Extrinsic semiconductors electron concentration

The carrier concentrations in doped or extrinsic semiconductors to which donor or acceptor atoms have been added can be deterrnined by considering the chemical kinetics or mass action of reactions between electrons and donor ions or between holes and acceptor ions. The condition for electrical neutraHty is given by equation 6. When the predominant dopants are donors, the semiconductor is... 

The equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

Thus, it follows that the Fermi level of p-1ype semiconductors ascends from an energy level near ea toward the middle of the band gap with decreasing acceptor concentration, N. From Eqns. 2-22 and 2-24, we obtain in general that the Fermi level is located at levels higher for n-type semiconductors and lower for p-type semiconductors than the middle of the band gap. As described in the foregoing, the concentration of electrons, n, in the conduction band is different from the concentration of holes, p, in the valence band in extrinsic semiconductors... 

The most probable donor level, ered, the most probable acceptor level, eox, and the standard Fermi level, e redox) of redox electrons are characteristic of individual redox particles but the Fermi level, e m dox), of redox electrons depends on the concentration ratio of the reductant to the oxidant, which fact is similar to the Fermi level of extrinsic semiconductors depending on the concentration ratio of the donor to the acceptor. 

The properties of semiconductors are extremely sensitive to the presence of impurities at concentrations as low as 1 part in 10 °. For this reason, silicon manufactured for transistors and other devices must be very pure. The deliberate introduction of a very low concentration of certain impurities into the very pure semiconductor, however, alters the properties in a way that has proved invaluable in constructing semiconductor devices. Such semiconductors are known as doped or extrinsic semiconductors. Consider a crystal of silicon containing boron as an impurity. Boron has one fewer valence electron than silicon. Therefore, for every silicon replaced by boron, there is an electron missing from the valence band (Figure 4.10) (i.e., positive holes occur in the valence band and these enable electrons near the top of the band to conduct electricity). Therefore, the doped solid will be a better conductor than pure silicon. A semiconductor like this doped with an element with fewer valence electrons than the bulk of the material is called a p type semiconductor because its conductivity is related to the number of positive holes (or empty electronic energy levels) produced by the impurity. 

Note. The Debye length (LD), although not introduced into the present simplified discussion, is a parameter frequently referred to in the gas-sensor literature. It was originally introduced into ionic solution theory and later applied to semiconductor theory where it is especially applicable to semi con -ductor/metal and semiconductor/semiconductor junctions. It is a measure of the distance beyond which the disturbance at the junction has effectively no influence on the electron distribution and therefore closely related to d (see Eq. (4.49)). It is a material parameter given by LD = (j kl /e2(, )12 where cQ is the undisturbed electron concentration, essentially the extrinsic electron concentration in the case of doped n-type tin oxide, and the other symbols have their usual meaning.)... 

The bulk electronic properties of extrinsic semiconductors are largely determined by the level of doping that is used to make the materials n-type or p-type. For non-degenerate semiconductors, the electron concentration in the conduction band and the hole concentration in the valence band are related to the Fermi energy EF and to the effective densities of states in the conduction and valence bands (Nc and Ny respectively) by... 

Extrinsic semiconductors ate those in which the carrier concentration, either holes or electrons, are controlled by intentionally added impurities called dopants. The dopants are termed shallow impurities because their energy levels lie within the band gap close to one or other of the bands. Because of thermal excitation, -type dopants (donors) are able to donate electrons to the conduction band and p-type dopants (acceptors) can accept electrons from the valence band, the result of which is equivalent to the introduction of holes in the valence band. Band gap widening/narrowingmay occur if the doping changes the band dispersion. At low temperamres, a special type of electrical transport known as impurity conduction proceeds. This topic is discussed in Section 7.3. 

The most popular semiconductor material is silicon (hence Silicon Valley). Fig. 12.9a is a schematic representation of a pure Si crystal. Each Si atom has rout-valence electrons and bonds to four other atoms to form Lewis octets. The crysttil can become a conductor if some of the valence electrons are shaken loose. This produces both negative and positive charge carriers—electrons and l-uilcs. Much more important are extrinsic semiconductors in which the Si crystal is doped with impurity atoms, usually at concentrations of several parts per million (ppm). For example, Si can be doped with P (or As or Sb) atoms, which has five valence electrons. As shown in Fig. 12.9b, a P atom can replace a Si atom in the lattice. The fifth electron on the P is not needed for bonding and becomes available as a current carrier. Thus, Si doped with P is a n-type semiconductor. The Si can instead be doped with B (or Ga or Al). which has only three valence eleetrons. As shown in Fig. 12.9c, a B atom replacing a Si atom leaves an electron vacancy in one of its four bonds. Such positive holes can likewise become current carriers, making Si doped with B a p-type semi con duetor. 

The transient effects consist essentially in the creation of excited electronic states and more particularly of free carriers. It can be shown that in the case of insulators, the properties related to the concentration of free carriers may undergo considerable modifications. In the case of extrinsic semiconductors only the properties depending on the concentration of carriers minority are altered, except in the case of irradiation of very high intensity. Finally, the properties depending on the concentration of carriers are the least modified in the case of intrinsic semiconductors. 

The main variables that determine the transport and screening (see below) of both intrinsic and extrinsic semiconductors are the mobile carrier densities n and 7A, Given the energetic information, that is, the electronic band structure, and the dopant concentrations, these densities can be evaluated from equilibrium statistical mechanics. For example, the density of electrons in the conduction band is... 

Single crystals of Hg,, Cd Te are grown by several different methods [4.42]. Almost regardless of the growth method or composition x in the above range, undoped ( pure ) crystals which are n-type at low temperatures have an extrinsic electron concentration near 10 cm" this is a relatively low carrier concentration for a semiconductor, and it is one of the major reasons for the success of Hg, j.Cd Te as a photoconductive infrared detector material. However, undoped crystals often turn out p-type with or have... 

In the extrinsic or doped semiconductor, impurities are purposely added to modify the electronic characteristics. In the case of silicon, every silicon atom shares its four valence electrons with each of its four nearest neighbors in covalent bonds. If an impurity or dopant atom with a valency of five, such as phosphorus, is substituted for silicon, four of the five valence electrons of the dopant atom will be held in covalent bonds. The extra, or fifth electron will not be in a covalent bond, and is loosely held. At room temperature, almost aU of these extra electrons will have broken loose from their parent atoms, and become free electrons. These pentavalent dopants thus donate free electrons to the semiconductor and are called donors. These donated electrons upset the balance between the electron and hole populations, so there are now more electrons than holes. This is now called an N-type semiconductor, in which the electrons are the majority carriers, and holes are the minority carriers. In an N-type semiconductor the free electron concentration is generally many orders of magnitude larger than the hole concentration. 

For an n-type extrinsic semiconductor, dependence of conductivity on concentration and mobility of electrons... 

A material of this type is said to be an n-type extrinsic semiconductor. The electrons are majority carriers by virtue of their density or concentration holes, on the other hand, are the minority charge carriers. For n-type semiconductors, the Fermi level is shifted upward in the band gap, to within the vicinity of the donor state its exact position is a function of both temperature and donor concentration. 

Most ceramic oxides are electrical msulatois, whose electronic corrduction is very weak (major exception superconductors), but whose ionic corrduction can be remarkable (for example, zirconia) those oxides that are semieonduetois are frequently extrinsic semiconductors, whose perfomrances vary cotrsiderably with the nature of the doping agents and their concentration. 

For a given semiconductor at temperature T, Equation (9.51) shows that as the number of free electrons increases, the number of holes proportionately decreases, so that their product remains the same. Thus the amount of the phosphorus dopant that is introduced controls the amount of both the electrons and the holes in the semiconductor. We call the carriers of higher concentration the majority carriers, while those of lower concentration are the minority carriers. Since electrons are the majority carrier when we dope silicon with phosphorous, we call this material an n-type semiconductor. When the number densities of minority and majority carriers are controlled by the amount of dopant, we say we have an extrinsic semiconductor. In the limit of small dopant concentrations, [P i] << p, there is no effect of the substitutional impurity of the electronic defects in the semiconductor, and it behaves similarly to an intrinsic semiconductor. 

The product composition, Tij oo2 o.ooiS2. is also consistent with the carrier concentration of 1.4 x 10 electrons/cm determined by Hall-coefficient measurements for similarly-prepared, highly stoichiometric TiS2. The carrier concentration for this extrinsic semiconductor is consistent with the contribution of four electrons per excess Ti to the host conduction band to produce its observed extrinsic semiconducting properties. ... 

Both electrons and holes are mobile charge carriers in semiconductors. The mobile charge carrier whose concentration is much greater than the other is called the majority carrier, and the minority carrier is in much smaller concentrations. In n-type semiconductors, the mcgority carriers are electrons in the conduction band and the minority carriers are holes in the valence band. The product of the concentrations of majority and minority carriers (electrons and holes) in a semiconductor of extrinsic type (containing impurities) equals the square of the concentration of electron-hole pairs, ni, in the same semiconductor of intrinsic type (containing no impurities) ... 

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