JPH10300432A - Ellipsometry and ellipsometer, shape measuring method, and manufacture of semiconductor device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To approximate a phase slippage and a displacement of principle axis as the function thereof and determine the thickness and refractive index of a thin film from the respective measured values by use of a specified expression (function) by measuring the phase slippage and the displacement of principle axis, and determining the measured values corresponding thereto, respectively. SOLUTION: A possible range of values of the phase slippage (Δ) and displacement of principle axis (Ψ) of a thin film to be applied is limited to a certain area, whereby the precision of approximation can be consequently enhanced to enhance the precision of calculation and measurement of refractive index (n) or thickness (d). As an intended variable, either one of the thickness (d) and the refractive index (n) is selected according to the purpose. The selected refractive index (n) or thickness (d) of the thin film is approximately expressed as the function of Δ and Ψ. Thereafter, within the range where a multiple regression expression is determined, the respective measured values δand ϕ are substituted to the multiple regression expression (IV) to calculate the refractive index (n) or thickness (d) of the thin film. Namely, by measuring Δ and Ψ, the refractive index (n) or thickness (d) of the thin film can be determined by one calculation.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an ellipsometer and an ellipsometer for measuring the thickness and the refractive index of a thin film, and in particular, the values of .DELTA. And .SIGMA. The present invention relates to an ellipsometer and an ellipsometer for obtaining a film thickness and a refractive index of a thin film using a multiple regression equation, and a method for manufacturing a semiconductor device using the ellipsometry.

[0002] In a thin film forming step in semiconductor manufacturing, whether or not the formed thin film is formed as desired,
In particular, it is an important inspection / evaluation item whether or not the formed thin film has a desired film thickness and whether or not it has desired physical properties and composition. For the inspection and evaluation, ellipsometry is often used as a simple and accurate method, and an ellipsometer is used as a device for ellipsometry.

[0003]

2. Description of the Related Art Ellipsometry is a technique in which polarized light is incident on a sample thin film surface to be measured in a slanting direction, the amount of change in the polarization state of reflected light and the amount of change in the polarization state of the previously incident light are determined, and analytical calculation is performed. In this method, the thickness and the refractive index of the sample thin film are determined from the amount of change.

In this case, there are two amounts of change in polarization. One is that when the polarized light is divided into two component waves, a p-component wave on the horizontal P coordinate plane (phase W _p ) and a s-component wave (phase W _s ) perpendicular thereto, reflection causes a reflection between them. This represents the resulting phase shift and is usually shown as Δ in the following equation (I).

[0005]

(Equation 5)

The other amount of change represents a change occurring in the principal axis direction of polarized light, and is usually represented by the following formula (II):
As shown.

[0007]

(Equation 6)

The change in the main axis direction is a p-component wave (intensity A _p )
S component wave (intensity A _s) in reflectance occurs difference in amplitude between the two because the different components (A _s of A _s / incident light and A _p of A _p / incident light of the reflected light reflected light) and This is because a change occurs as the combined polarized light. These Δ and Ψ are actually measured by an ellipsometer using ellipsometry. A thin film (refractive index n, film thickness d) to be evaluated is provided on a base substrate having a refractive index n ₃ , and light having a wavelength λ is emitted. Refractive index n ₁
When the light is incident at an incident angle θ in the atmosphere of the above, the following relational expression (III) is obtained.

[0009]

(Equation 7)

In the right-hand side parameters in the equation (III), n
₃ , λ, n ₁ and θ are known, and the measured Δ value and Ψ
If the value is used, the refractive index n of the thin film to be evaluated as an unknown
And the film thickness d.

[0011]

However, in general, equation (III) cannot be developed into a closed form with respect to the refractive index n or the film thickness d, and therefore, the δ and φ values, which are the actually measured values of Δ and Ψ, are substituted. And cannot be solved directly.
Therefore, conventionally, in order to obtain the refractive index n and the film thickness d corresponding to the measured δ value and φ value, the refractive index and the film thickness are variously changed and substituted into the equation (III) to obtain Δn. And Ψ are calculated, and the corresponding refractive index and film thickness when the calculated values match the actually measured δ and φ values are obtained. These values are used as the refractive index n and the film thickness d of the thin film. Use the method of finding out.

However, when such a method is used, there is a problem that the amount of calculation is large and it takes time to obtain the refractive index n and the film thickness d. In recent years, as the integration of semiconductors has progressed, the number of inspection / evaluation points for thin films on one semiconductor manufacturing substrate has been increasing. For example, the number of inspection / evaluation points for one substrate has reached tens of thousands. This is becoming a natural inspection process.

Under these circumstances, the measurement time that is too long is a problem that cannot be ignored in semiconductor manufacturing, and shortening the measurement time of the refractive index n and the film thickness d is a major problem in ellipsometry and, consequently, evaluation of a thin film on a substrate. . Therefore, an object of the present invention is to provide a new and useful ellipsometer and ellipsometer that solve the above-mentioned problems.

Another object of the present invention is to provide a method for measuring Δ
Value and Ψ value using multiple regression analysis to quickly determine the refractive index n of the thin film
It is an object of the present invention to provide an ellipsometer and an ellipsometer that use a method of calculating the thickness and the film thickness d to reduce the measurement time.

[0015]

According to the first aspect of the present invention,
The parameter of the elliptically polarized light reflected from the surface of the sample on which the thin film measurement is performed, and the phase shift (Δ) defined by the following equation
And the principal axis displacement (Ψ) are measured, and the thickness and the refractive index of the thin film are determined from the corresponding δ and φ values by ellipsometry.
And the thickness and refractive index of the thin film are determined from the δ and φ values using the function.

[0016]

(Equation 8)

[0017]

(Equation 9)

According to a second aspect of the present invention, in the ellipsometry according to the first aspect, a multiple regression equation obtained by multiple regression analysis using the δ value and the φ value is used as the function. The thickness and the refractive index of the thin film are obtained. According to a third aspect of the present invention, in the ellipsometry of the second aspect, the multiple regression equation is a polynomial of Δ and Ψ.

According to a fourth aspect of the present invention, in the ellipsometry according to the third aspect, the polynomial is a third-order polynomial having Δ and Ψ as variables. According to a fifth aspect of the present invention, in the ellipsometer, the phase shift (Δ) and the displacement (Ψ) of the principal axis, which are parameters of elliptically polarized light reflected from the sample surface on which the thin film measurement is performed, are defined by the following equations. Means for obtaining δ and φ values of the corresponding measured values, means for performing multiple regression analysis using the δ and Ψ values, and obtaining a multiple regression equation as a polynomial of Δ and Ψ, Means for determining the thickness and refractive index of the thin film using the equation and the δ and φ values.

[0020]

(Equation 10)

[0021]

[Equation 11]

According to a sixth aspect of the present invention, in the ellipsometer according to the fifth aspect, the multiple regression equation is a third-order polynomial using Δ and Ψ as variables. The invention according to claim 7 is a shape measuring method including a step of obtaining the n number of structural parameters by ellipsometry in a sample having a periodic structure including n number of structural parameters. / 2 times ellipsometry while changing measurement conditions to determine ellipsometric parameters Δ _i , Ψ _i (i = 1 to n / 2); and actually measuring n structural parameters on the standard sample And the step of expressing the n structural parameters as a function of the ellipsometric parameters; and performing ellipsometry on a measurement sample having a periodic structure including the n structural parameters, thereby obtaining ellipsometric parameters Δ _i , Ψ
_i (i = 1 to n / 2); and a step of obtaining a structural parameter of the measurement sample using the function.

According to an eighth aspect of the present invention, in the shape measuring method according to the seventh aspect, the function is an ellipsometric parameter Δ _i , obtained by using the actually measured structural parameter on the standard sample as a target variable. Ψ _i (i = 1 to n /
2) It is obtained by multiple regression analysis using explanatory variables as the variables. According to a ninth aspect of the present invention, in the shape measuring method according to the seventh or eighth aspect, the measurement condition is changed by changing an incident angle, an incident direction, or a wavelength of the light beam on the periodic structure. It is characterized by.

According to a tenth aspect of the present invention, in the shape measuring method according to any one of the seventh to ninth aspects, the structure parameter includes a parameter representing a process condition. An eleventh aspect of the present invention is the shape measuring method according to any one of the seventh to tenth aspects, wherein m of the n structural parameters of the measurement sample are actually measured, and the ellipsometry is measured. Change in measurement conditions is n
/ 2−m or more, and the remaining nm structural parameters are (n / 2−m) or more Δ, (n / 2−m) or more Ψ, and m structural parameters. Approximately expressed by

According to a twelfth aspect of the present invention, in the shape measuring method according to the eighth aspect, when the multiple regression analysis includes an error in an actually measured value of a structural parameter used as an objective variable, the ellipsometry is used. Extracting a constant value of a structural parameter other than the error-containing structural parameter among the obtained ellipso parameters, and using one of the extracted ellipso parameters as an explanatory variable, Performing a simple regression analysis as an objective variable, wherein the multiple regression analysis is performed with the predicted value obtained by the simple regression analysis for the structural parameter including the error as an actual measurement value. And

According to a thirteenth aspect of the present invention, a periodic structure including n structural parameters formed on a standard sample is given by n
/ 2 times ellipsometry is performed while changing the measurement conditions, and the ellipsometric parameters Δ _i , Ψ _i (i = 1 to n / 2)
), A step of actually measuring n structural parameters on the standard sample, a step of expressing the n structural parameters as a function of the ellipsometric parameters, Forming a plurality of patterns to be measured including parameters and forming the periodic structure, and performing ellipsometry on the periodic structure on the semiconductor substrate to obtain ellipsometric parameters Δ _i ,
A step of obtaining Ψ _i (i = 1 to n / 2); and a step of obtaining the structural parameters of a periodic structure on the semiconductor substrate using the function.

According to a fourteenth aspect of the present invention, in the method for manufacturing a semiconductor device according to the thirteenth aspect, the periodic structure is a resist pattern formed on a substrate. According to the first aspect of the present invention, the refractive index n and the thickness d of the thin film, which cannot be expressed as a function of Δ and Ψ, are approximated by Δ
The refractive index n and the film thickness d of the thin film can be obtained by substituting the measured values δ and φ corresponding to Δ and Ψ into the function.

Therefore, the calculation for obtaining the refractive index n and the film thickness d from the δ value and the φ value of the thin film can be completed in one time, and the calculation time in the measurement can be reduced. Therefore, in thin film evaluation, it is possible to provide an ellipsometry having a short measurement time even if the number of measurements is large. According to the second aspect of the present invention, by using a multiple regression equation based on multiple regression analysis using the δ and φ values of the thin film, the refractive index n and the thickness of the thin film that cannot be expressed as a function of Δ and Ψ d can be approximately represented by a function of Δ and Ψ.

Therefore, for the function based on the multiple regression equation,
By substituting the measured values δ and φ corresponding to Δ and Ψ, the refractive index n and the thickness d of the thin film can be obtained. Therefore, the calculation for obtaining the refractive index n and the film thickness d from the δ value and the φ value of the thin film can be completed in one time, and the calculation time in the measurement can be shortened. Ellipsometry can be provided.

According to the third and fifth aspects of the present invention, by using a multiple regression equation based on multiple regression analysis using the δ and φ values of the thin film, the thin film cannot be expressed as a function of Δ and Ψ. Can be approximately represented by the functions of Δ and Ψ. Then, the multiple regression equation is
By using a polynomial of Ψ and Ψ, the approximation of the refractive index n and the thickness d of the thin film to the functions of Δ and Ψ can be made more accurate.

Therefore, the refractive index n based on the δ and φ values of the thin film
The calculation for obtaining the film thickness d and the film thickness d can be completed at one time, the calculation accuracy is high, and the calculation time can be shortened and the measurement can be performed with high accuracy. Therefore, in thin film evaluation,
It is possible to provide an ellipsometer and an ellipsometer that have high accuracy and a short measurement time even when the number of measurements is large. Claim 4
And according to the invention of claim 6, by using a multiple regression equation by multiple regression analysis using the δ value and φ value of the thin film,
The refractive index n and the thickness d of the thin film, which cannot be expressed as functions of Δ and Ψ, can be approximately expressed by functions of Δ and Ψ.

At this time, by making the multiple regression equation a third-order polynomial composed of variables of Δ and Ψ, the approximation of the refractive index n and the thickness d of the thin film to the functions of Δ and Ψ can be made highly accurate. However, the calculation does not become too complicated, and the effect of shortening the calculation time can be maintained. Therefore, the δ of the thin film
The calculation for obtaining the refractive index n and the film thickness d from the value and the φ value can be completed in a single operation, and the calculation accuracy is high. As a result, an ellipsometer and an ellipsometer that can reduce the required time and measure with high accuracy can be obtained. Can be provided.

According to the seventh aspect of the present invention, the various structural parameters of the periodic structure are determined by ellipsometry using the correspondence between the structural parameters determined for the standard sample and the ellipsometric parameters, thereby enabling nondestructive analysis. so,
It is possible to obtain it efficiently. According to the invention of claim 8, it is possible to quickly obtain a function for converting data obtained by ellipsometry into structural data by multiple regression analysis.

According to the ninth aspect of the present invention, it is possible to easily realize a change in ellipsometry measurement conditions required for obtaining various parameters of the periodic structure.
According to the tenth aspect, it is possible to obtain even process parameters by ellipsometry. According to the eleventh aspect of the present invention, the number of changes in the necessary ellipsometry measurement conditions can be reduced by actually measuring a part of the structure data at the time of ellipsometry of the measurement sample. According to the simplification of the twelfth aspect of the invention, when performing multiple regression analysis, even if an error is included in the actual measurement value used as the objective variable,
The error can be removed, and a highly accurate multiple regression equation can be obtained.

According to the thirteenth aspect, by obtaining the structural parameters of the periodic structure by ellipsometry, various line and space patterns formed during the manufacturing process of the semiconductor device can be efficiently and non-destructively. Can be inspected well. According to the fourteenth aspect, the resist pattern on the substrate can be inspected by using ellipsometry.

[0036]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the present invention, the refractive index n or the film thickness d of a thin film, which cannot be expressed as a function of Δ and Ψ, is approximately expressed as a function of Δ and Ψ,
The measured values δ and φ, which are the measured results of Δ and Ψ of the thin film, are substituted into the equation, and can be obtained by calculation.

As an approximation method, the accuracy of the approximation does not greatly affect the accuracy of the measurement result, and as a result, the measurement accuracy is not inferior to that of the conventional ellipsometry. In terms of time, anything that is better than conventional ellipsometry can be used.
As a method most suitable as such a method, there is a method using a multiple regression equation using multiple regression analysis.

The method of applying the multiple regression analysis to ellipsometry is as follows. First, an approximate range of Δ and う る that can be indicated by a thin film to be inspected and measured in a manufacturing process of a target semiconductor or the like is determined, and a multiple regression analysis is performed within the range to obtain a multiple regression equation. In this way, a certain range is specified for all Δ and Ψ ranges at once.
The refractive index n or the thickness d of the thin film is approximately expressed as a function of Δ and Ψ because the thin film to which the present invention is applied and to which ellipsometry is to be applied is determined by a specified type and during a determined manufacturing process. This is a thin film having a thickness, and is expected to exhibit similar characteristics to some extent, so that it covers a wider range than necessary and is wasteful.

That is, as a range of values of Δ and う る that can be taken by the thin film to be applied, the range of values of Δ and Ψ is limited to a certain area. As a result, the accuracy of approximation is further improved, and the calculation and the As a specific method capable of increasing the accuracy of the measurement of the refractive index n or the film thickness d, first, other means,
For example, by conventional ellipsometry, etc., for one or a plurality of thin films having the same Δ and 薄膜 as the thin film to be measured and inspected, the refractive index or the film thickness is measured in advance from several points to several tens of points. And the corresponding δ and φ values are determined.

Then, one of the film thickness d and the refractive index n is selected as the objective variable. At this time, any of them can be selected and can be selected according to the purpose. Next, the refractive index n or the thickness d of the selected thin film is approximated by Δ and Ψ.
As a function of However, in that case, it is not known in advance what function to choose between Δ and Ψ, so it is possible to choose any function between Δ and Ψ. The multiple regression equation to be obtained can be a polynomial equation. As a result, accurate approximation can be performed, and desired results can be obtained.

Therefore, in each case of selecting the film thickness d or the refractive index n, it is desirable to select Δ and Ψ as the explanatory variables and the respective functions and the function consisting of Δ and Ψ. In addition, the dimensions of the variables Δ and 選 択 are selected, and the order of the polynomial is determined so that the calculation does not become too complicated as long as the approximation accuracy can be maintained. It is desirable to choose 2
It is desirable to select the next to fourth order as dimensions of the variables Δ and Ψ.

Next, a multiple regression analysis is performed by using the δ value and φ value corresponding to the film thickness d or the refractive index n of several to several tens of points determined above, and a multiple regression equation is obtained. Then, in order to prevent the calculation from becoming complicated, and to improve the calculation efficiency and speed, among the selected explanatory variables, the change in the value is used to calculate the refractive index n or the film thickness d of the thin film calculated by the obtained multiple regression equation. It is also possible to form a multiple regression equation by using only those that have a large effect and omitting variables that have little effect without using them.

Thereafter, for thin films having δ and φ values within the range obtained by the multiple regression equation, Δ and Ψ were measured,
Substituting the obtained δ value and φ value into the obtained multiple regression equation,
It is possible to calculate the refractive index n or the thickness d of the thin film. In other words, Δ and Ψ are measured, and the refractive index n or the thickness d of the thin film can be quickly obtained by one calculation.

It should be noted that, within the range of Δ and Ψ required for the measurement of the thin film, only one multiple regression equation is obtained, and it is not necessary to use only that formula. The necessary range of Δ and Ψ is subdivided into a plurality of ranges. It is also possible to obtain a multiple regression equation corresponding to the area (1) and select a corresponding area of Δ and か ら from a plurality of multiple regression equations for the evaluation of the thin film and use it in the calculation. In this case, since the applicable range of Δ and Ψ is further narrowed, the accuracy of approximation is further improved, and the accuracy of calculation and hence measurement of the refractive index n or the film thickness d can be further improved.

By the way, in a sample having a periodic structure such as a line and space pattern, if there are n parameters for designating the structure, to obtain the n structural parameters from Δ and Ψ, it is necessary to perform ellipsometry. The measurement conditions are changed by changing the incident angle or the wavelength of the light beam, and Δ and Ψ are measured at least n / 2 times (when n is an odd number, at least n / 2 + ／ times) (Δ ₁ , Δ ₂ ,...).・ ・
_{Δ n / 2, Ψ 1,} Ψ 2, ··· Ψ n / 2). Furthermore the samples having such a periodic structure, structural parameters alpha ₁ by another method, alpha _2, when measured in advance · · · alpha _n,
Ellipsometric parameters (Δ ₁ , Δ ₂ ,... Δn _{/ 2} ,
Ψ ₁ , Ψ ₂ ,... Ψ _{n / 2} ) can be expressed as a function of the structural parameters (α ₁ , α ₂ ,..., Α _n ).
Therefore, if such a function is obtained, the structure parameter can be obtained from the ellipso parameter by solving the function in reverse. In the embodiment described below, such a function is obtained by multiple regression analysis. In the structure parameter obtained by such a method, instead of a specific single value,
The average value of a certain area is obtained, and therefore, it is possible to obtain the average value by one measurement.

[0046]

【Example】

[First Embodiment] As a first embodiment of the present invention, an example will be described in which the film thickness d is represented by a multiple regression equation of Δ and 説明. First, Δ
Regions (1) and (2) were limited to the following ranges. 60 <Δ <90 28 <Ψ <34 Next, regression analysis is performed. Regarding Δ and Ψ corresponding to the target film thickness d, the problem of multicollinearity that reduces the reliability of the multiple regression equation is minimized. In order to avoid this, a combination of (d, Δ, １９) of 19 points having a small correlation between Δ and Ψ was selected.

FIG. 1 shows plots of Δ and Ψ for the 19 points used. As the explanatory variables, cubic expressions of Δ and Ψ were selected.
That is, Δ, Ψ, Δ ² , Ψ ² , ΔΨ, ΔΨ ² , ΨΔ ² , Δ
³ and Ψ ³ were selected. A multiple regression analysis is performed using these explanatory variables, and 変 数, ΔΨ, ΔΨ ² , Δ ³ ,
It was selected Ψ ³ of 5 variables.

The multiple regression equation was as follows. d = 107.03Ψ−2.7445ΔΨ−0.057 Ψ ³ +0.06408 ΔΨ ² +0.00179 Δ ³ +81.029 (IV) Next, the film thickness d is calculated using the multiple regression equation (IV), and the film thickness is approximated. The value was determined. Then, the approximate value was compared with a film thickness actually measured by another reliable method, and the measurement accuracy of the film thickness when multiple regression analysis was used was evaluated.

[0049]

[Table 1]

The approximate difference between the actual film thickness was ± 5 angstroms with 95% reliability. That is, the approximate value obtained by the multiple regression equation is 9 within ± 5 Å for a thin film having a thickness of 600 to 800 Å.
5% was included, demonstrating high accuracy. The multiple correlation coefficient representing the correlation coefficient between the actual value of the film thickness and the approximate value when multiple regression analysis is used is R = 0.
99943, again demonstrating its high accuracy.

Next, in the actual film thickness evaluation, evaluation was performed using the above-mentioned multiple regression equation (IV). By measuring Δ and Ψ of the film to be measured, and substituting the measured values into the multiple regression equation (IV), a highly accurate film thickness value was obtained by one calculation. When the same method was applied to the refractive index of the thin film, a highly accurate refractive index value was obtained by a single calculation, similarly to the case of the film thickness.

Next, as shown in FIG. 2, a thin film sample 4 was formed using a polarizer 1, a quarter-wave (λ / 4) plate 2 and an analyzer 3.
Measuring device 5 comprising a so-called PSCA optical system for measuring
Calculation device (CP) having both the function of calculating the refractive index and the film thickness from Δ and に よ る according to the conventional method and the function of obtaining the refractive index and the film thickness by the multiple regression analysis according to the present invention.
U) An ellipsometer 11 consisting of 7 was prepared.

A number of refraction indices and film thicknesses corresponding to the measurement of a substrate thin film in a semiconductor manufacturing process or the like performed using the ellipsometer 11 will be described. In each measurement, linearly polarized light is incident on the sample thin film from the polarizer 1 of the measuring device 5 of the ellipsometer 11 and elliptically polarized light reflected from the sample is detected by the detector 6, and the shape of the detected elliptically polarized light is detected. Then, the CPU 7 calculates Δ and 試 料 of the sample thin film, and obtains corresponding measured values of δ and φ.

The above measurement is performed many times, and a combination of several to several tens of points is selected from a large number of combinations of the actually measured values δ and φ obtained by the many measurements. The combination of the refractive index and Δ and 若 し く は or the combination of the refractive index and Δ and Ψ is obtained by the function of calculating the refractive index and the thickness from Δ and に よ る according to the conventional method provided in the CPU 7.

Next, using these combinations, C
Multiple regression analysis is performed by PU7, and a multiple regression equation is obtained as a third-order polynomial of Δ and Ψ. After the multiple regression equation is determined, the measured values δ and φ values that have already been obtained, and the actually measured values δ and φ values measured after that, the refractive index of the corresponding thin film using the multiple regression equation and Find the film thickness. In order to find the multiple regression equation, the refractive index and the film thickness were not calculated by the conventional method as described above, and Δ and Ψ were measured for a sample thin film having a known refractive index and a value in an appropriate range. It is also possible to obtain a multiple regression equation using a combination of a known refractive index or film thickness, an actual measurement value δ value, and a φ value. In this case, in the ellipsometer, the function of calculating the refractive index and the film thickness from Δ and Ψ in the conventional method in the CPU 7 may be omitted, and only the function of obtaining the refractive index and the film thickness by the multiple regression analysis according to the present invention may be used. .

Further, the multiple regression equation is stored in the CPU 7, and the multiple regression equation is not obtained in a normal manufacturing process or the like. It is also possible to calculate the refractive index and the film thickness of the thin film by using the δ value and the φ value obtained by the container, and to cope with the thin film evaluation. Next, the thickness of the sample thin film was actually measured using the ellipsometer according to the present example.

In the measurement, the same combination of 19 points (actual film thickness d, Δ, Ψ) as in the above example was used for the multiple regression analysis, and the multiple regression equation was the same as equation (IV). After that, measurement was performed on the sample thin film of unknown thickness. As a result of the measurement, a high-precision film thickness was obtained by a single calculation using the δ and φ values that are the actual measured values of Δ and に よ る. Value or refractive index value was obtained, and the calculation time was shortened and the measurement time was shortened as compared with the conventional ellipsometer. [Second Embodiment] Next, an example in which ellipsometry is used to determine the structural parameters of a periodic structure formed on a substrate will be described as a second embodiment of the present invention.

FIG. 3 shows an experiment according to a second embodiment of the present invention.
The configuration of the sample 20 used in the above is shown. Please refer to FIG.
In addition, the sample 20 has a registration formed on the Si substrate 21.
By performing electron beam exposure and development of the strike film,
0.3 μm pitch line and space pattern 22
Are formed. When exposing, use an electron beam
By changing the size, the resist pattern 21
The width is changed in the range of 0.1 to 0.2 μm,
Doses of 80, 100, 110 and 120 μC / cm ^Two
And change it in four ways. 25 combinations in total
A sample corresponding to the above was prepared.

FIG. 4 shows distributions of Δ and Ψ obtained by applying ellipsometry to the samples corresponding to the above 25 combinations using the apparatus of FIG. Next, SEM
With respect to the 25 samples, the resist pattern width L was measured, the target variable was L, and the explanatory variables were Δ, Ψ, Δ
As a result of performing multiple regression analysis with Ψ, Δ ² and Δ / Ψ,
The following multiple regression equation was determined. L = −0.0229Δ + 0.01833Ψ−2.392
× 10 ^-4 Ψ ² + 0.2797Δ / Ψ + 2.0450 × 1
0 ^-4 ΔΨ + 0.4906 However, the multiple regression equation above, term delta ² as a result of the T-test, since inconclusive that does not affect the purposes variable is omitted.

FIG. 5 and Table 2 show the relationship between the predicted value of the line width L based on the above multiple regression equation and the actually measured value by the SEM.

[0061]

[Table 2]

As can be seen from FIG. 5, the predicted value of the line width L and the measured value linearly correspond to each other. As can be seen from Table 2, the error (error / measured value) normalized by the measured value is It is at most 5% or less. In FIG. 5, the multiple correlation coefficient R is 0.99349, which is very good. The relationship between FIG. 5 and Table 2 shows that in the line and space pattern of FIG. 3, the line width L of the resist pattern can be represented by parameters Δ and Ψ obtained by ellipsometry. Conversely, by using the multiple regression equation described above, ellipsometry is applied to the measured sample having the same periodic line and space pattern as in FIG. 3, and from the parameters Δ and Ψ obtained as a result, S
Without performing EM measurement, the line width L of the sample to be measured
Means that it can be easily back calculated. Third Embodiment FIG. 6 shows the structure of a sample 30 used in an experiment according to a third embodiment of the present invention.

Referring to FIG. 6, a line and space pattern 32 having a pitch of 5 μm is formed on sample 30 by subjecting a resist film formed on Si substrate 31 to electron beam exposure and development. In the experiment of this embodiment, the electron beam dose at the time of exposure was 204 μC / c.
By changing m ⁻² , 170 μC / cm ⁻² and 136 μC / cm ⁻² , three types of samples having different doses were produced. Further, in the samples of each dose amount, the line width L of the line and space pattern was variously changed.

Next, Δ and Ψ were determined by applying ellipsometry using the apparatus of FIG. 2, and multiple regression analysis was performed on the resist pattern width L actually measured by SEM using these. However, at the time of the multiple regression analysis, only significant explanatory variables were selected by the T test, and as a result, the following multiple regression equation was obtained. L = −0.001118ΔΨ + 0.004005Ψ +
0.163487 FIG. 7 and Tables 3 to 5 show the relationship between the predicted value of the line width L based on the above-mentioned multiple regression equation and the actually measured value by the SEM.

[0065]

[Table 3]

[0066]

[Table 4]

[0067]

[Table 5]

As can be seen from FIG. 7, the predicted value of the line width L and the measured value linearly correspond to each other as in FIG. 5, and as can be seen from Table 3, the error (error /
(Measured value) is almost 2% or less, and at most 3.5% or less. In FIG. 7, the multiple correlation coefficient R is 0.9966.
7, which is even better than the case of FIG. FIG.
And the relationship between Table 3 and FIG.
In the line and space pattern of FIG. 6, the line width L of the resist pattern can be represented by parameters Δ and Ψ obtained by ellipsometry. This means that, conversely, by using the multiple regression equation, ellipsometry is applied to the sample to be measured, and from the obtained parameters Δ and Ψ, without performing SEM measurement,
This means that the line width L can be easily calculated backward.

The above-mentioned multiple regression equation is different from the multiple regression equation described above with reference to FIG. 5 because the pitch and exposure dose of the line and space pattern 32 in FIG. 6 are different from those in FIG. . That is, since the multiple regression equation changes each time the condition changes, it is necessary to obtain the condition for each condition. Fourth Embodiment FIG. 8 shows the structure of a sample 40 used in a fourth embodiment of the present invention.

Referring to FIG. 8, the sample 40 is a Si substrate 4
1, an HTO film 42 formed on a Si substrate 41, an SiN film 43 formed on the HTO film 42,
A line and space resist pattern 44 having a width W is formed on the iN film 43 at a uniform pitch. In this embodiment, the thickness t ₁ of the HTO film 42 is
Using the thickness t ₂ of the N film 43 and the pattern width W as structural parameters, 740 to 840 ° and 140 to 240, respectively.
Å and samples varied in the range of 0.30 to 0.37 μm were prepared.

In this embodiment, since the structural parameters include the film thicknesses t ₁ and t ₂ in addition to the width W, these three
Are obtained by ellipsometry.
It cannot be expressed only by the number of parameters (Δ, Ψ). For this reason, in this embodiment, ellipsometry measurement conditions are changed in three ways corresponding to the three structural parameters, and ellipsometry is executed for each of the three conditions. For example, in this embodiment, in the ellipsometer of FIG. 2, the incident angles of the incident light beam are changed to 55 °, 65 °, and 75 °, and ellipsometry is performed for each incident angle.

The Δ and the obtained at each incident angle
And (Ψ₁, Ψ₁), (Δ_Two, Ψ _Two) And (Δ_Three,
Ψ_Three), The film thickness t₁, Film thickness t_TwoAnd pattern width
For each of W_i, Ψ_i, Δ_i× Δ_j, Δ_i× Ψ
_j. Ψ_i× Ψ_j, Δ_i/ Ψ_j(I = 1 to 3, j = 1 to
A multiple regression equation with 3) as an explanatory variable is obtained. For example,
The multiple regression equation using the turn width W as an objective variable is: W = −0.00331Ψ_Three+ 0.48138Δ_Three/ Ψ_Two
+0.512903, and the multiple correlation coefficient R was 0.97374.

That is, the above-mentioned relationship is obtained by obtaining Ψ ₂ , Ψ ₃ and Δ ₃ for the sample to be measured having a periodic structure similar to the line and pattern having the configuration of FIG. it can. Generally, when there are a plurality of structural parameters of a periodic structure, for example, n,
If is an even number, it is necessary to perform ellipsometry by changing the measurement conditions at least n / 2 times, and to determine Δ and Ψ for each condition (when n is an odd number, at least n / 2 + ／ times) It is necessary to change the measurement).

Further, among the n structural parameters,
If m things are obtained in advance by another method,
The number of ellipsometry measurement conditions can be reduced to (n / 2-m) (or n / 2-1 / 2 when n is an odd number). In this case, the remaining nm structural parameters are approximately represented by n / 2-m or more Δ and n / 2-m or more Ψ, and m actually measured parameters. [Fifth Embodiment] By the way, in the second embodiment,
In establishing the relationship of FIG. 5, it is assumed that the line and space pattern 22 of the sample 20 of FIG. 3 is actually measured by SEM. However, the actual measurement of the line and space pattern by the SEM generally involves some errors. Therefore, in the present embodiment, in obtaining the multiple regression equation, such an error accompanying the actual measurement of the pattern width by the SEM is removed, and the accuracy of the predicted value when ellipsometry is applied to the sample to be measured is improved. With the goal.

When applying the ellipsometry to the sample 20 of FIG. 3 and keeping the exposure dose constant and changing only the line width L, the obtained distributions of Δ and Ψ are smooth as shown in FIG. Draw a simple curve. FIG. 9 shows an example in which the exposure dose is set to 120 μC / cm ² . Therefore, in the present embodiment, of the data obtained by performing ellipsometry on the sample in which the line width and the dose amount are variously changed, only the data with a constant dose amount is extracted. , A simple regression analysis is performed using the SEM actual measurement value of the line width L as an objective variable and Ψ as an explanatory variable.

FIG. 10 shows that the dose is set to 120 μC / cm ^2.
2 shows a simple regression curve when set to. Referring to FIG. 10, the measured value of the line width L fluctuates above and below the regression curve, but the true line width L should lie on a smooth curve. Is considered to indicate an error of the actually measured value.

[0077] Therefore, in this embodiment, further exposure dose to ^{80μC / cm 2, 100μC / cm} 2, 110μ
C / cm ² and the above single regression analysis is performed for each exposure dose. By using the regression equation thus obtained, a predicted value of the line width is obtained for each exposure dose. Further, when the multiple regression analysis described in the second embodiment is performed using the predicted value of the line width obtained in this manner, the obtained multiple correlation coefficient is R in the case of the second embodiment. From 0.9934 to 0.99933, and the standard deviation σ of the predicted value is also from 3.7 nm to 1.2 n.
m. That is, according to such a procedure, when performing the regression analysis, an error included in the objective variable is removed, and a highly accurate multiple regression equation is obtained.

Although the present invention has been described with reference to preferred embodiments, the present invention is not limited to such specific embodiments, and various modifications and alterations are possible within the scope of the appended claims. is there.

[0079]

According to the first aspect of the present invention, the calculation of the refractive index n and the thickness d from the δ and φ values of the thin film by the actual measurement of Δ and Ψ is completed in one operation, and the calculation time in the measurement is reduced. It can be shortened. Therefore, in thin film evaluation, it is possible to provide an ellipsometry having a short measurement time even if the number of measurements is large.

According to the second aspect of the present invention, the refractive index n and the film thickness d are obtained by using a multiple regression equation based on multiple regression analysis.
Is completed in one measurement, and the calculation time can be shortened. In thin film evaluation, ellipsometry with a large number of measurements and a short measurement time can be provided. According to the third and fifth aspects of the present invention, by using a multiple regression equation which is a polynomial of Δ and に よ る by multiple regression analysis, the refractive index n and the film thickness d from the δ and φ values of the thin film can be calculated. The calculation required is completed in one time. Then, the calculation accuracy is high, and the measurement time can be reduced and the measurement can be performed with high accuracy.

Therefore, in the thin film evaluation, it is possible to provide an ellipsometer and an ellipsometer which have high accuracy and a short measurement time even if the number of measurements is large. Claims 4 and 6
According to the invention described above, the multiple regression equation based on the multiple regression analysis is a cubic polynomial composed of variables of Δ and 、, thereby approximating the refractive index n and the thickness d of the thin film to the functions of Δ and Ψ. While keeping the accuracy high, without making the calculation too complicated,
It is possible to maintain the effect of shortening the calculation time.

Therefore, it is possible to provide an ellipsometer and an ellipsometer that can reduce the required time and perform highly accurate measurement. According to the invention of claim 7, by ellipsometry, various structural parameters of the periodic structure are used in a non-destructive and efficient manner by using the correspondence between the structural parameters obtained for the standard sample and the ellipsometric parameters. It will be possible to get better.

According to the eighth aspect of the present invention, a function for converting data obtained by ellipsometry into structural data can be quickly obtained by multiple regression analysis. According to the ninth aspect of the present invention, it is possible to easily realize a change in ellipsometry measurement conditions necessary for obtaining various parameters of the periodic structure. According to the tenth aspect, it is possible to obtain even process parameters by ellipsometry.

According to the eleventh aspect of the present invention, it is possible to reduce the number of changes in the required ellipsometry measurement conditions by actually measuring a part of the structure data at the time of ellipsometry of the measurement sample. According to the invention of claim 12, the measurement is simplified, when performing multiple regression analysis,
Even when an error is included in the measured value used as the objective variable, the error can be removed, and a multiple regression equation with high accuracy can be obtained.

According to the thirteenth aspect of the present invention, by obtaining the structural parameters of the periodic structure by ellipsometry, various line and space patterns formed during the manufacturing process of the semiconductor device can be efficiently and non-destructively. Can be inspected well. According to the fourteenth aspect, the resist pattern on the substrate can be inspected by using ellipsometry.

[Brief description of the drawings]

FIG. 1 is a diagram plotting Δ and Ψ corresponding to film thickness values used for multiple regression analysis in an example of the present invention.

FIG. 2 is a diagram schematically illustrating a main configuration of an ellipsometer according to an embodiment of the present invention.

FIG. 3 is a diagram showing a configuration of a sample used in a second embodiment of the present invention.

FIG. 4 is a diagram showing an example of ellipsometric parameters obtained for the sample of FIG.

5 is a diagram showing a correspondence between an actually measured value of a pattern width and a predicted value obtained by ellipsometry, obtained for the sample of FIG. 3;

FIG. 6 is a diagram showing a configuration of a sample used in a third embodiment of the present invention.

FIG. 7 is a diagram showing a correspondence between an actually measured value of a pattern width and a predicted value by ellipsometry, obtained for the sample of FIG. 6;

FIG. 8 is a diagram showing a configuration of a sample used in a fourth embodiment of the present invention.

9 shows Δ and Ψ appearing at a specific exposure dose for the ellipsometric parameters obtained for the sample of FIG.
FIG. 6 is a diagram showing a smooth relationship between

FIG. 10 shows the results of a simple regression analysis performed on the ellipsometric parameters obtained for the sample of FIG.

[Description of Signs] 1 Polarizer 2 λ / 4 plate 3 Analyzer 4 Thin film sample 5 Measuring instrument 6 Detector 7 CPU 11 Ellipsometer 20, 30, 40 Sample 21.31, 41 Substrate 22, 32, 44 Resist pattern 42 Oxidation Film 43 nitride film

Claims (14)

[Claims] 1. A parameter of elliptically polarized light reflected from the surface of a sample on which a thin film measurement is performed, wherein a phase shift (Δ) and a displacement (薄膜) of a main axis defined by the following equation are measured, and corresponding measured values are respectively measured. In ellipsometry for determining the film thickness and refractive index of the thin film from the δ and φ values of the above, the film thickness and the refractive index are approximated as functions of Δ and 、, and the δ value and φ are Ellipsometry, wherein the thickness and the refractive index of the thin film are determined from the values. (Equation 1) (Equation 2) 2. The ellipsometry according to claim 1, wherein a multiple regression equation obtained by multiple regression analysis using the δ value and φ value is used as the function, Ellipsometry characterized by determining the refractive index. 3. The ellipsometry according to claim 2, wherein said multiple regression equation is a polynomial of said Δ and Ψ. 4. The ellipsometry according to claim 3, wherein said polynomial is a third-order polynomial having said Δ and Ψ as variables. 5. A phase shift (Δ) and a displacement (Ψ) of a main axis, which are parameters of elliptically polarized light reflected from a sample surface on which a thin film measurement is performed, defined by the following equations, and correspond to actual measured values, respectively. Means for obtaining a δ value and a φ value of; a means for performing a multiple regression analysis using the δ value and the Ψ value to obtain a multiple regression equation as a polynomial of the Δ and Ψ; an ellipsometer comprising means for determining the thickness and refractive index of the thin film using the φ value. (Equation 3) (Equation 4) 6. The ellipsometer according to claim 5, wherein the multiple regression equation is a third-order polynomial with Δ and Ψ as variables. 7. A shape measuring method including a step of obtaining the n number of structural parameters by ellipsometry in a sample having a periodic structure including n number of structural parameters, wherein the periodic structure on a standard sample is n / 2 the times of ellipsometry, run while changing the measurement conditions, ellipsometric parameters delta _i, [psi _i and (i = 1~n / 2) obtaining a step of actually measuring the n-number of structural parameters of the upper standard sample Expressing the n number of structural parameters as a function of the ellipsometric parameter; and performing ellipsometry on a measurement sample having a periodic structure including the n number of structural parameters, thereby obtaining ellipsometric parameters Δ _i , Ψ _i (I = 1 to n / 2); and using the function to determine a structural parameter of the measurement sample. Condition measurement method. 8. The function is obtained by using an actually measured structural parameter on the standard sample as a target variable, and ellipsometric parameters Δ _i , Ψ _i (i = 1 to n) obtained for the standard sample.
The shape measuring method according to claim 7, wherein the shape measuring method is obtained by multiple regression analysis using (/ 2)) as an explanatory variable. 9. The shape measuring method according to claim 7, wherein the measurement condition is changed by changing an incident angle, an incident direction, or a wavelength of the light beam on the periodic structure. . 10. The apparatus according to claim 7, wherein said structural parameters include parameters representing process conditions.
The method for measuring a shape according to any one of the claims. 11. In the measurement sample, among the n structural parameters, m parameters are actually measured, and the change in the measurement conditions of the ellipsometry is set to n / 2−m times or more, and the remaining nm Number of structure parameters are (n / 2−
11. The method according to claim 7, wherein m) or more Δ, (n / 2−m) or more 近似, and m structural parameters are approximately represented. Shape measurement method. 12. The multiple regression analysis, when an error is included in a measured value of a structural parameter used as an objective variable, among ellipso parameters obtained by the ellipsometry, other than a structural parameter including the error. Extracting a constant structural parameter value, and performing a simple regression analysis using one of the extracted ellipso parameters as an explanatory variable, and using the structural parameter including the error as an objective variable. 9. The shape measuring method according to claim 8, wherein the regression analysis is performed by using a predicted value obtained by the simple regression analysis with respect to the structural parameter including the error as an actually measured value. 13. An ellipsometry of n / 2 times is performed on a periodic structure including n structural parameters formed on a standard sample while changing measurement conditions to obtain ellipsometric parameters Δ _i , Ψ _i (I = 1 to n / 2), a step of actually measuring n structural parameters on the standard sample, a step of expressing the n structural parameters as a function of the ellipsometric parameter, Forming a plurality of patterns to be measured on the substrate including the n structural parameters to form the periodic structure; and performing ellipsometry on the periodic structure on the semiconductor substrate to obtain ellipsometric parameters Δ _i , Ψ
_i . A method of manufacturing a semiconductor device, comprising: determining _i (i = 1 to n / 2); and determining the structural parameters of a periodic structure on the semiconductor substrate using the function. 14. The method according to claim 13, wherein the periodic structure is a resist pattern formed on the semiconductor substrate.