RU2079853C1 - Method of measurement of electrophysical parameters of semiconductor materials - Google Patents

Abstract

FIELD: measurement technology. SUBSTANCE: proposed method of determination of electrophysical parameters of semiconductor and semiinsulating materials is based on local nondestructive measurements of relaxation processes of electron-hole and trap systems in sample under conditions of their periodic excitation by light and quasi-equilibrium heating of sample. Method allows to measure time of relaxation of traps, their energy and concentration as well as their distribution in plane of plane and in depth. Concentration of equilibrium carriers and their distribution in depth and in plane of plate are determined in doped samples. EFFECT: improved authenticity of proposed method. 2 cl, 8 dwg

Description

 The invention relates to measuring equipment.

A known method of non-destructive measurement of the parameters of traps in semiconductors, which consists in measuring the intensity of the optical absorption spectra [1] The method is based on the absorption of light quanta when stimulating transitions, an impurity band, or a band zone. The disadvantages of the method include low sensitivity and, as a result, poor resolution (locality 1 mm). In the case of traps in a neutral state, the threshold concentration of the detected impurity exceeds 10 ¹⁶ 10 ¹⁷ cm ^-3 , which is associated with a small photoionization cross section of the impurity. In the case of impurity – zone transitions, the sensitivity threshold [2] does not exceed 10 ¹⁷ cm ^–3 . In the case of a deep impurity, the detection ability is 10 ¹⁶ cm ^-3 .

в процессе его квазиравновесного нагревания на полевой электрод подают периодическую систему импульсов обеднения и обогащения, регистрируя в период обеднения изменения емкости во времени; при этом время, в течение которого регистрируются изменения емкости, а также момент начала регистрации выбирают соответствующими максимумам изменения емкости а текущая температура образца является параметром, изменяющим соотношение между длительностью "временного окна" и характерными временами генерационно-рекомбинационных процессов, протекающих с участием измеряемых ловушек, обуславливающих динамику процесса изменения емкости.A known method for determining the parameters of traps in semiconductor materials, based on non-stationary spectroscopy of deep levels (GU), in which the excitation of GU is carried out by applying voltage pulses to the test cell [3] The test sample is made in the form of a capacitive cell containing a field electrode and an ohmic contact . Measurements are carried out in the following sequence. Cool the sample to a temperature

in the process of its quasi-equilibrium heating, a periodic system of impulse and enrichment pulses is fed to the field electrode, recording changes in capacity over time during the depletion period; the time during which the changes in the capacitance are recorded, as well as the moment of the beginning of the registration, are selected corresponding to the maxima of the capacitance changes and the current temperature of the sample is a parameter that changes the relationship between the duration of the “time window” and the characteristic times of the generation-recombination processes taking place with the participation of measured traps causing the dynamics of the process of changing capacity.

 The disadvantage of this method is the fact that it relates to destructive methods, since for measurements it is necessary to produce barrier and ohmic contacts on the sample. In addition, when diagnosing instrument structures on semi-insulating substrates, due to the need to produce a planar ohmic contact, the locality of the method is unsatisfactory (-1 mm). And finally, it is almost impossible to diagnose semi-insulating materials using this method.

 Of non-destructive methods for determining the concentration of equilibrium carriers in semiconductor materials, a method is known based on the absorption of long-wavelength radiation by free carriers [4]. The method allows, however, to carry out quantitative measurements only when using reference samples and is therefore used only to control the distribution of doping in the plane of the wafer.

 The aim of the invention is the implementation of a method of non-destructive measurements of the electrophysical parameters of semiconductor and semi-insulating materials, which allows to determine the parameters of deep levels, their distribution in the plane and depth of the plate, as well as the absolute measurements of the concentration of free carriers in semiconductors and their distribution in the plane of the plate.

и регистрируют зависимость от времени и от температуры величин U₁(t) и

пропорциональных току через конденсатор и среднему току, протекающему через конденсатор за время

при этом регистрирующие приборы к контролируемым цепям подключаются через усилитель, а средний ток

определяется по формуле

где
I₀ максимальный фототок через образец, τ_p время жизни носителей на ловушках, t текущее время, t_и длительность светового импульса, затем определяют температуру

соответствующую максимальной величине

после чего устанавливают другой период модуляции излучения

регистрируют соответствующую зависимость

и определяют температуру

отвечающую максимальной величине

затем для изолирующих и полуизолирующих образцов с концентрацией глубоких центров N_t, превышающей концентрацию равновесных носителей U₀, увеличивают интенсивность облучения до величины, соответствующей максимальной величине U^* сигнала U(t), а для образцов с концентрацией ловушек N_t, меньшей концентрации равновесных носителей n₀ (для полупроводников), монотонно увеличивают мощность облучения до величины P^*, при которой постоянная времени релаксации τ_o становится зависимой от интенсивности облучения, затем рассчитывают по формулам

время жизни носителей на ловушках при температурах

энергию ловушек

сечение захвата ловушек

концентрацию ловушек

концентрацию равновесных носителей

при этом

а используемые обозначения имеют следующий смысл: V_т тепловая скорость носителей, U $\genfrac{}{}{0ex}{}{\text{*}}{\text{вх}}$ напряжение на входе усилителя, соответствующее максимальной величине сигнала U(t), C_вх входная емкость усилителя, α коэффициент поглощения излучения в образце, g - элементарный заряд, P^x мощность излучения, приходящая на облучаемый участок образца Δx², f^* степень заполнения ловушек, τ_o постоянная времени релаксации фотопотенциала, β квантовая эффективность, ∈_c и ∈_п - диэлектрическая проницаемость окружающей среды и измеряемой среды соответственно, при этом тип ловушечных центров (ГУ) и тип полупроводника определяют по знаку регистрируемого фотопотенциала U(t) или по знаку функции

В случаях, когда концентрация носителей в образцах превышает концентрацию ловушек, а длительность возбуждающего импульса света превышает время релаксации измерительной системы и системы ловушек, при изменении интенсивности излучения регистрируют ту ее величину, которая отвечает моменту начала изменения постоянной времени релаксации фотопотенциала от интенсивности облучения и затем по приведенной выше формуле рассчитывают концентрацию свободных (равновесных) носителей.This goal is achieved by the fact that, when measuring the parameters of traps, a quasi-equilibrium heated sample is placed between the plates of a flat capacitor, and the controlled portion of the sample is irradiated with light (ℏν> E _d ) which varies in time according to a periodic law with a period

and register the dependence on time and temperature of the quantities U ₁ (t) and

proportional to the current through the capacitor and the average current flowing through the capacitor over time

at the same time, recording devices are connected to controlled circuits through an amplifier, and the average current

determined by the formula

Where
I _{0 the} maximum photocurrent through the sample, τ _p the lifetime of the carriers in the traps, t the current time, t _{and the} duration of the light pulse, then determine the temperature

corresponding to the maximum value

then set a different period of radiation modulation

register the corresponding dependence

and determine the temperature

corresponding to the maximum value

then, for insulating and semi-insulating samples with a concentration of deep centers N _t exceeding the concentration of equilibrium carriers U ₀ , the radiation intensity is increased to a value corresponding to the maximum value U ^{* of the} signal U (t), and for samples with a concentration of traps N _t lower than the concentration of equilibrium carriers n ₀ (for semiconductors) monotonically increase the irradiation power to a value of P ^* , at which the relaxation time constant τ _o becomes dependent on the irradiation intensity, then calculated by the formulas

lifetime of carriers in traps at temperatures

trap energy

trap capture section

concentration of traps

concentration of equilibrium carriers

wherein

and the notation used has the following meaning: V _{t is the} thermal velocity of the carriers, U $\genfrac{}{}{0ex}{}{\text{*}}{\text{in}}$ the voltage at the amplifier input corresponding to the maximum value of the signal U (t), C _{in is the} input capacitance of the amplifier, α is the radiation absorption coefficient in the sample, g is the elementary charge, P ^{x the} radiation power arriving at the irradiated portion of the sample Δx ² , f ^{* the} degree of trap filling , τ _o photovoltage relaxation time constant, β quantum efficiency, ∈ _{c p} ∈ and - the permittivity of the environment and the medium, respectively, wherein the type of trap centers (SU) and the type of the semiconductor is determined by the sign of registered photovoltage of U (t) or the sign function

In cases where the carrier concentration in the samples exceeds the concentration of traps, and the duration of the exciting light pulse exceeds the relaxation time of the measuring system and the trap system, when its radiation intensity is changed, its value is recorded that corresponds to the moment of the beginning of the change in the relaxation time constant of the photopotential from the radiation intensity and then the above formula calculates the concentration of free (equilibrium) carriers.

где
l^E эффективная длина экранирования (глубина зондирования),
E₀ величина напряженности поля в конденсаторе,

, l_э - длина дебаевского экранирования; в случае наличия глубоких доноров и компенсирующих акцепторов эффективная длина экранирования равна

Неразрушающий характер измерений обусловлен бесконтактным способом измерения тока через образец, связанного с фотопотенциалом, изменяющимся периодически во времени, а отсутствие контактов повышает локальность измерений.In cases of application to the plates of a flat concentrator of an electric field (voltage U ₀ ) during the above procedures determines the depth of the diagnosed area depending on the magnitude and polarity of the voltage U ₀ according to the formula (5)

Where
l ^E effective shielding length (sounding depth),
E _{0 the} value of the field strength in the capacitor,

, l _e - the length of the Debye screening; in the case of deep donors and compensating acceptors, the effective screening length is

The non-destructive nature of the measurements is due to the non-contact way of measuring the current through the sample, associated with the photopotential, which varies periodically in time, and the absence of contacts increases the locality of the measurements.

The measurement scheme (Fig. 1) includes:
sample 1, measuring capacitor 2, light source 3 (ℏ • ν> E _g ), power supply 4, broadband amplifier 5, synchrodetector 6, thermostat 7, temperature sensor 8, plotter 9 and 12, stroboscopic amplifier 10, scanning device for sample 11, the source of the external field 13.

 Measurements are carried out according to the following scheme (procedure).

частота следования импульсов света). Напряжение, возникающее на входе усилителя, пропорциональное току, протекающему через образец, усиливается широкополосным усилителем 5 и соответствующий сигнал преобразуется стробоскопическим усилителем-преобразователем 10 и подается на вход "y" графопостроителя 9; на вход "x" графопостроителя 9 подается сигнал временной развертки стробоскопического преобразователя 10. Параллельно сигнал с выхода широкополосного усилителя 5 подается на вход синхродетектора 6, а с его выхода сигнал

ставший пропорциональным среднему току, протекающему через образец за период

подается на вход "y" второго графопостроителя 12, на вход "x" которого подается сигнал, пропорциональный температуре образца, формируемый датчиком 8.Sample 1 is placed between the plates of the measuring capacitor 2, one of the plates of which is transparent to radiation, and the measured portion of the sample is irradiated with electromagnetic radiation from the source 3 with a varying intensity with a period of time

pulse repetition rate). The voltage occurring at the input of the amplifier, proportional to the current flowing through the sample, is amplified by a broadband amplifier 5 and the corresponding signal is converted by a stroboscopic amplifier-converter 10 and fed to the input "y" of the plotter 9; at the input "x" of the plotter 9, a time-sweep signal of the stroboscopic converter 10 is supplied. In parallel, the signal from the output of the broadband amplifier 5 is fed to the input of the synchrodetector 6, and the signal from its output

which has become proportional to the average current flowing through the sample over a period

fed to the input "y" of the second plotter 12, to the input "x" of which a signal is proportional to the temperature of the sample, generated by the sensor 8.

 Note that the same plotter can be used to measure time and temperature dependencies, since the measurement procedure allows both parallel and sequential time and temperature measurement cycles; in this case, in the case of choosing a sequential measurement option, the time-sweep output of the stroboscopic amplifier 10, or a signal from the temperature sensor 8, are switched to the input "x" of the plotter.

для двух различных периодов возбуждения

а затем, используя значения

а также равенства

по формулам для E_t и σ_t рассчитываем энергию ГУ и сечение захвата.In the process of measuring the energy parameters of the traps, quasi-equilibrium heating of the sample and registration of the signal from the output of the synchrodetector are performed 6

for two different periods of arousal

and then using the values

as well as equality

according to the formulas for E _t and σ _{t, we} calculate the GI energy and the capture cross section.

To measure the concentration, we produce a monotonic change in the intensity of the irradiation pulses. Moreover, in the case of semi-insulators (N _t > n ₀ ), we increase the irradiation intensity to a value corresponding to the maximum value of the photo signal (to “saturation”), and calculate the concentration of traps according to the formula for N _t . When measuring the concentration of free carriers (equilibrium) for the case N _t <n _{0, we} measure the relaxation time under conditions of weak excitations (linear recombination mode), then, increasing the irradiation monotonously, we register the irradiation power P ^* at which the relaxation time constant of the corresponding pulse the photopotential begins to depend on the intensity of irradiation, and we determine the concentration of equilibrium carriers by the formula for n ₀ .

В процессе диффузии и самоиндуцированного дрейфа носителей, а также дрейфа их в приповерхностном "контактном" электрическом поле (на границе раздела полупроводник/воздух), доминирующие неравновесные носители распространяются вглубь образца, существенно меняя картину равновесной заселенности глубоких уровней на длине дебаевского экранирования, либо на эффективной длине дебаевского экранирования (при наличии внешнего поля) и создавая объемный заряд. В результате за время освещения импульсом АДБ (рис. 2а) образуется дрейфово-диффузионный потенциал Φ_mDE (рис. 2б), приводящий при модулированном во времени освещении (облучении) к изменению во времени поверхностного потенциала Φ_DE (рис. 2в). Последний изменяется от максимальной величины Φ_m соответствующей моменту окончания импульса облучения, до величины Φ_o соответствующей моменту окончания времени задержки между световыми импульсами. Эта вариация потенциала δΦ= Φ_m-Φ_o создает во внешней цепи ток δj=δΦ/Z, где Z Z_i + Z_n есть сумма сопротивлений измерительной емкости Z_i и импеданса образца Z_n. При наличии ловушек динамика изменений поверхностного потенциала определяется их энергией и сечением захвата, а при больших интенсивностях облучения и концентрацией неравновесных носителей. При этом можно показать, что функция

аппаратно реализующаяся в представленной схеме измерения (имеется в виду режим синхродетектирования), будет иметь максимум при равенстве времени релаксации фотопотенциала и длительности периода следования импульсов световых f $\genfrac{}{}{0ex}{}{\text{-1}}{\text{т}}$ Действительно, так как I_з=I_o•[1-exp(-t/τ_з)] функция тока "зарядки", а I_р=I_o•exp(-t/τ )]_p функция тока "разрядки" (тока релаксации фотопотенциала в темноте), то величина протекающего за временной интервал заряда ("среднего" тока) будет иметь вид:

.The method is based on a physical effect associated with generation-recombination processes in a semiconductor, with the participation of deep levels, under conditions of excitation of nonequilibrium carriers in the sample by light pulses. The light incident on the sample penetrates to a depth of α ^-1 (a is the light absorption coefficient of the sample); in this case, in the region α ^-1 , the type of carriers that has a longer recombination time will prevail, which follows from the validity of the stationary equation

In the process of diffusion and self-induced drift of carriers, as well as their drift in a near-surface “contact” electric field (at the semiconductor / air interface), the dominant nonequilibrium carriers propagate deep into the sample, significantly changing the equilibrium population of deep levels along the Debye screening length, or on the effective the length of the Debye screening (in the presence of an external field) and creating a space charge. As a result, during the illumination by the ADB pulse (Fig. 2a), the drift-diffusion potential Φ _mDE (Fig. 2b) is formed, which, under time-modulated illumination (irradiation), changes in the surface potential Φ _DE in time (Fig. 2c). The latter varies from the maximum value Φ _m corresponding to the end of the irradiation pulse, to Φ _o corresponding to the end of the delay time between the light pulses. This variation of the potential δΦ = Φ _m -Φ _o creates a current δj = δΦ / Z in the external circuit, where ZZ _i + Z _n is the sum of the resistances of the measuring capacitance Z _i and the impedance of the sample Z _n . In the presence of traps, the dynamics of changes in the surface potential is determined by their energy and capture cross section, and at high irradiation intensities and the concentration of nonequilibrium carriers. Moreover, it can be shown that the function

hardware implemented in the presented measurement scheme (meaning the synchrodetection mode), will have a maximum if the relaxation time of the photopotential and the duration of the repetition period of light pulses f $\genfrac{}{}{0ex}{}{\text{-one}}{\text{t}}$ Indeed, since I _z = I _o • [1-exp (-t / τ _z )] the function of the “charging” current, and I _p = I _o • exp (-t / τ)] _{p is the} function of the “discharge” current ( of the relaxation potential of the photopotential in the dark), then the magnitude of the charge flowing over the time interval (the "average" current) will have the form:

.

). Значит в полученной зависимости

максимум функции соответствует температуре T_m, при которой f $\genfrac{}{}{0ex}{}{\text{-1}}{\text{т}}$ = τ(T_m) (рис. 3а). Таким образом, используя полученные на зависимостях

значения

, а также зная, что

, определяем энергию ГУ E_t и их сечение захвата σ_t. Действительно, так как

и τ_o= (U_t•σ_t•N_cv)^-1, то при двух периодах повторения

получаем:

, а так как

и

.For t _and <f $\genfrac{}{}{0ex}{}{\text{-one}}{\text{t}}$ or, for Δn≪ n _o , M, K, we obtain that the maximum of this quantity is realized under the condition τ = f $\genfrac{}{}{0ex}{}{\text{-one}}{\text{t}}$ (we obtain from

) So in the resulting relationship

the maximum of the function corresponds to the temperature T _m at which f $\genfrac{}{}{0ex}{}{\text{-one}}{\text{t}}$ = τ (T _m ) (Fig.3a). Thus, using the obtained dependencies

values

as well as knowing that

, we determine the energy of the PG E _t and their capture cross section σ _t . Indeed, since

and τ _o = (U _t • σ _t • N _cv ) ^-1 , then for two repetition periods

we get:

, and since

and

.

Эквивалентная схема измерения показана на фиг. 4.When measuring the concentration of PG, it is preferable to implement the following relations between the impedances of the measuring capacitance Z _c , the input impedance of the amplifier 5 Z _in and spreading resistance and the volume resistance of the measured sample Z _n : Z _c >> Z _n >> Z _in . It is easy to show that the aforementioned relations between the indicated impedances are realized in the region of repetition frequencies of the excitation pulses (10 ² 10 ⁶ Hz) and with the characteristic dimensions of the gap between the sample and the translucent lining of the capacitance 0.1 1.0 mm and its linear size 1 mm. In this case, between the photo-emf value and the voltage at the input of the amplifier, the following relation is valid:

An equivalent measurement circuit is shown in FIG. 4.

Учитывая что

, имеем

Отсюда окончательно имеем

Значит, для произведения концентрации ловушек на степень их заполнения можно написать следующее соотношение:

При определении концентрации свободных равновесных носителей n₀ (случай N_t<n₀) предлагаемый подход основан на следующем соотношении для стационарной концентрации неравновесных носителей: Δn_ст.= τ•β•I•α^-1.Then, since f $\genfrac{}{}{0ex}{}{\text{-one}}{\text{t}}$ ≫ τ from the _system and C from the _name << C _n , then for the current through the sample we can write the following relation:

Given that

, we have

From here we finally have

So, for the product of the concentration of traps by the degree of their filling, we can write the following relation:

When determining the concentration of free equilibrium carriers n ₀ (case N _t <n ₀ ), the proposed approach is based on the following relation for the stationary concentration of nonequilibrium carriers: Δn _Art. = τ • β • I • α ^-1 .

где P^* мощность светового облучения равная критической (пороговой) величине, β квантовая эффективность, t время жизни ловушек в возбужденном состоянии, ℏ постоянная Планка, ν частота электромагнитного излучения (ℏ•ν энергия кванта света), a коэффициент поглощения света образцом, Dx линейный размер пятна светового зонда.At low excitation levels (Δn <n _o ), a linear recombination regime is realized and τ is a constant. In the case of high excitation intensities (Δn> n _o ), τ becomes a function of the concentration of nonequilibrium carriers and decreases with a further increase in the irradiation intensity, Fig.3b. Thus, there is a critical value, above which τ ceases to be a constant value. Such a value of P ^* corresponds to a situation in which the concentration of nonequilibrium carriers becomes equal to the concentration of equilibrium carriers, Dn _Art. = n _o .
From here for the equilibrium concentration follows the ratio:

where P ^{* is the} light irradiation power equal to the critical (threshold) value, β is the quantum efficiency, t is the lifetime of the traps in the excited state,, is the Planck constant, ν is the frequency of electromagnetic radiation (ℏ • ν is the quantum energy of light), and the light absorption coefficient is sample, Dx is linear spot size of the light probe.

Note that the surface potential facilitates the separation of holes and electrons: holes in the field of the surface potential rush to the surface and recombine at high speed on its multiple defects, enhancing the correctness of the monopolar representation of the problem. Taking into account the contact potential does not affect the energy of traps and practically does not affect the capture rate at the GU, but will determine only the thickness of the diagnosed layer. And since the method for determining the concentration of PG proposed above is an estimate from below, and the true thickness of the probed layer is not α ^-1 , but equal to the screening length, the method of estimation accuracy increases and is no worse than 2 times.

 Examples of measurements.

, с периодом 100 мкс (период повторения импульсов) и длительностью 10 мкс. Монотонно увеличивает температуру образца и регистрируем U(t) и

(кривые 1, 2 рис. 5а,б).(a). We install a sample (N _t > n ₀ , a semi-insulating gallium arsenide substrate) in the measuring capacitor 2 and irradiate it with light pulses with

, with a period of 100 μs (pulse repetition period) and a duration of 10 μs. Monotonically increases the temperature of the sample and register U (t) and

(curves 1, 2 Fig. 5a, b).

We repeat this procedure with a light pulse repetition period of 300 μs and obtain curves 3 and 4 of Fig. 5ab. Using the relations obtained above for E _t and σ _t , we determine the energy and trapping capture cross section.

Используя вышеприведенные соотношения, получаем:

(отсчет ведется от E_c).As a result of measurements obtained:

Using the above relations, we obtain:

(counting is from E _c ).

Increasing the irradiation intensity, we record the maximum photopotential, U $\genfrac{}{}{0ex}{}{\text{*}}{\text{FP}}$ : U $\genfrac{}{}{0ex}{}{\text{*}}{\text{FP}}$ = 1500 μV. Given the geometry of the experiment (the diameter of the transparent lining of the measuring capacitor is 1 mm, the gap between the sample and the lining of the capacitance is 0.1 mm, the diameter of the light spot is 500 μm), we calculate
N _t ^o CN _t 5 • 10 ¹⁵ cm ^-3 .

(b) We install a sample (n ₀ > N _t ) of the semiconductor structure in the measuring capacitance, monotonically increase the amplitude of the irradiation pulses, measuring the relaxation time τ of the photopotential pulses, and record the irradiation power P ^* at which the relaxation time becomes dependent on the irradiation intensity. Measured: threshold light power 1.1 • 10 ^-4 W, relaxation time t _o in the area with linear recombination 2 ms (Fig. 6, 1, 2). Using the formula obtained above to determine n ₀ , we obtain values of 4 • 10 ¹⁵ cm ^-3 for equilibrium concentration. Control measurements of the image using the C – V method gave a value of 4.4 • 10 ¹⁵ cm ^-3 for the concentration of free carriers.

Источники информации, использованные при составлении заявки
1. W. Kohn. Sol. State Phys. v.5, p.257 (1957).In fig. 7 presents the measurement results of the inventive method of a semi-insulating substrate of gallium arsenide containing one acceptor center: E _t 0.82 eV, σ _t = 10 ^-13 cm ² , N _t 4 • 10 ¹⁴ cm ^-3 , τ _o = 0.6 ms.
Figure 8 shows the results of measurements of the semi-insulating gallium arsenide substrate containing donor and acceptor deep centers:

Sources of information used in the preparation of the application
1. W. Kohn. Sol. State Phys. v. 5, p. 257 (1957).

 2. J. Pankov. Optical processes in semiconductors. Ed. "World", 1973, ch. 3.

 3. D.V. Lang. J. appl. Phys. v. 75, N7, p. 3014 (1974).

 4. N.I. Feng. The absorption of infrared radiation in semiconductors. Advances in Physical Sciences, vol. 6, p. 316, 1958.

 5. Ginberg N. Brynskih P. The theory of light absorption by free carriers, covering quantum and classical domains. Physics and technology of semiconductors, v.5, v.7, p.1271 (1971).

Claims (1)

1. The method of determining the electrophysical parameters of semiconductor materials, which pre-cool the sample to a temperature

where E ^* and N $\genfrac{}{}{0ex}{}{\text{*}}{\text{t}}$ - approximate minimum values of the energy of traps and concentration of traps, respectively, selected from the range of possible values for a given measurement object;
k Boltzmann constant;
N _{c v the} density of states at the bottom of the conduction band - N _c and the ceiling of the valence band N _v ,
followed by quasi-equilibrium heating under conditions of periodic disturbance of the equilibrium of the electron-hole and trap systems in the sample, characterized in that the measured sample is placed between the plates of a flat capacitor and the controlled portion of the sample is irradiated with electromagnetic radiation with photon energy ℏv> E _g ,
where E _g the band gap of the test sample, which varies in time according to the periodic law with a period

and register the dependence on time and temperature of the quantities U ₁ (t) and

proportional to the current through the capacitor and the average current flowing through the capacitor over time

at the same time, recording devices are connected to controlled circuits through an amplifier, and the average current is determined by the formula

where I _{0 is the} maximum photocurrent through the sample;
τ _p is the lifetime of carriers on traps;
t current time;
t _{and the} duration of the light pulse, determine the temperature

corresponding to the maximum value

then set a different period of modulation of radiation

register the corresponding dependence

and determine the temperature

corresponding to the maximum value

then, for insulating and semi-insulating samples with a concentration of deep centers N _t exceeding the concentration of equilibrium carriers n ₀ , the radiation intensity is increased to a value U ^* corresponding to the maximum signal value U (t), and for samples with a concentration of traps N _t lower than the concentration of equilibrium carriers n ₀ , the irradiation power is monotonically increased to a value of P ^* , at which the relaxation time constant τ _o becomes dependent on the irradiation intensity, then the carrier lifetime per l is calculated using the formulas temperature-controlled

trap energy

trap capture section

concentration of traps

The concentration of equilibrium carriers

Where

v _t thermal velocity of the carriers;
U $\genfrac{}{}{0ex}{}{\text{*}}{\text{in}}$ - voltage at the input of the amplifier corresponding to the maximum value of the signal U (t),
C _{in x} output capacity of the amplifier;
α is the radiation absorption coefficient in the sample;
g elementary charge;
P ^* radiation power coming to the irradiated portion of the sample;
f ^* degree of trap filling;
t ₀ is the relaxation time constant of the photopotential;
β - quantum efficiency;
E _c and E _n are the dielectric permittivities of the environment and the medium being measured, respectively, while the type of trap centers and the type of semiconductor are determined by the sign of the detected photographic potential U (t) or by the sign of the function

2. The method according to p. 1, characterized in that the electrical voltage U ₀ is supplied to the plates of the flat capacitor and the depth of the diagnosed area is calculated depending on the magnitude of the voltage and its polarity.

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