The band structure of semiconductors is such that at low temperatures their allowed band of valence electrons is completely filled with electrons, and the nearest free conduction band is separated from it by a band gap of a certain size and is empty. The transfer of an electron to the conduction band can be carried out due to the energy of thermal motion, light or corpuscular radiation. If an electron is somehow transferred to the conduction band, then it can carry out charge transfer. After the transfer of electrons, empty spaces remain in the valence band - unfilled states of electrons, as a result of which the remaining electrons are able to move under the influence of the electric field, i.e. also contribute to the current. When describing such movement of electrons, it is more convenient to consider the movement not of the electrons themselves, but of empty spaces called holes. Holes behave as positive current carriers with a charge +e equal in absolute value to the charge of the electron and of a different sign from it. If holes are formed due to the transfer of electrons from the valence band to the conduction band, then the number of electrons in the semiconductor is equal to the number of holes. Such a semiconductor is called intrinsic (Fig. 2.4, a).
Rice. 2.4. Semiconductor energy diagrams:
a) own; b) electronic; c) hole;
E S– bottom of the conduction band; E V– ceiling of the forbidden zone; E d– donor level, E a– acceptor level
However, in any crystal there are various defects - foreign atoms, empty sites - vacancies, dislocations, etc. An electron localized near a defect has energy that falls just into the band gap, as a result of which an impurity level is formed in the band gap. If such a level lies close to the conduction band, then even with a slight increase in temperature, electrons will move from levels to the band, as a result of which they are able to move throughout the crystal.
A semiconductor in which electrons in the band are formed as a result of their transition from impurity levels is called an impurity electronic semiconductor (Fig. 2.4, b). A semiconductor may have local levels that are not normally occupied by electrons. If such levels are located close to the edge of the valence band, then with increasing temperature, electrons of the valence band can be captured by them, as a result of which mobile holes are formed in the valence band. A semiconductor with this type of impurity conductivity is a hole semiconductor (Fig. 2.4, c).
Thus, the current carriers in a semiconductor are electrons in the conduction band and holes in the valence band, and the electrical conductivity of a semiconductor can be expressed as follows:
where , – mobility of charge carriers;
n, p– concentrations of electrons and holes, respectively;
e– electron charge.
Thus, to find the dependence of electrical conductivity on temperature, it is necessary to find out how the concentrations of current carriers and their mobility change with temperature.
Conduction electrons in semiconductors obey the Fermi-Dirac distribution function:
which expresses the probability that an electron is in a quantum state with energy E at a temperature T. Here E F– Fermi energy, k– Boltzmann constant.
The electrical conductivity of an intrinsic semiconductor is determined by the electrons in the conduction band. Their concentration can be determined by the number of all states occupied by electrons n(E) in the conduction band:
Where g(E) – density of quantum states;
f(E) – Fermi-Dirac function;
E c– energy level corresponding to the bottom of the conduction band.
The final expression for the temperature dependence of the electron concentration in the conduction band of an intrinsic semiconductor has the form:
Where N V, N C– effective density of states in the valence band, conduction band.
Now let's consider the effect of temperature on the mobility of charge carriers. It is known that the mobility value is determined by the electron free path, i.e. processes of charge carrier scattering in a semiconductor:
where is the mean free path of the electron;
– average speed of thermal movement;
m* – effective mass of the carrier;
IN– some coefficient;
ζ – takes values 1/2, 3/2, 5/2 depending on the type of crystal lattice.
The general course of change in conductivity with temperature can be written as:
In this expression, the factor varies slowly with temperature, while the exponent varies strongly with temperature, E g>>kT. Therefore, for not too high temperatures, expression (2.6) can be replaced by the simpler one
If equation (2.7) is plotted graphically in ln coordinates σ from T -1 .
then the band gap E g can be determined from the slope of this linear relationship (Fig. 2.5, a).
Rice. 2.5. Semiconductor conductivity graphs:
a – intrinsic electrical conductivity; b – impurity electrical conductivity
If there are impurities in semiconductors, impurity conductivity is added to the intrinsic conductivity, and then the electrical conductivity σ can be represented as the sum of intrinsic and impurity conductivities:
where Δ E– impurity ionization energy.
Typically, the band gap is much greater than the ionization energy of the impurity, i.e. E g>>Δ E. This means that in the region of low temperatures the number of electrons released by lattice atoms is small. Therefore, at low temperatures, the electrical conductivity of an impurity semiconductor will be mainly due to the impurity electrons. At a sufficiently high temperature, almost all atoms will be ionized, and the actual increase in conductivity will occur only due to the semiconductor's own electrons. The ideal graph for an impurity semiconductor (Fig. 2.5, b) is depicted by a broken line with two straight sections corresponding to the electrical conductivity of the main lattice and the impurity.
Thus, from the slope of the straight lines one can determine the band gap E g and ionization energy of impurities. Indeed, the tangent of the angle of inclination of the straight line (Fig. 2.5)
Δ is determined similarly E.
Real graph of ln dependence σ =f( T-1) has a more complex nature, so it is better to calculate the angle of inclination along tangents drawn to the graph in the region of low and high temperatures.
Since electrons and holes in a semiconductor are a non-degenerate system, its conductivity can be considered from a classical point of view. The expression for the current density in scalar form is written as
Where n And p– electron and hole concentrations, u n And u p– their drift speeds. If the field strength is not too high, these velocities are proportional to its magnitude.
Here b n And b p– mobility of electrons and holes, respectively.
For the conductivity of metals in the classical theory, a formula was obtained, where the denominator is the mass of a free electron. On the other hand, from (8) and (9) one can obtain the conductivity in the form . Equating these expressions for conductivity, we obtain
, (10)
where the free path time τ is expressed through the average free path and the root mean square speed of thermal motion of electrons υ. Expression (10) is valid for electrons and holes in a semiconductor, if by mass we mean their effective masses.
At high temperatures, carrier scattering occurs predominantly through thermal vibrations of the lattice, i.e. phonons. The carrier path length is inversely proportional to temperature. In addition, the thermal speed of electrons υ is proportional to the root of temperature. Then mobility 
.
At low temperatures, carrier scattering occurs mainly on ionized impurity atoms. This process is similar to the scattering of particles on nuclei, studied in detail by E. Rutherford. A charged particle, flying past the nucleus, deviates from the original direction of motion so that the trajectory has the shape of a hyperbola. The free path is proportional to the fourth power of speed. In addition, the mean free path is inversely proportional to the concentration of impurities N, since the more impurity ions, the more often the carrier interacts with them. Then the mobility is proportional to the temperature to the power of 3/2. .
As shown above. Specific conductivity can be written as 
. The dependence of this quantity on temperature is due to the corresponding dependences of the concentration of carriers and their mobilities. The dependence of the mobility at all temperatures is power law. In those temperature ranges when the carrier concentration has an exponential dependence on temperature, it is this that determines the resulting dependence of conductivity on temperature.
The concentrations of electrons and holes in an intrinsic semiconductor have the expression:
, (11)
If a semiconductor is doped with impurities of a different valence, then the concentrations of electrons and holes in electron and hole semiconductors are given by the expressions:
, (12)
. (13)
Here E d And Nd is the activation energy of the impurity (the difference in the energy of the bottom of the conduction band and the donor level) and the concentration of donor impurity atoms, respectively, E g– band gap width. The effective masses of electrons and holes are denoted as m n And m p.
From all that has been said, we can conclude that the dependence of specific conductivity on temperature has the character
(14)
at low temperatures, when ionization of impurities occurs, or
(15)
at high temperatures, when their own carriers are intensively generated.
Activation energies are determined by the slope of the straight section of the graph depending on the inverse temperature T-1 . This is either the distance from the impurity level to the band boundary or the band gap.
Intrinsic conductivity occurs in well-purified semiconductors when impurities do not affect the electrical properties. At absolute zero temperature, the valence band is completely filled with electrons; in the conduction band, all levels are free and there is no electrical conductivity. As the temperature increases, the thermal generation of free charge carriers begins. Electrons, receiving energy from thermal vibrations of the lattice sufficient to overcome the band gap of width , are transferred from the valence conduction band (Figure 72.2), forming an equal number of holes in the valence band. Transitions occur at any temperature.
Thermal generation of charge carriers in an intrinsic semiconductor.
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W c – bottom of the conduction band; W V – valence band ceiling; ∆W – band gap; , ○ – electron and hole
Figure 72.2
The explanation of transitions at is associated with the static distribution of energy between the atoms of the body (the energy of thermal vibrations of individual atoms during some periods of time may be greater than its average value). Along with the excitation of carriers, reverse processes of their recombination also occur, consisting in the return of electrons from the conduction band to the valence band. In this case, electron-hole pairs disappear. The process of generation of free charge carriers is balanced by the process of recombination, and at each steady-state temperature the crystal is in a state of thermodynamic equilibrium, having a concentration of charge carriers corresponding to a given temperature. Statistical calculations show that the electron concentration n, and, consequently, the hole concentration p, increases rapidly with increasing temperature according to the exponential law
where A is a constant characteristic of a given semiconductor, independent of temperature to a first approximation; e – the base of the natural logarithm; k – Boltzmann constant; T – absolute temperature.
For example, in pure silicon, this dependence ensures that the electron concentration increases from when heated from room temperature to electron temperature.
In an intrinsic semiconductor, the electrical conductivity is:
where e is the electron charge; – electron mobility; – electron mobility.
The mobility of charge carriers, which is their drift speed in an electric field of unit strength, in semiconductors also depends on temperature. Most often, in the region of low temperatures, mobility increases due to scattering on impurities; in the region of high temperatures, where scattering on thermal vibrations of the lattice predominates, it decreases with increasing T. A typical graph of the dependence is shown in Figure 72.3. However, the temperature dependence of charge carrier concentration in semiconductors is usually much stronger than the temperature dependence of mobility. Therefore, the temperature dependence of mobility can be neglected and it can be assumed that changes in electrical conductivity with temperature are determined only by changes in the concentration of charge carriers. From formulas (1) and (2) for the dependence of specific electrical conductivity on temperature, the following expression follows:
where is a coefficient characteristic of a given semiconductor material and representing at .
Figure 72.3
It is convenient to depict the dependence on a semi-logarithmic scale. Really
This expression in coordinates gives a straight line, the slope of which is determined by the value of W. The graphs for the intrinsic semiconductor are given in Figure 72.4.
Figure 72.4
The resistance R of a sample of length and cross-sectional area S is expressed in terms of resistivity:
Then, according to (72.3),
The graph for an intrinsic semiconductor is a straight line, the slope of which is greater the wider the band gap of the semiconductor. In Figure 72.5, straight lines 1,2,3 correspond to semiconductors for which.
Figure 72.5
Impurities and lattice defects significantly affect the electrical properties of semiconductors. For example, adding boron to silicon in an amount of one atom per silicon atom increases the conductivity at room temperature by a thousand times compared to pure silicon.
Statistical calculations have shown that the concentration of majority charge carriers (electrons in n-type semiconductors and holes in p-type semiconductors) in the region of impurity conductivity also increases exponentially.
where is the ionization energy of the impurity; and are coefficients determined by the concentrations of donor and acceptor atoms, respectively.
The concentrations of minority charge carriers are much lower, and at any temperature.
where is the intrinsic concentration of charge carriers at this temperature in a given semiconductor. Thus, the larger n, the smaller p and vice versa.
Due to the weaker dependence of mobility on temperature than concentration on temperature, and in the region of impurity conductivity, the dependence is also determined by the temperature variation of concentration
where is a constant determined by the semiconductor material and the impurity concentration in it.
Taking logarithms of (72.9), we obtain
Figure 72.6 shows a graph of the specific electrical conductivity of an impurity semiconductor over a wide temperature range in semilogarithmic coordinates.
Temperature dependence of the electrical conductivity of an impurity semiconductor.
Figure 72.6
There are three sections in this graph. 1 - section of impurity conductivity, in which the concentration of the main charge carriers increases due to the ionization of impurity levels. The slope of the straight line is determined by the ionization energy of the impurity. At temperature T s all impurities turn out to be ionized and further up to T i the concentration of the main charge carriers remains approximately constant and equal to the concentration of impurity atoms - section 2. The temperature dependence in this region, when , is determined by the temperature dependence of mobility. At temperatures (section 3), electron-hole pairs are generated and the slope of the straight line is determined by the band gap.
If samples of the same semiconductor material are doped with different amounts of the same impurity, then with increasing impurity concentration (the concentration increases with increasing order number of the curve in Figure 72.7), the values in the region of impurity conductivity increase, the depletion of the impurity and the transition from impurity to intrinsic conductivity shift towards higher temperatures. At high concentrations of impurity atoms, they remain incompletely ionized up to the temperature at which intrinsic conductivity begins to predominate (curve 4).
Dependence of electrical conductivity of semiconductors on temperature at various impurity contents.
As we have already seen, specific conductivity is expressed by the formula
where n is the concentration of charge carriers that determine the conductive properties of a given body, and u is the mobility of these carriers. Charge carriers can be both electrons and holes. It is interesting to note that although, as is known, in most metals the free charge carriers are electrons, in some metals the role of free charge carriers is played by holes. Typical representatives of metals with hole conductivity are zinc, beryllium and some others.
To clarify the dependence of conductivity on temperature, it is necessary to know the temperature dependence of the concentration of free carriers and their mobility. In metals, the concentration of free charge carriers does not depend on temperature. Therefore, the change in the conductivity of metals depending on temperature is completely determined by the temperature dependence of carrier mobility. In semiconductors, on the contrary, the concentration of carriers depends sharply on temperature, and temperature changes in mobility are practically unnoticeable. However, in those temperature regions where the carrier concentration is constant (the region of depletion and the region of saturation of impurities), the course of the temperature dependence of conductivity is completely determined by the temperature change in carrier mobility.
The value of the mobility itself is determined by the processes of carrier scattering on various defects in the crystal lattice, that is, by a change in the speed of directional movement of carriers during their interaction with various defects. The most significant is the interaction of carriers with ionized atoms of various impurities and with thermal vibrations of the crystal lattice. In different temperature regions, the scattering processes caused by these interactions have different effects.
In the region of low temperatures, when thermal vibrations of atoms are so small that they can be neglected, scattering by ionized impurity atoms is of primary importance. In the region of high temperatures, when in the process of thermal vibrations the lattice atoms are significantly displaced from the position of stable equilibrium in the crystal, thermal dissipation comes to the fore.
Scattering by ionized impurity atoms. In impurity semiconductors, the concentration of impurity atoms is many times higher than the concentration of impurities in metals. Even at a sufficiently low temperature, most of the impurity atoms are in an ionized state, which seems quite natural, since the very origin of the conductivity of semiconductors is associated primarily with the ionization of impurities. Scattering of carriers by impurity ions turns out to be much stronger than scattering by neutral atoms. This is explained by the fact that if scattering of a carrier by a neutral atom occurs during a direct collision, then for scattering by an ionized atom it is enough for the carrier to fall into the region of the electric field created by the ion (Fig. 28). When an electron flies through the region of the electric field created by a positive ion, its flight path undergoes a change, as shown in the figure; in this case, the speed of its directional movement υ E, acquired due to the influence of the external field, will decrease to If the electron passes close enough to the ion, then after scattering the direction of motion of the electron may turn out to be completely opposite to the direction of action of the external electric field.
Considering the problem of the scattering of charged particles on charged centers, the outstanding English physicist E. Rutherford came to the conclusion that the mean free path of particles is proportional to the fourth power of their speed:
The application of this dependence to the scattering of carriers in semiconductors led to a very interesting and, at first glance, unexpected result: the mobility of carriers in the low-temperature region should increase with increasing temperature. In fact, the mobility of carriers turns out to be proportional to the cube of their speed of movement:
At the same time, the average kinetic energy of charge carriers in semiconductors is proportional to temperature and, therefore, the average thermal speed is proportional to the square root of 
Consequently, carrier mobility depends on temperature as follows:
At low temperatures, when scattering by ionized impurities plays the main role and when thermal vibrations of lattice atoms can be neglected, carrier mobility increases proportionally with increasing temperature (the left branch of the u(T) curve in Figure 29). Qualitatively, this dependence is quite understandable: the greater the thermal speed of the carriers, the less time they spend in the field of the ionized atom and the less distortion of their trajectory. Due to this, the free path of carriers increases and their mobility increases.
Dissipation by thermal vibrations. With increasing temperature, the average speed of thermal movement of carriers increases so much that the probability of their scattering by ionized impurities becomes very small. At the same time, the amplitude of thermal vibrations of the lattice atoms increases, so that the scattering of carriers by thermal vibrations comes to the fore. Due to the increase in scattering by thermal vibrations, as the semiconductor is heated, the free path of carriers and, consequently, their mobility decreases.
The specific course of the dependence in the high temperature region is not the same for different semiconductors. It is determined by the nature of the semiconductor, the band gap, the impurity concentration and some other factors. However, for typical covalent semiconductors, in particular for germanium and silicon, at not too high impurity concentrations, the u(T) dependence has the form:
(see the right branch of the curve in Figure 29).
So, the mobility of carriers in semiconductors in the region of low temperatures increases in direct proportion and in the region of high temperatures it decreases in inverse proportion
Dependence of semiconductor conductivity on temperature. Knowing the course of the temperature dependence of the mobility and concentration of carriers in semiconductors, it is possible to establish the nature of the temperature dependence of the conductivity of semiconductors. Schematically dependency 
is shown in Figure 30. The course of this curve is very close to the course of the dependence curve 
shown in Figure 25. Since the dependence of the carrier concentration on temperature is much stronger than the temperature dependence of their mobility, then in the regions of impurity conductivity (section ab) and intrinsic conductivity (section cd), the dependence of the specific conductivity σ(T) is almost completely determined by the dependence of the carrier concentration on temperature . The slope angles of these sections of the graph depend, respectively, on the ionization energy of donor impurity atoms and on the band gap of the semiconductor. The tangent of the tilt angle γ n is proportional to the energy of removal of the fifth valence electron of the donor impurity atom. Therefore, having experimentally obtained a graph of changes in the conductivity of a semiconductor upon heating in the impurity region ab, it is possible to determine the value of the activation energy of the donor level, that is, the energy distance of the donor level W d from the bottom of the conduction band (see Fig. 20). The tangent of the slope γ i is proportional to the energy of electron transition from the valence band to the conduction band, that is, the energy of creation of its own carriers in the semiconductor. Thus, having experimentally obtained the dependence of conductivity on temperature in its own region cd, it is possible to determine the band gap W g (see Fig. 17). The quantities W d and W g are the most important characteristics of a semiconductor.
The main difference between the dependences σ(T) and n(T) is observed in the section bc, located between the impurity depletion temperature T s and the temperature of transition to intrinsic conductivity T i . This region corresponds to the ionized state of all impurity atoms, and the energy of thermal vibrations is still insufficient to create its own conductivity. Therefore, the concentration of carriers, being practically equal to the concentration of impurity atoms, does not change with increasing temperature. The course of the temperature dependence of conductivity in this region is determined by the course of the temperature dependence of carrier mobility. In most cases, at moderate impurity concentrations, the main mechanism of carrier scattering in this temperature range is scattering by thermal vibrations of the lattice. This mechanism causes a decrease in carrier mobility and, consequently, the conductivity of semiconductors with increasing temperature in the bc region.
In degenerate semiconductors, due to the high concentration of impurities, which causes the overlap of the electric fields of ions, the scattering of carriers by ionized impurity atoms remains of primary importance up to high temperatures. And this scattering mechanism is precisely characterized by an increase in carrier mobility with increasing temperature.
The electrical conductivity of any material is determined by the concentration and mobility of free charge carriers, the values of which depend on temperature.
Mobility m of free charge carriers characterizes their scattering and is defined as the coefficient of proportionality between the drift velocity v dr and electric field strength e: v dr = m e.
Scattering free charge carriers, i.e. a change in their speed or direction of movement may occur due to the presence of structural defects in real semiconductor crystals (this includes, for example, impurity atoms and ions), and thermal vibrations of the crystal lattice.
It has been established that when charge carriers are scattered only by impurity ions, the mobility
The increase in the mobility of free charge carriers with increasing temperature is explained by the fact that the higher the temperature, the greater the thermal speed of movement of the free carrier and the less time it will be in the Coulomb field of the ion, which changes the trajectory of its movement, which means it will have less scattering and more high mobility. As the temperature rises, scattering by thermal vibrations of the crystal lattice becomes increasingly important, and at a certain temperature it becomes predominant.
Thermal vibrations of the crystal lattice increase with increasing temperature, carrier scattering also increases, and their mobility decreases. It has been established that in atomic semiconductors, when free charge carriers are scattered predominantly by thermal vibrations of the lattice
In Fig. Figure 4.10 shows the dependences of the mobility of free charge carriers in an n-type semiconductor with different donor impurity concentrations. With increasing temperature, when scattering on impurity ions, the mobility increases, and then, due to ever-increasing vibrations of the crystal lattice and the scattering caused by them, it decreases. The magnitude and position of the maximum of the m(T -1) curve depend on the impurity concentration. As it increases, the maximum shifts to the region of higher temperatures, and the entire curve moves down along the ordinate axis. At an impurity concentration equal to N D3, corresponding to a degenerate semiconductor, the mobility decreases with increasing temperature, similar to what happens in conductor materials (Section 3.8).
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Rice. 4.10. Dependence of the mobility of free electrons on temperature in an n-type semiconductor: N D1 At very low temperatures, when thermal vibrations of the crystal lattice are small and impurity atoms are weakly ionized, scattering of free carriers mainly occurs on neutral impurity atoms. With this scattering mechanism, mobility does not depend on temperature, but is determined by the impurity concentration. So, the concentration of free charge carriers in semiconductors increases with increasing temperature according to an exponential law, and the temperature dependence of mobility has, in general, the character of a curve with a maximum and a power law of change. In the general case, the specific electrical conductivity s of a semiconductor, in which the charge carriers are free electrons with mobility m n and free holes with mobility m p, is equal to: where e is the elementary charge. For native semiconductor Considering that the power-law dependence is weaker than the exponential one, we can write: Similarly for an n-type impurity semiconductor in the region of impurity conductivity: Relations (4.14) and (4.15) are valid only until complete ionization of the impurity occurs. Having obtained the experimental dependence of specific conductivity on temperature in the form lns(T -1), it is possible to determine the band gap of the semiconductor and the ionization energy of the impurity using relations (4.13) – (4.15). Let us consider the experimental curves of the temperature dependence of the electrical conductivity of silicon containing different amounts of donor impurity (Fig. 4.11). The increase in the specific conductivity of silicon with increasing temperature in the low temperature region is due to an increase in the concentration of free charge carriers - electrons due to the ionization of the donor impurity. With a further increase in temperature, a region of impurity depletion occurs—its complete ionization. The intrinsic electrical conductivity of silicon has not yet manifested itself noticeably. Under conditions of impurity depletion, the concentration of free charge carriers practically does not depend on temperature, and the temperature dependence of the specific conductivity of the semiconductor is determined by the dependence of carrier mobility on temperature. The decrease in silicon conductivity observed in this region with increasing temperature occurs due to a decrease in mobility when free charge carriers are scattered by thermal vibrations of the crystal lattice. Rice. 4.11. Temperature dependence of the electrical conductivity of silicon containing different amounts of donor impurity N D: 1 – 4.8×10 23 ; 2 – 2.7×10 24 ; 3 – 4.7×10 25 m -3 However, a case is also possible when the impurity depletion region is in the temperature range where the main scattering mechanism is scattering on impurity ions. Then the specific conductivity of the semiconductor will increase with increasing temperature: s~T 3/2. A sharp increase in specific conductivity with a further increase in temperature (Fig. 4.11) corresponds to the region of intrinsic electrical conductivity, in which the concentration increases exponentially [relation (4.4)], and mobility decreases according to the power law (4.10). In a degenerate semiconductor (curve 3 in Fig. 4.11), the concentration of free charge carriers does not depend on temperature and the temperature dependence of conductivity is determined by the dependence of their mobility on temperature (Fig. 4.10). 4.6. Optical and photoelectric phenomena Light absorption. Due to the reflection and absorption of light by a semiconductor, the intensity of monochromatic radiation incident on it with intensity I 0 decreases to a certain value I. In accordance with the Lambert–Bouguer law: where R is the reflection coefficient, x is the distance from the surface of the semiconductor along the direction of the beam (in the volume) to a given point; a is the absorption coefficient. The value of a -1 is equal to the thickness of the layer of substance, when passing through which the intensity of light decreases by e times (e is the base of the natural logarithm). The absorption of electromagnetic radiation energy by a semiconductor can be associated with various physical processes: disruption of covalent bonds between atoms of the material with the transition of electrons from the valence band to the conduction band; ionization of impurity atoms and the appearance of additional free electrons or holes; a change in the vibrational energy of lattice atoms; formation of excitons, etc. If the absorption of light by a semiconductor is due to the transitions of electrons from the valence band to the conduction band due to the energy of radiation quanta, then absorption is called own; if the emergence of free carriers due to the ionization of impurity atoms (donors or acceptors) – impurity. In a number of semiconductors, due to the absorption of a light quantum, such excitation of an electron in the valence band is possible, which is not accompanied by its transition to the conduction band, but a coupled electron-hole system is formed, moving within the crystal as a single whole. This system is called exciton. The optical absorption of a semiconductor, caused by the interaction of radiation with the vibrational motion of the crystal lattice, is called lattice. Regardless of the mechanism of absorption of radiation quanta, the process obeys the law of conservation of energy. Photoconductivity semiconductors is a phenomenon that always accompanies the process of absorption of electromagnetic radiation energy. When a semiconductor is illuminated, the concentration of free charge carriers in it can increase due to carriers excited by absorbed light quanta. Such carriers can be either their own electrons and holes, or carriers that have passed into a free state due to the ionization of impurity atoms. Illumination of a semiconductor with light for a sufficiently long time does not lead to an infinite increase in the concentration of excess (compared to equilibrium) charge carriers, since as the concentration of free carriers increases, the probability of their recombination increases. There comes a moment when recombination balances the process of generation of free carriers and an equilibrium state of the semiconductor is established with a higher conductivity s equal to that without illumination (s 0). Rice. 4.13. Absorption spectrum of a semiconductor and spectral distribution of photosensitivity: 1 – intrinsic absorption; 2 – impurity absorption; 3.4 – photocurrent With longer wavelength radiation, when the energy of light quanta E Ф is low (E f =hn, where h is Planck’s constant, n is the frequency), at l pr impurity absorption occurs and photoconductivity (photocurrent) occurs due to the ionization of impurities (curves 2, 4 , Fig. 4.13). At a shorter wavelength l i , i.e. With a higher energy of light quanta, commensurate with the band gap of the semiconductor DE 0, intrinsic (fundamental) absorption and photoconductivity (photocurrent) arise (curves 1.3, Fig. 4.13). This wavelength l i is called the intrinsic (fundamental) absorption edge of the semiconductor. The short-wavelength decrease in photoconductivity (curve 3, Fig. 4.13) is explained by the high absorption coefficient (curve 1, Fig. 4.13), i.e. Almost all the light is absorbed in a very thin surface layer of the material. As stated above, photoconductivity caused by the generation of free carriers is always accompanied by the absorption of electromagnetic radiation energy. In the process of recombination, on the contrary, energy is released. The released energy can be absorbed by the crystal lattice ( nonradiative recombination) or be emitted in the form of a light quantum ( radiative recombination). The latter phenomenon has found application in LEDs used in instrument making as light indicators.
, (4.11)
. (4.13)
. (4.15)
in semiconductors