What creates an electric current in semiconductors. Electric current in semiconductors

In semiconductors, this is the directed movement of holes and electrons, which is influenced by an electric field.

As a result of the experiments, it was noted that the electric current in semiconductors is not accompanied by the transfer of matter - they do not undergo any chemical changes. Thus, electrons can be considered current carriers in semiconductors.

The ability of a material to form an electric current in it can be determined. According to this indicator, conductors occupy an intermediate position between conductors and dielectrics. Semiconductors are various types of minerals, some metals, metal sulfides, etc. Electric current in semiconductors arises due to the concentration of free electrons, which can move in a direction in a substance. Comparing metals and conductors, it can be noted that there is a difference between the temperature effect on their conductivity. An increase in temperature leads to a decrease In semiconductors, the conductivity index increases. If the temperature in the semiconductor increases, then the movement of free electrons will be more chaotic. This is due to the increase in the number of collisions. However, in semiconductors, in comparison with metals, the concentration of free electrons increases significantly. These factors have the opposite effect on the conductivity: the more collisions, the lower the conductivity, the greater the concentration, the higher it is. In metals, there is no relationship between temperature and the concentration of free electrons, so that with a change in conductivity with increasing temperature, the possibility of an ordered movement of free electrons only decreases. With regard to semiconductors, the effect of increasing the concentration is higher. Thus, the more the temperature rises, the greater the conductivity will be.

There is a relationship between the movement of charge carriers and such a concept as electric current in semiconductors. In semiconductors, the appearance of charge carriers is characterized by various factors, among which the temperature and purity of the material are especially important. By purity, semiconductors are divided into impurity and intrinsic.

As for the intrinsic conductor, the influence of impurities at a certain temperature cannot be considered significant for them. Since the band gap in semiconductors is small, in an intrinsic semiconductor, when the temperature reaches, the valence band is completely filled with electrons. But the conduction band is completely free: there is no electrical conductivity in it, and it functions as a perfect dielectric. At other temperatures, there is a possibility that during thermal fluctuations certain electrons can overcome the potential barrier and find themselves in the conduction band.

Thomson effect

The principle of the Thomson thermoelectric effect: when an electric current is passed in semiconductors along which there is a temperature gradient, in addition to Joule heat, additional amounts of heat will be released or absorbed in them, depending on the direction in which the current flows.

Insufficiently uniform heating of a sample having a homogeneous structure affects its properties, as a result of which the substance becomes inhomogeneous. Thus, the Thomson phenomenon is a specific Pelte phenomenon. The only difference is that it is not the chemical composition of the sample that is different, but the eccentricity of the temperature causes this inhomogeneity.

Semiconductors are substances that are intermediate in electrical conductivity between good conductors and good insulators (dielectrics).

Semiconductors are also chemical elements (germanium Ge, silicon Si, selenium Se, tellurium Te), and compounds of chemical elements (PbS, CdS, etc.).

The nature of current carriers in different semiconductors is different. In some of them, charge carriers are ions; in others, the charge carriers are electrons.

Intrinsic conductivity of semiconductors

There are two types of intrinsic conduction in semiconductors: electronic conduction and hole conduction in semiconductors.

1. Electronic conductivity of semiconductors.

Electronic conductivity is carried out by directed movement in the interatomic space of free electrons that have left the valence shell of the atom as a result of external influences.

2. Hole conductivity of semiconductors.

Hole conduction is carried out with the directed movement of valence electrons to vacant places in pair-electron bonds - holes. The valence electron of a neutral atom located in close proximity to a positive ion (hole) is attracted to the hole and jumps into it. In this case, a positive ion (hole) is formed in place of a neutral atom, and a neutral atom is formed in place of a positive ion (hole).

In an ideally pure semiconductor without any foreign impurities, each free electron corresponds to the formation of one hole, i.e. the number of electrons and holes involved in the creation of the current is the same.

The conductivity at which the same number of charge carriers (electrons and holes) occurs is called the intrinsic conductivity of semiconductors.

The intrinsic conductivity of semiconductors is usually small, since the number of free electrons is small. The slightest traces of impurities radically change the properties of semiconductors.

Electrical conductivity of semiconductors in the presence of impurities

Impurities in a semiconductor are atoms of foreign chemical elements that are not contained in the main semiconductor.

Impurity conductivity- this is the conductivity of semiconductors, due to the introduction of impurities into their crystal lattices.

In some cases, the influence of impurities manifests itself in the fact that the "hole" mechanism of conduction becomes practically impossible, and the current in the semiconductor is carried out mainly by the movement of free electrons. Such semiconductors are called electronic semiconductors or n-type semiconductors(from the Latin word negativus - negative). The main charge carriers are electrons, and not the main ones are holes. n-type semiconductors are semiconductors with donor impurities.

1. Donor impurities.

Donor impurities are those that easily donate electrons and, consequently, increase the number of free electrons. Donor impurities supply conduction electrons without the appearance of the same number of holes.

A typical example of a donor impurity in tetravalent germanium Ge is pentavalent arsenic atoms As.

In other cases, the movement of free electrons becomes practically impossible, and the current is carried out only by the movement of holes. These semiconductors are called hole semiconductors or p-type semiconductors(from the Latin word positivus - positive). The main charge carriers are holes, and not the main - electrons. . Semiconductors of the p-type are semiconductors with acceptor impurities.

Acceptor impurities are impurities in which there are not enough electrons to form normal pair-electron bonds.

An example of an acceptor impurity in germanium Ge are trivalent gallium atoms Ga

Electric current through the contact of semiconductors of p-type and n-type p-n junction is the contact layer of two impurity semiconductors of p-type and n-type; The p-n junction is a boundary separating regions with hole (p) conduction and electronic (n) conduction in the same single crystal.

direct p-n junction

If the n-semiconductor is connected to the negative pole of the power source, and the positive pole of the power 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. Electrons, crossing the boundary, "fill" the holes, the current through the pn junction is carried out by the main charge carriers. As a result, the conductivity of the entire sample increases. With such a direct (throughput) direction of the external electric field, the thickness of the barrier layer and its resistance decrease.

In this direction, the current passes through the boundary of the two semiconductors.

Reverse pn junction

If the n-semiconductor is connected to the positive pole of the power source, and the p-semiconductor is connected to the negative pole of the power source, 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, the current through p -n-transition is carried out by minor charge carriers. This leads to a thickening of the barrier layer and an increase in its resistance. As a result, the conductivity of the sample turns out to be insignificant, and the resistance is large.

A so-called barrier layer is formed. With this direction of the external field, the electric current practically does not pass through the contact of the p- and n-semiconductors.

Thus, the electron-hole transition has one-sided conduction.

The dependence of the current on the voltage - volt - current characteristic of the p-n junction is shown in the figure (volt - current characteristic of the direct p-n junction is shown by a solid line, volt - ampere characteristic of the reverse p-n junction is shown by a dotted line).

Semiconductors:

Semiconductor diode - for rectifying alternating current, it uses one p - n - junction with different resistances: in the forward direction, the resistance of the p - n - junction is much less than in the reverse direction.

Photoresistors - for registration and measurement of weak light fluxes. With their help, determine the quality of surfaces, control the dimensions of products.

Thermistors - for remote temperature measurement, fire alarms.

Semiconductor- this is a substance in which the resistivity can vary over a wide range and decreases very quickly with increasing temperature, which means that the electrical conductivity (1 / R) increases.
- observed in silicon, germanium, selenium and in some compounds.

Conduction mechanism semiconductors

Semiconductor crystals have an atomic crystal lattice, where outer electrons are bound to neighboring atoms by covalent bonds.

At low temperatures, pure semiconductors have no free electrons and it behaves like a dielectric.

Semiconductors are pure (no impurities)

If the semiconductor is pure (without impurities), then it has own conductivity, which is small.

There are two types of intrinsic conduction:

1 electronic(conductivity "n" - type)

At low temperatures in semiconductors, all electrons are associated with nuclei and the resistance is large; as the temperature increases, the kinetic energy of the particles increases, the bonds break and free electrons appear - the resistance decreases.
Free electrons move opposite to the electric field strength vector.
The electronic conductivity of semiconductors is due to the presence of free electrons.

2. perforated(conductivity "p"-type)

With an increase in temperature, the covalent bonds between atoms are destroyed, carried out by valence electrons, and places with a missing electron are formed - a "hole".
It can move throughout the crystal, because. its place can be replaced by valence electrons. Moving a "hole" is equivalent to moving a positive charge.
The hole moves in the direction of the electric field strength vector.

In addition to heating, the breaking of covalent bonds and the appearance of intrinsic conductivity of semiconductors can be caused by illumination (photoconductivity) and the action of strong electric fields.

The total conductivity of a pure semiconductor is the sum of the conductivities of the "p" and "n" types
and is called electron-hole conductivity.

Semiconductors in the presence of impurities

They have own + impurity conductivity
The presence of impurities greatly increases the conductivity.
When the concentration of impurities changes, the number of carriers of the electric current - electrons and holes - changes.
The ability to control the current underlies the widespread use of semiconductors.

Exist:

1)donor impurities (giving away)

They are additional suppliers of electrons to semiconductor crystals, easily donate electrons and increase the number of free electrons in a semiconductor.
These are conductors "n" - type, i.e. semiconductors with donor impurities, where the main charge carrier is electrons, and the minority is holes.
Such a semiconductor has electronic impurity conductivity.

For example - arsenic.

2. acceptor impurities (host)

They create "holes" by taking electrons into themselves.
These are semiconductors "p" - type, those. semiconductors with acceptor impurities, where the main charge carrier is holes, and the minority is electrons.
Such a semiconductor has hole impurity conductivity.

For example, indium.

Electrical properties of "p-n" junction

"p-n" transition(or electron-hole transition) - the contact area of two semiconductors, where the conductivity changes from electronic to hole (or vice versa).

In a semiconductor crystal, such regions can be created by introducing impurities. In the contact zone of two semiconductors with different conductivities, mutual diffusion will take place. electrons and holes and a blocking electric layer is formed. The electric field of the blocking layer prevents the further transition of electrons and holes through the boundary. The barrier layer has an increased resistance compared to other areas of the semiconductor.

The external electric field affects the resistance of the barrier layer.
With the direct (transmission) direction of the external electric field, the electric current passes through the boundary of two semiconductors.
Because electrons and holes move towards each other to the interface, then the electrons, crossing the interface, fill the holes. The thickness of the barrier layer and its resistance are continuously decreasing.

Access mode p-n transition:

With the blocking (reverse) direction of the external electric field, the electric current will not pass through the contact area of the two semiconductors.
Because electrons and holes move from the boundary in opposite directions, then the blocking layer thickens, its resistance increases.

Blocking mode p-n transition.

>>Physics: Electric current in semiconductors

What is the main difference between semiconductors and conductors? What structural features of semiconductors have given them access to all radio devices, televisions and computers?
The difference between conductors and semiconductors is especially evident when analyzing the dependence of their electrical conductivity on temperature. Studies show that for a number of elements (silicon, germanium, selenium, etc.) and compounds (PbS, CdS, GaAs, etc.), the resistivity does not increase with increasing temperature, as in metals ( fig.16.3), but, on the contrary, decreases extremely sharply ( fig.16.4). Such substances are called semiconductors.

From the graph shown in the figure, it can be seen that at temperatures close to absolute zero, the resistivity of semiconductors is very high. This means that at low temperatures the semiconductor behaves like an insulator. As the temperature rises, its resistivity decreases rapidly.
The structure of semiconductors. In order to turn on the transistor receiver, you do not need to know anything. But to create it, one had to know a lot and have an extraordinary talent. To understand in general terms how a transistor works is not so difficult. First you need to get acquainted with the mechanism of conduction in semiconductors. And for this you have to delve into the nature of the connections holding the atoms of a semiconductor crystal next to 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 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-electron bond, called covalent bond. In the formation of this bond, one valence electron participates from each atom, which are separated from the atom to which they belong (collected by the crystal) and, during their movement, spend most of their time in the space between neighboring atoms. Their negative charge keeps the positive silicon ions near each other.
One should not think that the collectivized 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 the neighboring atom, it can move on to the next, and then further along the entire crystal. Valence electrons belong to the entire crystal.
Pair-electron bonds in a silicon crystal are strong enough and do not break at low temperatures. Therefore, silicon does not conduct electricity at low temperatures. The valence electrons involved in the bonding of atoms are, as it were, a “cementing solution” that holds the crystal lattice, and an external electric field does not have a noticeable effect on their movement. A germanium crystal has a similar structure.
electronic conductivity. When silicon is heated, the kinetic energy of the 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 in them is called electronic conductivity. As the temperature rises, the number of broken bonds, and hence the number of free electrons, increases. When heated from 300 to 700 K, the number of free charge carriers increases from 10 17 to 10 24 1/m 3 . This leads to a decrease in resistance.
hole conduction. When a bond is broken between semiconductor atoms, a vacancy is formed with a missing electron. He is called hole. The hole has an excess positive charge compared to the rest of the unbroken bonds (see Fig. 16.6).
The position of the hole in the crystal is not fixed. The following process is continuously going on. One of the electrons that provide the connection between atoms jumps to the place of the formed hole and restores the pair-electron 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 movement of holes, equivalent to the movement of positive charges, occurs randomly and therefore does not create an electric current. In the presence of an electric field, an ordered movement of holes occurs, and, thus, an electric current associated with the movement of holes is added to the electric current of free electrons. 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 (+) for one free electron (-). When a field is applied, a free electron is displaced against the field strength. One of the bound electrons also moves in this direction. It looks like the hole is moving in the direction of the field.
So, in semiconductors there are two types of charge carriers: electrons and holes. Therefore, semiconductors have not only electronic, but also hole conductivity.
We have considered the mechanism of conduction in pure semiconductors. Conductivity under these conditions is called own conductivity semiconductors.
The conductivity of pure semiconductors (intrinsic conductivity) is carried out by the movement of free electrons (electronic conductivity) and the movement of bound electrons to vacant sites of pair-electron bonds (hole conduction).

???
1. What bond is called covalent?
2. What is the difference between the dependence of the resistance of semiconductors and metals on temperature?
3. What mobile charge carriers are there in a pure semiconductor?
4. What happens when an electron meets a hole?

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics Grade 10

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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. The average energy of thermal motion of electrons and holes is equal to 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 increasing 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 be many times greater than the speed of directed 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 is 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 the 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 there is no external electric field in the 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 influence 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 the 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 the mean free path, l. The average thermal velocity can be directed in both positive and negative directions. These quantities are related to each other 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 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: