Gravitational singularity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Gravitational_singularity 

 

Animated simulation of gravitational lensing caused by a Schwarzschild black hole passing in a line-of-sight planar to a background galaxy. Around and at the time of exact alignment (syzygy) extreme lensing of the light is observed.

A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.

Gravitational singularities are mainly considered in the context of general relativity, where density would become infinite at the center of a black hole without corrections from Quantum Mechanics, and within astrophysics and cosmology as the earliest state of the universe during the Big Bang. Physicists are undecided whether the prediction of singularities means that they actually exist (or existed at the start of the Big Bang), or that current knowledge is insufficient to describe what happens at such extreme densities.

General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. The termination of such a geodesic is considered to be the singularity.

The initial state of the universe, at the beginning of the Big Bang, is also predicted by modern theories to have been a singularity. In this case, the universe did not collapse into a black hole, because currently-known calculations and density limits for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.

Interpretation

Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the ultraviolet catastrophe, re-normalization, and instability of a hydrogen atom predicted by the Larmor formula.

In classical field theories including special relativity, but not general relativity, one can say that a solution has a singularity at a particular point in spacetime where certain physical properties become ill defined, with spacetime serving as a background field to locate the singularity. A singularity in general relativity, on the other hand, is more complex because spacetime itself becomes ill defined, and the singularity is no longer part of the regular spacetime manifold. In general relativity, a singularity cannot be defined by "where" or "when".

Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist. This is also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that due to quantum gravity effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance.

Types

There are different types of singularities, each with different physical features which have characteristics relevant to the theories from which they originally emerged, such as the different shape of the singularities, conical and curved. They have also been hypothesized to occur without event horizons, structures which delineate one spacetime section from another in which events cannot affect past the horizon; these are called naked.

Conical

A conical singularity occurs when there is a point where the limit of some diffeomorphism invariant quantity does not exist or is infinite, in which case spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere the coordinate system is used.

An example of such a conical singularity is a cosmic string and a Schwarzschild black hole.

Curvature

A simple illustration of a non-spinning black hole and its singularity

Solutions to the equations of general relativity or another theory of gravity (such as supergravity) often result in encountering points where the metric blows up to infinity. However, many of these points are completely regular, and the infinities are merely a result of using an inappropriate coordinate system at this point. In order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. scalars) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.

An example is the Schwarzschild solution that describes a non-rotating, uncharged black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the event horizon. However, spacetime at the event horizon is regular. The regularity becomes evident when changing to another coordinate system (such as the Kruskal coordinates), where the metric is perfectly smooth. On the other hand, in the center of the black hole, where the metric becomes infinite as well, the solutions suggest a singularity exists. The existence of the singularity can be verified by noting that the Kretschmann scalar, being the square of the Riemann tensor i.e. ${\displaystyle R_{\mu \nu \rho \sigma }{R}^{\mu \nu \rho \sigma }}$, which is diffeomorphism invariant, is infinite.

While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, also known as a Kerr black hole, the singularity occurs on a ring (a circular line), known as a "ring singularity". Such a singularity may also theoretically become a wormhole.

More generally, a spacetime is considered singular if it is geodesically incomplete, meaning that there are freely-falling particles whose motion cannot be determined beyond a finite time, being after the point of reaching the singularity. For example, any observer inside the event horizon of a non-rotating black hole would fall into its center within a finite period of time. The classical version of the Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite spacetime curvature.

Naked singularity

Until the early 1990s, it was widely believed that general relativity hides every singularity behind an event horizon, making naked singularities impossible. This is referred to as the cosmic censorship hypothesis. However, in 1991, physicists Stuart Shapiro and Saul Teukolsky performed computer simulations of a rotating plane of dust that indicated that general relativity might allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed. However, it is hypothesized that light entering a singularity would similarly have its geodesics terminated, thus making the naked singularity look like a black hole.

Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum, if the angular momentum (${\displaystyle J}$) is high enough. Transforming the Kerr metric to Boyer–Lindquist coordinates, it can be shown that the coordinate (which is not the radius) of the event horizon is, ${\displaystyle r_{\pm }=\mu \pm {\left({\mu }^2-a^2\right)}^{1/2}}$, where ${\displaystyle \mu =GM/c^2}$, and ${\displaystyle a=J/Mc}$. In this case, "event horizons disappear" means when the solutions are complex for ${\displaystyle r_{\pm }}$, or ${\displaystyle {\mu }^2<a^2}$. However, this corresponds to a case where ${\displaystyle J}$ exceeds ${\displaystyle G{M}^2/c}$ (or in Planck units, ${\displaystyle J>M^2}$); i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.

Similarly, disappearing event horizons can also be seen with the Reissner–Nordström geometry of a charged black hole if the charge (${\displaystyle Q}$) is high enough. In this metric, it can be shown that the singularities occur at ${\displaystyle r_{\pm }=\mu \pm {\left({\mu }^2-q^2\right)}^{1/2}}$, where ${\displaystyle \mu =GM/c^2}$, and ${\displaystyle q^2=G{Q}^2/\left(4\pi {ϵ}_0{c}^4\right)}$. Of the three possible cases for the relative values of ${\displaystyle \mu }$ and ${\displaystyle q}$, the case where ${\displaystyle {\mu }^2<q^2}$ causes both ${\displaystyle r_{\pm }}$ to be complex. This means the metric is regular for all positive values of ${\displaystyle r}$, or in other words, the singularity has no event horizon. However, this corresponds to a case where ${\displaystyle Q/\sqrt{4\pi {ϵ}_0}}$ exceeds ${\displaystyle M\sqrt{G}}$ (or in Planck units, ${\displaystyle Q>M}$); i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values. Also, actual astrophysical black holes are not expected to possess any appreciable charge.

A black hole possessing the lowest ${\displaystyle M}$ value consistent with its ${\displaystyle J}$ and ${\displaystyle Q}$ values and the limits noted above; i.e., one just at the point of losing its event horizon, is termed extremal.

Entropy

Further information: Black hole, Hawking radiation, and Entropy

Before Stephen Hawking came up with the concept of Hawking radiation, the question of black holes having entropy had been avoided. However, this concept demonstrates that black holes radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore temperature. The loss of energy also implies that black holes do not last forever, but rather evaporate or decay slowly. Black hole temperature is inversely related to mass. All known black hole candidates are so large that their temperature is far below that of the cosmic background radiation, which means they will gain energy on net by absorbing this radiation. They cannot begin to lose energy on net until the background temperature falls below their own temperature. This will occur at a cosmological redshift of more than one million, rather than the thousand or so since the background radiation formed.

Ultra-high vacuum

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Ultra-high_vacuum 

Ultra-high vacuum (UHV) is the vacuum regime characterised by pressures lower than about 100 nanopascals (1.0×10⁻⁷ Pa; 1.0×10⁻⁹ mbar; 7.5×10⁻¹⁰ Torr). UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of a gas molecule is greater than approximately 40 km, so the gas is in free molecular flow, and gas molecules will collide with the chamber walls many times before colliding with each other. Almost all molecular interactions therefore take place on various surfaces in the chamber.

UHV conditions are integral to scientific research. Surface science experiments often require a chemically clean sample surface with the absence of any unwanted adsorbates. Surface analysis tools such as X-ray photoelectron spectroscopy and low energy ion scattering require UHV conditions for the transmission of electron or ion beams. For the same reason, beam pipes in particle accelerators such as the Large Hadron Collider are kept at UHV.

Overview

Maintaining UHV conditions requires the use of unusual materials for equipment. Useful concepts for UHV include:

• Sorption of gases
• Kinetic theory of gases
• Gas transport and pumping
• Vacuum pumps and systems
• Vapour pressure

Typically, UHV requires:

• High pumping speed — possibly multiple vacuum pumps in series and/or parallel
• Minimized surface area in the chamber
• High conductance tubing to pumps — short and fat, without obstruction
• Use of low-outgassing materials such as certain stainless steels
• Avoid creating pits of trapped gas behind bolts, welding voids, etc.
• Electropolishing of all metal parts after machining or welding
• Use of low vapor pressure materials (ceramics, glass, metals, teflon if unbaked)
• Baking of the system to remove water or hydrocarbons adsorbed to the walls
• Chilling of chamber walls to cryogenic temperatures during use
• Avoiding all traces of hydrocarbons, including skin oils in a fingerprint — gloves must always be used

Hydrogen and carbon monoxide are the most common background gases in a well-designed, well-baked UHV system. Both Hydrogen and CO diffuse out from the grain boundaries in stainless steel. Helium could diffuse through the steel and glass from the outside air, but this effect is usually negligible due to the low abundance of He in the atmosphere.

Measurement

Pressure

Main article: Pressure measurement

Measurement of high vacuum is done using a nonabsolute gauge that measures a pressure-related property of the vacuum, for example, its thermal conductivity. See, for example, Pacey. These gauges must be calibrated. The gauges capable of measuring the lowest pressures are magnetic gauges based upon the pressure dependence of the current in a spontaneous gas discharge in intersecting electric and magnetic fields.

UHV pressures are measured with an ion gauge, either of the hot filament or inverted magnetron type.

Leak rate

In any vacuum system, some gas will continue to escape into the chamber over time and slowly increase the pressure if it is not pumped out. This leak rate is usually measured in mbar L/s or torr L/s. While some gas release is inevitable, if the leak rate is too high, it can slow down or even prevent the system from reaching low pressure.

There are a variety of possible reasons for an increase in pressure. These include simple air leaks, virtual leaks, and desorption (either from surfaces or volume). A variety of methods for leak detection exist. Large leaks can be found by pressurizing the chamber, and looking for bubbles in soapy water, while tiny leaks can require more sensitive methods, up to using a tracer gas and specialized Helium mass spectrometer.

Outgassing

Main article: Outgassing

Outgassing is a problem for UHV systems. Outgassing can occur from two sources: surfaces and bulk materials. Outgassing from bulk materials is minimized by selection of materials with low vapor pressures (such as glass, stainless steel, and ceramics) for everything inside the system. Materials which are not generally considered absorbent can outgas, including most plastics and some metals. For example, vessels lined with a highly gas-permeable material such as palladium (which is a high-capacity hydrogen sponge) create special outgassing problems.

Outgassing from surfaces is a subtler problem. At extremely low pressures, more gas molecules are adsorbed on the walls than are floating in the chamber, so the total surface area inside a chamber is more important than its volume for reaching UHV. Water is a significant source of outgassing because a thin layer of water vapor rapidly adsorbs to everything whenever the chamber is opened to air. Water evaporates from surfaces too slowly to be fully removed at room temperature, but just fast enough to present a continuous level of background contamination. Removal of water and similar gases generally requires baking the UHV system at 200 to 400 °C (392 to 752 °F) while vacuum pumps are running. During chamber use, the walls of the chamber may be chilled using liquid nitrogen to reduce outgassing further.

Bake-out

Main article: Bake-out

In order to reach low pressures, it is often useful to heat the entire system above 100 °C (212 °F) for many hours (a process known as bake-out) to remove water and other trace gases which adsorb on the surfaces of the chamber. This may also be required upon "cycling" the equipment to atmosphere. This process significantly speeds up the process of outgassing, allowing low pressures to be reached much faster. After baking, to prevent humidity from getting back into the system after it is exposed to atmospheric pressure, a nitrogen gas flow that creates a small positive pressure can be maintained to keep the system dry.

System design

Pumping

There is no single vacuum pump that can operate all the way from atmospheric pressure to ultra-high vacuum. Instead, a series of different pumps is used, according to the appropriate pressure range for each pump. In the first stage, a roughing pump clears most of the gas from the chamber. This is followed by one or more vacuum pumps that operate at low pressures. Pumps commonly used in this second stage to achieve UHV include:

• Turbomolecular pumps (especially compound pumps which incorporate a molecular drag section and/or magnetic bearing types)
• Ion pumps
• Titanium sublimation pumps
• Non-evaporable getter (NEG) pumps
• Cryopumps
• Diffusion pumps, especially when used with a cryogenic trap designed to minimize backstreaming of pump oil into the systems.

Turbo pumps and diffusion pumps rely on supersonic attack upon system molecules by the blades and high speed vapor stream, respectively.

Airlocks

See also: Airlock

To save time, energy, and integrity of the UHV volume an airlock or load-lock vacuum system is often used. The airlock volume has one door or valve, such as a gate valve or UHV angle valve, facing the UHV side of the volume, and another door against atmospheric pressure through which samples or workpieces are initially introduced. After sample introduction and assuring that the door against atmosphere is closed, the airlock volume is typically pumped down to a medium-high vacuum. In some cases the workpiece itself is baked out or otherwise pre-cleaned under this medium-high vacuum. The gateway to the UHV chamber is then opened, the workpiece transferred to the UHV by robotic means or by other contrivance if necessary, and the UHV valve re-closed. While the initial workpiece is being processed under UHV, a subsequent sample can be introduced into the airlock volume, pre-cleaned, and so-on and so-forth, saving much time. Although a "puff" of gas is generally released into the UHV system when the valve to the airlock volume is opened, the UHV system pumps can generally snatch this gas away before it has time to adsorb onto the UHV surfaces. In a system well designed with suitable airlocks, the UHV components seldom need bakeout and the UHV may improve over time even as workpieces are introduced and removed.

Seals

See also: Vacuum flange

Metal seals, with knife edges on both sides cutting into a soft, copper gasket are employed. This metal-to-metal seal can maintain pressures down to 100 pPa (7.5×10⁻¹³ Torr). Although generally considered single use, the skilled operator can obtain several uses through the use of feeler gauges of decreasing size with each iteration, as long as the knife edges are in perfect condition. For SRF cavities, indium seals are more commonly used in sealing two flat surfaces together using clamps to bring the surfaces together. The clamps need to be tightened slowly to ensure the indium seals compress uniformly all around.

Material limitations

Many common materials are used sparingly if at all due to high vapor pressure, high adsorptivity or absorptivity resulting in subsequent troublesome outgassing, or high permeability in the face of differential pressure (i.e.: "through-gassing"):

• The majority of organic compounds cannot be used:
  • Plastics, other than PTFE and PEEK: plastics in other uses are replaced with ceramics or metals. Limited use of fluoroelastomers (such as Viton) and perfluoroelastomers (such as Kalrez) as gasket materials can be considered if metal gaskets are inconvenient, though these polymers can be expensive. Although through-gassing of elastomerics can not be avoided, experiments have shown that slow out-gassing of water vapor is, initially at least, the more important limitation. This effect can be minimized by pre-baking under medium vacuum. When selecting O-rings, permeation rate and permeation coefficients need to be considered. For example the penetration rate of nitrogen in Viton seals is 100 times lower than the penetration of nitrogen in silicon seals, which impacts the ultimate vacuum that can be achieved. 
  • Glues: special glues for high vacuum must be used, generally epoxies with a high mineral filler content. Among the most popular of these include asbestos in the formulation. This allows for an epoxy with good initial properties and able to retain reasonable performance across multiple bake-outs.
• Some steels: due to oxidization of carbon steel, which greatly increases adsorption area, only stainless steel is used. Particularly, non-leaded and low-sulfur austenitic grades such as 304 and 316 are preferred. These steels include at least 18% chromium and 8% nickel. Variants of stainless steel include low-carbon grades (such as 304L and 316L), and grades with additives such as niobium and molybdenum to reduce the formation of chromium carbide (which provides no corrosion resistance). Common designations include 316L (low carbon), and 316LN (low carbon with nitrogen), which can boast a significantly lower magnetic permeability with special welding techniques making them preferable for particle accelerator applications. Chromium carbide precipitation at the grain boundaries can render a stainless steel less resistant to oxidation.
• Lead: Soldering is performed using lead-free solder. Occasionally pure lead is used as a gasket material between flat surfaces in lieu of a copper/knife edge system.
• Indium: Indium is sometimes used as a deformable gasket material for vacuum seals, especially in cryogenic apparatus, but its low melting point prevents use in baked systems. In a more esoteric application, the low melting point of Indium is taken advantage of as a renewable seal in high vacuum valves. These valves are used several times, generally with the aid of a torque wrench set to increasing torque with each iteration. When the indium seal is exhausted, it is melted and reforms itself and thus is ready for another round of uses.
• Zinc, cadmium: High vapor pressures during system bake-out virtually preclude their use.
• Aluminum: Although aluminum itself has a vapor pressure which makes it unsuitable for use in UHV systems, the same oxides which protect aluminum against corrosion improve its characteristics under UHV. Although initial experiments with aluminum suggested milling under mineral oil to maintain a thin, consistent layer of oxide, it has become increasingly accepted that aluminum is a suitable UHV material without special preparation. Paradoxically, aluminum oxide, especially when embedded as particles in stainless steel as for example from sanding in an attempt to reduce the surface area of the steel, is considered a problematic contaminant.
• Cleaning is very important for UHV. Common cleaning procedures include degreasing with detergents, organic solvents, or chlorinated hydrocarbons. Electropolishing is often used to reduce the surface area from which adsorbed gases can be emitted. Etching of stainless steel using hydrofluoric and nitric acid forms a chromium rich surface, followed by a nitric acid passivation step, which forms a chromium oxide rich surface. This surface retards the diffusion of hydrogen into the chamber.

Technical limitations:

• Screws: Threads have a high surface area and tend to "trap" gases, and therefore, are avoided. Blind holes are especially avoided, due to the trapped gas at the base of the screw and slow venting through the threads, which is commonly known as a "virtual leak". This can be mitigated by designing components to include through-holes for all threaded connections, or by using vented screws (which have a hole drilled through their central axis or a notch along the threads). Vented Screws allow trapped gases to flow freely from the base of the screw, eliminating virtual leaks and speeding up the pump-down process.
• Welding: Processes such as gas metal arc welding and shielded metal arc welding cannot be used, due to the deposition of impure material and potential introduction of voids or porosity. Gas tungsten arc welding (with an appropriate heat profile and properly selected filler material) is necessary. Other clean processes, such as electron beam welding or laser beam welding, are also acceptable; however, those that involve potential slag inclusions (such as submerged arc welding and flux-cored arc welding) are obviously not. To avoid trapping gas or high vapor pressure molecules, welds must fully penetrate the joint or be made from the interior surface, otherwise a virtual leak might appear.

UHV manipulator

A UHV manipulator allows an object which is inside a vacuum chamber and under vacuum to be mechanically positioned. It may provide rotary motion, linear motion, or a combination of both. The most complex devices give motion in three axes and rotations around two of those axes. To generate the mechanical movement inside the chamber, three basic mechanisms are commonly employed: a mechanical coupling through the vacuum wall (using a vacuum-tight seal around the coupling: a welded metal bellows for example), a magnetic coupling that transfers motion from air-side to vacuum-side: or a sliding seal using special greases of very low vapor pressure or ferromagnetic fluid. Such special greases can exceed USD $400 per kilogram. Various forms of motion control are available for manipulators, such as knobs, handwheels, motors, stepping motors, piezoelectric motors, and pneumatics. The use of motors in a vacuum environment often requires special design or other special considerations, as the convective cooling taken for granted under atmospheric conditions is not available in a UHV environment.

The manipulator or sample holder may include features that allow additional control and testing of a sample, such as the ability to apply heat, cooling, voltage, or a magnetic field. Sample heating can be accomplished by electron bombardment or thermal radiation. For electron bombardment, the sample holder is equipped with a filament which emits electrons when biased at a high negative potential. The impact of the electrons bombarding the sample at high energy causes it to heat. For thermal radiation, a filament is mounted close to the sample and resistively heated to high temperature. The infrared energy from the filament heats the sample.

Typical uses

Ultra-high vacuum is necessary for many surface analytic techniques such as:

• X-ray photoelectron spectroscopy (XPS)
• Auger electron spectroscopy (AES)
• Secondary ion mass spectrometry (SIMS)
• Thermal desorption spectroscopy (TPD)
• Thin film growth and preparation techniques with stringent requirements for purity, such as molecular beam epitaxy (MBE), UHV chemical vapor deposition (CVD), atomic layer deposition (ALD) and UHV pulsed laser deposition (PLD)
• Angle resolved photoemission spectroscopy (ARPES)
• Field emission microscopy and Field ion microscopy
• Atom Probe Tomography (APT)

UHV is necessary for these applications to reduce surface contamination, by reducing the number of molecules reaching the sample over a given time period. At 0.1 millipascals (7.5×10⁻⁷ Torr), it only takes 1 second to cover a surface with a contaminant, so much lower pressures are needed for long experiments.

UHV is also required for:

• Particle accelerators The Large Hadron Collider (LHC) has three UH vacuum systems. The lowest pressure is found in the pipes the proton beam speeds through near the interaction (collision) points. Here helium cooling pipes also act as cryopumps. The maximum allowable pressure is 1×10⁻⁶ pascals (1.0×10⁻⁸ mbar)
• Gravitational wave detectors such as LIGO, VIRGO, GEO 600, and TAMA 300. The LIGO experimental apparatus is housed in a 10,000 cubic metres (350,000 cu ft) vacuum chamber at 1×10⁻⁷ pascals (1.0×10⁻⁹ mbar) in order to eliminate temperature fluctuations and sound waves which would jostle the mirrors far too much for gravitational waves to be sensed.
• Atomic physics experiments which use cold atoms, such as ion trapping or making Bose–Einstein condensates.

While not compulsory, it can prove beneficial in applications such as:

• Molecular beam epitaxy, E-beam evaporation, sputtering and other deposition techniques.
• Atomic force microscopy. High vacuum enables high Q factors on the cantilever oscillation.
• Scanning tunneling microscopy. High vacuum reduces oxidation and contamination, hence enables imaging and the achievement of atomic resolution on clean metal and semiconductor surfaces, e.g. imaging the surface reconstruction of the unoxidized silicon surface.
• Electron-beam lithography

Semiconductor

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Semiconductor 

An ingot of monocrystalline silicon

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 fabricating most electronic circuits.

Semiconductor devices can display a range of different useful properties, such as passing current more easily in one direction than the other, showing variable resistance, and having sensitivity to light or heat. Because the electrical properties of a semiconductor material can be modified by doping and by the application of electrical fields or light, devices made from semiconductors can be used for amplification, switching, and energy conversion.

The conductivity of silicon is increased by adding a small amount (of the order of 1 in 10⁸) of pentavalent (antimony, phosphorus, or arsenic) or trivalent (boron, gallium, indium) atoms. This process is known as doping, and the resulting semiconductors are known as doped or extrinsic semiconductors. Apart from doping, the conductivity of a semiconductor can be improved by increasing its temperature. This is contrary to the behavior of a metal, in which conductivity decreases with an increase in temperature.

The modern understanding of the properties of a semiconductor relies on quantum physics to explain the movement of charge carriers in a crystal lattice. Doping greatly increases the number of charge carriers within the crystal. When a doped semiconductor contains free holes, it is called "p-type", and when it contains free electrons, it is known as "n-type". The semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants. A single semiconductor device crystal can have many p- and n-type regions; the p–n junctions between these regions are responsible for the useful electronic behavior. Using a hot-point probe, one can determine quickly whether a semiconductor sample is p- or n-type.

A few of the properties of semiconductor materials were observed throughout the mid-19th and first decades of the 20th century. The first practical application of semiconductors in electronics was the 1904 development of the cat's-whisker detector, a primitive semiconductor diode used in early radio receivers. Developments in quantum physics led in turn to the invention of the transistor in 1947 and the integrated circuit in 1958.

Properties

Variable electrical conductivity

Semiconductors in their natural state are poor conductors because a current requires the flow of electrons, and semiconductors have their valence bands filled, preventing the entire flow of new electrons. Several developed techniques allow semiconducting materials to behave like conducting materials, such as doping or gating. These modifications have two outcomes: n-type and p-type. These refer to the excess or shortage of electrons, respectively. A balanced number of electrons would cause a current to flow throughout the material.

Heterojunctions

Heterojunctions occur when two differently doped semiconducting materials are joined. For example, a configuration could consist of p-doped and n-doped germanium. This results in an exchange of electrons and holes between the differently doped semiconducting materials. The n-doped germanium would have an excess of electrons, and the p-doped germanium would have an excess of holes. The transfer occurs until an equilibrium is reached by a process called recombination, which causes the migrating electrons from the n-type to come in contact with the migrating holes from the p-type. The result of this process is a narrow strip of immobile ions, which causes an electric field across the junction.

Excited electrons

A difference in electric potential on a semiconducting material would cause it to leave thermal equilibrium and create a non-equilibrium situation. This introduces electrons and holes to the system, which interact via a process called ambipolar diffusion. Whenever thermal equilibrium is disturbed in a semiconducting material, the number of holes and electrons changes. Such disruptions can occur as a result of a temperature difference or photons, which can enter the system and create electrons and holes. The process that creates and annihilates electrons and holes are called generation and recombination, respectively.

Light emission

In certain semiconductors, excited electrons can relax by emitting light instead of producing heat. These semiconductors are used in the construction of light-emitting diodes and fluorescent quantum dots.

High thermal conductivity

Semiconductors with high thermal conductivity can be used for heat dissipation and improving thermal management of electronics.

Thermal energy conversion

Semiconductors have large thermoelectric power factors making them useful in thermoelectric generators, as well as high thermoelectric figures of merit making them useful in thermoelectric coolers.

Materials

Main article: List of semiconductor materials

 

Silicon crystals are the most common semiconducting materials used in microelectronics and photovoltaics.

A large number of elements and compounds have semiconducting properties, including:

• Certain pure elements are found in group 14 of the periodic table; the most commercially important of these elements are silicon and germanium. Silicon and germanium are used here effectively because they have 4 valence electrons in their outermost shell, which gives them the ability to gain or lose electrons equally at the same time.
• Binary compounds, particularly between elements in groups 13 and 15, such as gallium arsenide, groups 12 and 16, groups 14 and 16, and between different group-14 elements, e.g. silicon carbide.
• Certain ternary compounds, oxides, and alloys.
• Organic semiconductors, made of organic compounds.
• Semiconducting metal–organic frameworks.

The most common semiconducting materials are crystalline solids, but amorphous and liquid semiconductors are also known. These include hydrogenated amorphous silicon and mixtures of arsenic, selenium, and tellurium in a variety of proportions. These compounds share with better-known semiconductors the properties of intermediate conductivity and a rapid variation of conductivity with temperature, as well as occasional negative resistance. Such disordered materials lack the rigid crystalline structure of conventional semiconductors such as silicon. They are generally used in thin film structures, which do not require material of higher electronic quality, being relatively insensitive to impurities and radiation damage.

Preparation of semiconductor materials

Almost all of today's electronic technology involves the use of semiconductors, with the most important aspect being the integrated circuit (IC), which are found in desktops, laptops, scanners, cell-phones, and other electronic devices. Semiconductors for ICs are mass-produced. To create an ideal semiconducting material, chemical purity is paramount. Any small imperfection can have a drastic effect on how the semiconducting material behaves due to the scale at which the materials are used.

A high degree of crystalline perfection is also required, since faults in the crystal structure (such as dislocations, twins, and stacking faults) interfere with the semiconducting properties of the material. Crystalline faults are a major cause of defective semiconductor devices. The larger the crystal, the more difficult it is to achieve the necessary perfection. Current mass production processes use crystal ingots between 100 and 300 mm (3.9 and 11.8 in) in diameter, grown as cylinders and sliced into wafers.

There is a combination of processes that are used to prepare semiconducting materials for ICs. One process is called thermal oxidation, which forms silicon dioxide on the surface of the silicon. This is used as a gate insulator and field oxide. Other processes are called photomasks and photolithography. This process is what creates the patterns on the circuit in the integrated circuit. Ultraviolet light is used along with a photoresist layer to create a chemical change that generates the patterns for the circuit.

The etching is the next process that is required. The part of the silicon that was not covered by the photoresist layer from the previous step can now be etched. The main process typically used today is called plasma etching. Plasma etching usually involves an etch gas pumped in a low-pressure chamber to create plasma. A common etch gas is chlorofluorocarbon, or more commonly known Freon. A high radio-frequency voltage between the cathode and anode is what creates the plasma in the chamber. The silicon wafer is located on the cathode, which causes it to be hit by the positively charged ions that are released from the plasma. The result is silicon that is etched anisotropically.

The last process is called diffusion. This is the process that gives the semiconducting material its desired semiconducting properties. It is also known as doping. The process introduces an impure atom to the system, which creates the p–n junction. To get the impure atoms embedded in the silicon wafer, the wafer is first put in a 1,100 degree Celsius chamber. The atoms are injected in and eventually diffuse with the silicon. After the process is completed and the silicon has reached room temperature, the doping process is done and the semiconducting material is ready to be used in an integrated circuit.

Physics of semiconductors

Energy bands and electrical conduction

Main articles: Electronic band structure and Electrical resistivity and conductivity

 

Filling of the electronic states in various types of materials at equilibrium. Here, height is energy while width is the density of available states for a certain energy in the material listed. The shade follows the Fermi–Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level E_F lies inside at least one band.

In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes.

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Semiconductors are defined by their unique electric conductive behavior, somewhere between that of a conductor and an insulator. The differences between these materials can be understood in terms of the quantum states for electrons, each of which may contain zero or one electron (by the Pauli exclusion principle). These states are associated with the electronic band structure of the material. Electrical conductivity arises due to the presence of electrons in states that are delocalized (extending through the material), however in order to transport electrons a state must be partially filled, containing an electron only part of the time. If the state is always occupied with an electron, then it is inert, blocking the passage of other electrons via that state. The energies of these quantum states are critical since a state is partially filled only if its energy is near the Fermi level (see Fermi–Dirac statistics).

High conductivity in material comes from it having many partially filled states and much state delocalization. Metals are good electrical conductors and have many partially filled states with energies near their Fermi level. Insulators, by contrast, have few partially filled states, their Fermi levels sit within band gaps with few energy states to occupy. Importantly, an insulator can be made to conduct by increasing its temperature: heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath the band gap (valence band) and the band of states above the band gap (conduction band). An (intrinsic) semiconductor has a band gap that is smaller than that of an insulator and at room temperature, significant numbers of electrons can be excited to cross the band gap.

A pure semiconductor, however, is not very useful, as it is neither a very good insulator nor a very good conductor. However, one important feature of semiconductors (and some insulators, known as semi-insulators) is that their conductivity can be increased and controlled by doping with impurities and gating with electric fields. Doping and gating move either the conduction or valence band much closer to the Fermi level and greatly increase the number of partially filled states.

Some wider-bandgap semiconductor materials are sometimes referred to as semi-insulators. When undoped, these have electrical conductivity nearer to that of electrical insulators, however they can be doped (making them as useful as semiconductors). Semi-insulators find niche applications in micro-electronics, such as substrates for HEMT. An example of a common semi-insulator is gallium arsenide. Some materials, such as titanium dioxide, can even be used as insulating materials for some applications, while being treated as wide-gap semiconductors for other applications.

Charge carriers (electrons and holes)

Main article: Electron hole

The partial filling of the states at the bottom of the conduction band can be understood as adding electrons to that band. The electrons do not stay indefinitely (due to the natural thermal recombination) but they can move around for some time. The actual concentration of electrons is typically very dilute, and so (unlike in metals) it is possible to think of the electrons in the conduction band of a semiconductor as a sort of classical ideal gas, where the electrons fly around freely without being subject to the Pauli exclusion principle. In most semiconductors, the conduction bands have a parabolic dispersion relation, and so these electrons respond to forces (electric field, magnetic field, etc.) much as they would in a vacuum, though with a different effective mass. Because the electrons behave like an ideal gas, one may also think about conduction in very simplistic terms such as the Drude model, and introduce concepts such as electron mobility.

For partial filling at the top of the valence band, it is helpful to introduce the concept of an electron hole. Although the electrons in the valence band are always moving around, a completely full valence band is inert, not conducting any current. If an electron is taken out of the valence band, then the trajectory that the electron would normally have taken is now missing its charge. For the purposes of electric current, this combination of the full valence band, minus the electron, can be converted into a picture of a completely empty band containing a positively charged particle that moves in the same way as the electron. Combined with the negative effective mass of the electrons at the top of the valence band, we arrive at a picture of a positively charged particle that responds to electric and magnetic fields just as a normal positively charged particle would do in a vacuum, again with some positive effective mass.^[12] This particle is called a hole, and the collection of holes in the valence band can again be understood in simple classical terms (as with the electrons in the conduction band).

Carrier generation and recombination

Main article: Carrier generation and recombination

When ionizing radiation strikes a semiconductor, it may excite an electron out of its energy level and consequently leave a hole. This process is known as electron-hole pair generation. Electron-hole pairs are constantly generated from thermal energy as well, in the absence of any external energy source.

Electron-hole pairs are also apt to recombine. Conservation of energy demands that these recombination events, in which an electron loses an amount of energy larger than the band gap, be accompanied by the emission of thermal energy (in the form of phonons) or radiation (in the form of photons).

In some states, the generation and recombination of electron-hole pairs are in equipoise. The number of electron-hole pairs in the steady state at a given temperature is determined by quantum statistical mechanics. The precise quantum mechanical mechanisms of generation and recombination are governed by the conservation of energy and conservation of momentum.

As the probability that electrons and holes meet together is proportional to the product of their numbers, the product is in the steady-state nearly constant at a given temperature, providing that there is no significant electric field (which might "flush" carriers of both types, or move them from neighbor regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature, being approximately exp(−E_G/kT), where k is Boltzmann's constant, T is the absolute temperature and E_G is bandgap.

The probability of meeting is increased by carrier traps – impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady-state.

Doping

Main article: Doping (semiconductor)

The conductivity of semiconductors may easily be modified by introducing impurities into their crystal lattice. The process of adding controlled impurities to a semiconductor is known as doping. The amount of impurity, or dopant, added to an intrinsic (pure) semiconductor varies its level of conductivity. Doped semiconductors are referred to as extrinsic. By adding impurity to the pure semiconductors, the electrical conductivity may be varied by factors of thousands or millions.

A 1 cm³ specimen of a metal or semiconductor has the order of 10²² atoms. In a metal, every atom donates at least one free electron for conduction, thus 1 cm³ of metal contains on the order of 10²² free electrons, whereas a 1 cm³ sample of pure germanium at 20 °C contains about 4.2×10²² atoms, but only 2.5×10¹³ free electrons and 2.5×10¹³ holes. The addition of 0.001% of arsenic (an impurity) donates an extra 10¹⁷ free electrons in the same volume and the electrical conductivity is increased by a factor of 10,000.

The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron acceptors or donors. Semiconductors doped with donor impurities are called n-type, while those doped with acceptor impurities are known as p-type. The n and p type designations indicate which charge carrier acts as the material's majority carrier. The opposite carrier is called the minority carrier, which exists due to thermal excitation at a much lower concentration compared to the majority carrier.

For example, the pure semiconductor silicon has four valence electrons that bond each silicon atom to its neighbors. In silicon, the most common dopants are group III and group V elements. Group III elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. When an acceptor atom replaces a silicon atom in the crystal, a vacant state (an electron "hole") is created, which can move around the lattice and function as a charge carrier. Group V elements have five valence electrons, which allows them to act as a donor; substitution of these atoms for silicon creates an extra free electron. Therefore, a silicon crystal doped with boron creates a p-type semiconductor whereas one doped with phosphorus results in an n-type material.

During manufacture, dopants can be diffused into the semiconductor body by contact with gaseous compounds of the desired element, or ion implantation can be used to accurately position the doped regions.

Amorphous semiconductors

Some materials, when rapidly cooled to a glassy amorphous state, have semiconducting properties. These include B, Si, Ge, Se, and Te, and there are multiple theories to explain them.

Early history of semiconductors

See also: Semiconductor device § History of semiconductor device development, and Timeline of electrical and electronic engineering

The history of the understanding of semiconductors begins with experiments on the electrical properties of materials. The properties of the time-temperature coefficient of resistance, rectification, and light-sensitivity were observed starting in the early 19th century.

Karl Ferdinand Braun developed the crystal detector, the first semiconductor device, in 1874.

Thomas Johann Seebeck was the first to notice an effect due to semiconductors, in 1821. In 1833, Michael Faraday reported that the resistance of specimens of silver sulfide decreases when they are heated. This is contrary to the behavior of metallic substances such as copper. In 1839, Alexandre Edmond Becquerel reported observation of a voltage between a solid and a liquid electrolyte, when struck by light, the photovoltaic effect. In 1873, Willoughby Smith observed that selenium resistors exhibit decreasing resistance when light falls on them. In 1874, Karl Ferdinand Braun observed conduction and rectification in metallic sulfides, although this effect had been discovered much earlier by Peter Munck af Rosenschold (sv) writing for the Annalen der Physik und Chemie in 1835, and Arthur Schuster found that a copper oxide layer on wires has rectification properties that ceases, when the wires are cleaned. William Grylls Adams and Richard Evans Day observed the photovoltaic effect in selenium in 1876.

A unified explanation of these phenomena required a theory of solid-state physics, which developed greatly in the first half of the 20th century. In 1878 Edwin Herbert Hall demonstrated the deflection of flowing charge carriers by an applied magnetic field, the Hall effect. The discovery of the electron by J.J. Thomson in 1897 prompted theories of electron-based conduction in solids. Karl Baedeker, by observing a Hall effect with the reverse sign to that in metals, theorized that copper iodide had positive charge carriers. Johan Koenigsberger classified solid materials like metals, insulators, and "variable conductors" in 1914 although his student Josef Weiss already introduced the term Halbleiter (a semiconductor in modern meaning) in his Ph.D. thesis in 1910. Felix Bloch published a theory of the movement of electrons through atomic lattices in 1928. In 1930, B. Gudden stated that conductivity in semiconductors was due to minor concentrations of impurities. By 1931, the band theory of conduction had been established by Alan Herries Wilson and the concept of band gaps had been developed. Walter H. Schottky and Nevill Francis Mott developed models of the potential barrier and of the characteristics of a metal–semiconductor junction. By 1938, Boris Davydov had developed a theory of the copper-oxide rectifier, identifying the effect of the p–n junction and the importance of minority carriers and surface states.

Agreement between theoretical predictions (based on developing quantum mechanics) and experimental results was sometimes poor. This was later explained by John Bardeen as due to the extreme "structure sensitive" behavior of semiconductors, whose properties change dramatically based on tiny amounts of impurities. Commercially pure materials of the 1920s containing varying proportions of trace contaminants produced differing experimental results. This spurred the development of improved material refining techniques, culminating in modern semiconductor refineries producing materials with parts-per-trillion purity.

Devices using semiconductors were at first constructed based on empirical knowledge before semiconductor theory provided a guide to the construction of more capable and reliable devices.

Alexander Graham Bell used the light-sensitive property of selenium to transmit sound over a beam of light in 1880. A working solar cell, of low efficiency, was constructed by Charles Fritts in 1883, using a metal plate coated with selenium and a thin layer of gold; the device became commercially useful in photographic light meters in the 1930s. Point-contact microwave detector rectifiers made of lead sulfide were used by Jagadish Chandra Bose in 1904; the cat's-whisker detector using natural galena or other materials became a common device in the development of radio. However, it was somewhat unpredictable in operation and required manual adjustment for best performance. In 1906, H.J. Round observed light emission when electric current passed through silicon carbide crystals, the principle behind the light-emitting diode. Oleg Losev observed similar light emission in 1922, but at the time the effect had no practical use. Power rectifiers, using copper oxide and selenium, were developed in the 1920s and became commercially important as an alternative to vacuum tube rectifiers.

The first semiconductor devices used galena, including German physicist Ferdinand Braun's crystal detector in 1874 and Indian physicist Jagadish Chandra Bose's radio crystal detector in 1901.

In the years preceding World War II, infrared detection and communications devices prompted research into lead-sulfide and lead-selenide materials. These devices were used for detecting ships and aircraft, for infrared rangefinders, and for voice communication systems. The point-contact crystal detector became vital for microwave radio systems since available vacuum tube devices could not serve as detectors above about 4000 MHz; advanced radar systems relied on the fast response of crystal detectors. Considerable research and development of silicon materials occurred during the war to develop detectors of consistent quality.

Early transistors

Main article: History of the transistor

 

John Bardeen, William Shockley and Walter Brattain developed the bipolar point-contact transistor in 1947.

Detector and power rectifiers could not amplify a signal. Many efforts were made to develop a solid-state amplifier and were successful in developing a device called the point contact transistor which could amplify 20dB or more. In 1922, Oleg Losev developed two-terminal, negative resistance amplifiers for radio, but he perished in the Siege of Leningrad after successful completion. In 1926, Julius Edgar Lilienfeld patented a device resembling a field-effect transistor, but it was not practical. R. Hilsch and R. W. Pohl in 1938 demonstrated a solid-state amplifier using a structure resembling the control grid of a vacuum tube; although the device displayed power gain, it had a cut-off frequency of one cycle per second, too low for any practical applications, but an effective application of the available theory. At Bell Labs, William Shockley and A. Holden started investigating solid-state amplifiers in 1938. The first p–n junction in silicon was observed by Russell Ohl about 1941 when a specimen was found to be light-sensitive, with a sharp boundary between p-type impurity at one end and n-type at the other. A slice cut from the specimen at the p–n boundary developed a voltage when exposed to light.

The first working transistor was a point-contact transistor invented by John Bardeen, Walter Houser Brattain, and William Shockley at Bell Labs in 1947. Shockley had earlier theorized a field-effect amplifier made from germanium and silicon, but he failed to build such a working device, before eventually using germanium to invent the point-contact transistor. In France, during the war, Herbert Mataré had observed amplification between adjacent point contacts on a germanium base. After the war, Mataré's group announced their "Transistron" amplifier only shortly after Bell Labs announced the "transistor".

In 1954, physical chemist Morris Tanenbaum fabricated the first silicon junction transistor at Bell Labs. However, early junction transistors were relatively bulky devices that were difficult to manufacture on a mass-production basis, which limited them to a number of specialised applications.