CN102980748A - Method for measuring optical constants of thin film with non-uniform refractive index - Google Patents

Abstract

The invention relates to a method for measuring optical constants of a thin film with a non-uniform refractive index. The method comprises the following steps: perfomring spectral measurement on transmissivity and reflectivity of the thin film to obtain spectral measurement data; performing variable-angle ellipsometry on the thin film to obtain ellipsometric parameters; and fitting the spectral data and the ellipsometric parameters, matching with a corresponding dispersion relation, and working out the optical constants of the thin film by using a non-uniform model. On the basis of separate use of the photometry and the ellipsometry, respective advantages of the photometry and the ellipsometry are flexibly taken, high sensitivity of measuring optical parameters of a film layer by the ellipsometry and intuition of measuring data by the photometry are fully played, and the photometry and the ellipsometry are combined with each other to obtain high-precision analytical data of the optical constants, so that the reliance of the photometry on the thickness of the thin film is improved and the difficulty for model calculation by the ellipsometry is reduced.

Description

A kind of measuring method of non-homogeneous index film optical constant

Technical field

The present invention relates to deep ultraviolet thin film optical technology application, particularly a kind of measuring method of non-homogeneous index film optical constant.

Background technology

In recent years, along with the ArF excimer laser in the numerous areas such as material retrofit, deep-UV lithography, material processed and quasi-molecule medical treatment more and more widespread use and tremendous development, so that the research of deep ultraviolet optical correlation technique has great society and economic worth.In the field of deep ultraviolet, no matter be ArF excimer laser or other associated optical system, all be unable to do without the coated optical element of deep ultraviolet wave band, therefore in the urgent need to developing the optical thin film of excellent performance in the deep ultraviolet wavelength band.

In order to prepare the thin film optical components that meets the demands, must accurately determine the optical constant (refractive index and extinction coefficient) of used membraneous material in corresponding wave band.When design and the characteristic of calculating optical thin-film component, usually bulk material respectively to the optical constant of constant as film, and film is simplified to have homogeneous refractive index, the rete of extinction coefficient and thickness.But the optical constant of material difference under filminess and under the block state is very large, heterogeneity, anisotropy that refractive index occurs, and the unevenness of extinction coefficient appearance and anisotropy etc.And the strong deposition process that adopts that relies on of optical constant, therefore under each concrete preparation condition, the optical constant of accurate Analysis film is to prepare an important ring of high performance thin film optical element.

The method of resolving optical constants has a lot, such as spectrophotometric method (photometry), Ellipsometric (ellipsometry), the prism-coupled method of utilizing wave guide principles, surface plasmons method and polarization state conversion method etc.Because high precision measuring instrument was in quick, the ripe development of deep ultraviolet wave band, so that photometry and ellipsometry become the common method of determining optical constant at the deep ultraviolet wave band in recent years.

Photometry is by measuring transmissivity and the reflectivity of film sample, a kind of method of its transmissivity and reflectivity being carried out match based on dispersion relation.And ellipsometry is to utilize the reflection of light beam on interface or film or the polarization conversion that occurs during transmission, according to the ellipsometric parameter that records, sets up corresponding dispersive model and carries out match.Photometry is thicker to the thickness requirement of film, in order to produce a plurality of interference extreme values, and larger on result's impact of resolving in the precision of measure spectrum reflectivity; Ellipsometry has very high measurement sensitivity and precision, and the ultrathin film of energy logarithm nanometer thickness is measured.But the mathematical computations of ellipsometry is complicated, relatively relies on the foundation of model when data fitting, and all there is relevance in two kinds of methods.For this reason, in the urgent need to outside above-mentioned analytic method, seek other effectively solution to the problems described above, realize the accurate Analysis of deep ultraviolet wave band Film Optics constant.

Summary of the invention

For the optical constant of accurate Analysis film at the deep ultraviolet wave band, by photometry and ellipsometry are analyzed, the invention discloses a kind of based on photometry and ellipsometry measuring method that combine, non-homogeneous index film optical constant.

In order to solve the problems of the technologies described above, technical scheme of the present invention is specific as follows:

A kind of measuring method of non-homogeneous index film optical constant may further comprise the steps:

Step a carries out transmitance and reflectance spectrum measurement to film, obtains spectrum measuring data;

Step b carries out the ellipsometric measurement of varied angle to film, obtains ellipsometric parameter;

Step c according to the measurement result of step a and b, with spectrum measuring data and ellipsometric parameter match, cooperates corresponding dispersion relation, uses the optical constant of non-homogeneous model solution film.

In the technique scheme, among the step c, described non-homogeneous model is the Schroeder model.

In the technique scheme, among the step b, ellipsometric measurement band selection 185nm-450nm.

In the technique scheme, among the step b, the ellipsometric measurement angle is selected respectively 65 °, 70 ° and 75 °.

In the technique scheme, also comprise step after the step c: calculate and actual conditions according to theory, the value of evaluation function σ is regarded as desired result less than 0.01, otherwise recomputates; σ is defined as

$\mathrm{\σ}=\frac{1}{2N-M}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[{\left(\frac{{\mathrm{\ψ}}_i^{\mathrm{mod}}-{\mathrm{\ψ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\ψ},i}^{\exp }}\right)}^2+{\left(\frac{{\mathrm{\Δ}}_i^{\mathrm{mod}}-{\mathrm{\Δ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\Δ},i}^{\exp }}\right)}^2+{\left(\frac{T_i^{\mathrm{mod}}-T_i^{\exp }}{{\mathrm{\σ}}_{T,i}^{\exp }}\right)}^2+{\left(\frac{R_i^{\mathrm{mod}}-R_i^{\exp }}{{\mathrm{\σ}}_{R,i}^{\exp }}\right)}^2]$

Wherein, N is ellipsometer and the simultaneously-measured number of wavelengths of photometer, namely obtains total logarithm of ellipsometric parameter ψ, Δ and spectrum measuring data T, R; M is the number of selected fitting parameter; ψ is that relative amplitude changes between polarized light reflection back/forth component, and Δ is the phase change between polarized light reflex time component;

With ,

With

The ψ and the Δ value that are respectively measurement and calculate according to model; With

Measuring error for ψ and Δ value; T represents the transmissivity of film, and R is the reflectivity of expression film;

With

,

With

The T and the R value that are respectively measurement and calculate according to model;

With

Measuring error for T and R value.

The advantage of the measuring method of non-homogeneous index film optical constant of the present invention is:

The measuring method of non-homogeneous index film optical constant of the present invention, by on the basis of using respectively photometry and ellipsometry to find the solution, adopted flexibly two kinds of methods advantage separately, give full play to ellipsometry and measure the high sensitivity of rete optical parametric and the intuitive of photometric measurement data, both mutually combine and then obtain high-precision optical constant resolution data, thereby have improved photometry to the dependence of film thickness and reduced the degree of difficulty that ellipsometry calculates model.

Description of drawings

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail.

Fig. 1 is the schematic flow sheet that refractive index inhomogeneity Film Optics constant of the present invention is resolved.

Embodiment

The present invention relates to by on the basis of comparative analysis photometry and ellipsometry, become hybrid algorithm in conjunction with combination of advantages separately, obtained the optical constant of refractive index inhomogeneity film, thereby improved the parsing precision of film at deep ultraviolet band of light mathematic(al) constant.

The measuring method of non-homogeneous index film optical constant of the present invention:

At first, will carry out spectral measurement to the film substrate that under specific process conditions, prepares, and need to consider in the weak absorption of the deep ultraviolet wave band substrate impact on film;

Secondly, measure at the ellipsometric parameter that film is carried out the measurement of transmitance and reflectance spectrum and varied angle, test band selection 185nm-450nm, the Ellipsometry Measurement angle is selected respectively 65 °, 70 ° and 75 °;

At last, theoretical model must be selected correctly, and the refractive index of membraneous material changes with the variation of its thickness, needs to adopt non-homogeneous model to process.The heterogeneity model cooperates corresponding dispersion relation then with spectrum measuring data and ellipsometric parameter, and uses the Schroeder model to carry out together COMPREHENSIVE CALCULATING.

Ultimate principle of the present invention mainly based on following some:

The basic reason of optical constant relevance appears in film photometry and ellipsometry match, be that the quantity of unknown number parameter is greater than equation number, make equation not have unique solution, this has directly caused different-thickness in the certain limit, refractive index and extinction coefficient combination all can produce preferably fitting result, and discreteness is larger as a result thereby make.Address this problem, can be from two aspects: the first, reduce unknown number.Can use the dispersion relation mathematical model during common ellipse inclined to one side match, as be applicable to the Caucy equation of transparent or weak absorbing material, and be applicable to the Drude model of metal, be applicable to semi-conductive Lorentz model, by the parametrization of optical constant, greatly reduced the number of unknown number.But the shortcoming of the method need to have the physical property of material certain understanding could determine to use which kind of model; And because material is usually completely different in different wavelength section optical properties, need select different models.The wrong choice of single model may cause neglecting the slight change of some optical constants.The second, the quantity of increase equation provides more qualifications.Although adopt multiple angles of incidence to obtain more data, often can not provide new qualifications, its role normally reduces experimental error, the correctness of checking fitting result.

By the analysis of front as can be known, the same optical constant that determines with film of the such intensive quantity of reflectivity of optical thin film and transmissivity.Thereby increase reflectivity and transmissivity, the information that are conducive to the optical constant Inversion Calculation can be provided more.Therefore optimal method is that this spline equation number can reduce the difficulty of calculating greatly greater than the unknown parameter number with the reflectivity of film and the simultaneously match of ellipsometric parameter of transmissivity and ellipsometer acquisition.

Can be seen by top ultimate principle:

At first, which kind of base material the present invention for adopting without limits, and the optical constant that is specially adapted to transparent dielectric film is resolved.

Secondly, the present invention does not limit the film of which kind of method and deposition process parameters preparation, is specially adapted to the fluoride film of the deep ultraviolet film of thermal evaporation preparation.

The 3rd, the present invention does not limit the film which kind of is used for the preparation of deep ultraviolet membraneous material, is specially adapted to LaF ₃, GdF ₃, MgF ₂And AlF ₃Deng the fluoride film material.

Below in conjunction with accompanying drawing the present invention is done to describe in detail.

This example is for the LaF that adopts hot boat Evaporation preparation ₃Film uses hybrid algorithm to resolve film in the optical constant of deep ultraviolet wave band.

Consult Fig. 1, the steps flow chart of the measuring method of non-homogeneous index film optical constant of the present invention mainly comprises:

(1) required transmissivity and the reflectivity of photometry of importing film imports the ellipsometric parameter that ellipsometer measurement obtains;

(2) scope of setup parameter, the initial value of setted wavelength scope, thickness and optical constant;

(3) because the refractive index of membraneous material changes with the variation of its thickness, therefore adopt non-homogeneous model (Schroeder model and dispersive model) to carry out match;

(4) calculate and actual conditions according to theory, final discrimination standard is that the evaluation function value is regarded as desired result less than 0.01, otherwise can turn back to the initial setting stage, continues to calculate after rational parameter is set again.

Evaluation function adopts square error σ (mean square error, MSE) to come the matching degree of evaluation model calculated value and experiment measuring value.In fact the inversion of parameters match is exactly the process of seeking the σ minimum value, and σ is less, and calculated value and experiment value error are less, and acquired results is more credible.σ is defined as

$\mathrm{\σ}=\frac{1}{2N-M}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[{\left(\frac{{\mathrm{\ψ}}_i^{\mathrm{mod}}-{\mathrm{\ψ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\ψ},i}^{\exp }}\right)}^2+{\left(\frac{{\mathrm{\Δ}}_i^{\mathrm{mod}}-{\mathrm{\Δ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\Δ},i}^{\exp }}\right)}^2+{\left(\frac{T_i^{\mathrm{mod}}-T_i^{\exp }}{{\mathrm{\σ}}_{T,i}^{\exp }}\right)}^2+{\left(\frac{R_i^{\mathrm{mod}}-R_i^{\exp }}{{\mathrm{\σ}}_{R,i}^{\exp }}\right)}^2]$

Wherein, N is ellipsometer and the simultaneously-measured number of wavelengths of photometer, namely obtains total logarithm of ellipsometric parameter ψ, Δ and spectrum measuring data T, R; M is the number of selected fitting parameter;

With

,

With

The ψ and the Δ value that are respectively measurement and calculate according to model.ψ is that relative amplitude changes between polarized light reflection back/forth component in the ellipsometric parameter, and Δ is the phase change between polarized light reflex time component;

With Measuring error for ψ and Δ value; With

,

With

The T and the R value that are respectively measurement and calculate according to model, T represents the transmissivity of film in the spectrum measuring data, R is the reflectivity of expression film;

With Measuring error for T and R value.

Obviously, above-described embodiment only is for example clearly is described, and is not the restriction to embodiment.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here need not also can't give all embodiments exhaustive.And the apparent variation of being extended out thus or change still are among the protection domain of the invention.

Claims (5)

1. the measuring method of a non-homogeneous index film optical constant is characterized in that, may further comprise the steps:

Step a carries out transmitance and reflectance spectrum measurement to film, obtains spectrum measuring data;

Step b carries out the ellipsometric measurement of varied angle to film, obtains ellipsometric parameter;

Step c according to the measurement result of step a and b, with spectrum measuring data and ellipsometric parameter match, cooperates corresponding dispersion relation, uses the optical constant of non-homogeneous model solution film.

2. measuring method according to claim 1 is characterized in that, among the step c, described non-homogeneous model is the Schroeder model.

3. measuring method according to claim 1 and 2 is characterized in that, among the step b, and ellipsometric measurement band selection 185nm-450nm.

4. measuring method according to claim 1 and 2 is characterized in that, among the step b, the ellipsometric measurement angle is selected respectively 65 °, 70 ° and 75 °.

5. measuring method according to claim 1 and 2 is characterized in that, also comprises step after the step c: calculate and actual conditions according to theory, the value of evaluation function σ is regarded as desired result less than 0.01, otherwise recomputates; σ is defined as

$\mathrm{\σ}=\frac{1}{2N-M}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[{\left(\frac{{\mathrm{\ψ}}_i^{\mathrm{mod}}-{\mathrm{\ψ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\ψ},i}^{\exp }}\right)}^2+{\left(\frac{{\mathrm{\Δ}}_i^{\mathrm{mod}}-{\mathrm{\Δ}}_i^{\exp }}{{\mathrm{\σ}}_{\mathrm{\Δ},i}^{\exp }}\right)}^2+{\left(\frac{T_i^{\mathrm{mod}}-T_i^{\exp }}{{\mathrm{\σ}}_{T,i}^{\exp }}\right)}^2+{\left(\frac{R_i^{\mathrm{mod}}-R_i^{\exp }}{{\mathrm{\σ}}_{R,i}^{\exp }}\right)}^2]$

Wherein, N is ellipsometer and the simultaneously-measured number of wavelengths of photometer, namely obtains total logarithm of ellipsometric parameter ψ, Δ and spectrum measuring data T, R; M is the number of selected fitting parameter; ψ is that relative amplitude changes between polarized light reflection back/forth component, and Δ is the phase change between polarized light reflex time component;

With

,

With

The ψ and the Δ value that are respectively measurement and calculate according to model;

With

Measuring error for ψ and Δ value; T represents the transmissivity of film, and R is the reflectivity of expression film;

With

,

With

The T and the R value that are respectively measurement and calculate according to model;

With

Measuring error for T and R value.

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