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Carrier Lifetime
A definition in semiconductor physics, carrier lifetime is defined as the average time it takes for a minority carrier to recombine. The process through which this is done is typically known as minority carrier recombination. The energy released due to recombination can be either thermal, thereby heating up the semiconductor (''thermal recombination'' or non-radiative recombination, one of the sources of waste heat in semiconductors), or released as photons (''optical recombination'', used in LEDs and semiconductor lasers). The carrier lifetime can vary significantly depending on the materials and construction of the semiconductor. Carrier lifetime plays an important role in bipolar transistors and solar cells. In indirect band gap semiconductors, the carrier lifetime strongly depends on the concentration of recombination centers. Gold atoms act as highly efficient recombination centers, silicon for some high switching speed diodes and transistors is therefore alloyed with ...
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Semiconductor Physics
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 fabrica ...
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Photovoltaic Effect
The photovoltaic effect is the generation of voltage and electric current in a material upon exposure to light. It is a physical property, physical and chemical phenomenon. The photovoltaic effect is closely related to the photoelectric effect. For both phenomena, light is absorbed, causing excitation of an electron or other charge carrier to a higher-energy state. The main distinction is that the term ''photoelectric effect'' is now usually used when the electron is ejected out of the material (usually into a vacuum) and ''photovoltaic effect'' used when the excited charge carrier is still contained within the material. In either case, an electric potential (or voltage) is produced by the separation of charges, and the light has to have a sufficient energy to overcome the potential barrier for excitation. The physical essence of the difference is usually that photoelectric emission separates the charges by ballistic conduction and photovoltaic emission separates them by diffusion, ...
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Transconductance
Transconductance (for transfer conductance), also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciprocal of resistance. Transadmittance (or transfer admittance) is the AC equivalent of transconductance. Definition Transconductance is very often denoted as a conductance, ''g''m, with a subscript, m, for ''mutual''. It is defined as follows: :g_m = \frac For small signal alternating current, the definition is simpler: :g_m = \frac The SI unit for transconductance is the siemens, with the symbol S, as in conductance. Transresistance Transresistance (for transfer resistance), also infrequently referred to as mutual resistance, is the dual of transconductance. It refers to the ratio between a change of the voltage at two output points and a related change of current through two input points, and is notated as ''r''m: :r_m = \frac ...
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Electrical Resistance And Conductance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ). The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather than inte ...
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Bipolar Junction Transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar transistor allows a small current injected at one of its terminals to control a much larger current flowing between the terminals, making the device capable of amplification or switching. BJTs use two p–n junctions between two semiconductor types, n-type and p-type, which are regions in a single crystal of material. The junctions can be made in several different ways, such as changing the doping of the semiconductor material as it is grown, by depositing metal pellets to form alloy junctions, or by such methods as diffusion of n-type and p-type doping substances into the crystal. The superior predictability and performance of junction transistors quickly displaced the original point-contact transistor. Diffused transistors, along wi ...
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Open-circuit Voltage
Open-circuit voltage (abbreviated as OCV or VOC) is the difference of electrical potential between two terminals of an electronic device when disconnected from any circuit. There is no external load connected. No external electric current flows between the terminals. Alternatively, the open-circuit voltage may be thought of as the voltage that must be applied to a solar cell or a battery to stop the current. It is sometimes given the symbol Voc. In network analysis this voltage is also known as the Thévenin voltage. The open-circuit voltages of batteries and solar cells are often quoted under particular conditions (state-of-charge, illumination, temperature, etc.). The potential difference mentioned for batteries and cells is usually the open-circuit voltage. The value of the open-circuit voltage of a transducer equals its electromotive force (emf), which is the maximum potential difference it can produce when not providing current. Example Consider the circuit: If w ...
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Time Derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t. Notation A variety of notations are used to denote the time derivative. In addition to the normal ( Leibniz's) notation, :\frac A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E. :\dot (This is called Newton's notation) Higher time derivatives are also used: the second derivative with respect to time is written as :\frac with the corresponding shorthand of \ddot. As a generalization, the time derivative of a vector, say: : \mathbf v = \left v_1,\ v_2,\ v_3, \ldots \right is defined as the vector whose components are the derivatives of the components of the original vector. That is, : \frac = \left \frac,\frac ,\frac , \ldots \right . Use in physics Time derivatives are a key concept in physics. For example, for a changing position x, its t ...
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Elementary Charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as e =  coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from bla ...
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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 amount of ...
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Voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named ''volt''. The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and transformers). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground of the system is used as one of the points. A voltage can represent either a source ...
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Electric Current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons. The SI unit of electric current is the ampere, or ''amp'', which is the flow of electric charge across a surface at the rate of one coulomb per second. The ampere (symbol: A) is an SI base unit. Electric current is measured using a device called an ammeter. Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers. In ordinary con ...
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Laser Diode Rate Equations
The laser diode rate equations model the electrical and optical performance of a laser diode. This system of ordinary differential equations relates the number or density of photons and charge carriers (electrons) in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain. The rate equations may be solved by numerical integration to obtain a time-domain solution, or used to derive a set of steady state or small signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers. The laser diode rate equations can be formulated with more or less complexity to model different aspects of laser diode behavior with varying accuracy. Multimode rate equations In the multimode formulation, the rate equationsG. P. Agrawal, "Fiber-Optic Communication Systems", Wiley Interscience, Chap. 3 model a laser with multiple optical modes. This formulation requires one equat ...
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