RU2377543C1 - Method of determining optical absorption losses in thin films - Google Patents

Abstract

FIELD: physics; optics.

SUBSTANCE: invention relates to measuring techniques. The method is characterised by that, a laser resonator radiation beam is directed onto an inclined face of a plane-parallel plate placed in the resonator at an angle θ₀ from the base. A test thin film is placed on one of the surfaces of the said plate in form of a wedge with vertex angle β, minimum thickness d and maximum thickness 3d. The plate is moved perpendicular the axis of the laser resonator and energy or power of the radiation coming out of the laser resonator is measured at different thicknesses of the wedge of the film at the point of reflection, and absorption of optical radiation by the film is determined from the maximum difference in the measured values.

EFFECT: more accurate determination of absorption losses in thin films.

3 dwg

Description

The invention relates to optical instrumentation and can be used to determine the parameters of various coatings used for the manufacture of optical elements and devices, including reflective, antireflective, beam-splitting and others.

A known method of measuring the reflection coefficient, which measure the light flux reflected from the surface of the test sample and the reference sample, which is a beam splitter plate (SU 135256 [1]). The disadvantage of this method is the need for independent determination of the transmittance of the beam splitter plate.

There is a method by which successive measurements of light fluxes reflected from the test sample and the reference sample made of non-absorbing and non-scattering material are made (SU 1402864 [2]). The disadvantage of this method is the low expressivity caused by the need to determine the transmission of the reference sample, which requires a change in the geometry of the measuring circuit and an additional number of measurements. This also reduces accuracy.

Closest to the technical nature of the proposed is a method known from RU 2033603 [3]. The method is as follows. Set the plate from the test substance into the light flux with intensity I _o and measure the signal I _Rx corresponding to the intensity of the flux reflected from the sample. In this case, the desired reflection coefficient

Then, a comparison sample is installed in the light beam reflected from the test sample, and a signal I _Te corresponding to the intensity of the light transmitted through the comparison sample is measured. To pass the sample comparison receive

After that, the test sample is removed, instead, a reference sample is installed in the same position and the signal l _Re corresponding to the intensity of light reflected from the reference sample is measured. For the reflection coefficient of the comparison sample get

For non-absorbing and non-scattering material of the reference sample, the relation

From equations (2) - (4), equation (1) is obtained for the desired reflection coefficient.

The disadvantage is the low accuracy and the impossibility of measuring optical absorption losses in thin films.

The inventive method is aimed at simplifying and improving the accuracy of measuring small optical absorption losses in thin films.

This result is achieved by the fact that the method for determining optical absorption losses in thin films is characterized by directing the laser radiation beam onto the inclined end of the plane-parallel plate installed in it with an angle at the base θ _o , on the part of one of the planes of which the test thin film is applied in in the form of a wedge with an angle at its apex β, minimum thickness d and maximum 3d, move the plate in the direction perpendicular to the axis of the laser resonator and measure the energy or power the radiation output from the laser resonator, when the beam is reflected from the film-free plane of the plate, and then from the part covered by the film, for different thicknesses of the film wedge at the reflection point and the maximum difference in the measured values judges the absorption of optical radiation by the film, while θ _about , d, and β are determined from the conditions:

θ _о + arcsin ((cos θ _o ) / n ₁ ) ≥arcsin (1 / n ₁ ),

Where

n ₁ is the refractive index of the plate;

n ₂ is the refractive index of the test film;

λ is the laser wavelength, m;

θ _{about the} angle between the plane of the plane-parallel plate and its inclined end, rad;

θ is the angle of incidence of radiation on the film, rad;

a is the diameter of the laser beam, m;

β is the angle at the top of the wedge of the test film, rad;

d is the thickness of the test film, m

The proposed solution, which consists in the direction of the laser radiation beam to the inclined end of the plane-parallel plate installed in it with an angle at the base θ _о , on the part of one of the planes of which the test thin film is deposited in the form of a wedge with an angle β at its apex, the minimum thickness d and the maximum 3d and moving the plate in the direction perpendicular to the axis of the laser resonator, it is possible to achieve the following goals: to simplify the process of measuring the small absorption of thin films and to increase the accuracy of such a measurement Niya.

Simplification of the measurement process is achieved due to the fact that the measurement process uses a simple, easily fabricated optical element (plane-parallel plate), onto which, using practically any of the known methods of film deposition (thermal, electron beam, etc.), investigated wedge-shaped film. In the measurement process, in addition to the named element, no other auxiliary elements (standards, plates, mirrors, etc.) are used and, therefore, do not perform additional measurements on these elements. The use of a laser resonator makes it possible to simplify the design of a device for measuring absorption in thin films. When measuring small absorption in the film, the level of the signal emerging from the laser cavity after multiple reflections from the film remains high due to the high brightness of the radiation and the high quality factor of the resonator. This means that measurement does not require complex signal amplification and detection systems. Since the divergence of laser radiation is small, there is no need for complex collecting and focusing optics.

Improving the accuracy of measuring the small absorption of thin films in the method is achieved due to the fact that the measured film is placed in the laser cavity, it is deposited on the face of the total internal reflection of the plate, and the absorption maximum in the film is reached. The use of a laser resonator with an active element equipped with means for pumping and controlling it, means for measuring the energy or power of laser radiation can significantly improve the accuracy of measuring optical absorption losses in thin films. This is explained by the fact that the measured film is placed in the laser resonator in the path of the beam and, due to this, when the resonator is tuned into resonance, the beam will repeatedly reflect and pass through the film (due to the phenomenon of impaired total internal reflection), and this provides a multiple increase in the total path by which radiation is absorbed by the film and, consequently, an increase in the total absorption of radiation by the film. Therefore, by measuring the energy or power of the laser radiation, large relative changes in energy or power will be recorded during measurements, which will increase the accuracy of their measurement, and as a result (see the formula for calculating the absorption of the film below), increase the accuracy of measuring low absorption of the film. In addition, during measurements, the high quality factor of the laser resonator is maintained, since the film is deposited on a part of the face of the total internal reflection of the plate, and, therefore, when a ray hits a portion of this face without a deposited film, no losses are introduced into the resonator during measurements (actually at this moment measurement of losses from the reference is performed). When the plate is moved in the direction perpendicular to the axis of the laser cavity, the laser beam moves along the face of the total internal reflection of the plate and enters a thin film. The film introduces into the laser cavity two types of losses: small absorption losses in the film (fundamental for the film material, defects in it, etc.) and losses caused by the violation of the total internal reflection by the film. Based on the laws describing the reflection and refraction of light (see M. Born, E. Wolf. "Fundamentals of Optics", M., 1970) it is easy to establish that the phenomenon of total internal reflection for the face of the base used in the method of the plate will be observed if the angle between its base and the inclined end face θ ₀ will satisfy the condition:

Where

n ₁ is the refractive index of the plate. The plane-parallel plate used in the proposed method is made with an angle between the base of the plate and its inclined end face θ ₀ satisfying condition (5). The application of a thin film with a refractive index of n ₂ (n ₁ ≠ n ₂ ) violates the total internal reflection at the "plate - film" boundary. In this case, the energy reflection, transmission, and absorption coefficients R, T, and A can be calculated from the following relationships (see M. Born, E. Wolf. "Fundamentals of Optics", M., 1970):

Where

r _{i + 1} and t _{i + 1} - Fresnel coefficients at the interfaces between the media with refractive indices n _i and n _{i + 1} ;

n _i is the refractive index of the material of the medium or film;

d _i is the film thickness;

θ _i is the angle of incidence or refraction on / in the film;

for i = 2

n ₂ is the refractive index of the film.

-ik₂, и k₂ - искомый показатель поглощения материала пленки, может быть вычислен из (6) - (13).Since the film absorbs, then n ₂ =

-ik ₂ , and k ₂ is the desired absorption coefficient of the film material, can be calculated from (6) - (13).

The system of equations (6) - (13) allows us to determine the absorption characteristics of the film from a number of measured values of R or T, or A. So they can be used to determine the absorption of the film of a given thickness or the absorption rate of the film material. But the exact solutions for this system in general are extremely difficult to find. As a rule, the curves of the dependences of absorption losses on the film thickness are preliminarily plotted for a certain range of absorption coefficient values. Then, by comparing the measured and calculated values of the absorption loss using numerical methods, the absorption characteristics are determined: either the absorption of the film of a given thickness, or the absorption coefficient of the film material. An example of the dependence of absorption losses on the film thickness for an absorbing TiO ₂ film (n ₂ = 2,3) and a glass plate (n ₁ = 1,5), for helium radiation - a neon gas laser (λ = 0.632 μm) and the angle of incidence of radiation on the film θ≈50 ° is shown in figure 2.

It is seen that these dependences are characterized by the presence of maxima of the total absorption (A _a ) of the film for a number of film thicknesses. From theory (see M. Born, E. Wolf. "Fundamentals of Optics", M., 1970) it is known that the presence of such maxima, their position and magnitude are explained by the interference of the rays repeatedly reflected and refracted from the film boundaries into which the incident radiation film, provided that the output boundary of the film is a surface of total internal reflection. It is clear that the maximum accuracy in determining the absorption loss in the film will be observed for the greatest of the extrema of the dependence of absorption loss for a given interval of film thicknesses, since in this case the largest relative changes in the measured energy or radiation power coming out of the resonator will be recorded. In the proposed method, the extremum, depending on the absorption loss on the film thickness for film thicknesses not exceeding λ, can be detected when scanning a wedge-shaped film from one end of the wedge (film thickness is d) to the other (film thickness is 3d).

The minimum (d) and maximum (3d) film thickness were selected based on the numerical analysis of equations (6) - (13). It was found that for small film thicknesses (d <λ) and small film absorption levels (k <10 ^-5 ), the absorption maximum lies in the thickness range determined by the condition 0.25≥δ _i ≤0.75 (see 13). From this condition, the minimum film wedge thickness d is determined as follows:

. Численное моделирование уравнений (6)-(13) показывает, что это требование обеспечивает достижение незначительного влияния набега фазы на диаметре луча лазера при наклонном его падении на пленку на точность измерения малых поглощений пленки предлагаемым способом.The choice of angle β is due to the need to limit the maximum phase incursion on the diameter of the laser beam when it is inclined to fall onto the film by a value equal to

. A numerical simulation of equations (6) - (13) shows that this requirement ensures the insignificant effect of phase incursion on the diameter of the laser beam when it is inclined to fall onto the film on the accuracy of measuring the small absorption of the film by the proposed method.

The essence of the proposed method is illustrated by examples of its implementation and drawings. Figure 1 presents a schematic diagram of a device with which the measurement process is carried out; figure 2 an example of the dependence of the absorption loss on the film thickness for an absorbing film TiO ₂ ; figure 3 an example of the dependence of the pump power on the absorption loss in the film.

The device with which the method is carried out includes a laser resonator with an active element 1, a dull mirror 2 and a translucent mirror 3. The laser contains means for pumping and controlling it (not shown in the drawing because of their popularity). The device is equipped with means for measuring the energy or power of laser radiation, which can be selected from among the known (not shown in the drawing). A plane-parallel plate 4 with an angle at the base of θ _{0 is} installed in the resonator with the possibility of its movement perpendicular to the beam of radiation incident on its inclined end face. A test thin film 5 is applied on a part of the surface of a plane-parallel plate in the form of a wedge with an angle β at its peak with a minimum thickness d and a maximum 3d.

The method is as follows.

First option. They turn on the pumping means of the active element 1 and, using the controls, achieve stable generation of radiation through a translucent mirror 3. After that, using known means, for example IMO-2H (Russia) or OPHIR-32 (USA), measure the energy or power of laser radiation. Then, a plane-parallel plate 4 is placed inside the resonator formed by mirrors 2 and 3, on one of the surfaces of which the test film 5 is applied in the form of a wedge. First, the plate 4 is installed so that after the laser beam enters it, it would be reflected from its surface on which the film is applied, but from its part free of the film. Measure the energy or power of the laser radiation and record the measured values.

Then, the plate 4 is displaced perpendicular to the beam of radiation incident on its inclined end (shown in the drawing by arrows) so that the radiation enters the plate at one of the edges of the film deposited on the outside, and the laser radiation power or energy is determined. And thus, the procedure is repeated so that the reflection of the beam inside the plate occurs at points with different film thicknesses at the reflection point and the maximum difference between the measured values of energy or power is recorded. Since a decrease in the energy or power of the laser radiation at the exit from the resonator indicates losses introduced into it, then the magnitude of the maximum difference between the measured power or energy of radiation at the exit of the resonator for surface areas of a plane-parallel plate with a film and without it can be used to judge the value of losses absorption in thin films. For this, the dependences of the absorption losses on the film thickness for a certain range of absorption coefficients are preliminarily constructed using equations (6) - (13). The obtained dependences are normalized for use in the resonator used according to a number of loss standards, measuring the radiation power or energy at the exit from the resonator when a laser beam is incident on a surface portion of a plane-parallel plate without a film. For example, pure plane-parallel glass plates can be used as loss standards. Then, by comparing the measured and previously calculated absorption loss values, the absorption loss values for the film of a given thickness or absorption coefficient of the film material are determined.

The second option. The means for pumping the active element 1 are turned on and, using the controls, they achieve stable generation of radiation through a translucent mirror 3. After that, a plane-parallel plate 4 is placed on the surface of the laser radiation inside the cavity formed by mirrors 2 and 3, on which surface 5 a wedge. First, the plate 4 is installed so that after the laser beam enters it, it would be reflected from its surface on which the film is applied, but from its part free of the film. After that, stable generation is again achieved with the minimum electric power supplied to the pumping means. Then, the plate 4 is displaced perpendicularly with respect to the radiation beam incident on its inclined end (shown in arrows in Fig. 1) so that the radiation falls inside the plate at one of the edges of the film deposited on the outside and determines the minimum electric power supplied to the pumping means necessary for sustainable generation. The difference required for pumping power in the case of reflection from the free surface and from the surface with the applied film is recorded. The procedure is repeated so that the reflection of the beam inside the plate occurs at points with different film thicknesses at the reflection point and the maximum of the difference required for pumping power in case of reflection from the free surface and at one of the points with the deposited film is fixed. Since the amount of losses in the resonator is directly related to the power supplied to the pumping means to ensure stable generation, the change in the supplied energy can also be used to judge the change in the amount of loss, and hence the amount of absorption loss in thin films. In the general case, the absorption coefficient of a film cannot be expressed explicitly in terms of the measured quantities. Therefore, it is necessary to first plot the dependences of the pump power on film losses. An example of such a dependence is shown in Fig. 3. Then, by comparing the measured and calculated values of the pump power, the values of the loss coefficient in the film material are determined using numerical methods.

Claims (1)

A method for determining optical absorption losses in thin films, characterized in that the laser beam is directed to the inclined end of the plane-parallel plate installed in it with an angle at the base θ ₀ , on the part of one of the planes of which the test thin film is applied in the form of a wedge with an angle at its vertex β, the minimum thickness d and the maximum 3d, move the plate in the direction perpendicular to the axis of the laser resonator, and measure the energy or power of the radiation emerging from the laser ezonatora, the reflection beam from the free to the film plane of the plate, and then from the part covered by the film, under different film thickness of the wedge at the reflection point, and the maximum difference in the measured values are judged on the absorption film of the optical radiation, and the magnitude of θ _0, d, and β are determined by the formulas:
θ ₀ + arcsin ((cos θ ₀ ) / n ₁ ) ≥arcsin (1 / n ₁ ),

where n ₁ is the refractive index of the plate;
n ₂ is the refractive index of the test film;
λ is the laser wavelength, m;
θ ₀ is the angle between the plane of the plane-parallel plate and its inclined end, rad;
θ is the angle of incidence of radiation on the film, rad;
a is the diameter of the laser beam, m;
β is the angle at the top of the wedge of the test film, rad;
d is the thickness of the test film, m

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