Electric current in semiconductors. Intrinsic and impurity conductivity

Intrinsic conductivity of semiconductors

In semiconductors, the main band is separated from the band of excited levels by a finite energy interval ($\triangle E$). The main band of a semiconductor is called the valence band, and the band of excited states is called the conduction band. At T=0 K, the valence band is completely filled, while the conduction band is free. Therefore, near absolute zero, semiconductors do not conduct current. Generally speaking, dielectrics and semiconductors differ from the point of view of band theory only in the band gap ($\triangle E$). Conventionally, dielectrics include semiconductors with $\triangle E>2eV.$

Note 1

In semiconductors, as the temperature increases, electrons exchange energy with ions in the crystal lattice. Because of this, the electron can acquire additional kinetic energy of size $\approx kT.\ $This energy may be enough to transfer some of the electrons to the conduction band. These electrons in the conduction band conduct current.

In the valence band, quantum states that are not occupied by electrons are released. Such states are called holes. Holes are current carriers. Electrons can recombine with holes (make quantum transitions to unfilled states, that is, holes). In this case, the former filled states are released, that is, they become holes. The latter recombine with new electrons, and holes are formed again. As a result of these processes, an equilibrium concentration of holes is established; this concentration is the same throughout the entire volume of the conductor if there is no external field. Quantum transition electron is accompanied by its movement against the field. It reduces the potential energy of the system. A transition associated with movement in the direction of the field increases the potential energy of the system. Transitions against the field prevail over transitions along the field, which means that current will begin to flow through the semiconductor in the direction of the applied electric field. In an open semiconductor, current will flow until the electric field compensates for the external field. The final result of the phenomenon is the same as if the current carriers were not electrons, but positively charged holes. Consequently, a distinction is made between electron and hole conductivity of semiconductors.

The true current carriers in metals and semiconductors are electrons; holes are introduced formally. Holes, like real positively charged particles, do not exist. However, it turned out that in an electric field, holes move in the same way as positively charged particles would move under classical consideration. Due to the small concentration of electrons in the conduction band and holes in the valence band, classical Boltzmann statistics can be used.

Note 2

The conductivity of semiconductors, both electronic and hole, is not related to the presence of impurities. It is called the intrinsic electrical conductivity of semiconductors.

In an ideally pure semiconductor without any impurities, each electron released by thermal movement or light would correspond to the formation of one hole, that is, the number of electrons and holes that participate in the creation of current would be the same.

Ideally pure semiconductors do not exist in nature; making them artificially is extremely difficult. Small traces of impurities qualitatively change the properties of semiconductors.

Impurity conductivity of semiconductors

Electrical conductivity of semiconductors, which is caused by the presence of impurities of other atoms chemical elements, is called impurity electrical conductivity. The smallest amounts of impurities can significantly increase the conductivity of semiconductors. In metals, the opposite phenomenon is observed. Impurities always reduce the conductivity of metals.

The increase in conductivity in the presence of impurities is explained by the fact that additional energy levels appear in semiconductors, which are located in the band gap of the semiconductor.

Donor impurities

Let additional levels in the band gap appear near the lower edge of the conduction band. If the energy interval that separates additional energy levels from the conduction band is small compared to the band gap, then the number of electrons in the conduction band, and therefore the conductivity of the semiconductor itself, will increase. Impurities that supply electrons to the conduction band are called donors (donor impurities). Additional energy levels are called donor levels.

Semiconductors with donor impurities are called electronic (n-type semiconductors).

Acceptor impurities

Let the introduction of an impurity cause additional levels to appear near the upper edge of the valence band. In this case, electrons from the valence band move to these additional levels. In this case, holes appear in the valence band, and this is how hole electrical conductivity of the semiconductor arises. Such impurities are called acceptors (acceptor impurities). Additional levels are called acceptor levels.

Semiconductors that have acceptor impurities are called hole semiconductors (p-type semiconductors). Mixed semiconductors may exist.

What type of conductivity a semiconductor has (electronic or hole) is judged by the sign of the Hall effect.

The process of introducing impurities is called doping. At very high concentrations of impurity levels, splitting of the impurity levels can be observed, as a result of which they can cover the boundaries of the corresponding energy bands.

Example 1

Assignment: Explain what type of impurity can be arsenic atoms and boron atoms in the silicon crystal lattice?

Consider silicon and arsenic. Silicon is a tetravalent atom, therefore, a silicon atom has four electrons. Arsenic is pentavalent, which means its atom contains five electrons. The fifth electron can be removed from the arsenic atom due to thermal motion. A positive arsenic ion can displace one of the silicon atoms from the lattice, taking its place. Thus, a conduction electron will appear between the lattice sites. Consequently, it turns out that arsenic is a donor impurity for silicon.

Let's consider boron as an impurity to silicon. The outer shell of a boron atom has three electrons. A boron atom can capture the missing fourth electron from some adjacent place in the silicon crystal. A hole appears in this place, and the resulting negative boron ion can displace the silicon atom from the crystal lattice and take its place. Hole conductivity occurs in a silicon crystal. Boron is an acceptor impurity.

Answer: Arsenic is a donor impurity in the silicon lattice, boron is an acceptor impurity for silicon.

Example 2

Assignment: In thermoelements, in some cases the current in the hot junction flows from the metal to the semiconductor, and in others from the semiconductor to the metal, explain why?

It is the difference between electron and hole conductivity of semiconductors that explains the process described in the task conditions.

In an electronic semiconductor, the speed of electrons at the hot end is greater than at the cold end. Consequently, electrons leak (diffuse) from the hot end to the cold until the electric field arising due to charge redistribution stops the flow of diffusing electrons. Once equilibrium is established, the hot end, which has lost electrons, has a positive charge, the cold end, which has gained an excess of electrons, therefore has a negative charge. This means that a potential difference (positive) appears between the hot and cold ends.

In a hole semiconductor, the reverse process occurs. Hole diffusion proceeds from the hot end to the cold end. In this case, the hot end receives a negative charge, and the cold end becomes positively charged. The sign of the potential difference between the hot and cold ends is negative.

The conductivity of chemically pure semiconductors is called own conductivity, and the semiconductors themselves are their own semiconductors. In a pure semiconductor, the number of free electrons and holes is the same. Under the influence of a voltage applied to a semiconductor, the speed of directional movement of free electrons in it is greater than that of holes. Therefore, the current strength of electronic conductivity I e is greater than the current strength of hole conductivity I d. The total current in a semiconductor I = I e + I d.

The intrinsic conductivity of a semiconductor increases with increasing temperature. At a constant temperature, a dynamic equilibrium occurs between the process of hole formation and recombination of electrons and holes. Under this condition, the number of conduction electrons and holes per unit volume remains constant.

The conductivity of semiconductors is greatly influenced by the presence of impurities in them. By introducing certain impurities into a semiconductor, one can obtain relatively a large number of free electrons with a small number of “holes” or, conversely, a large number of “holes” with a very small number of free electrons. The conductivity of conductors caused by impurities is called impurity conductivity, and the semiconductors themselves are impurity semiconductors. Impurities that easily give up their electrons to the main semiconductor and, therefore, increase the number of free electrons in it are called donor(giving off) impurities. Elements whose atoms have a greater number of valence electrons than the atoms of the main semiconductor are used as such impurities. Thus, in relation to germanium, arsenic and antimony impurities are donors.

To obtain arsenic impurities in germanium, they are mixed and melted. Germanium is a tetravalent element. Arsenic is pentavalent. When solidification occurs at a site of the germanium crystal lattice, the germanium atom is replaced by an arsenic atom. The electrons of the latter form strong covalent bonds with four neighboring germanium atoms (Fig. 102, a). The remaining fifth valence electron of arsenic, which is not involved in pair-electronic bonds, continues to move around the arsenic atom. Due to the fact that the dielectric constant of germanium ε = 16, the force of attraction of the electron to the nucleus decreases, the size of the electron’s orbit increases 16 times; its binding energy with the atom decreases by 256 times (i.e., ε 2 times), and the energy of thermal motion becomes sufficient to separate this electron from the atom. It begins to move freely in the germanium lattice, thus turning into a conduction electron.

An arsenic atom, located in a site of the germanium crystal lattice, having lost an electron, becomes a positive ion.

It is firmly bound to the germanium crystal lattice, therefore it does not take part in the formation of current.

The energy required to transfer an electron from the valence band to the conduction band (see Fig. 96) is called activation energy. For impurity current carriers it is usually many times less than for the current carrier of the main semiconductor. Therefore, with slight heating and illumination, mainly electrons of impurity atoms are released. In place of the lost electron, a hole is formed in the donor atom. However, almost no movement of electrons into holes is observed, i.e., the additional hole conductivity created by the donor is very small. This is explained as follows. Due to the small number of impurity atoms, its conduction electrons are rarely near the hole and cannot fill it. And the electrons of the atoms of the main semiconductor, although they are located near the holes, are not able to occupy them due to their much lower energy level.

A small addition of a donor impurity makes the number of free conduction electrons thousands of times greater than the number of free conduction electrons in a pure semiconductor under the same conditions. In a semiconductor with a donor impurity, the main charge carriers are electrons. n-type semiconductors.

Impurities that capture electrons from the main semiconductor and, therefore, increase the number of holes in it are called acceptor(receiving) impurities. Such impurities are elements whose atoms have fewer valence electrons than the atoms of the main semiconductor. Thus, in relation to germanium, indium and aluminum impurities are acceptor impurities.

To obtain indium impurities in germanium, they are mixed and melted. Germanium is a tetravalent element. Indium is trivalent. To form covalent bonds with the four nearest neighboring germanium atoms, the indium atom lacks one electron. Indium borrows it from the germanium atom (Fig. 102, b). To do this, the electrons of germanium atoms are given energy by heating, sufficient only to break covalent bond, after which the released electrons are captured by indium atoms. Being not free, these electrons do not participate in the formation of current. Indium atoms become negative ions; they are firmly bound to the germanium crystal lattice, and therefore do not take part in the formation of current.

In place of the electron that left the germanium atom, a hole is formed, which is a free carrier of a positive charge. This hole can be filled by electron A from a neighboring germanium atom, etc. In a semiconductor with an acceptor impurity, the main charge carriers are holes. Such semiconductors are called p-type semiconductors.

Thus, in contrast to intrinsic conductivity, which is carried out simultaneously by electrons and holes, impurity conductivity of a semiconductor is mainly due to carriers of the same sign: electrons in the case of a donor impurity and holes in the case of an acceptor impurity. These charge carriers in an impurity semiconductor are the majority ones. In addition to them, such a semiconductor contains minority carriers: in an electronic semiconductor - holes, in a hole semiconductor - electrons. Their concentration is significantly less than the concentration of the main carriers.

Semiconductors are a class of substances (solids) in which the valence band is completely occupied by electrons, separated from the conduction band by a narrow (about 1 eV) band gap. Their electrical conductivity is less than the electrical conductivity of metals, but greater than the electrical conductivity of dielectrics.

Semiconductors include elements (Si, Ge, As, Se, Te), chemical compounds(oxides, sulfides, selenides), alloys of elements of various groups.

The main feature that distinguishes semiconductors as a special class of substances is the strong influence of temperature and impurity concentration on their electrical conductivity.

There are intrinsic and impurity semiconductors. The electrical conductivity of pure semiconductors (which are completely free of impurities) is called intrinsic conductivity.

Intrinsic semiconductors include germanium and silicon. The molecular structure of silicon is shown in Fig. 8.8, where:

Core and internal electronic shells;

Hole, vacancy with missing connection;

Valence electrons that form a covalent bond.

Germanium and silicon have the same crystal lattice: each atom is surrounded by four atoms located at the vertices of a regular tetrahedron. The outer shell of an atom has four valence electrons, so each atom forms four covalent bonds with its four nearest neighbors.

In Fig. Figure 8.9 shows the energy structure of electrons in a semiconductor. At T=0, all levels of the valence band are occupied, and the Fermi level lies in the band gap separating the conduction band. In this case, there are no electrons in the conduction band. It is typical for semiconductors that the band gap is up to 10 kT. At room temperatures, the “blurring” of the Fermi-Dirac function overlaps , and the probability of transition of electrons from the valence band to the conduction band is not equal to 0.

Thus, in semiconductors (which fundamentally distinguishes them from dielectrics), relatively small energy effects caused by heating or irradiation can lead to the separation of some electrons from their atoms. This is the mechanism of carrier formation in pure semiconductors.

At temperature T=0 K and no other external factors intrinsic semiconductors behave like dielectrics. As the temperature increases, electrons from the upper levels of the valence band can move to the lower levels of the conduction band. When an electric field is applied, the electrons are mixed against the field. Electric current appears in the semiconductor. The conductivity of intrinsic semiconductors due to electrons is called electronic conductivity, or n-type conductivity.

Due to the thermal transition of electrons in the valence band, vacant states called holes appear. In an external electric field, an electron from a neighboring level can move to the place vacated by an electron, a hole, and a hole will appear in the place that the electron left, etc. This process of filling holes with electrons is equivalent to moving the hole in the direction opposite to the movement of the electron. The holes don't actually move. The conductivity of intrinsic semiconductors due to holes (quasiparticles) is called hole conductivity, or p-type conductivity.

Thus, two conductivity mechanisms are observed in intrinsic semiconductors: electronic and hole. The number of electrons in the conduction band is equal to the number of holes in the valence band. Consequently, if the concentration of conduction electrons and holes is equal to n e and n p, respectively, then n e = n p.

The conductivity of intrinsic semiconductors is always excited, i.e. appears only under the influence of external factors (increased temperature, irradiation, strong electric fields, etc.).

In an intrinsic semiconductor, the Fermi level is in the middle of the band gap. When an electron passes from the upper level of the valence band to the lower level of the conduction band, an activation energy equal to the band gap E is expended, which leads to the appearance of a hole in the valence band. The energy expended on the emergence of a pair of current carriers must be divided into two equal parts. Therefore, the origin for each of these processes must be in the middle of the bandgap. The Fermi energy in an intrinsic semiconductor is the energy from which electrons and holes are excited.

In physics solid it is proved that the electron concentration in the conduction band

, (8.17)

where W 2 is the energy corresponding to the bottom of the conduction band;

W F – Fermi energy;

T – thermodynamic temperature;

C 1 is a constant depending on temperature and effective mass of the conduction electron.

Note. Effective mass is a quantity that has the dimension of mass. It characterizes the dynamic properties of conduction electrons and holes. Allows you to take into account the effect on conduction electrons not only of the external field, but also of the internal periodic field of the crystal, to consider their movement in the external field as the movement of free particles, without taking into account the interaction of conduction electrons with the lattice.

Hole concentration in the valence band

, (8.18)

where C 2 is a constant depending on temperature and effective mass of holes;

W 1 – energy corresponding to the upper boundary of the valence band. The excitation energy in this case is counted down from the Fermi level, so the values in the exponential factor are different.

According to the fact that n e = n p , we have

. (8.19)

If the effective masses of electrons and holes are equal, then at a given temperature C 1 = C 2 and, therefore,

. (8.20)

Thus, the Fermi level in an intrinsic semiconductor is indeed located in the middle of the band gap.

Since for intrinsic semiconductors DW>>kT, the Fermi-Dirac distribution has the form

, (8.21)

Where – average number of fermions in a state with energy Wi;

m – chemical potential.

Under these conditions, the Fermi-Dirac distribution transforms into the Maxwell-Boltzmann distribution:

, (8.22)

Thus we have:

. (8.23)

Replacing (W - W F) = DW/2 in formula (8.23), we get

. (8.24)

Since the number of electrons transferred to the conduction band, and therefore the number of holes formed, is proportional to , then the specific conductivity of intrinsic semiconductors

where g o is a constant characteristic of a given semiconductor.

Electrical resistivity of semiconductors

The increase in the conductivity of semiconductors with increasing temperature is explained by the fact that with increasing temperature, the number of electrons in semiconductors increases, which, due to thermal excitation, move into the conduction band and participate in conduction.

In semiconductors, in addition to the process of generating electrons and holes, the process of their recombination is possible. Electrons can move from the conduction band to the valence band, giving excess energy to the lattice and emitting quanta of electromagnetic radiation. As a result, for each temperature a certain equilibrium in the concentration of electrons and holes is established, depending on the temperature.

The recombination rate, i.e. the number of electron-hole pairs disappearing per unit time is determined by the properties of the semiconductor; in addition, it is proportional to the concentration of electrons and holes, since the greater the number of charge carriers, the more likely their meeting, resulting in recombination. Thus, the recombination rate

« Physics - 10th grade"

Why does the resistance of conductors depend on temperature?
What phenomena are observed in the state of superconductivity?

Semiconductors- substances whose resistivity has an intermediate value between the resistivity of metals (10 -6 -10 -8 Ohm m) and the resistivity of dielectrics (10 8 -10 13 Ohm m).

The difference between conductors and semiconductors is especially evident when analyzing the dependence of their electrical conductivity on temperature. Research shows that for a number of elements (silicon, germanium, selenium, indium, arsenic, etc.) and compounds (PbS, CdS, GaAs, etc.) the resistivity does not increase with increasing temperature, as with metals (see Fig. 16.3 ), but, on the contrary, decreases extremely sharply (Fig. 16.4).

This property is inherent specifically in semiconductors.

From the graph shown in the figure, it is clear that at temperatures close to absolute zero, the resistivity of semiconductors is very high. This means that at low temperatures the semiconductor behaves like a dielectric. As the temperature increases, its resistivity decreases rapidly.

Structure of semiconductors.

In order to turn on a transistor receiver, you don’t need to know anything. But to create it, you had to know a lot and have extraordinary talent. Understanding in general terms how a transistor works is not so difficult. First, you need to become familiar with the conduction mechanism in semiconductors. And for this you will have to delve into nature of connections, holding the atoms of a semiconductor crystal near each other.

For example, consider a silicon crystal.

Silicon is a tetravalent element. This means that in the outer shell of its atom there are four electrons that are relatively weakly bound to the nucleus. The number of nearest neighbors of each silicon atom is also four. A diagram of the structure of a silicon crystal is shown in Figure (16.5).

The interaction of a pair of neighboring atoms is carried out using a pair-electronic bond called covalent bond. In the formation of this bond, one valence electron from each atom participates; the electrons are separated from the atom to which they belong (collected by the crystal), and during their movement they spend most of the time in the space between neighboring atoms. Their negative charge holds the positive silicon ions near each other.

One should not think that a collective pair of electrons belongs to only two atoms. Each atom forms four bonds with its neighbors, and any valence electron can move along one of them. Having reached a neighboring atom, it can move on to the next one, and then further along the entire crystal. Valence electrons belong to the entire crystal.

Pair-electron bonds in a silicon crystal are quite strong and do not break at low temperatures. Therefore, silicon at low temperatures does not conduct electric current. The valence electrons involved in the bonding of atoms are like a cementing solution that holds the crystal lattice, and the external electric field does not have a noticeable effect on their movement. The germanium crystal has a similar structure.

Electronic conductivity.

When heating silicon kinetic energy particles increases and individual bonds break. Some electrons leave their “beaten paths” and become free, like electrons in a metal. In an electric field, they move between lattice nodes, creating an electric current (Fig. 16.6).

The conductivity of semiconductors due to the presence of free electrons is called electronic conductivity.

As the temperature increases, the number of broken bonds, and therefore free electrons, increases. When heated from 300 to 700 K, the number of free charge carriers increases from 10 17 to 10 24 1/ml 3. This leads to a decrease in resistance.

Hole conductivity.

When the bond between the atoms of a semiconductor is broken, a vacant place with a missing electron is formed, which is called hole.

The hole has an excess positive charge compared to other unbroken bonds (see Fig. 16.6).

The position of the hole in the crystal is not constant. The following process occurs continuously. One of the electrons that ensures the connection of atoms jumps to the place of the formed hole and restores the pair-electronic bond here, and where this electron jumped from, a new hole is formed. Thus, the hole can move throughout the crystal.

If the electric field strength in the sample is zero, then the holes move randomly and therefore do not create an electric current. In the presence of an electric field, an ordered movement of holes occurs.

The direction of movement of holes is opposite to the direction of movement of electrons (Fig. 16.7).

In the absence of an external field, there is one hole (+) per free electron (-). When a field is applied, the free electron is displaced against the field strength. One of the bound electrons also moves in this direction. This looks like moving the hole in the direction of the field.

So, in semiconductors there are two types of charge carriers: electrons and holes.

Conduction caused by the movement of holes is called hole conductivity semiconductors.

We examined the conduction mechanism of pure semiconductors.

The conductivity of pure semiconductors is called own conductivity.

Impurity conductivity.

The intrinsic conductivity of semiconductors is usually low, since the number of free electrons is small: for example, in germanium at room temperature n e = 3 10 13 cm -3. At the same time, the number of germanium atoms per 1 cm 3 is of the order of 10 23.

Thus, the number of free electrons is approximately one ten-billionth of total number atoms.

The conductivity of semiconductors can be significantly increased by introducing an impurity into them. In this case, along with its own conductivity, an additional one arises - impurity conductivity.

The conductivity of conductors, caused by the introduction of impurities (atoms of foreign chemical elements) into their crystal lattices, is called impurity conductivity.

Donor impurities.

Let's add a small amount of arsenic to silicon. Arsenic atoms have five valence electrons. Four of them are involved in creating a covalent bond between a given atom and surrounding silicon atoms. The fifth valence electron appears to be weakly bound to the atom. It easily leaves the arsenic atom and becomes free (Fig. 16.8).

When one ten-millionth of arsenic atoms is added, the concentration of free electrons becomes equal to 10 16 cm -3. This is a thousand times greater than the concentration of free electrons in a pure semiconductor.

Impurities that easily give up electrons and, therefore, increase the number of free electrons are called donor(giving) impurities.

Free electrons move through a semiconductor in the same way that free electrons move in a metal.

Semiconductors that have donor impurities and therefore have a large number of electrons (compared to the number of holes) are called n-type semiconductors(from English word negative - negative).

In an n-type semiconductor, electrons are the main charge carriers, and holes are non-core.

Acceptor impurities.

If indium, whose atoms are trivalent, is used as an impurity, then the nature of the conductivity of the semiconductor changes. To form normal pair-electronic bonds with its neighbors, the indium atom lacks one electron, which it takes from a neighboring atom of the crystal. As a result, a hole is formed. The number of holes in the crystal is equal to the number of impurity atoms (Fig. 16.9).

Impurities in a semiconductor that create an additional concentration of holes are called acceptor(receiving) impurities.

In the presence of an electric field, holes move directionally and an electric current arises due to hole conductivity.

Semiconductors with a predominance of hole conductivity over electron conductivity are called p-type semiconductors(from the English word positive - positive).

The majority charge carriers in a p-type semiconductor are holes, and the minority charge carriers are electrons.

By changing the impurity concentration, you can significantly change the number of charge carriers of one or another sign. Thanks to this, it is possible to create semiconductors with a predominant concentration of one of the current carriers, electrons or holes. This feature of semiconductors opens up wide possibilities for their practical application.

§ 3 Intrinsic conductivity of semiconductors

Internal structure of semiconductors.

Semiconductors include a large number of substances that, in their electrical properties, occupy an intermediate position between conductors and dielectrics. For semiconductors j=1 2¸ 1 0 - 8 S/m (j - electrical conductivity). For conductors j = 1 4¸ 1 0 3 Sm/m; for dielectrics j< 10 -12 S/m. The most important property and a sign of semiconductors is the dependence of their electrical properties on external conditions T, E, R etc. Feature semiconductors is to reduce their resistivity with increasing temperature. It is typical for semiconductors crystalline structure with covalent bonds between atoms.

Intrinsic conductivity of semiconductors.

Under the influence of external factors, some valence electrons of atoms acquire energy sufficient to free themselves from covalent bonds.

The release of an electron from a covalent bond in the energy diagram corresponds to the transition from the valence band to the conduction band. When an electron is released from a covalent bond, a free space appears in the latter, possessing an elementary positive charge equal in absolute value to the charge of the electron. This vacated place in electronic communications was conventionally called hole, and the process of pair formation is called generation of charges. The hole, having a positive charge, attaches to itself an electron from an adjacent filled covalent bond. As a result one connection is restored(this process is called recombination) And the neighboring one is destroyed. Then we can talk about the movement of a positive charge - a hole - across the crystal. If an electric field acts on a crystal, the movement of electrons and holes becomes ordered and an electric current arises in the crystal. In this case, hole conductivity is called conductivity R-type ( positive - positive), and electronic conductivityn-type (negative - negative).

In a chemically pure semiconductor crystal (the number of impurities is 10 16 m -3), the number of holes is always equal to the number of free electrons and the electric current in it is formed as a result of the simultaneous transfer of charge of both signs. This electron-hole conductivity is called intrinsic conductivity of the semiconductor.

j = j n+ j p

j- electron current density (n) and holes ( R).

In an intrinsic semiconductor, the Fermi level is in the middle of the band gap. Because activation energy, equal to the band gap, is used to transfer an electron from the upper level of the valence band to the lower level of the conduction band and at the same time to create a hole in the valence band. Those. the energy spent on the formation of a pair of current carriers is divided into two equal parts, and thus the origin of reference for each of these processes (the transition of an electron to the creation of a hole) must be in the middle of the band gap.

Number of electrons transferred to the conduction band and number of holes formed~

Thus, the conductivity of intrinsic semiconductors

γ is a constant determined by the type of substance.

Those. with increasing T, γ increases, since from the point of view of band theory, the number of electrons increases, which, as a result of thermal excitation, move into the conduction band.

those.

According to the slope of the line ln γ it is possible to determine the bandgap width D E.

§ 4 Impurity conductivity of semiconductors

In semiconductors containing impurities, electrical conductivity consists of intrinsic and impurity.

Conductivity, caused by the presence in the semiconductor crystal of impurities from atoms with different valency called impurity. Impurities that cause an increase in free electrons in a semiconductor are called donor, and causing an increase in holes - acceptor.

The different effects of impurity atoms are explained as follows. Let us assume that in a germanium crystal ( Ge 4+ ) whose atoms have 4 valence electrons, we introduce pentavalent arsenic As 5+ . In this case, the arsenic atoms, with their 4th out of five valence electrons, enter into a bond. The 5th valence electron of arsenic will be unbound, i.e. becomes a free electron. Semiconductors whose electrical conductivity has increased due to the formation of an excess of free electrons when an impurity is introduced are called electronically conductive semiconductors (semiconductor n -type),A donor impurity (donating an electron).

Introduction to a 4-valence semiconductor of a 3-valence element, for example ( In 3+ ) indium leads, on the contrary, to an excess of holes over free electrons. In this case, the covalent bonds will not be completely completed and the resulting holes can move around the crystal, creating hole conduction. Semiconductors whose electrical conductivity is mainly due to the movement of holes are called hole-conducting semiconductors or semiconductors R-type, and an admixture - acceptor (exciting electron from a covalent bond or from the valence band). The energy levels of these impurities are called acceptor levels- located above the valence band.

The energy levels of donor impurities are called donor levels- located below the lower level of the conduction band.

In impurity semiconductors, charge carriers are main(electrons in a conductorn-type) and not the main ones(holes in the semiconductor R-type, electrons in a semiconductorn-type).

The presence of impurity levels in semiconductors significantly changes the position of the Fermi level E F . In a semiconductorn-type at T= 0 K E F located midway between the bottom of the conduction band and the donor level. With increasing T An increasing number of electrons move from the donor level to the conduction band, but due to thermal excitation, some electrons from the valence band move to the conduction band. Therefore, with increasing T The Fermi level shifts down to the middle of the band gap.

In semiconductors R-type at T = 0 TO,E F midway between the acceptor level and the top of the valence band. With increasing T E F shifts to the middle of the band gap.

The dependence of the conductivity of semiconductors on temperature has the form shown in the figure (for more details, see laboratory work 8.6.).