JP4587690B2 - Ultrathin film and thin film measurement method - Google Patents

Description

  The present invention processes a data obtained by using a spectroscopic ellipsometer using a local minimum calculation method (hereinafter referred to as “BLMC”) to accurately measure an ultra-thin film, a film thickness, an optical constant, and the like of the thin film. The present invention relates to a surface ultrathin film and a thin film measurement method.

The amount of change in polarization of incident light and reflected light is measured using a spectroscopic ellipsometer, and the film thickness (d) and complex refractive index N (N = n−ik) can be calculated from the results. The amount of change in polarization (ρ) is expressed by ρ = tan Ψ exp (iΔ) and depends on parameters such as wavelength (λ), incident angle ( φ), film thickness, complex refractive index, and the relationship is as follows: become.
(D, n, k) = f (Ψ, Δ, λ, φ)

When the incident angle is fixed, the single wavelength ellipsometer can measure only two independent variables for the three unknowns (d, n, k), so one of d, n, k is known. Need to be fixed as. The measurement variables also vary the angle of incidence at a single wavelength is increased. However, since there is a strong correlation between (ψ (φ ₁ ) , Δ (φ ₁ ) ) and (ψ (φ ₂ ) , Δ (φ ₂ ) ) due to the difference in incident angle ( φ), d, n, k It is difficult to accurately obtain
JA Woollam et al., 5 authors, “Overview of Variable Angle Spectroscopic Ellipsometry (VASE), Part I: Basic Theory,” and Typical Applications "" Proceedings of SPIE ", Vol.CR72, p.3-28, July 1999

The information (Ψ _E , Δ _E ) spectrum of the amount of change in polarization of the multilayer thin film formed on the substrate measured using a spectroscopic ellipsometer is obtained from the n, k information of the substrate and the n, k, d information of each layer. Includes everything. However, thin film analysis is not possible for the following reasons.

Polarization change amount, the volume which light passes, can be represented by (an area of the phase angle × beam diameter). If the beam diameter is constant, the amount of change in polarization is proportional to a mathematical formula obtained by multiplying the film thickness (d), the complex refractive index N, and the incident angle (φ). Therefore, the value of the amount of change in polarization also changes depending on the correctness of the incident angle. By correctly determining the incident angle, it is possible to correctly determine the value of the amount of polarization change.

As described above, the information (Ψ _E , Δ _E ) spectrum of the polarization change amount of the multilayer thin film includes all of the n, k information of the substrate and the n, k, d information of each layer. From this, it is not possible to calculate a unique combination of the n, k information of the substrate and the n, k, d information of each layer. Therefore, an optimum model is determined by fitting parameters using a dispersion formula. The dispersion formula is a formula showing the wavelength dependence of the dielectric constant of a substance. In the near infrared to ultraviolet range, this dielectric constant ε (λ) is determined from the bonding mode of the constituent atoms of the material. As a dispersion formula, a calculation formula based on a harmonic oscillator, a calculation formula based on quantum mechanics, an empirical formula, and the like are known, and usually includes two or more parameters. By calculating (fitting) this parameter, the dielectric constant ε (λ) of the material can be obtained. An object of the present invention is to set a combination model such as a film thickness and a complex refractive index, calculate a simulation spectrum thereof, and perform fitting between the simulation spectrum and a measurement spectrum using a minimum value calculation method (BLMC). Accordingly, an object of the present invention is to provide an ultra-thin film and a thin-film measurement method using a spectroscopic ellipsometer based on a minimum value calculation method (BLMC) for determining the ultra-thin film and the structure of the thin film.

The ultrathin film and thin film measurement method according to the present invention is an ultrathin film and thin film measurement method on a substrate surface to be measured using a spectroscopic ellipsometer based on a minimum value calculation method (BLMC). Ψ _E , Δ _E spectrum measurement step for obtaining measurement spectra Ψ _E (λ _i ) and Δ _E (λ _i ) which are changes in polarization of incident light and reflected light for each wavelength λ _i by changing the wavelength of (N ₀ (n ₀ , k ₀ )) of the substrate and (N (n, k)) of the thin film on the substrate are assumed using a dispersion formula that is a formula showing the wavelength dependence of the dielectric constant of the substance, further plurality of thickness within the expected range (d ± mΔd), a plurality of mixing ratios shown the volume fraction of the plurality of object substance that is mixed in the range expected (Vf ± mΔVf), and Set multiple incident angles (φ ± mΔφ) within the expected range and corresponding simulation Calculating spectrum [psi _M a (lambda _i) and Δ _M (λ _i), the angle of incidence, based on a combination of the mixing ratio and thickness, performs fitting dispersion equation parameters, obtained by the fitting Using the parameters of the dispersion formula as the optical constants of the film, the Ψ _E (λ _i ) and Δ _E (λ _i ) are calculated from the Ψ _M (λ _i ) and Δ _M (λ _i ) spectra calculated therefrom. A first step of selecting a film thickness (d _best ), a mixing ratio (Vf _best ), an incident angle (φ _best ), and a dispersion fitting result (DSP _best ) with the smallest difference between Using the selected angle of incidence (φ _best ) as a definite value, the fitting of the film thickness (d _best ), the mixing ratio (Vf _best ), and the dispersion equation (DSP _best ) obtained by the fitting is performed again to obtain the most suitable model. Consists of a second step to select Characterized in that it is.

  According to the present invention, ultrathin films and thin film structures, which have been difficult in the past, can be accurately and accurately measured by using a model and further fitting using a local minimum calculation method (BLMC).

  Embodiments of the method according to the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing the configuration of an ellipsometer used in the method of the present invention. The spectroscopic ellipsometer shown in this block diagram executes spectroscopic measurement data acquisition step 10 of the method described later.

  The Xe lamp 1 is a so-called white light source including a large number of wavelength components. The light emitted from the Xe lamp 1 is guided to the polarizer 3 through the optical fiber 2. The light polarized by the polarizer 3 is incident on the surface of the sample 4 to be measured at a specific incident angle (for example, φ = 75.00 °). The reflection from the sample 4 is guided to the analyzer 6 through a photoelastic modulator (PEM) 5. Phase modulation is performed at a frequency of 50 kHz by a photoelastic modulator (PEM) 5 to produce linear to elliptically polarized light. Therefore, Ψ and Δ can be determined with a resolution of several milliseconds. The output of the analyzer 6 is connected to the spectroscope 8 via the optical fiber 7. The output data of the spectroscope 8 is taken into the data take-in unit 9 and the spectroscopic measurement data acquisition step 10 is completed. The position of the PEM 5 can be either after the polarizer 3 or before the analyzer 6.

Next, a case where the incident angle near the nominal incident angle φ ₀ is measured as a parameter will be described. Polarization change amount as described above ([rho) is expressed by ρ = tan Ψ exp (iΔ) , wavelength (lambda), the angle of incidence (phi), dependent thickness, on the parameters of the complex refractive index, etc., the relationship Is as follows. (D, n, k) = f (Ψ, Δ, λ, φ)

The nominal angle of incidence phi ₀ shown in FIG. 1, setting a model, by delicate shape of the surface of the sample, the incident angle phi ₀ is anticipated that it is better to slightly increase or decrease, the above-mentioned [psi _E, Δ _E also, those who think that it is reasonable person that it was a measurement data depending on the angle you modify the φ ₀ is good.

That is, the thin film measurement method using the spectroscopic ellipsometer, the [psi _E, the nominal angle of incidence of delta _E spectrum measurement step and phi _0, the [psi _M, at delta _M Moderushi simulation spectrum calculation step, a function the phi ₀ simulation spectrum [psi _M0 to (λ _i), in the vicinity of Δ _M0 (λ _i) further the nominal angle of incidence and phi ₀ phi _k The simulation spectrum Ψ _Mk (λ _i) as a function and obtaining Δ _{Mk (λ i).} The Moderushi a simulation spectrum calculated in Step _{2 1 Ψ E (λ i)} , is compared with Δ _E (λ _i).

FIG. 2 is a flowchart showing a first embodiment of a thin film measuring method according to the present invention.
(Step 10) Measurement is performed with the apparatus shown in FIG.
(Step 20) This step is a step of converting spectroscopic measurement data into comparison data. The spectroscopic measurement data acquired in the aforementioned spectroscopic measurement data acquisition step 10 is converted into comparison data in the form of Ψ _E (λ) and Δ _E (λ).

(Step 21) This step 21 is a step for modeling a spectroscopic measurement object. This is a step of creating a model in consideration of the manufacturing process of the measurement object converted into the comparison data in the step 20.
A plurality of film thicknesses (d ± mΔd) within the expected range, a dispersion formula that matches the material produced on the substrate, and a plurality of incident angles (φ ± mΔφ) within the expected range are set.
In this embodiment, it is assumed that the substrate is Si, and the first layer SiON is three layers of 20 mm, 25 mm and 30 mm on the substrate, and the incident angle for measurement is changed from 75.00 ° to 0.01 ° every 75.degree. Prepare a large number of models up to 05 °.
(Step 22) In this step 22, Ψ _M , Δ _M calculated from the model and measurement data Ψ _E , Δ _E are displayed together.

(Step 23) Fitting is performed for each model.
(Step 24) The result of fitting the variance value for each model is shown. The columns 24a, 24b, and 24c show the results of fitting the parameters (ε _s , ω _t ) of the dispersion equation (DSP) corresponding to the incident angles with respect to SiON of 20Å, 25Å, and 30Å. Here, N measurement data pairs Exp (i = 1, 2,..., N) and corresponding N model calculation data pairs Mod (i = 1, 2,..., N) of the model. If the measurement error has a normal distribution and the standard deviation is σ _i , the mean square error (χ ² ) is given as follows.

  Here, P is the number of parameters.

(Step 25) In this step, the first selection of one incident angle and film thickness is performed.
In the case of the film thickness of 20 mm shown in the column 24a, the result of fitting shows the smallest χ ² value 0.0315 when the incident angle is 75.02 ° (see the column 24d). In the case of the film thickness of 25 mm shown in the column 24b, the result of fitting shows the smallest χ ² value 0.0242 when the incident angle is 75.03 ° (see the column 24e). In the case of the film thickness of 30 mm shown in the column 24c, the result of fitting shows the smallest χ ² value 0.0297 when the incident angle is 75.04 ° (see the column 24f). Among these, the model of 24e (φ _best = 75.03 °, d _best = 25Å) showing the smallest χ ² value 0.0242 is selected.
(Step 26) Using the incident angle ( φ _best ) selected in the first step as a definite value, the film thickness (d _best ) and dispersion parameters (ε _s , ω _t ) are fitted. In the example, the incident angle ( φ _best ) = 75.03 ° is set as a definite value, and the fitting of the film thickness (d _best ) = 25 mm and the dispersion equation parameters (ε _s , ω _t ) = (2.00, 12.58) is performed. Do. This is the second stage.
(Step 27) The fitting result of the second stage is shown. In the example, the final result is the film thickness d (final result) = 24.24 mm, and the dispersion equation parameters (ε _s , ω _t ) = (2.09, 13.24).
(Step 28) The data calculated in the above step is stored.
(Step 29) It is confirmed whether the stored data is not physically unnatural.

  (Step when data obtained by fitting is not valid) It is possible that the result obtained in any of the first and second steps is not physically or empirically valid. In that case, it is determined that the model setting is not good, and a model is further added or changed to set a different model, and fitting is performed again. Steps 22 → 21, steps 25 → 21, and steps 27 → 21 in FIG. 2 correspond to this.

  Next, in the ultrathin film and thin film measurement method on the surface of the substrate to be measured using a spectroscopic ellipsometer based on the minimum value calculation method (BLMC), the film on the surface of the substrate is uneven or discontinuous, or some materials are mixed. An embodiment in the case of being present will be described. For a medium composed of a plurality of substances that are sufficiently smaller than the wavelength order and physically mixed, a model is estimated using effective medium approximation (EMA). Effective medium approximation (EMA) when substance A and substance B are mixed is the dispersion formula or reference data for the volume fraction of substance A, the volume fraction of substance B, the film thickness of the A + B mixed layer, and the dielectric constant. Etc. are estimated and fitted and evaluated.

In this example, a mixed layer of SiO ₂ and SiN formed on a Si substrate is measured. (Measurement Step) A measurement spectrum Ψ that is a change in the polarization of incident light and reflected light for each wavelength λ _i by changing the wavelength of incident light on the thin film (SiO ₂ and SiN mixed layer) on the surface of the substrate to be measured _E (λ _i ) and Δ _E (λ _i ) are obtained. The measuring device is the same as described above.

(Target model formation step)
In this step, to form a model when a thin film on the substrate is in the mixed layer of SiO ₂ and SiN.
The (N ₀ ( n ₀ , k ₀ )) of the substrate Si is easily determined because the substrate is bulk. In order to use the effective medium approximation (EMA), (N (n, k)) of the thin film on the substrate is modeled by using some dispersion formulas or reference data.
The initial value of the thin film model is the mixing ratio (V f ): SiO ₂ (30%) + SiN (70%)
Thickness (d): 20 mm. Further from here, a plurality of film thicknesses (d ± mΔd) within an expected range and a plurality of mixing ratios (V f ± mΔV f ) within an expected range such as the dispersion formula used in the model, A plurality of incident angles ( φ ± mΔφ) within the expected range are set.
The mixing ratio (Vf) is an abbreviation for “Volume fraction”, and is used to mean volume fraction.

(Distributed parameter fitting step)
The parameters of the dispersion formula (ε _s , ω _t ) are fitted based on the combination of the incident angle, the film thickness, and the mixing ratio.
(First selection step)
Of each Ψ _M (λ _i ) and Δ _M (λ _i ) obtained by the fitting, the film thickness (d _best ) where the difference between Ψ _E (λ _i ) and Δ _E (λ _i ) is the smallest. ), An incident angle (φ _best ), and a model fitting result (DSP _best ) in which a combination of the mixture ratio (V f _best ) is set.

(Second selection step)
Using the incident angle ( φ _best ) selected in the first step as a definite value, the fitting of the film thickness (d _best ), the mixing ratio (V f _best ), and the dispersion formula (DSP _best ) is performed. As a result, in the example, SiO ₂ (57.1%) + SiN (42.9%)
Thickness (d): 32.5 mm is obtained as a result.

  (Step when data obtained by fitting is not valid) It is possible that the result obtained in any of the first and second steps is not physically or empirically valid. It is judged that the setting of the model is not good, and further, the constituent substances of the model are added or changed, a different model is set and fitting is performed again, and the process is repeated until a correct result is obtained. This step is indispensable in reality, but it is an artificial judgment and is not a part of the invention.

Various modifications can be made to the embodiments described in detail within the scope of the present invention. In order to facilitate understanding, Ψ and Δ have been consistently described in relation to data acquisition and model setting. Similar measurements and fittings are possible using the following data pairs well known to those skilled in the art and are within the scope of the present invention.
(N, k), (ε _i , ε _r ), (tan Ψ, cos Δ), (I _s , I _c )
Moreover, although the example which forms one SiON layer on a board | substrate was shown, it can utilize similarly for the measurement of a different multilayer structure, and the measurement of the film thickness of a wide range. The substrate is also exemplified by Si, but other materials (glass, quartz, compound semiconductor, etc.) can be used as well.

  In the example, the fitting is described as fitting all the parameters at the same time. However, the fitting may be performed separately, and this is also included in the technical scope of the present invention. In the example, the fitting is written with a combination of the incident angle and the film thickness, but depending on the software, the incident angle may be fitted simultaneously with the dispersion formula, and this is also included in the technical scope of the present invention.

  Similarly, when the incident angle is fixed without fitting, it is also included in the technical range. In the above-described embodiment, the classical (classical mechanics) formula is used as the dispersion formula. However, other formulas and parameters can be used in the same manner, and these formulas are included in the technical scope of the present invention.

It is a block diagram which shows the structure of the spectroscopic ellipsometer used in step 10 of acquisition of the spectroscopic measurement data of the method of this invention. It is a flowchart for demonstrating the thin film measuring method by this invention.

Explanation of symbols

1 Xe lamp 2 Optical fiber 3 Polarizer 4 Sample 5 Photoelastic modulator (PEM)
6 Analyzer 7 Optical Fiber 8 Spectrometer 9 Data Acquisition Unit 10 Spectroscopic Measurement Step 20 Spectrometric Comparison Data Generation Step 21 Model Comparison Data Generation Step 22 Simulation Step 23 Fitting Step 24 Fitting Process Step 25 One Incidence Angle and Film First step of selecting a combination of thicknesses 26 Fitting step (second step)
27 Result acquisition step 28 Data storage step 29 Confirmation step

Claims (1)

In the ultrathin film and thin film measurement method on the surface of the substrate to be measured using the spectroscopic ellipsometer by the local minimum calculation method (BLMC),
Measurement spectrum Ψ _E (λ _i ) and Δ _E (λ _i ), which is the change in polarization of incident light and reflected light for each wavelength λ _i , is obtained by changing the wavelength of incident light on the thin film on the surface of the substrate to be measured Ψ _E , Δ _E spectrum measurement step;
Assuming that (N ₀ (n ₀ , k ₀ )) of the substrate and (N (n, k)) of the thin film on the substrate are based on a dispersion formula that is a formula showing the wavelength dependence of the dielectric constant of the substance. A plurality of film thicknesses (d ± mΔd) that are further within the expected range, a plurality of mixing ratios (Vf ± mΔVf) that indicate the volume fractions of the mixed substances that are within the expected range, and Setting a plurality of incident angles (φ ± mΔφ) within an expected range and calculating corresponding simulation spectra Ψ _M (λ _i ) and Δ _M (λ _i );
Based on the combination of the incident angle, the mixing ratio, and the film thickness, the parameters of the dispersion equation are fitted, the parameters of the dispersion equation obtained by the fitting are used as the optical constants of the film, and each Ψ calculated from the parameters _The film thickness (d _best ) and the mixture ratio (Vf _best ) in which the difference between Ψ _E (λ _i ) and Δ _E (λ _i ) is the smallest among the _M (λ _i ) and Δ _M (λ _i ) spectra. And a first step of selecting an incident angle (φ _best ) and a dispersion fitting result (DSP _best ),
Using the incident angle (φ _best ) selected in the first step as a definite value, the film thickness (d _best ), the mixing ratio (Vf _best ), and the dispersion formula (DSP _best ) obtained by the fitting are again fitted. An ultra-thin film and a thin-film measurement method on the surface of a substrate to be measured using a spectroscopic ellipsometer based on a minimum value calculation method (BLMC) comprising the second step of selecting the most suitable model.

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