Key Properties and Functions of Phonons in Semiconductors
The concept of phonon was introduced by soviet physicist Igor Tamm in 1932. The word phonon was derived from the Greek word phone, which refers to the meaning of sound or voice because long-wavelength phonons result in the production of sound. The name and the word are analogous to the photon. In analogy with the quantum energy, photon, in the electromagnetic field, the name phonon was suggested for the quantum lattice vibrational energy by Frenkel in 1935. Thus, phonons are the quanta of sound just like a photon is a quanta or the packet of energy for electromagnetic waves.
In this article, we are going to learn about the concept of phonons, what phonons are and a deep insight into the meaning of phonons for better understanding.
What is Phonon?
Solid crystal consists of atoms bound into a specific repeating three-dimensional spatial pattern called a lattice.
The solids execute elastic behaviour at the atomic level, the bond between the atoms and the intermolecular bonds are elastic.
The atoms act like they are connected with a spring, just like coupled harmonic oscillators and the thermal energy generated or any external forces will cause the atoms and molecules to oscillate. This will generate mechanical waves that carry heat and sound through the material.
A packet of these waves can travel throughout the crystal with definite momentum and energy known as phonons.
Now, what is phonon? The quantum of energy is a phonon. In other words, we can say, a phonon is the quantum energy of the lattice vibration, just like photons are the quantum energy of electromagnetic radiations. The energy of each phonon is given by:
⇒ E = hv
⇒E = ħ(2π)v
⇒ E = ħω……. (1)
Where,
ω -The angular frequency
ħ - The reduced Planck’s constant
Phonon Meaning
According to the phonon definition, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules condensed specifically in solids and some liquids. In other words, a phonon can be defined as a discrete unit of vibrational mechanical energy, the phonons exist with a discrete amount of energy given by E=ħ.
Phonons play an important role in many of the physical properties of solid states, such as they play a key role in thermal conductivity and electrical conductivity. The study of phonons is an essential concept in condensed matter physics or solid-state physics.
Phonon Vector: When a phonon with a wave vector is created by elastic scattering of a photon or neutron from wave vector K to K', the wave vector selection rule that governs the process is given by:
⇒ K = K' + G
Where,
G -The reciprocal lattice vector
Types of Phonon
When the unit cell consists of more than one atom, the crystal will contain two types of phonons. Thus, there are two types of phonons that we study in condensed matter physics:
Acoustic Phonon: In acoustic phonons, both positive and negative ions swing together.
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Optical Phonon: In optical phonons, both positive and negative ions swing against each other. The optical phonons are excited easily by light.
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Phonon Energy
Since, the atoms in the unit cell are behaving like a coupled oscillator, according to the quantum theory, the energy of the harmonic oscillator is given by
\[\Rightarrow E = (1+\frac{1}{2}\bar{h}\omega)\]
Where,
ω -The angular frequency
ħ - The reduced Planck’s constant
Phonon Momentum
The phonon momentum is given by ħK, it is not the momentum of the phonon, it is often referred to as crystal momentum in general.
Properties of Phonons
Phonons are often used as a quasiparticle, some popular research has shown that phonons and protons may indeed have some kind of mass and be affected by gravity.
phonons are said to have a kind of negative mass and negative gravity.
phonons are known to travel faster (with maximum velocity) in denser materials.
It is projected that phonons would deflect away as it detects the difference in densities, exhibiting the qualities of a negative gravitational field.
Phonons have also been predicted to play a key role.
They can also be used as quasiparticles.
They can be affected by gravity.
They tend to have negative energy and negative mass.
They travel faster in denser material (with higher velocity).
Phonons in Semiconductors
The lattice thermal conductivity of a number of semiconductors along with InSb, GaAs, GaSb, CdTe, and CdS has been measured between temperatures 1.7 and 300°K. This, together with previous works and experiments on Si and Ge, is used to investigate the validity of the relaxation time expressions for the scattering of phonons by boundaries, atomic impurities and electrons, and to discuss phonon-phonon interactions and resonance scattering effects.
The obtained results indicate that the boundary scattering and isotope scattering relaxation times lead to accurately calculated values of thermal conductivity only when the materials are exceptionally pure. And the structure, which has been identified as due to resonance scattering, has been observed in the data for most of the materials. Electron-phonon scattering has been noted in GaSb but the complexity of the problems make the analysis only qualitative. The phonon-phonon scattering is further studied into two more processes known as the U-process and N-process.
The limit scattering and isotope scattering unwinding times lead to precisely determined upsides of warm conductivity just when the materials are uncommonly unadulterated. Also, the construction, which has been distinguished because of reverberation scattering, has been seen in the information for the majority of the materials. Electron-phonon scattering has been noted in GaSb however the intricacy of the issues makes the examination just subjective. The phonon-phonon scattering was additionally examined into two additional cycles known as the U-interaction and N-process.
Did You Know?
Phonons are analogous to photons, in fact, both possess almost identical properties. The following points will elaborate on why phonons are analogous to photons:
Both phonons and photons are bosons. That means, both particles with integral spins.
Both photons and phonons are the quanta of energy. Photons are the quanta of energy described for electromagnetic waves, whereas phonons are the quanta of energy for the lattice vibrations.
Photons and phonons are not conserved entities.
FAQs on What Are Phonons? Understanding Their Types and Importance
1. What is a phonon in the context of solid-state physics?
A phonon is a quantum of vibrational energy that arises from the collective oscillation of atoms within a crystal lattice. In simple terms, just as a photon is a discrete packet of light energy, a phonon is a discrete packet of vibrational or sound energy in a solid. It is a quasiparticle used to describe how vibrations, like sound and heat, propagate through a periodic structure of atoms.
2. What is the primary difference between a phonon and a photon?
While both are quanta of energy, phonons and photons differ fundamentally:
- Nature: A phonon is a quantum of a mechanical wave (lattice vibration), whereas a photon is a quantum of an electromagnetic wave.
- Medium: Phonons require a medium, such as a solid crystal lattice, to exist and propagate. Photons can travel through a vacuum.
- Speed: Phonons travel at the speed of sound within the material, which is much slower than photons, which travel at the speed of light.
3. Is a phonon a real particle or simply a wave?
A phonon is best described as a quasiparticle. It is not a fundamental particle like an electron or proton. Instead, it is a convenient and powerful concept in physics used to describe the collective, particle-like behaviour of a wave. A lattice vibration is a wave, but when we quantize its energy, the resulting energy packet (the phonon) exhibits properties like energy and momentum, allowing it to be treated like a particle in interactions.
4. What are the main types of phonons found in crystal lattices?
There are two primary types of phonons, distinguished by the motion of atoms in the lattice:
- Acoustic Phonons: These correspond to atoms vibrating in-phase with their neighbours, moving together. These vibrations are responsible for the propagation of sound through the solid.
- Optical Phonons: These occur when adjacent atoms vibrate out-of-phase, moving against each other. They are called 'optical' because, in ionic crystals, this opposing motion can be excited by infrared radiation (light).
5. How are phonons created in a solid?
Phonons are created when the atoms in a crystal lattice are displaced from their equilibrium positions. This can be caused by thermal energy (which makes atoms vibrate randomly) or by an external force. Because the atoms are connected by interatomic bonds (acting like tiny springs), the vibration of one atom is passed on to its neighbours, creating a collective wave of motion. The quantized energy modes of these collective vibrations are what we call phonons.
6. How do phonons explain the thermal conductivity of materials?
In electrically insulating solids, heat is transferred almost entirely by phonons. When one part of a solid is heated, its atoms vibrate more intensely, creating more phonons. These phonons travel through the lattice, colliding with other atoms and transferring their energy, effectively conducting heat from the hotter region to the colder region. The thermal conductivity of the material depends on how easily these phonons can propagate without being scattered.
7. What is the formula to calculate the energy of a phonon?
The energy of a phonon is quantized and is directly proportional to its vibrational frequency. The formula is identical in form to that for a photon: E = ħω, where:
- E is the energy of the phonon.
- ħ (h-bar) is the reduced Planck constant.
- ω (omega) is the angular frequency of the lattice vibration.
This relationship highlights the quantum nature of lattice vibrations.
8. Why are optical phonons named 'optical' if they relate to lattice vibrations?
Optical phonons are named for their ability to interact with electromagnetic radiation, specifically light (often in the infrared spectrum). This happens in crystals with more than one type of atom, like sodium chloride (NaCl). The out-of-phase vibration of the positive (Na+) and negative (Cl-) ions creates an oscillating electric dipole. This oscillating dipole can either absorb or emit a photon, directly coupling the lattice vibration to light. Acoustic phonons do not have this property.
9. Can phonons exist in liquids or gases?
The concept of a phonon is most clearly defined for crystalline solids because of their ordered, periodic lattice structure. While collective vibrational modes can exist in amorphous solids and liquids, the lack of long-range order makes the phonon description more complex. In gases, where particles move randomly and are not bound in a lattice, the concept of a phonon as a collective lattice vibration does not apply.
