Upload
dao-van-hoat
View
214
Download
0
Embed Size (px)
Citation preview
7/30/2019 Light and Solide, Rat Hay-1
1/32
1
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)
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
ElectromagneticElectromagnetic Wave in vacuumWave in vacuum
/10x31 8 smc
oo
==
Speed of light related to
electric permittivity andmagnetic permeability
7/30/2019 Light and Solide, Rat Hay-1
2/32
2
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Electromagnetic WaveElectromagnetic Wave
v=1
c=
1
o
n= c
v=
o
= r
r n r
= permittivity = permeability
o - in a
vacuum
r - relative
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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 ?
7/30/2019 Light and Solide, Rat Hay-1
3/32
3
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
The spectrumThe spectrum
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
4/32
4
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
5/32
5
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
6/32
6
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption
optical spectroscopy cangive an idea of band-gap
Absorption by electronic excitationAbsorption by electronic excitation
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
7/32
7
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
optical spectroscopy cangive an idea of band-gap
Absorption by electronic excitationAbsorption by electronic excitation
insulator = gap in VUVinsulator = gap in VUV semicon. = gap atsemicon. = gap at
border IR/vis.border IR/vis.
7/30/2019 Light and Solide, Rat Hay-1
8/32
8
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption by electronic excitationAbsorption by electronic excitation
insulator = gap in VUVinsulator = gap in VUV semicon. = gap atsemicon. = gap at
border IR/vis.border IR/vis.
peaks above threshold: exciton
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
excitons
EoptEg
electron:-ve
hole: +ve
Frenkel or Wannierexcitons....
......details come in
Ch. 7
Band gaps & excitons (nonBand gaps & excitons (non--metals)metals)
7/30/2019 Light and Solide, Rat Hay-1
9/32
9
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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)
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
10/32
7/30/2019 Light and Solide, Rat Hay-1
11/32
11
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
12/32
12
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
13/32
13
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
14/32
14
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption phenomenaAbsorption phenomena
Electronic Polarization
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Solid State Physics VUSolid State Physics VU
Metal-insulator transition in metalhydrides
7/30/2019 Light and Solide, Rat Hay-1
15/32
15
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
16/32
16
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Visualisation of H diffusion in YDen Broeder, van der Molen et al, Nature 394 (1998) 656
Y
Y2O3 Pd
H
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
1
H/Y
0
2
3
hcp-
insulator
hcp-
metal
7/30/2019 Light and Solide, Rat Hay-1
17/32
17
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
18/32
18
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)
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
;)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
7/30/2019 Light and Solide, Rat Hay-1
19/32
19
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
;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.
Some remarks on optics
;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)( =
7/30/2019 Light and Solide, Rat Hay-1
20/32
20
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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.
Some remarks on optics
xnkxnikeeExE
"'
000)(
=
Complex index of refractionComplex index of refraction
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()
7/30/2019 Light and Solide, Rat Hay-1
21/32
21
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
xnkxnikeeExE
"'
000)(
=
Absorption coefficientAbsorption coefficient
Decay of wave amplitude
)('
)(""2"2
*)(
0
0
"22
00
cnn
cnk
eIeEEExIxxnk
===
===
""'2'"'
"')(
22
==
+=
nnnn
innn
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
xnkxnikeeExE
"'
000)(
=
Absorption coefficientAbsorption coefficient
Decay of wave amplitude
)(')('
)(""2"2
*)(
0
0
0
"2
00
nccnn
cnk
eIeEEExIxxnk
====
===
""'2
'"'
"')(
22
=
=
+=
nn
nn
innn
;'''*0
+=
+= ii
7/30/2019 Light and Solide, Rat Hay-1
22/32
22
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
n
n
E
E
I
R
+
=
1
1
Complex index of refractionComplex index of refraction
ET
ER
EI
Matching the amplitudes at
the boundary: EI = ET+ ER
Matching Hy: -nET=ER- EI
Ratio of complex amplitudes
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Complex index of refractionComplex index of refraction
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
7/30/2019 Light and Solide, Rat Hay-1
23/32
23
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
absorbing mode:electron on a spring
force constant:vibrational frequency 0
interaction with surroundings:damping, decay time '
Absorption: simple modelAbsorption: simple model
0
7/30/2019 Light and Solide, Rat Hay-1
24/32
24
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Dilute collection of N such modes(e.g. gas phase) has absorptioncoefficient :
single line centred at 0 with width ca. 1/'
Absorption: simple modelAbsorption: simple model
0
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption: simple modelAbsorption: simple model
0
Now put the oscillators in the solid,with N per unit volume
() has real ( ') and imaginary (") partsabsorption now peaked at max. of "
7/30/2019 Light and Solide, Rat Hay-1
25/32
25
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
= plasma frequency
Absorption: simple modelAbsorption: simple model
0
Now put the oscillators in the solid,with N per unit volume
() has real ( ') and imaginary (") partsabsorption now peaked at max. of "
nn
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
In many structures both electronic andvibronic absorption is seen
opt is determined by the bandgap
Absorption and reflectivityAbsorption and reflectivity
0
strongest absorptionstrongest absorption
nn
Added contribution due to slow lattice vibrations
7/30/2019 Light and Solide, Rat Hay-1
26/32
26
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Gross structure (for solid with a singleabsorption mode):
high transmission at low E
absorption band
high reflectivity
transmission againincreasing
orE
Absorption and reflectivityAbsorption and reflectivity
0
strongest absorptionstrongest absorption
nn
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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....?
7/30/2019 Light and Solide, Rat Hay-1
27/32
27
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
strongest absorptionstrongest absorption
nn
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption and reflectivity: metalsAbsorption and reflectivity: metals
A metal has no gap: absorption frequency 0=0
High reflection already at =00
nn
7/30/2019 Light and Solide, Rat Hay-1
28/32
28
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
Absorption and reflectivity: metalsAbsorption and reflectivity: metals
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
()
photonfrequency ()
reflects transmits
for E < plasma frequency, metals reflect
dielectric const.negative
n purelyimaginary
n'=0
nn == nn '' -- ii nn ''''
Absorption and reflectivity: metalsAbsorption and reflectivity: metals
7/30/2019 Light and Solide, Rat Hay-1
29/32
29
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
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
7/30/2019 Light and Solide, Rat Hay-1
30/32
7/30/2019 Light and Solide, Rat Hay-1
31/32
31
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
MgMg22NiHNiHxx: a case study: a case study
Reflective metal
Transparant semiconductor
Reflection and transmission is low!
High absorption! ?
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
MgMg22NiHNiHxx: a case study: a case study
Front and back of the sample is not the same!
This is not due to the thin Pd caplayer!
7/30/2019 Light and Solide, Rat Hay-1
32/32
C M S M a s t e r s : Electronic Structure and Chemistry of Sol ids.
Some remarks on optics
MgMg22NiHNiHxx: a case study: a case study
A double layer is formed of transparant
Mg2NiH4 and reflective Mg2Ni layers
A high tunable reflection/absorbtion
over the whole solar range