RU2439541C1 - Method for determination of conductivity and thickness of semiconductor layers - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method consists in exposure of semiconductor layer to SHF range radiation and measurement of dependence of SHF-range reflection coefficient in selected frequency range at the first and second values of temperature, calculation of parameters for semiconductor layer (d, σ) at which theoretical dependence of electromagnetic radiation reflection coefficient has the closest value to the measured one; using known temperature dependence a target couple of parameters (d, σ) is determined at which theoretical frequency dependence of electromagnetic radiation reflection coefficient has the closest value to the measured one at the second temperature value.

EFFECT: possibility of simultaneous determination of conductivity and thickness of semiconductor layer.

3 dwg, 2 tbl

Description

The invention relates to measuring technique, and can be used to determine the conductivity and thickness of the semiconductor layer on the surface of the dielectric and can be used in various industries for controlling the properties of semiconductor layers.

To determine the electrophysical parameters of dielectric and semiconductor materials and structures, one can use the results of measurements of the reflection spectra of the microwave radiation interacting with them, provided that their theoretical description is known. Simultaneous determination of the parameters of semiconductor layers such as electrical conductivity and thickness is not possible at the present level of technology because of the fact that with different combinations of the values of these parameters, the same frequency dependence of the reflection coefficient of microwave radiation can be observed.

A known method for determining the properties of a controlled material using two-electrode or three-electrode capacitive converters (see Bugrov A.V. High-frequency capacitive converters and quality control devices. - M: Mechanical Engineering, 1982. P. 44). In the general case, the properties of the transducer depend both on the size, configuration and relative position of the electrodes, as well as on the shape, electrophysical properties of the material being monitored and its location with respect to the electrodes.

This method has the following disadvantages:

- does not allow high-speed scanning of large surfaces;

- there is no possibility of separation of the pathogen of the scanning field and the receiving device;

- requires special methods of detuning from the gap;

- the method does not provide simultaneous measurement of dielectric constant and thickness;

- when measuring thickness, it is required to use a metal surface as an electrode, in this case, the measurements depend on the variation of the dielectric constant.

A known method for determining the thickness of dielectric coatings on an electrically conductive basis (see Devices for non-destructive testing of materials and products. Handbook edited by V.V. Klyuyev. - 2nd edition, revised. And add. - M.: Engineering, 1988. C .120-125), which consists in the creation of eddy currents in an electrically conductive substrate and the subsequent registration of complex voltages U or resistances Z of the eddy current transducer as a function of the electrical conductivity of the substrate and the gap value.

The disadvantages of this method are

- additional error caused by loose fit of the eddy current sensor;

- there is no possibility of measuring the electrical conductivity of the coating;

- sensitive to changes in the parameters of the substrate (electrical conductivity and magnetic permeability).

The prototype adopted a method of measuring structure parameters, including irradiation of the structure with microwave radiation using a waveguide system. measuring the frequency dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure in the selected frequency range. Further, according to the obtained dependences, the conductivity or thickness of the metal film is determined (see patent for the invention of the Russian Federation No. 2326368, IPC G01N 22/00, G01B 15/02).

This method has the following disadvantages:

- not suitable for simultaneous measurement of two parameters: electrical conductivity and layer thickness;

- not suitable for measuring the thickness of semiconductor coatings.

The task of the invention is to enable the simultaneous determination of electrical conductivity σ and thickness d of the semiconductor layer.

The technical result of the invention is the expansion of functionality: simultaneous determination of electrical conductivity σ and layer thickness d of the semiconductor layer.

The problem is solved in that in the method for determining the parameters of the semiconductor layer, which consists in irradiating the structure with microwave radiation, measuring the frequency dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured layer in the selected frequency range at the first temperature value, according to the solution, for the first value temperatures find pairs of values of the interdependent parameters of the semiconductor layer (d, σ) at which the theoretical frequency dependence of the coefficient of the electromagnetic radiation reflection is closest to the measured one, then the temperature of the semiconductor layer is changed, the frequency dependence of the reflection coefficient of electromagnetic radiation is measured at the second temperature value and, using the known temperature dependences, pairs of parameter values (d , σ) for the second temperature value, after which the desired pair of parameter values (d, σ) is determined at which the theoretical frequency dependence of the coefficient the reflection coefficient of electromagnetic radiation is closest to that measured at the second temperature value.

The invention is illustrated by drawings:

Figure 1 - diagram of the installation for measuring the frequency dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure of the dielectric-semiconductor;

Figure 2 - dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure of the dielectric-semiconductor at a temperature of 294 K;

Figure 3 - dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure of the dielectric-semiconductor at a temperature of 314 K.

The positions in the drawings indicate:

1 - oscillating frequency generator,

2 - coaxial waveguide transducer,

3 - waveguide,

4 - valve

5 - dielectric layer in the composition of the investigated structure,

6 - semiconductor layer in the composition of the investigated structure,

7 - matched load.

8 - directional couplers,

9 - detectors,

10 - indicator of the coefficient of the standing wave voltage and attenuation

11 - analog-to-digital Converter

12 is a computer.

A - the measured dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure of the dielectric-semiconductor at a temperature of 294 K;

B is the calculated dependence of the reflection coefficient of electromagnetic radiation of the microwave range on the measured dielectric-semiconductor structure at a temperature of 294 K;

C is the measured dependence of the reflection coefficient of electromagnetic radiation of the microwave range on the measured structure of the dielectric-semiconductor at a temperature of 314 K;

D is the calculated dependence of the reflection coefficient of electromagnetic radiation of the microwave range on the measured dielectric-semiconductor structure at a temperature of 314 K.

The measured structure is placed in the waveguide, completely filling its cross section. Next, using the oscillating frequency generator, the measured structure is irradiated with microwave radiation, and using the VSWR indicator and attenuation, the frequency dependence of the microwave reflection coefficient on the measured structure is measured at the first temperature value.

Adding a dielectric with known parameters to the structure makes it possible to realize a minimum in the frequency dependence of the reflection coefficient and thereby increase the sensitivity of the measurement method.

Next, we determine the pairs of values of the interdependent parameters of the semiconductor layer (d, σ) at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to the measured one.

To do this, build the functional:

,

решаем систему из двух уравнений.and set the partial derivatives to zero

,

we solve a system of two equations.

We compile a table of pairs of values of the parameters of the semiconductor layer (d, σ) at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to the measured one.

Then change the temperature of the semiconductor layer, temperature control is carried out using a thermocouple. Then again measure the frequency dependence of the reflection coefficient of electromagnetic radiation at a second temperature value.

Then, using the known temperature dependences and the values of the parameters (d, σ) for the first temperature value, pairs of parameter values (d, σ) for the second temperature value are calculated.

When the temperature changes, the conductivity of the semiconductor material changes according to the well-known law:

,

,

; a, b - аппроксимационные константы, которые меняют свои значения в зависимости от используемого температурного диапазона: при очень низких температурах можно учитывать только рассеяние на атомах примеси и дислокациях (подвижность растет пропорционально Т^3/2). С повышением температуры роль этих механизмов уменьшается по сравнению с рассеянием на ионах примеси. При высоких температурах доминирующим становится рассеяние на фононах (подвижность растет пропорционально Т^-3/2).where ΔW is the activation energy of the impurity in the region of impurity conductivity or the band gap in the region of intrinsic conductivity; k is the Boltzmann constant,

; a , b are approximation constants that change their values depending on the temperature range used: at very low temperatures, only scattering by impurity atoms and dislocations can be taken into account (mobility increases proportionally to T ^3/2 ). With increasing temperature, the role of these mechanisms decreases compared to scattering by impurity ions. At high temperatures, phonon scattering becomes dominant (mobility increases in proportion to T ^-3/2 ).

The thickness of the sample varies according to the law of linear expansion:

Δd = α · ΔT · d ₀ ,

where Δd is the absolute change in thickness, α is the coefficient of linear expansion, ΔT is the change in temperature, d ₀ is the initial thickness.

A new table of pairs of parameter values (d, σ) is compiled for the second temperature.

Then determine the desired pair of parameter values (d, σ), at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to that measured at the second temperature value.

The determination was made by the minimum value of the residual function:

If it was necessary to determine the parameters (d, σ) of the semiconductor layer for the first temperature, recalculate these parameters according to the given temperature relationships.

Example

Antimony doped silicon was used as the test sample, and fluoroplastic was chosen as the dielectric. The temperature was recorded using a thermocouple.

Curve A represents the frequency dependence of the reflection coefficient of electromagnetic radiation from the measured structure, measured at a temperature of 294 K.

For the first temperature value, pairs of values of the interdependent parameters of the semiconductor layer (d, σ) are found at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to the measured one. The values are presented in table 1.

Table 1 No. d _Si , μm σ, Ohm ^-1 · cm ^-1 one 357 1,095 2 358 1,092 3 359 1,090 four 360 1,087 5 361 1,084 6 362 1,081 7 363 1,078

Curve B represents the frequency dependence of the reflection coefficient of electromagnetic radiation from the measured structure, calculated for the parameters of the semiconductor layer shown in Table 1.

Then, the temperature of the semiconductor layer was changed to a value of 314 K, and the frequency dependence of the reflection coefficient of electromagnetic radiation was measured at a second temperature value.

Curve C represents the frequency dependence of the reflection coefficient of electromagnetic radiation from the measured structure, measured at a temperature of 314 K.

Further, using the known temperature dependences, from the values of the parameters (d, σ) for the first temperature value from Table 1, we calculated pairs of parameter values (d, σ) for the second temperature value.

When the temperature changes, the conductivity of the semiconductor material changes according to the well-known law:

; a, b - аппроксимационные константы. В окрестностях комнатной температуры в полупроводниках преобладает рассеяние на фононах, а концентрация носителей заряда остается неизменной, поэтому было использовано следующее соотношение:where ΔW is the activation energy of the impurity in the region of impurity conductivity or the band gap in the region of intrinsic conductivity; k is the Boltzmann constant,

; a , b are approximation constants. In the vicinity of room temperature, scattering by phonons predominates in semiconductors, and the concentration of charge carriers remains unchanged; therefore, the following relation was used:

.

.

The thickness of the sample varies according to the law:

Δd = α · ΔT · d ₀ ,

where Δd is the absolute change in thickness, α is the coefficient of linear expansion, ΔT is the change in temperature, d ₀ is the initial thickness.

For fluoroplastic, α≈10 ^-5 K ^-1 , for silicon α≈2.33 · 10 ^-6 K ^-1 . At the initial silicon layer thickness of 360 μm, the absolute change in thickness with a temperature change of 20 K is 16 nm, and the absolute change in the thickness of the fluoroplastic layer with its initial thickness of 2 cm is 4 μm. In the framework of the problem to be solved, such small changes in the layer thicknesses can be neglected.

Table 2 presents the pairs of values of the parameters of the semiconductor layer for a temperature of 314 K, corresponding to the pairs of values presented in table 1.

After that, we determined the desired pair of parameter values (d, σ) at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to that measured at the second temperature value.

table 2 No. d, μm σ, Ohm ^-1 · cm ^-1 one 357 0,992 2 358 0,990 one 359 0.987 four 360 0.985 5 361 0.982 6 362 0.979 7 363 0.977

Curve D represents the frequency dependence calculated for the parameters of the semiconductor layer at which the theoretical frequency dependence of the reflection coefficient of electromagnetic radiation is closest to that measured at the second temperature value.

Thus, as a result of solving the inverse problem by the least squares method, the following values of the sought parameters were found: the semiconductor layer thickness (d _pp ) was 0.36 mm, and the electrical conductivity σ = 1.087 Ohm ^-1 cm ^-1 , which corresponds to independent thickness measurements method, and the result of solving the one-parameter problem of finding electrical conductivity at a known thickness.

Claims (1)

The method of determining the parameters of the semiconductor layer in the measured dielectric-semiconductor structure, which consists in irradiating the structure with microwave radiation, measuring the frequency dependence of the reflection coefficient of electromagnetic radiation of the microwave range from the measured structure in the selected frequency range at the first temperature value, characterized in that for the first value temperatures find pairs of values of the interdependent parameters of the semiconductor layer: thickness (d) and electrical conductivity (σ) at which cally frequency dependence of the reflectance of electromagnetic radiation is the closest to the measured, then the temperature change of the semiconductor layer, measured the frequency dependence of the reflection coefficient of the electromagnetic radiation at a second temperature and from the temperature dependence of the electrical conductivity σ (T) = σ _o T ^3/2 where σ _of is the coefficient constant for a given temperature range, and T is the temperature, taking into account that within the framework of the problem to be solved, changes in the thickness of the layers of the dielectric and semiconductor and the temperature change can be neglected, from the values of the parameters (d, σ) for the first temperature value, pairs of parameter values (d, σ) for the second temperature value are calculated, after which the desired pair of parameter values (d, σ) is determined at which the theoretical frequency the reflection coefficient of electromagnetic radiation is closest to that measured at the second temperature value.

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