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SSPD_Chapter1_Part 11 is a continuation of Solid State of Matter. This describes indirect band gap material and its non-radiative transition charactistics and direct band gap material and its radiative transition characteristics.

SSPD_Chapter 1_Part 11_Continued_Direct and indirect Band gap Semiconductors.


Silicon and Germanium are indirect band-gap materials as shown in Figure(1.58.a and b). Whereas compound semiconductors are direct band-gap materials, as shown in Figure (1.59.), with the exception of GaP which need special doping to become direct band gap. When the top of the valence band and bottom of the conduction band occurs at k=0 then we have Direct Band Gap material. Here direct transition occurs hence it is radiative transition . Photons can mediate direct transitions. But when the bottom of the conduction band occurs at k= π/a and bottom of the valence band occurs at k=0 then indirect transition occurs. The extra momentum ћk = ћ.(π/a)= h/(2a) cannot be removed by photon. Phonon has larger momentum and phonon mediates an indirect transition. This leads to increase in thermal vibration of crystal lattice. Phonon is a quanta of lattice vibrational energy. Hence indirect transition is non-radiative. If the edge of conduction band is made of s-orbital electrons then we have direct band-gap material. If the edge of conduction band is made of p-orbital then we have indirect band-gap material.

Figure.1.58 and 59. E-k diagram of Ge, Si and GaAs PHONONS.

A quanta of lattice vibrational energy is known as phonon. A Crystal Lattice System can be treated as lattice centers interconnected with bonds equivalent to elastic springs. These springs, representing the atomic bonds, behave like harmonic oscillators which has quantized energies E n = (n+1/2)ћω. At 0K, the Zero Point Energy of the lattice is (1/2)ћω. The Lattice vibrations propogate like coupled vibrations or as cooperative vibrations of many atoms. Lattice vibrations are longitudinal (atomic vibrations are in the same direction as that of propogation) as well as transverse (atomic vibrations are at right angle to the direction of propogation) as shown in Figure (1.60). These lattice vibrations travel as lattice waves. They occur at 4×10 12 Hz and at 14×10 12 Hz .At 4×10 12 Hz the phonons are known as Transverse Acoustical (TA) Waves and as Longitudinal Acoustical (LA) Waves. At 14×10 12 Hz, these are known as Transverse Optical (TO) Waves and as Longitudinal Optical (LO) Waves.

The velocity of propogation = √(B/ρ)

where B is the elastic bulk modulus and ρ is the density of the crystal.

Substituting the appropriate values B= 70Gpa and ρ= 2.7 gm-cm -3 for Aluminium:

Velocity of propogation is 5092m/s in Aluminum.

The frequency of oscillation is ~ 10 13 Hz.

Therefore λ phonon =velocity/ frequency= 5 A°;

Linear momentum of phonons = p phonons = h/λ= 10 -24 Kg-m/sec = ћk;

Therefore k phonons = 10 -24 Kg-m/sec/ћ= 2π×10 10 radians/m ;

Figure 1.60. Crystal Lattice System represented as Coupled Harmonic Oscillators. PHOTONS.

Photon is a quanta of optical energy. If we examine Green colored photons of wavelength λ = 500nm

then p photons = h/λ = 13.26×10 -28 Kg-m/sec ;

We see that p photons <<p phonons;

Also k photons = 2π×10 7 radians/m ;

In a indirect band-gap material, at the bottom of the conduction band, conducting electrons have k = π/a = π/(5×10 -10 ) therefore k= (π/5) ×10 10 radians/m whereas holes have k=0. Therefore in in-direct transition the mediating particle must take away the energy as well as momentum. Conservation of momentum can be achieved only through the mediation of phonons (k phonons = 2π×10 10 radians/m) because of significant excess momentum present during in-direct transition. Hence in-direct transition is accompanied with the emission of phonons rather than photons. Therefore in-direct transition is non-radiative whereas direct transition is radiative. Therefore Direct Band Gap materials are suitable for light sources. RADIATIVE AND NON-RADIATIVE TRANSITION.

Indirect Transition(momentum as well as energy has to be accounted for):

conducting electron + hole = phonons (non-radiative);

Direct Transition (momentum is zero for both carriers and only energy has to be accounted for :

conducting electron + hole = photons (radiative);

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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