Lebedev A.I. Physics of semiconductor devices

From your physics course you know that there are conductors, dielectrics and semiconductors. Conductors are characterized by a conductivity of 10 2 -10 8 S/cm 3 (Sm - Siemens = 1/Ohm), for dielectrics - 10 -10 S/cm 3 and less. The interval from 10 -10 to 10 2 S/cm 3 is occupied by semiconductors. Characteristic feature What distinguishes semiconductors from metals is the increase in electrical conductivity with increasing temperature.

Semiconductor devices are electrical converting devices whose operating principle is based on phenomena occurring in the semiconductor itself or at the interface of two semiconductors with different types of conductivity.

Semiconductor devices include:

Rectifier diodes

RF and microwave diodes

Zener diodes or reference diodes

Tunnel diodes

Varicaps

Thyristors

Bipolar and field-effect transistors, etc.

For the manufacture of real semiconductor devices, germanium, silicon and gallium arsenide are usually used.

As you know, a semiconductor has a three-dimensional lattice. For simplicity, we will consider a flat lattice. Silicon atoms are connected to each other by a covalent bond. At a temperature of 0 o K, all semiconductors are ideal insulators because there are no free electrons in their structure.

Under the influence external factors(change in temperature, radiation, light radiation, etc.) the crystal structure receives external energy, which can lead to the breaking of a covalent bond and a free electron will appear in the structure, i.e. The resistance of the semiconductor will decrease.

A semiconductor can be represented in terms of energy levels (valence band, band gap, conduction band). Here DW is the band gap, the potential barrier that an electron must overcome to enter the conduction band. For the most common semiconductors, DW = 0.1-3 eV, and for dielectrics - 6 eV. For germanium DW = 0.72 eV, for silicon DW = 1.12 eV.

At the site of the bond break, a hole appears, which has the same charge as the electron, but with the opposite sign. In an ideal semiconductor, the concentration of electrons and holes is the same. If n n is the electron concentration, and n p is the hole concentration, then for an ideal semiconductor n n = n p is the intrinsic conductivity of the semiconductor.

Real semiconductor devices use impurity semiconductors. If a 5-valence element is introduced into a semiconductor as an impurity, then this semiconductor will be a semiconductor with electronic conductivity or n-type, and the impurity is called a donor impurity. In this case, the electron concentration Nn will be much greater than the hole concentration Np, i.e. N n >> N p . Thus, electrons will be the majority charge carriers, and holes will be minority charge carriers.

If a 3-valence element is introduced into a semiconductor as an impurity, then free holes will appear in the valence band. In this case, the hole concentration will be much greater than the electron concentration N p >> N n - this is a semiconductor with hole conductivity or p-type, and the impurity is called acceptor. Here the main charge carriers are holes.

ELECTRON-HOLE TRANSITION

When two semiconductors with different types of conductivity come into contact, as a result of diffusion, electrons move into the p-layer, and holes, on the contrary, into the n-layer. At the interface of the contact of two semiconductors, as a result of recombination, a region of stationary space charges (ions) is formed, which create an electric field that prevents further transition of the main charge carriers. A p-n junction is a region depleted of charge carriers and, therefore, it has an increased resistance, which determines electrical resistance the entire system.

There are also two pn junction capacitances:

It is therefore obvious that the properties of a pn junction depend on the frequency of the voltage applied to the pn junction.

The current-voltage characteristic of the p-n junction is as follows:

Where I o is the reverse current of the p-n junction (thermal current). The p-n junction current in the forward direction is determined by the formula:

j T - temperature potential

From the current-voltage characteristic it is obvious that the p-n junction conducts well in the forward direction and poorly in the reverse direction, i.e. has valve properties. The current-voltage characteristic is nonlinear, which means that when alternating signals pass through a p-n junction, the signal spectrum is transformed.

On the reverse branch of the current-voltage line, the dotted line shows a sharp increase in current, i.e. breakdown of the p-n junction occurs.

Electrical breakdown is a reversible breakdown, which is used to produce special devices - zener diodes. Electrical breakdowns include tunnel, avalanche and surface.

Tunnel breakdown is when, with an increase in the reverse voltage Urev, a sharp curvature of the energy zones occurs. In this case, the level of the valence band of the n-type semiconductor turns out to be at the level of the conduction band of the p-type semiconductor, i.e. a tunnel for charges appears, which leads to a sharp increase in current.

Avalanche breakdown occurs at higher p-n junction voltages than tunnel breakdown, as a result of which an avalanche-like multiplication of charge carriers begins in the p-n junction, which also leads to a sharp increase in current.

Thermal breakdown is irreversible.

EQUIVALENT ELECTRICAL DIAGRAM

p-n-junction

r - differential resistance

Usually the equivalent circuit is used for variable signals and therefore differential parameters are used.

Rk - resistance of contacts and leads

r - resistance of the p-n junction in direct or reverse switching

C is the diffusion capacitance for direct connection or the barrier capacitance for reverse connection of the p-n junction.

From the diagram it follows that when high frequency signal, the valve properties of the p-n junction deteriorate.

DEPENDENCE OF RN-JUNCTION PARAMETERS ON TEMPERATURE

The parameters are highly dependent on the ambient temperature. As the temperature increases environment both forward and reverse currents increase. The reverse parameters change especially strongly, for example, r arr sharply decreases, which can reduce the breakdown voltage U breakdown. An increase in temperature enhances the generation of minority charge carriers and, consequently, sharply increases their concentration in the semiconductor. This is a significant drawback of the pn junction and all semiconductor devices.

SEMICONDUCTOR DIODES

A semiconductor diode is an electrical converting device whose properties depend on the properties and characteristics of the p-n junction. Diodes are distinguished by frequency range and power dissipation.

Based on the conversion frequency, there are low-frequency (LF) diodes (rectifier and power), high-frequency (HF) diodes and pulse diodes.

Special diodes include zener diodes, stabilizers, varicaps and tunnel diodes.

Based on the dissipation power, low-power diodes (up to 0.25 W), medium power (0.25 to 1 W) and high power (over 1 W) are distinguished.

RECTIFIER DIODES

Consider a rectifier diode. Here, the emitter is understood as a region with a high concentration of charge carriers, and the base is a region with a low charge concentration, i.e. the base is high resistance.

In the figure of the current-voltage characteristic, the dotted line indicates an ideal p-n junction.

DU b is the voltage drop across the high-resistance base.

In real semiconductor devices, the current-voltage characteristic is shifted to the right. Rectifier diodes are also characterized by differential parameters: r pr, r arr, C diff, C bar.

For rectifier diodes, the capacitance usually lies in the range C = (10 - 100) pF. The capacitance depends on the area of ​​the p-n junction.

To characterize rectifier diodes, enter the following parameters:

I pr.max - direct maximum current,

U rev.add. - permissible reverse voltage, at which there is still no thermal breakdown.

Just like a pn junction, the parameters and characteristics of a rectifier diode are highly dependent on temperature.

An example of the use of a rectifier diode is a half-wave rectifier. Where the average value of the rectifier current is:

Then the input current will have a sinusoidal character then

A capacitor is usually connected in parallel to the load, which smoothes out current pulses.

ZENER DIRECTION (REFERENCE DIODE)

Rectifier diodes are capable of rectifying current from units of mA to 1000A at voltages from units of volts to 1000 V. For high currents and voltages, diode assemblies are used.

Zener diodes serve to stabilize DC voltage. The working section of the current-voltage characteristic of the zener diode is the reverse branch. It has three characteristic sections. Section I is the usual reverse current of a real diode - thermal current or generation current. Section II is the section of electrical breakdown - tunnel 1 or avalanche 2 in nature; it is this section of the current-voltage characteristic that is the working section of the zener diode. In section III, thermal breakdown occurs.

As the reverse voltage increases, the current through the diode increases, as well as the power released in the p-n junction, which leads to an increase in the temperature of the p-n junction. Increasing the diode temperature increases the generation of minority charge carriers, which in turn increases the reverse current. Thus, the temperature rises even more, which leads to the destruction of the p-n junction.

I min - selected at the initial moment of the breakdown.

I max - determined from the permissible power dissipation.

The operating point of the zener diode is usually selected in the middle of the working branch of the zener diode. As the current decreases, the operating point shifts to the region where the differential resistance of the zener diode increases, which leads to deterioration of stabilization. With a significant change in the stabilization current, the stabilization voltage Ust changes little.

The main parameters of the zener diode (nominal values) are - U st - stabilization voltage, I st - stabilization current and r diff - differential resistance.

The lower the differential resistance, the higher the quality of the zener diode. For real zener diodes, the stabilization resistance is in the range of 1 - 100 Ohms.

This is a relative change in the stabilization voltage DU st / U st to the absolute change in temperature DT. For zener diodes, TKN can be greater or less than zero. Typically, low-voltage tunnel diodes have a negative TKN, while higher-voltage avalanche diodes have a positive TKN. The dependence of TKN on stabilization voltage is shown in the figure.

The presence of negative and positive TKN in zener diodes makes it possible to carry out thermal compensation and the total TKN in this case is significantly less. In particular, you can connect an additional diode in series with the zener diode, whose TKN is negative, or you can choose two zener diodes with the same TKN, but with different signs. In this case, the circuit of two zener diodes will be more stable and the stabilization voltage will change little when the ambient temperature changes.

PARAMETRIC VOLTAGE STABILIZER

where E is an unstabilized power source;

R b - ballast resistance;

R n - load resistance;

I n - load current;

I st - stabilization current;

VD - the zener diode is turned on in the opposite direction.

According to Kirchhoff's second law:

Suppose that as a result of external factors the voltage of the power supply has changed to DE, then

Obviously, the expression in the denominator is always greater than one, i.e. the voltage at the output of a parametric stabilizer is significantly less than the change in voltage at the input. In order to reduce DU st, you need to reduce r st and increase R b. As R b increases, most of the power source voltage will drop across the ballast resistance R b and to maintain the stabilization voltage in a given range, it will be necessary to increase the power source voltage. In addition, the useful power of the source will also drop at the ballast resistance.

It is desirable that no more than 2 V drop across the ballast resistance Rb.

RF DIODES

Typically, radio engineering devices (detector, frequency converter, frequency mixer) use RF diodes. RF diodes differ from rectifier diodes by the small capacitance of the pn junction.

Typically, RF diodes use a point p-n junction, which has a small p-n junction area and, therefore, a small p-n junction capacitance, but also small currents through the p-n junction and low reverse voltage.

Point diodes are obtained as follows. They take an n-type semiconductor crystal, a metal needle, at the tip of which there is an acceptor impurity. A powerful current pulse of short duration is passed through the needle and crystal. A p-n junction is formed at the point of contact. The capacitance of RF diodes lies in the range C = 1 - 10 pF. The smaller the capacitance of the pn junction, the higher the frequency range of the RF diode.

PULSE DIODES

Pulsing diodes are widely used in modern digital pulse devices. They belong to the class of RF diodes, but time restrictions are introduced for them. The input signal for them is a rectangular pulse, which has a very wide signal spectrum.

At moment t 1 the voltage changes sign. In this case, a sharp jump in the reverse current "I d" is observed. In the interval from t 1 to t 2, the current drops to I o - the reverse current of the diode.

treset is called the recovery time of the reverse resistance of the p-n junction, i.e. - this is the time of resorption of minority charge carriers in the base of the diode.

When switched back on, the time t rise is affected by the barrier capacitance, which is charged to the value of the reverse voltage. The current in the capacitance leads the voltage by 90 o. As the barrier capacitance is charged, the current in the capacitance decreases according to an exponential law and at time t 2 the current takes on a steady value I arr = I o.

t east "(0.1 - 1) µs - for pulse diodes.

The capacitance of the p-n junction for pulsed diodes is units of pF.

If the input pulse has a long duration t U , then the recovery time t rise is short. If t U is small, then t rise increases.

In the case of direct connection of the diode at the time of arrival of a single current pulse t 1, the current voltage on the diode reaches the maximum value U max, and then drops to a steady value equal to the single level U 1.

Then t mouth = t 1 - t 2 - time of establishment of forward voltage.

This happens because the base is high-resistance and drops across the diode maximum voltage. As charge carriers are injected from the emitter into the base, the base resistance drops, the potential barrier decreases, and this leads to a voltage drop to a steady-state value equal to U 1 .

t mouth - determined by voltage from U max to a value of 1.2 from the unit level U 1. Typically t mouth is on the order of units of microseconds.

Thus, the main parameters of a pulse diode are: I max imp pr, U arr. add. (1 - 100V), C, t east, t set.

MESADIODES

In integrated technology, it is convenient to obtain a mesadiode, which belongs to the pulse diodes and is capable of operating with very short pulses.

They are obtained as follows. An n-type substrate is taken and an acceptor impurity is introduced by diffusion or sputtering, thereby creating a p-type region. Further using machining or etching create mesadiodes with a small pn junction area. The plate is then cut.

The parameters of mesadiodes are the same as those of pulsed diodes, i.e. I max imp pr, U arr. add. , C, t east, t mouth.

TUNNEL DIODE

If there is a high concentration of impurities in a semiconductor, this leads to bending of the energy bands. In this case, a tunnel appears through which charge carriers move from the valence band to the conduction band.

If no external voltage is applied to the tunnel diode, then the total current through the p-n junction is zero.

The section from O to A is a section of a pronounced tunnel effect (up to approximately 0.2 V). Section AB, with an increase in voltage greater than U 1, the energy zones are even more bent, which leads to a decrease in the tunnel effect current (U 2 is approximately equal to 0.4 - 0.6 V).

With a further increase in voltage (section BC), the diffusion process begins, as in a conventional diode.

Section AB is a negative differential resistance, which makes it possible to use the tunnel effect in amplifier circuits, electronic generators and pulse switching devices (multivibrator, trigger, etc.), but the power of such diodes is usually low.

Parameters: I max /I min »5, I max i.e. , I min i.e. , - r, U 1(max i.e.) , U 2(min i.e.) , DU - voltage change during direct connection, when the maximum current of the tunnel effect becomes equal to the diffusion current.

VARICAPE

A varicap is a semiconductor diode with controlled capacitance. To describe the operation of a varicap, the capacitance-voltage characteristic is used, i.e. dependence of capacitance on applied voltage.

The characteristic is nonlinear and only part of it is used when the diode is turned back on. As the reverse voltage U reverse decreases, the capacitance increases, i.e. in a varicap a barrier capacitance is used.

Varicap parameters: C max, C max /C min ³10.

Varicaps are used in selective devices, for example in a parallel oscillatory circuit.

With section - does not allow the DC component to pass into the circuit.

By changing the voltage, we thereby change the capacitance of the varicap and, consequently, the resonant frequency of the circuit. In receivers with AFC, it is the varicap that is used.

NOTATION

D9A - high-frequency, low-power diode.

Here D means diode, 9 means series, A means features electrical parameters. In this case, D9A is a germanium diode.

KD220 K - silicon diode, series 220.

An analogue of this designation is 2D220. The first digit here means 1 - germanium, 2 - silicon, 3 - gallium arsenide.

BIPOLAR TRANSISTORS

A transistor is an electrical converting device with two or more p-n junctions. There are two types of transistors: n-p-n-type and p-n-p-type.

The emitter is an area with a very high concentration of charge carriers. The middle region - the base - has a different type of conductivity, the concentration of carriers in it is much less than the concentration in the emitter, i.e. as in diodes, the base is high-resistance.

The collector extracts carriers from the base by external voltage. The carrier concentration in the collector is high, but slightly lower than in the emitter.

If a voltage is applied to the transistor to the emitter junction in the forward direction, and to the collector junction in the reverse direction, with E to >>E e, then the emitter junction becomes narrower, its resistance decreases and the injection of charge carriers from the emitter to the base begins.

The collector junction is closed to the majority charge carriers, but since the electrons in the base are minority carriers, under the influence of the collector voltage Ek they pass into the collector and create a current Ik in the external circuit - the collector current.

Thus, the emitter current flows in the external circuit of the emitter, which is equal to:

I e = I k + I b

Moreover, as a first approximation, we can assume that I e = I k, because The base current I b is very small. In real transistors, there are minority charge carriers in the emitter, base and collector. Therefore, a current of minority charge carriers of the collector I o, or a thermal current, flows through a closed collector junction, i.e.

I e =I k + I o

In the diagrams, transistors are designated as follows

For a transistor, it is important to know the relationship between the input current I in and the output current I out, so the current transfer coefficient is introduced. In the scheme with common base(our example) this is a - current transfer coefficient or emitter current transfer coefficient.

It is equal to a = I k /I e "(0.96 - 0.999) - in real transistors, i.e. a circuit with a common base does not amplify the current because a<1.

THREE TRANSISTOR CONNECTION DIAGRAMS

Connection diagram with a common base. Here the base is the common electrode for the input and output.

I in = I e, I out = I k

U in = U eb, U out = U kb

Scheme with common emitter.

I in = I b, and I out = I k

U in = U e U out = U e

Circuit with a common collector.

I in = I b, I out = I e

U in = U bk U out = U eq

The most common circuits are those with a common base and a common emitter.

VOLTAMPER CHARACTERISTICS OF THE TRANSISTOR

Let's consider a family of input and output current-voltage characteristics, although there are also transient characteristics and characteristics feedback CVC.

The input current-voltage characteristic of a transistor in a connection circuit with a common base is the dependence of the input current on the input voltage Iin = f(Uin) with Uout = const or otherwise

I e = f(U eb) at U kb = const.

This is a characteristic of an open emitter junction. The current-voltage characteristic is affected by the voltage at the collector p-n junction. The higher the voltage on it, the more to the right the input current-voltage characteristic of the transistor shifts. This occurs as a result of modulation of the base thickness. If the base decreases in thickness, then its resistance increases.

The output current-voltage characteristic is the dependence of the output current on the output voltage Iout = f(Uout) at Iin = const. The family of output characteristics are the characteristics of a closed collector p-n junction.

Here Iko is the thermal collector saturation current.

As the input current increases, the output current increases proportionally (I e4 > I e3 > I e2 > I e1 > 0). The output collector current is practically independent of the output voltage U kb.

The range of voltage values ​​at U kb kb = 0 collector current in the output circuit is due to the presence of the electric field of the high-resistance base, the potential difference of which is similar to the potential difference of the previously considered p-n junction.

SCHEME PARAMETERS WITH A COMMON BASE

at U KB = const. r e - differential resistance of the emitter junction.

Base diffusion resistance

Volume resistance of the base (depends on the concentration of carriers in the base)

at I e = const. r k is the differential resistance of the collector junction.

This is the voltage feedback factor.

Note that the feedback ratio is the ratio of the input voltage to the output voltage. The ratio of the output voltage to the input voltage is the forward transfer factor (or gain?)

at U kb = const - this is the coefficient of direct current transfer.

EQUIVALENT ELECTRICAL DIAGRAM OF A TRANSISTOR

Usually the equivalent circuit is used on alternating current. Here C e is the diffusion capacitance of the emitter p-n junction; it is usually neglected.

mU kb - equivalent current (voltage?) generator.

mU kb = U eb

B’ is the internal point of the base.

r b = r’ b + r” b

m = (10 -3 - 10 -5) - therefore, in real transistors it is neglected.

The output circuit includes rk, barrier capacitance Ck and an equivalent current generator aI e = Ik. The barrier capacitance Ck cannot be neglected, because The resistance of the collector junction r to is high. As a result, the equivalent electrical circuit of the transistor is simplified.

The parameters r e, r b, r k, C k are given in reference books.

VOLTAMPER CHARACTERISTICS OF A COMMON EMITTER CIRCUIT

Input characteristics are the dependence of the base current on the voltage between the base and the emitter I b = f (U b e) at U k e = const. These are the characteristics of an open pn junction.

At a voltage of less than 0.3 V, a reverse current I o flows in the base circuit. With increasing voltage between the collector and emitter Uke, the characteristic shifts to the left, i.e. value of the specified input current appears at a lower base-emitter voltage U be, because part of the voltage Uke is also applied to the emitter junction.

Output current-voltage characteristics are the dependence of the output collector current on the output voltage, i.e. in this case I c = f(U b e) with a constant input base current I b = const. These are the characteristics of a closed collector p-n junction.

I brass is the through saturation current in a circuit with a common emitter. This is zero through collector current, it flows through the entire transistor.

As the input current increases, the output current also increases (I b4 > I b3 > I b2 > I b1 >0). Moreover, the greater the input current, the greater the dependence of the collector current Ik on the output voltage Uke.

As for the parameters of the equivalent circuit, it is important to know the relationship between the input and output currents. By analogy with a common base circuit, we can imagine the following equivalent circuit. Here the parameters r b, r e, r k, C k are the same as in the scheme with a common base, but this scheme is not convenient, because there is no connection between the input current I b and the output current I c. You can write

I e = I k + I b From the scheme with a common base I k = aI e + I k, we substitute the previous one into this expression, then

I k = aI e + aI b + I k and from here we get

And a is the current transfer coefficient in a circuit with a common base, then

b is the flux transfer coefficient in a circuit with a common emitter.

The physical principles of operation of the most important classes of modern semiconductor devices are considered: diodes, bipolar and field-effect transistors, thyristors, microwave devices with negative differential resistance (Gunn diodes, avalanche-flight and injection-flight diodes), charge-coupled devices, optoelectronic devices (photodetectors, LEDs, injection lasers, etc.). The basic theoretical relationships that determine the characteristics of these devices are derived. Much attention is paid to describing the features of modern high-speed devices with submicron and nanometer dimensions, including devices that use heterojunctions, quantum wells and quantum dots. In addition, the book examines the basics of planar technology, describes the technological problems that have arisen recently and indicates promising ways to solve them.
For senior students, graduate students and researchers working in the field of semiconductor physics.
recommended by the Educational Institution for Classical University Education of the Russian Federation as a textbook for university students studying in specialties 010701 - “Physics”, 010704 - “Physics of Condensed Matter”, 010803 - “Microelectronics and Semiconductor Devices*.

Current-voltage characteristics of a thin p-n junction.

In this section, we will obtain an analytical expression for the current-voltage characteristic of an ideal p-n junction, which was derived by Shockley in 1949, which is not only unusual from a scientific point of view, but also very promising from a technological point of view; in particular, they are very effective for use as solar energy converters and for the creation of new electronic devices. For chemists and physicists - scientists, specialists in the synthesis of new organic substances, developers in the areas of application of synthetic conductive materials.

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Hamakawa, editor. Amorphous semiconductors and devices based on them. 1986 376 pp. djvu. 4.6 MB.
The structure and classification of amorphous semiconductors, their electronic structure, structural defects and impurities, optical and electrical properties, and optically stimulated phenomena in chalcogenide glasses are considered. Data on the growth and properties of amorphous silicon hydrides are presented. The areas of application of amorphous semiconductors are shown.
For scientists and specialists in the metallurgical, mechanical engineering, aviation, and shipbuilding industries, dealing with issues of materials science, semiconductor and electronic engineering.

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H. Herman. Semiconductor superlattices. 1989 238 pp. PDF. 33.3 MB.
The book by the Polish scientist M. Herman is an introduction to new area semiconductor physics – physics of multilayer semiconductor microstructures, so-called superlattices, which have found important application in picosecond semiconductor electronics. The electrical conductivity of superlattices is considered, the prospects for their application are discussed, as well as manufacturing technologies and the results of experimental studies. The book contains a fairly complete presentation of the problem and can serve as a reference and educational tool.
For specialists in semiconductor physics, engineers and technologists, as well as for undergraduate and graduate students.

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Shalimova. Physics of semiconductors. 390 pages. Size 7.0 MB. PDF.

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2. Semiconductors. Semiconductor devices

2.1. General information

Semiconductors are substances whose conductivity is intermediate between the conductivities of metals and dielectrics. Semiconductors are both poor conductors and poor dielectrics. The boundary between semiconductors and dielectrics is arbitrary, since dielectrics high temperatures ah can behave like semiconductors, and pure semiconductors at low temperatures behave like insulators. In metals, the electron concentration is practically independent of temperature, and in semiconductors, charge carriers appear only when the temperature increases or when energy is absorbed from another source.

Typical semiconductors are carbon (C), germanium (Ge) and silicon (Si). Germanium is a brittle, grayish-white element discovered in 1886. The source of powdered germanium dioxide, from which solid pure germanium is obtained, is the ash of certain types of coal.

Silicon was discovered in 1823. It is widely distributed in the earth's crust in the form of silica (silicon dioxide), silicates and aluminosilicates. Sand, quartz, agate and flint are rich in silicon dioxide. Pure silicon is obtained from silicon dioxide chemically. Silicon is the most widely used semiconductor material.

Let us consider in more detail the formation of conduction electrons in semiconductors using silicon as an example. A silicon atom has serial number Z=14 V periodic table D. I. Mendeleev. Therefore, its atom contains 14 electrons. However, only 4 of them are on the unfilled outer shell and are weakly bound. These electrons are called valence electrons and give rise to the four valences of silicon. Silicon atoms are able to combine their valence electrons with other silicon atoms using what is called a covalent bond (Figure 2.1). In covalent bonding, valence electrons are shared between different atoms, resulting in the formation of a crystal.

As the temperature of the crystal increases, thermal vibrations of the lattice lead to the breaking of some valence bonds. As a result, some of the electrons that previously participated in the formation of valence bonds are split off and become conduction electrons. In the presence of an electric field, they move against the field and form an electric current.

However, when an electron is released in the crystal lattice, an unfilled interatomic bond is formed. Such “empty” spaces with missing bonding electrons are called “holes.” The appearance of holes in a semiconductor crystal creates additional opportunity for charge transfer. Indeed, the hole can be filled by an electron transferred under the influence of thermal vibrations from a neighboring atom. As a result, normal communication will be restored in this place, but a hole will appear in another place. Any of the other bond electrons, etc., can in turn go into this new hole. The sequential filling of a free bond with electrons is equivalent to the movement of a hole in the direction opposite to the movement of electrons. Thus, if in the presence of an electric field electrons move against the field, then holes will move in the direction of the field, i.e. the way positive charges would move. Consequently, in a semiconductor there are two types of current carriers - electrons and holes, and the total conductivity of the semiconductor is the sum of electronic conductivity (n-type, from the word negative) and hole conductivity (p-type, from the word positive).

Along with transitions of electrons from a bound state to a free state, there are reverse transitions in which a conduction electron is captured in one of the vacant positions of bond electrons. This process is called electron-hole recombination. In a state of equilibrium, such a concentration of electrons (and an equal concentration of holes) is established at which the number of direct and reverse transitions per unit time is the same.

The considered conduction process in pure semiconductors is called intrinsic conductivity. Intrinsic conductivity increases rapidly with increasing temperature, and this is a significant difference between semiconductors and metals, whose conductivity decreases with increasing temperature. All semiconductor materials have a negative temperature coefficient of resistance.

Pure semiconductors are an object of mainly theoretical interest. Major semiconductor research concerns the effects of adding impurities to pure materials. Without these impurities, most semiconductor devices would not exist.

Pure semiconductor materials such as germanium and silicon contain small numbers of electron-hole pairs at room temperature and can therefore conduct very little current. Alloying is used to increase the conductivity of pure materials.

Doping is the addition of impurities to semiconductor materials. Two types of impurities are used. Impurities of the first type - pentavalent - consist of atoms with five valence electrons, for example, arsenic and antimony. The second type of impurity - trivalent - consists of atoms with three valence electrons, for example, indium and gallium.

When a pure semiconductor material is doped with a pentavalent material such as arsenic (As), some of the semiconductor atoms are replaced by arsenic atoms (Figure 2.2). The arsenic atom introduces four of its valence electrons into covalent bonds with neighboring atoms. Its fifth electron is weakly bound to the nucleus and can easily become free. The arsenic atom is called a donor atom because it donates its extra electron. The doped semiconductor material contains a sufficient number of donor atoms, and therefore free electrons, to maintain the current.

At room temperature, the number of additional free electrons exceeds the number of electron-hole pairs. This means that the material has more electrons than holes. Therefore, electrons are called majority carriers. Holes are called minority carriers. Since majority carriers have a negative charge, such a material is called an n-type semiconductor.

When a semiconductor material is doped with trivalent atoms, such as indium (In) atoms, these atoms will place their three valence electrons among three neighboring atoms (Figure 2.3). This will create a hole in the covalent bond.

The presence of additional holes will allow electrons to easily drift from one covalent bond to another. Since holes easily accept electrons, atoms that introduce additional holes into a semiconductor are called acceptor atoms.

Under normal conditions, the number of holes in such a material significantly exceeds the number of electrons. Therefore, holes are the majority carriers and electrons are minority carriers. Because the majority carriers have a positive charge, the material is called a p-type semiconductor.

N- and p-type semiconductor materials have significantly higher conductivity than pure semiconductors. This conductivity can be increased or decreased by changing the amount of impurities. The more heavily doped a semiconductor material is, the lower its electrical resistance.

The contact of two semiconductors with different types of conductivity is called a p-n junction and has a very important property– its resistance depends on the direction of the current. Note that such a contact cannot be achieved by pressing two semiconductors against each other. A p-n junction is created in one semiconductor wafer by forming regions with different types of conductivity in it. Methods for obtaining p-n junctions are described below.

So, in a piece of a single-crystal semiconductor, a p-n junction is formed at the boundary between two layers with different conductivities. There is a significant difference in the concentrations of charge carriers. The concentration of electrons in the n-region is many times greater than their concentration in the p-region. As a result, electrons diffuse into the region of their low concentration (in the p-region). Here they recombine with holes and in this way create a spatial negative charge of the ionized acceptor atoms, which is not compensated by the positive charge of the holes.

At the same time, diffusion of holes into the n-region occurs. Here, a spatial positive charge of the donor ions, which is not compensated by the electron charge, is created. Thus, a double layer of space charge is created at the boundary (Fig. 2.4), depleted of the main current carriers. A contact electric field Ek arises in this layer, preventing the further transition of electrons and holes from one region to another.

The contact field maintains a state of equilibrium at a certain level. But even in this case, under the influence of heat, a small part of electrons and holes will continue to pass through the potential barrier caused by space charges, creating a diffusion current. However, at the same time, under the influence of the contact field, minority charge carriers of the p- and n-regions (electrons and holes) create a small conduction current. In a state of equilibrium, these currents cancel each other out.

If an external current source is connected to the p-n junction, then the voltage indicated in Fig. 2.5 Reverse polarity will cause external field E, coinciding in direction with the contact field Eк. As a result, the width of the double layer will increase, and there will be practically no current due to the majority carriers. Only a small current is possible in the circuit due to minority carriers (reverse current Irev).

When the voltage of direct polarity is turned on, the direction of the external field is opposite to the direction of the contact field (Fig. 2.6). The width of the double layer will decrease, and a large forward current Ipr will arise in the circuit. Thus, the p-n junction has pronounced one-way conductivity. This is expressed by its current-voltage characteristic (Fig. 2.7).

When a forward voltage is applied to a pn junction, the current increases rapidly with increasing voltage. When a reverse voltage is applied to the p-n junction, the current is very small, quickly reaches saturation and does not change up to a certain limiting value of the reverse voltage Urev, after which it increases sharply. This is the so-called breakdown voltage at which breakdown occurs p-n junction and it collapses. It should be noted that in Figure 2.7 the scale of the reverse current is a thousand times smaller than the scale of the forward current.

All solids, in accordance with their electrical properties, can be divided into metals, semiconductors and dielectrics. Resistivity (p) of various solids varies within very wide limits: for metals p< 10 -4 Ом см, для полупроводников р - 10~ 4 -Ю 10 Ом*см, для диэлектриков р >10 ohm cm. These differences in p values ​​are due to the peculiarities of the energy structure for different types of crystalline solids. The structures of the energy states of semiconductors and dielectrics (Fig. 1.1) are not fundamentally different from each other; all differences are due only to the difference in the band gap (A E e): in semiconductors usually AE 3^ 3 eV, and in dielectrics AE 3 > 3 eV.

Semiconductor materials, which are divided into own(pure, unadulterated) and impurities. Both in intrinsic and impurity semiconductors (energy

Rice. 1.1

diagrams of the latter are shown in Fig. 1.2) there are two types of free charge carriers - electrons And holes. Free charge carriers Such carriers are called whose kinetic energy is greater than their potential binding energy with atoms. The concentration of free carriers is determined by two opposing processes - their generation And recombination. The generation of charge carriers, i.e., the formation of free electrons and holes, is carried out when a semiconductor is exposed to thermal energy, light, ionizing radiation, beams of charged particles and other energy factors. Under thermodynamic equilibrium conditions (at temperatures T > O K) there is always thermal generation of carriers, the intensity of which increases with increasing temperature. In the intrinsic semiconductor, electron-hole pairs are formed during the generation process.

On the energy diagram of an intrinsic semiconductor (see Fig. 1.1), this process is illustrated by arrow 1, which shows the transition of an electron from the valence band, the upper limit of which corresponds to the energy E in y to the conduction band (E p- its lower limit). In the valence band, when an electron passes to the conduction band, a hole remains. (Let us denote the concentration of electrons and holes feast respectively.) Thus, in a state of equilibrium in the intrinsic semiconductor p = p = p 17 i.e.

Where n 1- equilibrium concentration of free charge carriers in the intrinsic semiconductor at a given temperature.

In a state of equilibrium, the processes of generation of electron-hole pairs in the intrinsic semiconductor are balanced

Rice. 1.2

military recombination processes. Equilibrium concentrations of electrons and holes for an intrinsic semiconductor with a band gap &E. L can be calculated according to the following expression:

Where N p = 2(2k in t p kT/k 2) 3/2, LH B = 2(2k t r kT /K 2) 312 - effective densities of energy states in the conduction band and valence band, respectively; w p And t r- effective masses of electrons and holes; To= 1.38 10 23 J/K - Boltzmann constant; To~ 6.6 10~ 34 J s - Planck’s constant; T- temperature in degrees Kelvin (K).

In expression (1.2), the exponential factor causes a sharp increase in the concentration of free charge carriers with increasing temperature T or reducing the band gap D E 3. The effect of the band gap on the concentration of carriers in intrinsic semiconductors can be illustrated using the example of silicon (81) and gallium arsenide (GaAb), which are most widely used in semiconductor technology: when T= 300 K AE 3= 1.12 eV for B1 and AE 3= 1.42 eV for CaAb, and the concentration of intrinsic carriers, respectively, is 1.4 10 10 and 1.8 * 10 6 cm“ 3. This example shows that a difference in band gap of only 1.27 times leads to a change in carrier concentration by four orders of magnitude.

Impurity semiconductors can be donor, acceptor And compensated. In donor semiconductors, or in n-type semiconductors(they contain a pentavalent donor impurity, such as phosphorus or arsenic for silicon), electronic conductivity predominates. This means that the concentration of free electrons p p0 y which in this case are called main carriers in an equilibrium state at not too high temperatures T(such that £!G <&. E 3) is many orders of magnitude higher than the concentration of its own carriers l 1 and holes p l0, which in this case are non-major media.

At not too high temperatures, the overwhelming number of electrons in an l-type semiconductor arises due to thermal ionization of donor atoms; As a result, donor atoms turn into positively charged ions, and electrons removed from them become free charge carriers.

In Fig. 1.2, A this process is illustrated by an arrow and corresponds to the transition of an electron from the donor level E l into the conduction zone. Level E d is formed by donor impurity atoms in the band gap. Energy difference A E l = E i - E d equal to the ionization energy of donors. Due to the low ionization energy (hundredths of an electron volt or less) at room temperature (G = 300 K; CT= 0.026 eV) almost all donor atoms are ionized and the concentration of majority carriers (electrons in this case) is equal to the donor concentration n n0~ DO D, and the concentration of minority carriers (holes) is determined law of mass action p p0 p p0 = p, and is equal to

In a state of equilibrium in impurity semiconductors, as well as in intrinsic semiconductors, the processes of generation and recombination of free carriers occur simultaneously. As a result, equilibrium concentrations of electrons and holes are established. Using expressions (1.2) and (1.3), the concentration of minority carriers (holes) in the donor semiconductor in the equilibrium state can be determined by the following formula:

When an acceptor impurity with a concentration of /Va is introduced into a semiconductor n 1= p 4 hole conductivity will predominate in it. Such a semiconductor is called holey or p-type semiconductor. Holes in this case arise due to the ionization of acceptor atoms, i.e., as a result of the addition of electrons to them that arise when bonds are broken in the atoms of the own semiconductor.

On the energy diagram (see Fig. 1.2, b) the described process corresponds to the transition of an electron from the valence band to the acceptor level E a, located in the band gap near the ceiling E in valence band. As a result, free levels are formed in the valence band, and the acceptor atom turns into a negative ion. Similar to a donor semiconductor, in an acceptor semiconductor, due to the low ionization energy at room temperature, almost all acceptor atoms are ionized and the concentration of the majority carriers p/R) (in this case, holes) is equal to the concentration of acceptors 7V a, i.e. r r O" N a. Equilibrium

concentration of minority carriers - electrons Prts- let us determine from a relation similar to formula (1.3)

Taking (1.2) into account, it leads to an expression “symmetrical” to formula (1.4):

In semiconductor devices, the concentration of LG D donors and acceptors varies within a wide range from 10 13 to 10 21 cm -3. At a high concentration of impurity atoms, due to the strong interaction between them, impurity levels ( E l or E a) are split into sublevels, as a result of which an impurity band is formed, which, at concentrations of 7U a, 7U D more than 10 20 cm~ 3, overlaps with the conduction band for donor semiconductors and with the valence band for acceptor semiconductors. When impurity levels overlap with the conduction band or valence band, the ionization energy of the impurity decreases to zero and a partially filled band appears. As in metals, in this case in semiconductors conductivity exists even at T= O K. Such semiconductors are called degenerate.

In real conditions, semiconductors usually contain both donor and acceptor impurities. If N d > ./U a, the result is an l-type semiconductor, and with LG a > # d - a p-type semiconductor. In the first case, the effective concentration of donors is important N d- LG a, and in the second case, the effective concentration of LG acceptors a - A^ d. When LG a = LG D, the semiconductor is called compensated. The concentration of free carriers in it is the same as in the native semiconductor.

Atoms of some impurities can form energy levels in the band gap at a considerable distance from E p And E p; such atoms are called traps. Energy levels corresponding to donor traps are located above the middle of the band gap, and acceptor levels are located below. A donor trap is neutral if its corresponding energy level is filled (occupied by an electron), and turns into a positive ion if the level is empty. Acceptor traps are neutral when the level is free and negatively charged (negative ions) when it is filled.

Temperature dependence of the concentration of free charge carriers. The carrier concentration in impurity semiconductors, as well as in intrinsic semiconductors, depends significantly on temperature. Let us consider the temperature dependence of the electron concentration in silicon using the example of an i-type semiconductor (Fig. 1.3). Three areas can be distinguished on it. At low temperatures (region 1) with increasing temperature, the concentration of free electrons (i ~ p p) increases as the number of ionized donors increases. Dependence of electron concentration on 1 /T is determined by an exponential function of the form exp [-AE A /(2kT)]> therefore, on a semi-logarithmic scale it is depicted by a straight line, the slope of which is proportional to the ionization energy of donors D E d, In area 2 almost all donors are ionized, and the concentration of intrinsic electrons n i is insignificant, therefore, with increasing temperature, the total number of free electrons changes insignificantly, and their concentration can be considered equal to the donor concentration: i ~ n n0 ~ N.. In the high temperature region (region 3) intense ionization of the semiconductor's own atoms occurs, so that the concentration of intrinsic carriers becomes greater than the concentration of the main impurity carriers,

Rice. 1.3

i.e. n 1 > n n0~ ^U d. In the region under consideration, the carrier concentration is determined by the dependence n ~ n 1 ~ exp(-D £ 3 /(2/rm which on a semi-logarithmic scale is depicted by a straight line with a slope angle p, and tg p is proportional to the band gap &E y

An increase in the concentration of impurities leads not only to an increase in the concentration of majority carriers, but also to a proportional decrease in the concentration of minority carriers, in accordance with expressions (1.3) and (1.5), which is associated with an increase in the probability of their recombination, proportional to the product of the noted concentrations.

Most semiconductor devices operate normally in the temperature range corresponding to the region 2 in Fig. 1.3. Maximum temperature in this region Tmax is approximately determined from the condition yy, = N d(for l-type semiconductor). It is proportional to the band gap and increases with increasing impurity concentration (see Fig. 1.3, curves a, b).

The concentration of minority carriers in region 2, in contrast to the concentration of majority carriers, increases strongly with increasing temperature according to expressions (1.4) and (1.6), respectively, for an electronic semiconductor (where holes are minority carriers) and for a hole semiconductor (minority carriers are electrons). Instrument parameters, which depend on the concentration of minority carriers, will also change with temperature even in the region of complete ionization of impurities (region 2 in Fig. 1.3), and maximum working temperature such devices may be noticeably lower than the temperature determined by the conditions n 1= AG D or n 1 =(For electron or hole semiconductors).

Fermi level. Free carriers in a solid fill energy states with significantly different probabilities. According to quantum statistics, the probability of an electron filling an energy level with energy E determined Fermi-Dirac function G(E)> which is calculated according to the following formula:

Where E f- energy corresponding to the Fermi level. In any equilibrium system, no matter how heterogeneous it may be, the Fermi level is the same for all its parts. As calculations show, in an intrinsic semiconductor at t p V t r The Fermi level lies in the middle of the band gap E f = E f = 0,5(E p 4- E p). IN non-degenerate l-type semiconductor (L^n " P l.) Fermi level E f is located closer to the conduction band, and in a non-degenerate p-type semiconductor the Fermi level E f located closer to the valence band. At room temperature (Г® 300 K) it lies, as a rule, below the level of donors and above the level of acceptors for semiconductors P- and p-type, respectively. If in impurity semiconductors the Fermi level lies in the band gap at a distance of at least (2 G)/^^ from its corresponding

boundaries, then the concentrations of electrons and holes will be equal:

With rising temperatures in impurity semiconductor(at t p " 25 ™ p) The Fermi level approaches the middle of the band gap, since in this case the intrinsic conductivity begins to dominate over the impurity one. The dependence of the Fermi level position on temperature for silicon with different concentrations of donor and acceptor impurities is shown in Fig. 1.4, where E = E f - E i.

Rice. 1.4

If i = A^n or p = A^b (degenerate semiconductor), i.e., the concentration of carriers is commensurate with the concentration of allowed states, then, due to the Pauli principle, electrons cannot arbitrarily occupy energy levels. The Fermi level in this case lies either in the band gap at a distance of less than (2...3) from its boundaries, or in the conduction band for an π semiconductor or in the valence band for a p semiconductor. For highly degenerate semiconductors, the position of the Fermi level, as well as the concentration of majority carriers, does not depend on temperature.