Introduction to Optical PropertiesBW, 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 radiationIf 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:

AbsorptionLooks at the number of absorbed photons (intensity) vs.photon frequency ω

ReflectionLooks at the number of reflected photons (intensity) vs.photon frequency ω

TransmissionLooks at the number of transmitted photons (intensity)vs. photon frequency ω

EmissionLooks 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 isvery rich, complicated, & varied!

• Understanding such spectra gives

huge amounts of information about:electronic energy bands, vibrational

properties, defects, …

1. Refraction

2. Transmission

3. Reflection

a. Specular

b. Total internal

c. Diffused

4. ScatteringThere is also Dispersion

where different colors bend differently

1. Refraction

2. Transmission

3. Reflection

a. Specular

b. Total internal

c. Diffused

4. ScatteringThere is also Dispersion

where different colors bend differently

41

3b

2

3a

3c

Incident light

“Semi- transparent” material

Interaction Between Light & Bulk Material Many different possible processes can occur!

A Quick Review of “Light” & Photons History: Newton & Huygens on Light

• Light as waves• Light as particles

Christiaan Huygens

Isaac Newton

They They strongly strongly disagreeddisagreed with with

each other!each other!

Light – Einstein & Planck• 1905 Einstein – Related the wave & particle

properties of light when he looked at thePhotoelectric 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.

(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 .

(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 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:

Changes in the fieldspropagate through free space with speed c.

H,tc

1H,

2

2

22

Light as an Electromagnetic Wave

(E, H) 2

(E, H)

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 wavelength in the mediumr relative magnetic permeability of the medium r relative electric permittivity of the medium

rrn

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 SpectrumShorter

Wavelengths

Longer Wavelengths

Increasing Photon

Energy (eV)

Color & Energy Violet ~ 3.17eV Blue ~ 2.73eV Green ~ 2.52eV Yellow ~ 2.15eVOrange ~ 2.08eV Red ~ 1.62eV

Visible Light• Light that can be detected by the human eye has

wavelengths in the range λ ~ 450nm to 650nm & is called visible light:

• The human eye can detect light of many different colors. • Each color is detected with different efficiency.

3.1eV 1.8eV

Spectral Response of Human Eyes

Eff

icie

ncy,

100

%

400nm 600nm 700nm500nm

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.

NormallyHigh resistivity materials (Insulators) are Transparent

High conductivity materials (Metals) have a “Metallic

Luster” & are Opaque

Semiconductors can be opaque or transparentThis & 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 – 3.1eVSo, 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?

•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.

To Answer This:

Colors of Semiconductors

I B G Y O R

EEvisvis= 1.8eV = 1.8eV 3.1eV 3.1eV

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 intensityx = 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 Processes in Semiconductors

Important region:

Ab

sorp

tion

coe

ffic

ien

t (

, cm

-1)

Photon Energy (eV)

Absorption spectrum of a semiconductor.

Vis

Eg ~ Evis

Wavelength (m)

IRUV

Lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllll

AbsorptionAn 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 orAbsorption Threshold.

Valence Band – Conduction Band Absorption(Band to Band Absorption)

Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy

EC - EV = h = Egap

Valence Band – Conduction Band Absorption(Band to Band Absorption)

Valence Band – Conduction Band Absorption(Band to Band Absorption)

Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy

EC - EV = h = Egap

If h > Egap then obviously a transition can happen. Electrons are then excited to the

conduction band.

After the Absorption Then What? 2 Primary Absorption Types

Direct Absorption & Indirect Absorption• All absorption processes must satisfy:

Conservation of Total EnergyConservation 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

K (wave number)h

Conservation of Energyh = EC(min) - Ev (max) = Egap

Conservation of Momentum

Kvmax + qphoton = kc

EA Direct Vertical

Transition!

The Photon Momentum is Negligible

Indirect Band Gap Absorption

E

K (wave number) h

• 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

Another Viewpoint

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

• This effect is called Photoconductivity

• Want conductivity to be controlled by 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

Light, when it travels in a

medium can be absorbed and

reemitted by every atom in its path.

Refraction, Reflection &Dispersion

Defined by refractive index; n

Small n

High n

n1 = refractive index of material 1

n2 = refractive index of material 2

Total Internal Reflection

n2

i

n1 > n

2i

Incidentlight

t

Transmitted(refracted) light

Reflectedlight

k t

i>cc

TIR

c

Evanescent wave

k i k r

(a) (b) (c)

Light wave travelling in a more dense medium strikes a less dense medium. Depending onthe incidence angle with respect to c, which is determined by the ratio of the refractiveindices, 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?