Mott–Schottky Equation
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Mott–Schottky Equation
The Mott–Schottky equation relates the capacitance to the applied voltage across a semiconductor-electrolyte junction. \frac = \frac (V - V_ - \frac) where C is the differential capacitance \frac, \epsilon is the dielectric constant of the semiconductor, \epsilon_0 is the permittivity of free space, A is the area such that the depletion region volume is w A, e is the elementary charge, N_d is the density of dopants, V is the applied potential, V_ is the flat band potential, k_B is the Boltzmann constant, and T is the absolute temperature. This theory predicts that a Mott–Schottky plot will be linear. The doping density N_d can be derived from the slope of the plot (provided the area and dielectric constant are known). The flatband potential can be determined as well; absent the temperature term, the plot would cross the V-axis at the flatband potential. Derivation Under an applied potential V, the width of the depletion region is w = (\frac ( V - V_ ) )^\frac Using ...
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Capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: ''self capacitance'' and ''mutual capacitance''. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operations of the capacitor, a device designed for this purpose as an elementary linear electronic component. Capacitance is a function only of the geometry of the design of the capacitor, e.g., the opposing surface area of the plates and the distance between them, and the permittivity of the dielectric material between the plates. For many dielectric materials, the permittivity and thus the capacitance, is ...
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Potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple release of energy by objects to the realization of abilities in people. The philosopher Aristotle incorporated this concept into his theory of potentiality and actuality, a pair of closely connected principles which he used to analyze motion, causality, ethics, and physiology in his ''Physics'', ''Metaphysics'', '' Nicomachean Ethics'', and '' De Anima'', which is about the human psyche. That which is potential can theoretically be made actual by taking the right action; for example, a boulder on the edge of a cliff has potential to fall that could be actualized by pushing it over the edge. Several languages have a potential mood, a grammatical construction that indicates that something is potential. These include Finnish, Japanese, and ...
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Semiconductor
A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. Its conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common semiconductor and is used in laser diodes, solar cells, microwave-frequency integrated circuits, and others. Silicon is a critical element for ...
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Electrolyte
An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dissolving, the substance separates into cations and anions, which disperse uniformly throughout the solvent. Solid-state electrolytes also exist. In medicine and sometimes in chemistry, the term electrolyte refers to the substance that is dissolved. Electrically, such a solution is neutral. If an electric potential is applied to such a solution, the cations of the solution are drawn to the electrode that has an abundance of electrons, while the anions are drawn to the electrode that has a deficit of electrons. The movement of anions and cations in opposite directions within the solution amounts to a current. Some gases, such as hydrogen chloride (HCl), under conditions of high temperature or low pressure can also function as elect ...
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Electrical Junction
{{Unreferenced, date=June 2019, bot=noref (GreenC bot) An electrical junction is a point or area where multiple conductors or semiconductors make physical contact. Electrical junctions types include thermoelectricity junctions, metal–semiconductor junctions and p–n junctions. Junctions are either rectifying or non-rectifying. Non-rectifying junctions are called ohmic contacts. Electronic components employing rectifying junctions include p–n diodes, Schottky diodes and bipolar junction transistors. (Electrical outlets ) See also * Break junction * Depletion region, also called junction region ** Junction voltage * Heterojunction * Homojunction * Josephson junction * Nodal analysis In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between " nodes" (points where elements or branches connect) in an electrical circuit i ... * p–n junction isolation Electricity Se ...
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Journal Of Chemical Education
The ''Journal of Chemical Education'' is a monthly peer-reviewed academic journal available in both print and electronic versions. It is published by the Division of Chemical Education of the American Chemical Society and was established in 1924 by Neil Gordon Neil Elbridge Gordon (October 7, 1886 – May 30, 1949) was an American chemist and educator. He is known for founding the Journal of Chemical Education (c. 1924) and establishing the Gordon Research Conferences (c. 1931). He held several Chair .... The journal covers research on chemical education, and its target audience includes instructors of chemistry from middle school through graduate school and some scientists in commerce, industry, and government. References External links * Chemical education journals American Chemical Society academic journals Monthly journals Publications established in 1924 English-language journals {{chemistry-journal-stub ...
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Dielectric Constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering as well as in chemistry. Definition Relative permittivity is typically denoted as (sometimes ...
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Permittivity Of Free Space
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: : (farads per meter), with a relative uncertainty of It is a measure of how dense of an electric field is "permitted" to form in response to electric charges, and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: :F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/4 \pi \varepsilon_0 (known as the Coulomb constant, ''k''e) is ap ...
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Depletion Region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have been diffused away, or have been forced away by an electric field. The only elements left in the depletion region are ionized donor or acceptor impurities. This region of uncovered positive and negative ions is called the depletion region due to the depletion of carriers in this region. The depletion region is so named because it is formed from a conducting region by removal of all free charge carriers, leaving none to carry a current. Understanding the depletion region is key to explaining modern semiconductor electronics: diodes, bipolar junction transistors, field-effect transistors, and variable capacitance diodes all rely on depletion region phenomena. Formation in a p–n junction A depletion region ...
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Flat Band Potential
In semiconductor physics, the flat band potential of a semiconductor defines the potential at which there is no depletion layer at the junction between a semiconductor and an electrolyteSixto Giménez and Juan Bisquert. Photoelectrochemical Solar Fuel Production. Springer, Switzerland, 2016. or p-n-junction. This is a consequence of the condition that the redox Fermi level of the electrolyte must be equal to the Fermi level of the semiconductor and therefore preventing any band bending of the conduction and valence band. An application of the flat band potential can be found in the determining the width of the space charge region in a semiconductor-electrolyte junction.M Sharon. An Introduction to the Physics and Electrochemistry of Semiconductors. John Wiley & sons, inc and Scrivener Publishing LLC, New Jersey and Beverly, 2016. Furthermore, it is used in the Mott-Schottky equation to determine the capacitance of the semiconductor-electrolyte junction K. Gelderman, L. Lee, an ...
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Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of ...
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Absolute Temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as manifestations of the kinetic energy of free motion of microscopic particles such as atoms, molecules, and electrons. From the thermodynamic viewpoint, for historical reasons, because of how it is defined and measured, this microscopic kinetic definition is regarded as an "empirical" temperature. It was adopted because in practice it can generally be measured more precisely than can Kelvin's thermodynamic temperature. A thermodynamic temperature reading of zero is of particular importance for the third law of thermodynamics. By convention, it is reported on the '' Kelvin scal ...
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