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Phonon Scattering
Phonons can scatter through several mechanisms as they travel through the material. These scattering mechanisms are: Umklapp phonon-phonon scattering, phonon-impurity scattering, phonon-electron scattering, and phonon-boundary scattering. Each scattering mechanism can be characterised by a relaxation rate 1/\tau which is the inverse of the corresponding relaxation time. All scattering processes can be taken into account using Matthiessen's rule. Then the combined relaxation time \tau_ can be written as: :\frac = \frac+\frac+\frac+\frac The parameters \tau_, \tau_, \tau_, \tau_\text are due to Umklapp scattering, mass-difference impurity scattering, boundary scattering and phonon-electron scattering, respectively. Phonon-phonon scattering For phonon-phonon scattering, effects by normal processes (processes which conserve the phonon wave vector - N processes) are ignored in favor of Umklapp processes (U processes). Since normal processes vary linearly with \omega and umklapp proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phonons
A phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined as phonons as long as the modal wavelength of the oscillation is smaller than the size of the object. A type of quasiparticle in physics, a phonon is an excited state in the quantum mechanical Quantization (physics), quantization of the mode of vibration, modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves. The study of phonons is an important part of condensed matter physics. They play a major role in many of the physical properties of condensed matter systems, such as thermal conductivity and electrical conductivity, as well as in models of neutron scattering and related effects. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Umklapp Scattering
In crystalline materials, Umklapp scattering (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written ''k'') which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed as a point inside the zone. So, the wave vector is then mathematically transformed to a point inside the first Brillouin zone. This transformation allows for scattering processes which would otherwise violate the conservation of momentum: two wave vectors pointing to the right can combine to create a wave vector that points to the left. This non-conservation is why crystal momentum is not a true momentum. Examples include electron-lattice potential scattering or an anharmonic phonon-phonon (or electron-phonon) scattering process, reflecting an electronic state or creating a phonon with a momentum ''k''-vector outside the first Brillouin zone. Umklapp scatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron-longitudinal Acoustic Phonon Interaction
The electron-longitudinal acoustic phonon interaction is an interaction that can take place between an electron and a longitudinal acoustic (LA) phonon in a material such as a semiconductor. Displacement operator of the LA phonon The equations of motion of the atoms of mass M which locates in the periodic lattice is : M \frac u_ = -k_ ( u_ + u_ -2u_ ), where u_ is the displacement of the ''n''th atom from their equilibrium positions. Defining the displacement u_ of the \ellth atom by u_= x_ - \ell a, where x_ is the coordinates of the \ellth atom and a is the lattice constant, the displacement is given by u_= A e^ Then using Fourier transform: : Q_ = \frac \sum_ u_ e^ and : u_ = \frac \sum_ Q_ e^. Since u_ is a Hermite operator, : u_ = \frac \sum_ (Q_ e^ + Q^_ e^ ) From the definition of the creation and annihilation operator a^_ = \frac (M\omega_Q_-iP_), \; a_ = \frac (M\omega_Q_+iP_) : Q_ is written as : Q_ = \sqrt (a^_+a_) Then u_ expressed as : u_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matthiessen's Rule
In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility. Electron and hole mobility are special cases of electrical mobility of charged particles in a fluid under an applied electric field. When an electric field ''E'' is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity, v_d. Then the electron mobility ''μ'' is defined as v_d = \mu E. Electron mobility is almost always specified in units of cm2/( V⋅ s). This is different from the SI unit of mobility, m2/( V⋅ s). They are related by 1 m2/(V⋅s) = 104 cm2/(V⋅s). Conductivity is proportional to the product of mobility and carrier concentration. For example, the same conductivity could come from a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grüneisen Parameter
In condensed matter, Grüneisen parameter is a dimensionless thermodynamic parameter named after German physicist Eduard Grüneisen, whose original definition was formulated in terms of the phonon nonlinearities. Because of the equivalences of many properties and derivatives within thermodynamics (e.g. see Maxwell relations), there are many formulations of the Grüneisen parameter which are equally valid, leading to numerous interpretations of its meaning. Some formulations for the Grüneisen parameter include: \gamma = V \left(\frac\right)_V = \frac = \frac = \frac = -\left(\frac\right)_S where is volume, C_P and C_V are the principal (i.e. per-mass) heat capacities at constant pressure and volume, is energy, is entropy, is the volume thermal expansion coefficient, K_S and K_T are the adiabatic and isothermal bulk moduli, v_s is the speed of sound in the medium, and is density. The Grüneisen parameter is dimensionless. Grüneisen constant for perfect crystals with pair i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the Elasticity (physics), elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel\ \frac = \frac = \frac where :\tau_ = F/A \, = shear stress :F is the force which acts :A is the area on which the force acts :\gamma_ = shear strain. In engineering :=\Delta x/l = \tan \theta , elsewhere := \theta :\Delta x is the transverse displacement :l is the initial length of the area. The derived SI unit of shear modulus is the Pascal (unit), pascal (Pa), although it is usually expressed in Pascal (unit), gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional analysis, dimensional form is M1L−1T−2, replacing ''force'' by ''mass'' times ''acceleration''. Explanation The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye Frequency
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific heat ( heat capacity) in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box in contrast to the Einstein photoelectron model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence of the heat capacity of solids, which is proportional to the cube of temperature – the Debye ''T'' 3 law. Similarly to the Einstein photoelectron model, it recovers the Dulong–Petit law at high temperatures. Due to simplifying assumptions, its accuracy suffers at intermediate temperatures. Derivation The Debye model treats atomic vibrations as phonons confined in the solid's volume. It is analogous to Planck's law of black body radiation, which treats electromagnetic radiation as a photon gas confined in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanostructures
A nanostructure is a structure of intermediate size between microscopic and molecular structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...s. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimensions in the volume of an object which are on the nanoscale. Nanotextured surfaces have ''one dimension'' on the nanoscale, i.e., only the thickness of the surface of an object is between 0.1 and 100 nm. Nanotubes have ''two dimensions'' on the nanoscale, i.e., the diameter of the tube is between 0.1 and 100 nm; its length can be far more. Finally, spherical nanoparticles have ''three dimensions'' on the nanoscale, i.e., the particle is between 0.1 and 100 nm in each spat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Conductivity
The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials such as mineral wool or Styrofoam. Metals have this high thermal conductivity due to free electrons facilitating heat transfer. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications, and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is \mathbf = - k \nabla T, where \mathbf is the heat flux, k is the thermal conductivity, and \nabla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Scattering
Lattice scattering is the scattering of ions by interaction with atoms in a lattice. This effect can be qualitatively understood as phonons colliding with charge carriers. In the current quantum mechanical picture of conductivity the ease with which electrons traverse a crystal lattice is dependent on the near perfectly regular spacing of ions in that lattice. Only when a lattice contains perfectly regular spacing can the ion-lattice interaction (scattering) lead to almost transparent behavior of the lattice. In the quantum understanding, an electron is viewed as a wave traveling through a medium. When the wavelength of the electrons is larger than the crystal spacing, the electrons will propagate freely throughout the metal without collision. See also * Ionized impurity scattering *Phonon scattering Phonons can scatter through several mechanisms as they travel through the material. These scattering mechanisms are: Umklapp phonon-phonon scattering, phonon-impurity scattering, p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
