Why is it called transistor theory
2 MOS transistor theory
1 2.1 Semiconductor properties Page 1 2 MOS-Trasistortheorie I an itegrated circuit, small circuit elements are made from Si-semiconductor material and connected. In order to understand the IC technology, the development process and the properties of the IC, the basis for the semiconductor properties and the structural elements of the circuit, the resistors, the coders, the diodes (vetiles), the trasistore (switches and amplifiers) and the Connection technology put together. 2.1 Semiconductor properties Integrated circuits are almost invariably manufactured on the basis of crystalline silicon (Si), a semiconductor material that can be made from quartz sad (SiO 2). Semiconductors et ma the material because the electrical conduction mechanism ad the conductivity can be set in a targeted manner by technology-specific processes (doping) ad the adjustable conductivity sweeps over the area between the metals ad the insulators. The prerequisite for the technical mastery and the utilization of the semiconductor properties was the development and the understanding of the semiconductor physics and the necessary chemistry. The macroscopic properties can therefore be derived from the properties of the microscopic, non-visible atomic components of matter. Location ad energy model silicon is an element that is classified in the fourth skin of the eriodic system of elements. It thus has four 3d electrons in the outermost electrical shell. Excerpt from the Periodic System of Elements (PSE) Grue III IV V VI Period2 BCNO 3 Al Si P 4 Ga Ge As 5 I Sb From atomic physics and chemistry it is known that for connections between two or more atoms, the expressed electrical envelope is in between en Atoms play an important role. The state in which the outermost shell is occupied by 8 electrons is particularly favorable in terms of energy and thus the driving force for the construction of the connection (so-called closed shell). In the silicon crystal, each Si atom is connected to its nearest neighbor through four covalent (electrical) bidugs. (covalent bidug = uolar, directed bidug by Elektroeaar). The Si crystal lattice is constructed in such a way that the closest neighbor of each Si atom sits on the corner of a tetrahedron pyramid (picture). The distance between two Si atoms is of the order of magnitude of Agström units (A = m = 0.1 m): one cubic centimeter of the silicon crystal contains the unimaginably large number of Si atoms (10 22 / cm -3)! In order to visualize the Leitugsmechaismus in the crystal instead of the 3-dimesioale
2 2.1 Semiconductor properties Page 2 Representation of the crystal lattice a schematic 2-dimensional representation is used, which takes over the essential properties of the Bidugsmechaismus. The Doelbidug mediated by the Elektroeaar is marked by a line. Electrical conductivity arises on the basis of the thermal movement (Schwiguge of the atoms), which leads to an occasional rupture of a large part of the Biduge. In silicon at 300 K, this is a very good biduge. As a result, approximately 3 electric pairs (ELP) are generated (Geeratio vo ELPe). An electric is released from the bidug. It becomes free to move and can diffuse through the crystal. Furthermore, the electrically neutral point where the bidug has broken open is also positively charged on the outside by the removal of the electrical system due to the positive kerladug. This positively charged state (= open bidug) can be pulled over by bidugelectro from a neighboring bidug, whereby the bidug is closed again, but the adjacent bidug is opened. In this way, an positively charged gap (so-called) can also move freely through the crystal. Electro Geeratio eies ELP through thermal energy or radiation energy (E> Eg) Si covalent electrical doelbidug Through the thermal movement there are i the same number of freely movable positive ud egative charge carriers. A pre-applied electric field (suction source) leads these charge carriers to an electric current flow (electric conductivity). If an electric hits an egg, the open bidug is closed again and the energy stemming from the movement is emitted as silence energy a the grid (so-called light-emitting recombination). In thermal equilibrium, the number of ELPs generated by geeratio and the number of ELPs lost again by recombiation are balanced, so that with a certain thermal movement there is a temperature-dependent number of free ELPs in the crystal. When the crystal is heated, the silence energy is increased and thus the number of ELPs and the conductivity also increase. In addition to the thermal geeratio from ELPe, there is also geeratio through radiation. The so-called photoe play a role in the interaction between the bidugelectroe and the radiation. This is the smallest unit of electromagnetic radiation, similar to how electrons are the smallest unit of electrical charges. In the atomic range, electromagnetic radiation has both wave and particle character. In contrast to Elektroe, however, the Photoe has no rest mass, it moves within a medium with a costly speed of the speed of light, and consequently it cannot be secured. An energy is assigned to each photo or quarter of a radiation of the frequency for the wave length λ via the Plack relation. (h = Plack's effect quatum) hc 1240 W = hf = W / ev = λ λ / m If u falls on the Si crystal, electromagetic radiation, the energy of which is sufficient to break up Biduge, W hoto> W Bidug, then ELPe is generated and thus increases the electrical conductivity of the crystal. For silicon, this requirement is already met for radiation from the visible range with a wave length of λ <800 m. So light is absorbed by silicon. Part of the light is on the other hand reflected because of the electrical conductivity and the material properties (ε r = 11, = (ε r) r = (-1) 2 / (+ 1) 2). A silicon crystal is therefore otically transparent and has a gray metallic glaze.
3 2.1 Semiconductor properties Page 3 In addition to the schematic representation of the electrons in the 2-dimensional spatial space of the semiconductor, a representation of the energy conditions is also common and helpful. In the semiconductor crystal, the electrons are distributed to energy levels similar to that of egg atoms. Due to the large number of electrons, however, the energy levels are arbitrarily close. The Rumfelektroe and the Bidugselektroe occupy the energy in the so-called Valezbad. If the biduge is broken open, there are free electrics and holes. The energy levels of the free electrons lie in the so-called conductivity bath, which is above the Valez bath by the amount of energy required to break up the biduge. This so-called Badabstad has the value W g = 1.1 ev for silicon. The energy difference between free electrons and holes is therefore equal to the Badabstad. The energy levels are located in the Valezbad. For the free electrons in the conductive bath there is a state density fuctio, N (W), W = Eergy, which increases with the root of the distance of Eergy to Badkate. N (W) Etsrechedes applies to the holes. The free electrons have thermal kinetic energy and exchange energy due to shocks. The result is an energy distribution in which the frequency for low energy is greatest and the frequency decreases with increasing energy (Fermi energy distribution): established Elektroegas. As the temperature rises, there are more electrons with higher energy (see fig.) The energy at which the probability of the value reaches 50% is referred to as the Fermi level or Fermi energy W F. WW cf, N / NT 1
4 2.1 Semiconductor properties Page 4 Si P Si Si Electro fixed, positive charge of the Doatorrumfes When building a pentavalent atom i the Si lattice, four of the five external electrons of the foreign atom are needed to form the covalent biduge in the lattice. The fifth electric is therefore very weak a the foreign atom building ad is detached (dissociated) due to thermal energy ad is freely movable. A locally fixed, positive excess charge remains at the location of the foreign atom. If e.g. Only every 10 6th silicon atom is replaced by a foreign atom, the number of free electrons increases by 10 6 times compared to that in the i-si (i i-si is broken up every th bidug). In the -Si the electrics are so-called majority load carriers. The white holes are geat priority cargo carriers. Their number immt against the Kozetratio in the i-si with increasing Koz. of the foreign atoms N D, since the recombination rate increases with N D or the number of free electrons. -Si Doctor level W Majority load carrier Wc Wd W F Wg Elektro Wv Priority load carrier 0 50% 100% f etsreched sid the conditions in -Si. -Si Elektro Si Si B Si stationary egative charge of the Akzetorrumfes
5 2.1 Semiconductor properties Page 5 -Si W Priority load carrier Wc Wg Akzetoriveau Elektro Wa Wv Majority load carrier W F 0 50% 100% f
6 2.1 Semiconductor properties Page 6 Quatitatives for conductivity: vv µ i N d = drift speed of the electrons = µ = drift speed of the holes = µ, N, µ a = 3, = concentration of the electrons or holes (i number / cm) = itrisis Coz of electrons and holes = 1.5 10 e = 1, mobility of electrons or holes 3 = cozetratio of doors or accetors (i number / cm) -19 coul EE 10 cm -3 at room temperature E Q (e) (v) ta + ev ta U U I = = = e (µ + µ) A = t t l R 1 l R = κ = e (µ + µ) sec. Conductivity I κ A itrisic i-si: (no doping) = = i ud i = i0 ex (Eg / kt) A -Si l, U -doping: -doping: i N d ud = << 2 i N a ud = << 2 To the image on the next page As a function of the doping co-tration, it should be noted that the mobility for electrons is about 3 times greater than that for holes. This would mean that construction elements, in which the conduction is based on the movement of electrics (i form of the majority load carrier) should be a factor of 3 times faster than those in which the holes take over this function.In the MOS-Trasistor (MOSFET), however, the conditions are slightly modified, since conduction takes place here near the surface of the semiconductor. The surface is covered with oxide. The way of proximity to the regular surface with its not completely saturated biduge ad surface conditions impairs the mobility in relation to the bulk and the difference between electrics ad hole mobility is more than a factor of two. For this reason, with the same structure, -Kaal MOSFETs (NMOS) are about 2x faster than -MOSFETS (PMOS). In Figure 2 it can be seen that the mobility depends on the doping concentration. The life of the load carrier means the averaged time that elapses between the image and the recombination of a free load carrier. (See picture)
7 2.1 Semiconductor properties page 7
8 2.1 Semiconductor properties Page 8 Fermi distribution The next image from [Paul] shows once again the beam model for the semiconductors. etsreched the possible number of the (standing) electric wave: particle-wave dualism of the electric). The so-called Fermian distributionfuktio f (W) gives for a certain energy the ratio of the number of electrons, which are in states with an energy between W and W + dw, to the total number of electrons a, or in other words: f (W) dW is equal to the probability that the electrical energy has a value between W ud W + dW. Since a limited number of levels are available for each energy and the lower levels are first largely filled, this function for low energy up to a For the holes, which are caused by the lack of electrical power, the following applies to D (W) and f (W) in each case with a different course to D (W) and f (W), i.e. D (W) = -D (Wi -W) ud f (W) = 1- f (W). The Fermi energy or the Fermi level is the energy value at which the Fermifuctio de value ½: f (w F) = 1/2. The Fermifuktio is symmetrical to W F. As the temperature rises, there would be more and more electrics and higher energy levels. For the Fermifuktio this means that the slope vo f (w) at W F becomes flatter and the values vo f (w) for energy W> W F agehobe ad for W 9 2.1 Semiconductor properties Page 9 The following applies: i-si: WF = W i, -Si: WF 10 2.1 Semiconductor properties Page 10 Other binary, terary and quaterary compound semiconductors GaP, IP output material (substrate material) in the manufacture of crystals for ute terary and quaterary semiconductors. Ga As 1-x P x for LEDs in the range from green to red Ga x Al 1-x As for lasers in the near infrared (λ = 0.8 µm to λ = 1.0 µm) (Ga x I 1-x) ( As y P 1-y) for laser and photodiode in the second and third infrared window of the quartz glass fiber (λ = 1.3 µm and λ = 1.6 µm)
9 2.1 Semiconductor properties Page 9 The following applies: i-si: WF = W i, -Si: WF
10 2.1 Semiconductor properties Page 10 Other binary, terary and quaterary compound semiconductors GaP, IP output material (substrate material) in the manufacture of crystals for ute terary and quaterary semiconductors. Ga As 1-x P x for LEDs in the range from green to red Ga x Al 1-x As for lasers in the near infrared (λ = 0.8 µm to λ = 1.0 µm) (Ga x I 1-x) ( As y P 1-y) for laser and photodiode in the second and third infrared window of the quartz glass fiber (λ = 1.3 µm and λ = 1.6 µm)
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