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Variable-range Hopping
Variable-range hopping is a model used to describe carrier transport in a disordered semiconductor or in amorphous solid by hopping in an extended temperature range. It has a characteristic temperature dependence of :\sigma= \sigma_0e^ where \sigma is the conductivity and \beta is a parameter dependent on the model under consideration. Mott variable-range hopping The Mott variable-range hopping describes low-temperature conduction in strongly disordered systems with localized charge-carrier states and has a characteristic temperature dependence of :\sigma= \sigma_0e^ for three-dimensional conductance (with \beta = 1/4), and is generalized to ''d''-dimensions :\sigma= \sigma_0e^. Hopping conduction at low temperatures is of great interest because of the savings the semiconductor industry could achieve if they were able to replace single-crystal devices with glass layers. Derivation The original Mott paper introduced a simplifying assumption that the hopping energy depends in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amorphous Solid
In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("without"), and ''morphé'' ("shape, form"). In some older articles and books, the term was used synonymously with glass. Today, "glassy solid" or "amorphous solid" is considered the overarching concept. Polymers are often amorphous. Structure Amorphous materials have an internal structure comprising interconnected structural blocks that can be similar to the basic structural units found in the corresponding crystalline phase of the same compound. Unlike crystalline materials, however, no long-range order exists. Localized order in amorphous materials can be categorized as short or medium range order. By convention, short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings. Medium range order is then def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nevill Francis Mott
Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. The award was shared with Philip W. Anderson and J. H. Van Vleck. The three had conducted loosely related research. Mott and Anderson clarified the reasons why magnetic or amorphous materials can sometimes be metallic and sometimes insulating. Education and early life Mott was born in Leeds to Lilian Mary Reynolds and Charles Francis Mott and grew up first in the village of Giggleswick, in the West Riding of Yorkshire, where his father was Senior Science Master at Giggleswick School. His mother also taught Maths at the School. The family moved (due to his father's jobs) first to Staffordshire, then to Chester and finally Liverpool, where his father had been appointed Director of Education. Mott was at first educated at home by his mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Conduction
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter ( sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Localization
In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc. This phenomenon is to be distinguished from weak localization, which is the precursor effect of Anderson localization (see below), and from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is ''not'' due to disorder, but to a strong mutual Coulomb repulsion of electrons. Introduction In the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Function
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer , \Gamma(n) = (n-1)!\,. Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: \Gamma(z) = \int_0^\infty t^ e^\,dt, \ \qquad \Re(z) > 0\,. The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles. The gamma function has no zeroes, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: \Gamma(z) = \mathcal M \ (z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Of States
In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states in the system of volume V whose energies lie in the range from E to E+\delta E. It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation. Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often referr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb Gap
First introduced by M. Pollak, the Coulomb gap is a soft gap in the single-particle density of states (DOS) of a system of interacting localized electrons. Due to the long-range Coulomb interactions, the single-particle DOS vanishes at the chemical potential, at low enough temperatures, such that thermal excitations do not wash out the gap. Theory At zero temperature, a classical treatment of a system gives an upper bound for the DOS near the Fermi energy, first suggested by Efros and Shklovskii. The argument is as follows: Let us look at the ground state configuration of the system. Defining E_i as the energy of an electron at site i , due to the disorder and the Coulomb interaction with all other electrons (we define this both for occupied and unoccupied sites), it is easy to see that the energy needed to move an electron from an occupied site i to an unoccupied site j is given by the expression: :\Delta E=E_j-E_i-e^2/r_ . The subtraction of the last term accounts fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Level
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''µ'' or ''E''F for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from. A precise understanding of the Fermi level—how it relates to electronic band structure in determining electronic properties, how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics. In band structure theory, used in solid state physics to analyze the energy levels in a solid, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a ''50% probability of being occupied at any given time''. The position of the Fermi level in relation to the band energy levels is a crucial factor in determining electrical properties. The Fermi le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexei L
Alexey, Alexei, Alexie, Aleksei, or Aleksey (russian: Алексе́й ; bg, Алексей ) is a Russian language, Russian and Bulgarian language, Bulgarian male first name deriving from the Greek language, Greek ''Aléxios'' (), meaning "Defender", and thus of the same origin as the Latin Alexius. Alexey may also be Romanization of Russian, romanized as ''Aleksei'', ''Aleksey'', ''Alexej'', ''Aleksej'', etc. It has been commonly westernized as Alexis (given name), Alexis. Similar Ukraine, Ukrainian and Belarus, Belarusian names are romanized as Oleksii (Олексій) and Aliaksiej (Аляксей), respectively. The Russian Orthodox Church uses the Old Church Slavonic version, Alexiy (Алексiй, or Алексий in modern spelling), for its Saints and hierarchs (most notably, this is the form used for Patriarchs Partiarch Alexius I, Alexius I and Patriarch Alexius II, Alexius II). The common hypocoristic is Alyosha (other), Alyosha () or simply Lyosha () ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Shklovskii
Boris Ionovich Shklovskii (born 1944) is a theoretical physicist, at the William I Fine Theoretical Physics Institute, University of Minnesota, specializing in condensed matter. Shklovskii earned his A.B. degree in Physics, in 1966 and a Ph.D. in condensed matter theory, in 1968 from Leningrad University.UMN BIO physics Shklovskii Retrieved 28 April 2019. Shklovskii is known for the Efros–Shklovskii variable-range hopping conductivity, a model for the temperature dependence of the electrical conductivity in the variable-range hopping regime. He has also made important contributions to the theory of the |
Mobility Edge
In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc. This phenomenon is to be distinguished from weak localization, which is the precursor effect of Anderson localization (see below), and from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is ''not'' due to disorder, but to a strong mutual Coulomb repulsion of electrons. Introduction In the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Phenomena
This is a list of electrical phenomena. Electrical phenomena are a somewhat arbitrary division of electromagnetic phenomena. Some examples are: * Biefeld–Brown effect — Thought by the person who coined the name, Thomas Townsend Brown, to be an anti-gravity effect, it is generally attributed to electrohydrodynamics (EHD) or sometimes electro-fluid-dynamics, a counterpart to the well-known magneto-hydrodynamics. * Bioelectrogenesis — The generation of electricity by living organisms. * Capacitive coupling — Transfer of energy within an electrical network or between distant networks by means of displacement current. *Contact electrification — The phenomenon of electrification by contact. When two objects were touched together, sometimes the objects became spontaneously charged (οne negative charge, one positive charge). * Corona effect — Build-up of charges in a high-voltage conductor (common in AC transmission lines), which ionizes the air and produces visib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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