Semiconductors are materials that, under normal conditions, are insulators, but with increasing temperature become conductors. That is, in semiconductors, as the temperature increases, the resistance decreases.

The structure of a semiconductor on the example of a silicon crystal

Consider the structure of semiconductors and the main types of conductivity in them. As an example, consider a silicon crystal.

Silicon is a tetravalent element. Therefore, in his outer shell There are four electrons that are loosely bound to the nucleus of an atom. Each one has four more atoms in its neighborhood.

Atoms interact with each other and form covalent bonds. One electron from each atom participates in such a bond. The silicon device diagram is shown in the following figure.

picture

Covalent bonds are strong enough and low temperatures do not break. Therefore, there are no free charge carriers in silicon, and it is a dielectric at low temperatures. There are two types of conduction in semiconductors: electron and hole.

Electronic conductivity

When silicon is heated, additional energy will be imparted to it. The kinetic energy of the particles increases and some covalent bonds are broken. This creates free electrons.

In an electric field, these electrons move between nodes crystal lattice. In this case, an electric current will be created in silicon.

Since free electrons are the main charge carriers, this type of conduction is called electronic conduction. The number of free electrons depends on the temperature. The more we heat silicon, the more covalent bonds will break, and consequently, more free electrons will appear. This leads to a decrease in resistance. And silicon becomes a conductor.

hole conduction

When a covalent bond breaks, a vacancy is formed in place of the ejected electron, which can be occupied by another electron. This place is called a hole. The hole has an excess positive charge.

The position of a hole in a crystal is constantly changing, any electron can take this position, and the hole will move to where the electron jumped from. If a electric field no, then the motion of the holes is random, and therefore no current occurs.

If it is present, there is an orderliness in the movement of holes, and in addition to the current that is created by free electrons, there is also a current that is created by holes. The holes will move in the opposite direction to the electrons.

Thus, in semiconductors, the conductivity is electron-hole. Current is generated both by electrons and by holes. This type of conduction is also called intrinsic conduction, since the elements of only one atom are involved.

Carrier transport in semiconductors

Introduction

Current carriers in semiconductors are electrons and holes. Current carriers move in the periodic field of crystal atoms as if they were free particles. The effect of the periodic potential affects only the carrier mass. That is, under the action of the periodic potential, the mass of the carrier changes. In this regard, solid state physics introduces the concept of the effective mass of an electron and a hole. Average energy thermal motion electrons and holes is kT/2 for each degree of freedom. The thermal velocity of an electron and a hole at room temperature is about 10 7 cm/s.

If an electric field is applied to a semiconductor, then this field will cause the drift of current carriers. In this case, the carrier velocity will first increase with an increase in the field, reach the average value of the velocity, and then stop changing, since the carriers are scattered. Scattering is caused by defects, impurities, and emission or absorption of phonons. The main reason for carrier scattering is charged impurities and thermal vibrations of lattice atoms (absorption/emission of phonons). Interaction with them leads to a sharp change in the speed of the carriers and the direction of their movement. The change in the direction of the carrier velocity is random. An additional mechanism for the scattering of current carriers is the scattering of carriers on the surface of a semiconductor.

In the presence of an external electric field, the random nature of the movement of carriers in a semiconductor is superimposed by the directed movement of carriers under the action of the field in the intervals between collisions. And even despite the fact that the speed of random movement of carriers can many times exceed the speed of directional movement of carriers under the action of an electric field, the random component of the movement of carriers can be neglected, since with random movement the resulting carrier flow zero. The acceleration of carriers under the action of an external field obeys the laws of Newton's dynamics. Scattering leads to a sharp change in the direction of movement and the magnitude of the velocity, but after scattering, the accelerated motion of the particle under the action of the field resumes.

The net effect of the collisions is that the particles do not accelerate, but the particles quickly reach a constant speed of motion. This is equivalent to introducing a decelerating component into the equation of motion of a particle characterized by a time constant t. During this period of time, the particle loses momentum mv determined by the average speed v. For a particle that has a constant acceleration between collisions, this time constant is equal to the time between two successive collisions. Let us consider in more detail the mechanisms of current carrier transport in semiconductors.

driftingcurrent(Drift Current)

The drift motion of carriers in a semiconductor under the action of an electric field can be illustrated by Figure XXX. The field tells the carriers the speed v.

Fig. Movement of carriers under the action of the field .

If we assume that all carriers in a semiconductor move at the same speed v, then the current can be expressed as the ratio of the total charge transferred between the electrodes to the time t r passing this charge from one electrode to another, or:

where L – distance between electrodes.

The current density can now be expressed in terms of the concentration of current carriers n in semiconductor:

where BUT is the cross-sectional area of ​​the semiconductor.

Mobility

The nature of the movement of current carriers in a semiconductor in the absence of a field and under the action of an external electric field is shown in Figure XXX. As already noted, the thermal velocity of electrons is on the order of 10 7 cm/s, and it is much higher than the drift velocity of electrons.

Fig. Random nature of the motion of current carriers in a semiconductor in the absence and presence of an external field.

Consider the motion of carriers only under the action of an electric field. According to Newton's law:

where the force includes two components - the electrostatic force and minus the force that causes the loss of momentum during scattering, divided by the time between collisions:

Equating these expressions and using the expression for average speed, we get:

Let us consider only the stationary case, when the particle has already accelerated and reached its average constant velocity. In this approximation, the speed is proportional to the electric field strength. The coefficient of proportionality between the last values ​​is defined as the mobility:

Mobility is inversely proportional to the mass of the carrier and directly proportional to the mean free path.

The drift current density can be written as a function of mobility:

As already noted, in semiconductors, the mass of carriers is not equal to the mass of an electron in vacuum, m and the formula for mobility should use the effective mass, m * :

Diffusion of current carriers in semiconductors.

Diffusion current

If external electric field is absent in a semiconductor, then there is a random movement of current carriers - electrons and holes under the action of thermal energy. This random movement does not lead to directional movement of carriers and the formation of current. Always instead of the carrier who left any place, another one will come in his place. Thus, a uniform carrier density is maintained throughout the volume of the semiconductor.

But the situation changes if the carriers are distributed unevenly over the volume, i.e. there is a concentration gradient. In this case, under the action of the concentration gradient, a directed movement of carriers occurs - diffusion from the region where the concentration is higher to the region with a low concentration. Directional movement of charged carriers under the action of diffusion creates a diffusion current. Let's consider this effect in more detail.

We obtain a relation for the diffusion current. We will proceed from the fact that the directional movement of carriers under the action of the concentration gradient occurs as a result of thermal motion (at a temperature
according to Kelvin, for each degree of freedom of a particle, there is an energy
), i.e. diffusion is absent at zero temperature (carrier drift is also possible at 0K).

Despite the fact that the random nature of the movement of carriers under the action of heat requires a statistical approach, the derivation of a formula for the diffusion current will be based on the use of average values ​​characterizing the processes. The result is the same.

Let us introduce the average values ​​- the average thermal velocity v th, mean time between collisions,  , and average length free run, l. The average thermal velocity can be directed in both positive and negative directions. These quantities are interconnected by the relation

Consider the situation with an inhomogeneous distribution of electrons n(x) (see Figure XXX).

Fig. one Carrier density profile used to derive the current diffusion expression

Consider the flow of electrons through a plane with coordinate x = 0. Carriers come to this plane as from the left side of the coordinate x = - l, and to the right from the side of the coordinate x = l. The flow of electrons from left to right is

where the coefficient ½ means that half of the electrons are in the plane with the coordinate x = - l moves to the left and the other half moves to the right. Similarly, the flow of electrons through x = 0 coming from the right side x = + l will be equal to:

The total flow of electrons passing through the plane x = 0 from left to right, will be:

Assuming that the mean free path of electrons is sufficiently small, we can write down the difference in electron concentrations to the right and left of the coordinate x = 0 through the ratio of the concentration difference to the distance between the planes, i.e. through the derivative:

The electron current density will be equal to:

Usually, the product of the thermal velocity and the mean free path is replaced by a single factor, called the electron diffusion coefficient, D n .

Similar relationships can also be written for the hole diffusion current:

It should only be remembered that the charge of holes is positive.

There is a relationship between the diffusion coefficient and mobility. Although at first glance it may seem that these coefficients should not be related, since the diffusion of carriers is due to thermal motion, and the drift of carriers is due to an external electric field. However, one of the main parameters, the time between collisions, should not depend on the cause that caused the carriers to move.

We use the definition of thermal velocity as,

and the conclusions of thermodynamics that for each degree of freedom of electron motion there is thermal energy kT/2, equal to the kinetic:

From these relations, one can obtain the product of the thermal velocity and the mean free path, expressed in terms of the carrier mobility:

But we have already defined the product of the thermal velocity and the mean free path as the diffusion coefficient. Then the last relation for electrons and holes can be written in the following form:

These relations are called the Einstein relations.

Total current

The total current through a semiconductor is the sum of the drift and diffusion current. For the electron current density, we can write:

and similarly for holes:

The total current density through the semiconductor is equal to the sum of the electron and hole current:

The total current through the semiconductor is equal to the product of the current density and the area of ​​the semiconductor:

The current can also be written in the following form:

Equilibrium condition for an inhomogeneously doped semiconductor

(condition of no current through the semiconductor)

Semiconductors occupy an intermediate position in electrical conductivity (or resistivity) between conductors and dielectrics. However, this division of all substances according to their electrical conductivity property is conditional, since under the influence of a number of reasons (impurities, irradiation, heating), the electrical conductivity and resistivity of many substances change very significantly, especially for semiconductors.

In this regard, semiconductors are distinguished from metals by a number of features:

1. The resistivity of semiconductors under normal conditions is much greater than that of metals;

2. the specific resistance of pure semiconductors decreases with increasing temperature (for metals, it increases);

3. when semiconductors are illuminated, their resistance decreases significantly (light has almost no effect on the resistance of metals):

4. An insignificant amount of impurities has a strong effect on the resistance of semiconductors.

Semiconductors include 12 chemical elements in the middle part of the periodic table (Fig. 1) - B, C, Si, P, S, Ge, As, Se, Sn, Sb, Te, I, compounds of elements of the third group with elements of the fifth group, many oxides and sulfides of metals, a number of others chemical compounds, some organic substances. Germanium Ge and silicon Si have the greatest application for science and technology.

Semiconductors can be pure or doped. Accordingly, intrinsic and impurity conductivity of semiconductors are distinguished. Impurities, in turn, are divided into donor and acceptor.

Self electrical conductivity

To understand the mechanism of electrical conduction in semiconductors, let us consider the structure of semiconductor crystals and the nature of the bonds that hold crystal atoms near each other. Crystals of germanium and other semiconductors have an atomic crystal lattice (Fig. 2).

A flat diagram of the structure of germanium is shown in Figure 3.

Germanium is a tetravalent element, in the outer shell of the atom there are four electrons that are weaker connected to the nucleus than the rest. The number of nearest neighbors of each germanium atom is also 4. Four valence electrons of each germanium atom are connected with the same electrons of neighboring atoms by chemical pair electrons ( covalent) connections. In the formation of this bond, one valence electron participates from each atom, which are split off from the atoms (collectivized by the crystal) and, during their movement, spend most of their time in the space between neighboring atoms. Their negative charge keeps the positive germanium ions near each other. This kind of connection can be conditionally depicted by two lines connecting the nuclei (see Fig. 3).

But the itinerant pair of electrons belongs to more than just two atoms. Each atom forms four bonds with its neighbors, and a given valence electron can move along any of them (Fig. 4). Having reached the neighboring atom, it can move on to the next, and then further along the entire crystal. Collectivized valence electrons belong to the whole crystal.

The covalent bonds of germanium are quite strong and do not break at low temperatures. Therefore, germanium does not conduct electricity at low temperatures. The valence electrons participating in the bonding of atoms are firmly attached to the crystal lattice, and the external electric field does not have a noticeable effect on their movement. A silicon crystal has a similar structure.

The electrical conductivity of a chemically pure semiconductor is possible when covalent bonds in crystals are broken and free electrons appear.

The extra energy that must be spent to break the covalent bond and make the electron free is called activation energy.

Electrons can obtain this energy by heating the crystal, by irradiating it with high-frequency electromagnetic waves etc.

As soon as the electron, having acquired the necessary energy, leaves the localized bond, a vacancy is formed on it. This vacancy can be easily filled by an electron from the neighboring bond, on which, therefore, a vacancy is also formed. Thus, due to the movement of bond electrons, vacancies move throughout the crystal. This vacancy behaves in exactly the same way as a free electron - it moves freely through the bulk of the semiconductor. Moreover, given that both the semiconductor as a whole and each of its atoms are electrically neutral with unbroken covalent bonds, we can say that an electron leaving a bond and the formation of a vacancy is actually equivalent to the appearance of an excess positive charge on this bond. Therefore, the resulting vacancy can be formally considered as a positive charge carrier, which is called hole(Fig. 5).

Thus, the departure of an electron from a localized bond generates a pair of free charge carriers - an electron and a hole. Their concentration in a pure semiconductor is the same. At room temperature the concentration of free carriers in pure semiconductors is low, about 10 9 ÷ 10 10 times less than the concentration of atoms, but it rapidly increases with increasing temperature.

• Compare with metals: there the concentration of free electrons is approximately equal to the concentration of atoms.

In the absence of an external electric field, these free electrons and holes move randomly in a semiconductor crystal.

In an external electric field, electrons move in the direction opposite to the direction of the electric field strength. Positive holes move in the direction of the electric field strength (Fig. 6). The process of movement of electrons and holes in an external field occurs throughout the entire volume of the semiconductor.

The total electrical conductivity of a semiconductor is the sum of the hole and electron conductivities. In this case, in pure semiconductors, the number of conduction electrons is always equal to the number of holes. Therefore, pure semiconductors are said to have electron-hole conductivity, or own conductivity.

With an increase in temperature, the number of breaks in covalent bonds increases and the number of free electrons and holes in the crystals of pure semiconductors increases, and, consequently, the electrical conductivity increases and the resistivity of pure semiconductors decreases. A graph of the dependence of the resistivity of a pure semiconductor on temperature is shown in fig. 7.

In addition to heating, the breaking of covalent bonds and, as a result, the appearance of intrinsic conductivity of semiconductors and a decrease in resistivity can be caused by illumination (photoconductivity of a semiconductor), as well as by the action of strong electric fields.

Impurity conductivity of semiconductors

The conductivity of semiconductors increases with the introduction of impurities, when, along with intrinsic conductivity, an additional impurity conductivity arises.

impurity conductivity semiconductors is called conductivity, due to the presence of impurities in the semiconductor.

Impurity centers can be:

1. atoms or ions of chemical elements embedded in a semiconductor lattice;

2. excess atoms or ions embedded in lattice interstices;

3. various other defects and distortions in the crystal lattice: empty nodes, cracks, shifts that occur during crystal deformations, etc.

By changing the concentration of impurities, one can significantly increase the number of charge carriers of one sign or another and create semiconductors with a predominant concentration of either negatively or positively charged carriers.

Impurities can be divided into donor (donating) and acceptor (receiving).

Donor impurity

• From the Latin "donare" - to give, donate.

Let us consider the mechanism of electrical conductivity of a semiconductor with a donor pentavalent impurity of arsenic As, which is introduced into a crystal, for example, silicon. The pentavalent arsenic atom donates four valence electrons to form covalent bonds, and the fifth electron is unoccupied in these bonds (Fig. 8).

The detachment energy (ionization energy) of the fifth valence electron of arsenic in silicon is 0.05 eV = 0.08⋅10 -19 J, which is 20 times less than the detachment energy of an electron from a silicon atom. Therefore, already at room temperature, almost all arsenic atoms lose one of their electrons and become positive ions. Positive arsenic ions cannot capture the electrons of neighboring atoms, since all four of their bonds are already equipped with electrons. In this case, the movement of the electron vacancy - "hole" does not occur and the hole conductivity is very low, i.e. practically absent.

Donor impurities- these are impurities that easily donate electrons and, consequently, increase the number of free electrons. In the presence of an electric field, free electrons come into ordered motion in a semiconductor crystal, and electronic impurity conduction arises in it. As a result, we get a semiconductor with predominantly electronic conductivity, called an n-type semiconductor. (From Latin negativus - negative).

Since the number of electrons in an n-type semiconductor is significantly more number holes, the electrons are the majority charge carriers, and the holes are the minor ones.

Acceptor impurity

• From the Latin "acceptor" - receiver.

In the case of an acceptor impurity, for example, trivalent indium In, the impurity atom can give its three electrons for covalent bonding with only three neighboring silicon atoms, and one electron is “missing” (Fig. 9). One of the electrons of neighboring silicon atoms can fill this bond, then the In atom will become an immobile negative ion, and a hole will form in place of the electron that left one of the silicon atoms. Acceptor impurities, capturing electrons and thereby creating mobile holes, do not increase the number of conduction electrons. Major charge carriers in a semiconductor with an acceptor impurity are holes, and minority carriers are electrons.

Acceptor impurities are impurities that provide hole conductivity.

Semiconductors in which the concentration of holes exceeds the concentration of conduction electrons are called p-type semiconductors (from Latin positivus - positive.).

It should be noted that the introduction of impurities into semiconductors, as in any metals, disrupts the structure of the crystal lattice and hinders the movement of electrons. However, the resistance does not increase due to the fact that increasing the concentration of charge carriers significantly reduces the resistance. Thus, the introduction of a boron impurity in the amount of 1 atom per hundred thousand silicon atoms reduces the specific electrical resistance silicon by about a thousand times, and the admixture of one indium atom per 10 8 - 10 9 germanium atoms reduces the electrical resistivity of germanium by millions of times.

If both donor and acceptor impurities are simultaneously introduced into a semiconductor, then the nature of semiconductor conductivity (n- or p-type) is determined by an impurity with a higher concentration of charge carriers.

Electron-hole transition

An electron-hole transition (abbreviated p-n-junction) occurs in a semiconductor crystal that simultaneously has regions with n-type (contains donor impurities) and p-type (with acceptor impurities) conductivities at the boundary between these regions.

Suppose we have a crystal in which on the left there is a semiconductor region with hole (p-type), and on the right - with electronic (n-type) conductivity (Fig. 10). Due to thermal motion during the formation of a contact, electrons from an n-type semiconductor will diffuse into the p-type region. In this case, an uncompensated positive donor ion will remain in the n-type region. Having passed into the region with hole conductivity, the electron very quickly recombines with the hole, and an uncompensated acceptor ion is formed in the p-type region.

Like electrons, holes from the p-type region diffuse into the electronic region, leaving an uncompensated negatively charged acceptor ion in the hole region. Having passed into the electronic region, the hole recombines with the electron. As a result, an uncompensated positive donor ion is formed in the electronic region.

As a result of diffusion, a double electric layer of oppositely charged ions is formed at the boundary between these regions, the thickness l which does not exceed fractions of a micrometer.

An electric field arises between the layers of ions with a strength E i. The electric field of the electron-hole junction (p-n-junction) prevents the further transition of electrons and holes through the interface between two semiconductors. The blocking layer has an increased resistance compared to the rest of the volumes of semiconductors.

External electric field with intensity E affects the resistance of the blocking electric field. If the n-semiconductor is connected to the negative pole of the source, and the plus of the source is connected to the p-semiconductor, then under the action of an electric field, the electrons in the n-semiconductor and the holes in the p-semiconductor will move towards each other to the semiconductor interface (Fig. 11). Electrons, crossing the boundary, "fill" the holes. With such forward direction external electric field, the thickness of the barrier layer and its resistance continuously decrease. In this direction, electric current passes through the p-n junction.

The considered direction of the p-n-junction is called direct. The dependence of the current on the voltage, i.e. volt-ampere characteristics direct transition, shown in Fig. 12 as a solid line.

If the n-semiconductor is connected to the positive pole of the source, and the p-semiconductor is connected to the negative, then the electrons in the n-semiconductor and holes in the p-semiconductor under the action of an electric field will move from the interface in opposite directions (Fig. 13). This leads to a thickening of the barrier layer and an increase in its resistance. The direction of the external electric field that expands the barrier layer is called locking (reverse). With this direction of the external field, the electric current of the main charge carriers does not pass through the contact of two p- and p-semiconductors.

The current through the p-n junction is now due to the electrons that are in the p-type semiconductor and the holes from the n-type semiconductor. But there are very few minority charge carriers, so the conductivity of the transition turns out to be insignificant, and its resistance is large. The considered direction of the p-n-junction is called reverse, its current-voltage characteristic is shown in Fig. 12 dashed line.

Please note that the current measurement scale for forward and reverse transitions differ by a thousand times.

Note that at a certain voltage applied in the opposite direction, there is breakdown(i.e., destruction) of the p-n junction.

Semiconductors

Thermistors

The electrical resistance of semiconductors is highly dependent on temperature. This property is used to measure temperature by current strength in a circuit with a semiconductor. Such devices are called thermistors or thermistors. A semiconductor substance is placed in a metal protective case, in which there are isolated leads for including the thermistor in an electrical circuit.

The change in the resistance of thermistors when heated or cooled allows them to be used in temperature measuring instruments to maintain a constant temperature in automatic devices- in closed chambers-thermostats, to ensure fire alarm etc. Thermistors exist for measuring both very high ( T≈ 1300 K) and very low ( T≈ 4 - 80 K) temperatures.

A schematic representation (Fig. a) and a photograph (Fig. b) of the thermistor are shown in Figure 14.

Rice. fourteen

Photoresistors

The electrical conductivity of semiconductors increases not only when heated, but also when illuminated. The electrical conductivity increases due to the breaking of bonds and the formation of free electrons and holes due to the energy of light incident on the semiconductor.

Devices that take into account the dependence of the electrical conductivity of semiconductors on illumination are called photoresistors.

Materials for the manufacture of photoresistors are compounds such as CdS, CdSe, PbS and a number of others.

The small size and high sensitivity of photoresistors make it possible to use them for recording and measuring weak light fluxes. With the help of photoresistors, the quality of surfaces is determined, the dimensions of products are controlled, etc.

A schematic representation (Fig. a) and a photograph (Fig. b) of the photoresistor are shown in Figure 15.

Rice. fifteen

semiconductor diode

The ability of a p-n junction to pass current in one direction is used in semiconductor devices called diodes.

Semiconductor diodes are made from germanium, silicon, selenium and other substances.

To prevent harmful effects air and light, a germanium crystal is placed in a hermetic metal case. Semiconductor diodes are the main elements of rectifiers alternating current(more precisely, they are used to convert alternating current into a pulsating direct current.)

A schematic representation (Fig. a) and a photograph (Fig. b) of a semiconductor diode are shown in Figure 16.

Rice. 16

LEDs

Light-emitting diode or light emitting diode- a semiconductor device with a p-n junction that creates optical radiation when an electric current is passed through it.

The emitted light lies in a narrow range of the spectrum, its spectral characteristics depend, among other things, on chemical composition semiconductors used in it.

Literature

1. Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 300-308.
2. Burov L.I., Strelchenya V.M. Physics from A to Z: for students, applicants, tutors. - Minsk: Paradox, 2000. - S. 219-228.
3. Myakishev G. Ya. Physics: Electrodynamics. 10 - 11 cells: a textbook for in-depth study of physics / G.Ya. Myakishev, A.Z. Sinyakov, B.A. Slobodskov. - M.: Bustard, 2005. - S. 309-320.
4. Yavorsky BM, Seleznev Yu. A. A reference guide to physics for those entering universities and self-education. - M.: Nauka, 1984. - S. 165-169.

Semiconductors occupy an intermediate place in electrical conductivity between conductors and non-conductors of electric current. The group of semiconductors includes many more substances than the groups of conductors and non-conductors taken together. The most characteristic representatives of semiconductors that have found practical use in technology, are germanium, silicon, selenium, tellurium, arsenic, cuprous oxide and a huge number of alloys and chemical compounds. Almost all inorganic substances the world around us are semiconductors. The most common semiconductor in nature is silicon, which makes up about 30% of the earth's crust.

The qualitative difference between semiconductors and metals is manifested primarily in the dependence of resistivity on temperature. With decreasing temperature, the resistance of metals decreases. In semiconductors, on the contrary, with decreasing temperature, the resistance increases and near absolute zero they practically become insulators.

In semiconductors, the concentration of free charge carriers increases with increasing temperature. The mechanism of electric current in semiconductors cannot be explained within the free electron gas model.

Germanium atoms have four loosely bound electrons in their outer shell. They are called valence electrons. In a crystal lattice, each atom is surrounded by four nearest neighbors. The bond between atoms in a germanium crystal is covalent, that is, it is carried out by pairs of valence electrons. Each valence electron belongs to two atoms. The valence electrons in a germanium crystal are much more strongly bonded to atoms than in metals; therefore, the concentration of conduction electrons at room temperature in semiconductors is many orders of magnitude lower than in metals. Near absolute zero temperature in a germanium crystal, all electrons are engaged in the formation of bonds. Such a crystal does not conduct electricity.

As the temperature rises, some of the valence electrons can gain enough energy to break covalent bonds. Then free electrons (conduction electrons) will appear in the crystal. At the same time, vacancies that are not occupied by electrons are formed at the sites of bond breaking. These vacancies are called "holes".

At a given semiconductor temperature, a certain number of electron-hole pairs are formed per unit time. At the same time, the reverse process is going on - when a free electron meets a hole, the electronic bond between germanium atoms is restored. This process is called recombination. Electron-hole pairs can also be produced when a semiconductor is illuminated due to the energy of electromagnetic radiation.

If a semiconductor is placed in an electric field, then not only free electrons are involved in the ordered movement, but also holes, which behave like positively charged particles. Therefore, the current I in a semiconductor is the sum of the electronic I n and hole I p currents: I = I n + I p.

The concentration of conduction electrons in a semiconductor is equal to the concentration of holes: n n = n p . The electron-hole mechanism of conduction manifests itself only in pure (i.e., without impurities) semiconductors. It is called intrinsic electrical conductivity of semiconductors.

In the presence of impurities, the electrical conductivity of semiconductors changes greatly. For example, adding impurities phosphorus into crystal silicon in the amount of 0.001 atomic percent reduces the resistivity by more than five orders of magnitude.

A semiconductor in which an impurity is introduced (i.e., part of the atoms of one type is replaced by atoms of another type) is called doped or doped.

There are two types of impurity conduction, electron and hole conduction.

Thus, when doping a four-valent germanium (Ge) or silicon (Si) pentavalent - phosphorus (P), antimony (Sb), arsenic (As) an extra free electron appears at the location of the impurity atom. In this case, the impurity is called donor .

When doping four valent germanium (Ge) or silicon (Si) trivalent - aluminum (Al), indium (Jn), boron (B), gallium (Ga) - there is a line hole. Such impurities are called acceptor .

In the same sample of a semiconductor material, one section may have p-conductivity, and the other n-conductivity. Such a device is called a semiconductor diode.

The prefix "di" in the word "diode" means "two", it indicates that the device has two main "details", two semiconductor crystals closely adjacent to each other: one with p-conductivity (this is the zone R), the other - with n - conductivity (this is the zone P). In fact, a semiconductor diode is one crystal, in one part of which a donor impurity is introduced (zone P), into another - acceptor (zone R).

If a constant voltage is applied from the battery to the diode "plus" to the zone R and "minus" to the zone P, then free charges - electrons and holes - will rush to the boundary, rush to the pn junction. Here they will neutralize each other, new charges will approach the boundary, and a D.C.. This is the so-called direct connection of the diode - the charges move intensively through it, a relatively large forward current flows in the circuit.

Now we will change the polarity of the voltage on the diode, we will carry out, as they say, its reverse inclusion - we will connect the “plus” of the battery to the zone P,"minus" - to the zone R. Free charges will be pulled away from the boundary, electrons will go to the "plus", holes - to the "minus" and, as a result, the pn - junction will turn into a zone without free charges, into a pure insulator. This means that the circuit will break, the current in it will stop.

Not a large reverse current through the diode will still go. Because, in addition to the main free charges (charge carriers) - electrons, in the zone P, and holes in the p zone - in each of the zones there is also an insignificant amount of charges of the opposite sign. These are their own minority charge carriers, they exist in any semiconductor, appear in it due to the thermal movements of atoms, and it is they who create the reverse current through the diode. There are relatively few of these charges, and the reverse current is many times less than the direct one. The magnitude of the reverse current is highly dependent on: temperature environment, semiconductor material and area pn transition. With an increase in the transition area, its volume increases, and, consequently, the number of minority carriers appearing as a result of thermal generation and the thermal current increase. Often CVC, for clarity, is presented in the form of graphs.

Many semiconductors are chemical elements(germanium, silicon, selenium, tellurium, arsenic, etc.), a huge number of alloys and chemical compounds. Almost all inorganic substances of the world around us are semiconductors. The most common semiconductor in nature is silicon, which makes up about 30% of the earth's crust.

The qualitative difference between semiconductors and metals is manifested in temperature dependence of resistivity(fig.9.3)

Band model of electron-hole conductivity of semiconductors

At education solids a situation is possible when the energy band that has arisen from the energy levels of the valence electrons of the initial atoms turns out to be completely filled with electrons, and the nearest ones available for filling with electrons energy levels separated from valence band E V an interval of unresolved energy states - the so-called forbidden zone E g.Above the band gap is the zone of energy states allowed for electrons - conduction band E c .

The conduction band at 0 K is completely free, while the valence band is completely occupied. Similar band structures are characteristic of silicon, germanium, gallium arsenide (GaAs), indium phosphide (InP) and many other semiconductor solids.

With an increase in the temperature of semiconductors and dielectrics, electrons are able to receive additional energy associated with thermal motion. kT. For some electrons, the energy of thermal motion is sufficient for the transition from the valence band to the conduction band, where electrons under the action of an external electric field can move almost freely.

In this case, in a circuit with a semiconductor material, as the temperature of the semiconductor rises, an electric current will increase. This current is associated not only with the movement of electrons in the conduction band, but also with the appearance vacancies from electrons that have gone into the conduction band in the valence band, the so-called holes . A vacant place can be occupied by a valence electron from a neighboring pair, then the hole will move to a new place in the crystal.

If a semiconductor is placed in an electric field, then not only free electrons are involved in the ordered movement, but also holes, which behave like positively charged particles. Therefore, the current I in a semiconductor is made up of an electronic I n and hole Ip currents: I= I n+ Ip.

The electron-hole mechanism of conduction manifests itself only in pure (i.e., without impurities) semiconductors. It is called own electrical conductivity semiconductors. Electrons are thrown into the conduction band with Fermi level, which turns out to be located in its own semiconductor in the middle of the forbidden zone(Fig. 9.4).

It is possible to significantly change the conductivity of semiconductors by introducing very small amounts of impurities into them. In metals, an impurity always reduces the conductivity. Thus, the addition of 3% phosphorus atoms to pure silicon increases the electrical conductivity of the crystal by a factor of 105.

Slight addition of dopant to the semiconductor called doping.

Necessary condition A sharp decrease in the resistivity of a semiconductor with the introduction of impurities is the difference in the valency of the impurity atoms from the valence of the main atoms of the crystal. The conductivity of semiconductors in the presence of impurities is called impurity conductivity .

Distinguish two types of impurity conduction – electronic and hole conductivity. Electronic conductivity occurs when pentavalent atoms (for example, arsenic, As) are introduced into a germanium crystal with tetravalent atoms (Fig. 9.5).

The four valence electrons of the arsenic atom are involved in the formation of covalent bonds with four neighboring germanium atoms. The fifth valence electron turned out to be redundant. It easily detaches from the arsenic atom and becomes free. An atom that has lost an electron turns into a positive ion located at a site in the crystal lattice.

An admixture of atoms with a valency greater than the valency of the main atoms of a semiconductor crystal is called donor impurity . As a result of its introduction, a significant number of free electrons appear in the crystal. This leads to a sharp decrease in the resistivity of the semiconductor - by thousands and even millions of times.

Conductor resistivity with great content impurities can approach the resistivity of a metallic conductor. Such conductivity, due to free electrons, is called electronic, and a semiconductor with electronic conductivity is called n-type semiconductor.

hole conduction occurs when trivalent atoms are introduced into a germanium crystal, for example, indium atoms (Fig. 9.5)

Figure 6 shows an indium atom that has created covalent bonds with only three neighboring germanium atoms using its valence electrons. The indium atom does not have an electron to form a bond with the fourth germanium atom. This missing electron can be captured by an indium atom from a covalent bond of neighboring germanium atoms. In this case, the indium atom turns into a negative ion located at a site of the crystal lattice, and a vacancy is formed in the covalent bond of neighboring atoms.

An admixture of atoms capable of capturing electrons is called acceptor impurity . As a result of the introduction of an acceptor impurity in the crystal, many covalent bonds are broken and vacant sites (holes) are formed. Electrons can jump to these places from neighboring covalent bonds, which leads to random wandering of holes around the crystal.

The concentration of holes in a semiconductor with an acceptor impurity significantly exceeds the concentration of electrons that arose due to the mechanism of intrinsic electrical conductivity of the semiconductor: np>> n n. This type of conduction is called hole conductivity . An impurity semiconductor with hole conductivity is called p-type semiconductor . Major free charge carriers in semiconductors p-type are holes.

Electron-hole transition. Diodes and transistors

In modern electronic technology, semiconductor devices play an exceptional role. Over the past three decades, they have almost completely replaced electrovacuum devices.

Any semiconductor device has one or more electron-hole junctions. . Electron-hole transition (or n–p-transition) - is the contact area of ​​two semiconductors with different types conductivity.

At the boundary of semiconductors (Fig. 9.7), a double electric layer is formed, the electric field of which prevents the process of diffusion of electrons and holes towards each other.

Ability n–p-transition to pass current in almost only one direction is used in devices called semiconductor diodes. Semiconductor diodes are made from silicon or germanium crystals. During their manufacture, an impurity is melted into a crystal with a certain type of conductivity, which provides a different type of conductivity.

Figure 9.8 shows a typical volt-ampere characteristic of a silicon diode.

Semiconductor devices with not one but two n-p junctions are called transistors . Transistors are of two types: p–n–p-transistors and n–p–n-transistors. in transistor n–p–n-type basic germanium plate is conductive p-type, and the two regions created on it - by conductivity n-type (Figure 9.9).

in transistor p–n–p- it's kind of the opposite. The plate of a transistor is called base(B), one of the regions with the opposite type of conductivity - collector(K), and the second - emitter(E).