J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
The Electromagnetic Properties of Materials
• Electrical conduction – Metals – Semiconductors – Insulators (dielectrics) – Superconductors
• Magnetic materials – Ferromagnetic materials – Others
• Photonic Materials (optical) – Transmission of light – Photoactive materials
• Photodetectors and photoconductors • Light emitters: LED, lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
The Optical Properties of Materials: Photonic Materials
• Beauty: one-half of the earliest materials science – Pottery glazes(the origin of metals), paints and cosmetics – Jewelry - the development of metals and metalworking
• Information – Window glass – Optical fibers (rapidly replacing copper wire)
• Light – The electric light – LEDs and Lasers – Photodetectors and photoconductors
• Power – Photovoltaics (solar cells) – Laser power transmission (welding, surface treatments)
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
The Optical Properties of Materials: Photonic Materials
• “Optical” means the whole electromagnetic spectrum – From radio waves to γ-rays – Can be regarded as
• Waves in space • Particles with quantized energies
• Light as waves – Refraction and reflection at an interface (windows, light pipes, solarium) – Absorption and scattering (optical fibers) – Diffraction (x-ray and electron crystallography)
• Light as particles – Transmission and absorption – Photodetectors and photoconductors: switches, photocopiers – Photoemitters: LEDs and lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Electromagnetic Waves in Free Space
• Wave carries electric and magnetic fields – Oriented perpendicular to the direction of propagation – Wave:
– Particle:
E
H
¬
€
E = E0 exp −i kx −ωt( )[ ]
€
k =2πλ
(λ = wavelength)
€
ω = 2πν
€
ωk
= νλ = c
(ν = frequency)
c = speed
€
ε = hν = ω
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
The Electromagnetic Spectrum
-10
-8
-6
-4
-2
0
2
4
6
8
1 km
1 m
1 mm
1 µm
1 nm1 Å
4
2
0
-2
-4
-6
-8
-10
-12
-14
4
6
8
10
12
14
16
18
20
22
radio
microwave
infrared
ultraviolet
x-ray
©- ray
visible
0.4 µm
0.5 µm
0.6 µm
0.7 µm
violet
blue
green
yellow
orange
red
log[fr
eque
ncy(
Hz)]
log[en
ergy(
eV)]
log[w
avele
ngth(
m)]
• Visible light: – λ ~ 0.4-1 µm – E ~ 1.2-3 eV
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Light as a Wave
• Propagation through free space at velocity, c
• When light enter a material, it is – Refracted – Reflected – Attenuated
incident
reflected
transmitted
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Refraction and Reflection at an Interface: Normal Incidence
• Refraction: – Wave “drags” charges – Friction slows propagation
• Index of refraction (n) – Property governing refraction – Related to dielectric
constant:
– Depends on frequency (dispersion)
incident
reflected
transmitted
€
E = E 0 exp[−i(kx −ωt)]
Inside material:
€
k = nko ⇒ λ =λ0n
€
v =ωk
=cn
€
n = ε
€
n = n(ω) = ε(ω)
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Refraction at an Interface
• Snells’ Law
– Light bends toward low-n region
• The critical angle – Light cannot exist region 1 if
– Principle of “light pipe”
Φ2
d
Φ1
n2
n1 €
n1 sinφ1 = n2 sinφ2
φ2 > φc = sin−1 n1
n2
Optical fiber confines light by reflection
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
incident
reflected
transmitted
Reflection at an Interface
• Normal incidence from n1 to n2 – Δn ⇒ reflection – Intensity thrown back
• Reflected intensity
• Transmitted intensity
• Note: depends on Δn – Not transparency
€
T =ItIi
=1− R =4n2
(n1 + n2)2€
R =IrIi
=(n2 − n1)
2
(n2 + n1)2
n1
n2
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Exploiting the Light as a Wave: Examples
• Optical fibers – Transparent pipes that transmit light – Note that “light” need not be visible
• GaAs systems operate in the infrared
• Greenhouses and solar heaters – Glass containers that let light in, – Then trap its energy for heat
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Optical Fibers
• Require – Small diameter to minimize surface loss – Perfect cylinder to minimize surface scattering – Exceptional purity to suppress absorption – Exceptional uniformity to suppress Rayleigh scattering
• Gradient fibers – Rays that reflect from surface travel farther than rays on-axis
• Loss of coherence and information – Want gradient in n such that n lower on outside
• Rays that reflect from surface move faster – Can adjust n with solute additions
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Propagation of Light: Attenuation
• IT is gradually attenuated
• Mechanisms of attenuation – Absorption – Rayleigh scattering
• Mechanisms of absorption – Conduction electrons – Phonons – Electronic transitions
• Valence • Core
I
x
incident
reflected
transmitted
€
IT = I0 exp −ηx[ ]
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Attenuation: Rayleigh Scattering
• Light scatters from heterogeneities – Density fluctuations – Chemical heterogeneities – Defects and second-phase particles
• Only recently is it possible to produce clear, uniform glass – “As through a glass - darkly”
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Absorption: Insulator or Semiconductor
• Absorption by – Optical phonons (solar panels) – Ionic transitions (color) – Band transitions (photoconductivity) – Core transitions (x-ray spectroscopy)
Optical phonons
Ionic transitions
E
x
conduction band
valence band
E
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Absorption: The “Greenhouse” Effect
• Absorption by – Optical phonons (solar panels) – Ionic transitions (color) – Band transitions (photoconductivity) – Core transitions (x-ray spectroscopy)
Optical phonons
Ionic transitions
E
x
conduction band
valence band
E
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
The Solarium and Solar Heater
• Mechanism is glass – transparent in the visible – Opaque in the infrared
• Sunlight enters – Rays are absorbed and re-emitted in the infrared – Re-emitted rays cannot penetrate glass – Solar energy is trapped inside
glass
earth
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Diffraction
• Waves reflected from successive planes – Destructive interference unless
– Bragg’s Law ⇒ strong intensity peak
• Pattern of diffraction peaks identifies crystal structure – Use x-rays or electrons with λ of a few Å
d
œ œ
€
nλ = 2d sinθ (Bragg’s Law)
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Electron Diffraction of “Intercritically Tempered Steel”
• Electron microscopy – Photograph – Diffraction pattern
• Diffraction pattern – Peaks from crystal planes – Pattern identifies phases – Ex.: bcc and fcc Fe present
• Combined analysis – “Bright field” microstructure – Diffraction pattern shows phases – “Dark field” locates phases
• Image diffraction spot
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Light as a Particle: Photons
• Transparency and color
• Photodetectors – Photoconductors – Photoelectronics – Photocopiers
• Photoemitters – Phosphors – Light-emitting diodes (LED) – Lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Light as a Particle: Photons
• Transparency and color
• Photodetectors – Photoconductors – Photoelectronics – Photocopiers
• Photoemitters – Phosphors – Light-emitting diodes (LED) – Lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Transparency and Color
• Materials are opaque to all radiation for which ћω>EG – All materials with EG < about 2.5 eV are opaque to visible light
• Radiation with hν=Ei is also absorbed – For all internal excitations (donors, acceptors, ionic excitations) – Leads to “colored” or “dimmed” light
e -
intrinsic excitation
e -
extrinsic excitations ionic
excitations
intrinsic extrinsic
EGEDEG
hˆ hˆ
˙ ˙
EI
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Light as a Particle: Photons
• Transparency and color
• Photodetectors – Photoconductors – Photoelectronics – Photocopiers
• Photoemitters – Phosphors – Light-emitting diodes (LED) – Lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Photoconductivity
• Light of suitable wavelength excites carriers – σ = neµ (n = steady state density from optical excitations) – Semiconductor or insulator becomes metal
• Note two kinds of semiconductor – “direct gap” produces carriers at EG – “indirect gap” excitation requires phonons at E<Ed - messy
behavior
Ó∑
e-
intrinsicexcitation
e-
extrinsicexcitations
EGE
k
EGE
k
conduction band
valence band
conduction band
valence band
Ed
“direct gap” “indirect gap”
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Photoconductors
• Light creates current – “Electric eye” circuits – Photodetecters (need multiple conductors to detect
frequency)
• Photoelectronic transistors – Switch “on” when light “on” – Illumination plays the part of positive voltage at the base
E
x
e e e e e e
-e ee
Ó∑G
+
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Photocopiers
• Charge photoconductor plate
• Reflect light from page – Reflection from white spaces – Removes charge ⇒ Creates map of original print
• Pass through “toner” – Ink sticks to charge on plate
• Print – Press against paper to transfer ink ⇒ Faithful copy of original
• Color copying – Passes for the 3 primary colors
+ + + + + + + + + + + + + +
- - - - - - - - - - - - - -ÎV
(a)
+ + + + + + + + + + + + + +
- - - - - - - - - - - - - -ÎV
(b)
+ + + + + + + + +
- - - - - - - - -ÎV
(c)
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Light as a Particle: Photons
• Transparency and color
• Photodetectors – Photoconductors – Photoelectronics – Photocopiers
• Photoemitters – Phosphors – Light-emitting diodes (LED) – Lasers
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Photoemitters: Phosphors
• A phosphor is an ionic emitter – Incident radiation (ћωi=Ei) excites ion – Excited ion relaxes in lattice, changing energy – Excited state returns to ground state, emitting photon with Ee = ћω’ – Since ω’ ≠ ωI, photon is emitted from the material
• Phosphors used in monitors, etc. – Multiple phosphors used for color images
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Photoemitters: Light Emitting Diodes (LED)
• To generate light from a p-n junction: – Use a “direct-gap” semiconductor in forward bias – Charge recombinations generate photons
• “Color” set by band gap – Long search for “blue” LED solved by GaN
EGE
k
EGE
k
conduction band
valence band
conduction band
valence band
Ed
E
x
e e e e e e
-e
Ó∑G
+
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Lasers: Light Amplification by Stimulated Emission of Radiation
• Three-level laser (ruby): – Excite with incident radiation – Transition to level with difficult transition to ground state (inverted population) – Transitions stimulate further transitions, create beam of photons “in phase”
• Light emission from laser – Mirrors used for multiple reflections to amplify “in phase” beam – Mechanism such as “half-silvered” mirror to emit amplified light
mirror half-silvered mirror
stimulated emission
1
2
3
Ó∑12
phonon
Ó∑13
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Lasers: Four-Level Lasers
• Three-level laser: Problem – ћω13 can stimulate transition 1→3 – One photon lost for each transition - loss of efficiency
• Four-level laser: Solution – Lasing transition to transient state 4 – Immediate transition 4 →1 empties level 4 ⇒ High efficiency since ћω14 has nothing to excite
J.W. Morris, Jr. University of California, Berkeley
MSE 200A Fall, 2008
Semiconductor Lasers
• Use direct-gap semiconductor (GaAs) – Note GaAs gap such that “light” is infrared
• Create “well” where electrons are trapped
• Pump high density of carriers ⇒ exceed recombination rate
• Recombination enhanced by stimulated emission ⇒ laser
Heterojunction GaAs Laser
e e e e e e e
GaAs (n) GaAs (p) GaAlAs (p)
+ -
ћωG
