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Black's Equation
Black's Equation is a mathematical model for the mean time to failure (MTTF) of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement (movement) in the solid phase caused by an electromagnetic field. The equation is: R. L. de OrioDissertation: "Electromigration Modeling and Simulation" 2010. R.L. de Orio, H. Ceric, S. Selberherr"Physically based models of electromigration: From Black’s equation to modern TCAD models"Microelectronics Reliability journal. 2010. MTTF = \frac e^\left(\frac\right) A is a constant j is the current density n is a model parameter Q is the activation energy k is Boltzmann's constant T is the absolute temperature in K The model is abstract, not based on a specific physical model, but flexibly describes the failure rate dependence on the temperature, the electrical stress, and the specific technology and materials. More adequately described as descriptive than prescriptive, the values for ''A'', ''n'', and ''Q'' are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Time Between Failure
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The term is used for repairable systems while mean time to failure (MTTF) denotes the expected time to failure for a non-repairable system. The definition of MTBF depends on the definition of what is considered a failure. For complex, repairable systems, failures are considered to be those out of design conditions which place the system out of service and into a state for repair. Failures which occur that can be left or maintained in an unrepaired condition, and do not place the system out of service, are not considered failures under this definition. In addition, units that are taken down for routine scheduled maintenance or inventory control are not considered within the definition of failure. The higher the MTBF, the longer a system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromigration
Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in microelectronics and related structures. As the structure size in electronics such as integrated circuits (ICs) decreases, the practical significance of this effect increases. History The phenomenon of electromigration has been known for over 100 years, having been discovered by the French scientist Gerardin. The topic first became of practical interest during the late 1960s when packaged ICs first appeared. The earliest commercially available ICs failed in a mere three weeks of use from runaway electromigration, which led to a major industry effort to correct this problem. The first observation of electromigration in thin films was made by I. Blech.I. Blech: ''Electromigration in Thin Aluminum Fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Phase
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See ) The term ''phase'' is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the term ''phase'' is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Because ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siegfried Selberherr
Siegfried Selberherr (* 3. August 1955 in Klosterneuburg) is an Austrian scientist in the field of microelectronics. He is a professor at the Institute for Microelectronics of the Technische Universität Wien (TU Wien). His primary research interest is in modeling and simulation of physical phenomena in the field of microelectronics. Biography Since 1988 Siegfried Selberherr is a chair professor for software technology of microelectronic systems at the TU Wien. He studied electrical engineering at the TU Wien, where he received the degree of Diplom-Ingenieur and the doctoral degree in technical sciences in 1978 and 1981, respectively, and the Habilitation in 1984. Afterwards he was a visiting researcher with the Bell-Labs for some time. Between 1996 and 2020 Prof. Selberherr was a Distinguished Lecturer of the IEEE Electron Devices Society. For many years, Prof. Selberherr was a leader of the Institute for Microelectronics at the TU Wien (now this Institute is headed by his you ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Current Density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Definition Assume that ''A'' (SI unit: m2) is a small surface centred at a given point ''M'' and orthogonal to the motion of the charges at ''M''. If ''I'' (SI unit: A) is the electric current flowing through ''A'', then electric current density ''j'' at ''M'' is given by the limit: :j = \lim_ \frac = \left.\frac \_, with surface ''A'' remaining centered at ''M'' and orthogonal to the motion of the charges during the limit process. The current density vector j is the vector whose magnitude is the electric current density, and whose dire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Activation Energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Activation energy can be thought of as the magnitude of the potential barrier (sometimes called the energy barrier) separating minima of the potential energy surface pertaining to the initial and final thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy. The term "activation energy" was introduced in 1889 by the Swedish scientist Svante Arrhenius. Other uses Although less commonly used, activation energy also applies to nuclear reactions and various other physical phenomena. Te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann's 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 scale'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point. Historically, the Kelvin scale was developed by shifting the starting point of the much-older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant to be exactly . Hence, one kelvin is equal to a change in the thermodynamic temperature that results in a change of thermal energy by . The temperature in degree Celsius is now defined as the temperature in kelvins minus 273.15, meaning t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Temperature Operating Life
High-temperature operating life (HTOL) is a reliability test applied to integrated circuits (ICs) to determine their intrinsic reliability. This test stresses the IC at an elevated temperature, high voltage and dynamic operation for a predefined period of time. The IC is usually monitored under stress and tested at intermediate intervals. This reliability stress test is sometimes referred to as a "lifetime test", "device life test" or "extended burn in test" and is used to trigger potential failure modes and assess IC lifetime. There are several types of HTOL: * AEC Documents. * JEDEC Standards. * Mil standards.Mil standard Design considerations The main aim of the HTOL is to age the device such that a short experiment will allow the lifetime of the IC to be predicted (e.g. 1,000 HTOL hours shall pr ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
