http://www.wiretechworld.com/the-future-of-optical-fibres/

EE 443 Optical Fiber Communications

Dr. Donald EstreichFall Semester

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Lecture 9

Semiconductors – II

2

From Lecture 8 (September 17, 2019)

1. Atoms have discrete energy levels (for outer electrons) but solidshave energy bands where electrons and holes reside

2. Electrons in conduction band from thermal generation or from donoratoms in lattice

3. Holes in valence band from thermal generation or from acceptor atomsin lattice

4. Electrons and holes viewed as wave packets in motion (can’t localizethese charge carriers) with separate effective masses (m*)

5. Semiconductors have forbidden bandgaps which dominate theirphysical properties

6. Holes have positive charge and electrons have negative charge whichunder low doping conditions can be treated as classical particles(but don’t look too closely at the “particle”)

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Representing the Density of States of Semiconductor Bands

https://en.wikipedia.org/wiki/Band_gap

Valence band iscompletely filledby electrons at

T = 0 K

Conduction band is empty at T = 0 K

No electron statesin the bandgap

For a semiconductor

Note: A filled band can’t conduct current

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https://www.scienceabc.com/innovation/what-are-semiconductors-and-how-do-they-work.html

Electron-hole pair creation

Conduction & Valence Bands in Semiconductors

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Electron-Hole Pairs in Intrinsic Semiconductor

https://vidyarthiacademy.in/vidyarthiacademy/cbsenotes/xiiphys/12-phys-cbsenotes-14-semiconductors.php

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Intrinsic Concentration

in

midgap energyFE =

electrons

holes

EG

Fermi energyor

Fermi level

Ferm

i-D

irac

Sta

tist

ical

Dis

trib

uti

on

Probability0 1

ExponentialSection

Fermi Energy Level in Intrinsic Semiconductor

https://physics.stackexchange.com/questions/332045/why-is-the-fermi-dirac-distribution-defined-between-energy-bands

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Fermi-Dirac Distribution for Electrons in a Material

Fermi Level

https://sites.google.com/site/puenggphysics/home/unit-5/fermi-dirac-function

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Direct Bandgap vs. Indirect Bandgap Semiconductors

http://edetec106.blogspot.com/2016/01/differentiate-between-direct-and.html

2k

=

E- k diagrams

Wave VectorOr

CrystalMomentum

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Fermi-Dirac Distribution and Maxwell-Boltzmann Approximation

http://www.iue.tuwien.ac.at/phd/mwagner/node28.html

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The Formation of a PN-Junction

http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/pnjun.html

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The Formation of a PN-Junction

https://www.electronics-tutorials.ws/diode/diode_2.html

Eo

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Majority Carriers and Minority Carriers in Doped Semiconductor

https://www.pveducation.org/pvcdrom/pn-junctions/equilibrium-carrier-concentration

Law of Mass Action

In silicon the intrinsic carrier concentration at T = 300 K is

3 10 3

2 6 20 3 2

2

(cm ) 1.01 10 pairs/cm

( ) 1.02 10 (pairs/cm )i

i

in

n cm

pn n

−

−

=

=

=

Based upon the Boltzmann distribution.

po = NAno = ND

DepletionRegion

pono

n-typep-type

NeutralRegion Neutral

Region

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The Potential Barrier in a PN-Junction

https://www.researchgate.net/figure/Abrupt-p-n-junction-in-thermal-equilibrium-adapted-from-Ref-51-a-Space-charge_fig3_283081246

14https://giphy.com/gifs/work-ei2AYYW8qdZyo

Semiconductor PN-Junction Both Forward and Reverse Bias

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Spontaneous Emission From Recombination at PN-Junction

ED

EA

n-region

p-region

From: Section 6.3.4, Figure 6.11, in Senior

A pn-junction under forward bias giving spontaneous emission of photons.

16From: Section 6.3.4, in Senior

Spontaneous Emission From Electroluminescence

We require a direct bandgap semiconductor and the transition isknown as “band-to-band” recombination. Under forward bias thethe excess minority carrier populations decay from band-to-bandrecombination. Thus, the energy of the photon is approximatelyequal to the bandgap energy EG.

velocity of light

wavelength

1.24[μm]=

[eV]

G

G

hcE hf

c

E

= =

=

=

Called electroluminescence (from spontaneous emission) in diode.

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https://www.researchgate.net/figure/Band-structure-in-momentum-space-A-direct-band-gap-semiconductor-Electron-hole_fig1_280063964

Band Structure in Momentum Space (k Space)

Direct Bandgap Indirect Bandgap > L

Indirect BandgapL >

EG

e.g., Si and Ge e.g., GaAs

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Quantized Lattice Vibrations – Phonons

https://mappingignorance.org/2018/01/18/what-the-heck-is-a-phonon/ http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/phonon.html

A phonon is an excited state in the quantum mechanical quantization

of the modes of vibrations of elastic structures of interacting particles.

19From: Section 6.3.3, Figure 6.13 (page 314), in Senior

Energy-Momentum Diagrams Showing Transitions

Phonon

Direct Bandgap Indirect Bandgap

PhotonPhoton

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https://ecee.colorado.edu/~bart/book/book/chapter4/ch4_6.htm

Maintaining Conservation of Energy and Momentum

photon photonphoton

Direct Bandgap Indirect Bandgap Indirect Bandgap

Scenario 1 Scenario 2

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Photon Emission Unlikely in Indirect Gap Materials

From Section 6.3.3, pp. 313 to 316 in Senior

The radiative minority carrier lifetime is

where Br is recombination coefficient (cm3sec-1), and n and p are the respectiveminority carrier and majority carrier concentrations.

Example 6.4 (page 315)Compare a direct gap semiconductor (Si) with a direct bandgap semiconductor (GaAs).Assume for both that (n + p) = 1 1018 cm-3.

For silicon, Br = 1.79 10-15 cm3sec-1, thus

For gallium arsenide, Br = 7.21 10-10 cm3sec-1, thus

1

( )r

rB n p =

+

15 18

1 1 1(Si) 0.56 milliseconds

( ) 1.79 10 (1 10 ) 1790r

rB n p

−= = = =

+

10 18 8

1 1 1(GaAs) 1.39 nanoseconds

( ) 7.21 10 (1 10 ) 7.21 10r

rB n p

−= = = =

+

slow

fast

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https://www.ee.co.za/article/choose-laser-based-sensor.html/ret-april-2016-fig2

Sources for Coherent and Incoherent Light

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• Coherence: It is a crucial property of laser, that exists due to stimulated emission. It simply denotes that the wavelength of the waves of emitted

light is in phase. With an ordinary light source (e.g., LED), it is not coherent

because it is generated by spontaneous emission of photons.

• Monochromaticity: Monochrome means it has a single wavelength. Waves having single wavelength denotes a single color.

• Brightness: Brightness of a light is basically the power per unit surface area per unit solid angle. Due to continuous reflections, a light of high intensity and more power is produced by laser diodes.

• Directionality: A laser light is highly directional this means it does not exhibit much beam divergence. Directionality in a laser diode is achieved because the emitted photons undergo multiple reflections between the mirrors.

Properties of a Laser Diode

https://circuitglobe.com/laser-diode.html

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https://www.slideshare.net/KamalKhan822/solids-conductors-insulators-semiconductors

Direct Bandgap Semiconductor With Stimulated Emission Possible

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https://elprocus.wordpress.com/2013/07/25/led-architecture-and-design-concepts/

Light Emitting Diodes and Commonly Found Packaging

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https://www.skipprichard.com/ask-questions-to-improve-your-leadership/