the electromagnetic properties of materials · the electromagnetic properties of materials ... •...

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


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)


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


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


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


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


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)


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


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


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


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


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[ ]


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”


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


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


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


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)


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


MSE 200A Fall, 2008

Light as a Particle: Photons

•  Transparency and color

•  Photodetectors –  Photoconductors –  Photoelectronics –  Photocopiers

•  Photoemitters –  Phosphors –  Light-emitting diodes (LED) –  Lasers


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


MSE 200A Fall, 2008






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”


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

+


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)


MSE 200A Fall, 2008






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


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

+


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


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


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

the electromagnetic properties of materials · the electromagnetic properties of materials ... •...

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