CN112285063A - Characterization method of infrared optical constant of ultrathin metal film - Google Patents

Characterization method of infrared optical constant of ultrathin metal film Download PDF

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CN112285063A
CN112285063A CN202011012332.3A CN202011012332A CN112285063A CN 112285063 A CN112285063 A CN 112285063A CN 202011012332 A CN202011012332 A CN 202011012332A CN 112285063 A CN112285063 A CN 112285063A
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film
metal film
ultrathin metal
optical constant
infrared
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CN112285063B (en
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杨霄
刘华松
刘丹丹
姜玉刚
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Tianjin Jinhang Institute of Technical Physics
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55Specular reflectivity
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/59Transmissivity
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55Specular reflectivity
    • G01N2021/558Measuring reflectivity and transmission

Abstract

The application provides a characterization method of an infrared optical constant of an ultrathin metal film, which is characterized in that a special characterization sample of the optical constant of the ultrathin metal film is prepared, the spectral characteristics of the sample are increased, and the accurate infrared optical constant of the ultrathin metal film is obtained by utilizing a film optical constant inversion calculation method. The method is suitable for representing the accurate infrared optical constants of the common metal films with the thickness of less than 100nm, such as gold, silver, aluminum, chromium and the like, and provides an important technical support for the design and preparation of the infrared film containing the ultrathin metal film material.

Description

Characterization method of infrared optical constant of ultrathin metal film
Technical Field
The application specifically discloses a characterization method of an infrared optical constant of an ultrathin metal film.
Background
Compared with a dielectric film, the ultrathin metal film has larger refractive index and extinction coefficient, and is widely applied to metal-dielectric composite optical film elements such as a reflection filter, an induction transmission filter, an attenuation sheet and the like in modern film design. In the above film design process, the optical constants between the metal and dielectric layers and the thickness of each layer must be strictly matched. The thickness of the ultrathin metal film is often smaller than the average electron free path of the metal, and the optical constant of the ultrathin metal film has a certain correlation with the thickness of the ultrathin metal film, namely the ultrathin metal films with different thicknesses have different optical constants.
The premise for completing the design of a reliable metal-dielectric film at one time is to obtain the accurate optical constant of the metal film under a certain thickness. However, since the thickness of the ultra-thin metal film is very small (<80nm), when the ultra-thin metal film is applied to an infrared band, the ultra-thin metal film is far smaller than an action wavelength (>2000nm), and infrared transmission and reflection spectrums of the ultra-thin metal film have no obvious characteristics, the infrared optical constants of the ultra-thin metal film cannot be accurately obtained by a conventional method for inverting the infrared transmission and reflection spectrums. In addition, when a single-layer metal film sample prepared for obtaining the optical constants of the metal film sample is placed in the air, the metal film can react with oxygen and water vapor in the air, and the accuracy of the optical constant test result is further influenced.
Disclosure of Invention
In view of the above-mentioned drawbacks and deficiencies of the prior art, the present application is directed to a method for characterizing infrared optical constants of an ultra-thin metal film, which facilitates accurate acquisition of infrared optical constants of the ultra-thin metal film, as compared to the prior art.
A characterization method of infrared optical constants of an ultrathin metal film comprises the following steps:
s1: preparing an ultrathin metal film characterization sample, wherein the sample structure is as follows: Sub/M xH/Air; wherein: sub is a substrate; air is Air; m is an ultrathin metal film layer; h is an infrared transparent dielectric film; x is the optical thickness of the dielectric film;
s2: establishing a Drude dielectric function dispersion model of the ultrathin metal film;
s3: establishing a film interference physical model of an ultrathin metal film characterization sample;
s4: and measuring the reflectivity spectrum and the transmissivity spectrum of the characterization sample of the ultrathin metal film.
S5: and (3) obtaining the thickness and the optical constant of the ultrathin metal film in the ultrathin metal film characterization sample by taking the measured reflectivity spectrum and the measured transmissivity spectrum as targets, based on the film interference physical model, using a film optical constant inversion calculation method and combining with an evaluation function of film optical constant inversion calculation.
According to the technical scheme provided by the embodiment of the application, the evaluation function of the inversion calculation of the optical constants of the thin film is as follows:
Figure BDA0002697900410000021
wherein: MSE is the mean square error of the measured value and the theoretical model calculation value, N is the number of the measured wavelengths, M is the number of variables,
Figure BDA0002697900410000022
and
Figure BDA0002697900410000023
measured values of spectral transmittance and spectral reflectance at i wavelengths respectively,
Figure BDA0002697900410000024
and
Figure BDA0002697900410000025
respectively calculated values of i wavelength spectral transmittance and spectral reflectance,
Figure BDA0002697900410000026
and
Figure BDA0002697900410000027
i wavelength spectral transmittance and spectral reflectance measurement errors, respectively.
According to the technical scheme provided by the embodiment of the application, in step S3, a thin film interference physical model is constructed by using the optical constants of the Sub substrate, the optical constants of the H-layer dielectric film in step S1 and the Drude dielectric function dispersion model of the M-layer ultrathin metal thin film established in step S2.
According to the technology provided by the embodiment of the applicationThe technical scheme is that H is Ge, ZnS or Al2O3、YbF3、MgF2Any one of them.
According to the technical scheme provided by the embodiment of the application, the Sub is any one of Si, Ge, ZnS and ZnSe.
In summary, the present application provides a characterization method for infrared optical constants of an ultrathin metal film, aiming at the problem that the optical constants of the ultrathin metal film in the infrared band are not accurately tested, which comprises the steps of preparing a special characterization sample of the optical constants of the ultrathin metal film, increasing the spectral characteristics of the sample, and obtaining the accurate infrared optical constants of the ultrathin metal film by using a film optical constant inversion calculation method. The method is suitable for representing the accurate infrared optical constants of the common metal films with the thickness of less than 100nm, such as gold, silver, aluminum, chromium and the like, and provides an important technical support for the design and preparation of the infrared film containing the ultrathin metal film material.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 is a schematic diagram of infrared optical constants of a Si substrate;
FIG. 2 is a schematic diagram of infrared optical constants of a Ge film;
FIG. 3 is a schematic diagram of an inversion result of an infrared transmittance spectrum of an ultrathin Al film sample to be characterized;
FIG. 4 is a schematic diagram of an inversion result of an infrared reflectance spectrum of an ultrathin Al film sample to be characterized;
fig. 5 is a graph showing the result of optical constant characterization of the ultra-thin Al film.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Specific application examples are as follows: and (3) characterizing the infrared optical constant of the ultrathin Al film.
A characterization method of infrared optical constants of an ultrathin metal film comprises the following steps:
s1: preparing an ultrathin metal film characterization sample, wherein the sample structure is as follows: Sub/M2H/Air.
In this example:
sub is a Si substrate, the optical constants of which are shown in fig. 1.
M is the ultra-thin Al film to be characterized.
H is an infrared transparent Ge film with optical constants shown in FIG. 2 and an optical thickness of 2
Figure BDA0002697900410000033
Center wavelength λ0=4300nm。
S2: and establishing a Drude dielectric function dispersion model of the ultrathin Al film.
S3: and establishing a film interference physical model of the ultra-thin metal film characterization sample.
Wherein:
the Sub optical constant and the thickness and optical constant of the H layer are known, and the thickness and optical constant of the M layer are unknown.
In step S3, a film interference physical model is constructed by using the optical constant of the Sub substrate in step S1, the optical constant of the H-layer dielectric film and the Drude dielectric function dispersion model of the M-layer ultrathin metal film established in step S2, and an expression of the transmittance and reflectance of the ultrathin metal film characterization sample is obtained.
The film characteristic matrix of the ultrathin metal film characterization sample is as follows:
Figure BDA0002697900410000031
wherein the content of the first and second substances,
Figure BDA0002697900410000032
is the phase thickness of the M layers, nM、kMThe refractive index and the extinction coefficient of the M-layer film are respectively, and the expression can be obtained based on a Drude dispersion model.
Figure BDA0002697900410000041
Is the phase thickness of the H layer, nH、kHThe refractive index and extinction coefficient of the H-layer film are respectively.
dM、dHThe physical thicknesses of the M-layer film and the H-layer film, respectively.
θM、θHThe incident angles of the light rays in the M-layer film and the H-layer film, respectively (in this example, the test is performed under the condition of vertical incidence, and the values are both 0).
λ is the wavelength of the incident light, η in the case of normal incidenceM=nM-ikM、ηH=nH-ikH、ηsub=nsub-iksub
The expression of B and C can be calculated from the matrix and substituted into the following formula to obtain the single-side transmittance T of the coated surface of the sample1And single-sided reflectance R1
Figure BDA0002697900410000042
Figure BDA0002697900410000043
According to the Fresnel formula, from the optical parameter n of the substratesub、ksubThe single-sided transmittance T of the uncoated surface (substrate surface) of the sample can be obtained2And single-sided reflectance R2. Using the following formula, a sample was obtainedDouble-sided transmission T and R:
Figure BDA0002697900410000044
Figure BDA0002697900410000045
s4: and measuring the reflectivity spectrum and the transmissivity spectrum of the characterization sample of the ultrathin metal film. Specifically, the transmittance and reflectance spectra of the ultra-thin Al thin film characterization samples were measured using a brook infrared fourier analysis spectrometer.
S5: the measured reflectivity spectrum and the measured transmissivity spectrum are taken as targets, based on a film interference physical model, a film optical constant inversion calculation method is used, and the thickness d of the ultrathin metal film in the ultrathin metal film characterization sample is obtained by combining an evaluation function of the film optical constant inversion calculationMAnd an optical constant nM、kM
Specifically, those of J.A.Woollam, USA are used
Figure BDA0002697900410000046
And (3) performing inversion calculation on the optical constant of the film by software, wherein the effect after spectrum inversion is shown in fig. 3 and 4, the MSE value is 1.964, the accurate parameters in the Drude model of the ultra-thin Al film characterization sample are obtained, the thickness of the ultra-thin Al film is 40.318nm, and the optical constant is shown in fig. 5.
The method in the embodiment is suitable for representing the accurate infrared optical constants of the common metal films with the thickness of less than 100nm, such as gold, silver, aluminum, chromium and the like, and provides an important technical support for the design and preparation of the infrared film containing the ultrathin metal film material.
In any preferred embodiment, the evaluation function of the numerical inversion calculation of the optical constants of the thin film is as follows:
Figure BDA0002697900410000051
wherein:
MSE is the mean square error of the measured value and the theoretical model calculation value, N is the number of the measured wavelengths, M is the number of variables,
Figure BDA0002697900410000052
and
Figure BDA0002697900410000053
measured values of spectral transmittance and spectral reflectance at i wavelengths respectively,
Figure BDA0002697900410000054
and
Figure BDA0002697900410000055
respectively calculated values of i wavelength spectral transmittance and spectral reflectance,
Figure BDA0002697900410000056
and
Figure BDA0002697900410000057
i wavelength spectral transmittance and spectral reflectance measurement errors, respectively.
Optionally, the H is Ge, ZnS, Al2O3、YbF3、MgF2Any one of them.
Optionally, the Sub is any one of Si, Ge, ZnS, and ZnSe.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.

Claims (5)

1. A characterization method of an infrared optical constant of an ultrathin metal film is characterized by comprising the following steps:
the method comprises the following steps:
s1: preparing an ultrathin metal film characterization sample, wherein the sample structure is as follows: Sub/MxH/Air; wherein: sub is a substrate; air is Air; m is an ultrathin metal film layer; h is an infrared transparent dielectric film; x is the optical thickness of the dielectric film;
s2: establishing a Drude dielectric function dispersion model of the ultrathin metal film;
s3: establishing a film interference physical model of an ultrathin metal film characterization sample;
s4: measuring the reflectivity spectrum and the transmissivity spectrum of the ultra-thin metal film characterization sample;
s5: and (3) obtaining the thickness and the optical constant of the ultrathin metal film in the ultrathin metal film characterization sample by taking the measured reflectivity spectrum and the measured transmissivity spectrum as targets, based on the film interference physical model, using a film optical constant inversion calculation method and combining with an evaluation function of film optical constant inversion calculation.
2. The method for characterizing the infrared optical constants of the ultrathin metal film as claimed in claim 1, wherein the method comprises the following steps:
the evaluation function of the inversion calculation of the optical constant of the film is as follows:
Figure FDA0002697900400000011
wherein: MSE is the mean square error of the measured value and the theoretical model calculation value, N is the number of the measured wavelengths, M is the number of variables,
Figure FDA0002697900400000012
and
Figure FDA0002697900400000013
measured values of spectral transmittance and spectral reflectance at i wavelengths respectively,
Figure FDA0002697900400000014
and
Figure FDA0002697900400000015
respectively calculated values of i wavelength spectral transmittance and spectral reflectance,
Figure FDA0002697900400000016
and
Figure FDA0002697900400000017
i wavelength spectral transmittance and spectral reflectance measurement errors, respectively.
3. The method for characterizing the infrared optical constants of the ultrathin metal film as claimed in claim 1, wherein the method comprises the following steps: in step S3, a thin film interference physical model is constructed by using the optical constant of the Sub substrate in step S1, the optical constant of the H dielectric film and the Drude dielectric function dispersion model of the ultrathin metal thin film established in step S2.
4. The method for characterizing the infrared optical constants of the ultrathin metal film as claimed in any one of claims 1 to 3, wherein the method comprises the following steps: h is Ge, ZnS or Al2O3、YbF3、MgF2Any one of them.
5. The method for characterizing the infrared optical constants of the ultrathin metal film as claimed in any one of claims 1 to 3, wherein the method comprises the following steps: the Sub is any one of Si, Ge, ZnS and ZnSe.
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