Galvanomagnetic effects in semiconductors

Galvanomagnetic effects in semiconductors are called such phenomena that occur when a semiconductor is simultaneously exposed to electric and magnetic fields.

All galvanomagnetic effects are divided into transverse (the action of electric and magnetic fields is found on the faces of the semiconductor, parallel to the electric and magnetic fields) and longitudinal (manifested along the sample).

The transverse effects include the Hall and Ettingshausen effects, while the parallel ones include the change in the resistance of the sample in a magnetic field and the Nernst effect (longitudinal temperature difference).

Consider only the Hall effect. If a semiconductor, along which an electric current flows, is placed in a magnetic field perpendicular to

direction of the current, then a transverse electric field will appear in the semiconductor, perpendicular to the current and the magnetic field. This phenomenon is called the Hall effect, and the resulting transverse EMF is called the Hall EMF.

On fig. 8.8 shows an n-type semiconductor plate. The electric field E is directed parallel to the Z axis, and the magnetic

the field H is along the Y axis. An electron moving in a magnetic field is affected by the Lorentz force, which deflects it in a direction perpendicular to the direction of the magnetic field. As a result, electrons will accumulate at one of the ends of the sample. On the opposite face, a positive uncompensated charge will be created due to the ions of the donor impurity. Such an accumulation of charges will occur until the action of the electric field that has arisen as a result of such a process balances the Lorentz force acting on the electron. The equilibrium condition for the force acting on an electron in scalar form can be written as

where Vn is the average speed of the directed motion of an electron;

B is the magnetic induction in the sample; Ex is the strength of the resulting transverse electric field.

Assuming that the transverse electric field is uniform, we obtain

(8.23)

where a is the plate width; Ux – Hall EMF. It is also known that j = sigma E or

(8.24)

where j u003d I (ab) is the density of the current flowing in the sample under the action of an external electric field E.

Using (8.24), from (8.22) we obtain

(8.25)

The Rx value is called the Hall coefficient and is determined

as

(8.26)

The Hall emf in an n-type semiconductor can be determined by the formula

The minus sign reflects the fact that charge carriers in this semiconductor are electrons. For p -type semiconductors, a similar expression is obtained, only the concentration n will be replaced by p and the direction of the transverse electric field will be opposite, i.e., the Hall emf will be positive. This circumstance is used to determine the type of electrical conductivity of semiconductors.

If we express the current in A, the magnetic field strength in A / m, the Hall voltage in V, the sample thickness in cm, then the Hall coefficient is (cm 3 /k)

Thus, by measuring the Hall potential difference Ux at a known current I, magnetic field strength H , and sample thickness b , we calculate Rx. Further, if the Hall coefficient Px and electrical conductivity are known, it is easy to calculate the concentration of charge carriers and the value of mobility.

The Hall effect is interesting not only as a method for determining the characteristics of semiconductor materials, but also as the principle of operation of a number of semiconductor devices that have found technical application.

6. Electron-hole transition (p-n- transition)

The main structural element of most types of semiconductor devices is an electrical transition layer – a transition layer in a semiconductor material between two regions with different types of electrical conductivity or different values

specific electrical conductivity, and one of the regions may be a metal.

An electrical transition between two regions of a semiconductor. one of which has a p-type electrical conductivity, and the other –

n-type, called an electron-hole transition or pn-transition.

It is impossible to create a p-n junction by mechanically connecting two semiconductors with different types of electrical conductivity; electron-hole junctions are obtained by introducing donor and acceptor impurities into the semiconductor in such a way that one part of the semiconductor has electronic and the other has hole electrical conductivity.

Let us consider two separately taken regions of electronic and hole semiconductors shown in Figs. 8.9, a. The main charge carriers in an n-type semiconductor are electrons (marked with a minus sign in Fig. 8.9, o), and holes in a p-type semiconductor (in Fig. 8.9, a , marked with a plus sign). The ionized atoms of the donor and acceptor impurities are denoted by plus and minus signs in circles, respectively. Minority carriers in electron and hole semiconductors are not indicated, since their concentration is very low in comparison with the concentration of majority carriers.

We will conditionally assume that the p- and p-semiconductors are brought into perfect contact (Fig. 8.9. b). Since there are many electrons in the n-semiconductor, and there are many holes in the p -semiconductor, an intensive exchange of charge carriers will begin between the semiconductors. Due to the difference in concentrations, electrons from the n-type semiconductor diffuse into the p-type semiconductor, leaving an uncompensated positive charge of donor impurity ions in the near-contact region of the n-type semiconductor. holes, in turn,

diffuse into the n-type semiconductor, as a result of which a negative charge of acceptor impurity ions appears in the near-contact layer of the p-type semiconductor. Thus, the interface between n- and p-type semiconductors will be depleted of free charge carriers and, despite the small width d = 10 -6 – 10 -8 m, will have a high resistance, many times greater than the resistance of the rest of the semiconductors. The presence of negative and positive space charges leads to the formation of an electric field, which prevents further diffusion flow of charge carriers. The system comes to an equilibrium state under the condition that the flows of free charge carriers caused by the gradient of their concentrations and the dielectric field of the space charge are equal. Now consider what happens if an external voltage is applied to the p -n junction. Let a positive power pole be attached to the p-region, and a negative power pole to the n-region. Such an external field will be directed towards the electric field due to space charges. In this case, the majority charge carriers in p- and n-semiconductors, which have the highest energy, are able to penetrate through the depleted layer into the region where they turn out to be minority charge carriers and recombine. Such a directed movement of charge carriers is an electric current, and it can be said that an electron-hole junction with such a polarity of the external voltage will be “opened” and a direct current will flow through it.

When the polarity of the external voltage is reversed, the electric field of space charges and the external field will coincide in direction. As a result of the action of the total electric field, the majority carriers will move away from the junction and only minority carriers will be able to cross the junction. Since the number of minor carriers is many times less than the main ones, the current due to them will also be small compared to that which will be obtained with direct connection. With this inclusion, the electron-hole transition is “locked” and only a small reverse current of minority carriers can flow through it.

On fig. 8.10 shows the relationship between the current flowing through the p-n junction and the external voltage, which is called the current-voltage characteristic. The current-voltage characteristic of the pn junction is described by the following expression:

I = Is (e qU/(kT) –1) (8.29)

where Is is the saturation current (when the pn junction is turned on again, this current is equal to the reverse current); U is the applied voltage;

q/(kT) = 40 V -1 at room temperature.

Simple semiconductors

a) Germanium. Germanium is one of the most carefully studied semiconductors, and many of the phenomena characteristic of semiconductors were first observed experimentally on this material.

The existence and basic properties of germanium were predicted by D. I. Mendeleev in 1870, calling it ekasilicium. In 1886, the German chemist K. Winkler discovered a new element in mineral raw materials, which he called germanium. Germanium proved to be equivalent to exasilicon. The content of germanium in the earth’s crust is small, but it occurs naturally in many parts of the world. Germanium is isolated from germanium-containing ore most often as a result of chemical processing of raw materials using concentrated HCL in the form of germanium tetrachloride GeCL 4 . Germanium tetrachloride is a volatile liquid that is subjected to deep purification using extraction and rectification methods. After purification of GeCl 4 , it is hydrolyzed with water, resulting in germanium dioxide GeO 2 – a white powder. After drying, GeO 2 is reduced in a stream of purified hydrogen at a temperature of 650 ° C to elemental germanium, which is a gray powder. The germanium thus reduced is etched in a mixture of acids and fused into ingots. Ingots are used as a starting material for the production of high-purity germanium by zone melting or the direct production of single crystals by melt pulling.

The essence of the zone melting method is that. that a narrow molten zone moves along a horizontally located sample located in a graphite or quartz boat. Impurities present in the sample are pushed to the end of the ingot. For high-quality cleaning, the whole process is repeated many times or more advanced installations are used, which make it possible to create simultaneously four or five melted zones along the ingot.

To obtain a single crystal by the melt pulling method, germanium thoroughly purified from impurities is melted in an installation, the scheme of which is shown in Fig. 8.11. The working volume is a hermetic water-cooled chamber, inside which a vacuum of the order of 10 -4 Pa is created, or a protective gaseous medium (from hydrogen or high purity argon). The material (M) is placed in a crucible (A) mounted on the end of a water-cooled rod (B-1). Rod B-1 is driven by an electric drive at a strictly constant speed. Also, it can be dropped

or raise to select the optimal position of the crucible with the melt in relation to the heating element B. As a heating element, a resistance furnace or a high-frequency induction heating source is usually used. Through the upper flange of the chamber, coaxially with the lower rod B-1, the upper rod B-2 is inserted, at the lower end of which a single-crystal seed of the material to be crystallized is attached. The seed is introduced into the melt and kept in it until the surface melts. When this happens, the seed, rotating, begin to slowly raise. Behind the seed is a liquid column of melt held by surface tension. Getting into the area of low temperatures above the surface of the crucible, the melt solidifies, forming one whole with the seed. This method currently produces germanium single crystals with a diameter of up to 100 mm, and sometimes more.

Pure germanium has a metallic luster and is characterized by relatively high hardness and brittleness. It crystallizes in the structure of diamond, melts at a temperature of 937 ° C, the density at 25 ° C is 5.33 g / cm 3 . In the solid state germanium is a typical covalent crystal. Crystalline germanium

chemically stable in air at room temperature. Powdered germanium, when heated in air to a temperature of about 700 ° C, easily forms germanium dioxide GeO 2 . Germanium is slightly soluble in water and practically insoluble in hydrochloric and dilute sulfuric acid. The active solvents of germanium under normal conditions are a mixture of nitric and hydrofluoric acids and a solution of hydrogen peroxide. When heated, germanium reacts intensively with halogens, sulfur and sulfate compounds.

The main physical properties of germanium, silicon and selenium are given in Table. 8.1.

The temperature dependences of the resistivity of germanium at different donor impurity contents are shown in Figs. 8.12. Germanium, used in semiconductor devices, has a resistivity from millionths of an ohm-m to values close to the resistivity of its own germanium

The electrical properties of germanium are strongly influenced by heat treatment. So, if an n-type sample is heated to a temperature above 550 ° C, and then abruptly cooled (quenched), then the type of electrical conductivity will change. A similar heat treatment of p-type germanium leads to a decrease in resistivity, without changing the type of electrical conductivity. Annealing of hardened samples at a temperature of 500-550°C restores not only the type of electrical conductivity, but also the original resistivity. If germanium is melted, then its resistivity becomes close to the resistivity of liquid metals, such as mercury (pw = 6.5 10 -7 Ohm). An example of marking germanium is GDG 075/05, where the first letter indicates the name of the material (G – germanium), the second is the type of electrical conductivity (E – electronic, D – hole), the third is the name of the dopant (in this case, gallium). The numerator of the fraction indicates the value of the resistivity (0.75 Ωcm), the denominator indicates the diffusion length of the minority charge carriers (0.5 mm).

Germanium is used for the manufacture of various types of diodes, transistors, Hall EMF sensors, strain gauges. The optical properties of germanium allow it to be used for the manufacture of photodiodes and phototransistors, light modulators, optical filters, and nuclear particle counters. The operating temperature range of germanium devices is from -60 to +70 °C.

B) Silicon. In contrast to germanium, silicon is one of the most abundant elements in the earth’s crust; its content in it is about 29%. However, it does not occur in a free state in nature, but is present only in compounds in the form of an oxide and in salts of silicic acids. The purity of natural silicon oxide in the form of quartz single crystals sometimes reaches 99.9%; in a number of deposits, the purity of sand reaches 99.8–99.9%.

Technical silicon, obtained by the reduction of natural dioxide Si0 2 (silica) in an electric arc between graphite electrodes, is widely used in ferrous metallurgy as an alloying element (for example, transformer steel) and as a deoxidizer in steel production. Technical silicon is a fine-crystalline sinter containing about 1% impurities, and cannot be used as a semiconductor. It is the feedstock for the production of silicon of semiconductor purity, the content of impurities in which should be less than 10 -6 %.

The technology for obtaining silicon of semiconductor purity includes the following operations:

I) the transformation of technical silicon into a highly volatile compound, which, after purification, can be easily restored; 2) purification of the compound by physical and chemical methods; 3) restoration of the compound with the release of pure silicon; 4) final purification of silicon by the method of crucible-free zone melting; 5) growth of single crystals.

In semiconductor production, the method of hydrogen reduction of trichlorosilane SiHCI 3 is most widely used. It is obtained by processing crushed technical silicon with dry hydrogen chloride at a temperature of 300 – 400 0 С:

Si-3HCI u003d SiHCI 3 + H 2 ;.

Trichlorosilane is a liquid with a boiling point of 32 0 C. Therefore, it is easily purified by extraction, adsorption and rectification methods.

Unlike germanium, the main purification of silicon from impurities is carried out by chemical methods. Crystallization methods are aimed at converting chemically obtained semi-crystalline silicon into single crystals with certain electrophysical properties. Bulk silicon crystals are grown by melt growth and crucibleless vertical zone melting. The first method is used, as a rule, to obtain large single crystals with a relatively low resistivity (< 2.5 Ohm). The second method is used to obtain high-resistance silicon single crystals with a low content of residual impurities. It should be noted that in terms of technology, silicon is a more complex material than germanium, since it has a high melting point of 1412 °C and is chemically very active in the molten state (reacts with almost all crucible materials).

The melt-stretching method has been previously described. A significant disadvantage of this method when used to grow silicon single crystals is the contamination of the crystals with oxygen. The source of oxygen is a quartz crucible, which interacts with the melt in accordance with the reaction

SiO 2 ( tv ) + Si ( l ) – 2SiO.

The dissolution of quartz into silicon not only leads to saturation with oxygen, but also other impurities are introduced that contaminate silicon.

Vertical crucibleless zone melting provides purification of silicon crystals from impurities and the possibility of growing silicon single crystals with a low oxygen content. In this method, a narrow molten zone is held between the solid parts of the ingot due to surface tension forces. The melting of the ingots is carried out using a high-frequency inductor (Fig. 8.13) operating at a frequency of 5 MHz. High-frequency heating makes it possible to carry out the process of crucible-free zone melting in vacuum and in a protective atmosphere.

Silicon crystals with a diameter of up to 100 mm are currently obtained by the method of vertical crucibleless melting. Silicon crystals of n- and ,0-types are obtained by introducing appropriate impurities during growth, among which phosphorus and boron are most often used. Such crystals of electronic and hole silicon are labeled KEF and KDB, respectively.

The main physical properties of silicon are presented in Table. 8.1. The conductivity of silicon, like germanium, varies greatly with the presence of impurities. On fig. 8.14 shows the dependences of the resistivity of silicon and germanium on the concentration of impurities. Due to the wider band gap, the intrinsic resistivity of silicon is more than three orders of magnitude greater than that of germanium.

C) silicon carbide. It is the only binary compound formed by semiconductor elements of group IV of the periodic table. This is a semiconductor material with a large band gap of 2.8–3.1 eV (depending on modifications). Silicon carbide is used for the manufacture of semiconductor devices operating at high temperatures up to 700 °C.

Technical silicon carbide is produced in electric furnaces by reducing silicon dioxide (quartz sand) with carbon:

SiO 2 + 3C – SiC + 2CO.

Intergrown packages of SiC crystals, called druses, form in the furnace. Most of the crystals in druse are small, but there are crystals with an area of up to 1.5-2 cm 2 . Silicon carbide powder is obtained from druse by crushing. Silicon carbide crystals of semiconductor purity are obtained by sublimation in furnaces with graphite heaters and screens. The crystallization process is carried out in an argon atmosphere at a temperature of 2400-2600 °C. The resulting crystals usually have a lamellar shape with a diameter of about 1 cm. Silicon carbide is one of the hardest substances, it is resistant to oxidation up to temperatures above 1400 ° C. At room temperature, silicon carbide does not interact with any acids. When heated, it dissolves in alkali melts, and also interacts with phosphoric acid and a mixture (HNO 3 + HF).

The electrical conductivity of SiC crystals at normal temperature is impurity. The type of electrical conductivity and the color of silicon carbide crystals depend on foreign impurities or are determined by an excess of Si or C atoms over the stoichiometric composition. Pure silicon carbide of stoichiometric composition is colorless. Impurities of elements of group V (N, P, As, Sb, Bi) and iron in carbide give a green color and electrical conductivity / r-type, elements of groups II (Ca, Mg) and III groups (B, Al, Ga, In) – blue and violet coloration and p-type electrical conductivity. An excess of Si leads to electronic electrical conductivity of SiC, and an excess of C leads to hole conductivity.

D) Binary compounds. Among binary compounds, compounds A III B V , A II B VI , A IV B IV .

Semiconductor compounds A III B V , are the closest analogs of silicon and germanium. They are formed as a result of the interaction of elements III-6 of the subgroup of the periodic table (boron, aluminum, gallium, indium) with elements of the V-6 subgroup (nitrogen, phosphorus, arsenic, antimony). Compounds A III B V , it is customary to classify according to the metalloid element. Accordingly, nitrides, phosphides, arsenides and antimonides are distinguished. These compounds are obtained either from a melt that contains elements in equal atomic concentrations, or from a solution of a compound that has an excess of Group III elements, and also from the gas phase. Crystals of antimonides, gallium and indium arsenides are usually grown from a melt by drawing on a seed from an inert flux. A layer of liquid transparent flux under pressure of an inert gas provides complete sealing of the crucible and suppresses the evaporation of a volatile component from the melt. The single crystals obtained from the melt have insufficiently high chemical purity. For purification, the same methods are used as for the purification of germanium and silicon.

Some parameters of the considered compounds are given in table. 8.2.

Gallium arsenide among compounds A PI B V occupies a special position. Large band gap (1.4 eV). high electron mobility [0.85 m 2 /Vs)! make it possible to create on its basis devices operating at high temperatures and high frequencies. The first semiconductor was GaAs, on which an injection laser was created in 1962. It is used to make LEDs, tunnel diodes, Gaip diodes, transistors, solar cells and other devices. For the manufacture of detectors in the infrared region of the spectrum, Hall sensors, thermoelectric generators, strain gauges, indium anti-monide is used, which has a very small band gap (0.17 eV) and a very high electron mobility – 7.7 m 2 / (Vs). Gallium phosphide, which has a large band gap (2.25 eV), has found wide application in the mass production of LEDs. Unlike other compounds of group A III B V , gallium antimonide has an extremely high sensitivity to mechanical stresses. The specific resistance of GaSb doubles when exposed to a pressure of 4-10 8 Pa. At the same pressure applied to GaAs and InP crystals, their resistivity changes by only 3%. Due to its high sensitivity to deformations, gallium antimonide is used in the manufacture of strain gauges.

Semiconductor compounds A II B VI include zinc , cadmium and mercury chalcogenides. Among them, sulfides, selenides and tellurides can be distinguished.

The main physical properties of these compounds are listed in Table. 8.3.

Table 8.3

The technology for growing single crystals of A II B V I compounds has been developed much less fully than the technology for semiconductors of the A III B V type . melting. The growth of such materials in most cases is carried out by recrystallization of a preliminarily synthesized compound through the vapor phase in sealed quartz ampoules. A II B VI compounds are used in most cases to create industrial phosphors, photoresistors, highly sensitive Hall sensors and far infrared radiation receivers.

Among semiconductor compounds of type A IV B V I the most studied are lead chalcogenides: PbS. PbSe, PbTe. Lead sulfide, selenide, and telluride naturally occur as the minerals galena, claustalite, and altaite. The first mineral is one of the most common ores of lead, the other two are found quite rarely in nature. Single crystals of PbS, PbSe, PbTe are obtained mainly by vapor deposition, by melt growth or by slow cooling of the melt using the natural temperature gradient of the furnace. The main physical properties of lead chalcogenides are given in Table. 8.4.

Table 8.4

From Table. 8.4 shows that these compounds are narrow-gap semiconductors. Lead chalcogenides are used to manufacture photoresistors in infrared technology, infrared lasers, strain gauges, and thermogenerators operating in the temperature range from room temperature to 600°C.

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