Transcript ENGR-45_Lec-13_Optical-Prop

Engineering 45
Optical
Properties
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
[email protected]
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-13_Optical_Properties.ppt
Learning Goals – Optical Props
 Learn How Light and Solid Materials Interact
 Why materials have characteristic colors
 Why some materials transparent
and others not
 Optical applications:
• Luminescence
• Photoconductivity
• Solar Cell
• Optical Fiber
Communications
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Properties of Solid Materials
 Mechanical: Characteristics of
materials displayed when forces are
applied to them.
 Physical: Characteristics of materials
that relate to the interaction of materials
with various forms of energy.
 Chemical: Material characteristics that
relate to the structure of a material.
 Dimensional: Size, shape, and finish
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Material Properties
Chemical
Composition
Microstructure
Phases
Grain Size
Corrosion
Crystallinity
Molecular Weight
Flammability
Physical
Melting Point
Thermal
Magnetic
Electrical
Optical
Acoustic
Gravimetric
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Mechanical
Dimensional
Tensile properties
Toughness
Ductility
Fatigue
Hardness
Standard Shapes
Standard Sizes
Surface Texture
Stability
Mfg. Tolerances
Creep
Compression
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ElectroMagnetic Radiation
 Energy associated with Light, Radio Signals,
X-rays and Others is Transmitted as
ElectroMagnetic (EM) Radiation (EMR)
 Electromagnetic radiation
Transmits energy in the form of
a Sinusoidal wave Which
Contains ELECTRICAL &
MAGNETIC Field-Components
 The EM waves Travel in
Tandem, and are
perpendicular to
• Each Other
• The Direction Of Propagation
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The EM Spectrum
 EM Waves Cover a Wide Range of
WAVELENGTHS, , and FREQUENCIES, 
• : miles→femtometers
 “Light” is generally divided
into Three Segments
• UltraViolet: 0.001→0.35 µm
– NOT Visible, High in Energy
• Visible: 0.35→0.7 µm
– A VERY Small Slice
of the EM spectrum
• InfraRed: 0.7-1000 µm
– Not Visible; carries “sensible”
energy (heat)
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EM Radiation Quantified
 All EM Waves
Travel at the Speed
of Light, c
 c is a Universal
Constant with a
value of 300 Mm/s
(186 000 miles/sec)
 c is related to the
Electric & Magnetic
Universal Constants
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c  1  0 0
• Where (Recalling
From Previous
Lectures)
– 0  ELECTRIC
Permittivity of Free
Space (a vacuum)
– µ0  MAGNETIC
Permeability of Free
Space (a vacuum)
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EM Radiation Quantified
 The Wavelength
and Frequency of
EM waves are
related thru c
c   
• Where
–   WaveLength in
meters per cycle
–   Frequency in
Hertz (cycles/sec)
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 EM radiation has a
Wave↔Particle
Duality
 The Energy, E, of a
Light Particle
E  h  hc  
• Where h 
Planck’s Constant
(6.63x10-34 J-s)
 h is the
PHOTON Energy
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EM-Solid Interaction
 Consider EM
Radiation with
Intensity I0 (in W/m2)
Impinging on a Solid
 The EM-Solid
interaction Alters the
incident Beam by
3 possible
Phenomena
• The EM Beam can
be
– Reflected
– Absorbed
– Transmitted
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EM-Solid Interaction cont
 Mathematically
I 0  I R  I A  IT
• Where all the IK are
Intensities in W/sq-m
 An Energy Balance
on the Solid:
• E-in = E-reflected +
E-absorbed +
E-transmitted
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 Now Divide
E-Balance Eqn by I0
1 R  AT
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EM-Solid Interaction cont.2
1 R  AT
• Where:
– R  REFLECTANCE
(IR/I0)
– A  ABSORBANCE
(IA/I0)
– T  TRANSMITTANCE
(IT/I0)
 Using R, A, T, Classify
EM-Solid Behavior
• Opaque → T = 0
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IR
I0
IA
IT
• Transparent →
– T >> A+R
– Light Not Scattered
• Translucent→
– T > A+R
– Light Scattered
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Metals – Optical Absorption
 Metals Interact with Light Thru QUANTIZED Photon
Absorption by Electrons
 Metals have Very
Closely Spaced eEnergy Levels
Io
Energy of electron
unfilled states
DE = h required
filled states
• Thus Almost ALL incident
Photons are ABSORBED
within about 100 nm of
the surface
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Metals – Optical Reflection
 The Absorbed Energy is ReEmitted by e- “falling”
back to Lower Energy states
 Since Metals have Very
Closely Spaced eEnergy Levels The Light
Energy of electron
is emitted at many ’s
IR
re-emitted
photon from
material
surface
• Thus Outgoing Light Looks
About the Same as Incoming
Light → High Reflectance
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unfilled states
“conducting” electron
DE
filled states
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Light Absorbtion/Reflection
 Amount of NON-Reflected
Light Absorbed by a Matl
IT I 0 e

 = absorption coefficient, cm-1
 = sample thickness, cm
I 0 = NonReflected incident
light intensity
IT = transmitted light intensity
 For normally incident
2
light passing into a Rreflectivi ty  ns  1 
 n 1
solid having an
 s

index of refraction n:
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Cu Bar
 Metals also ABSORB
Some Photons
• Dissipated as heat
 Metals that Absorb few, or
in broad-spectrum, reflect “WHITE” Light and
Appear Silvery
Sn-Plated Cu Bar
Metals - Colors
 Some Metals absorb Preferentially, and the
Reflected Light is Colored due the absence of
the Absorbed light
• e.g., Cu Absorbs in the Violet-Blue; leaving
Reflected light rich in Orange-Red
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Total Transmission
 Combining External and Internal
Reflection, along with Beer’s Absorbtion
Yields the TOTAL Transmission Eqn
IT  I 0 1  R  e
2  
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Total-T Example
 For the Situation at
Right Determine the
thickness, d77, that
will produce a total
Transmittance of
77%
 From Tab 21.1 Find
Pyrex ns = 1.47
 Next find R using
Eqn (21.13)
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Quartz
Pyrex
0.86I 0
I0
13
23 mm
mm
2
 ns  1   1.47  1 
  
R  

 ns  1   1.47  1 
R  3.621%
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Total-T Example
Quartz
Pyrex
 Recall total
Transmission Eq
IT  I 0 1  R  e
2
 Now Solve for β
0.86I 0
I0
 
13
23 mm
mm
IT
 

e
2
 IT I 0 
I 0 1  R 
 
   ln 
2 

1  R 


IT


ln 
  
2 
 I 0 1  R  
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Total-T Example
Quartz
Pyrex
 Thus


0.86
 23mm
   ln 
2 
 1  0.03621 
  3.350 meter
 Solving Total-T Eqn
for the length
 IT I 0 

   ln 

2 
 1  R  
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0.86I 0
I0
13
23 mm
mm
 Then d77

 0.00335
0.77

d 77   ln 
2 
mm
 1  0.03621 
d 77  56.0 mm
Bruce Mayer, PE
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NonMetals – Selective Absorb.
 In The Case of Materials with “Forbidden” Gaps in
the Band Structure, Absorption Occurs only if h>Egap
Energy of electron
blue light: h 3.3 ev
unfilled states
red light: h 1.8 ev
 For These
Materials there
is Very little
ReEmission
incident photon
energy h
Io
Egap
filled states
• The Material Color
Depends on the
Width of the BandGap
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Color Cases – BandGap Matls
 Egap < 1.8 eV
• ALL Visible Light Absorbed; Solid Appears
Gray or Black in Color
– e.g., Si with Egap = 1.1 eV
 Egap > 3.3 eV
• NO Visible Light Absorbed; Solid Appears Clear
and Transmissive
– e.g., Diamond Egap = 5.45 eV, SiO2 Egap = 8-9 eV
 1.8 eV < Egap < 3.3 eV
• Some Light is absorbed and Material has a color
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NonMetal Colors
 Color determined by
sum of frequencies
• transmitted light
• re-emitted light from
electron transitions
• Red/yellow/orange is
transmitted and
gives it this color
 e.g., Cadmium
Sulfide (CdS)
• Egap = 2.4eV
• Absorbs higher
energy visible light
(blue, violet),
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 CdS
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NonMetal Colors cont.
 Ex: Ruby =
Sapphire (Al2O3) +
0.5-2 at% Cr2O3
• red is transmitted
 Result: Ruby is
deep Red in color
• Sapphire is colorless
(i.e., Egap > 3.1eV)
 adding Cr2O3
• alters the band gap
• blue light is
absorbed
• yellow/green is
absorbed
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Wavelength vs. Band Gap
 Example: What is the maximum
wavelength absorbed by Ge?
 Find Ge BandGap: Eg = 0.67 eV
• Thus Need Ephoton = hc/λmax ≥ Eg
 Use the Photon Energy Eqn:
max
hc (6.62x10 34 J  s )(3 x 108 m/s )
 
 1.85m
19
E g (0.67eV )(1.60x10 J/eV )
note : for Si E g 1.1eV max 1.13 m
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Light Refraction
 When Light Encounters a Matter-Containing
Environment, it SLOWS DOWN Due to
Interaction with Electrons
no
transmitted
light
+
transmitted
light
electron
cloud
distorts
+
 Define the INDEX of REFRACTION, n
n  Spd of Light in Vacuum  Spd of Light in Matl 
c
Or n 
v
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Light Refraction cont
 The slowing of light in a Non-Vacuum Medium
Results in Refraction, or Bending of the light Path
 Light Refracts per Snell’s Law :
n1 sin 1  n2 sin 2
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Bruce Mayer, PE
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Refraction Physics
 Recall
c
n
v
 Now the relations for
v and c
v  1 
• Where ε & µ are
respectively the
Permittivity &
Permeability of the
Material
 Now Recall
c  1  0 0
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 Thus n

c
n 
  r r
v
 0 0
 Most Matls are NOT
magnetic → µr  1
• So
n  r
 e.g. Germanium
• n = 3.97 → n2 = 15.76
• r = 16.0 (very close)
Bruce Mayer, PE
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Application  Luminescence
 Based on EM Induced e− excitation, and then
Relaxation with Broad-Spectrum h Emission
Energy of electron
Energy of electron
unfilled states
unfilled states
Incident
Radiation
h0
Egap
Egap
emitted light
h1+ h2+...
filled states
Electron
Excitation
 e.g.
fluorescent
lamps
Re-emission
Occurs
glass
coating
e.g.; -alumina,
doped w/
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filled states
UV
radiation
“white” light
Bruce Mayer, PE
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Application  PhotoConduction
 h Absorption by NO-Junction SemiConductors
results in the Elevation of an e- to the
Conduction Band Where it Can Carry an
E-Field Driven Current
+
+
Energy of electron
Energy of electron
unfilled states
unfilled states
semi
conductor:
Egap
Incident
radiation
filled states
filled states
-
A. No incident radiation:
little current flow
 e.g. Cadmium Sulfide
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Conducting e-
Egap
-
B. Incident radiation:
Increased current flow
Bruce Mayer, PE
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Application  Si Solar Cell
 Recall The
PN Junction
P-doped Si
conduction
Si
electron
Si P Si
• An incident PHOTON produces
HOLE-ELECTRON pair.
• Typically 0.5-0.7 V potential
– Theoretical Max = 1.1 V (Egap).
• Current INCREASES with
INCREASED Light INTENSITY
Si
n-type Si
p-njunction
p-type Si
– Need to Minimize Reflectance
n
Si
B
+E-
Si
hole
Si
Si
B-doped Si
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 Operation for Si Cell:
p
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Application – Heat Mirror
 Natural SunLight is
Very Pleasant
• However, In Sunny
Climes Windows that
Admit Visible Light
ALSO transmit InfraRed
EM radiation that Heats
the Building; increasing
AirConditioning costs
 Soln → “Heat” Mirror
Window
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Application – Heat Mirror cont
 A Perfect Heat Mirror
Would
• Transmit 100% of EM
radiation (light) in the
visible 350-700 nm
Wavelength range
• Reflect 100% of
EMR over 700 nm
 HM Film Stack →
dielectric / metal /
dielectric (D/M/D)
 Heat Mirror Windows
• e.g., 300Å TiO2 /
are Constructed from
130Å Ag / 300Å TiO2
thin-film coated
“window glass”
http://www.cerac.com/pubs/cmn/cmn6_4.htm
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All Done for Today
The
Solar
Spectrum
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WhiteBoard Work
 Derive Eqns
• 21.18
IT  I 0e
 d
– Thick, Strongly Absorbing
Medium of thickness d
• 21.19


IT  I 0 1  R e
2
d
– Weakly Absorbing (transparent) medium
with Reflection, R, and thickness d
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Heat Mirror
Hot Miror (Heat Reflecting)
What - These "hot mirror" filters transmit the visible spectrum
and reflect the infrared. At any specified angle of incidence,
the average transmission is more than 93% from 425 to 675
nm. The average reflectance of our standard Hot Mirror is
more than 95% from 750 to 1150 nm.
Extended Hot Mirror: The average reflectance is more than
90% from 750 to 1600 nm.
Long IR Hot Mirror The average reflectance is more than 90%
from 1700 to 3000 nm
Cold Mirror (Heat Transmitting)
These "cold mirror" filters reflect the visible spectrum
and transmit heat (infrared). At any specified angle of
incidence, average reflectance is more that 95% from
450 to 675 nm. Transmission is more than 85% from
800 to 1200 nm.
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[email protected] • ENGR-45_Lec-13_Optical_Properties.ppt