Temperature level of electrical conductivity of metals. Electrical conductivity versus temperature Temperature conductivity

Yak was intended in At the end of the day, As the temperature rises, the conductor will experience more delays free flow of electrical charge– electrons in the conduction zone and electrons in the valence zone. Since the external electric field is daily, a number of charged particles are carried chaotic character And the flow through any cross-section of the expression is equal to zero. Average fluidity of particles - so called. "thermal fluidity" can be expressed using the same formula as the average thermal fluidity of the molecules of an ideal gas

de k- Boltzmann postion; m-Effective mass of electronics or parts.

When the external electric field is stagnant, a signal is sent to the conductor, "Dreifova" fluidity component - Along the field near the roads, across the field - near the electronics, then. Electrical fluid leaked through the eye. Stream thickness j develop from the strengths of the “electronic” j n and "dirochnogo" j p strumiv:

de n, p- concentration of free electrons and particles; υ n , υ p- Drift speed of the charge nose.

Here it is important to remember that if you want to charge the electron and the dirk - the side behind the sign, and also the vectors of drift fluids in the direction of the proximal side, so that the total stream is actually the sum of the modules of the electronic and dik strum.

It's obvious that it's cool υ n і υ p themselves lie under the external electric field (in the simplest form - linearly). We have introduced proportionality coefficients μ nі μ p, as they call “rukhomy” noses charge

And let’s rewrite formula 2 to look like this:

j = en n E+ep p E= n E+ p E= E.(4)

Here  - electrical conductivity of the conductor, and  n і  p- These are electronic and physical warehouses, obviously.

It is obvious from (4) that the electrical conductivity of the conductor is determined by the concentrations of high charge carriers in each of its fragility. This will also be true for the electrical conductivity of metals. Ale in metals the concentration of electrons is very high
and keep at eye temperature. Looseness electrons in metals changes with temperature This is due to an increase in the number of electrons colliding with thermal collisions of crystalline oxides, which leads to a change in the electrical conductivity of metals due to increases in temperature. U Newswires and the main contribution to the temperature and electrical conductivity is reduced storage depending on temperature and concentration Noses in charge.

Let's take a look at the process of thermal activation ( generation) electrons from the valence band of the conductor to the conduction band. I want the average energy of thermal collision of crystal atoms
For example, at a room temperature of only 0.04 eV, which is much less than the width of the shielded zone of most of the conductors among the atoms of the crystal there will be such, the energy of which can be equalized with g. When energy is transferred from these atoms to electrons, they remain in the conduction zone. Number of electrons in the energy interval from ε to ε + dε conductivity zones can be written as:

de
- Strength of energy levels (6);

- level of population density with energy ε electron ( Fermi subdivision function). (7)

In formula (7) the symbol F designated sov. farm rhubarb. Metals have Fermi rhubarb - remaining busy with electrons rhubarb at absolute zero temperature (div. Introduction). True, f(ε ) = 1 at ε < Fі f(ε ) = 0 at ε > F (Fig.1).

Fig.1. Rozpodil Fermi-Dirak; often at a temperature of absolute zero and “dissolve” at terminal temperatures.

At the conductors, As we are pleased to hear, the Fermi’s zeal is expected to meet near the fenced area, tobto. na nomu nomozhe buti elektron. However, in the conductors at T = 0, all stations that lie lower than the Fermi level are filled, and those that are higher than the Fermi level are empty. Beyond the end temperature, the level of population of electrons with energy ε > F is no longer equal to zero. However, the concentration of electrons in the conductivity zone of the conductor is still much less than the number of high energy sources in the zone, then.
. Todi in the sign (7) can be marked with one and the function of division can be written down in the “classical” neighbor:

. (8)

The electron concentration at the conductivity zone can be calculated by integrating (5) over the conductivity zone from the bottom - E 1 to the top - E 2 :

In the integral (9), the bottom of the conductivity zone is taken to be zero, and the upper boundary is replaced by
through a change in the exponential multiplier due to the increase in energy.

After calculating the integral, we can remove:

. (10)

Calculation of the concentration of oxides at the valence band is given by:

. (11)

For the conductor, there is no house near the warehouse, so called. Vlasny conductor, the concentration of electrons in the conductivity zone is responsible for the concentration of diodes in the valence zone ( mind of electroneutrality). (It is significant that nature does not have such conductors, but at low temperatures and concentrations, houses can be supplied with an influx of the remaining ones at the mercy of the conductor). The same, equal to (10) and (11), is removed for the level of the Farm from the moisture distributor:

. (12)

Tobto. at absolute zero temperature Fermi's Vlasny for sure in the middle of the fenced area,і pass near the middle of the fenced area at not too high temperatures, sprat shifting start ringing at b_k conductivity zones(the effective mass of particles is, as a rule, greater than the effective mass of electrons (div. Introduction). Now, substituting (12) in (10), for the concentration of electrons we subtract:

. (13)

A similar relationship emerges for the concentration of wood:

. (14)

Formulas (13) and (14) with sufficient accuracy allow one to determine the concentration of charge carriers in to the powerful conductor. The concentration values calculated for these relationships are called powerful concentrations. For example, for germanium Ge, silicon Si and gallium arsenide GaAs at T=300 K the smell becomes consistent. In practice, for the preparation of conductor devices, conductors with significantly higher concentrations of charge carriers (
). The greater, equalized with moisture, concentration of noses is due to the administration of the navigator electrically active houses(I'm still talking about the so-called amphoteric Households introduced by a provider do not change the concentration of noses in a person). Depending on the valence and ionic (covalent) radius, home atoms can be differently included in the crystalline elements of the conductor. Some of them can replace the atom of the main speech at vuzli grati - houses substitution It is important for others to grow up at interuniversities grati - houses vprovadzhennya. The diversity and inflow of the power of the conductor.

It is acceptable that in a crystal with almost valence silicon atoms, some of the Si atoms are replaced by atoms of a pentavalent element, for example, phosphorus atoms R. Most of the valence electrons of the phosphorus atom form a covalent bond with the closest silicon atoms. The fifth valence electron of the phosphorus atom will be bound to the ion brush Coulomb interaction. In general, this pair with the phosphorus ion with the charge +e and the coulombic interaction of the electron associated with it is a predictable water atom, which is why such houses are also called hydrogen-like little houses. Coulomb interaction Crystal will have a meaning weakened through electrical polarization in extra household ions of neighboring atoms. Energy of ionization such a home center can be estimated using the following formula:

, (15)

de - The first ionization potential for the water atom is 13.5 eV;

χ – dielectric penetration of crystal ( χ =12 for silicon).

Substituting in (15) the values and values of the effective mass of electrons in silicon - m n = 0,26 m 0 is taken for the energy of ionization of the phosphorus atom in the crystal lattice of silicon ε I = 0.024 eV, which is significantly less than the width of the shielded zone and generates less than the average thermal energy of atoms at room temperature. This means, first of all, that household atoms are much easier to ionize than the atoms of the main speech, and, in other words, at room temperature, these household atoms will be ionized. Appearance in the conductivity zone of the conductor of electrons that passed there from Domishkovykh Rivniv, not related to the opening of the hole in the valence zone. Therefore concentration main noses the concentration of electrons in a given particle can be increased by several orders of magnitude non-main noses- Darok. Such carriers are called electronic or by phone carriers n -Like, and the houses that notify the transmitter of electronic conductivity are called donors. If crystal silicon introduces a house of atoms of a trivalent element, for example, boron B, then one of the covalent bonds of the house atom with the vessel atoms is lost to silicon unfinished. The burying of this bond of an electron from one of the neighboring silicon atoms will lead to the appearance of a hole at the valence band, then. The crystal has to be careful about its conductivity (conductor p -Like). Houses that eat electrons are called acceptors. On the energy diagram of the conductor (Fig. 2), the donor rhubarb is located below the bottom of the conductivity zone by the amount of the donor ionization energy, and the acceptor rhubarb is located above the bottom of the valence band by the energy onization of the acceptor. For water donors and acceptors, such as those in silicon elements of groups V and III of the Mendelev periodic table, the ionization energies are approximately equal.

Fig.2. Energy diagrams of electronic (left-handed) and manual (right-handed) transmitters. The position of the Fermi levels for temperatures close to absolute zero is shown.

Calculating the concentration of carrier charge in the conductor with the regulation of home electronic systems is not easy to achieve and analytical solutions can be avoided in many cases.

Let's take a look at the n-type conductor when temperature, enough low. And here you can take advantage of your ability. All electrons in the conductivity zone of such a conductor are electrons that have passed there from donor levels:

. (16)

Here
- Concentration of donor atoms;

- Number of electrons that were lost at donor sites :

. (17)

From the point of view (10) and (17) level 16 we write down:

. (18)

Virishyuchi tse kvadratne rіvnyannya shodo
, cancelable

Let's look at the solution for very low temperatures (in practice, mean temperatures around tens of degrees Kelvin), if the other addition under the square root sign is more than one. Not very well in singles, let’s take it away:

, (20)

tobto. for low temperatures, the farm’s rave grows approximately in the middle between the donor rave and the bottom of the conductivity zone (at T = 0K – exactly in the middle). By substituting (20) with the formula for electron concentration (10), we can see that the electron concentration increases with temperature following an exponential law

. (21)

Exhibitor Showcase
indicates that in a given temperature range the electron concentration increases exponentially Ionization of donor houses

For higher temperatures - for such, if the moisture conductivity is still insignificant, but the mind is reduced
, the other addition under the root will be less than one and vikorystic relationship

+…., (22)

The position of the Fermi level is taken away

, (23)

and for the electron concentration

. (24)

All donors are already ionized, the concentration of atoms near the conductivity zone is the same as the concentration of donor atoms - this is the so-called. area of the interior of the house. At higher temperatures there is an intense deflection from the conduction zone of electrons from the valence band (ionization of atoms of the main substance) and the concentration of charge carriers again begins to increase following the exponential law (13), characteristic of areas with moisture conductivity. How to reveal the degree of concentration of electrons as a function of temperature in coordinates
, you can see a laman line, which consists of three sections, corresponding to the higher temperature ranges (Fig. 3).

R IS.3. Temperature level of electron concentration in a conductor-type.

Similar relationships, up to a multiplier, are obtained when calculating the concentration of oxides in a p-type conductor.

At very high concentrations of the house (~10 18 -10 20 cm -3), the conductor transforms into so called. virogene mill. The houses of the village are splintered into house zone, which can often overlap with the conductivity zone (in electronic conductors) or with the valence band (in dielectrics). In which the concentration of the charge charge actually ceases to lie at temperatures up to very high temperatures, then. the conductor is driven like metal ( quasi-metallic conductivity). The Rhubarb Fermi in the degenerate conductors will be either very close to the edge of the conductor zone, or the conductors will be in the middle of the permissible energy zone, so that the zone diagram of such a conductor will be similar to the zone d Igram metal (div. Fig. 2a Introduction). To increase the concentration of the charge in such conductors, the function of the subsection of the trace is taken over the view (8), as the system worked, and the view of the quantum function (7). Integral (9) in this case is calculated using numerical methods and is called Fermi-Dirac integral Tables of Fermi-Dirac integrals for induced values, for example, in the monograph by L.S. Stilbans.

At
The stage of generation of the electronic (dirty) gas of the floor is high, so that the concentration of the nozzles does not lie at a temperature up to the melting temperature of the conductor. Such “virgins” of transmitters are used in the production of low electronic devices, among some of the most important ones. Injection lasers and tunnel diodes.

Singing, although smaller in size, the temperature of the electrical conductivity is introduced temperature level of friability Noses in charge. Looseness, the “macroscopic” meaning given by us in (3), can be expressed through the “microscopic” parameters – the effective mass an hour of relaxation to the impulse – average hour of free run of an electron (hole) between two last stops with defects in crystal mounts:

, (25)

and the electrical conductivity with the relationship between (4) and (25) will be written as:

. (26)

Yak defects - Centers of Rossiyuvannya Thermal damage of crystalline mounts – acoustic and optical – may occur phononi(div. methodological textbook “Structure and dynamics ...”), house atoms– ionized and neutral, atomic areas of the crystal – dislocations, surface Krystal that between grains in polycrystals, etc. The process itself of dissecting the charge on defects can be spring-loadedі non-spring - in the first phase there is no change in quasi-impulse electron (dirk); in another way – a change in both quasi-impulse and energy of the part. As the process of dispersing the charge on the lattice defects - spring, that hour of relaxation of the impulse can be represented by the appearance of static content in the energy of the section:
. So, for the most important types of spring dissipation of electrons on acoustic phonons and ions of the house.

(27)

і
. (28)

Here
- quantities that do not lie in the energy;
- Concentration ionized house of any type.

The average relaxation time is based on the following formula:

;
. (29)

We reject the rules (25)-(29):

. (30)

Since, in any temperature range, the contribution to the looseness of noses, which is attributable to different dissipation mechanisms, can be equated by value, then the looseness is measured by the formula:

, (31)

de index i It corresponds to the singing mechanism of dispersion: on house centers, acoustic phonons, optical phonons, etc.

The typical level of fragility of electrons (frames) in the conductor as a function of temperature is shown in Fig. 4.

Fig.4. Typical retention depending on the temperature of the nose's friability to the charge of the conductor.

At very low temperatures (in the area of absolute zero) the houses are not yet ionized, dissolution is carried out at neutral home centers and fragility is practical don't lie low type of temperature (Fig. 4, panel a-b). As the temperature increases, the concentration of ionized compounds increases according to an exponential law, and the looseness falls zgіdno (30) – dilyanka b-v. In the area interior of the house the concentration of ionized house centers does not change, and the friability increases, as
(Fig. 4, c-d). With a further increase in temperature, the dispersion on acoustic and optical phonons begins to become more important and the friability decreases again (g-d).

The temperature range of the looseness is important - a static function of temperature, and the temperature range of the concentration is exponential, so the temperature variation of electrical conductivity in the main rice is a repeatable temperature range of the concentration of the charge. u. This makes it possible to accurately determine, based on temperature and electrical conductivity, the most important parameter of the conductor – the width of its protected zone, which is intended to be produced in this robot.

For chargers with one charge, the electrical conductivity γ is determined by the

de n - Concentration of free charge carriers, m -3; q is the value of the skin charge; μ − charge carrying speed, which is equal to the average charge carrying speed (υ) up to the field strength (E): υ/E, m 2 /(B∙c).

The temperature of the concentration of noses is presented for the little one 5.3.

In the area of low temperatures, the plot of land between points a and b characterizes the concentration of plants, called houses. With increasing temperatures, the number of noses supplied by houses increases, until the electronic resources of house atoms are exhausted (point b). At the site of the b-v house, it is already visible, and the transition of electrons from the main conductor through the shielded area is still visible. The section of the curve with a steady concentration of charge carriers is called the area of the empty house. Next, the temperature rises, which begins to increase the concentration of particles due to the passage of electrons through the shielded zone (division v-g). The height of the plot characterizes the width of the fenced zone of the filler (the tangent of the edge gives the value ΔW). Nahila plots a-b to lie under the energy of ionization of houses ΔW p.

Small 5.3. Typical concentration of charge concentration

at the provider's temperature

The little one 5.4 shows the temperature level of the friability of the nose charge for the conductor.

Small 5.4. Temperature level of nose friability

charge in the conductor

The increased fluidity of the free-running wear charge with temperature changes is explained by the fact that the higher the temperature, the greater the thermal fluidity of the free-running wear charge. However, with a further increase in temperature, the thermal oscillation of the burrs and the charge carrier begin to stick to it more and more often, and the friability decreases.

For the little one 5.5 the temperature level of the power supply for the conductor is presented. This storage capacity is foldable, because the electrical conductivity depends on the fragility and number of noses:

In the AB section, the increase in the pet's electrical conductivity due to increased temperatures is determined by the house (behind the direct effect on this section is indicated the activation energy of the house W p). At the end of the BV period, saturation occurs, as the capacity of the noses does not increase, and the conductivity drops due to a change in the friability of the noses of the charge. In the context of VG, the increase in conductivity is due to an increase in the number of electrons of the main conductor, which flows into the shielded zone. According to the height, the straight line indicates the width of the fenced-in area of the main pipeline. For nearby ruptures, you can quickly use the formula

Where the width of the fenced zone W is calculated as eB.

Small 5.5. Temperature range of the feedstock electrical conductivity

for a telephone director

The laboratory robot is monitoring the silicon conductor.

Silicon, Like Germany, is included in group IV of table D.I. Mendelev. It is one of the most abundant elements in the earth's crust, accounting for approximately 29%. However, in nature, the veins do not converge.

Technical silicon (about one hundred houses), which is extracted from dioxide (SiO 2) in an electric discharge between graphite electrodes, is widely used in ferrous metallurgy as an alloying element ( for example, electrical steel). Technical silicon as a conductor of vicors cannot. Wine is the output product for the production of silicon of conductor purity, instead of which it may be less than 10 -6%.

The technology for stripping silicon of conductor purity is very complex and includes a number of stages. The end purification with silicon can be formed using the zone melting method, which poses a number of difficulties, since the melting temperature of silicon is very high (1414 ° C).

Silicon is the main material for the production of conductor devices: diodes, transistors, zener diodes, thyristors, etc. At silicon, the upper limit of the operating temperature of the devices can be set at a material purification stage of 120-200 degrees, which is significantly higher than in Germany.

Conductors are materials whose main feature is the supply of electrical conductivity from external energy inputs, as well as the concentration and type of house.

The clear importance of the authorities of the air carriers and pro-
Water carriers are identified by the type of their chemical bonds. In metals, the valence electrons of atoms of crystalline oxides are partly a group of equal charge carriers, called electron gas (metal bond). The number of noses
bodies of charge, which indicates the number of atoms per unit
There is no information about the crystalline orates. It is impossible to significantly change this concentration of carriers in the charge by the influx of external factors (temperature, changes, introduced housework, deformation, etc.). Consider all the features of the conductivity of conductors: positive temperature coefficient of the power supply, independence of the concentration of charge carriers in the home at the gates, conductivity, etc.

In the conductors, all the valence electrons of the atoms take part in the creation of a covalent (or ion-covalent) saturated chemical bond. With conductor crystals, there is no need for quasi-strong charge carrying, which is due to the direct influence of the external factor, so that at a temperature of absolute zero the conductor does not have any electrical conductivity. The value of the covalent (ionic-covalent) bond (bonding energy) indicates the width of the shielded zone of the conductor. At temperatures below 0 K, some of the charge carriers, hydrated by thermal energy, can create a chemical bond to create an equal number of electrons in the conductivity zone. Irok is near the valence band. the charge of their concentration is assigned to the relationship

where i - The effective strength of the joints is directed from the bottom of the conductivity zone to the wall of the free zone.

To control the type of electrical conductivity and the conductivity values of the conductor at the site of the crystal lattice, introduce at a low concentration of the house with valency,
varies on the larger or smaller side depending on the valence of the main atoms of the conductor. Such houses in the barrier zone of the conductor are indicated by additional energy levels: donor - near the bottom of the conductivity zone and acceptor - near the bottom of the valence zone. The energy required for thermal generation of charge carriers, the formation of the presence of houses (ionization energy of houses) is 50-100 times less than the width of the protected zone:

The process of thermogeneration of house noses is also quite simple and is described by the formulas

de - concentration of donor houses, and - acceptor houses While the temperature is low, not all houses are ionized and the concentration of the hosts is determined by formulas (4). However, in typical episodes, even at a temperature significantly lower than the room temperature (close to -60 0 C), all components are ionized and with further heating the concentration does not change and remains the same as the concentration of the introduced components. (kozhen atom of the house “dav” one charge at a time. Therefore, in any temperature range, the nose concentration practically does not lie below the temperature (region II in Fig. 4). However, at a significant increase in temperature (for silicon, for example, close to 120 0 C), the breakdown of moisture bonds begins behind the mechanism represented by formula (3) and the concentration of charge carriers begins to increase sharply. Take a look at the illustration in Fig. 4, on any representation of the temperature range, the concentration of charge carriers is on a nearly logarithmic scale relative to the return temperature (the significance of such a scale becomes obvious after the logarithm of expressions (3) and (4)).

Here - the temperature of the interior of the house - the temperature of the transition to moisture conductivity. Formulas for races

Small 4. Temperature level of the concentration of the main carriers of the charge in the house conductor n- Like. I- area of weak ionization of the house (house electrical conductivity) (); II- area of the interior of the house (); III- Area of moisture conductivity ().

Having made friends, the temperatures have been lowered. In the area .III The generation of charge carriers is consistent with formula (3). At lower temperatures this process is even smaller, and therefore in the area .I The generation of noses is indicated by formula (4). As it flows from expressions (3) and (4), the greater the greater the width of the shielded zone of the conductor, and the greater the greater the greater the ionization energy of the donors (acceptors). Vakhovuyuchi scho, lay, scho >.

Quasi-strong charge carriers (electronics and dirs), powered by average thermal energy, produce a chaotic collapse with thermal fluidity. , it is important to comply with the applied action. Due to the external action of the electric field, the straightening of the charge carriers is caused - drift. At what thickness of the drift stream

de – electrical conductivity, – concentration of charge carriers, – fluidity of the direct flow under the influx of external electric field tension E.

As a rule, if Ohm's law applies, E - do not direct the charge without changing its energy (weak fields). In this way, the fluidity of the flow of the charge noses is deprived of equal, and the fluidity of the drift, which characterizes the effectiveness of the direct flow of the charge of the charge, lies in the fact that there is a strong respect for the flow of defects in the crystalline material. and decide. The parameter that characterizes the effectiveness of a direct charge carrier is called ruddability:

Obviously, there are more defects in the crystal lattice that take part in the Russian charge, then less. Under consideration, understand the change in the quasi-pulse of the direct flow of the charge, caused by the influx of defects. In addition, the fragments in the crystal are always present in various types of defects (thermal vibration of atoms, houses, etc.), then the fragility of the charge is “controlled” by the most effective dissolution mechanism:

where m Σ is the resulting looseness of the charge in the conductor; m i - looseness, equipped i dissolution mechanism. So, for example, in the region of high temperatures m Σ is controlled by the contribution of thermal vibrations of the lattice and changes with increasing temperature. In the region of low temperatures, if the deposits of garnet dispersion in m Σ are small, carrying a charge that lasts a little, they immediately find themselves in the field of Coulomb forces (gravity or displacement) of ionized houses. This very mechanism of dispersion “controls” m Σ in the conductors at low temperatures. Therefore, the looseness of the nose charge when stored depending on the temperature is determined by the following empirical relationships:

de aі b- Constant quantities.

The acidity lnm Σ(T) in crystals of the form (7) is presented in Fig. 5. In this picture, curves 1 and 2 illustrate the fact that the concentration of houses is increasing ( N pr1<N pr2) does m change? in the region of low temperatures, the mechanism of glaze dispersion in the crystal remains unchanged.

Good analysis of acoustic phonons is more important when T> 100 K. If there is a house in the area, if possible

Small 5. Temperature level of friability of charge carriers
in carriers with different concentrations of the house. N pr1

Therefore, electrical conductivity can change due to increased temperature due to changes in nose friability m Σ ( T) through the dispersion of charges on acoustic phonons.

MESSAGE FOR ROZRAKHUNOVO-GRAPHIC

ROBOTI

KAZAN STATE ENERGY CENTER

UNIVERSITY

Department of Physics

Essay

Temperature depth of the conductivity of the conductor

Vikonav: Romanov A.V. - Group ZES-1-04___________ (date, signature)

Verified by: ________________________________________ (date, signature)

Home addresses:

m. Yelabuga

vul. Okruzhne Shosse bud. 35 sq. 69

Date of overpowering:

Kazan 2006

Conductors are substances that oscillate at room temperature and have electrical conductivity in the range of 10 -8 to 10 6 Ohm -1 m -1 , which is highly deposited in view of the size of the house and the structure of the substance , as well as from external minds: temperature, lighting , external electric and magnetic fields, changes. The electrical conductivity of solids in modern physics is explained in terms of the band theory. In Fig. I displays are simplified by diagrams of the energy zones of the moisture, acceptor and donor conductors.

The crystals of the conductors inevitably stir in real minds the song of a third-party house, which suggests that it is necessary to remove material of even a high level of purity. Houses are also specially introduced either during the growth of crystals with the method of removing the conductor from the given electrical authorities, or during the preparation of adjacent structures. Such conductors are called alloyed or house-shaped. The atoms of the houses, which differ from the atoms of the main crystal by valency, create equal amounts of the allowed energy of electrons in the barrier zone, which can supply electrons to the conductivity zone, or accept electrons and from the valence band. We will look at this process from afar. This section of us has an idealized model of a water conductor in every day's home. Such guides are called powerful.

When heated, the conductivity of the conductors increases sharply. Temperature range of conductivity s The moisture carrier is indicated by a change in concentration n and fragility of electronics m - and wood m + type of temperature:

s = e ( n - m - + n + m +) (1)

The friability of the charge carriers in the conductors is kept at an equally low temperature and changes according to the law m~T –3/2. This means that with the increase in temperature, the strength of the current per hour increases, as a result of which the fluidity of the direct flow of the charge carrier to a field of the same voltage changes.

Let's take a look at the donor conductor. Due to the low concentration of electrons in the conductivity of the conductors, the conductors are ordered by the classical Maxwell-Boltzmann statistics. Therefore, in the region of low temperatures for the concentration of electrons in the conductivity zone with one type of house we can:

n = A T 3/2 e - D W / kT , (2)

where A is a coefficient that does not lie under T; DW is the activation energy of the house, which is the energy interval between the donor level and the lower edge of the conductivity zone (Fig. Ic)K - Boltzmann position.

Let's take a look at the simplified zone model of its conductor, shown in Fig. 1. This model is mainly used in the future. In this model, the energy of electrons is positive and increases along the ordinate axis. The energy of the trees is negative and flows downward. The abcis is always dependent on spatial coordinates, and also along this axis, depending on the minds of the world, temperature, concentration of the house, and the direction of the electric field can be reflected. The valence band is a zone of conductivity surrounded by straight lines, which means: E v – the line of the valence band; E c – bottom of the conductivity zone. The energy of the electron is sufficient, which means it is absorbed from the valence band. The width of the fenced zone is calculated as the difference E g = E c - E v.

Let's now look at what the physical reason is for the sharp change in the temperature range of the conductivity of conductors and metals.

Small 1. A simple zone model of a valence conductor: E v – valence band column; E c – bottom of the conductivity zone.

E g = E c – E v – width of the fenced area. G - generation of electron-dyk pair, R - recombination of electron-dyk pair.

The squiggly arrows show the processes of photon degradation and vibration during light generation and vibrational recombination in parallel.

At a temperature T > 0, the average phonon energy is similar (k - Boltzmann's constant), for example, at room temperature T = 300 K it is similar to 0.039 eV. However, through the Maxwell-Boltzmann division it is clear that the phonon has energy Eg, which can significantly exceed the average, and this certainty is proportional. The electrons gradually exchange energy with phonons during the closing process. Naturally, in stationary systems the electronic subsystem as a whole is in thermal equilibrium with the vibrations of the lattice, and around the electronics they can generate much more energy than average. Thermal excitation of an electron is the act of transferring energy from a phonon to an electron such that the rupture of a covalent bond occurs.

If an electron takes back an energy greater or equal to Eg from a phonon, it can “throw itself” from the valence band into the conduction band, where it becomes free and can take part in the transferred charge with the addition of external energy electric field. Simultaneously with the transition of the electron to the conductivity zone, a new hole is created near the valence band, which also takes part in the electrical conductivity. Thus, in power conductors, free electrons and cores are generated in pairs, this process is called the generation of electron-core pairs (Fig. 1). In this case, a reversal process occurs - the mutual annihilation of electrons and particles when the electron rotates around the valence band. This process is called recombination of electron-core pairs. The number of generation (recombination) pairs of charge carriers in one unit per hour is called the generation rate G (recombination - R). In stationary brains, the rates of thermal generation and recombination are equal, so G = R (1)

It is important that the generation of electron-core pairs can also occur when the conductor is driven by a light frequency v such that the photon energy satisfies the mind

During light generation, the electron fades the photon (Fig. 1). During the reversal process of recombination, the energy that has been released, equal to Eg, can either be transferred from the electron back to the lattice (phonon), or carried by the photon. Phonons and photons can also be instantly popularized, or else, by virtue of the law of conservation, their partial energy is less than Eg. When energy is carried away by a photon, the process is called viprominental recombination. Light generation and vibrational recombination are the basis for the operation of a whole class of optoelectronic conductor devices - the components of vibrational recombination, which we will not be able to examine in this course and.

Obviously, due to thermal generation, there are rapid transitions of electrons from one of the upper levels of the valence band, which are occupied by electrons, from one of the lower levels of the conductor zone. bottoms, - since they stink, the fragments of such transitions require less energy. The star shows that the generation rate G is proportional to: the number of possible occupied electron positions N v near the valence band wall; the number of unoccupied rivers N c near the bottom of the conductivity zone (physical displacement N v and N c will be considered further) and the availability of electron energy E g:

de, a is the proportionality coefficient that lies under the frequency of the connection of phonons and electrons. On the other hand, the rate of recombination R is proportional to the density of the “sharpness” of the noses, then. addition of electron concentration n and dirok p (g - proportionality coefficient):

fragments for your carrier n = p. In a stationary fall there is a place of jealousy (2), then

The conductivity of the crystal is (6) proportional to the concentration of electrons and friability. As can be seen from expression (7), the concentration n in a moisture conductor increases exponentially with increasing temperature, while the temperature content of the friability in conductivity plays a less significant role. Thus, the conductivity of the moisture conductor in the first place increases with the temperature according to the same law as the concentration of electrons and particles (until the dissipation of charge carriers on the thermal vibrations of the lattice becomes noticeable). This can be written:

(8)

Also, from a phenomenological point of view, conductivity of conductors in metals shows that conductivity of conductors in conductors increases rapidly with temperature changes. The physical reason for this lies in the increased rate of thermal generation of electron-core pairs due to temperature increases. If you prologarithmuvati viraz (8), then I’ll see

Therefore, if on the graph we plot lns along the ordinate axis, and the return temperature along the abcis axis, we can take it directly from the slope Eg/2k, as shown in Fig. 2. Thus, knowing the value of the direct line, you can determine the most important characteristic of the conductor - the width of the fenced zone. The value of Eg determined in this way is called the thermal width of the fenced zone, the fragments of which are also determined from the optical dimming spectra of the clay and the calculation of Eg, on the basis of virus (9).