The change in the band gap of native silicon can be expressed by the function:

where T is the lattice temperature, E g (0) is the band gap at 0 K (for silicon it is 1.166). The change in band gap with temperature is equally distributed between the conduction band and the valence band.

The bandgap energy of semiconductors tends to decrease as temperature increases. This behavior can be explained by considering that the interatomic distance increases when the amplitude of atomic vibrations increases due to an increase in thermal energy. This effect can be measured using the coefficient of linear expansion of a material (a value that characterizes the relative amount of change in volume or linear dimensions body with an increase in temperature by 1 K at constant pressure). In silicon, the temperature coefficient of linear expansion is 2.33·10 -6 K -1, below 120 K it becomes negative. By increasing the interatomic distance, it decreases potential energy electrons in the material, which in turn reduces the size of the band gap.

The band gap can also change from the applied mechanical stress, due to compression or expansion of the semiconductor.

For the first time, the dependence of the band gap on temperature was obtained by R. McFarlan from measurements of optical absorption. It can be seen that in a wide temperature range DE depends linearly on temperature, but at a temperature tending to 0, the band gap tends to a constant value.

Rice. 1.

Conclusion

Thus, in this work, one of the main parameters of a semiconductor was considered - the band gap, in particular its dependence on temperature in silicon. Band gap is a fundamental parameter in semiconductor physics. It is necessary to take into account its change relative to external influences, such as temperature or applied mechanical stress, which can change the size of E g and thereby the properties of the semiconductor.

List of sources

1. Pavlov P.V. Solid state physics / Pavlov P.V., A.F. Khokhlov - Textbook. 3rd ed., ster. - M.: Higher. school, 2000. - 494 p.

Bandgap:

A semiconductor is called intrinsic or type i(intrinsic) if it does not contain any impurities. In this case, free electrons and holes are formed in pairs only due to thermal generation and also recombine in pairs. Therefore, in the intrinsic semiconductor the concentration free electrons equal to the hole concentration. Since the band gap of a semiconductor depends on temperature, we determine it using the dependence

Options GaAs Let's take from table 2: , , . For a temperature of 170 K, the band gap is equal to

Concentration of intrinsic charge carriers

The concentration of intrinsic charge carriers is defined as

, .

According to the law of “active masses”, therefore

Effective densities of states:

Let us determine the effective densities of states in the conduction band and valence band

Knowing the effective densities of states, one can determine the intrinsic concentration of charge carriers

Fermi level position:

Let us determine the position of the Fermi level in the intrinsic semiconductor. The charge carrier concentrations in the intrinsic semiconductor are equal to

, .

Since in an intrinsic semiconductor the electron concentration is equal to the hole concentration, we equate these expressions and express the Fermi level

Let us find the position of the Fermi level relative to the middle of the band gap. Since the energy of the levels is measured in electron volts (eV), we take the Boltzmann constant , we get

Consequently, the Fermi level in the intrinsic semiconductor lies above the middle of the band gap by 0.021 eV.

Charge carrier mobilities:

The mobilities of electrons and holes in real semiconductors, due to scattering processes, are lower than the mobilities in crystals with an ideal lattice. In semiconductors, charge carriers are scattered mainly by acoustic phonons and impurity ions. In different temperature ranges, one or another scattering mechanism will dominate, and it will determine the magnitude and temperature dependence of the mobility. At low temperatures ah ( T < 100 K) характер зависимости подвижности обусловлен рассеянием на ионах примесей. В области высоких температур (T> 100 K), mobility decreases with increasing temperature due to scattering by acoustic phonons, and the dependence of mobility on temperature can be represented by a semi-empirical model

,

where K, A– parameter determined empirically. Values ​​for GaAs parameters

determined according to table 2. Then:

Specific electrical resistance:

Specific electrical resistance is inversely proportional to specific electrical conductivity, which is equal to

Attitude apparent current flowing through

semiconductor to hole current:

The total current through the semiconductor is equal to the sum of the hole and electron components of the drift and diffusion currents. Since there is no injection or extraction of charge carriers, the semiconductor is in an equilibrium state and there is no diffusion component of the current (the concentration gradient is zero). Therefore, the total current is equal to the drift current, which consists of hole and electron components.

Where E– applied tension electric field. The ratio of the total current to the hole component will be equal to

Task 2.

For semiconductor p-type with a concentration of acceptor impurities determine the concentration of major and minority charge carriers; Fermi level position; electrical resistivity; the ratio of the total current flowing through a semiconductor to the hole current.

Currently, experimental and theoretical methods for studying band structure solids cover the energy range up to ~25 eV. For theoretical calculations of the band structure, methods are used quantum theory(linear combination of atomic orbitals, orthogonalized plane waves, pseudopotential, etc.). The accuracy of theoretical calculations of Eg usually does not exceed ~0.5 eV. The latter, however, can be increased by using experimental reference points in theoretical calculations. Nowadays, for many solids, a good qualitative understanding of the band pattern has been achieved in a fairly large energy range, and in some cases, semi-quantitative knowledge of band structures in the range 10-20 eV, where the accuracy can reach 0.5-1.0 eV, that is, 5-10%. At the same time, theoretical calculations of the band structure of solids are still too rough to unambiguously interpret, for example, electrical reflectance spectra (the experimental resolution of spectral peaks exceeds ~0.01-0.001 eV) or predict the gaps between the extrema of the valence band and conduction band, where required accuracy more than ~0.1 eV. Therefore, to reliably determine Eg, experimental research methods are used, the accuracy of which reaches ~0.1 eV (sometimes up to ~0.01 eV).

Experimentally, the value of E g is determined from the analysis of various physical effects associated with the transitions of electrons from the conduction band to the valence band under the influence of thermal activation (E g term) or light quanta (E g opt). Typically, E g term is determined from the temperature variation of electrical resistance or Hall coefficient R in the region of intrinsic conductivity, and E g opt is determined from the edge of the absorption band and the long-wavelength boundary of photoconductivity (Photo). The value of E g can also be estimated from measurements of magnetic susceptibility, thermal conductivity (bipolar component), tunneling experiments at low temperatures, etc. There are also some empirical relationships for qualitatively assessing the band gap E g of materials, for example:

(here N X , M and A X , M is the number and atomic numbers of the valence electrons of the anion and cation, C = 43 is a constant), having an auxiliary character. An estimate of E g is also used by extrapolation (usually linear or quadratic) in homologous series of known compounds or phases of variable composition. Most often, E g is determined experimentally by the temperature variation of electrical resistance:

here e is the electron charge,

m is the mobility of electrons in the region of the crystal’s own conductivity, when the concentration of current carriers in the conduction zone increases with temperature as a result of thermal activation according to the exponential law:

here C is a constant depending on the parameters of the conduction and valence bands,

k o - Boltzmann constant,

T- absolute temperature, E a = (E g /2) - activation energy (coefficient 1/2 shows that the Fermi level should be located in the middle of the band gap). The method requires accounting temperature dependence electron mobility m.

The value of E g is also determined by measuring the dependence of the Hall coefficient on temperature in the region of intrinsic conductivity according to the formula:

where R is the Hall coefficient,

T is the absolute temperature.

The main errors in determining E g using these methods are associated with:

1) failure to reach the region of intrinsic conductivity, the influence of activation of impurity levels and the contribution of impurity conductivity;

2) failure to take into account the temperature dependence of mobility m in formula (3);

3) insufficient length of the used temperature range DT;

4) change chemical composition samples and the extent of the homogeneity region of compounds at high temperature and other factors.

The determination of E g from the edge of a semiconductor's intrinsic light absorption and photoconductivity is based on the excitation of a valence electron into the conduction band due to the absorbed photon energy. Direct (vertical) optical transitions are possible (k 2 = k 1 + g, or k 2 ~ k 1, here k 1 and k 2 are the electron wave vector in the final and initial states, g is the phonon wave vector) and indirect (non-vertical) optical transitions involving phonons ((k 2 ~ k 1 + K ph, here K ph is the phonon momentum). The intrinsic absorption edge is determined for direct and indirect transitions, respectively, by the relations:

here u* is the cutoff frequency of photon absorption,

u phonon - frequency of absorbed (+) and emitted (-) phonon, E g opt and

Eg term - optical and thermal band gap. From these expressions it follows that the value of E g opt = E g term for the case of direct vertical optical transitions; in the case of indirect optical transitions, the value of E g opt can be both less (the case of phonon absorption) and more (the case of phonon emission) minimum distance between the valence band and the conduction band (E g term = E g), and the measured values ​​of E g opt can significantly depend on the crystallographic direction in the sample. Typically E g opt = E g term in covalent crystals, E g opt > E g term in ionic crystals, E g opt< E g term в случае экситонного поглощения света (образования связанных электрона и дырки). Экситонная ширина запрещенной зоны рассчитывается из соотношения:

where DE X is the exciton binding energy (eV); in some cases, the measured values ​​of E g opt and E g term can differ several times. The indicated relations (6) and (7) are correct for the case when the Fermi level is in the band gap of the crystal. In heavily doped p-type semiconductors (semimetals), the excitation of electrons into the conduction band occurs from the Fermi level located in the valence band of the compound, and the value of E g opt will additionally increase to E g opt ~ E g term + E F .

Ministry of Education of the Russian Federation

Tomsk State University of Control Systems

and radio electronics (TUSUR)

Department of Physics

Report

Laboratory work for the course of general physics

“DETERMINATION OF THE BANDGAND WIDTH OF A SEMICONDUCTOR

BY TEMPERATURE DEPENDENCE OF DIODE REVERSE CURRENT”

Checked: Completed by students of group 122-1:

A.V. Front _________ Izotov S.I.

"__" _______ 2011 _________ Miller A.A.

Trenkal E.I.

"__" ____________ 2011

1. INTRODUCTION

The band gap is the most important characteristic of a semiconductor, largely determining its scope of application. Figure 1.1 shows the band diagram of an intrinsic (i.e., pure unimpurity) semiconductor, which shows some of the basic parameters that the band theory of semiconductors operates on.

Figure 1.1. - Band diagram of the intrinsic semiconductor

The electrical conductivity of intrinsic semiconductors occurs when electrons move from the valence band to the conduction band. Transition probability for non-degenerate semiconductors and
equal to

Taking the logarithm of (1.2) and making the simplest transformations, we get:

By measuring the dependence own semiconductor on temperature, and plotting the dependence
, from the slope of the straight line expressing this dependence, one can determine
.

However, the band gap of a semiconductor can be measured quite accurately by examining the temperature dependence of the reverse current of a standard diode made from this semiconductor. Definition
This way is the purpose of this work.

2. USING A DIODE FOR MEASUREMENT
SEMICONDUCTOR

The basis of any semiconductor diode is
transition,
a transition is formed by introducing, for example, a semiconductor crystal on one side - type of acceptor impurity.

Band diagrams of doped semiconductors at 0 K

Figure 2.1

Electronic ( -type) conductivity is formed when a donor impurity is introduced into an intrinsic semiconductor. The donors are atoms of the fifth group of the periodic table. The energy level corresponding to the donor impurity lies in the band gap. Therefore, already at room temperatures all donors will be ionized, i.e. The “extra” electrons of the donor impurity atoms will move into the conduction band. The electron concentration in the conduction band is approximately equal to the concentration of impurity atoms. Electrons for an n-type semiconductor are the main charge carriers. Ionized donor atoms become positive ions.

The position of the Fermi level is determined by the temperature and concentration of donor impurity atoms (N2)

Figure 2.2 - Fermi level in doped semiconductors depending on temperature

When the temperature increases above 40-50 °C, an intensive transition of electrons from the valence band to the conduction band begins. In this case, the electron concentration in the conduction band increases sharply, but the hole concentration in the valence band also increases by the same amount. When Ep reaches the middle of the band gap, the type of conductivity is compensated - the impurity semiconductor becomes similar to its own.

A p-n junction is formed when p- and n-type semiconductors are connected. Near the contact boundary, at the mean free path, electrons and holes encounter each other and recombine. The remaining uncompensated impurity ions form a space charge region, which, with its electric field, prevents the diffusion of the main carriers: holes from the p - region, electrons from the n - region.

3. Basic calculation formulas.

(3.1)

Where a – straight line slope coefficient

k – Boltzmann constant.

where: E is the width of the band gap.

where: T – temperature inside the rheostat;

T 0 – temperature in the laboratory, K;

 - proportionality coefficient (1.5 deg/μA);

J OBR – current through P2, µA.

(3.4)

Where σ( ln ( I )) – Confidence interval value

γ – microammeter accuracy class (γ = 1.5)

X N – normalizing value (X N = 100 µA)

I – current through P2.

4. experimental setup diagram

Figure 3.1

5. completing of the work

Table 4.1 - Measurement results

Let's estimate the measurement error and build a graph on which we plot confidence intervals:

Rice. Dependence ln I arr =f(1/T)

Using the least squares method, we determine the slope A= -18076,9

Using formula 3.1, we calculate the band gap, as well as its error ∆E=1.6±0.11 eV.

6. CONCLUSION

After conducting the experiment, we measured the volt-ampere, from which we studied the dependence of the reverse current of the Ge diode on temperature, constructed a graph from which we determined the slope, and calculated the band gap. From the experiment it follows that the band gap of the Ge diode decreases with increasing temperature.

Study of the temperature dependence of the electrical conductivity of semiconductors.

Goal of the work:

become familiar with the basic theoretical models of electrical conductivity of crystalline bodies

acquainted with experimental methods determining the band gap of semiconductors;

study the temperature dependence of the electrical conductivity of intrinsic and impurity semiconductors;

Basic concepts of band theory of crystalline bodies.

The band gap is one of the main parameters of semiconductor materials that determine its properties. According to the band theory of crystals, in the case of a semiconductor, the lower, completely filled energy band, which is formed by a number of levels of the valence electrons of the atom, is called valence zone. The next, located above, zone of permitted energy values, free when absolute zero temperature, called zone conductivity. The band of energy values ​​forbidden for an electron that separates these two zones is called prohibited zones (Fig. 1).

Rice. 1. Band (energy) diagram of semiconductors.

In the presence of impurity atoms in the crystal lattice, the valence electrons of foreign atoms can have local energy levels, the so-called impurities levels located in the prohibited area. In this case, when these levels are occupied by electrons and can donate electrons to the conduction band, they are called donor, if the levels are free and can capture electrons from the valence band, then they are called acceptor. The minimum energy that must be imparted to an electron to transfer it from the donor level to the conduction band, or from the valence band to the acceptor level, is called the ionization energy of the impurity.

The ionization energy of the impurity and the band gap can be found from measurements of the dependence of the electrical conductivity or Hall constant on temperature, as well as from the spectral distribution of the optical absorption coefficient or photocurrent of the semiconductor. In this work, the band gap of a semiconductor is determined based on the temperature dependence of electrical conductivity.

Method for determining the band gap of a semiconductor.

The specific electrical conductivity of substances, as is known, depends on the concentration of charge carriers and their mobility.

For an impurity semiconductor, the electrical conductivity is:

For metals σ=qnμ n, and the electron concentration is practically independent of temperature and can be considered constant.

According to the condition of electrical neutrality in the intrinsic semiconductor, the equality n=p=n i is satisfied, where the index i indicates belonging to the intrinsic semiconductor:

The band gap of most semiconductors decreases with increasing temperature from the value ΔE g (0) at T=0. At sufficiently high temperatures (but< 200К) эту зависимость можно списать линейной аппроксимацией:

where N=(N c N v) 1/2 = 2(2πm 0 kT/h 2) 3/2, N c, N v is the effective density of quantum states in the conduction band and valence band, respectively. (at room temperature N = 2.41 * 10 19 cm -3).

Let us consider a semiconductor containing impurity atoms of the donor type. Let the main substance of the semiconductor be composed of atoms of group IV periodic table elements, and impurity atoms are elements of group V. The presence of an impurity leads to the appearance in the band gap of local energy levels E d located near the conduction band (Fig. 1), that is (E c -E d)<<ΔE g , поэтому при низких температурах можно пренебречь ионизацией основного вещества и считать, что концентрация носителей заряда в зоне проводимости определяется процессом ионизации донорных атомов:

where N d is the concentration of donor impurity; g is the spin degeneracy factor; g = 2 for a monovalent donor impurity; g = 4 for a monovalent acceptor impurity in germanium and silicon.

The electron concentration in the conduction band is described by formula (3) in the so-called “freezing out” region of the impurity, that is, in the range from T = 0 to the temperature range where complete ionization (“depletion”) of impurity atoms is observed. In the depletion region, the electron concentration in the conduction band does not depend on temperature and n=N d . The temperature boundary of the areas of freezing and depletion of impurities is designated T s.

With a further increase in temperature, an intensive transfer of charge carriers from the valence band to the conduction band begins and, starting from a certain temperature Ti, the intrinsic concentration of charge carriers prevails over the impurity one. Thus, at T > T i the conductivity of the impurity semiconductor can be considered intrinsic. The dependence of the charge carrier concentration of an impurity semiconductor on temperature is shown in Fig. 2, where the areas of freezing, impurity depletion and intrinsic conductivity are designated by numbers 1, 2, 3, respectively.

In the region of high temperatures (T>T i), the dependence of the concentration of charge carriers on temperature is determined by the factor exp(-ΔE g / 2kT), and in the region of low temperatures (T<Т s) - множителемexp[- (E c -E d)/2kT]. Чем выше концентрация примесейN d , тем больше область температур, в которой концентрация электронов в зоне проводимости не зависит от температуры, и тем при более высокой температуре начинается рост концентрации носителей заряда, обусловленный переходами из валентной зоны полупроводника через запрещённую зону, то есть ионизации её основного вещества.

Rice. 2. Temperature dependence of the electrical conductivity of an impurity semiconductor

The dependence of the mobility of charge carriers in a semiconductor on temperature is determined by the mechanism of carrier scattering and is a power function of temperature. In the region of high temperatures, mobility is determined by the scattering of charge carriers on thermal vibrations of the lattice and decreases with increasing temperature according to the law μ~T 3/2 when scattering by acoustic phonons, and in the region of low temperatures, when the amplitude of vibrations of lattice atoms is small, mobility is determined by the scattering of carriers charge on ionized impurity atoms, and in this region μ~T 3/2. Therefore, the dependence of the mobility of charge carriers in a semiconductor on temperature is represented by a curve with a maximum, and the position of the maximum depends on the impurity concentration (Fig. 3).

In accordance with (1), the dependence of specific conductivity on temperature σ(T) is determined by the temperature dependences of the mobility and concentration of charge carriers. Comparing the dependences of concentration and mobility on temperature, it can be noted that the dependence of mobility on temperature will determine the temperature dependence of conductivity only in the temperature range (T i > T > T s) where the concentration of charge carriers is constant; at other temperatures, the temperature dependence of conductivity is determined mainly by the temperature dependence of the charge carrier concentration. The graph of the dependence of the conductivity of a semiconductor on temperature in coordinates lnσ(1/T) convenient for further calculations has the form shown in Fig. 4.

Rice. 3. Temperature dependence of charge carrier mobility.

Rice. 4. Methodology for determining the activation (energy) parameters of the electrical conductivity process.

For comparison, in Fig. Figure 5 shows a graph of σ(T) for metals; This dependence is explained by an increase in electron scattering on thermal vibrations of the lattice with increasing temperature and a corresponding decrease in the mobility of charge carriers in the metal.

Rice. 5. Temperature dependence of the resistivity of metals.

Thus, for an intrinsic semiconductor, from expressions (1) and (2) it follows:

where (lnσ 0 +α/2k)=const, and -ΔE g о /2k is the slope linear function(5). This coefficient can be determined graphically by calculating the slope of the graph of the experimental dependence lnσ(1/T) in the section of intrinsic conductivity (Fig. 4, section 3).

Indeed, in this area:

By substituting the value ΔE g o in (2) with the value α corresponding to the given substance, we can calculate the band gap of the semiconductor at a given temperature.

Similar reasoning is valid for impurity semiconductors in the low temperature region (section 1, Fig. 4), when the ionization energy of the acceptor ΔE a = E a -E v or donor ΔE d =E c -E d impurity can be determined from an expression of the form:

Experimental points of the lnσ(1/T) dependence in section 3. It is recommended to approximate with a computer using the least squares method. The angular coefficient of the linear approximation determined in this case is the tgβ value necessary for calculating the bandgap width.

Methodology for conducting experimental studies

In this work, to study the temperature dependence of the resistivity ρ (or conductivity σ) of a semiconductor (germanium) and a metal (copper), it is necessary to measure voltage U on the sample, current I through the sample and temperature T of the material in accordance with the well-known expression:

where S- cross section sample, l is the length of the sample (in work this is the distance between zones).

Calculations of ρ(orσ) according to (9) are carried out at each given value of the sample temperature.

A schematic diagram of the setup for measuring the temperature dependence of electrical conductivity is shown in Fig. 6.

R is. 6. Scheme of the setup for measuring the temperature dependence of the electrical conductivity of semiconductors.

S1 – current switch through the sample; S2 – switch for measuring current (position a) and measuring voltage on the sample (position b); S3 – polarity switch PPTV-1; S4 – switch; R1 – resistance store (P-33); R2 – reference resistance (100 Ohm); PV1 – PPTV-1; PV2 – millivoltmeter; GB1 – power supply.

The installation consists of a DC power supply GB1, a source switch S4, a resistance store R1, a reference resistor R2, a milliammeter PI1, a voltage meter PV1, switches S1, S2, S3, a thermocouple and a millivoltmeter PV2, a chamber with a furnace and a sample holder, and a transformer T1. The vertical panel contains: milliammeter PV1, switches S1, S2, S3, S4, resistor R2 and terminals for connecting R1, PV1 and sample conductors. Source GB1 is connected to the circuit at the back of the panel.

To determine the voltage on the sample, a two-probe compensation measurement method is used. The essence of the two-probe method is that the voltage drop U is measured using metal probes between two internal points A and B of a semiconductor sample through which current I flows, supplied through external contacts 1 and 2. In this way, electrical isolation is achieved between the power source and the measuring circuit.

The use of the compensation method is due to the possibility of errors when measuring the voltage drop between contacts A and B due to the transition resistance of these contacts (the most significant errors are caused by metal-semiconductor contacts).

These errors are eliminated by using the PPTV-1 potentiometer as a voltage meter (PV1 in Fig. 6; PPTV is a high-resistance DC potentiometer). Indeed, the potential difference between zones A and B is compensated by the opposite voltage of the potentiometer U n, and if the circuit is balanced (U = U n), then the current flowing through the galvanometer of the PPTV-1 meter is zero. Since there is no current, there is no voltage drop at the probe-semiconductor contact. In this case, the contact resistances do not affect the accuracy of resistivity measurement.

Another source of errors in measuring the temperature dependence of resistivity is the thermo-EMF that appears on the measuring probes due to a certain temperature gradient of the sample, which occurs due to uneven heating of the material. The influence of thermo-EMF is eliminated as follows. Measuring the voltage on the sample (between the probes) must be done at two different directions of current through the sample, for which the laboratory setup has a switch S1 that swaps contacts 1 and 2 of the sample; in this case, the direction of the current in the circuit external to the sample (in particular, through the reference resistor R2) does not change.

Since the PPTV-1 meter is polar, when changing the direction of the current through the sample, its inputs must be swapped, which is done by switch S3, that is, in the voltage measurement mode on the sample, S1 and S3 are switched together. Since the actual value of thermo-EMF ΔU is less than absolute value than the voltage drop between the probes U, and the sign of ΔU is determined by the temperature gradient and does not depend on the direction of the current, then the measured voltage drops U 1 and U 2 for different current directions will be respectively equal:

The amount of current through the sample is approximately set according to the readings of the milliammeter PI1 using the voltage regulator of the power supply GB1. For convenience of calculations, it is recommended to maintain the current value constant and equal to 5 mA at all temperature conditions. To more accurately set the current, it is necessary to switch the PPTV-1 meter to the reference resistor R2 = 100 Ohm (S2 is set to position a), and then set the PPTV-1 value to Uet = 0.5 V (5 mA * 100 Ohm = 0.5 V) and using a PPTV galvanometer. This procedure, that is, current control, is performed before each voltage measurement.

In this work, it is possible to conduct research in the temperature range from room temperature to 250 degrees C. The samples are heated in a special chamber with an electric furnace. The temperature inside the chamber is determined using a thermocouple, a PV2 millivoltmeter and a calibration table, providing an accuracy of 1 degree. Millivoltmeter readings PV2 (U T) way. The thermo-EMF values ​​in the calibration table (in millivolts) are located at the intersection of the columns corresponding to tens of degrees. These tens and units of degrees are summed up and added to the readings of the room thermometert k. The obtained values ​​are entered into the measurement table and then converted into an absolute temperature scale.

The procedure for performing laboratory work.

Familiarize yourself with the laboratory installation for measuring the temperature dependence of electrical conductivity, perform necessary connections elements.

Read the operating instructions for the PPTV-1 potentiometer and prepare it for operation.

Make measurements of the necessary parameters of the semiconductor sample at room temperature t k (thermocouple emf Ut = 0):

1. Turn on the power supply GB1 (switch S4).

   Set the current direction switch S1 to position a.

   Using the voltage regulator of the power supply GB1, set the approximate current value of 5 mA according to the readings of the milliammeter PI1.

   Set more precisely the current value through the sample I = 5mA, for which:

set S2 to the voltage measurement mode on the reference resistor (position a), aS3 to position;

use the potentiometer knobs to set the value U R 2 =0.5 V in the windows of the top panel;

Using the resistance magazine R1, by pressing first the “50000 Ohm” button and then the “0” button of the potentiometer, achieve an equilibrium position of the galvanometer needle. In this case, the accuracy of setting the voltage U R 2 reaches 0.03%.

Switching S2 to position b, aS 3 to position a, measure the voltage drop across the sample U 1.

Change the direction of the current through the sample by setting S1 to position b, and control the current value by repeating paragraph 3.4.

Switch S 2 and S 3 to position b and measure the voltage drop across the sample U 2.

results measurements t,U 1 ,U 2 and calculations T, 1/T,U avg,σ,lnσ should be entered in Table 1. (The dimensions of physical quantities in calculations must correspond to the SI system of units.)

Table 1.

Registration of measurement results and calculations for laboratory work.

Repeat the measurements (clauses 3.2…3.7), changing the temperature of the material being tested. To heat the sample, it is necessary to turn on the chamber oven by connecting transformer T1 (LATR) to the ~ 220 V network and turning the LATR output voltage regulator knob clockwise to the limiter. The EMF of the thermocouple U T should be fixed in the range from 0.5 mV to 4.0 mV every 0.5 mV. At each fixed value of U T for the duration of measurements, it is necessary to turn on the furnace heater by turning the LATR regulator knob counterclockwise until it stops. After taking the appropriate measurements, the handle returns to its original heating position.

Plot the dependence lnσ(1/T) and determine the band gap of the semiconductor at room temperature using the method described in section 2. Present the final result of the calculation ΔE g in joules and electron volts.

At the next lesson, repeat the necessary measurements and calculations for the copper sample, while paragraphs 3.6 and 3.7 are not performed. The results of measurements t, U 1 = U and calculations T, ρ are included in table 1.

Based on the analysis, construct a graph of the temperature dependence of the electrical conductivity and resistivity of the studied semiconductor.

Formulate conclusions regarding the results obtained from the analysis of experimental research data.

Test questions and assignments

Explain the mechanism of formation of band energy diagrams in crystalline bodies(metals, semiconductors).

Why is the electrical conductivity of intrinsic semiconductors equal to zero when the energy bands are completely filled?

Estimate the width of impurity levels (donor, acceptor) in doped semiconductors.

Explain the mechanism of electrical conductivity in intrinsic and impurity semiconductors.

How can activation energy parameters in semiconductors be determined based on experimental data?

What particles are equilibrium charge carriers in intrinsic and impurity semiconductors?

Explain the temperature dependence of charge carrier concentration in semiconductors and metals.

Explain the temperature dependence of charge carrier mobility in semiconductors and metals.

What explains the different behavior of the temperature dependence of electrical conductivity in metals and semiconductors?

Bibliography

Pasynkov V.V., Chirkin L.K. Semiconductor devices. –M., Ed. "Lan". 2002. 385 p.

Epifanov G.I. Physical Basics microelectronics. – M., “Higher. school". 1997 407 p.