JP3293211B2 - Laminate film evaluation method, film evaluation apparatus and thin film manufacturing apparatus using the same - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION In the field of semiconductors, liquid crystal displays, or magnetic files, non-destructively evaluate the thickness, density, and interface state of each layer of materials and devices with multiple layers laminated on a substrate. The present invention relates to a method for evaluating a laminate by an X-ray reflectivity method which is suitable for the above.

[0002]

2. Description of the Related Art In many fields such as semiconductors, materials and elements in which a number of thin films are laminated on a substrate are used. Since the thickness and density of the formed film, or the state of the interface often affect the characteristics, it is important to control the film with high accuracy. For that purpose, accurate evaluation of these is essential.
For this reason, the film thickness and film quality have been conventionally evaluated by various methods. For example, methods such as a probe method, cross-sectional observation observation with an electron microscope, and ellipsometry are generally used. In recent years, attempts have been made to evaluate film thickness and film quality from X-ray reflectance.

[0003] Among them, a method using X-ray reflectivity can be performed in the air, a system having no transparency to light, for example, Si.
It is possible to evaluate the film thickness and interface state in a system in which a metal film is formed on a substrate or a glass substrate, and there is an advantage that the sample is not destroyed. However, when a multi-layer thin film is formed on a substrate, the X-ray reflectivity profile becomes very complicated and the film thickness starts, and accurate analysis of the reflection profile is required for accurate evaluation of density and interface state It is. For this reason, the paper “K. Sakurai and A. Iida: Jpn.J. Appl. Phys. 31 (1
992) L113 ”, and a method using curve fitting between experimental reflectance and theoretical reflectance to evaluate density and interface state (for example, JM Baribeau: Appl.
Phys. Lett. 57 (1990) 1748).

[0004]

As described above, the evaluation of thin films by X-ray reflectivity can be applied to any object, and the Fourier transform method and curve fitting method as analysis methods are very difficult to obtain film thickness and the like. It is valid. Among these analysis methods, it is most important to accurately extract the vibration structure occurring in the X-ray reflectivity in the Fourier transform method, and to the true value as the initial value with the correct film structure model in the curve fitting method as the initial value. It is important to set close values and to be able to fit only arbitrary parameters. However, in the conventional method, X
In extracting a vibration structure occurring in the linear reflectance, a baseline is applied by a function such as a polynomial, and correction is performed by this. For this reason, there is a problem that a good baseline cannot always be obtained over the entire measurement area depending on the function used, and that it takes time. Further, in the conventional curve fitting, calculation is performed while changing parameters by trial and error, so that there is a problem that much time is required.

An object of the present invention is to provide a method for efficiently obtaining a baseline for extracting a vibration structure in a short time and with the judgment of an analyst when performing an analysis by Fourier transform. Secondly, it is an object of the present invention to provide an analysis method in which fitting parameters are freely selected when performing analysis by curve fitting so that a highly reliable result can be obtained.

[0006]

An analysis method of the present invention for achieving the above object will be described below.

First, in a method of obtaining a baseline prior to Fourier transform, when calculating an arbitrary base, an equal average of a plurality of points on both sides of the point is calculated and used as a base value of the point. Do. Although the measurement points used for averaging are insufficient at the end, the averaging is performed by excluding the insufficient points. This process can be repeated an arbitrary number of times, and the result is displayed on the display once or every predetermined number of times, so that the analyst can determine whether or not to perform an even average. It is characterized by making the algorithm such that

In the second curve fitting method, a value obtained by a Fourier analysis in advance is set as an initial value, and an algorithm that allows an analyst to arbitrarily select a parameter to be fitted and a parameter to be fixed. It is characterized by the following.

According to the present invention, the average of the X-ray reflectivities at the measurement points is obtained.
Repeating the averaging process an arbitrary number of times
Displays the result of the averaging process every time the averaging process is performed
And whether to perform further averaging by external input.
To perform the averaging process
If the averaging process is repeated
And average if you choose not to perform averaging.
Outputting the result of the average processing as a baseline
And X-ray reflectance pattern by the output baseline
Correcting the vibration component and extracting the vibration component; and
And Fourier transforming the vibration component.
This is a characteristic X-ray reflectance analysis method.

Further, the present invention relates to the above X-ray reflectance analysis method.
Average processing to find the average of X-ray reflectivity
X-ray reflectance analysis method characterized by using
is there.

Further, the present invention relates to the above-mentioned X-ray reflectance analysis method.
In addition, the averaging process for obtaining the average of the X-ray reflectance is a weighted average
Or a combination of weighted average and even average
X-ray reflectance analysis method, characterized in that
You.

Further, the present invention relates to the above-mentioned X-ray reflectance analysis method.
In the above, the step of Fourier transforming the vibration component includes:
First, fast Fourier transform is performed, and the result of fast Fourier transform is obtained.
X-ray characterized by performing a Fourier transform based on the result
This is a reflectance analysis method.

Further, the present invention provides an X-ray reflectivity analysis method as described above.
The thickness of each layer of the laminate determined using
X-ray refractive index and interface roughness
X-ray incident angle of the laminate based on physical parameters such as
Calculating the X-ray reflectivity for
Measured X-ray reflectivity and calculated X-ray reflectivity
To the nonlinear least-squares fitting method based on the emissivity
The film thickness of the laminate, the refractive index for X-rays, and the interface
Obtaining physical parameters such as funnels.
This is an X-ray reflectivity analysis method characterized by the following.

Further, the present invention relates to the above-mentioned X-ray reflectance analysis method.
In the above, the film thickness of each layer of the obtained laminate is given in advance.
Index of refracted X-rays and interface roughness given
Displaying a list of physical parameters such as nesting,
From the displayed list of physical parameters,
The physical parameters to be optimized by the fitting method
Steps and optimized physical parameters as initial values
Selected using a non-linear least squares fitting method
Obtaining a physical parameter.
X-ray reflectance analysis method.

Further, the present invention relates to a thin film manufacturing apparatus,
Repeat the average processing of the X-ray reflectivity at the measurement point any number of times
Display means for displaying the result of the averaging process, and the displayed result
To select whether to perform further averaging based on the results.
A means to determine the baseline using the algorithm and the measured
Based on the obtained X-ray reflectivity and the baseline
Means for extracting a vibration component of the measured X-ray reflectivity
And means for performing a Fourier transform on the extracted vibration component.
A thin film manufacturing apparatus characterized in that:

Further, the present invention relates to the above thin film manufacturing apparatus.
And the film thickness obtained by the Fourier transform method
Index of refraction for given X-rays,
X-ray incidence on laminate based on physical parameters such as funes
Means for calculating the X-ray reflectivity for the angle by calculation;
X-rays determined by calculation and X-ray reflectivity determined
Nonlinear least squares fitting method based on reflectance
The thickness of the laminate, the refractive index for X-rays, and the interface
Means for determining physical parameters such as roughness
Feedback physical parameters to the deposition conditions
And means for controlling the process.
This is a thin film manufacturing apparatus.

Further, the present invention relates to an X-ray reflectometer.
Averaging the X-ray reflectivity at the measurement point an arbitrary number of times
Display means for displaying the result of the averaging process.
Using an algorithm that can select whether to perform averaging
Means to determine the baseline by using the measured X-ray reflectivity
And X measured based on the determined baseline
Means for extracting a vibration component of the linear reflectance, and the extracted vibration
Means for Fourier transforming the components.
X-ray reflectometer.

Further, the present invention provides the above-mentioned X-ray reflectance measuring apparatus.
In, the film thickness obtained by the Fourier transform method,
Index of refraction for a given x-ray, and given
Based on physical parameters such as interface roughness,
A method for calculating the X-ray reflectivity with respect to the X-ray incident angle by calculation
Step, measured X-ray reflectivity and calculated
Based on the X-ray reflectivity, a nonlinear least squares fite
The thickness of the laminate, the refractive index for X-rays, and the
And means for determining physical parameters such as interface roughness.
An X-ray reflectivity measuring apparatus characterized by having:

Further, the present invention relates to the above-mentioned X-ray reflectance analysis method.
In addition, for a laminate in which a plurality of films are laminated, an X-ray counter
Based on physical parameters such as film thickness obtained by emissivity analysis
And calculate the X-ray reflectivity of the laminate with respect to the X-ray incidence angle.
And the measured X-ray incidence angle
Based on the X-ray reflectivity and the calculated X-ray reflectivity
Of the stack by the nonlinear least squares fitting method
Thickness, refractive index to X-rays, interface roughness, etc.
Determining a logical parameter.
X-ray reflectance analysis method.

Further, the present invention relates to an X-ray reflectometer.
Averaging the X-ray reflectivity at the measurement point an arbitrary number of times
Means to repeat and averaging every time averaging is performed any number of times
Display means for displaying the result of the
Means for selecting whether or not to perform averaging processing;
If averaging is selected, further averaging is optional.
To repeat the number of times and not to perform averaging
Output the result of averaging as a baseline
Means and X-ray reflectivity by the output baseline
Means for correcting a pattern and extracting a vibration component, and a vibration component
Means for outputting the result of Fourier transform of
Calculate physical parameters such as film thickness based on the result
Based on the means and the physical parameters such as the determined film thickness
By calculating the X-ray reflectivity for the X-ray incident angle of the laminate
Means for obtaining the calculated X-ray reflectivity and calculation.
Nonlinear least squares fit based on the measured X-ray reflectivity
The thickness of the laminate, the refractive index for X-rays,
And means for determining physical parameters such as interface roughness
An X-ray reflectometer comprising:

[0021]

According to the present invention, the above object is achieved by the following operations.

FIG. 1 shows a procedure for obtaining a baseline in Fourier analysis and performing Fourier transform using the baseline.

FIG. 2 shows the result on the display in the process of obtaining the baseline. At the first stage, the vibration structure still remains at the baseline, and it is easily understood that the vibration structure is inappropriate as the baseline. Further, the uniform averaging is repeated, and at the third stage, the baseline is smooth over the entire measurement range, which indicates that this is sufficient. Thereafter, if the measured value is corrected with this baseline, the vibration structure can be extracted over the entire reflectance profile, and a more correct Fourier transform can be performed.

Next, the procedure of the second curve fitting method is shown in FIG. When setting the initial value, it is used that all parameters relating to the film are positive. That is, a minus sign is given to an initial value of a parameter to be fixed, and a plus sign is given to a parameter to be fitted. After reading these initial values by the analysis program, the sign is determined, only the + sign is taken out, a new number is given, and the values are sequentially rearranged. After that, it is possible to optimize only the fitting parameters by a normal fitting program, for example, a nonlinear least-squares fitting method using the Marquardt method.

[0025]

【Example】

Example 1 As an example of the X-ray reflectivity analysis method according to claim 1, a carbon film is formed by sputtering on a fused quartz substrate having a copper film having a thickness of about 80 nm formed on the surface by vapor deposition. And the thickness of the copper film.

The measurement of the X-ray reflectivity is performed by using a Cu target as an X-ray source, separating the generated X-ray Ge (111)
and the incident X-ray taken out uKα _1. The measurement angle range is 0.
The angle was 1 ° to 1.1 °, the angle step was 0.001 °, and the number of measurement points was 1001. FIG. 1 is a flowchart showing an example of a data processing procedure of the present method. FIG. 3 shows an angle dependence curve 1 of the reflectance obtained by normalizing the measured X-ray reflection intensity by the total reflection intensity.

The reflectance curve 1 shown in FIG.

[0028]

(Equation 1)

From equation (1), the X-ray reflectance curve shows a carbon film,
Vibration components resulting from the layer structure of the copper film and the carbon film + the copper film are superimposed. The thickness d of each layer and the refractive index δ contribute to the period of these vibration components.

In analyzing these vibration components by the Fourier transform, since the structure other than the vibration components hinders the analysis, the components other than the vibration components are removed by baseline correction.

Here, the measured value of the reflectance curve 1 is represented by a data set of {N} points {θ _n , R (θ _n ), where n = 1, N}. X-ray reflectance curve R (theta _n) baseline curve B (θ _n) as the number 2 for the R a (theta _n) obtained by equally average.

[0032]

(Equation 2)

In equation (2), by increasing L, the smoothing efficiency can be improved, but the amount of calculation theoretically increases. However, by adopting an equal average instead of a weighted average, the equation (3) is obtained. B (θ _n ) can be obtained very quickly because the relational expression of ( ₁ ) can be used and efficiency can be improved.

[0034]

(Equation 3)

In Equation 2, n <L and n> NL
In the calculation of B (θ _n ) in the vicinity of the end point where L (θ _{n + a} ) before and after L used for averaging are not uniform, (2L +
1) It is not possible to take an even average at a point. Therefore, in the present embodiment, the average is calculated by excluding the missing parts.
That is, at the end points of n = 1 and n = NL, B (θ _n ) is obtained by averaging (L + 1) data. In addition, in addition to the above, L values are supplemented before the end point to make (2L + 1) in the entire area.
It is also possible to use a method of taking an even average at points.

Now, since B (θ) is the baseline,
It is not desirable to include information on the periodic structure that is useful for analysis. However, in reality, it is not rare that the periodic structure remains in B (θ) in one equal average calculation. Therefore, as shown in Expression 4, the average of the baseline curve B (θ) is repeatedly taken to calculate a baseline that does not include the periodic structure.

[0037]

(Equation 4)

FIG. 4 shows an example in which L = 12 and 25 points are averaged equally. Baselines 2, 3, and 4 in FIG. 4 are baselines when the number of repetitions m is 3, 6, and 9, respectively. Baselines 3 and 4 are intentionally shifted downward. As shown in FIG. 2, the profile of such an intermediate baseline is displayed on the screen so as to be superimposed on the X-ray reflectance measurement result, and an operator is inquired whether the baseline is sufficient. At this time, the result corrected by the baseline at that stage can also be displayed as a criterion. In the first stage of FIG. 2, since the periodic structure still remains, the operator inputs NO in response to the question as to whether or not the baseline is sufficient, and continues the uniform averaging. This is repeated, and when the third stage is reached, the baseline is smooth over the entire measurement range. If the operator inputs YES at this time, the correction is performed according to Equation 5, and the vibration structure is extracted. You.

[0039]

(Equation 5)

The reason for taking the log value in Equation 5 is, in part, to bring the center of the vibration structure closer to zero level for the purpose of purely extracting the vibration component.

Although an example has been shown in which an operator's judgment is required so that any system can be flexibly dealt with,
It is of course possible to make the computer determine the validity of the obtained baseline and automate this operation. The criteria for determining the validity of the baseline include, for example, the degree of the vibration component included in the baseline itself, and the degree of change of the baseline due to repetition of the uniform average.

Here, data of all regions cannot be used for analysis by Fourier transform. The periodic structure does not occur at θ smaller than the critical angle θ _{c, the} reflectance decreases as θ increases, and the structure is buried in noise, and applying Fourier transform including these lowers the accuracy Cause. Therefore, an area to be Fourier-transformed is specified in order to perform analysis with high accuracy.

As an actual procedure, the corrected profile 5 is displayed on the display as shown in FIG. 5, and the operator is caused to designate an upper limit and a lower limit of θ used for the Fourier transform using a keyboard or a mouse.

Here, it is assumed that the operator has designated the area 6 in FIG.

In the analysis, first, attention is paid to the carbon film. At this time, Θ is defined by Expression 6.

[0046]

(Equation 6)

At this time, the value of δ of the carbon film is used as δ. As a result, the periodic component caused by the carbon film becomes
By converting the horizontal axis into Θ, the period of the periodic structure caused by the carbon film becomes a completely constant value.

[0048]

(Equation 7)

Under such conditions, Fourier analysis becomes truly effective. However, at this time, since δ uses the value of the carbon film, it is clear that the period is not constant with respect to the periodic structure of the copper film, and the period is slightly shifted.

In actual measurement, since θ is changed at regular intervals and data sampling is performed, the measured values of Θ do not become regular intervals. The Fourier transform is a numerical integration, and it is desirable for calculation that the horizontal axes are arranged at equal intervals. In particular, when using the fast Fourier transform algorithm, the data on the horizontal axis must be arranged at equal intervals. When fast Fourier transform is assumed, the number of data points must be a power of two.

Therefore, if it is possible to measure the power of 2 and I (Θ) while changing Θ at equal intervals, it is convenient in terms of analysis, but such a scan is practically impossible. Therefore, for an arbitrary θ section 6 in which the periodic structure specified in FIG. 5 is clearly observed, the horizontal axis is converted from θ to Θ, and the specified section is equally divided so that the number of data points is 2 powers. Θ was reset so that I (Θ) was calculated by the data interpolation method. There are various interpolation algorithms, but in this embodiment, the combination of the measured data closest to the θ ′ value to be interpolated ｛Θ, I (Θ) か ら
(Θ) was determined in the form of a quadratic function, and a method of calculating I (Θ) corresponding to Θ set at equal intervals was used.

At this time, the refractive index δ of the carbon film is required. The angle θ _{c at which the} reflectivity sharply decreases as shown in the enlarged view at the lower left of FIG. 2 is a critical angle at which total reflection occurs on the surface of the carbon film. The number 8 is established between the critical angle theta _c and a refractive index [delta].

[0053]

(Equation 8)

Since the critical angle θ _{c of} carbon is about 0.21 ° as read from FIG. 3, the refractive index δ is
An approximate value of 000672 is obtained. Using the refractive index thus obtained, the horizontal axis is converted to 、, and Θ is converted to a data set with equal intervals by the above-described interpolation method, and the result of Fourier transform is shown by the solid line in FIG.

The peak indicates a periodic component, and the film thickness is converted using the number 9 from the number of channels x.

[0056]

(Equation 9)

Although the result using the Fourier transform by numerical integration is shown here, it is naturally possible to use an algorithm of the fast Fourier transform. At that time, it is convenient to make Θ equal intervals and to make the number of data a power of 2 when performing interpolation.

The peak 7 and the peak 8 are 3
This corresponds to a film thickness of 4.7 nm and 89.8 nm. From the preparation conditions of the sample, it is considered that the peak 8 is for the copper film and the peak 7 is for the carbon film.

Next, attention is paid to the copper film for analysis. The critical angle θ _{c of} copper is not clearly obtained in FIG. In such a case, δ can be approximated by Expression 10.

[0060]

(Equation 10)

The specific gravity of copper is 8.93 and the atomic number is 2
9. Since the atomic weight is 63.546, δ is 0.0000261 as δ.
Is obtained. Using the value of the refractive index, the horizontal axis is converted in the same manner as when focusing on the carbon film, and the result of Fourier transform is shown by the dotted line in FIG. Peak 9 and peak 10 correspond to the film thickness of 28.1 nm and 78.0 nm, respectively, from Formula 9 The peak 10 is considered to be due to the copper film, similarly to the peak 8, and the peak 1 in which the refractive index of the copper film was used to correct Θ.
At 0, the Fourier transform strength increases. On the other hand, since the peaks 7 and 9 are due to the carbon film, the Fourier transform intensity is high at the peak 7 where the refractive index of the carbon film is used for correcting Θ.

It is necessary to use the refractive value of each film to determine the film thickness of each layer, and the validity of the refractive index is reflected in the Fourier transform intensity. In this example, the peaks 7 and 10 are effective, the carbon film is 34.7 nm, and the copper film is 78.0.
It can be evaluated as nm.

As described above, a baseline is quickly obtained by repeating the uniform averaging of 20 or more points, a periodic component can be easily extracted from an actually measured value, and efficient film thickness evaluation by Fourier transform can be realized.

Embodiment 2 As an embodiment of the second X-ray reflectivity analysis method, the film thicknesses of the carbon film and the copper film are obtained by using the same sample and the measurement data as in the embodiment 1.

FIG. 7 is a flowchart showing an example of a data processing procedure of the present method. In this method, a baseline for extracting a periodic structure of vibration is obtained by repeatedly performing weighted averaging with an arbitrary point as a start point. FIG. 8 shows the obtained baseline (solid line) and measured value (dotted line). FIG.
Solid line designates an incident angle of 0.42 ° as the starting point,
7-point weighted average of the weighted average of 7 points, the repetition of the average operation
This is a baseline obtained by repeating 1200 times by a method of selecting whether or not to continue . FIG. 9 shows the result of correction based on the thus obtained baseline. According to this method, there is an advantage that distortion of the baseline at a small incident angle is small. In addition, a means for obtaining a baseline by repeatedly fixing an arbitrary point and taking an equal average from that point, and a means for obtaining a weighted average of a part and obtaining a uniform average by repeating the rest also correspond to the data profile. Of course, it is possible to use them properly.

From the correction values thus obtained, the upper limit and the lower limit of θ used for the Fourier transform are specified in the same method and range as in the first embodiment. Further, as in the first embodiment, the refractive indices of both the carbon film and the copper film are specified. FIG. 10 shows the result of Fourier transform in which the horizontal axis is transformed using δ and interpolation is performed with Θ being equally spaced. The solid line is the result using the refractive index of the carbon film, and the dotted line is the result using the refractive index of the copper film.

The peak 11 and the peak 12 correspond to the film thicknesses of 34.7 nm and 89.8 nm, respectively, from Equation 9. From the preparation conditions of the sample, it is considered that the peak 12 is for the copper film and the peak 11 is for the carbon film. The peaks 13 and 14 correspond to the numbers 9 to 28.1 nm and 78.0 n, respectively.
m. Since the peaks 12 and 14 are due to the copper film, the Fourier transform intensity is high at the peak 14 where the refractive index of the copper film is used for correcting Θ. On the other hand, since the peaks 11 and 13 are due to the carbon film, the Fourier transform intensity is high at the peak 11 where the refractive index of the carbon film is used for correcting Θ.

Since the thickness of each layer needs to be determined by using the refractive index of each film, peaks 11 and 14 are effective in this example. The carbon film has a thickness of 34.7 nm and the copper film has a thickness of 78.0 nm. We can evaluate that there is.

As described above, an arbitrary point is selected and the value is fixed.
By repeating weighted averaging with this point as a starting point, a baseline with a small incident angle and a small distortion can be obtained, a periodic component can be easily extracted from an actual measurement value, and efficient film thickness evaluation by Fourier transform can be realized. .

Embodiment 3 As an embodiment of the third X-ray reflectivity analysis method, the case where the thicknesses of a carbon film and a copper film are obtained by using the same sample and measurement data as in the embodiment 1 will be considered. FIG. 11 shows an example of the flowchart.

As shown in the first embodiment, the correction is performed using the baseline obtained by repeating the uniform averaging, the horizontal axis is converted into Θ, and the data obtained by performing interpolation so that the data are arranged at equal intervals is subjected to Fourier transform. When evaluating the film thickness, first, a Fourier transform is performed by a fast Fourier transform algorithm that can calculate all the periodic components at high speed. At this time, the intervals were divided so that the number of interpolation data points was a power of two. Figure 1 shows the results.
It is displayed on the screen like the result of the fast Fourier transform of 2. At this time, it is naturally possible to use the method of repeating the weighted average shown in the second embodiment for the baseline correction.

The operator designates a peak or an area to be Fourier-transformed in more detail among the peaks on the screen,
Fourier transform is performed in more detail on the vicinity of the specified peak or in the area by Fourier transform by numerical integration, and the result is displayed on the screen. For example, in the result of the fast Fourier transform in FIG. 12, a large peak is seen when the number of channels x is around 15. Therefore, the result of the Fourier transform obtained by subdividing the vicinity of the number of channels 15 by 20 in FIG. 12 by numerical integration and displaying it as shown in FIG. The solid line in FIG. 13 is the result of Fourier transform by numerical integration in detail, and the dotted line is the result of fast Fourier transform.

The Fourier transform by numerical integration enables a detailed analysis, but it is disadvantageous for calculating a wide periodic region because the calculation time is extremely long. On the other hand, the fast Fourier transform can quickly calculate the entire region, and thus is suitable for estimating a region in which a peak exists, but cannot be used for detailed analysis. Therefore, fast Fourier transform is first performed as in this method, the profile of the entire periodic area is obtained, the required peak is picked up, and a detailed Fourier transform is performed on only that portion, thereby quickly and efficiently analyzing the peak. Becomes possible.

Example 4 As an example of the fourth X-ray reflectivity analysis method, an example in which the refractive index of a copper film was obtained using the same sample and measurement data as in Example 1 will be described.

FIG. 14 is a flowchart showing an example of a data processing procedure of the present method.

Fourier transform is performed in the same procedure as in Example 1 while changing the value of the refractive index δ, and the Fourier transform intensity of the peak caused by the copper film is obtained. The Fourier transform of the peak caused by the refractive index δ and the copper film is performed. FIG. 15 shows the result of calculating the intensity correlation. Since the Fourier transform intensity becomes maximum when δ = 0.000024, it can be seen by the present method that δ of the copper film is 0.000024. The thickness of the copper film using this δ is 79.
9 nm. When the refractive index δ is not clearly understood, it can be approximated by Expressions 8 and 10, but a more accurate value can be obtained by this method. Further, by using the refractive index δ and Equation 10 determined by this method, it is possible to easily evaluate the density ρ of the ultrathin film.

As another example using this method, an example in which an organic film whose refractive index δ and thickness d are unknown on a silicon substrate is evaluated. FIG. 16 shows the measured X-ray reflectance curve of this sample. The X-ray reflectivity measurement condition is such that the measurement range is an incident angle of 0.2.
It is the same as Example 1 except that it is 5 to 1.0 °. The refractive index δ of the organic substance is usually in the range of 0.000004 to 0.000006. FIG. 17 shows the Fourier transform result obtained by assuming 0.0000045 as δ and using the same calculation procedure as in the first embodiment. A peak is observed near the number of channels x = 16, and it is considered that this is due to the organic film because the sample is a single-layer film. The Fourier transform intensity of this peak was determined while changing the refractive index δ, and the correlation between them was obtained as shown in FIG.
8 is shown. From this result, the refractive index of the organic film is about 0.000004
8. The film thickness was found to be 94.3 nm. From δ thus obtained and Equation 10, the density ρ of the organic film is approximately 1.
It is estimated to be 50 (Z / A can be approximately approximated to 0.5). Further, it is expected that a slight shift occurs in the incident angle when the sample is set, but it is difficult to evaluate the value of the shift. However, it is possible to perform this analysis by considering the deviation in the horizontal axis conversion (θ → Θ). FIG. 18 shows a profile of the Fourier transform intensity when the correction value Δθ of the incident angle is changed. From this profile, the deviation of the incident angle in the main measurement data is about 0.008 °. The accuracy of the analysis can be improved by correcting the deviation of the incident angle.

Example 5 A carbon film was formed by a sputtering method on a fused quartz substrate on which a copper film having a thickness of about 80 nm was formed by a vapor deposition method. The roughness of the interface with the layer was determined by applying the least-squares fitting method of the X-ray reflectance profile.

The X-ray reflectivity was measured by using a Cu target as the X-ray source, separating the generated X-ray Ge (111)
and the incident X-ray taken out uKα _1. The measurement angle range is 0.
1 ° ≦ θ ≦ 1.1 °, and the angle step is 0.001.
°, the number of measurement points was 1001 points. The following physical parameters of the substrate and each film affect the X-ray reflectivity profile.

Quartz substrate: real and imaginary parts of refractive index, copper /
Roughness of quartz substrate interface Copper film: Real part and imaginary part of refractive index, film thickness, carbon film
/ Film interface roughness Carbon film: Real and imaginary parts of refractive index, film thickness, roughness of carbon film surface In order to fit the experimental reflectance and the theoretical reflectance, besides the above physical parameters, it is necessary to use the experimental parameters. It is necessary to fit parameters such as the zero-point correction amount of the X-ray incident angle and the scale factor of the intensity, which are parameters. That is, the number of parameters is 13. It is very difficult to fit these at the same time, and even if it converges to a certain value, the certainty of the obtained value remains questionable. In addition, the parameters of well-examined substances such as the refractive index of a fused silica substrate or Cu, or the imaginary part of the refractive index of a substance composed of a light element are generally very small, and the change is hardly reflected in the reflectance. It is thought that fixing parameters that have no effect will lead to more correct results.

In the present embodiment, therefore, the real part of the refractive index of carbon, whose film quality is considered to change depending on the desired film thickness of copper and carbon, the roughness of the carbon surface and the interface between carbon and copper, and the production conditions. Are the physical parameters to be fitted, and the two parameters in the experiment are added to these parameters to perform nonlinear least squares fitting. Other physical parameters were fixed at conventionally known values. Fig. 20 shows the fitting procedure.
Table 1 shows initial values for fitting.

[0082]

[Table 1]

The thicknesses of carbon and copper were determined in Examples 1-4.
The value obtained by the Fourier transform by the method described in (1) above was set as the initial value, and the roughness was unknown and was set to 6.0 ° in each case. When reading initial values, the parameters to be fixed are-
Signs are given to the parameters to be fitted with + signs, the sign of the parameters is determined in the program, and only the positive parameters are numbered sequentially from 1 and rearranged in numerical order to perform least squares fitting. Optimization by least squares used the well-known Marquardt method. The fitting was performed with the logarithm of the reflectance in order to effectively reflect the experimental result on the high angle side. Table 2 shows the optimum values of the parameters obtained after the fitting.

[0084]

[Table 2]

FIGS. 21 and 22 show the results before and after fitting. The dotted line indicates the measured reflectance, and FIG.
The solid line in the middle is the reflectance calculated using the parameter before fitting, that is, the initial value, and the solid line in FIG. 22 is the reflectance calculated using the value after fitting. Before the fitting, the vibration period is slightly well shifted on the high angle side, but agrees well, but the amplitude is greatly shifted. The reason why the periods of the vibrations coincide well is that the Fourier transform result is used as the initial value, and the large deviation of the amplitude is because the roughness of the surface or interface or the value of the refractive index of the carbon film is incorrect. On the other hand, after the fitting, the measured reflectivity and the calculated reflectivity match very well, indicating that the fitting parameters are correctly optimized.
In contrast to the above results, the real parts of the refractive indices of copper and fused silica were added to the fitting parameters with initial values different from the values shown in Table 1. It diverged and did not converge.

According to the present method as shown in the above embodiment,
The physical parameter that affects the X-ray reflectivity is 1
Although the experimental parameters are 2 in total of 13, the fitting parameters can be selected, so only the necessary and important 7 parameters need to be fitted. The fitting time can be reduced and the nonlinear least squares method can be used. There is an effect that a stable fitting process can be obtained without causing a numerical overflow that often occurs. Also, there is an effect that the reliability of the value obtained by reducing the number of parameters increases.

Sixth Embodiment In the first embodiment, parameters to be fitted and parameters to be fixed are distinguished from each other by adding signs to the initial values. In the present embodiment, this distinction is made more visually and more easily. That is, a list of physical parameters affecting the reflectance is displayed on the display, and the parameter to be optimized can be selected on the display screen. An example is shown in FIG. The first column is a film number numbered from the surface of the subject, and the second, third, and fourth columns are the real part, the imaginary part, the film thickness, and the roughness of the film upper surface of the refractive index, respectively. Initial values are given, and only the items to be optimized are selected and displayed in a frame. If it is a color display, it may be displayed in color. After the selection, the result is read by a computer, the selected parameters are numbered and sorted in numerical order, and optimization is performed by the procedure shown in FIG.

According to the present embodiment, parameters to be optimized and parameters to be fixed can be visually distinguished, and a procedure without errors can be provided more easily.

Embodiment 7 When a single-layer film is formed on a substrate, the X-ray reflectivity has a simple vibration pattern. In such a simple case, the real part of the film thickness and the refractive index of the film can be easily obtained from the angle of the vibration peak occurring in the reflectance by the method of Examples 1 to 4 . That is, in the angle region where the reflection intensity is sufficiently smaller than 1, if the angle of the n-th peak is θ _n ,
The following equation holds with good accuracy.

[0090]

[Equation 11]

Here, d is the film thickness, δ is the real part of the refractive index of the film, and λ is the wavelength of the incident X-ray. In order to determine d and δ from Equation 11, it is necessary to accurately determine the order n of the peak. However, in general, the vibrating structure is generated near the total reflection angle of the film, and when the total reflection angle of the substrate is larger than that of the film, the reflection intensity has a complicated behavior near this angle. It is very difficult to decide exactly.

Therefore, in this embodiment, the difference between the peak angles is used. That is, when a temporary number is assigned to the peak and the angle of the n-th peak is θ _n and the angle of the n + m-th peak is θ _{n + m} , d and δ can be expressed by the following equations, respectively.

[0093]

(Equation 12)

[0094]

(Equation 13)

From the above equation, m is appropriately set, and the initial values d ₀ and δ ₀
Are given as appropriate and are repeatedly calculated to obtain Equations 12 and 13
Can be determined at the same time. Hereinafter, this method is referred to as an adjacent peak method.

In this embodiment, the above-mentioned adjacent peak method was applied to a system in which amorphous Si was formed on glass. X-ray reflectivity is C
measured in 0.001 ° steps with uKα _1. Table 3 shows the results obtained by repeatedly calculating with m = 2, 3, and 4 from the ten peaks read.

[0097]

[Table 3]

[0098] The values agree with each other with fairly good accuracy, indicating that d and δ are correctly obtained by the adjacent peak method.

According to this method, there is no need to prepare a special system for data processing, and it is only necessary to read the position of the peak, and it is very easy to obtain the peak. Example 8 The above-described laminated body analysis method was applied to a thin film device production line. A mechanism is provided for transporting and setting a product to an X-ray reflectometer in a thin film device manufacturing line, and X-ray reflectivity is measured. Further, the data processing described in Examples 1 to 7 is applied to the measurement data, and the film thickness, refractive index,
Roughness and the like were monitored, and when those values greatly deviated from specified values, they were excluded as defective. This has made it possible to manufacture thin-film devices of uniform quality. Further, the film thickness of each layer of the device,
By monitoring the refractive index, roughness, and the like, and feeding back the results to the film forming conditions, rapid process control has become possible. As described above, an accurate thin film manufacturing apparatus can be realized by this method. Also, instead of evaluating all products online, extract and evaluate dummy products every few points, or place a dummy substrate during the manufacture of thin film devices and evaluate the film quality of the dummy substrate to evaluate thin film devices. Can be managed for each lot, and in this case, the evaluation time can be shortened and the product throughput can be increased. In addition, one or several model products can be accurately measured for film thickness, refractive index,
Evaluate the roughness, etc., and evaluate the evaluated product by other simpler evaluation means, such as absorption spectroscopy, and compare the results with the previously evaluated film thickness, refractive index, roughness, etc. It is also possible to create a calibration curve from the correlations and evaluate the film quality from the calibration curve, thereby realizing simpler monitoring means.

[0100]

As described above, according to the present invention,
The thickness, refractive index, and roughness of a thin film can be evaluated quickly and accurately. In addition, it is possible to easily evaluate the density of the thin film and to evaluate the displacement of the sample setting.

Further, by introducing this method to a thin film manufacturing apparatus, defective products can be removed and a uniform product can be manufactured.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a procedure of an X-ray reflectivity analysis of the present invention.

FIG. 2 is an explanatory diagram of a display of a baseline obtained in the present invention.

FIG. 3 is a diagram showing measured values of X-ray reflectivity measured as examples.

FIG. 4 is an explanatory diagram of the progress of a baseline.

FIG. 5 is an explanatory diagram of a baseline correction result and an area setting.

FIG. 6 is a diagram showing a result of Fourier transform.

FIG. 7 is a flowchart showing a procedure of X-ray reflectance analysis of the present invention.

FIG. 8 is an explanatory diagram of the obtained baseline.

FIG. 9 is an explanatory diagram of a baseline correction result.

FIG. 10 is a diagram showing a result of Fourier transform.

FIG. 11 is a flowchart illustrating a procedure of X-ray reflectivity analysis according to the present invention.

FIG. 12 is a diagram showing a result of fast Fourier transform.

FIG. 13 is a diagram showing a detailed Fourier transform result.

FIG. 14 is a flowchart showing a procedure of X-ray reflectance analysis of the present invention.

FIG. 15 is a diagram showing a correlation between a refractive index δ and Fourier transform intensity.

FIG. 16 is a diagram showing measured values of X-ray reflectivity of an organic film on silicon.

FIG. 17 is a diagram showing a result obtained by processing the data of FIG. 16 and performing a Fourier transform;

FIG. 18 is a diagram showing a correlation between a refractive index δ and Fourier transform intensity.

FIG. 19 is a diagram showing a correlation between an incident angle correction value Δθ and Fourier transform intensity.

FIG. 20 is a flowchart showing a fitting procedure according to the present invention.

FIG. 21 is a diagram showing calculated values and actual measured values before fitting.

FIG. 22 is a diagram showing calculated values and actual measured values before fitting.

FIG. 23 is an explanatory diagram of selection of an optimization parameter in the present invention.

[Explanation of symbols]

1 ... Measured X-ray reflectivity curve, 2 ... Middle progress of the baseline (three repetitions), 3 ... Middle progress of the base line (6 repetitions), 4 ... Middle progress of the baseline ( 9 times of repetition), 5: Baseline corrected result, 6: Area used for Fourier transform, 7: Peak due to carbon film (using δ of carbon film), 8: Peak due to copper film (of carbon film) δ), 9: peak due to carbon film (use δ of copper film), 10: peak due to copper film (use δ of copper film), 1
1 ... peak due to carbon film (using δ of carbon film), 12 ... peak due to copper film (using δ of carbon film), 13 ... peak due to carbon film (using δ of copper film), 14 ... due to copper film Peak (using copper film δ).

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-4-50715 (JP, A) WO 91/19989 (WO, A1) "Fourier Analysis of Interference Structure in X-R" Low angle x-ray reflection study of ultrathin Ge (58) Fields studied (Int. Cl. ⁷ , DB name) G01B 15/02

Claims (12)

(57) [Claims] From X-ray reflectivity to claim 1 wherein X-ray incidence angle measured for the laminate in which a plurality of films are laminated in an X-ray reflectivity analysis to determine the thickness of the laminate by the Fourier transform method, measurement Perform the averaging process to find the average of the X-ray reflectivity
Repeat the number of times and display the result of the averaging process every time the averaging process is performed any number of times
And whether to perform further averaging by external input
Steps and further averaging if averaging is selected
Is repeated an arbitrary number of times, and if no averaging process is selected,
Outputting the result of the average processing as a baseline
And correcting the X-ray reflectance pattern by the baseline,
Extracting a vibration component, and performing a Fourier transform on the extracted vibration component.
An X-ray reflectivity analysis method comprising: 2. The method according to claim 1, wherein the averaging process is a process using uniform averaging.
X-ray reflectance analysis method as a feature. 3. The method according to claim 1, wherein the averaging process is a process using a weighted average or a weighted average.
It is characterized by processing that combines average and even average.
X-ray reflectance analysis method. 4. The method of claim 1, before Symbol step of Fourier transforming the vibration component performs a fast Fourier transform on the first, X-rays reflections and performing a Fourier transform on the basis of the result of the Fast Fourier transform Rate analysis method. 5. A method according to claim 1, wherein said product is obtained by using said X-ray reflectance analysis method .
The thickness of each layer, based on the refractive index, and physical parameters of the interface roughness, etc. previously given with respect to the X-ray previously given, a step of determining by calculation the X-ray reflectance with respect to the X-ray incidence angle of the stack, the Based on the measured X-ray reflectivity and the X-ray reflectivity obtained by the above calculation, physical parameters such as the film thickness of the laminate, the refractive index for X-rays, and the interface roughness are determined by a nonlinear least square fitting method. An X-ray reflectance analysis method. 6. A method according to claim 1, wherein said product is obtained by using said X-ray reflectance analysis method.
The thickness of each layer, the refractive index for a given X-ray, and
Displaying a list of the physical parameters of the interfacial roughness such previously given beauty, the steps of selecting a physical parameter to be optimized in a non-linear least square fitting method from the list of the physical parameters, the physical parameter as an initial value Obtaining the selected physical parameter using a non-linear least squares fitting method. 7. A film thickness of each layer of the laminated body is obtained by a Fourier transform method from an X-ray reflectance with respect to an X-ray incident angle measured for a laminated body in which a plurality of films are laminated. By feeding back to the film forming conditions, in the thin film manufacturing apparatus for controlling the process, an averaging process of the X-ray reflectance at the measurement point is repeated an arbitrary number of times, and a display means for displaying a result of the averaging process;
Means for obtaining a baseline using an algorithm capable of selecting whether or not to perform further averaging based on the indicating means; and a vibration of the measured X-ray reflectivity based on the measured X-ray reflectivity and the baseline. thin film manufacturing apparatus characterized by comprising means for extracting components, and means for Fourier-transforming the extracted said vibration component. 8. The laminated body according to claim 7, wherein the film thickness, the refractive index with respect to a predetermined X-ray, and the predetermined physical parameters such as interface roughness are determined by the Fourier transform method. Means for calculating an X-ray reflectivity with respect to a line incident angle, based on the measured X-ray reflectivity and the X-ray reflectivity obtained by the calculation, based on the nonlinear least-squares fitting method. thickness, the refractive index with respect to X-rays, and means for determining the physical parameters of the interface roughness, etc., by feeding back the physical parameters obtained in the film formation conditions, a thin film manufacturing apparatus characterized by comprising a means for process control . 9. An X-ray reflectivity of a laminate in which a plurality of films are laminated with respect to an X-ray incident angle is measured, and a film thickness of each layer of the laminate is obtained from the measured X-ray reflectivity by a Fourier transform method. In the X-ray reflectance measuring device, the average processing of the X-ray reflectance at the measurement point is repeated an arbitrary number of times,
Said display means for displaying the result of the averaging processing, based means for determining a baseline using an algorithm that can be selected whether to average processing further, the measured X-ray reflectance and the base line, the means for extracting vibration components of the measured X-ray reflectance, X-rays reflectivity measuring apparatus characterized by having a means for Fourier transforming the extracted vibration component. 10. The laminated body according to claim 9, wherein the thickness of the laminate is determined based on a physical parameter such as a film thickness, a predetermined refractive index for X-rays, and a predetermined interface roughness. Means for calculating an X-ray reflectivity with respect to a line incident angle, based on the measured X-ray reflectivity and the X-ray reflectivity obtained by the calculation, based on the nonlinear least square fitting method, An X-ray reflectivity measuring device comprising means for obtaining physical parameters such as a film thickness, a refractive index for X-rays, and interface roughness. 11. The X-ray of the laminate according to claim 1, based on a physical parameter such as a film thickness of the film obtained by the X-ray reflectance analysis method for the laminate in which a plurality of films are laminated. Calculating the X-ray reflectivity with respect to the incident angle by calculation; based on the X-ray reflectivity with respect to the X-ray incident angle measured for the laminate and the X-ray reflectivity obtained by the calculation, nonlinear least squares Determining a physical parameter such as a film thickness of the laminate, a refractive index to X-rays, and interface roughness by a fitting method. 12. A measurement of a laminate in which a plurality of films are laminated.
From the X-ray reflectivity for a specified X-ray incidence angle,
X-ray reflectance analysis to evaluate physical parameters such as body thickness
In the device, repeat the averaging process of the X-ray reflectivity at the measurement point any number of times.
Display the result of the averaging process every time the averaging process is performed an arbitrary number of times
Display means to perform the averaging process based on the display means.
And means for selecting whether or not to perform the averaging process.
When averaging is selected, further averaging
And a means for selecting whether or not to perform the averaging process.
If you choose not to perform averaging,
Means for outputting a processing result as a baseline, and correcting the X-ray reflectance pattern by the baseline,
Means for extracting a vibration component, and means for outputting a result of Fourier transform of the vibration component
And physical parameters such as film thickness based on the result of the Fourier transform.
Means for determining a meter, means for calculating an X-ray reflectivity with respect to an X-ray incident angle of the laminate based on physical parameters such as the determined film thickness, and X-ray reflection measured for the laminate. Means for obtaining physical parameters such as the film thickness of the laminate, the refractive index for X-rays, and the interface roughness by a nonlinear least-squares fitting method based on the reflectance and the X-ray reflectivity obtained by the calculation. An X-ray reflectance measuring device, characterized in that: