CN112595673A - Method for measuring optical constant of single crystal diamond substrate - Google Patents

Method for measuring optical constant of single crystal diamond substrate Download PDF

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CN112595673A
CN112595673A CN202011296318.0A CN202011296318A CN112595673A CN 112595673 A CN112595673 A CN 112595673A CN 202011296318 A CN202011296318 A CN 202011296318A CN 112595673 A CN112595673 A CN 112595673A
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diamond substrate
single crystal
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optical constants
crystal diamond
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崔长彩
李子清
陆静
胡中伟
徐西鹏
黄辉
黄国钦
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Huaqiao University
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    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/21—Polarisation-affecting properties
    • G01N21/211—Ellipsometry
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/21—Polarisation-affecting properties
    • G01N21/211—Ellipsometry
    • G01N2021/213—Spectrometric ellipsometry

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Abstract

The invention discloses a method for measuring optical constants of a monocrystalline diamond substrate, which comprises the following steps: respectively measuring the single crystal diamond substrate by adopting a transmission type ellipsometry measurement mode and a reflection type ellipsometry measurement mode; the transmission spectra (ψ) were obtained by the above measurements, respectivelyt、Δt) And reflection spectrum (psi)r、Δr) (ii) a Obtaining spectral data according to the measurement, and respectively calculating by adopting a Cauchy model to obtain substrate optical constants at least comprising a substrate refractive index n and an extinction coefficient k; evaluating the fitting error sigma, and optimizing the optical model or the dielectric function when the fitting error exceeds a preset condition; and comparing the fitting errors of the optimized models, and selecting a model and a measurement mode to determine the optical constant of the diamond substrate. It has the following advantages: the optical constant measurement is more accurate.

Description

Method for measuring optical constant of single crystal diamond substrate
Technical Field
The invention relates to the technical field of optical constant measurement, in particular to a method for measuring an optical constant of a monocrystalline diamond substrate.
Background
The existing method for testing the ultra-wideband optical constant of the optical film, such as CN106706521A, includes: s1, firstly, depositing an optical film with a preset thickness on a silicon substrate; s2, measuring the ultraviolet to near infrared band elliptical polarization spectrum and infrared band transmission spectrum of the deposited optical film; s3, selecting a transparent area of a section of film according to the spectral data of the optical film, and calculating by adopting a Cauchy model to obtain the refractive index n and the thickness d1 of the film within the waveband range; s4, establishing an optical constant model with an optical constant ranging from ultraviolet to infrared wide spectrum, adding a dielectric constant vibrator model in an absorption spectrum area, wherein the center frequency of a vibrator is the absorption position, and the amplitude and the width of the vibrator are adjusted according to spectrum data; s5, taking an ultraviolet to near-infrared waveband elliptical polarization spectrum and an infrared waveband transmission spectrum as a composite target, performing inversion operation on the optical constant of the film in an ultraviolet to infrared full spectrum range, wherein the initial value of the thickness is set as d1, an evaluation function MSE is preset, the MSE is the mean square error of a measured value and a theoretical model calculated value, and fitting the MSE to make the MSE smaller and better; and S6, obtaining each parameter of the dielectric constant model according to the MSE fitting result, and further obtaining the optical constant of the film in the ultraviolet-infrared ultra-wideband spectrum range, wherein the optical constant comprises the refractive index n, the extinction coefficient k and the physical thickness d of the film. The measurement method only obtains the result according to the measurement of the elliptical polarization measurement mode, so the accuracy of obtaining the constant is to be enhanced.
Disclosure of Invention
The invention provides a method for measuring an optical constant of a monocrystalline diamond substrate, which overcomes the defects of an optical film ultra-wideband optical constant measuring method in the background technology.
In order to solve the technical problem, the invention provides a method for measuring optical constants of a single crystal diamond substrate, which comprises the following steps:
s1, respectively measuring the single crystal diamond substrate by adopting a transmission type ellipsometry measuring method and a reflection type ellipsometry measuring method;
s2, respectively obtained by the above measurementTransmission spectrum (psi, delta)t) And reflection spectrum (psi)r、Δr) Phi represents the amplitude ratio of the emergent light to the incident light, delta represents the phase difference between the emergent light and the incident light, the lower corner mark t represents the transmission ellipsometry, and the lower corner mark r represents the reflection ellipsometry;
s3, obtaining spectral data according to the measurement, and respectively calculating by adopting a Cauchy model to obtain substrate optical constants, wherein the optical constants at least comprise a substrate refractive index n and an extinction coefficient k;
s4, evaluating the fitting error sigma, and optimizing the optical model or the dielectric function when the fitting error exceeds a preset condition;
s5, comparing the fitting error of the optimized model, selecting a model and a measuring mode to determine the optical constant of the diamond substrate.
In one embodiment: in this step S2, the transmission spectrum (ψ)t、Δt) Is defined as:
Figure RE-GDA0002947207420000021
reflectance spectrum
Figure RE-GDA0002947207420000022
Is defined as:
Figure RE-GDA0002947207420000023
t represents the polarization amplitude transmission coefficient, r represents the polarization amplitude reflection coefficient, and the lower indices p and s represent p-polarized light and s-polarized light, respectively, resolved from a natural light beam.
In one embodiment: in step S3, the calculation formula of the Cauchy model is:
Figure RE-GDA0002947207420000024
Figure RE-GDA0002947207420000025
wherein n is the refractive index, An、BnAnd CnIs Cauchy model parameter, lambda is wavelength, extinction coefficient k is from Ak、BkAnd EbDescription of three parameters, Eb＝1240/λb，EbAssociated with the substrate material. .
In one embodiment: in step S4, the fitting error σ is calculated by the following formula:
Figure RE-GDA0002947207420000031
ρ ═ tan Φ exp (i Δ), M is the number of measurement points, P is the number of parameters, the lower subscript ex indicates experimental data, and the lower subscript cal indicates calculated data of the fit.
In one embodiment: in step S3, obtaining spectral data according to the above measurements, and calculating with a Cauchy model to obtain optical constants of the substrate in the wavelength range, wherein the optical constants further include the thickness d of the substratet、 dr。
In one embodiment: the wave band range is 210 nm-1650 nm.
In one embodiment: in step S4, the optimized optical model includes a multilayer structure.
In one embodiment: the multilayer structure includes a roughness layer calculated using Bruggeman Effective Medium Approximation (EMA) theory.
Compared with the background technology, the technical scheme has the following advantages:
1. through two measurement modes of a transmission type and a reflection type of an ellipsometer, the single crystal diamond substrate is respectively measured to obtain a transmission spectrum and a reflection spectrum, then calculation is carried out according to an optical model established by combining the transmission spectrum and the reflection spectrum, fitting analysis is carried out to obtain a final optical constant of the single crystal diamond substrate, more information can be extracted, and the obtained optical constant is more accurate.
2. Transmission spectrumIs defined as
Figure RE-GDA0002947207420000032
The reflection spectrum is defined as
Figure RE-GDA0002947207420000033
Cauchy model has the calculation formula of
Figure RE-GDA0002947207420000034
Figure RE-GDA0002947207420000035
The fitting error sigma is calculated by the formula
Figure RE-GDA0002947207420000036
The optical constants are more accurate by establishing a model through the five formulas.
Detailed Description
In order to further explain the objects, technical solutions and features of the present invention, a method for measuring optical constants of a single crystal diamond substrate is described in detail with reference to specific embodiments.
A method for measuring optical constants of a single crystal diamond substrate, comprising:
s1, respectively measuring the single crystal diamond substrate by adopting a transmission type ellipsometry measuring mode and a reflection type ellipsometry measuring mode, wherein the measuring mode can adopt an ellipsometer for measuring, and the ellipsometer is an optical measuring instrument for detecting the thickness, the optical constant and the material microstructure of the thin film;
s2, obtaining transmission spectra (psi) by the above measurementt、Δt) And reflection spectrum (psi)r、Δr) Phi represents the amplitude ratio of the emergent light to the incident light, delta represents the phase difference between the emergent light and the incident light, the lower corner mark t represents the transmission ellipsometry, and the lower corner mark r represents the reflection ellipsometry; wherein:
transmission spectrum (psi)t、Δt) Is defined as:
Figure RE-GDA0002947207420000041
the reflection spectrum (ψ r, Δ r) is defined as:
Figure RE-GDA0002947207420000042
in equations (1) and (2): t represents a polarization amplitude transmission coefficient, r represents a polarization amplitude reflection coefficient, and lower corner marks p and s respectively represent p-polarized light and s-polarized light decomposed by a beam of natural light;
s3, obtaining spectrum data according to the above measurement, and calculating respectively by Cauchy model (Cauchy model) to obtain substrate optical constants including at least substrate refractive index nt、nr；
The Cauchy model has the calculation formula as follows:
Figure RE-GDA0002947207420000043
Figure RE-GDA0002947207420000044
in equation (3): n is the refractive index, An、BnAnd CnIs Cauchy model parameter, lambda is wavelength,
in equation (4): extinction coefficient k is represented by Ak、BkAnd EbDescription of three parameters, Eb＝1240/λbAssociated with the substrate material;
s4, evaluating the fitting error sigma, and optimizing the optical model or the dielectric function when the fitting error exceeds a preset condition;
the fitting error σ is calculated as:
Figure RE-GDA0002947207420000051
in equation (5): ρ ═ tan ψ exp (i Δ), M is the number of measurement points, P is the number of parameters (one point is measured multiple times, the number of measurements corresponds to the number of P), the lower subscript ex represents experimental data, and the lower subscript cal represents fitting calculation data; wherein: in ellipsometry, corresponding parameters are characterized and analyzed by means of a matrix, the number of measurements is related to the number of matrix elements, for example, if the mueller matrix is 4 x 4, at least 16 measurements are performed to solve the parameters;
s5, comparing the fitting error of the optimized model, selecting a model and a measuring mode to determine the optical constant of the diamond substrate.
Optionally, in step S4, the optimized optical model comprises a multilayer structure including a roughness layer calculated using Bruggeman' S Effective Medium Approximation (EMA) theory.
In this embodiment: whether the error exceeds a predetermined condition such as: judging the goodness of fit of the fitting curve and the measuring curve, wherein if the goodness of fit is large, the error is large, and if the goodness of fit is small, the error is small; or, calculating an evaluation index MSE value, and then judging whether the MSE value is larger than a preset value, wherein if the MSE value is larger than the preset value, the error is large, and if the MSE value is smaller than the preset value, the error is small.
According to the requirement, in step S3, spectral data are obtained according to the above measurement, and the optical constants of the substrate in the waveband range are obtained by respectively calculating with a Cauchy model, and if the substrate surface has other film layers, the thickness d of the surface film layer can be obtained by fitting. The wave band ranges from 210nm to 1650nm, and the thickness d of the film layer is used as a variable parameter to be fitted with A, B, C of a Cauchy model.
The above description is only a preferred embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any person skilled in the art can make insubstantial changes in the technical scope of the present invention within the technical scope of the present invention, and the actions infringe the protection scope of the present invention are included in the present invention.

Claims (8)

1. A method for measuring optical constants of a single crystal diamond substrate is characterized in that: the method comprises the following steps:
s1, respectively measuring the single crystal diamond substrate by adopting a transmission type ellipsometry measuring method and a reflection type ellipsometry measuring method;
s2, obtaining transmission spectra (psi) by the above measurementt、Δt) And reflection spectrum (psi)r、Δr) Phi represents the amplitude ratio of the emergent light to the incident light, delta represents the phase difference between the emergent light and the incident light, the lower corner mark t represents the transmission ellipsometry, and the lower corner mark r represents the reflection ellipsometry;
s3, obtaining spectral data according to the measurement, and respectively calculating by adopting a Cauchy model to obtain substrate optical constants, wherein the optical constants at least comprise a substrate refractive index n and an extinction coefficient k;
s4, evaluating the fitting error sigma, and optimizing the optical model or the dielectric function when the fitting error exceeds a preset condition;
s5, comparing the fitting error of the optimized model, selecting a model and a measuring mode to determine the optical constant of the diamond substrate.
2. A method of measuring optical constants of a single crystal diamond substrate according to claim 1, wherein: in this step S2, the transmission spectrum (ψ)t、Δt) Is defined as:
Figure RE-FDA0002947207410000011
the reflection spectrum (ψ r, Δ r) is defined as:
Figure RE-FDA0002947207410000012
t represents the polarization amplitude transmission coefficient, r represents the polarization amplitude reflection coefficient, and the lower indices p and s represent p-polarized light and s-polarized light, respectively, resolved from a natural light beam.
3. A method of measuring optical constants of a single crystal diamond substrate according to claim 1, wherein: in step S3, the calculation formula of the Cauchy model is:
Figure RE-FDA0002947207410000013
Figure RE-FDA0002947207410000021
wherein n is the refractive index, An、BnAnd CnIs Cauchy model parameter, lambda is wavelength, extinction coefficient k is from Ak、BkAnd EbDescription of three parameters, Eb＝1240/λb，EbAssociated with the substrate material.
4. A method of measuring optical constants of a single crystal diamond substrate according to claim 1, wherein: in step S4, the fitting error σ is calculated by the following formula:
Figure RE-FDA0002947207410000022
ρ ═ tan ψ exp (i Δ), M is the number of measurement points, P is the number of parameters, the lower subscript ex denotes experimental data, and the lower subscript cal denotes calculation data of fitting.
5. A method of measuring optical constants of a single crystal diamond substrate according to claim 1, wherein: in step S3, obtaining spectral data according to the above measurements, and calculating with a Cauchy model to obtain optical constants of the substrate in the wavelength range, wherein the optical constants further include the thickness d of the substratet、dr。
6. A method of measuring optical constants of a single crystal diamond substrate according to claim 5, wherein: the wave band range is 210 nm-1650 nm.
7. A method of measuring optical constants of a single crystal diamond substrate according to claim 1, wherein: in step S4, the optimized optical model includes a multilayer structure.
8. A method for measuring optical constants of a single crystal diamond substrate according to claim 7, wherein: the multilayer structure includes a roughness layer calculated using Bruggeman Effective Medium Approximation (EMA) theory.
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CN113654995A (en) * 2021-07-08 2021-11-16 南京大学 Method for measuring elliptical polarization spectrum under packaging condition
CN114324184A (en) * 2021-12-30 2022-04-12 广州粤芯半导体技术有限公司 Spectroscopic floating model of ellipsometer and establishing method

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