Semiconductor devices. Lebedev A.I. Physics of semiconductor devices. Current-voltage characteristic of the transistor

All solids, in accordance with their electrical properties, can be divided into metals, semiconductors and dielectrics. Resistivity (p) of various solids varies within very wide limits: for metals p< 10 -4 Ом см, для полупроводников р - 10~ 4 -Ю 10 Ом*см, для диэлектриков р >10 ohm cm. These differences in p values are due to the peculiarities of the energy structure for different types of crystalline solids. The structures of the energy states of semiconductors and dielectrics (Fig. 1.1) are not fundamentally different from each other; all differences are due only to the difference in the band gap (A E e): in semiconductors usually AE 3^ 3 eV, and in dielectrics AE 3 > 3 eV.

Greatest application in electronic devices found semiconductor materials, which are divided into own(pure, unadulterated) and impurities. Both in intrinsic and impurity semiconductors (energy

Rice. 1.1

diagrams of the latter are shown in Fig. 1.2) there are two types of free charge carriers - electrons And holes. Free charge carriers Such carriers are called whose kinetic energy is greater than their potential binding energy with atoms. The concentration of free carriers is determined by two opposing processes - their generation And recombination. The generation of charge carriers, i.e., the formation of free electrons and holes, is carried out when a semiconductor is exposed to thermal energy, light, ionizing radiation, beams of charged particles and other energy factors. Under thermodynamic equilibrium conditions (at temperatures T > O K) there is always thermal generation of carriers, the intensity of which increases with increasing temperature. In the intrinsic semiconductor, electron-hole pairs are formed during the generation process.

On the energy diagram of an intrinsic semiconductor (see Fig. 1.1), this process is illustrated by arrow 1, which shows the transition of an electron from the valence band, the upper limit of which corresponds to the energy E in y to the conduction band (E p- her bottom line). In the valence band, when an electron moves to the conduction band, a hole remains. (Let us denote the concentration of electrons and holes feast respectively.) Thus, in a state of equilibrium in the intrinsic semiconductor p = p = p 17 i.e.

Where n 1- equilibrium concentration of free charge carriers in the intrinsic semiconductor at a given temperature.

In a state of equilibrium, the processes of generation of electron-hole pairs in the intrinsic semiconductor are balanced

Rice. 1.2

military recombination processes. Equilibrium concentrations of electrons and holes for an intrinsic semiconductor with a band gap &E. L can be calculated according to the following expression:

Where N p = 2(2k in t p kT/k 2) 3/2, LH B = 2(2k t r kT /K 2) 312 - effective densities of energy states in the conduction band and valence band, respectively; w p And t r- effective masses of electrons and holes; To= 1.38 10 23 J/K - Boltzmann constant; To~ 6.6 10~ 34 J s - Planck's constant; T- temperature in degrees Kelvin (K).

In expression (1.2), the exponential factor causes a sharp increase in the concentration of free charge carriers with increasing temperature T or reducing the band gap D E 3. The effect of the band gap on the concentration of carriers in intrinsic semiconductors can be illustrated using the example of silicon (81) and gallium arsenide (GaAb), which are most widely used in semiconductor technology: when T= 300 K AE 3= 1.12 eV for B1 and AE 3= 1.42 eV for CaAb, and the concentration of intrinsic carriers, respectively, is 1.4 10 10 and 1.8 * 10 6 cm“ 3. This example shows that a difference in band gap of only 1.27 times leads to a change in carrier concentration by four orders of magnitude.

Impurity semiconductors can be donor, acceptor And compensated. In donor semiconductors, or in n-type semiconductors(they contain a pentavalent donor impurity, such as phosphorus or arsenic for silicon), electronic conductivity predominates. This means that the concentration of free electrons p p0 y which in in this case are called main carriers, in an equilibrium state at not too high temperatures T(such that £!G <&. E 3) is many orders of magnitude higher than the concentration of its own carriers l 1 and holes p l0, which in this case are non-major media.

At not too high temperatures, the overwhelming number of electrons in an l-type semiconductor arises due to thermal ionization of donor atoms; As a result, donor atoms turn into positively charged ions, and electrons removed from them become free charge carriers.

In Fig. 1.2, A this process is illustrated by an arrow and corresponds to the transition of an electron from the donor level E l into the conduction zone. Level E d is formed by donor impurity atoms in the band gap. Energy difference A E l = E i - E d equal to the ionization energy of donors. Due to the low ionization energy (hundredths of an electron volt or less) at room temperature (G = 300 K; CT= 0.026 eV) almost all donor atoms are ionized and the concentration of majority carriers (electrons in this case) is equal to the donor concentration n n0~ DO D, and the concentration of minority carriers (holes) is determined law of mass action p p0 p p0 = p, and is equal to

In a state of equilibrium in impurity semiconductors, as well as in intrinsic semiconductors, the processes of generation and recombination of free carriers occur simultaneously. As a result, equilibrium concentrations of electrons and holes are established. Using expressions (1.2) and (1.3), the concentration of minority carriers (holes) in the donor semiconductor in the equilibrium state can be determined by the following formula:

When an acceptor impurity with a concentration of /Va is introduced into a semiconductor n 1= p 4 hole conductivity will predominate in it. Such a semiconductor is called holey or p-type semiconductor. Holes in this case arise due to the ionization of acceptor atoms, i.e., as a result of the addition of electrons to them that arise when bonds are broken in the atoms of the own semiconductor.

On the energy diagram (see Fig. 1.2, b) the described process corresponds to the transition of an electron from the valence band to the acceptor level E a, located in the band gap near the ceiling E in valence band. As a result, free levels are formed in the valence band, and the acceptor atom turns into a negative ion. Similar to a donor semiconductor, in an acceptor semiconductor, due to the low ionization energy at room temperature, almost all acceptor atoms are ionized and the concentration of the majority carriers p/R) (in this case, holes) is equal to the concentration of acceptors 7V a, i.e. r r O" N a. Equilibrium

concentration of minority carriers - electrons Prts- let us determine from a relation similar to formula (1.3)

Taking (1.2) into account, it leads to an expression “symmetrical” to formula (1.4):

In semiconductor devices, the concentration of LGD donors and acceptors varies widely from 10 13 to 10 21 cm -3. At a high concentration of impurity atoms, due to the strong interaction between them, impurity levels ( E l or E a) are split into sublevels, as a result of which an impurity band is formed, which, at concentrations of 7U a, 7U D more than 10 20 cm~ 3, overlaps with the conduction band for donor semiconductors and with the valence band for acceptor semiconductors. When impurity levels overlap with the conduction band or valence band, the ionization energy of the impurity decreases to zero and a partially filled band appears. As in metals, in this case in semiconductors conductivity exists even at T= O K. Such semiconductors are called degenerate.

In real conditions, semiconductors usually contain both donor and acceptor impurities. If N d > ./U a, the result is an l-type semiconductor, and with LG a > # d - a p-type semiconductor. In the first case, the effective concentration of donors is important N d- LG a, and in the second case, the effective concentration of LG acceptors a - A^ d. When LG a = LG D, the semiconductor is called compensated. The concentration of free carriers in it is the same as in the native semiconductor.

Atoms of some impurities can form energy levels in the band gap at a considerable distance from E p And E p; such atoms are called traps. Energy levels corresponding to donor traps are located above the middle of the band gap, and acceptor levels are located below. A donor trap is neutral if its corresponding energy level is filled (occupied by an electron), and turns into a positive ion if the level is empty. Acceptor traps are neutral at the free level and negatively charged ( negative ions) when filling it out.

Temperature dependence of the concentration of free charge carriers. The carrier concentration in impurity semiconductors, as well as in intrinsic semiconductors, depends significantly on temperature. Let us consider the temperature dependence of the electron concentration in silicon using the example of an i-type semiconductor (Fig. 1.3). Three areas can be distinguished on it. At low temperatures(region 1) with increasing temperature, the concentration of free electrons (i ~ p p) increases as the number of ionized donors increases. Dependence of electron concentration on 1 /T is determined by an exponential function of the form exp [-AE A /(2kT)]> therefore, on a semi-logarithmic scale it is depicted by a straight line, the slope of which is proportional to the ionization energy of donors D E d, In area 2 almost all donors are ionized, and the concentration of intrinsic electrons n i is insignificant, therefore, with increasing temperature, the total number of free electrons changes insignificantly, and their concentration can be considered equal to the donor concentration: i ~ p p0 ~ N.. In the high temperature region (region 3) intense ionization of the semiconductor's own atoms occurs, so that the concentration of intrinsic carriers becomes greater than the concentration of the main impurity carriers,

Rice. 1.3

i.e. n 1 > n n0~ ^U d. In the region under consideration, the carrier concentration is determined by the dependence n ~ n 1 ~ exp(-D £ 3 /(2/rm which on a semi-logarithmic scale is depicted by a straight line with a slope angle p, and tg p is proportional to the band gap &E y

An increase in the concentration of impurities leads not only to an increase in the concentration of majority carriers, but also to a proportional decrease in the concentration of minority carriers, in accordance with expressions (1.3) and (1.5), which is associated with an increase in the probability of their recombination, proportional to the product of the noted concentrations.

Majority semiconductor devices works normally in the temperature range corresponding to the area 2 in Fig. 1.3. Maximum temperature in this region Tmax is approximately determined from the condition yy, = N d(for l-type semiconductor). It is proportional to the band gap and increases with increasing impurity concentration (see Fig. 1.3, curves a, b).

The concentration of minority carriers in region 2, in contrast to the concentration of majority carriers, increases strongly with increasing temperature according to expressions (1.4) and (1.6), respectively, for an electronic semiconductor (where holes are minority carriers) and for a hole semiconductor (minority carriers are electrons). Instrument parameters, which depend on the concentration of minority carriers, will also change with temperature even in the region of complete ionization of impurities (region 2 in Fig. 1.3), and maximum working temperature such devices may be noticeably lower than the temperature determined by the conditions n 1= AG D or n 1 =(For electron or hole semiconductors).

Fermi level. Free carriers in a solid fill energy states with significantly different probabilities. According to quantum statistics, the probability of an electron filling an energy level with energy E determined Fermi-Dirac function G(E)> which is calculated according to the following formula:

Where E f- energy corresponding to the Fermi level. In any equilibrium system, no matter how heterogeneous it may be, the Fermi level is the same for all its parts. As calculations show, in an intrinsic semiconductor at t p V t r The Fermi level lies in the middle of the band gap E f = E f = 0,5(E p 4- E p). IN non-degenerate l-type semiconductor (L^n " P l.) Fermi level E f is located closer to the conduction band, and in a non-degenerate p-type semiconductor the Fermi level E f located closer to the valence band. At room temperature (Г® 300 K) it lies, as a rule, below the level of donors and above the level of acceptors for semiconductors P- and p-type, respectively. If in impurity semiconductors the Fermi level lies in the band gap at a distance of at least (2 G)/^^ from its corresponding

boundaries, then the concentrations of electrons and holes will be equal:

With increasing temperature in an impurity semiconductor (at t p " 25 ™ p) The Fermi level approaches the middle of the band gap, since in this case the intrinsic conductivity begins to dominate over the impurity one. The dependence of the Fermi level position on temperature for silicon with different concentrations of donor and acceptor impurities is shown in Fig. 1.4, where E = E f - E i.

Rice. 1.4

If i = A^n or p = A^b (degenerate semiconductor), i.e., the concentration of carriers is commensurate with the concentration of allowed states, then, due to the Pauli principle, electrons cannot arbitrarily occupy energy levels. The Fermi level in this case lies either in the band gap at a distance of less than (2...3) from its boundaries, or in the conduction band for an r-semiconductor or in the valence band for a p-semiconductor. For highly degenerate semiconductors, the position of the Fermi level, as well as the concentration of majority carriers, do not depend on temperature.

2. Semiconductors. Semiconductor devices

2.1. General information

Semiconductors are substances whose conductivity is intermediate between the conductivities of metals and dielectrics. Semiconductors are both poor conductors and poor dielectrics. The boundary between semiconductors and dielectrics is arbitrary, since dielectrics at high temperatures can behave like semiconductors, and pure semiconductors at low temperatures behave like dielectrics. In metals, the electron concentration is practically independent of temperature, and in semiconductors, charge carriers appear only when the temperature increases or when energy is absorbed from another source.

Typical semiconductors are carbon (C), germanium (Ge), and silicon (Si). Germanium is a brittle, grayish-white element discovered in 1886. The source of powdered germanium dioxide, from which solid pure germanium is obtained, is the ash of certain types of coal.

Silicon was discovered in 1823. It is widely distributed in the earth's crust in the form of silica (silicon dioxide), silicates and aluminosilicates. Sand, quartz, agate and flint are rich in silicon dioxide. Pure silicon is obtained from silicon dioxide chemically. Silicon is the most widely used semiconductor material.

Let us consider in more detail the formation of conduction electrons in semiconductors using silicon as an example. The silicon atom has the serial number Z=14 in the periodic table of D.I. Mendeleev. Therefore, its atom contains 14 electrons. However, only 4 of them are on empty outer shell and are weakly coupled. These electrons are called valence electrons and give rise to the four valences of silicon. Silicon atoms are able to combine their valence electrons with other silicon atoms using what is called a covalent bond (Figure 2.1). In covalent bonding, valence electrons are shared between different atoms, resulting in the formation of a crystal.

As the temperature of the crystal increases, thermal vibrations of the lattice lead to the breaking of some valence bonds. As a result of this, some of the electrons that previously participated in the formation of valence bonds are split off and become conduction electrons. In the presence of an electric field, they move against the field and form electricity.

However, when an electron is released in the crystal lattice, an unfilled interatomic bond is formed. Such “empty” spaces with missing bonding electrons are called “holes.” The appearance of holes in a semiconductor crystal creates additional opportunity for charge transfer. Indeed, the hole can be filled by an electron transferred under the influence of thermal vibrations from a neighboring atom. As a result, normal communication will be restored in this place, but a hole will appear in another place. Any of the other bond electrons, etc., can in turn go into this new hole. The sequential filling of a free bond with electrons is equivalent to the movement of a hole in the direction opposite to the movement of electrons. Thus, if in the presence of an electric field electrons move against the field, then holes will move in the direction of the field, i.e. the way positive charges would move. Consequently, in a semiconductor there are two types of current carriers - electrons and holes, and the total conductivity of the semiconductor is the sum of electronic conductivity (n-type, from the word negative) and hole conductivity (p-type, from the word positive).

Along with transitions of electrons from a bound state to a free state, there are reverse transitions in which a conduction electron is captured in one of the vacant positions of bond electrons. This process is called electron-hole recombination. In a state of equilibrium, such a concentration of electrons (and an equal concentration of holes) is established at which the number of straight lines and reverse transitions per unit time is the same.

The considered conduction process in pure semiconductors is called intrinsic conductivity. Intrinsic conductivity increases rapidly with increasing temperature, and this is a significant difference between semiconductors and metals, whose conductivity decreases with increasing temperature. All semiconductor materials have a negative temperature coefficient resistance.

Pure semiconductors are an object of mainly theoretical interest. Major semiconductor research concerns the effects of adding impurities to pure materials. Without these impurities, most semiconductor devices would not exist.

Pure semiconductor materials such as germanium and silicon are kept at room temperature a small amount of electron-hole pairs and can therefore conduct very little current. Alloying is used to increase the conductivity of pure materials.

Doping is the addition of impurities to semiconductor materials. Two types of impurities are used. Impurities of the first type - pentavalent - consist of atoms with five valence electrons, for example, arsenic and antimony. The second type of impurity - trivalent - consists of atoms with three valence electrons, for example, indium and gallium.

When a pure semiconductor material is doped with a pentavalent material such as arsenic (As), some of the semiconductor atoms are replaced by arsenic atoms (Figure 2.2). The arsenic atom introduces four of its valence electrons into covalent bonds with neighboring atoms. Its fifth electron is weakly bound to the nucleus and can easily become free. The arsenic atom is called a donor atom because it donates its extra electron. The doped semiconductor material contains a sufficient number of donor atoms, and therefore free electrons, to maintain the current.

At room temperature, the number of additional free electrons exceeds the number of electron-hole pairs. This means that the material has more electrons than holes. Therefore, electrons are called majority carriers. Holes are called minority carriers. Since majority carriers have a negative charge, such a material is called an n-type semiconductor.

When a semiconductor material is doped with trivalent atoms, such as indium (In) atoms, these atoms will place their three valence electrons among three neighboring atoms (Figure 2.3). This will create a hole in the covalent bond.

The presence of additional holes will allow electrons to easily drift from one covalent bond to another. Since holes easily accept electrons, atoms that introduce additional holes into a semiconductor are called acceptor atoms.

Under normal conditions, the number of holes in such a material significantly exceeds the number of electrons. Therefore, holes are the majority carriers and electrons are minority carriers. Because the majority carriers have a positive charge, the material is called a p-type semiconductor.

N- and p-type semiconductor materials have significantly higher conductivity than pure semiconductors. This conductivity can be increased or decreased by changing the amount of impurities. The more heavily doped a semiconductor material is, the less electrical resistance.

Contact of two semiconductors with different types conductivity is called a p-n junction and has a very important property– its resistance depends on the direction of the current. Note that such a contact cannot be achieved by pressing two semiconductors against each other. A p-n junction is created in one semiconductor wafer by forming regions with different types of conductivity in it. Methods for obtaining p-n junctions are described below.

So, in a piece of a single-crystal semiconductor, a p-n junction is formed at the boundary between two layers with different conductivities. There is a significant difference in the concentrations of charge carriers. The concentration of electrons in the n-region is many times greater than their concentration in the p-region. As a result, electrons diffuse into the region of their low concentration (in the p-region). Here they recombine with holes and in this way create a spatial negative charge of the ionized acceptor atoms, which is not compensated by the positive charge of the holes.

At the same time, diffusion of holes into the n-region occurs. Here, a spatial positive charge of the donor ions, which is not compensated by the electron charge, is created. Thus, a double layer of space charge is created at the boundary (Fig. 2.4), depleted of the main current carriers. A contact electric field Ek arises in this layer, preventing the further transition of electrons and holes from one region to another.

The contact field maintains a state of equilibrium at a certain level. But even in this case, under the influence of heat small part electrons and holes will continue to pass through the potential barrier caused by space charges, creating a diffusion current. However, at the same time, under the influence of the contact field, minority charge carriers of the p- and n-regions (electrons and holes) create a small conduction current. In a state of equilibrium, these currents cancel each other out.

If you connect to the p-n junction external source current, then the voltage indicated in Fig. 2.5 Reverse polarity will cause external field E, coinciding in direction with the contact field Eк. As a result, the width of the double layer will increase, and there will be practically no current due to the majority carriers. Only a small current is possible in the circuit due to minority carriers (reverse current Irev).

When the voltage of direct polarity is turned on, the direction of the external field is opposite to the direction of the contact field (Fig. 2.6). The width of the double layer will decrease, and a large forward current Ipr will arise in the circuit. Thus, the pn junction has pronounced one-way conductivity. This is expressed by its current-voltage characteristic (Fig. 2.7).

When applied to the p-n junction forward voltage, then the current increases rapidly with increasing voltage. When a reverse voltage is applied to the p-n junction, the current is very small, quickly reaches saturation and does not change up to a certain limiting value of the reverse voltage Urev, after which it increases sharply. This is the so-called breakdown voltage at which breakdown occurs p-n junction and it collapses. It should be noted that in Figure 2.7 the scale reverse current a thousand times smaller scale direct current.

The basic semiconductor devices of modern microelectronics and physical processes that ensure their work. The static, frequency and impulse characteristics of devices are analyzed, methods of circuit modeling of devices are considered and their equivalent circuits. The limiting parameters of modern microelectronic devices are considered. For each device it is done short review modern methods their structural implementation in integrated circuits Oh. For students studying in the direction 210100 "Electronics and microelectronics" (210100.62 - bachelor, 210100.68 - master) and in engineering specialties 210104.65 "Microelectronics and solid-state electronics", 210108.65 "Microsystem technology", 010803.65 "Microelectronics and semiconductor nic devices", 210601.65 "Nanotechnologies in electronics." The material in the book can also be useful to scientists, engineers and graduate students seeking to gain the necessary professional knowledge

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NEW. Kireev P.S. Physics of semiconductors. 2nd ed. 1975 586 pp. PDF. 34.3 MB.
The book examines elements of the electronic theory of conductivity and semiconductor conductivity; band theory based on perturbation theory; statistics of electrons and holes; kinetic phenomena in semiconductors; scattering theory, contact and nonequilibrium phenomena based on the continuity equation; theories of optical and photoelectric phenomena in semiconductors.
The first edition of Semiconductor Physics, published in 1969, quickly sold out. Wide use books in educational process and specialists in practical work showed the feasibility of a second edition of the manual. Since in the years that have passed since the publication of the first edition, there have been no fundamental changes in our ideas about physical phenomena in semiconductors, the material has not been subjected to significant processing. The main changes are related to additions that either reveal greater possibilities of mathematical relationships for the analysis of physical phenomena, or highlight the physical content of the conclusions obtained. The number of examples of experimental dependencies has been significantly increased. Two new paragraphs have been added that discuss the Faraday effect and spin-orbit splitting of energy levels and bands.

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Aut I., Gentsov D., German K. Photoelectric phenomena. 1980 210 pp. djvu. 3.0 MB.
The book briefly and at the same time clearly sets out the fundamentals of the theory of photoelectric phenomena in semiconductors. The properties of the most important semiconductor materials and photovoltaic semiconductor circuit elements are also described.
Designed for scientists, engineers and students interested in the physics of semiconductors and their issues practical application.

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Anselm. Introduction to the theory of semiconductors. 615 pp. djvu. Size 7.6 MB.
The main attention in the book is paid to the issues of vibrations of the crystal lattice, the laws of electron motion in ideal and perturbed periodic fields, the kinetic equation and transfer phenomena (current passage). To read the book, familiarity with mathematics, quantum mechanics and statistical physics is required in the scope of the programs of the physics department of a university or the physics and mathematics department of a polytechnic institute.
It is not necessary to have a detailed knowledge of these courses, but it is assumed that the reader is able to understand the relevant paragraphs of the educational books if reference is made to them. The peculiarity of the book is that, on the basis of these simple knowledge, all formulas are derived and, as I hope, in sufficient detail to make it accessible to the above circle of people.

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B.M. Askerov, Electronic transfer phenomena in semiconductors. 1985 320 pp. PDF. 6.1 MB.
Dedicated to a systematic and detailed presentation linear theory stationary electronic transfer phenomena in semiconductors. Both classical and quantum theories of galvanic and thermomagnetic effects are presented. Various real band models are considered: arbitrary isotropic and anisotropic nonparabolic bands, as well as a hole germanium type band. The entrainment of current carriers by phonons in an arbitrary non-quantizing magnetic field is taken into account. Great place occupied by the theory of carrier scattering. A separate chapter is devoted to size effects in films.
For scientists, engineers and graduate students involved in semiconductor research, as well as senior students in physics and engineering physics.