semiconductor

semiconductor,

solid material whose electrical conductivity at room temperature is between that of a conductor and that of an insulator (see conductionconduction,
transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity.
..... Click the link for more information. ; insulationinsulation
, use of materials or devices to inhibit or prevent the conduction of heat or of electricity. Common heat insulators are, fur, feathers, fiberglass, cellulose fibers, stone, wood, and wool; all are poor conductors of heat.
..... Click the link for more information. ). At high temperatures its conductivity approaches that of a metal, and at low temperatures it acts as an insulator. In a semiconductor there is a limited movement of electrons, depending upon the crystal structure of the material used. The substances first used for semiconductors were the elements germanium, silicon, and gray tin. It was found that the incorporation of certain impurities in them enhances their conductive properties. The impurities either add free electrons or create holes (electron deficiencies) in the crystal structures of the host substances by attracting electrons. Thus there are two types of semiconductor: the N-type (negative), in which the current carriers (electrons) are negative, and the P-type (positive), in which the positively charged holes move and carry the current. The process of adding these impurities is called doping; the impurities themselves are called dopants. Dopants that contribute mobile electrons are called donor impurities; those that cause holes to form are acceptor impurities. Undoped semiconductor material is called intrinsic semiconductor material. Certain chemical compounds, including gallium arsenide, indium antimonide, and aluminum phosphide are semiconductors. Semiconductors are used to produce such electronic devices as diodesdiode
, two-terminal electronic device that permits current flow predominantly in only one direction. Most diodes are semiconductor devices; diode electron tubes are now used only for a few specialized applications.
..... Click the link for more information. , transistorstransistor,
three-terminal, solid-state electronic device used for amplification and switching. It is the solid-state analog to the triode electron tube; the transistor has replaced the electron tube for virtually all common applications.
..... Click the link for more information. , and computer memory devices. The field of solid-state physicssolid-state physics,
study of the properties of bulk matter rather than those of the individual particles that compose it. Solid-state physics is concerned with the properties exhibited by atoms and molecules because of their association and regular, periodic arrangement in
..... Click the link for more information. includes the study of semiconductors. See also integrated circuitintegrated circuit
(IC), electronic circuit built on a semiconductor substrate, usually one of single-crystal silicon. The circuit, often called a chip, is packaged in a hermetically sealed case or a nonhermetic plastic capsule, with leads extending from it for input, output,
..... Click the link for more information. .

Semiconductor

A solid crystalline material whose electrical conductivity is intermediate between that of a metal and an insulator. Semiconductors exhibit conduction properties that may be temperature-dependent, permitting their use as thermistors (temperature-dependent resistors), or voltage-dependent, as in varistors. By making suitable contacts to a semiconductor or by making the material suitably inhomogeneous, electrical rectification and amplification can be obtained. Semiconductor devices, rectifiers, and transistors have replaced vacuum tubes almost completely in low-power electronics, making it possible to save volume and power consumption by orders of magnitude. In the form of integrated circuits, they are vital for complicated systems. The optical properties of a semiconductor are important for the understanding and application of the material. Photodiodes, photoconductive detectors of radiation, injection lasers, light-emitting diodes, solar-energy conversion cells, and so forth are examples of the wide variety of optoelectronic devices. See Laser, Light-emitting diode, Semiconductor diode, Thermistor, Transistor

Conduction in semiconductors

The electrical conductivity of semiconductors ranges from about 10³ to 10^-9 ohm^-1 cm^-1, as compared with a maximum conductivity of 10⁷ for good conductors and a minimum conductivity of 10^-17 ohm^-1 cm^-1 for good insulators. See Electric insulator

The electric current is usually due only to the motion of electrons, although under some conditions, such as very high temperatures, the motion of ions may be important. The basic distinction between conduction in metals and in semiconductors is made by considering the energy bands occupied by the conduction electrons. See Band theory of solids, Ionic crystals

At absolute zero temperature, the electrons occupy the lowest possible energy levels, with the restriction that at most two electrons with opposite spin may be in the same energy level. In semiconductors and insulators, there are just enough electrons to fill completely a number of energy bands, leaving the rest of the energy bands empty. The highest filled energy band is called the valence band. The next higher band, which is empty at absolute zero temperature, is called the conduction band. The conduction band is separated from the valence band by an energy gap, which is an important characteristic of the semiconductor. In metals, the highest energy band that is occupied by the electrons is only partially filled. This condition exists either because the number of electrons is not just right to fill an integral number of energy bands or because the highest occupied energy band overlaps the next higher band without an intervening energy gap. The electrons in a partially filled band may acquire a small amount of energy from an applied electric field by going to the higher levels in the same band. The electrons are accelerated in a direction opposite to the field and thereby constitute an electric current. In semiconductors and insulators, the electrons are found only in completely filled bands at low temperatures. In order to increase the energy of the electrons, it is necessary to raise electrons from the valence band to the conduction band across the energy gap. The electric fields normally encountered are not large enough to accomplish this with appreciable probability. At sufficiently high temperatures, depending on the magnitude of the energy gap, a significant number of valence electrons gain enough energy thermally to be raised to the conduction band. These electrons in an unfilled band can easily participate in conduction. Furthermore, there is now a corresponding number of vacancies in the electron population of the valence band. These vacancies, or holes as they are called, have the effect of carriers of positive charge, by means of which the valence band makes a contribution to the conduction of the crystal. See Hole states in solids

The type of charge carrier, electron or hole, that is in largest concentration in a material is sometimes called the majority carrier and the type in smallest concentration the minority carrier. The majority carriers are primarily responsible for the conduction properties of the material. Although the minority carriers play a minor role in electrical conductivity, they can be important in rectification and transistor actions in a semiconductor.

Intrinsic semiconductors

A semiconductor in which the concentration of charge carriers is characteristic of the material itself rather than of the content of impurities and structural defects of the crystal is called an intrinsic semiconductor. Electrons in the conduction band and holes in the valence band are created by thermal excitation of electrons from the valence to the conduction band. Thus an intrinsic semiconductor has equal concentrations of electrons and holes. The carrier concentration, and hence the conductivity, is very sensitive to temperature and depends strongly on the energy gap. The energy gap ranges from a fraction of 1 eV to several electronvolts. A material must have a large energy gap to be an insulator.

Extrinsic semiconductors

Typical semiconductor crystals such as germanium and silicon are formed by an ordered bonding of the individual atoms to form the crystal structure. The bonding is attributed to the valence electrons which pair up with valence electrons of adjacent atoms to form so-called shared pair or covalent bonds. These materials are all of the quadrivalent type; that is, each atom contains four valence electrons, all of which are used in forming the crystal bonds. See Crystal structure

Atoms having a valence of +3 or +5 can be added to a pure or intrinsic semiconductor material with the result that the +3 atoms will give rise to an unsatisfied bond with one of the valence electrons of the semiconductor atoms, and +5 atoms will result in an extra or free electron that is not required in the bond structure. Electrically, the +3 impurities add holes and the +5 impurities add electrons. They are called acceptor and donor impurities, respectively. Typical valence +3 impurities used are boron, aluminum, indium, and gallium. Valence +5 impurities used are arsenic, antimony, and phosphorus.

Semiconductor material “doped” or “poisoned” by valence +3 acceptor impurities is termed p-type, whereas material doped by valence +5 donor material is termed n-type. The names are derived from the fact that the holes introduced are considered to carry positive charges and the electrons negative charges. The number of electrons in the energy bands of the crystal is increased by the presence of donor impurities and decreased by the presence of acceptor impurities. See Acceptor atom, Donor atom

At sufficiently high temperatures, the intrinsic carrier concentration becomes so large that the effect of a fixed amount of impurity atoms in the crystal is comparatively small and the semiconductor becomes intrinsic. When the carrier concentration is predominantly determined by the impurity content, the conduction of the material is said to be extrinsic. Physical defects in the crystal structure may have similar effects as donor or acceptor impurities. They can also give rise to extrinsic conductivity.

Materials

The group of chemical elements which are semiconductors includes germanium, silicon, gray (crystalline) tin, selenium, tellurium, and boron. Germanium, silicon, and gray tin belong to group 14 of the periodic table and have crystal structures similar to that of diamond. Germanium and silicon are two of the best-known semiconductors. They are used extensively in devices such as rectifiers and transistors.

A large number of compounds are known to be semiconductors. A group of semiconducting compounds of the simple type AB consists of elements from columns symmetrically placed with respect to column 14 of the periodic table. Indium antimonide (InSb), cadmium telluride (CdTe), and silver iodide (AgI) are examples of III–V, II–IV, and I–VI compounds, respectively. The various III–V compounds are being studied extensively, and many practical applications have been found for these materials. Some of these compounds have the highest carrier mobilities known for semiconductors. The compounds have zincblende crystal structure which is geometrically similar to the diamond structure possessed by the elemental semiconductors, germanium and silicon, of column 14, except that the four nearest neighbors of each atom are atoms of the other kind. The II–VI compounds, zinc sulfide (ZnS) and cadmium sulfide (CdS), are used in photoconductive devices. Zinc sulfide is also used as a luminescent material. See Luminescence, Photocon-ductivity

The properties of semiconductors are extremely sensitive to the presence of impurities. It is therefore desirable to start with the purest available materials and to introduce a controlled amount of the desired impurity. The zone-refining method is often used for further purification of obtainable materials. The floating zone technique can be used, if feasible, to prevent any contamination of molten material by contact with the crucible.

For basic studies as well as for many practical applications, it is desirable to use single crystals. Various methods are used for growing crystals of different materials. For many semiconductors, including germanium, silicon, and the III–V compounds, the Czochralski method is commonly used. The method of condensation from the vapor phase is used to grow crystals of a number of semiconductors, for instance, selenium and zinc sulfide. See Crystal growth

The introduction of impurities, or doping, can be accomplished by simply adding the desired quantity to the melt from which the crystal is grown. When the amount to be added is very small, a preliminary ingot is often made with a larger content of the doping agent; a small slice of the ingot is then used to dope the next melt accurately. Impurities which have large diffusion constants in the material can be introduced directly by holding the solid material at an elevated temperature while this material is in contact with the doping agent in the solid or the vapor phase.

A doping technique, ion implantation, has been developed and used extensively. The impurity is introduced into a layer of semiconductor by causing a controlled dose of highly accelerated impurity ions to impinge on the semiconductor.

An important subject of scientific and technological interest is amorphous semiconductors. In an amorphous substance the atomic arrangement has some short-range but no long-range order. The representative amorphous semiconductors are selenium, germanium, and silicon in their amorphous states, and arsenic and germanium chalcogenides, including such ternary systems as Ge-As-Te. Some amorphous semiconductors can be prepared by a suitable quenching procedure from the melt. Amorphous films can be obtained by vapor deposition.

Rectification in semiconductors

In semiconductors, narrow layers can be produced which have abnormally high resistances. The resistance of such a layer is nonohmic; it may depend on the direction of current, thus giving rise to rectification. Rectification can also be obtained by putting a thin layer of semiconductor or insulator material between two conductors of different material.

A narrow region in a semiconductor which has an abnormally high resistance is called a barrier layer. A barrier may exist at the contact of the semiconductor with another material, at a crystal boundary in the semiconductor, or at a free surface of the semiconductor. In the bulk of a semiconductor, even in a single crystal, barriers may be found as the result of a nonuniform distribution of impurities. The thickness of a barrier layer is small, usually 10^-3 to 10^-5 cm.

A barrier is usually associated with the existence of a space charge. In an intrinsic semiconductor, a region is electrically neutral if the concentration n of conduction electrons is equal to the concentration p of holes. Any deviation in the balance gives a space charge equal to e(p - n), where e is the charge on an electron. In an extrinsic semiconductor, ionized donor atoms give a positive space charge and ionized acceptor atoms give a negative space charge.

Surface electronics

The surface of a semiconductor plays an important role technologically, for example, in field-effect transistors and charge-coupled devices. Also, it presents an interesting case of two-dimensional systems where the electric field in the surface layer is strong enough to produce a potential wall which is narrower than the wavelengths of charge carriers. In such a case, the electronic energy levels are grouped into subbands, each of which corresponds to a quantized motion normal to the surface, with a continuum for motion parallel to the surface. Consequently, various properties cannot be trivially deduced from those of the bulk semiconductor. See Surface physics

Semiconductor

a substance whose electrical conductivity σ is intermediate between that of a metal and a good dielectric. At room temperature, the electrical conductivity of metals ranges from about 10⁶ to 10⁴ (ohm-cm)^-1; in the case of good dielectrics at room temperature, σ < 10^-10-10^–12 (ohm-cm)^-1. The electrical conductivity of semiconductors, unlike that of metals, increases as the temperature is raised. This increase is generally exponential over a rather broad temperature range:

(1) σ = σ0 exp (–ℰA/kT)

Here k is the Boltzmann constant, is the activation energy of the electrons in the semiconductor, and σ0 is a proportionality factor; σ0 actually depends on temperature, but less rapidly than exponentially. As the temperature rises, thermal motion breaks the bonds of the electrons, which become free charge carriers. The number of electrons that become free charge carriers is proportional to exp (— ℰA/kT).

An electronic bond can be broken not only by thermal motion but also by such external factors as light, a flux of fast particles, or a strong electric field. Semiconductors are therefore characterized by a high sensitivity of their electrical conductivity to external factors and to the impurity content and crystal defects, since in many cases ℰ_A is considerably smaller for electrons localized near impurities or defects than in an ideal crystal of the given semiconductor. Semiconductors have many different applications because their electrical conductivity can be controlled within wide limits by, for example, the variation of temperature or the introduction of impurities.

Semiconductors and dielectrics; classification of semiconductors. The difference between semiconductors and dielectrics is more quantitative than qualitative. Equation (1) applies equally to dielectrics, whose conductivity may become appreciable at high temperatures. Instead of placing semiconductors in a separate class, it would be more accurate to speak of the semiconducting state of nonmetallic substances and to classify as true dielectrics only those substances in which, because of the large values of and small values of σ₀, the conductivity can reach appreciable values only at temperatures at which the substances completely vaporize.

The term “semiconductor,” however, is often interpreted in a narrower sense as one of several typical groups of substances whose semiconductor properties are quite evident even at room temperature (300°K). Examples of these groups follow.

THE ELEMENTS GERMANIUM AND SILICON OF GROUP IV OF MENDELEEV’S PERIODIC SYSTEM OF THE ELEMENTS. Germanium and silicon have been the elements most thoroughly studied as semiconductors and are widely used in semiconductor electronics. Their atoms have four valence electrons and form diamond-type crystal lattices with covalent bonding of the atoms. Diamond itself has the properties of a semiconductor, but the value of ℰ_A is much greater for it than for Ge and Si, and its intrinsic electrical conductivity—that is, conductivity not due to impurities or external factors—at T = 300°K is therefore extremely small.

DIAMOND-LIKE SEMICONDUCTORS. Diamond-like semiconductors include compounds consisting of group III elements (Al, Ga, In) and group V elements (P, As, Sb). Such compounds are referred to as A^IIIB^V semiconductors and are exemplified by GaAs, InSb, GaP, and InP. Since group III atoms have three valence electrons and group V atoms have five, the average number of valence electrons per atom is, as in Ge and Si, equal to four in these compounds. Each atom forms four valence bonds with its nearest neighbors. A crystal lattice results that is similar to the diamond lattice except that the nearest neighbors of an A^III atom are B^V atoms and the nearest neighbors of a B^V atom are A^III atoms. Because of the partial redistribution of electrons, the A^III and B^V atoms in this structure are oppositely charged. The bonds in A^IIIB^V crystals are therefore not completely covalent but partially ionic. Covalent bonding, however, predominates and determines the structure of these crystals. For this reason, such crystals are very close analogues of Ge and Si in many of their properties.

Compounds of group II and group VI elements, such as ZnTe, ZnSe, CdTe, and CdS, are denoted A^IIB^VI. They also have an average of four valence electrons per atom, but the ionic character of the bonding is much more pronounced. In some of them, the covalent bond predominates over the ionic; in others, it is weaker. In both cases, however, the compound has the properties of a semiconductor, although not so markedly as in the preceding types.

The concept of average tetravalence and diamond-like semiconductors has proved fruitful in the search for new semiconductors of, for example, the type A^IIB^IVC^V₂, such as ZnSnP₂ and CdGeAs₂. Many diamond-like semiconductors form alloys that are also semiconductors, such as Ge-Si and GaAs-GaP.

GROUP VI AND GROUP V ELEMENTS AND THEIR ANALOGUES. The group VI elements Te and Se were known as semiconductors before Ge and Si. Se was used extensively in rectifiers and photocells. The group V elements As, Sb, and Bi are semimetals that are close in properties to semiconductors. Their closest analogues are compounds of the type A^IVB^VI, such as PbS, PbTe, SnTe, and GeTe. Such compounds have an average of five valence electrons per atom and form one of the most important groups of semiconductors, which is known above all for the use of PbS, PbSe, and PbTe as infrared detectors. In general, there are many semiconductors among compounds of group VI elements (O, S, Se, Te) with elements of groups I through V. Most of them have been little studied. Cu₂O, which is used in copper oxide rectifiers, and Bi₂Te₃, which is used in thermocouples, are examples that have been studied more and have practical application.

COMPOUNDS OF GROUP VI ELEMENTS WITH TRANSITION OR RARE-EARTH METALS, SUCH AS TI, V, MN, FE, NI, SM, AND EU. Ionic bonding predominates in semiconductors that are compounds of group VI elements with transition or rare-earth metals. Most such semiconductors have some type of magnetic ordering and are ferromagnets or antiferromagnets. The combination of semiconductor and magnetic properties and the mutual action of these properties are interesting both from the theoretical standpoint and for many practical applications. Some of the compounds, such as V₂O₃, Fe₃O₄, NiS, and EuO, can move from the semiconductor state to the metallic state; this transition occurs very abruptly as the temperature changes.

ORGANIC SEMICONDUCTORS. Many organic compounds also have the properties of semiconductors. Their electrical conductivity is generally small: σ ~ 10^-10 (ohm-cm)^-1. It increases markedly on exposure to light. Some organic semiconductors, however, have at room temperature a σ comparable to that of good inorganic semiconductors. Examples are crystals and polymers based on compounds of tetracyanquinodimethane (TCNQ) and complexes based on phthalocyanine, perylene, and violanthrene.

Electrons and holes in semiconductors. Since the atoms or ions in a solid are separated by a distance of the order of an atomic radius, valence electrons may move from one atom to another. Such electron transfer can result in the formation of a covalent bond if the electron shells of neighboring atoms overlap considerably and electron transitions between atoms occur sufficiently often. This picture is fully applicable to such a typical semiconductor as Ge. All the Ge atoms are neutral and are covalently bound to each other. Electron transfer between atoms, however, does not lead directly to electric conduction, since the electron density distribution as a whole is rigidly fixed: there are two electrons per bond between each pair consisting of an atom and its nearest neighbor. In order to produce conduction in such a crystal, at least one of the bonds must be broken—for example, by heating or by the absorption of a photon. When an electron is removed from the bond, it must be transferred to some other cell of the crystal where all the bonds are filled, and it will be an excess electron. Such an electron subsequently can move freely from cell to cell, since for this electron all cells are equivalent. Being everywhere excess, it is carrying an excess negative charge —that is, it becomes a conduction electron. The broken bond also begins to wander through the crystal as a hole, since under the conditions of strong exchange an electron of one of the neighboring bonds quickly occupies the place of the departed electron, thus leaving broken the bond from which it came. An electron deficiency in one of the bonds indicates that the atom, or pair of atoms, has a unit positive charge, which thus is transferred together with the hole.

In the case of ionic bonding, there is less overlapping of the electron shells, and electron transfer is less frequent. When a bond is broken, a conduction electron and a hole are also formed; the conduction electron is an excess electron in one of the cells of the crystal, and the hole is an uncompensated positive charge in another cell. They both can move through the crystal by passing from one cell to another.

The presence of two oppositely charged types of current carriers—electrons and holes—is a common property of semiconductors and dielectrics. In ideal crystals these carriers are always paired. The excitation of a bound electron and its conversion to a conduction electron inevitably cause a hole to appear; thus the concentrations of the two types of carriers are equal. Electrons and holes do not, however, necessarily make equal contributions to the electrical conductivity, because their mobility, or rate of transfer from cell to cell, may differ. In real crystals, which contain impurities and structural defects, the equality of the concentrations of electrons and holes may be disturbed, so that electrical conduction is accomplished essentially by just one type’ of carrier.

Band structure of semiconductors. A complete and rigorous description of the nature of charge carriers in semiconductors and of the laws governing the motion of charge carriers is given within the framework of the quantum theory of the solid state. The principal results of the theory are as follows:

(1) In crystals, the energy spectrum of the electrons consists

Figure 1. Occupancy of energy bands at absolute zero temperature: (a) in dielectrics, (b) in metals. The allowed bands are hatched; the filled bands, or parts of bands, are crosshatched.

of energy ranges, called allowed bands, that are completely filled with energy levels. The allowed bands are separated from each other by energy gaps (called forbidden bands), in which there are no electronic levels (Figure 1).

(2) The different states of an electron within each band are characterized not only by the energy of the electron but also by the quasimomentum p, which can assume any values within certain limited regions in momentum space (p-space) called Brillouin zones. The shape and dimensions of a Brillouin zone are determined by the symmetry of the crystal and by the crystal’s interatomic distances d: p_max ≲ h/d, where h is Planck’s constant. The equation of motion of a conduction electron in a crystal is similar to the equation of motion of an electron in vacuo but with the important difference that the relations ℰ = p²/2m₀ and v_p = p/m₀ (where m₀ is the mass of the free electron and ℰ is its energy, p its momentum, and v its velocity) are replaced by the more complicated function ℰ(p): v_p = ∂ℰp/∂p, which is specific for each crystal and each energy band.

(3) At the absolute zero of temperature the electrons fill the lowest energy levels. By virtue of the Pauli exclusion principle, only one electron can be located in each state characterized by a definite energy, quasimomentum, and one of two possible spin orientations. Therefore, depending on the concentration of electrons in the crystal, the electrons occupy some of the lowest allowed bands and leave the higher bands empty. If at T = 0°K part of the lower bands in a crystal are entirely occupied while the higher bands are empty, the crystal is a dielectric or a semiconductor (Figure 1, a). It is a metal only if at least one of the allowed bands is only partially filled even at T = 0°K (Figure 1, b).

In semiconductors and dielectrics, the upper filled allowed bands are called valence bands, and the lowest of the empty bands are called conduction bands. For T > 0°K, thermal motion raises some of the electrons from the valence band into the conduction band—that is, it breaks some of the chemical bonds. When this occurs, holes appear in the valence band (Figure 2).

Figure 2. Occupancy of energy bands in a semiconductor. Only a valence band and a conduction band are shown. The solid circles represent electrons in the conduction band, and the white circles indicate holes in the valence band.

The charge carriers in semiconductors are generally concentrated in rather narrow energy regions. The electrons are near the lower edge, or bottom, ℰ_c of the conduction band; they are at energy distances of ~kT from the bottom, where kT is the energy of thermal motion. The holes are in a region of the same width near the upper edge, or top, ℰ_v of the valence band. Even at very high temperatures (~1000°), kT ~ 0.1 electron volt (eV), and the width of allowed bands is usually of the order of 1–10 eV. In these narrow regions of width ~kT, the complicated functions ℰ(p) generally assume a simpler form. For example, for electrons near the bottom of the conduction band

Here, the subscript i denotes the coordinate axes, and p_oi are the quasimomenta corresponding to ℰ_c in the conduction band or ℰ_r in the valence band. The quantities m_i^e are called the effective masses of the conduction electrons. They play the same role in the equation of motion for a conduction electron as does m₀ in the equation of motion for a free electron. For holes in the valence band, we have similarly

The effective masses of electrons (m^e) and holes (m^h) do not coincide with m₀ and are generally anisotropic. Under different conditions the same carrier therefore behaves as a particle with different effective masses. For example, in an electric field E directed along the z-axis, it is accelerated as a particle with charge e and mass m_z^e and in a magnetic field H directed along the z-axis it moves in an ellipse in a plane perpendicular to H with the cyclotron frequency

From the quantum standpoint, such cyclic motion of electrons and holes in a crystal with frequency ω_c indicates the presence of energy levels called Landau levels that are separated from one another by ħω_c. The values of the effective masses of electrons and holes in different semiconductors range from hundredths of m₀ to hundreds of m₀.

The width of the energy gap Δℰ, that is, the minimum energy separating a filled band from an empty band, also varies over a broad range. Thus, when T → 0°K, Δℰ = 0.165 eV in PbSe, 0.22 eV in InSb, 0.33 eV in Te, 0.745 eV in Ge, 1.17 eV in Si, 1.51 in GaAs, 2.32 eV in GaP, 2.58 eV in CdS, and 5.6 eV in diamond. Gray tin is an example of a semiconductor in which Δℰ = 0—that is, the upper edge of the valence band coincides exactly with the lower edge of the conduction band (a semimetal). More complex compounds and alloys of semiconductors that are close in structure permit semiconductors with any Δℰ from 0 to 2–3 eV to be obtained.

The band structure has been studied most thoroughly for diamond-like semiconductors, primarily Ge, Si, and A^IIIB^V compounds. Much is also known about, for example, Te and A^IVB^VI compounds. A typical example is the band structure of Ge (Figure 3), in which two valence bands touch near the upper edge. This indicates the existence of two types of holes: heavy holes and light holes with effective masses 0.3m₀ and 0.04m₀, respectively. Yet another valence band is located 0.3 eV lower, but holes generally do not fall into it. The presence of three types of minima of the function ℰ (p) is characteristic of the conduction band of Ge: L, T, and A. The lowest of these is the L-minimum located at the boundary of the Brillouin zone in the direction of the crystallographic axis [III]. Its distance from the upper edge of the valence band is the width of the energy gap, which is Δ ℰ = 0.74 eV at temperatures close to absolute zero (Δℰ decreases somewhat with increasing temperature). The effective masses near the L-minimum are strongly anisotropic: 1.6m₀ for motion in the [III] direction and 0.08m₀ for perpendicular directions. Four equivalent L-minima correspond to the four equivalent directions of [111] (the diagonals of the cube) in the Ge crystal. The T-minimum and Δ-minimum are located at p= 0 and in the direction of the [100] axis. They are higher in the energy than the L-minimum by 0.15 eV and 0.2 eV, respectively. The number of conduction electrons in them, therefore, is generally much smaller than in the L-minimum.

Figure 3. Energy band diagram for Ge: (Δε) width of the energy gap; (L), (Γ), and (A) three minima of the function ε(p) in the conduction band along the [100] (Δ and Γ) and [111] (L) axes

The band structures of other diamond-like semiconductors are similar to the structure of Ge, with some differences. Thus, in Si, GaP, and diamond, the Δ-minimum is the lowest; in InSb, InAs, and GaAs, however, the Γ-minimum is the lowest. Isotropic and extremely small effective masses are characteristic of this second group: 0.013m₀ in InSb and 0.07m₀ in GaAs. The structures of the valence bands of many diamond-like semiconductors are similar, but may differ considerably from semiconductors of other groups.

Noncrystalline semiconductors. Ideal crystal ordering of the atoms is absent in liquid, amorphous, and vitreous semiconductors, but the immediate neighborhood of each atom is approximately preserved. The short-range order, however, is not always the same as in the crystal phase of the same substance. For example, in covalent semiconductors, such as Ge, Si, and A^IIIB^V, each atom has not four but eight nearest neighbors after melting; this is because the covalent bonds, which are extremely sensitive both to the interatomic distance and to the mutual orientation of the bonds, are broken by the intense thermal motion of the atoms in the liquid. As a result of this restructuring of the short-range order, in melts substances of the mentioned types become metals.

In other semiconductors, however, such as Te, Se, and A^IVB^VI, the short-range order apparently does not change when melting occurs, and the substances remain semiconductors in the melts. As applied to them and to amorphous semiconductors, the concepts of band theory require considerable changes and additions. The absence of strict ordering in the atomic arrangement creates local fluctuations of density and interatomic distances; these fluctuations make the energies of an electron slightly different near different atoms of the same kind. The transfer of an electron from atom to atom is thus hindered since such transfer is now associated with a change in energy. This circumstance does not lead to any qualitative changes for carriers whose energies lie in the allowed bands sufficiently far from the bands’ edges, inasmuch as such carriers have energies large enough to surmount comparatively easily the energy barriers between different atoms of the same kind. The picture, however, undergoes a qualitative change for carriers with energies near the band edges. The carriers no longer have enough energy to surmount the energy differences between neighboring atoms and therefore may become localized—that is, lose the ability to migrate. As a result, there arise electronic levels in the energy range that corresponds to the energy gap in the crystal. The electrons located in these levels are localized near the corresponding fluctuations, and such concepts of band theory as quasi-momentum are no longer applicable to them. The very concept of the energy gap changes. This energy region is now filled with electronic states, but the nature of these states is not the same as in the allowed bands because the states are localized. For this reason, we speak of a pseudo-forbidden band.

Optical properties of semiconductors. The mechanism of the absorption of light by a semiconductor is associated with the structure of the energy bands. The absorption process most characteristic of a semiconductor is its intrinsic absorption. In this process, when one of the electrons in the valence band with quasimomentum p absorbs a light quantum, it moves to an unoccupied state of one of the conduction bands with quasimomentum p″. The relation between the energy of the photon ħω(ω = 2πc/λ, where ω is the frequency of the light and λ is the wavelength) and the energies of the electron in the initial state (ℰⁱ) and final state (ℰ^f) is given by the equation

(5) ℏω = ℰ_f(p″) – ℰ_i(p)

The quasimomenta are governed by a law of conservation analogous to the law of conservation of momentum:

(6) p″ = p + ℏq ≈ p

where q is the wave vector of the photon. In practice, the momentum of a photon q is negligibly small compared with the quasimomenta of the electron. The approximate equality p″ ≈ p is therefore valid.

The intrinsic absorption of light is impossible at a photon energy ℏω smaller than the width Δℰ of the energy gap (the minimum energy of the absorbed quanta ℏω = Δℰ is called the absorption threshold, or edge). Consequently, for wavelengths

(7) λ > λ_max = 2πℏc/Δℰ.

an intrinsic semiconductor is transparent. Strictly speaking, the minimum energy of quanta absorbed by a given semiconductor may be greater than Δℰ if the edges of the conduction band ℰ_c a and valence band ℰ_v correspond to different values of p. A transition between the edges does not satisfy the requirement p = p″, and the absorption therefore begins at larger ℏω—that is, at shorter wavelengths. For Ge, for example, this would mean transitions to the Γ-minimum of the conduction band (see Figure 3).

Transitions for which p = p″, however, are still possible if the electron simultaneously absorbs or emits a phonon when it absorbs a light quantum. If the phonon frequency is ω_f and the momentum is equal to (p — p″), then the law of conservation of energy has the form

ℏω = ℰ_f(p″) – ℰ_i(p) ± ℏω_f

Since the phonon energies are small (ℏω_f ~ 10^-2 eV) compared with AS, their contribution to (8) is small. Optical transitions in which an electron undergoes a considerable change in quasimomentum are called indirect transitions, in contrast to direct transitions, which satisfy the condition p = p″. The necessity of the emission or absorption of a phonon makes indirect transitions much less probable than direct transitions. The light absorption coefficient K for indirect transitions is of the order of 10³ cm^-1, whereas in the region of direct transitions the absorption coefficient reaches 10⁵ cm^-1. Nonetheless, in all semiconductors in which the edges of the conduction and valence bands correspond to different p, there exists a wavelength region near λ_max where only indirect transitions are observed.

The light absorption coefficient in semiconductors is defined as the product of the probability of photon absorption by each electron and the number of electrons capable of absorbing quanta of the given energy. The study of the frequency dependence of the absorption coefficient therefore gives information on the density distribution of the electronic states in the bands. Thus, in the case of direct transitions, the absorption coefficient near the absorption edge is proportional to the density of states .

The presence of broad and intense bands in the absorption spectrum in the region of ℏω of the order of Δℰ indicates that a large number of valence electrons are weakly bound. Since a weak bond is readily deformed by an applied electric field, it follows that the crystal has a high polarizability. Indeed, large values of the dielectric constant ∊ are characteristic of many semiconductors, such as diamond-like and A^IVB^VI semiconductors. Thus, in Ge, ∊ = 16; in GaAs, ∊ = 11; and in PbTe, ∊ = 30. Because of the large values of ∊, the Coulomb interaction of charged particles, particularly electrons and holes, with each other or with charged impurities is considerably weakened if the particles are separated by a distance exceeding the dimensions of the unit cell. As a result, in many cases the motion of each carrier can be considered independently of the others. Otherwise, the free charge carriers would tend to form complexes consisting of an electron and a hole or charged impurity particle with binding energies of ~ 10 eV. It would be practically impossible to break these bonds through thermal motion in order to obtain appreciable conductivity at temperatures of ~300°K.

Pairwise binding of electrons and holes into complexes, however, still occurs, but this binding is weak (ℰ_pb ~ 10^-2 eV) and easily broken by thermal motion. Such bound states of an electron and a hole in a semiconductor are called excitons. They give rise in absorption spectra to narrow lines shifted by ℰ_pb from the absorption edge toward energies smaller than the photon energies. Excitons are formed when an electron that has absorbed a photon and left a hole in its place in the valence band does not move away from the hole but, held back by Coulomb attraction, remains near the hole.

The transparency of semiconductors in a narrow range of frequencies near the intrinsic-absorption edge can be varied by means of external magnetic and electric fields. By accelerating the electrons, an electric field can impart additional energy to an optical transition; this energy is small, since the transition time is very short. As a result, transitions from the valence band to the conduction band under the action of quanta with an energy somewhat smaller than Δℰ become possible. When this is the case, the sharp edge of the intrinsic absorption region of semiconductors becomes slightly blurred and is shifted toward lower frequencies.

A magnetic field alters the nature of the electronic states. As a result, the frequency dependence of the absorption coefficient assumes, instead of the smooth relation , the form of narrow absorption peaks associated with electronic transitions between the Landau levels of the valence band and the conduction band. In addition to the intrinsic absorption in semiconductors, absorption of light by free carriers, which is associated with transitions within a band, is also possible. Such intraband transitions occur only through the participation of phonons. The contribution of these transitions to the absorption is small, since the number of free carriers in a semiconductor is always very small in comparison with the total number of valence electrons. Absorption by free carriers accounts for the absorption of radiation with ℏω < Δℰ in intrinsic semiconductors. In a magnetic field, carrier transitions between Landau levels of the same band become possible; such transitions are evidenced by a sharp peak in the frequency dependence of the absorption coefficient at the cyclotron frequency ωc. Given fields of ~ 10³—10⁵ oersteds (Oe) and an effective mass of ~(1–0.01) m₀, ωc = 10¹⁰—10¹³ sec^-1. This range of values corresponds to superhigh frequencies or the far infrared.

Absorption bands associated with the excitation by photons of vibrations of oppositely charged ions wth respect to each other are observed in the far infrared (ℏω ~ 10^-2 eV) in semiconductors with an appreciable fraction of ionic bonding.

Role of impurities and defects in semiconductors. The electrical conductivity of a semiconductor may be due to the electrons of the substance’s own atoms or to the electrons of impurity atoms. In the former case we speak of intrinsic conduction, and in the latter case of extrinsic, or impurity, conduction. Sources of charge carriers include not only impurities but also various structural defects, such as vacancies and interstitial atoms, and a deficiency or excess of atoms of one of the components of a semiconductoring compound (deviations from stoichiometric composition), such as a Ni deficiency in NiO or a S deficiency in PbS.

Impurities and defects are divided into donors and acceptors. Donors contribute excess electrons to the bulk of the semiconductor and thus create n-type (electron) conduction. Acceptors capture valence electrons of the substance into which they are introduced; as a result, holes are formed, and p-type (hole) conduction arises (Figure 4). Typical examples of donors are impurity atoms of group V elements (P, As, Sb) in Ge and Si. When a donor atom enters the crystal lattice, it replaces a Ge atom in one of the cells. Four of its five valence electrons form covalent bonds with neighboring Ge atoms. The fifth electron is an excess electron for the lattice, since all the bonds are already saturated. It is not localized in any unit cell and becomes a conduction electron. When this occurs, the impurity atom acquires a charge of +1 and attracts an electron. A bound state of the electron and the impurity ion may result. This bond, however, is very weak because the electrostatic attraction of the electron to the impurity ion is reduced by the high polarizability of the semiconductor, and the dimensions of the region near the impurity in which the electron is localized are several tens of times greater than the size of the crystal’s unit cell. The ionization energy of an impurity is ~0.01 eV in Ge and ~0.04 eV in Si. Even at a temperature of 77°K, most of the impurities are ionized—that is, the semiconductor contains conduction electrons whose concentration is determined by the concentration of the donor impurities.

Figure 4. Electronic transitions that give rise to electric conduction in a semiconductor: (1) donor ionization (n-type conduction), (2) capture of valence electrons by acceptors (p-type conduction), (3) production of electron-hole pairs (intrinsic conduction), (4) impurity compensation

Similarly, atoms of group III elements (B, Al, Ga, In) are typical acceptors in Ge and Si. By capturing one of the valence electrons of Ge to complement their three valence electrons, they form four covalent bonds with their nearest neighbors, the Ge atoms, and become negatively charged ions. At the position of the captured electron there remains a hole, which, like an electron near a donor ion, can be held in the vicinity of the acceptor ion by Coulomb attraction, but at a large distance and with a very small binding energy. The holes are therefore free at not very low temperatures.

In the case of A^IIIB^V compounds, such similar considerations explain the donor action of impurities of some group VI elements (S, Se, Te), which replace a B^V atom, and the acceptor action of group II elements (Be, Zn, Cd), which replace an A^III atom. In Ge the same Zn is a doubly charged acceptor, since in order to form four valence bonds with its neighbors it may capture two more electrons to complement its own two valence electrons— that is, it may create two holes. Cu and Au atoms can exist in Ge in the neutral, singly charged, doubly charged, and triply charged states, thus forming one, two, or three holes.

The examples considered above pertain to substitutional impurities. Li is an example of an interstitial impurity in Ge and Si. Since the Li⁺ ion is small, it is located in the interstice between Ge atoms without significantly disrupting the lattice structure. It attracts very weakly and gives up readily its outer valence electron, which moves at a much greater distance. The Li⁺ ion is thus a typical donor. In many A^IVB^VI semiconductors the sources of free holes are vacancies in A^IV atoms, and B^VI vacancies are the sources of conduction electrons. It is clear from the above that doping, or the introduction of certain impurities, is an effective method of obtaining semiconductors with various required properties.

Heavily doped semiconductors. When impurities or defects are in high concentrations, their interaction results in qualitative changes in the properties of the semiconductor. This effect may be observed in heavily doped semiconductors containing impurities in such high concentrations N_im that the mean distance between the impurities, which is proportional to N_im^1/3, becomes less than or of the order of the mean distance a separating the impurity from the electron or hole captured by it. Under such conditions, a carrier may not be localized in general at any center, since it is always located at a comparable distance from several identical impurities at the same time. Moreover, the effect of impurities on the motion of electrons is generally small, since the large number of carriers with a charge sign opposite to the charge of the impurity ions screens—that is, greatly attenuates—the electric field of the ions. Consequently, all carriers introduced with these impurities are free even at very low temperatures.

The condition for heavy doping is N_im^1/3 × a~ 1 and is easily achieved for impurities that create shallow levels, that is, levels with a small binding energy. For example, in Ge and Si doped with impurities of group III or group V elements, this condition is satisfied even at N_im ~ 10¹⁸-10¹⁹ cm^-3, whereas these impurities can be introduced in concentrations up to N_im ~ 10²¹ cm^-3 when the atomic density of the host material is — 5 × 10²² cm^-3. Vacancies of one of the components in A^IVB^VI semiconductors are almost always present in high concentration (≥10^l7-10¹⁸ cm^-3), and the energies binding the carriers to these vacancies are small; thus the condition N_im^1/3 × a ~ 1 is nearly always satisfied.

Equilibrium concentrations of charge carriers in semiconductors. In the absence of external factors, such as illumination or an electric field, the electron and hole concentrations in a semiconductor are determined entirely by the temperature, the width AS of the energy gap, the effective masses of the carriers, the concentrations and spatial distribution of impurities and defects, and the energies binding electrons and holes to impurities and defects. In this case, we speak of equilibrium carrier concentrations.

At temperatures near T = 0°K, all the intrinsic electrons of a semiconductor are located in the valence band, which they completely fill, and the impurity electrons are localized near impurities or defects. Free carriers are thus absent. When donors and acceptors are present in a specimen, electrons from the donors can move over to the acceptors. If the donor concentration N_d is greater than the acceptor concentration N_a, then the specimen will contain N_a negatively charged acceptor ions and the same number of positively charged donors. Only N_d — N_a donors remain neutral and capable of surrendering their electrons to the conduction band as the temperature increases. Such a specimen is an n-type semiconductor with a carrier concentration N_d — N_a. Similarly, in the case where N_a > N_d, the semiconductor has p-type conductivity. The binding of donor electrons by acceptors is called impurity compensation, and semiconductors that contain donors and acceptors in comparable concentrations are said to be compensated.

As the temperature increases, thermal motion ejects electrons from donor atoms and the valence band into the conduction band (n-type conduction is meant here). If, however, the ionization energy of the donor is ℰ_d ≪ Δℰ (as is usually the case) and the temperature is not too high, then the first of these processes is dominant, even though the number of donors is many times smaller than the number of valence electrons. The semiconductor displays appreciable extrinsic n-type conductivity, which increases rapidly with temperature. In this case, the concentration of electrons in the conduction band is many times greater than the concentration of holes in the valence band. Under such conditions, the electrons are called majority carriers, and the holes are called minority carriers. It may be noted that the reverse is the case in a p-type semiconductor: here the majority carriers are holes, and the minority carriers are electrons. The increase in free carrier concentration with temperature continues until all the donors are ionized. Thereafter, the concentration remains nearly constant over a broad temperature range and is equal to n = N_d — N_a. The number of electrons thrown by thermal motion from the valence band into the conduction band, however, continues to increase exponentially and at some temperature becomes comparable to the concentration of impurity electrons. It subsequently becomes many times greater—that is, a rapid temperature-dependent increase in the total concentration of free carriers begins again. This region is the intrinsic conduction region of the semiconductor, where the electron concentration n and hole concentration p are practically the same: n = p = n_i. The increase in the number of intrinsic charge carriers continues to very high temperatures. At T = 1000°K, the concentration of intrinsic charge carriers may be only one to three orders of magnitude smaller than the concentration of conduction electrons in good metals. The temperature at which the transition from extrinsic to intrinsic conduction occurs depends on the relation between ℰ_d and Δℰ and on the concentrations N_d and N_a. In Ge with an impurity of group V elements, complete ionization of donors occurs already at T — 10° K ifN_d ~ 10¹³ cm^-3 and at T = 30°K if N_d ~ 10¹⁶ cm^-3. The transition to intrinsic conduction occurs at T = 300°K for N_d ~ 10¹³ cm^-3 and at T = 450°K for N_d ~ 10¹⁶ cm^-3 (Figure 5).

Figure 5. Temperature dependence of charge-carrier concentration n in moderately doped (1) and heavily doped (2) semiconductors: (I) region of partial ionization of impurities, (II) region of complete ionization of impurities, (III) region of intrinsic conduction

The determination of equilibrium charge-carrier concentrations in semiconductors is based on the Fermi distribution of electrons over the energy states (in the bands and impurity levels). The probability f of occupancy of an energy state ℰ by an electron is given by the formula

Here, ℰ_F is the Fermi level, which is the energy separating preferentially filled levels (f > ½) from preferentially vacant levels (f < ½).

If the Fermi level lies in the energy gap at a distance >kT from the bottom of the conduction band and from the top of the valence band, then in the conduction band f ≪ 1—that is, there are few electrons—and in the valence band 1 — f ≪ 1—that is, there are few holes. In this case, we say that the electrons and holes are nondegenerate. In the case of degeneracy, on the other hand, the Fermi level lies within one of the allowed bands, for example, in the conduction band at a distance ≫ kT from its bottom. This means that all the states in the band from the bottom to the Fermi level are filled with charge carriers with a probability f(ℰ) ~ 1.

The position of the Fermi level depends on the temperature and the doping. Within the bulk of a three-dimensional homogeneous semiconductor, the position is determined by the condition of conservation of the total number of electrons, that is, by the condition of electric neutrality:

Here, is the concentration of ionized donors and is the concentration of acceptors that have captured an electron.

In heavily doped semiconductors, the carrier concentration remains constant and equal to (N_d — N_a) at all temperatures up to the intrinsic conduction region, where such semiconductors do not differ from other semiconductors, as is shown by curve 2 in Figure 5. At low temperatures, the carriers in heavily doped semiconductors are degenerate, and such semiconductors should formally be classified as poor metals. Indeed, they display a number of metallic properties, such as superconductivity (SrTiO³, GeTe, SnTe) at very low temperatures.

Nonequilibrium charge carriers. An important characteristic of semiconductors is that the carrier concentrations in a semiconductor can be varied relatively easily with respect to the equilibrium values—that is, additional, nonequilibrium (excess) electrons and holes can be introduced. This characteristic determines many of the applications of semiconductors. Excess carriers can be produced by illumination, irradiation with a beam of fast particles, the application of a strong electric field, or, finally, injection through contacts with another semiconductor or metal.

Photoconductivity. The photoconductivity of a semiconductor is the increase in the semiconductor’s electrical conductivity under the action of light. It is generally caused by the appearance of additional nonequilibrium carriers as a result of the absorption by electrons of photons with an energy exceeding the electrons’ binding energy. A distinction is made between intrinsic and extrinsic photoconductivity. In the former case, a photon is absorbed by a valence electron with the result that an electron-hole pair is produced. It is apparent that such a process can occur on exposure to light with a wavelength corresponding to the intrinsic absorption region of the semiconductor: ℏω ≥ Δℰ Electron-hole pairs may also be created by photons with an energy slightly smaller than AS since there can occur processes in which an electron, on absorbing a photon, acquires additional energy from the thermal motion of the crystal lattice or from an equilibrium charge carrier. For example, the energy ℏω is sufficient to create an exciton, which subsequently, as a result of thermal motion, decays into a free electron and a free hole. Photoconductivity arises under the action of light of considerably longer wavelengths only in the presence of impurities that create local levels in the energy gap. Such photoconductivity is associated with the transition of an electron either from a local level to the conduction band or from the valence band to a local impurity level (hole production).

The phenomenon of photoconductivity permits the electrical conductivity of a semiconductor to be varied over a broad range in a short time, which may be of the order of microseconds or nanoseconds. It also permits high charge-carrier concentrations to be produced in semiconductors in which, because of a relatively large Δℰ and the absence of appropriate impurities, appreciable equilibrium concentrations of carriers cannot be obtained. The use of the photoconductivity of semiconductors with different AS and different depths of impurity levels—such as Si, Te, InSb, PbS, CdS, PbTe, Ge, and doped Zn or Au—makes possible the construction of highly sensitive light detectors for various regions of the spectrum from the far infrared to the visible.

Passage of fast particles through semiconductors. When a fast particle passes through a semiconductor, a considerable portion of the particle’s energy (approximately 30 percent) is expended on the production of electron-hole pairs whose number is thus of the order of the ratio of Δℰ. to the particle’s energy. For particles with energies ranging from 10 keV to 10 MeV, this ratio is ~ 10⁴—10⁷. This phenomenon can be made use of to count and measure the energy of fast particles.

Recombination; trapping of free carriers by impurities or defects. Recombination is any process that causes the transition of an electron from a conduction band to a valence band with the filling of some hole state and thus results in the disappearance of the electron and the hole as carriers. The transition of an electron from the conduction band to a state localized near an impurity or defect is called the trapping, or capture, of the electron. The trapping of a hole means the transition of an electron from an impurity level to a state unoccupied by electrons in the valence band. At thermodynamic equilibrium, the thermal production of carriers and the ionization of donors and acceptors balance the processes of recombination and trapping. The relation between the rates of these mutually inverse processes yields the Fermi energy distribution for electrons.

If nonequilibrium carriers appear in the semiconductor, the number of recombination and trapping events increases. When the external action ceases, recombination occurs more rapidly than production. Thus, the carrier concentration begins to decrease and approaches its equilibrium value. The average time that nonequilibrium carriers exist is called the lifetime τ of the carriers. It is inversely proportional to the rate of recombination or trapping by impurities. The lifetime of carriers in semiconductors ranges from 10^-3 to 10^–10 sec. Even in the same semiconductor the values of τ may vary by several orders of magnitude as a function of temperature, impurity or defect concentration, and the nonequilibrium-carrier concentration.

Recombination and capture always mean the transition of a carrier to lower energy levels (to the valence band or the energy gap). Different mechanisms of recombination differ in where and how the energy released in such a transition is transferred. In particular, the energy may be radiated as a photon. Such radiative recombination is observed in any semiconductor. The total number of radiative-recombination events per second is proportional to the product np, and, for small carrier concentrations, this recombination mechanism is not very effective. At high concentrations (~10¹⁷ cm^-3), however, some semiconductors become efficient light sources in a narrow range of wavelengths close to λ_max and we speak of recombination radiation. The width of the spectrum, ~kT, is due to the energy difference of the recombining carriers and is much smaller than the average energy of the photons. By using different semiconductors, it is possible to create light sources of virtually any wavelength in the visible and near-infrared regions of the spectrum. For example, if the GaP content in the alloy GaAs-GaP is varied from 0 to 100 percent, the visible spectrum can be covered from the red through the green regions inclusively.

If the concentration of nonequilibrium carriers is so high that degeneracy sets in—that is, if the probability of occupancy of each state near the edge of the corresponding band by a carrier is greater than ½—then an inverse population of energy levels is possible. When this occurs, the higher levels at the bottom of the conduction band are filled with electrons to a greater extent than are the lower levels at the upper edge of the valence band. The induced radiation of photons then exceeds the absorption of photons, and the amplification and generation of light may result. The operation of the semiconductor laser is based on this principle.

In nonradiative recombination the energy released is ultimately converted into thermal energy of the crystal. When the carrier concentrations are not high, the most important mechanism of nonradiative recombination is recombination through intermediate states in the energy gap that are localized around impurities or defects. First, one of the carriers is captured by an impurity, whose charge is thereby increased or decreased by unity. The same impurity then captures an oppositely charged carrier. As a result, both captured carriers disappear, and the impurity center returns to its initial state. If the concentration of nonequilibrium carriers is small compared with the equilibrium concentration of majority carriers, the lifetime is determined by the rate of capture of minority carriers, which are holes in n-type semiconductors and electrons in p-type semiconductors. The minority carriers are used here because they are far fewer in number than the majority carriers, and the time required for one of them to strike an impurity center is the longest part of the recombination process. Capable of acting as recombination centers are many impurities, such as Cu in Ge, and defects that have levels lying deep in the energy gap and that effectively trap electrons from the conduction band in one charge state and holes from the valence state in the other. Not all impurities and defects have this property. Some can effectively capture only one carrier. When the temperature is not loo low, they throw the carrier back into the band from which it was captured before they trap a carrier of opposite charge. Such impurities and defects are called traps, or trapping centers. They can considerably lengthen the lifetime of nonequilibrium carriers. The reason for this is that if, for example, all nonequilibrium minority carriers are captured by traps, the excess majority carriers have nothing with which to recombine, and other impurities acting as recombination centers prove ineffective.

Surface recombination has the same mechanism as recombination at impurities, but the centers through which recombination proceeds are associated with the surface of the crystal rather than with impurities. Auger recombination is another mechanism of nonradiative recombination that should be mentioned. In this process, when an electron and a hole recombine, they give the released energy ~Δℰ to a third carrier. This process is significant only for very high concentrations of free carriers, since it requires the collision of three carriers—that is, the simultaneous entrance of these carriers into a region whose size is of the order of the unit cell of the crystal.

Electrical conductivity of semiconductors. If a semiconductor is placed in an electric field, the field causes drift, or the directed motion of carriers, which produces a current flow in the semiconductor. The concept of carrier mobility is basic for a range of problems connected with the transmission of an electric current in a semiconductor. The mobility μ is defined as the ratio of the drift velocity v_d—that is, the average velocity of the carriers’ directed motion caused by an electric field—to the strength E of the field:

(11) μ = v_d/E

The mobilities of different types of carriers in the same semiconductor are different, and the mobilities of each type of carrier for different field directions are different in anisotropic semiconductors. The drift velocity that arises in an electric field is added to the velocity of the random thermal motion, which does not contribute to the current. In a given field, a carrier has a constant drift velocity v_d and does not accelerate indefinitely because of the presence of retardation processes due to scattering. In an ideal crystal, even in the absence of a field, every carrier would have a definite velocity v_d that would be invariant in both magnitude and direction. Impurities and various structural defects, however, exist in a real crystal. Each time a carrier collides with them, it undergoes a change in the direction of its velocity—that is, it is scattered. As a result, the carrier’s motion becomes random. Under the action of a field, a carrier is effectively accelerated only up to the moment of the next collision. When it is scattered, it loses energy and its direction of motion. Acceleration in the direction of the field E then begins anew and continues until the next collision. Thus, the average velocity of the carrier’s directed motion is acquired only over the time interval Δt between two successive collisions, which is called the mean free time. This average velocity is equal to v̄_d = eEΔt/m. It follows that

(12) μ = eΔt/m

The processes of carrier scattering are diverse. The most general process for all substances is scattering by lattice vibrations (phonons), which cause displacements of the crystal’s atoms from the atoms’ equilibrium positions in the lattice and thereby also disrupt the ordering of the lattice. When a carrier emits or absorbs phonons, it undergoes a change in quasimomentum and, consequently, velocity—that is, it is scattered. The average collision frequency 1/Δt depends on the nature of the crystal, the intensity and type of the crystal’s vibrations, the content of impurities and defects in the crystal, and the energy of the carriers. Therefore, μ is temperature-dependent. At temperatures T ~ 300°K, the dominant type of scattering is generally scattering by phonons. With decreasing temperature, however, the probability of this process decreases, since the intensity of thermal lattice vibrations is reduced. Moreover, because of their low thermal energy, the carriers are not able to emit every type of phonon possible in the given crystal; they can emit only the small proportion of phonons that have sufficiently small energies (frequencies). Under these conditions, scattering by charged impurities or defects becomes dominant for not very pure crystals. The probability of such scattering increases with decreasing carrier energy. In heavily doped semiconductors the scattering of charge carriers by each other can apparently play an important role.

Mobility varies over a broad range in different semiconductors. For example, the range extends from 10⁵ to 10^–3 cm²/sec or less at T = 300°K. Mobilities of 10⁵ to 10² cm²/sec, which are higher than in good metals, are characteristic of semiconductors of the first three groups listed above. Thus, at T = 300°K in Ge, μ^e = 4 × 10³ cm²/sec for electrons and μ^h = 2 × 10³ cm²/sec for holes; in InSb, μ^e = 7 × 10⁴ cm²/sec and μ^h = 10³ cm²/sec. These values of μ correspond to Δ t ~ 10^-12–10^–13 sec. The corresponding mean free paths l = vΔ t, where v is the velocity of thermal motion, are hundreds or thousands of times greater than the interatomic distances in the crystal.

The concept of free carrier motion interrupted only rarely by scattering events is, however, applicable solely to semiconductors where μ, is not too small—that is, where μ > 1 cm²/sec. For a lower mobility, l becomes smaller than the dimensions of the unit cell of the crystal (~ 10^-8 cm) and loses meaning since the very concept of the “free” motion of carriers in a crystal is connected with the passage of the carriers from cell to cell (within each cell an electron moves as in an atom or molecule). Such small values of μ are characteristic of many chemical compounds of the transition and rare-earth metals with group VI elements and also of most organic semiconductors. The strong interaction of carriers with local deformations of the crystal lattice is, apparently, responsible for this situation. When a carrier localized in a unit cell strongly interacts with the atoms forming this cell and the neighboring cells, the atoms are displaced by it from the positions they occupy when no carrier is present. The energy of a carrier in such a deformed cell (a polaron) is lower than in neighboring undeformed cells, and the passage of the carrier to a neighboring cell requires the expenditure of energy, which the carrier can obtain from some thermal fluctuation. When the carrier crosses over to a neighboring cell, the cell abandoned by it returns to the undeformed state, and the cell to which it moves is deformed. Its subsequent passage to a third cell, therefore, will again require an activation energy. This mechanism of motion is called the hopping mechanism and contrasts with the band mechanism considered above, which is associated with the free motion of carriers in allowed bands and does not require the expenditure of energy for passage from cell to cell. In the hopping mechanism, such concepts of the band theory of solids as quasi-momentum, effective mass, mean free time, and mean free path are meaningless. The concept of average drift velocity under the action of a field and the concept of mobility remain valid, although they are no longer described by formula (12).

The hopping mechanism of electrical conduction is characteristic of many amorphous and liquid semiconductors. Carriers with energies in the region of the pseudo-forbidden band move from a state localized near one fluctuation to a state localized near another through such activated jumps. They move in this way because the energies of the states near different fluctuations differ, since the fluctuations themselves are random in both location and magnitude. In semiconductors with high mobility, hopping conduction is sometimes observed at low temperatures (if the overwhelming majority of carriers are localized at impurities, the carriers can jump from impurity to impurity). Transfer phenomena in low-mobility semiconductors remain less well understood than are transfer phenomena in semiconductors with the band mechanism of conduction.

Carrier diffusion. Connected with the concept of mobility is the concept of the diffusion coefficient D of carriers whose random motion in the absence of a field creates a tendency toward uniform distribution of the carriers within the semiconductor— that is, toward the equalization of the carrier concentrations. If a semiconductor specimen contains regions of increased and reduced concentrations, the carriers “overflow” since the number of particles leaving any region as a result of random motion is proportional to the number of particles located in the region, and the number of incoming particles is proportional to the number of particles in neighboring regions. The diffusion fluxes j_d that equalize the concentrations n are proportional to the intensity of the thermal motion and to the drop in concentrations and are in the direction of decreasing concentration:

(13) j_d = –D grad n

This equation defines the concept of the diffusion coefficient D. The connection between D and the mobility μ, is given by the Einstein relation, which is universal if the charge carriers are not degenerate:

(14) D = kTμ/e

This equation reflects in particular the relation of diffusion to the intensity of the thermal motion.

The diffusion length l_D is an important characteristic of nonequilibrium carriers. It is the distance the carriers traverse by diffusion in their lifetime τ:

The magnitude of l_D may vary. It reaches 0.1 cm in intrinsic semiconductors with high mobility, such as Ge at 300°K.

Galvanomagnetic phenomena, Galvanomagnetic effects in semiconductors are phenomena associated with the influence of a magnetic field on current flow. A magnetic field H perpendicular to an electric field E deflects drifting carriers in a transverse direction. These carriers accumulate on a side face of the specimen so that the transverse electric field generated by them compensates the deflecting action of the magnetic field. This phenomenon is called the Hall effect. The ratio of the induced transverse field to the product of the current density and the magnetic field is called the Hall constant. In the simplest case of carriers of one type with an isotropic effective mass and a mean free time independent of energy, the Hall constant is equal to 1/nec—that is, it determines directly the carrier concentration n. Magneto resistance is absent in this case, since the Hall electromotive force completely counterbalances the Lorentz force.

Galvanomagnetic phenomena are much more complicated in semiconductors than in metals for several reasons. Semiconductors contain two types of carriers. Indeed, there may be more than two types: for example, heavy holes, light holes, and electrons. Moreover, the mean free times of carriers in a semiconductor are substantially dependent on energy, and the carriers’ effective masses are anisotropic. Since the electrons and holes drift in opposite directions, the magnetic field deflects them in one direction. Their charges and the induced field are therefore partially compensated depending on the ratio of their concentrations and mobilities. If the relaxation time is energy-dependent, the drift velocity and the contribution of carriers of different energies to the total current are not the same. The effects of the magnetic and the induced transverse electric fields compensate each other only on the average. They do not compensate for every carrier, since the Lorentz force is proportional to the velocity, and the electric force is independent of the velocity— that is, the twisting action of the magnetic field decreases, as it were, the mean free path of the faster drifting particles and thus reduces the current. Because of the anisotropy of their effective masses, the carriers move in the direction of the field, and the whole picture of their deflection by the magnetic field is altered.

The study of galvanomagnetic effects in semiconductors provides much informaton on carrier concentrations, the structure of the energy bands of semiconductors, and the nature of scattering processes.

Thermoelectric phenomena. The possibility of making use of thermoelectric phenomena in semiconductors is promising for the direct conversion of thermal energy into electrical energy and for cooling. With semiconductor thermocouples it is possible to obtain a conversion efficiency of ~10 percent or cooling to 230°K. The values of the thermoelectromotive force and the Peltier coefficient in semiconductors are several orders of magnitude greater than in metals. The reason for these large values is the relative smallness of the carrier concentration. When an electron moves from the bottom of the conduction band ℰ_c to the Fermi level ℰ_f of a metal in contact with a given semiconductor, it releases the energy, called Peltier heat, Π = ℰ_c — ℰ_F. When the electron undergoes the reverse transition it absorbs this energy. From the thermodynamic viewpoint, ℰ_F is the chemical potential of the electron, and it therefore must be the same on both sides of the contact. In a semiconductor, the value of Π = ℰ_c — ℰ_F in the extrinsic conduction region is determined by the condition n_Π = N_d — N_a. When the impurity concentration is not too high, Π may be large (Π = ℰ_c — ℰ_F ≫ kT) and increase relatively rapidly with temperature. This situation ensures large values of Π and the thermoelectromotive force a, which is related to Π by the equation Π = kT.

In metals, ℰ_F lies deep in the allowed band, and, because of the very strong degeneracy, only electrons with energies very close to ℰ_F participate in current transfer. The average change in the energy of an electron on passing through a contact between two metals is therefore very small: Π ~ kT.

Contact phenomena; the p-n junction. Semiconductor-metal or semiconductor-semiconductor contacts sometimes have rectifying properties —that is, they pass a current much more efficiently in one direction than in the opposite direction. These properties arise because the concentration or even the type of charge carriers changes in the contact region—that is, there is formed a space charge that provides the contact potential difference necessary for equalizing (in the state of equilibrium) the Fermi levels on both sides of the contact. In contrast to metals, in semiconductors this region is broad enough to ensure the necessary potential drop when the carrier concentration is small. If the sign of the contact potential difference is such that the carrier concentration in the contact region becomes smaller than in the bulk of the semiconductor, then the contact layer determines the electrical resistance of the entire system. If an external potential difference is added to the contact potential, it further reduces the number of carriers in the contact region; if, on the other hand, the external potential is of opposite sign, it increases the carrier concentration. Thus, the resistance of the contact is quite different for currents in the forward and reverse directions. This fact accounts for the rectifying properties of the contact (the Schottky barrier).

Such contacts were the first semiconductor devices and were used in rectifiers and detectors. The development of semiconductor electronics, however, began only after p-n junctions had been created. Such junctions are contacts between semiconducting regions with different types of conduction within a single semiconductor crystal. The contact potential difference in this case is close to the width of the energy gap, since ℰ_F lies near the bottom of the conduction band ℰ_c in the n-region and near the top of the valence band E_r in the p-region. An external potential difference, which reduces the contact potential, causes diffusion flows of electrons into the p-region and of holes into the n-region. This phenomenon is known as the injection of minority carriers). A p-n junction passes virtually no current in the reverse direction, since both types of carriers are drawn away from the junction region. In semiconductors with a large diffusion length, such as Ge and Si, excess carriers injected by one p-n junction may reach another nearby p-n junction and substantially determine the current across it. The current across a p-n junction can be varied by creating excess carriers near it in some other manner, for example, by illumination. Of these two possibilities for controlling the current of a p-n junction, the first, carrier injection, is the physical basis for the action of the transistor, and the second, the photoelectromotive force, is the basis for solar batteries.

Hot carriers; nonlinear phenomena in semiconductors. The concentration and average energy of free carriers in semiconductors are relatively small as compared with metals. Moreover, the mean free paths of free carriers are long. As a result not only the concentrations but also the energy distribution of charge carriers in the corresponding band can be varied comparatively easily over a wide range by various external factors. Besides the carrier energy, other characteristics also change, such as effective mass, mean free time, and mobility.

The most important factor is the action of strong electric fields capable of changing the carrier distribution with respect to energies and concentration. Fields of ~ 100–1,000 volts per centimeter (V/cm), and sometimes even weaker fields, are often sufficient for this purpose. When an electron is scattered by impurities and in the process completely loses its directionality of motion with respect to the field, it does not give up energy at all; when it emits phonons, it gives up only a small fraction of its energy: δ ≪ 1. Therefore, when the energy eEl, acquired by the carrier through acceleration by the field E over the mean free path l, becomes so great that eEl > kT, then the electron is no longer capable of completely giving up its energy for excitation of lattice vibrations, and its mean energy begins to increase. It is significant that the energy of random motion increases because of the random change of velocity when scattering occurs, whereas the velocity of directed motion remains, as before, relatively small. In such a case we speak of carriers. Moreover, because of the rise in the number of collisions with phonons, as the carrier energy increases the increase in V_D may slowed down with increasing field strength and may subsequently stop altogether. As a result, the heating of current carriers by the field leads to deviations from Ohm’s law. The nature of these deviations differs greatly for different semiconductors and even for the same semiconductor, depending on such factors as temperature, the presence of specific impurities, and the presence of a magnetic field (Figure 6). Semiconductors with nonlinear characteristics find wide application in various devices of semiconductor electronics.

Figure 6. Various types of nonlinear dependences of current density j = env_D on electric field strength E in semiconductors: (a) saturable, (b) N-shaped, (c) S-shaped

If the drift velocity in some region of the field decreases with the growth of the field E, then uniform current distribution throughout the specimen for fields stronger than some critical field is unstable. In place of uniform current distribution there spontaneously arise regions, or domains moving in the direction of the current. The field is many times stronger in these domains than in the rest of the specimen, and the carrier concentration also differs greatly from its average value for the specimen. The passage of domains is accompanied by strong periodic oscillations of the current. Under such conditions, the semiconductor is a generator of electrical oscillations, which are sometimes of extremely high frequency (~10¹¹ hertz). This phenomenon, which is connected with an N-shaped characteristic for the semiconductor (Figure 6, b), is called the Gunn effect and is observed in n-type GaAs and some A^IIIB^V compounds. The reason for this effect is that electrons located at the T-minimum of the conduction band, where their effective mass is small, acquire under the action of the field an energy sufficiently large (—0.35 eV) for a transition to theΔ-minimum, where their effective mass is much larger. As a result, their drift velocity decreases.

In semiconductors with piezoelectric properties (A^IIIB^V, A^II-B^VI, Te), where elastic waves in the crystal lattice are accompanied by the appearance of an electric field that increases their interaction with carriers, analogous nonlinear effects also appear because of the deviation from an equilibrium distribution of phonons. In these substances, the carrier flux becomes an intense radiator of elastic waves when the carrier drift velocity exceeds the speed of sound. The electric potential of an elastic wave of sufficiently large amplitude traps the carriers—that is, it forces the carriers to collect in regions where the potential has a minimum—so that the carriers move with the wave. If the drift velocity of a carrier cluster exceeds the wave velocity, then the wave slows the carriers with its field; it takes energy from the carriers and is therefore itself amplified. As a result, on reaching the speed of sound the drift velocity ceases to increase with the field, and all further expenditures of the energy of the external field go into the amplification of elastic waves. In this regime, piezoelectric semiconductors are used to amplify and generate ultrasound.

Deviations from Ohm’s law, including the characteristics illustrated in Figure 6, can be caused not only by a nonlinear dependence of v_D on E but also by a change in the carrier concentration under the action of the electric field. Such a change, for example, can result from a change in the rate of trapping of carriers by some impurities under the conditions of induction heating. The most widespread mechanism of variation of carrier concentration in a strong field is impact ionization. In impact ionization, when hot carriers that have acquired an energy greater than the width of the semiconductor’s energy gap collide with valence-band electrons, they eject the electrons into the conduction band and thereby produce new electron-hole pairs.

In a sufficiently strong field, the excess carriers produced by impact ionization can also produce new pairs in their lifetime, and the process of the rise in carrier concentration then takes on an avalanche character—that is, breakdown occurs. In contrast to dielectric breakdown, the breakdown of semiconductors is not accompanied by fracture of the crystal. The reason for this is that the breakdown fields for a semiconductor with an energy-gap widthΔℰ ~ 1–1.5 eV are relatively small: ≲ 10⁵ V/cm. In InSb they are ≲ 250 V/cm. A type of breakdown peculiar to semiconductors is associated with the impact ionization of impurities that have a small ionization energy; this type of breakdown occurs at low temperatures in fields of ~1–10 V/cm.

An electric field can also transfer a valence electron directly into the conduction band—that is, it can produce electron-hole pairs. This effect is quantum mechanical in nature and is connected with the tunnel effect—that is, the penetration of the electron under the action of an external field through the energy gap. It is usually observed only in extremely strong fields: the wider the energy gap, the stronger the field. Such fields, however, are realized in many semiconductor devices, and in many cases the tunnel effect determines the characteristics of the devices.

Most widely used experimental methods of investigating semiconductors. The width of the energy gapΔℰ, like the position of higher allowed bands, can be determined from light absorption or reflection spectra. Optical techniques are especially effective when combined with the effects, for example, of an electric field or deformations of the crystal, in this case they are known as modulation techniques. The minimum width of the energy gap can also be determined from the temperature dependence of the intrinsic conductivity or from the position of the red limit of the intrinsic photoconductivity. The most complete and accurate information on effective masses is given by investigations of cyclotron resonance and magneto-optical effects. For semiconductors in which these techniques cannot be employed because of, for example, low carrier mobility, the mass and density of states can be estimated from the magnitude of the thermoelectromotive force. In some cases, investigations of galvanomagnetic effects in strong magnetic fields are effective, especially in degenerate semiconductors, where various quantum oscillations of the same type as in the Shubnikov-De Haas effect are observed. The Hall effect is the basis of the principal method of measuring the carrier concentration and determining the sign of carriers in the case of extrinsic conduction. The sign of the carriers can also be determined from the direction of the thermoelectromotive force. When combined with conductivity measurements, the Hall effect also permits estimates of carrier mobility. The position of impurity levels in the energy gap is determined from the red limit of the photoconductivity or, more often, from the temperature dependence of the extrinsic conductivity. Photoconductivity and injection from contacts are used to determine the lifetime and diffusion length of excess carriers.

L. V. KELDYSH

Historical survey. Semiconductors as a separate class of materials were known by the end of the 19th century. Not until the development of quantum theory, however, could the characteristics of dielectrics, semiconductors, and metals be understood; a crucial role here was played by the British physicist A. H. Wilson (1931). Such important semiconductor characteristics as current rectification at a metal-semiconductor contact and photoconductivity had been observed, and the first devices based on them built, long before then. O. V. Losev demonstrated the possibility of using semiconductor contacts to amplify and generate oscillations in crystal detectors. In subsequent years, however, crystal detectors were supplanted by electron tubes. Not until the early 1950’s, after the discovery of the transistor effect by Bardeen, Brattain, and Shockley of the USA in 1948, did the extensive use of semiconductors, chiefly Ge and Si, in electronics begin. The intensive study of semiconductor physics began at the same time. It was stimulated by advances in the technology of crystal purification and doping. Interest in the optical properties of semiconductors increased when induced radiation in GaAs was discovered by D. N. Nasledov, A. A. Rogachev, S. M. Ryvkin, and B. V. Tsarenkov of the USSR in 1962. This led to the creation of semiconductor lasers. There first appeared p-n junction lasers, which resulted from the work of the American physicist Hall and such Soviet physicists as B. M. Vul and A. P. Shotov. Heterojunction lasers followed; they were a result of work by such physicists as Zh. I. Alferov.

Extensive research on semiconductors began in the USSR as early as the late 1920’s under the direction of A. F. Ioffe at the Physicotechnical Institute of the Academy of Sciences of the USSR. Many of the basic theoretical concepts of semiconductor physics were first formulated by, among others, la. I. Frenkel’, I. E. Tamm, B. I. Davydov, E. F. Gross, V. A. Zhuze, V. E. Lashkarev, and V. M. Tuchkevich. These scientists also made an important contribution to the study and application of semiconductors.

REFERENCES

Ioffe, A. F. Fizika poluprovodnikov. Moscow-Leningrad, 1957.
Shockley, W. Teoriia elektronnykh poluprovodnikov. Moscow, 1953. (Translated from English.)
Smith, R. Poluprovodniki. Moscow, 1962. (Translated from English.)
Poluprovodniki. Collection of articles edited by N. B. Hannay. Moscow, 1962. (Translated from English.)
Ansel’m, A. I. Vvedenie v teoriiu poluprovodnikov. Moscow-Leningrad, 1962.
Blatt, F. Fizika elektronnoi provodimosti v tverdykh telakh. Moscow, 1971, (Translated from English.)
Stil’bans, L. S. Fizika poluprovodnikov, Moscow, 1967.
Pikus, G. E. Osnovy teorii poluprovodnikovykh priborov. Moscow, 1965.
Gutman, F. and L. Lyons. Organicheskie poluprovodniki. Moscow, 1970. (Translated from English.)
Ostin, I., and D. Iluell. “Magnitnye poluprovodniki.” Uspekhi fizicheskikh nauk, 1972, vol. 106, issue 2.
Alekseev, A. A., A. A. Andreev, and V. Ia. Prokhorenko. “Elektricheskie svoistva zhidkikh metallov i poluprovodnikov.”
Uspekhi fizicheskikh nauk, 1972, vol. 106, issue 3.

semiconductor

[¦sem·i·kən¦dək·tər] (solid-state physics) A solid crystalline material whose electrical conductivity is intermediate between that of a conductor and an insulator, ranging from about 10⁵ mhos to 10^-7 mho per meter, and is usually strongly temperature-dependent.

Semiconductor

A solid crystalline material whose electrical conductivity is intermediate between that of a metal and an insulator. Semiconductors exhibit conduction properties that may be temperature-dependent, permitting their use as thermistors (temperature-dependent resistors), or voltage-dependent, as in varistors. By making suitable contacts to a semiconductor or by making the material suitably inhomogeneous, electrical rectification and amplification can be obtained. Semiconductor devices, rectifiers, and transistors have replaced vacuum tubes almost completely in low-power electronics, making it possible to save volume and power consumption by orders of magnitude. In the form of integrated circuits, they are vital for complicated systems. The optical properties of a semiconductor are important for the understanding and the application of the material. Photodiodes, photoconductive detectors of radiation, injection lasers, light-emitting diodes, solar-energy conversion cells, and so forth are examples of the wide variety of optoelectronic devices. See Integrated circuits, Laser, Light-emitting diode, Photoelectric devices, Semiconductor rectifier, Thermistor, Transistor, Varistor

Conduction in semiconductors

At absolute zero temperature, the electrons occupy the lowest possible energy levels, with the restriction that at most two electrons with opposite spin may be in the same energy level. In semiconductors and insulators, there are just enough electrons to fill completely a number of energy bands, leaving the rest of the energy bands empty. The highest filled energy band is called the valence band. The next higher band, which is empty at absolute zero temperature, is called the conduction band. The conduction band is separated from the valence band by an energy gap, which is an important characteristic of the semiconductor. In metals, the highest energy band that is occupied by the electrons is only partially filled. This condition exists either because the number of electrons is not just right to fill an integral number of energy bands or because the highest occupied energy band overlaps the next higher band without an intervening energy gap. The electrons in a partially filled band may acquire a small amount of energy from an applied electric field by going to the higher levels in the same band. The electrons are accelerated in a direction opposite to the field and thereby constitute an electric current. In semiconductors and insulators, the electrons are found only in completely filled bands, at low temperatures. In order to increase the energy of the electrons, it is necessary to raise electrons from the valence band to the conduction band across the energy gap. The electric fields normally encountered are not large enough to accomplish this with appreciable probability. At sufficiently high temperatures, depending on the magnitude of the energy gap, a significant number of valence electrons gain enough energy thermally to be raised to the conduction band. These electrons in an unfilled band can easily participate in conduction. Furthermore, there is now a corresponding number of vacancies in the electron population of the valence band. These vacancies, or holes as they are called, have the effect of carriers of positive charge, by means of which the valence band makes a contribution to the conduction of the crystal.

Intrinsic semiconductors

Extrinsic semiconductors

Semiconductor material “doped” or “poisoned” by valence +3 acceptor impurities is termed p‐type, whereas material doped by valence +5 donor material is termed n-type. The names are derived from the fact that the holes introduced are considered to carry positive charges and the electrons negative charges. The number of electrons in the energy bands of the crystal is increased by the presence of donor impurities and decreased by the presence of acceptor impurities.

Materials

Rectification in semiconductors

Surface electronics

semiconductor

1. a substance, such as germanium or silicon, that has an electrical conductivity that increases with temperature and is intermediate between that of a metal and an insulator The behaviour may be exhibited by the pure substance (intrinsic semiconductor) or as a result of impurities (extrinsic semiconductor) 2. a. a device, such as a transistor or integrated circuit, that depends on the properties of such a substance b. (as modifier): a semiconductor diode

semiconductor

(electronics)A material, typically crystaline, which allowscurrent to flow under certain circumstances. Commonsemiconductors are silicon, germanium, gallium arsenide.Semiconductors are used to make diodes, transistors andother basic "solid state" electronic components.

As crystals of these materials are grown, they are "doped"with traces of other elements called donors or acceptorsto make regions which are n- or p-type respectively for theelectron model or p- or n-type under the hole model.Where n and p type regions adjoin, a junction is formed whichwill pass current in one direction (from p to n) but not theother, giving a diode.

One model of semiconductor behaviour describes the dopingelements as having either free electrons or holes danglingat the points in the crystal lattice where the doping elementsreplace one of the atoms of the foundation material. Whenexternal electrons are applied to n-type material (whichalready has free electrons present) the repulsive force oflike charges causes the free electrons to migrate toward thejunction, where they are attracted to the holes in the p-typematerial. Thus the junction conducts current.

In contrast, when external electrons are applied to p-typematerial, the attraction of unlike charges causes the holes tomigrate away from the junction and toward the source ofexternal electrons. The junction thus becomes "depleted" ofits charge carriers and is non-conducting.

semiconductor

A solid state material that can be electrically altered. Certain elements in nature, such as silicon, perform like semiconductors when chemically combined with other elements. Various optical materials can also change their state (see phase change disc).

When electricity or light is applied to semiconductors, they change their state between conductive and non-conductive or reflective and non-reflective. The most significant semiconductor is the transistor, which in digital circuits works like an on/off switch. For analog applications, it may be an on/off switch as well, but is more likely used as an amplifier, taking in a low-voltage signal and outputting a higher voltage. See n-type silicon, doping, transistor concept and chip.

Like an On/Off Switch

In most types of transistors, the semiconductor material normally acts as an insulator. When it is pulsed with electricity, it becomes electrically conductive for that moment and acts like an electrical bridge.

semiconductor

sem·i·con·duc·tor

semiconductor

sem•i•con•duc•tor

sem·i·con·duc·tor

semiconductor

semiconductor

semiconductor,

Semiconductor

Conduction in semiconductors

Intrinsic semiconductors

Extrinsic semiconductors

Materials

Rectification in semiconductors

Surface electronics

Semiconductor

REFERENCES

semiconductor

Semiconductor

Conduction in semiconductors

Intrinsic semiconductors

Extrinsic semiconductors

Materials

Rectification in semiconductors

Surface electronics

semiconductor

semiconductor

semiconductor

semiconductor

sem·i·con·duc·tor

sem·i·con·duc·tor

Semiconductor

Semiconductor

semiconductor

Synonyms for semiconductor

noun a substance as germanium or silicon whose electrical conductivity is intermediate between that of a metal and an insulator

Synonyms

Related Words

noun a conductor made with semiconducting material

Synonyms

Related Words