Transcript Lecture 35

Introduction to Optical Properties
BW, Chs 10 & 11; YC, Chs 6-8; S, Chs 11-13
• Recall: Semiconductor Bandgaps Eg are
usually in the range: 0 < Eg < 3 eV
(up to 6 eV if diamond is included)
• Also, at equilibrium, at temperature T = 0,
the valence band is full & the
conduction band is empty.
• Now, consider what happens if electromagnetic
radiation (“light”) is shined on the material.
• In the photon representation of this radiation
If hν  Eg, some electrons can be promoted
to the conduction band leaving some holes in
the valence band.
• Now, consider some of the various possible types of
spectra associated with this process:
Absorption
Looks at the number of absorbed photons (intensity) vs.
photon frequency ω
Reflection
Looks at the number of reflected photons (intensity) vs.
photon frequency ω
Transmission
Looks at the number of transmitted photons (intensity)
vs. photon frequency ω
Emission
Looks at the number of emitted photons (intensity) vs.
photon frequency ω
• A (non-comprehensive) list of
Various Spectra Types:
Absorption, Reflection,
Transmission, Emission
• Each of these types of spectra is
very rich, complicated, & varied!
• Understanding such spectra gives
huge amounts of information about:
electronic energy bands, vibrational
properties, defects, …
Interaction Between Light & Bulk Material
Many different possible processes can occur!
3c
Incident
light
“Semitransparent”
material
4
1. Refraction
2. Transmission
3. Reflection
a. Specular
1
b. Total internal
3a
c. Diffused
3b
4. Scattering
2
There is also
Dispersion
where different colors
bend differently
A Quick Review of “Light” & Photons
History: Newton & Huygens on Light
• Light as waves
• Light as particles
Christiaan Huygens
Isaac Newton
They strongly
disagreed with
each other!
Light – Einstein & Planck
• 1905 Einstein – Related the wave & particle
properties of light when he looked at the
Photoelectric Effect.
• Planck – Solved the “black body” radiation
problem by making the (first ever!) quantum
hypothesis: Light is quantized into quanta
(photons) of energy
E = h. Wave-Particle duality.
(particles) (waves)
• Light is emitted in multiples of a certain minimum
energy unit. The size of the unit – the photon.
• Explains how an electron can be emitted if light
is shined on a metal
• The energy of the light is not spread but propagates
like particles .
Photons
• When dealing with events on the atomic scale, it is often
best to regard light as composed of quasi- particles:
PHOTONS
Photons are Quanta of light
Electromagnetic radiation is quantized
& occurs in finite "bundles" of energy 
Photons
• The energy of a single photon in terms of its
frequency , or wavelength  is,
Eph = h = (hc)/
Maxwell – Electromagnetic Waves
Light as an Electromagnetic Wave
• Light as an electromagnetic wave is characterized by a
combination of a time-varying electric field (E) & a
time-varying magnetic field (H) propagating through space.
• Maxwell’s Equations give the result that E & H satisfy
the same wave equation:
 
1
H)  
(E,
H)



 , H

,
H
2 
2 
c  t 
2(E,
2
2

Changes in the fields
propagate through free space with speed c.
Speed of Light, c
•
•
The frequency of oscillation, of the fields & their
wavelength, o in vacuum are related by: c = o
In any other medium the speed, v is given by: v = c/n = 
n  refractive index of the medium
n  r r
  wavelength in the medium
r  relative magnetic permeability of the medium
r  relative electric permittivity of the medium
The speed of light in a medium is related to the
electric & magnetic properties of the medium. The
speed of light c, in vacuum, can be expressed as
The Electromagnetic Spectrum
Shorter
Wavelengths
Increasing
Photon
Energy (eV)
Color & Energy
Violet ~ 3.17eV
Blue ~ 2.73eV
Green ~ 2.52eV
Yellow ~ 2.15eV
Orange ~ 2.08eV
Red ~ 1.62eV
Longer
Wavelengths
Visible Light
•
Light that can be detected by the human eye has
wavelengths in the range λ ~ 450nm to 650nm
& is called visible light:
•
Spectral Response of Human Eyes
Efficiency, 100%
•
1.8eV
3.1eV
The human eye can detect light of many different colors.
Each color is detected with different efficiency.
400nm 500nm 600nm 700nm
Visual Appearance of
Insulators, Metals, & Semiconductors
•
A material’s appearance & color depend on the interaction
between light with the electron configuration of the material.
Visual Appearance of
Insulators, Metals, & Semiconductors
•
A material’s appearance & color depend on the interaction
between light with the electron configuration of the material.
Normally
High resistivity materials (Insulators) are Transparent
High conductivity materials (Metals) have a “Metallic
Luster” & are Opaque
Semiconductors can be opaque or transparent
This & their color depend on the material band gap
•
For semiconductors the energy band diagram can explain
the appearance of the material in terms of both luster &
color.
Question
Why is Silicon Black & Shiny?
To Answer This:
•
We need to know that the energy gap of Si is:
Egap = 1.2eV
•
We also need to know that, for visible light, the
photon energy is in the range:
Evis ~ 1.8 – 3.1eV
So, for Silicon, Evis is larger than Egap
•
So, all visible light will be absorbed & Silicon appears black
So, why is Si shiny?
•
The answer is somewhat subtle: Significant photon
absorption occurs in silicon, because there are a significant
number of electrons in the conduction band. These
electrons are delocalized. They scatter photons.
Why is GaP Yellow?
To Answer This:
• We need to know that the energy gap of GaP is:
Egap = 2.26 eV
This is equivalent to a
•
•
•
Photon of Wavelength  = 549 nm.
So photons with E = h > 2.26 eV (i.e. green, blue,
violet) are absorbed.
Also photons with E = h < 2.26eV (i.e. yellow,
orange, red) are transmitted.
Also, the sensitivity of the human eye is greater for yellow
than for red, so
GaP Appears Yellow/Orange.
Colors of Semiconductors
Evis= 1.8eV
I
3.1eV
B
G
Y
O
R
If the Photon Energy is Evis > Egap 
Photons will be absorbed
If the Photon Energy is Evis < Egap 
Photons will transmitted
If the Photon Energy is in the range of Egap
those with higher energy than Egap will be absorbed.
We see the color of the light being transmitted.
If all colors are transmitted the light is White
Why is Glass Transparent?
•
Glass is an insulator (with a huge band gap). Its is difficult
for electrons to jump across a big energy gap: Egap >> 5eV
Egap >> E(visible light) ~ 2.7- 1.6eV
•
All colored photons are transmitted, with no absorption, hence the
light is transmitted & the material is transparent.
•
Define transmission & absorption by
Lambert’s Law: I = Ioexp(-x)
Io = incident beam intensity, I = transmitted beam intensity
x = distance of light penetration into material from a surface
  total linear absorption coefficient (m-1)
 takes into account the loss of intensity from scattering
centers & absorption centers.  approaches zero for a
pure insulator.
What happens during the photon
absorption process?
Photons interact with the lattice
Photons interact with defects
Photons interact with
valence electrons
Photons interact with …..
Absorption coefficient (, cm-1)
Absorption Processes in Semiconductors
Vis
Wavelength
(m)
UV
IR
Important region:
Eg ~ Evis
Photon Energy (eV)
Absorption spectrum of a semiconductor.
Lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
lllllllllllllllllll
Absorption
An Important Phenomena in the Description of
the Optical Properties of Semiconductors
• Light (electromagnetic radiation) interacts with
the electronic structure of the material.
The Initial Interaction is Absorption
•
•
This occurs because valence electrons on the
surface of a material absorb the photon energy &
move to higher-energy states.
The degree of absorption depends, among many
other things, on the number of valence
electrons capable of receiving the photon energy.
•
The photon-electron interaction process
obviously depends strongly on the photon energy.
•
Lower Energy Photons interact principally by
ionization or excitation of the solid’s valence electrons.
•
Low Energy Photons (< 10 eV) are in the infrared
(IR), visible & ultraviolet (UV) in the EM spectrum.
High Energy Photons (> 104 eV) are in the X-Ray
& Gamma Ray region of the EM spectrum.
•
•
The minimum photon energy to excite and/or
ionize a solid’s valence electrons is called the
Absorption Edge or
Absorption Threshold.
Valence Band – Conduction Band Absorption
(Band to Band Absorption)
Conduction Band, EC
Egap
h = Ephoton
Valence Band, EV
Valence Band – Conduction Band Absorption
(Band to Band Absorption)
This process obviously requires that the minimum energy of a
photon to initiate an electron transition must satisfy
EC - EV = h = Egap
Conduction Band, EC
Egap
h = Ephoton
Valence Band, EV
Valence Band – Conduction Band Absorption
(Band to Band Absorption)
This process obviously requires that the minimum energy of a
photon to initiate an electron transition must satisfy
EC - EV = h = Egap
Conduction Band, EC
If h > Egap then
obviously a transition
can happen. Electrons
are then excited to the
conduction band.
Egap
h = Ephoton
Valence Band, EV
After the Absorption Then What?
2 Primary Absorption Types
•
Direct Absorption & Indirect Absorption
All absorption processes must satisfy:
Conservation of Total Energy
Conservation of Momentum or Wavevector
•
The production of electron-hole pairs is very
important for electronics devices especially
photovoltaic & photodetector devices.
•
The conduction electrons produced by the absorbed
light can be converted into a current in these devices.
Direct Band Gap Absorption
A Direct Vertical Transition!
E
Conservation of Energy
h = EC(min) - Ev (max) = Egap
K (wave number)
The Photon
Momentum
is Negligible
Conservation of
Momentum
Kvmax + qphoton = kc
h
Indirect Band Gap Absorption
E
K (wave number)
h
Another Viewpoint
• If a semiconductor or insulator does not have many
impurity levels in the band gap, photons with energies
smaller than the band gap energy can’t be absorbed
– There are no quantum states with energies in the band gap
• This explains why many insulators or wide band gap
semiconductors are transparent to visible light, whereas
narrow band semiconductors (Si, GaAs) are not
Some of the many applications
– Emission:
light emitting diodes (LED) & Laser Diodes (LD)
– Absorption:
– Filtering: Sunglasses, ..
Si filters (transmission of infra red light with simultaneous
blocking of visible light)
• If there are many impurity levels the photons with
energies smaller than the band gap energy can be
absorbed, by exciting electrons or holes from these
energy levels into the conduction or valence band,
respectively
– Example: Colored Diamonds
Photoconductivity
• Charge carriers (electrons or
holes or both) created in the
corresponding bands by
absorbed light can also
participate in current flow,
and thus should increase the
current for a given applied
voltage, i.e., the conductivity
increases
• Want conductivity to be controlled by
• This effect is called
Photoconductivity
light. So want few carriers in dark → A
semiconductor
• But want light to be absorbed, creating
photoelectrons
• → Band gap of intrinsic
photoconductors should be smaller than
the energy of the photons that are
absorbed
Refraction, Reflection &Dispersion
Light, when it
travels in a
Small n
medium can be
absorbed and
reemitted by every
atom in its path.
High n
Defined by refractive index; n
n1 = refractive index of
material 1
n2 = refractive index of
material 2
Total Internal Reflection
t
ki
i
i
Transmitted
(refracted) light
kt
n2
n 1 > n2
kr
Evanescent wave
c c
i >c
TIR
Incident
light
Reflected
light
(a)
(b)
(c)
Light wave travelling in a more dense medium strikes a less dense medium. Depending on
the incidence angle with respect to  c, which is determined by the ratio of the refractive
indices, the wave may be transmitted (refracted) or reflected. (a) i < c (b)  i = c (c) i
>  c and total internal reflection (TIR).
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Mechanism & Applications of TIR
Optical fiber for
communication
What kinds of materials
do you think are suitable
for fiber optics cables?