Optical properties of thin films (n,k values). Determination of optical constants of films on silicon substrates

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Sat. Proceedings Scientific session of SUAI. Part 1. Technical sciences. - St. Petersburg: GUAP, 2013. P.167-170

UDC 535.321: 535.32: 539.238

E.N. Kotlikov (Doctor of Physics and Mathematics, Prof.) Head of the Department of Physics, V.M.Andreev -st. Lecturer at the Department of Physics, Yu.A. Novikova postgraduate student of the Department of Physics.

DETERMINATION OF OPTICAL CONSTANTS OF FILMS ON SILICON SUBSTRATES

Among the fundamental characteristics of matter, one of the main places belongs to optical constants (OC) - the refractive index n and absorption rate k . The refractive and absorption indices of a medium are functions of frequency electromagnetic radiation, and in the case of anisotropic media they also depend on the direction of radiation propagation. The OC of thin films depends both on the method of producing films and on technological conditions, for example, substrate temperature, deposition rate, residual pressure or pressure of the reactive medium in a vacuum chamber, and differ from the optical constants of the original single crystals. Therefore, to design multilayer interference coatings, it is necessary to first study the OK of films of the substances used.

There are a number of methods for studying OK: ellipsometric methods based on measuring the limiting angle of total internal reflection, calorimetric and spectrophotometric methods. The most common are the latest (spectrophotometric) methods, which are based on measuring the spectral values of reflectance coefficients Rλ and/or or transmission Tλ . They are traditional for studying the optical constants of thin films and are well covered in the literature. Spectrophotometric methods make it possible to obtain the dispersion characteristics of the refractive and absorption indices of the film in the entire required infrared (IR) spectral range. Accuracymethod is determined by two factors. Firstly, the error in measuring the transmittance (or reflection) coefficients, i.e. measurement technique. Secondly, the difference in the refractive indices of the film and the substrate. The larger this difference, the greater the amplitude in the transmission (reflection) extrema and, accordingly, the smaller the measurement error.

Currently there is no single universal method determination of optical parameters of real films from spectrophotometric data. In terms of used mathematical methods processing the results of spectra, spectrophotometric methods for searching for OK can be divided into two groups: analytical and numerical. The first group of methods involves searching for convenient analytical expressions for direct calculation optical constants in various special cases. An example of this approach is work. In it, the transmission spectrum is divided, depending on the absorption value, into a transparency region and a regionweak absorption.

The second group of methods is based on various numerical methods. In work [ 3 ] the method of successive approximations is used. The work uses Newton's iterative method; the work uses the method of minimizing the quality function. The works propose to conduct a search based on solving a system of nonlinear equations for energy coefficients reflection and transmission of the film-substrate system at a wavelengthλ . It is usually called ( T, R) method.

One of the most suitable materials for studying films on it is silicon ( Si ). Its transparency range (1-100 microns) exceeds other common materials. Zinc selenide ( ZnSe ) transparent in the range of 0.6-16 microns, germanium ( Ge ) in the range of 1.8-30 microns. Silicon ( Si ) is cheaper than the above materials, easy to process and widely distributed. Its disadvantage is the presence of a number of absorption bands, which are caused by silicon oxide embedded in the matrix.

Spectrophotometric methods for searching for OCs, proposed in a number of works, do not allow effective search for OC films in the presence of strong absorption bands, so we developed our own method, which is outlined below.

Let's consider optical system, consisting of a substrate with a thin film deposited on it, surrounded on both sides by air. Let us express the reflection coefficients ( R ) and transmittance (T ) through the parameters of this system. In this case, we will assume that light (with a wavelengthλ ) falls normally from the film side. Parameters related to the substrate will be denoted with a subscript S, related to film index f.

The geometric thickness of the film will be denoted by d , geometric thickness of the substrate through d s , refractive and absorption indices of the substrate, respectively, through n s, k s . We will also assume that the (relative) magnetic permeabilities of the film and substrate are equal to 1. Since the incidence of light is normal, the reflectance and transmittance are independent of polarization. Let be, . The direction of the beam incident on the optical system under consideration, i.e. the direction from the film to the substrate will be called positive. We will call the opposite direction negative. Reflectance coefficients(R f ) and transmittance (T f ) films for a beam traveling in the positive direction are obtained using known formulas through the characteristic matrix [ 7 ].

, (1)

, (2)

, (3)

The reflection and transmittance coefficients of the substrate-air interface for light traveling in the positive direction are equal

, (4)

Let us take the intensity of light incident on the system as 1 (i.e., we will measure all other intensities in units of intensity of the incident wave). The intensity of light emerging from the film is equal to R f . Assuming that there is no interference of light in the substrate, and assuming the values listed above, we obtain the following expressions:

, (5)

. (6)

Let all the parameters of the optical system be known, except, And , and, also, measured values and. The goal of this problem is to find, And. As stated above, an analytical solution to this problem is impossible. Search OK was carried out in several stages. We know that there is absorption in both the film and the substrate, which can be found:. Therefore, we previously determined the substrate constants using the spectrophotometric method from the transmission () and reflection () spectra.Absorption in the substrate was determined: Then, without absorption, transmission () and reflection () are found according to the formulas:

I (7)

where and are functions that are calculated analytically using formulas (1-6), and are absorption in the film and in the substrate.

From these spectra, the refractive index () and absorption index () of the substrate are found. In Fig. Figure 1 shows the dependence of the measured refractive index and absorption on the wavelength in the silicon substrate. T ok how systematic error depends to a greater extent on the normalization used in the spectrophotometer and reaches 1-2%, and the error in transmittance measurement is 0.1-0.3%, then, dTo eliminate additional errors, transmission in the entire spectrum was first normalized to T+R taken in areas free from absorption ( 1.8 2.5 and 4-6 microns). The absorption in the substrates of the silicon we use for the specified range with a substrate thickness of 400 microns lies at the level of 0.1-0.2%, and it can be neglected. Therefore, in the future, we assumed that the absorption of the substrate in the ranges of 1.8 2.5 and 4-6 µm is equal to zero.

At the next stage, the transmission and absorption spectra in the film-substrate system were determined and the transmission spectra were normalized. The absorption spectrum included both absorption in the film and absorption in the substrate. In Fig. Figure 2 shows the transmission spectrum of the film CaF2 , 8 microns thick on a silicon substrate. It includes absorption in the substrate and film, and is also determined by dispersion relations, i.e. refractive index () and absorption index () in the region of strong bands:. The absorption spectra of fluorides, like those of silicon, are close to zero in the range of 0.4-2.5 µm and 3.5-5 µm. These areas were used for additional spectrum normalizations. At zero absorption in the substrate and film, its transmittance at wavelengths is a multiple of the transmission of the substrate, where is the reflection of one side of the substrate (see formula 6).

The transmittance of the substrate in the range of 2-6 µm varies from 0.535 to 0.538. The normalization of the transmission spectrum was that the minimum transmission in areas free from absorption for half-wave films is taken in this range to be equal to the transmission of the substrate. A similar normalization was done for the reflection spectrum.

Based on the normalized spectra, absorption in the film was found(). The criterion for the correctness of normalization was in absorption-free regions of the spectrum. In Fig. Figure 1 shows the dependence of the absorption coefficient on the wavelength of the film-substrate system. It can be seen that in the range of 1.6 -2.6 µm the average absorption value is low. The increase in noise at wavelengths below 2 μm is associated with noise in the recording part of the spectrophotometer. In the region of 3.5 -7 µm, absorption is also minimal. From the absorption spectrumyou can find the dispersion of the extinction coefficient for all wavelengths: , where is the absorption coefficient of the film, k imaginary part of the complex film absorption index.

Rice. 1. Refractive indices ( ns) and

absorption (ks) of silicon (Si)

Rice. 2. Transmission spectrum

CaF 2 films on a Si substrate

At the next stage, the transmission spectra are corrected for absorption in the film. To do this, the absorption in the transmission (or reflection) spectrum of the film is calculated taking into account the obtained dependence of the absorption coefficient () on the wavelength (). Refractive index dispersion has little effect on the absorption spectrum. The main influence comes from the thickness of the film, which is already taken into account in the transmission and reflection spectra. The absorption spectrum in transmission (reflection) was calculated. The resulting absorption spectrum is added to the transmission (or reflection) spectrum.

In Fig. Figure 3 shows an example of a transmission spectrum corrected for absorption. From Fig. 3 it can be seen that the spectrum represents a sinusoid with slightly varying period and amplitude. Their changes are determined only by the dispersion of the refractive index. Minimum values transmittance in the range of 5000 - 700 cm-1 correspond to substrate transmittance = 0.536-0.538. The distortion of the curve in the region of more than 20 μm is due to the hardware features of the spectrophotometer.

Solving the inverse problem finding dispersion curves from the corrected spectrum for the refractive index becomes a much more correct problem than for the spectrum shown in Fig. 3. In this case, the parameters of the substrate, the absorption of the film (equal to zero), and variable refractive index and film thickness.

Analysis of the spectrum shows that in the region (900-6000) cm-1 The refractive index depends weakly on wavelength. Increase in transmittance to 0.545 at a wavelength of 1400 cm-1 can be explained by the heterogeneity of the film. Its density decreases as the film thickness increases, and the transmittance also decreases from maximum to minimum. Such a gradient film acts as a partially antireflective coating, which leads to a slight increase in transmission at the point corresponding to two half-wave films. In the region of 3 µm (3300 cm-1 ) transmittance is also above average. This indicates that the refractive index of the film increases in the region of a strong absorption band, caused by both water vapor and water absorbed on the surface of the film.

The dispersion of the refractive index was determined from the amplitude of the extrema using the program FilmMgr. In Fig. Figure 4 shows the dependence of the refractive index CaF 2 by wavelength . Its general course corresponds to the dispersion of a single crystal, taking into account the lower refractive index of the film. The difference is observed only in the peak at a wavelength of 3 μm. It is associated with the presence of an absorption band of absorbed water at 3 μm.

A technique for processing spectra on an absorbing substrate is proposed using the example CaF2 . This technique involves a number of corrections:

Transmission and reflection spectra possible errors spectrophotometric measurements;

Correction for absorption in the substrate;

Correction of transmission spectra to eliminate absorption in the film.

The corrections made make it possible to reduce the number of variables and, thereby, reduce errors in determining the dispersion constants of the film.

Bibliography

Havens, O.S. . Measurement of optical constants of thin films for applications / In the book: Physics of thin films. - M.: Mir, 1967. T.2.S. 136185.
Konovalova, O.P. Determination of optical constants of weakly absorbing dielectric layers on a transparent substrate / O.P. Konovalova, I.I. Shaganov // Optical-mechanical industry, 1988. No. 8. P.3941.
Kotlikov, E.N. . The problem of reducing optical losses in fluoride films / E.N. Kotlikov, E.V. Khonineva, V.N. Prokashev. St. Petersburg: Optical Journal, 2004. T.71. P.8487.
Kotlikov, E.N. Study of the optical constants of films used for the synthesis of broadband antireflective coatings / E.N. Kotlikov, G.V. Tereshchenko //Optics and spectroscopy, 1997.-T.82. AT 4. P.653-659.
Kotlikov, E.N. . Film-forming materials for the terahertz spectral range / E.N. Kotlikov, V.A. Ivanov, A.N. Tropin. SPb.: Sat. proceedings of the SUAI scientific session. Part 1., 2010. - pp. 153-155.
Ritter E. Film dielectric materials for optical applications // In the book. Physics thin films M.: Mir, 1978.- T.8. P.7-60.
Born, M. Fundamentals of optics / M. Born, E. Wolf, trans. from English edited by G.P. Motulevich. M.: Nauka, 1970. 856s.

Transparent thin dielectric and semiconductor films exhibit interference phenomena when light falls on them (Fig. 18).

Fig. 18. Schematic ray path through the transparent film-substrate system

Under certain conditions, when combining reflected or transmitted beams, interference will be observed with an increase or decrease in intensity, and the transmission (reflection) spectrum will look like this (Fig. 19).

Fig. 19. Transmission spectrum of the film-substrate system

Without considering the mathematical derivation of the formulas, we note that in the transmission spectrum of the film-substrate system at normal radiation incidence, extreme values are observed under the condition npl ·d=m·/4,

where npl is the refractive index of the film;

d-film thickness;

m - interference order;

 wavelength at the extremum.

The maximum values of the transmittance correspond to even m, the minimum to odd. For two neighboring extrema with even m, we can write:

n pl ·d=m· m /4=(m+2)· m +2 /4,

 m and  m +2 - wavelengths corresponding to neighboring extrema with even m.

From here

If the refractive index of the film is unknown, then it is found from the expression:

where T is the transmittance of the film-substrate system for odd m;n pl - the refractive index of the film;

n p is the refractive index of the substrate;

Having determined m, n p, n pl, determine the film thickness d.

3. Measuring the transmittance of metal films

Unlike dielectrics and semiconductors, in metals a large number of electrons are weakly bound to the metal atoms, and these electrons are considered free. Availability free electrons The features of light reflection from a metal surface are explained. Secondary waves caused by forced oscillations free electrons, generate a strong reflected wave, the intensity of which can reach 95% (or even more) of the incident intensity, and a relatively weak wave going into the metal. Since the density of free electrons is very significant (~ 10 22 in 1 cm 3), even very thin layers of metal reflect most of the light incident on them. That part of the light energy that penetrates into the metal is absorbed by it.

What fraction of light is not transmitted by the metal due to reflection and what is retained in it due to absorption depends on its conductivity. In an ideal conductor, absorption is zero, so the incident light is completely reflected. Silver films approach this ideal. In metals that are less conductive, for example, in iron, reflection can be only 30-40%, so that an opaque film of iron no more than a fraction of a micron thick absorbs about 60% of the light incident on it.

Thus, characteristic feature metal, consisting in its high reflectivity and manifested in the presence of a special “metallic” luster of a clean surface, is associated with its electrical conductivity. The higher the electrical conductivity coefficient, the higher, in general, the reflectivity of metals.

In our laboratory, the reflectivity of metals can be measured using a HeNe laser at a wavelength of 630 nm. Literature data for a similar wavelength give the following relationship between the reflectance of a metal film at a wavelength of 600 nm and resistivity:

But high reflectance values can only be obtained for films obtained under optimal conditions. Factors influencing the reflection coefficient are: deposition speed, pressure during deposition, thickness of the deposited film, substrate temperature, angle of incidence of the substance, degree of purity of the evaporated material and, finally, aging of the resulting coating in air.

The absorption of light by metals can be used to estimate the thickness of a metal film. The passage of light through conductive substances is determined by the relationship:

I=I 0 exp(-4πnkd/),

where d is the thickness of the absorbing layer;

n - refractive index for wavelength;

k is the absorption index for the wavelength;

I 0 - intensity of incident radiation;

I is the intensity of transmitted radiation.

Measuring the transmittance of a translucent metal film (I/I 0) will allow you to estimate its thickness using the above formula.

Table 2.1

Material
Material

Determination of transmittance using the LMF-72M photometer

The LMF-72 type photometer is intended for measuring transmittance and optical density in the spectral range from 365 to 750 nm and determining the concentration of solutions using calibration graphs, as well as as an indicator when carrying out nephelometric and fluorimetric analysis. The optical diagram of the photometer is shown in Fig. 20.

Fig.20. Optical design of the LMF-72M photometer

1-incandescent lamp;

2-condenser;

3-lens;

4-slit diaphragm;

5-modulator;

6-replaceable interference or absorption filter;

7-thermal filter;

8-measured sample;

9-absorption filter; "

10-protective glass;

11-photomultiplier.

The laboratory photometer is made according to a single-beam scheme with modulation of the light flux and direct reading. When measuring transmittance, the luminous flux from an incandescent lamp (1), formed by a condenser consisting of lenses (2) and an objective (3) into a parallel beam, through a continuously adjustable diaphragm slit (4), modulator luminous flux(5), the interference filter (6) passes through the sample being measured and hits the photocathode of the light detector.

Operating procedure

1. Connect the photometer to the network. Warm-up time for the device is 10-15 minutes.

2. Calibrate the T scale. To do this, insert an interference filter with the required wavelength at maximum transmission into the “filter” socket, and the cuvette holder in position “0”. Press the "U" button and, rotating the "0-precise" knob, align the arrow of the indicating device with the "0" mark on the scale. Set the cuvette holder to the “100” position, use the “diaphragm” knob to move the instrument arrow to the “100” mark on the scale, then use the “100-precise” knob to align the arrow with the “100” mark.

3. Transmittance measurement. Set the cuvette holder to position "0". Remove the cover and insert the sample to be measured into the holder. Close the lid, move the cuvette holder to the “100” position and count on the scale measuring instrument(transmittance in percent).

4. Turn off the photometer.

When working on a photometer, it is prohibited:

Change filters in position "100".

Perform measurements with the measuring chamber open.

Study of transmission and absorption spectra in the ultraviolet and visible regions of the spectrum on the device "Specord UV- VIS"

"SpecordUV-VIS" is an automatic dual-beam spectrophotometer that records linear transmittance or extinction of samples as a function of wavenumber. Representation of spectra in terms of wave number is convenient, since according to the relation E=hν=hc/=hc , Where

E-energy;

h is Planck's constant;

c is the speed of light;

ν - frequency;

 - wavelength;

- wave number,

energy is directly proportional to the wave number.

The basic optical diagram of the spectrophotometer "SpecordUV-VIS" is shown in Fig. 21.

A deuterium lamp is used as a light source in the ultraviolet region of the spectrum, and an incandescent lamp in the visible region. The light beam enters the entrance slit of the monochromator, from where the monochromatic beam is directed to the mirror chopper, where it is divided into two streams, forming a measurement channel and a comparison channel. Light falls on the radiation detector, which is an antimony-cesium photomultiplier, either from the sample channel or from the comparison channel. Spectra are recorded using a pen on a special form.

The design of the spectrophotometer provides various registration parameters. Currently the device is equipped with: wave number scale - 12.5mm/1000 cm -1 ; spectrum registration time - 4.4 min/sheet; registration speed is 5000 cm -1 /min.

Fig.21. Optical diagram of the spectrophotometer "SpecordUV-VIS"

The wave number is counted using the vernier. When working, the following ordinate scales are used:

0 – 100% transmittance, standard area;

0 – 20% transmittance, ordinate stretching for samples with low permeability;

0.1 - +1.4 extinction.

Operating procedure for the spectrophotometer "SpecordUVVIS"

1. Plug the device into the mains. Click the "Network" button.

2. Turn on the lamp (light source) for the corresponding part of the spectrum.

3. Insert the recorder pen.

4. Using the “Fast forward” and “Fast back” buttons, set the integer against zero using the vernier (for example, 21000 cm -1). Place the registration sheet on the recorder carriage so that, with the measurement channel closed, the recorder pen is at the intersection of the horizontal zero line and the vertical line.

5. Check the zero position and the correct installation of the registration sheet by conducting a test registration (press the "Start" button).

6. Set the 100% line. Open the measurement channel and carry out a test recording. If the recorded line runs parallel to 100%, then it is output to 100% using the 100% correction knob.

7. Press the "Quick Back" button. The carriage moves quickly to the right, and the recording device takes the leftmost position.

8. Place the sample to be measured in the cuvette compartment in the near channel.

9. Press the "Start" key. A registration started in this way can be interrupted at any point by pressing the "Stop" key.

10. Take out the registration sheet, turn off the lamp, press the "Network" button.

Push-button control on the front panel

Fast forward. The carriage moves quickly to the left, and at the same time the wave number runs.

Quickly back. The carriage moves quickly to the right.

Registration with automatic carriage return.

Start. Start of spectrum recording.

Stop. The recording device stops.

Radiation source.

2.7.2 Reflection in the ultraviolet region of the spectrum

Optical studies of thin doped layers of silicon and other semiconductors would be much easier and more accurate using radiation that is highly absorbed by the semiconductor material. This, for example, is ultraviolet radiation with a wavelength of 0.2 - 0.4 microns, which is almost completely absorbed by silicon layers only 0.05 - 0.1 microns thick. However, changing the concentration of free charge carriers in a semiconductor over a very wide range has virtually no effect on its optical properties in the short-wavelength region of the spectrum. Reflection spectra in the ultraviolet region helped to establish the features of the band structure of semiconductors. Reflection bursts characteristic of many semiconductor materials are explained by a sharp increase in the absorption coefficient, which is caused by interband transitions with a large band gap in those regions depending on , where 0 .

Using ultraviolet reflectance spectra, it is also possible to very finely control the quality of mechanical and chemical polishing of the surface of semiconductor crystals, which is clearly seen from the spectral dependences of the specular reflectance on the depth of defects remaining after polishing on the surface of silicon and gallium arsenide shown in Figures 15 and 16. Only after the depth of the damage as a result of additional polishing becomes less than the wavelength of ultraviolet (0.2 - 0.4 µm) and visible (0.4 - 0.75 µm) radiation used in the measurements (performed on SF-4 spectrophotometers , SF-10, SF-20, SF-26), the reflectance in these regions of the spectrum ceases to change (Figure 16).

The high efficiency of optical monitoring is facilitated by the presence of reflection peaks present in silicon and gallium arsenide in the ultraviolet region of the spectrum. For example, monitoring the state of the silicon surface is best done at a wavelength of 0.28 μm, where the reflectance of well-polished silicon reaches 70%. To increase the difference between the reflectances of plates with different processing surface, it is useful to use a device to observe multiple reflections of ultraviolet radiation from a set of plates with the same surface treatment (Figure 17). In the same device, another set of well-polished wafers makes it possible to isolate ultraviolet radiation with a wavelength of 0.28 microns, which is most useful for monitoring the condition of the silicon surface, from the source spectrum.

Instruments used to monitor the state of the surface, in which the selection of the required spectral interval was carried out using quartz prisms, diffraction gratings, parabolic and rotating mirrors, are more complex in design

1-3 µm; 2 - 1 µm; 3 - 1 µm; 4 - 0.1-0.2 microns;

1, 2, 4 - polishing time 1 hour; 3 - 2 hours

Figure 15. - Spectral dependence of reflectance

silicon surfaces after mechanical polishing with diamond pastes and abrasive powders with different diameters grains:

Figure 16. - Spectral dependence of the reflectance

gallium arsenide after treatment in a polishing etchant

and for remaining surface disturbances at different depths:

1 - 1 µm; 2, 3 - 0.2-0.3; 4 - less than 0.2 microns

1 - hydrogen lamp; 2 - quartz lens; 3 - filter made of silicon wafers treated with -chromium oxide; 4 - flat mirrors; 5 - device body with dividing curtains; 6 - plates under study; 7- photomultiplier tube type FEU-57 or FEU-39 with a quartz input window; 8 - photocurrent recording unit; 9 - modulator; 10 - power supply for a hydrogen lamp

Figure 17. - Diagram of a device for optical monitoring of the depth of defects on the surface of semiconductors

3Calculation of the antireflective coating of a solar cell

3.1 Reflectance coefficient of antireflective coating

Let's now move on to a real photocell. The reflectance of the semiconductor surface is determined by the formula

=
, (94)

Where - refractive index, which for most semiconductors lies in the range of 3 - 4 and does not depend very much on the wavelength. For silicon = 3.5 and from (94) it turns out
= 30%, i.e. = 70%. To enhance it, antireflection is used, i.e. a thin film with a refractive index is applied to the surface and thickness , which are selected in such a way that the light wave reflected from the front surface of the coating is canceled out by interference by the wave reflected from the boundary between the film and the semiconductor material. The reflectance of a film-coated semiconductor can be calculated using the following set of formulas:

=
; (95)

=
, =
, =
, (96)

- refractive index of the medium from which the light falls (for vacuum = 1); - refractive index of the film; - its thickness, and - the wavelength at which enlightenment is carried out. The minimum value of the reflection coefficient, equal to zero, is achieved when
= -1 and = . From the first condition it follows that
=, 3, 5. It is advisable to choose =, since in this case it turns out that the bleaching condition is better satisfied for neighboring wavelengths than at = 3, 5. etc. From the first condition it follows that the film thickness should be equal

=
(97)

The second condition, as can be verified by direct substitution, is satisfied when

=
. (98)

Since (97) is satisfied only at one wavelength, it is clear that for other wavelengths the reflection coefficient will be different from zero. To obtain zero reflection in the wavelength range, multilayer (several tens of layers) antireflection films are used, but due to great technological difficulties in manufacturing, they have not found application in photoenergetic devices.

Typically, a heat-regulating coating is applied to the antireflective film, having a refractive index in the range of 1.5 - 1.4 and a fairly significant thickness. Quartz or glass coatings are often used and bonded to the solar cells. These coatings simultaneously provide radiation protection. When calculating an antireflection film, it would be necessary to consider not a two-layer, but a three-layer optical system, which would lead to formulas that are much more cumbersome than (95). However, since the reflection coefficient at the interface between the vacuum and the heat-regulating coating is relatively small, to simplify calculations one can consider a two-layer system, but assume that the light falls from a medium with a refractive index , equal to the refractive index of the heat-regulating coating. It should be taken into account that the possible composition of antireflection films is limited by various technological and operational requirements. Thus, films must have sufficient mechanical strength, chemical resistance, good adhesion to the photoconverter material, resistance to irradiation with ultraviolet light, resistance to thermal cycling, and must be transparent in the wavelength range etc. In this regard, it is not always possible to select a material with a theoretically optimal value of the refractive index and one has to be content with values close to it. In addition, the refractive index of thin films may differ from the refractive index of the material taken in the form of thick samples. Optimal from the point of view of obtaining maximum efficiency. photocell, the antireflective film should also be selected taking into account the spectral composition of solar radiation and the values of the collection coefficient at different wavelengths.

In one of the first works devoted to the antireflection of silicon photocells, a film ( = 1.44) was used as a coating, which made it possible to increase the photocurrent of the element by 20 - 25%. This film was applied by oxidizing the surface of the photocell in air at elevated temperature. The chemical method for producing antireflective film from is described in. Thick films (5 - 7 microns), obtained by chemical and electrochemical methods, can be used as heat-regulating coatings. The paper discusses the possibility of using multilayer interference filters for clearing and proposes using glass plates glued to photoconverters as a heat-regulating coating. To combine antireflective and heat-regulating properties, films made of (=1.9) and glass plates glued on top were used, acting as a heat-regulating coating. Vacuum spray coatings from
(=1,36),
(=2,0), (= 2,2),
(=2.3). For the most favorable film thickness (= 0.15 µm), the theoretical increase in photocurrent reaches 40 - 45%. Experimental results show an increase in photocurrent up to 27%. The patent proposes an interference filter applied to glass in which layers alternate,
(=2.3) and
(=1.9) and which allows you to reflect radiation with wavelengths shorter than =0.4 µm and larger =1.1 µm.

In the laboratory, to study the optical properties of transparent films, a Specord UV-VIS spectrophotometer is used, designed to work in the ultraviolet and visible regions of the spectrum, and an LMF-72M photometer. Let's consider specific tasks, which can be solved using photometric instruments.

1. Determination of the refractive index of a transparent substrate

The refractive index is one of the main optical characteristics. It determines the speed of propagation of a light wave in a substance. Knowledge of it is necessary for materials used in optics.

When radiation of intensity I 0 is incident on a transparent substrate, one part of the beam is reflected (IR), the other passes through it (IT) (Fig. 17). Without taking into account the absorption of radiation inside the substrate, we note that the proportion of transmitted and reflected radiation depends on the refractive index:

Rice. 17. Schematic ray path when light falls on a transparent substrate

The transmittance (T) and reflectance of the substrate (R) at wavelength l can be calculated as follows:

Where

n n is the refractive index of the substrate at wavelength l.

Thus, by measuring the transmittance at the desired wavelength, the refractive index of the substrate can be obtained from this expression. The incidence of light on the substrate should be close to normal.

2. Determination of thickness transparent film on a transparent backing

Transparent thin dielectric and semiconductor films exhibit interference phenomena when light falls on them (Fig. 18).

Fig. 18. Schematic ray path through the transparent film-substrate system

Fig. 19. Transmission spectrum of the film-substrate system

where npl is the refractive index of the film;

d-film thickness;

m - interference order;

l wavelength at the extremum.

The maximum values of the transmittance correspond to even m, the minimum to odd. For two neighboring extrema with even m, we can write:

n pl d = m l m /4=(m+2) l m+2 /4,

l m and l m+2 are wavelengths corresponding to neighboring extrema with even m.

From here

If the refractive index of the film is unknown, then it is found from the expression:

where T is the transmittance of the film-substrate system for odd m; npl is the refractive index of the film;

n p is the refractive index of the substrate;

Having determined m, n p, n pl, determine the film thickness d.

3. Measuring the transmittance of metal films

Unlike dielectrics and semiconductors, in metals a large number of electrons are weakly bound to the metal atoms, and these electrons are considered free. The presence of free electrons explains the peculiarities of light reflection from a metal surface. Secondary waves caused by forced vibrations of free electrons generate a strong reflected wave, the intensity of which can reach 95% (or even more) of the incident intensity, and a relatively weak wave traveling into the metal. Since the density of free electrons is very significant (~ 10 22 in 1 cm 3), even very thin layers of metal reflect most of the light incident on them. That part of the light energy that penetrates into the metal is absorbed by it.

Thus, the characteristic feature of a metal, consisting in its high reflectivity and manifested in the presence of a special “metallic” luster of a clean surface, is associated with its electrical conductivity. How higher coefficient electrical conductivity, the higher, in general, the reflectivity of metals.

But high reflectance values can only be obtained for films obtained in optimal conditions. Factors influencing the reflection coefficient are: deposition speed, pressure during deposition, thickness of the deposited film, substrate temperature, angle of incidence of the substance, degree of purity of the evaporated material and, finally, aging of the resulting coating in air.

The absorption of light by metals can be used to estimate the thickness of a metal film. The passage of light through conductive substances is determined by the relationship:

I=I 0 exp(-4πnkd/l),

where d is the thickness of the absorbing layer;

n is the refractive index for wavelength l;

k is the absorption index for wavelength l;

I 0 - intensity of incident radiation;

I is the intensity of transmitted radiation.

Measuring the transmittance of a translucent metal film (I/I 0) will allow you to estimate its thickness using the above formula.

Table 2.1

Determination of transmittance using the LMF-72M photometer

Fig.20. Optical design of the LMF-72M photometer

1-incandescent lamp;

2-condenser;

3-lens;

4-slit diaphragm;

5-modulator;

6-replaceable interference or absorption filter;

7-thermal filter;

8-measured sample;

9-absorption filter; "

10-protective glass;

11-photomultiplier.

The laboratory photometer is made according to a single-beam scheme with modulation of the light flux and direct reading. When measuring transmittance, the luminous flux from an incandescent lamp (1), formed by a condenser consisting of lenses (2) and an objective lens (3) into a parallel beam, through a continuously adjustable diaphragm slit (4), a luminous flux modulator (5), and an interference filter (6) passes through the sample being measured and hits the photocathode of the light detector.

Operating procedure

1. Connect the photometer to the network. Warm-up time for the device is 10-15 minutes.

3. Transmittance measurement. Set the cuvette holder to position "0". Remove the cover and insert the sample to be measured into the holder. Close the lid, move the cuvette holder to position “100” and read on the scale of the measuring device (transmittance in percent).

4. Turn off the photometer.

When working on a photometer, it is prohibited:

Change filters in position "100".

Perform measurements with the measuring chamber open.

Study of transmission and absorption spectra in the ultraviolet and visible regions of the spectrum using the Specord UV-VIS device

"Specord UV-VIS" is an automatic dual-beam spectrophotometer that records linear transmittance or extinction of samples as a function of wavenumber. Representation of spectra in terms of wave number is convenient, since according to the relation E = hν = hc/l = hc, where

E-energy;

h - Planck's constant;

c is the speed of light;

ν - frequency;

l - wavelength;

Wave number,

energy is directly proportional to the wave number.

The basic optical diagram of the Specord UV-VIS spectrophotometer is shown in Fig. 21.

Fig.21. Optical diagram of the spectrophotometer "Specord UV-VIS"

The wave number is counted using the vernier. When working, the following ordinate scales are used:

0 – 100% transmittance, standard area;

0 – 20% transmittance, ordinate stretching for samples with low permeability;

0.1 - +1.4 extinction.

Operating procedure for the spectrophotometer "Specord UV VIS"

1. Plug the device into the mains. Click the "Network" button.

2. Turn on the lamp (light source) for the corresponding part of the spectrum.

3. Insert the recorder pen.

5. Check the zero position and the correct installation of the registration sheet by conducting a test registration (press the "Start" button).

6. Set the 100% line. Open the measurement channel and carry out a test recording. If the recorded line runs parallel to 100%, then it is output to 100% using the 100% correction knob.

7. Press the "Quick Back" button. The carriage moves quickly to the right, and the recording device takes the leftmost position.

8. Place the sample to be measured in the cuvette compartment in the near channel.

9. Press the "Start" key. A registration started in this way can be interrupted at any point by pressing the "Stop" key.

10. Take out the registration sheet, turn off the lamp, press the "Network" button.

Push-button control on the front panel

Fast forward. The carriage moves quickly to the left, and at the same time the wave number runs.

Quickly back. The carriage moves quickly to the right.

Registration with automatic carriage return.

Start. Start of spectrum recording.

Stop. The recording device stops.

Radiation source.

Optical properties thin films (n,k values)

The refractive index is one of the main optical characteristics. It determines the speed of propagation of a light wave in a substance. Knowledge of it is necessary for materials used in optics.

Thus, the characteristic feature of a metal, consisting in its high reflectivity and manifested in the presence of a special “metallic” luster of a clean surface, is associated with its electrical conductivity. The higher the electrical conductivity coefficient, the higher, in general, the reflectivity of metals.

The experimentally obtained table of metal reflectivity was measured using a helium-neon laser at a wavelength of 600 nm: