Light and Solide, Rat Hay-1

7/30/2019 Light and Solide, Rat Hay-1

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C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.

Some remarks on optics

When light meets a solid.When light meets a solid.

Tot

A qualitative approach to reflection/absorption

Some basics

Some applications al intensity equals:

Transmitted

Absorbed

Reflected

T+A+R = 1 (fraction transmitted, absorbed and reflected = 1)



ElectromagneticElectromagnetic Wave in vacuumWave in vacuum

/10x31 8 smc

oo

==

Speed of light related to

electric permittivity andmagnetic permeability


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Electromagnetic WaveElectromagnetic Wave

v=1

c=

1

o

n= c

v=

o

= r

r n r

= permittivity = permeability

o - in a

vacuum

r - relative



OpticalOptical PropertiesProperties

Electrical properties and optical properties are related!

interrogate einterrogate e--structure of solids with lightstructure of solids with light

Human perception of solids depends on their interaction

with visible light (1.5-3 eV):

why are metals shiny and 'metallic' ?

why are diamonds transparent ?

why is white paint white ?


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The spectrumThe spectrum



Energy scalesEnergy scales

1eV ~ 10000K (24 meV ~ 300 K)

1eV/atom ~ 100 kJ/mol (1eV~ 96 kJ/mol)

k= 2/ = 2= /hc

= 1m = 104 cm-1

= 1 m = 1.24 eV


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Power input/outputPower input/output

Black body power output

5 < < 50 mm

Solar power input within

0.25 < < 2 m

Optimal atmospheric

adsorptance around 10 m

Sensitivity of the

human eye



Optical Properties & Band StructureOptical Properties & Band Structure

Reflection

Scattering at interface between materials with different n

Absorption

Electronic Polarization

Electron excitation to defect levels in the band gap

Electron excitation across the band gap

Band

Valence

Conduction

Band

T+A+R = 1


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Absorption by electronic excitationAbsorption by electronic excitation

Absorption or emission due to excitation or relaxation of

the electrons in the atoms

http://www.nhn.ou.edu/~kieran/reuhome/vizqm/figs/hydrogen.gif



Absorption in a gas or liquid by electronic excitationAbsorption in a gas or liquid by electronic excitation

Weak interaction between gas/liquid molecules

Analogous to the absorption of a single atom/molecule


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Absorption

optical spectroscopy cangive an idea of band-gap




0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8

Wavelength (m)

In0.53Ga0.47As

Ge

Si

In0.7Ga0.3As0.64P0.36

InP

GaAs

a-Si:H

123450.9 0.8 0.7

103

104

105

106

107

108

P o o e e gy (eV)

1.0

(m

-1)

Fig. 9.19: Absorption coefficient () vs. wavelength () forvarious semiconductors (Data selectively collected and combinedfrom various sources.)From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

http://Materials.Usask.Ca

The absorption coefficients of various semiconductorsThe absorption coefficients of various semiconductors

x = lnI

I0


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Band Gap Energy and ColorBand Gap Energy and Color

.

Ba

ndgap

energy(eV)

Color thatcorresponds toband gap energy

Apparent colorof material(unabsorbed light)

4

3

2

1

red

yellow

greenblue

violet

colorless

black

yellow

orange

ultraviolet

infrared

red



optical spectroscopy cangive an idea of band-gap


insulator = gap in VUVinsulator = gap in VUV semicon. = gap atsemicon. = gap at

border IR/vis.border IR/vis.


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insulator = gap in VUVinsulator = gap in VUV semicon. = gap atsemicon. = gap at

border IR/vis.border IR/vis.

peaks above threshold: exciton



excitons

EoptEg

electron:-ve

hole: +ve

Frenkel or Wannierexcitons....

......details come in

Ch. 7

Band gaps & excitons (nonBand gaps & excitons (non--metals)metals)


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excitons

mean that the optical spectra don't give

the true band-gap

photoconductivityphotoconductivity

or

PESPES -- IPES:IPES:

Eopt

N+1N+1NN--11EEgg

PESPES--IPESIPES= 3.5 eV= 3.5 eV

Band gaps & excitons (nonBand gaps & excitons (non--metals)metals)



ImpuritiesImpurities givegive large bandgaplarge bandgap--crystals colorcrystals color

Corundum

Al2O3

Ruby, sapphire, topaz,

amethyst

Colorless in pure form

Impurities result in different

colors

The Cr levels give strong absorptions at

400nm (green) and 600nm (blue) leaving

only red to be transmitted


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Inhomogeneities: translucencyInhomogeneities: translucency

Translucency is due to light scattered within the material

grain boundaries in poly-crystalline materials

fine pores in ceramics

different phases of materials




Reflection


Absorption




Band

Valence

Conduction

Band

T+A+R = 1


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Absorption by polarizationAbsorption by polarization

The index of refraction n is a measure for the reduced

speed of light in a medium

This retardation is due to electronic polarization

Polarisation causes energy losses

Electronic polarization increases for larger atoms: add Pb to glass




Reflection


Absorption




Band

Valence

Conduction

Band


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Why are Metals Shiny?Why are Metals Shiny?

Metals Eg = 0 e V

All light with above X-ray wavelengths absorbed by continuousnumber of unoccupied states above Ef.

Light is reemitted with exact energy of absorption as electrons fall

back into lowest state. Metals appear reflective as the light we see is

reemitted.

emissionabsorption

Ef



Reflection byReflection by metalsmetals

In terms of electrostatics, the field of the radiation causes

the free electrons to move and a moving charge emits

electromagnetic radiation

Since there is a very high concentration of electrons,

practically all the light is absorbed within about 0.1Jm of

the surface

Penetration depths (I/I0 = 1/e) for some materials are:

water: 32 cm

glass: 29 cm

graphite: 0.6 Jm

gold: 0.15Jm


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Absorption phenomenaAbsorption phenomena


interaction with electron cloud induces electronic polarization

(some) energy lost in absorption

slows light down (seen as refraction)

Electron Transitions

electrons excited to higher unoccupied states

absorption threshold



Solid State Physics VUSolid State Physics VU

Metal-insulator transition in metalhydrides


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0 500 1000 1500 2000

0.1

1

10

Resistivity(m

cm)

Time (s)

0.2

0.4

0.6

0.8

1.0

Transmission(a.u.)

YH0 YH2 YH3

Huiberts et al. Nature

380 (1996) 231


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Visualisation of H diffusion in YDen Broeder, van der Molen et al, Nature 394 (1998) 656

Y

Y2O3 Pd

H



1

H/Y

0

2

3

hcp-

insulator

hcp-

metal


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Solid State Physics VUSolid State Physics VU

Metal-insulator transition in metalhydrides

Applications

switchable mirrors for office building windows

switchable absorbers for solar collectors

optical hydrogen sensors

indicator in the search for new hydrogen storage materials

Complex, light-weigth metal hydrides appear to be

insulating.

Their bandgap can be used for identification



A phase diagram image is created by

depositing thin film gradients of metals

A, B, C using tilted sputter sources

Measure optical properties using

CCD video camera during gas loading

up to 10 bar and 300 oC

A

B C

Complex hydride storage materials

become transparant

Thin film combinatorial chemistry as a tool to findThin film combinatorial chemistry as a tool to find

new hydrogen storage materialsnew hydrogen storage materials


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When light meets a solid.When light meets a solid.

Tot

A qualitative approach to reflection/absorption

Some basics

Some applications al intensity equals:

Transmitted

Absorbed

Reflected

T+A+R = 1 (fraction transmitted, absorbed and reflected = 1)



;)1( 00000 =+=+=+= EEEEPED ee

;)1( 00000 =+=+=+= HHHHMHB mm

t

EJ

t

DJH

+=

+= 0

t

H

t

BE

=

=

r

0

Maxwell equations

Maxwells equationsMaxwells equations

00 permeabilitypermeability

of vacuumof vacuum

00 permittivitypermittivityof vacuumof vacuum

c = (c = (0.0.00))--1/21/2


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;0

00

+==

iEiEiEH

;0HiE =

Assume

;

;

0

0

ti

ti

eEE

eHH

!=

!=

Dielectric constant is a complex quantity

The imaginary part is due to conductivity.

;'''*0

+

=

+

=

i

i

Complex dielectric constant.Complex dielectric constant.

C M S M a s t e r s : Electronic Structure and Chemistry of Solids.


;t

DJH

+=

;t

BE

=

Maxwell equations

Maxwells equationsMaxwells equations

0

=

i

EH

EE "=

02 =+" EkE

Assume

;

;

0

0

ti

ti

eEE

eHH

!=

!=

00=k

For 1-dimensional case the solution is ikxeExE 0)( =


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Complex index of refractionComplex index of refraction

nxikeExE 00)( =

#=n

ck

nkkkk

==

=#==

000

00000

;'''0

i

i+=

+=

nxikti eeExE 0')( 0

=

C M S M a s t e r s : Electronic Structure and Chemistry of Solids.


xnkxnikeeExE

"'

000)(

=


nxikeExE 00)( = #=n ;'''*

0

+=

+= ii

""'2

'"'

"')(

22

=

=

+=

nn

nn

innn

Decay of wave amplitude

If has imaginary parts due to the conductivity in the sample, therefractive index is complex: n=n-in and-dependent: n()


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xnkxnikeeExE

"'

000)(

=

Absorption coefficientAbsorption coefficient


)('

)(""2"2

*)(

0

0

"22

00

cnn

cnk

eIeEEExIxxnk

===

===

""'2'"'

"')(

22

==

+=

nnnn

innn



xnkxnikeeExE

"'

000)(

=

Absorption coefficientAbsorption coefficient


)(')('

)(""2"2

*)(

0

0

0

"2

00

nccnn

cnk

eIeEEExIxxnk

====

===

""'2

'"'

"')(

22

=

=

+=

nn

nn

innn

;'''*0

+=

+= ii


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n

n

E

E

I

R

+

=

1

1


ET

ER

EI

Matching the amplitudes at

the boundary: EI = ET+ ER

Matching Hy: -nET=ER- EI

Ratio of complex amplitudes




ET

ER

EI

Matching the amplitudes at

the boundary: EI = ET+ ER

Matching Hy: -nET=ER- EI

( )

( ) 22222

"1'

"1'

1

1

nn

nn

n

nR

++

+=

+

=

Reflection coefficient R


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proportion of light reflected by a solid, R :

R is large when:

(if n"=0) n' & 0

n" is very strong

n ' = normal refractionn '' = absorption

occurs for E > Eoccurs for E > Egg (non(non--metal) or E < Emetal) or E < Eplasmaplasma in a metalin a metal

Si: ESi: Egg = 1.1 eV= 1.1 eV

in vis. light it'sin vis. light it's

reflective andreflective and'metallic'.....'metallic'.....

( )

( ) 22222

"1'

"1'

1

1

nn

nn

n

nR

++

+=

+

=

Absorption and reflectivityAbsorption and reflectivity



absorbing mode:electron on a spring

force constant:vibrational frequency 0

interaction with surroundings:damping, decay time '

Absorption: simple modelAbsorption: simple model

0


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Dilute collection of N such modes(e.g. gas phase) has absorptioncoefficient :

single line centred at 0 with width ca. 1/'


0




0

Now put the oscillators in the solid,with N per unit volume

() has real ( ') and imaginary (") partsabsorption now peaked at max. of "


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= plasma frequency


0

Now put the oscillators in the solid,with N per unit volume

() has real ( ') and imaginary (") partsabsorption now peaked at max. of "

nn



In many structures both electronic andvibronic absorption is seen

opt is determined by the bandgap


0

strongest absorptionstrongest absorption

nn

Added contribution due to slow lattice vibrations


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Gross structure (for solid with a singleabsorption mode):

high transmission at low E

absorption band

high reflectivity

transmission againincreasing

orE


0


nn



E gap > 3 eV

high reflectivity in visible

n' (thus ()) as big as possible

absorption edge just above 3eV

strong scatterer (as powder, for instance)

rutile: TiO2

!! also cheap and non-toxic

The best white pigment....?The best white pigment....?


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decreasing Egfrom blue end

If a system has an energy gap in the visible(1.5 - 3 eV), it will appear coloured:

yelloworangereddark, shiny ('metallic')

if gap > 3eV no absorption in visibletransparent (if a good crystal)

Energy gap in the visibleEnergy gap in the visible

0


nn



Absorption and reflectivity: metalsAbsorption and reflectivity: metals

A metal has no gap: absorption frequency 0=0

High reflection already at =00

nn


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Reducing also the damping to zero

14.7

15.8

Al

3.93

8.98

Ag

4.406.058.04E(calculated)

4.155.946.64E(measured)

KNaLiMetal



()

photonfrequency ()

reflects transmits

for E < plasma frequency, metals reflect

dielectric const.negative

n purelyimaginary

n'=0

nn == nn '' -- ii nn ''''



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Reflectivity ofReflectivity ofmetals, damping includedmetals, damping included

Reflectivity of the metal with respect to

vacuum

Damping (') affects the reflectivity and the frequencywidth of the transition

1p''''=((((

p''''=100

p''''=10

/p1

R

Transparent



depends on electron density, N

for most metals, p is in the far UV

high reflectivity in visible

= 'shiny'

low N metal:e.g. doped metal oxideSn1-xSbxO2 (x=3%)

p in IR: transparent

Plasma frequencyPlasma frequency

EELS


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MgMg22NiHNiHxx: a case study: a case study

Reflective metal

Transparant semiconductor

Reflection and transmission is low!

High absorption! ?




Front and back of the sample is not the same!

This is not due to the thin Pd caplayer!


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A double layer is formed of transparant

Mg2NiH4 and reflective Mg2Ni layers

A high tunable reflection/absorbtion

over the whole solar range

Documents

Light and Solide, Rat Hay-1