e
e→ffective mass of electron
m*→e
h
ffective mass of hole

n →quantum number (n = corresponds to unbound state)

n=1 →lowestenergygroundstate


When the particle radius is ~ few times the exciton radius the exciton levels decide the
energy levels

When the dimension of the particle is < exciton radius →exciton ceases to exist.
With reducing size of the particle the density of states becomesmore quantized and the band
gap shifts to higher energies (shorter wavelengths) →the absorption spectrum shows a blue
shift

35. Variation of Emission spectra of
CdSequantum dots with size