WO2007078088A1

WO2007078088A1 - Method for processing and analyzing data of synchrotron grazing incidence x-ray scattering apparatus

Info

Publication number: WO2007078088A1
Application number: PCT/KR2006/005777
Authority: WO
Inventors: Moon-Hor Ree; Byeong-Du Lee; Jin-Hwan Yoon; Kyeong-Sik Jin; Kyu-Young Hoe; Sang-Woo Jin
Original assignee: Postech Academy-Industry Foundation
Priority date: 2005-12-30
Filing date: 2006-12-27
Publication date: 2007-07-12

Abstract

In order to correct scattering data obtained from synchrotron grazing incidence X-ray scattering apparatus on a thin film sample and to accurately analyze them, the present invention provides a method for processing and analyzing data of a synchrotron grazing incidence X-ray scattering apparatus, the method including converting two-dimensional scattering data on a thin film sample, that are obtained from a signal detector of the synchrotron grazing incidence X-ray scattering apparatus, into one-dimensional scattering data for a specific scattering angle, and acquiring quantitative information on the internal structure of the thin film sample and the surface thereof with respect to a specific direction by comparing and analyzing the one-dimensional scattering data.

Description

TITLE OF THE INVENTION

Method for Processing and Analyzing Data of Synchrotron Grazing

Incidence X-ray Scattering Apparatus

Field of the invention

The present invention relates to a method for processing and analyzing data

of a synchrotron grazing incidence X-ray scattering apparatus, and more particularly,

to a method for properly processing and accurately analyzing data obtained

therefrom on a thin film sample.

Background art

Synchrotron radiation sources, especially an X-ray beam, provide

information on microstructure that is not obtained by visible light, so an X-ray

scattering method is one of the major tools for analysis on polymer structure.

However, for a thin film sample with a thickness of less than 1 μm, the

previous transmission X-ray scattering method is not suitable for structural analysis.

It is not possible to obtain strong scattering intensity due to the small

scattering volume of the thin film, and in addition, an X-ray having enough energy to

penetrate the substrate as well as the thin film is required due to the thin film formed

on the substrate that is opaque to the X-ray.

A strong scattering intensity may be obtained due to the large scattering volume in the case that the X-ray is incident on the thin film at the critical angle,

however this method has a shortcoming in that the scattering signals may be distorted

by refraction and reflection of the incident X-ray beam.

DETAILED DESCRIPTION OF THE INVENTION

Technical objectives

The present invention provides a method for processing and analyzing data

from a synchrotron grazing incidence X-ray scattering apparatus that is capable of

correcting the distortion of the scattering data from a thin film sample.

In addition, the present invention provides a method for processing and

analyzing data from a synchrotron grazing incidence X-ray scattering apparatus that

is capable of accurately analyzing the scattering data on a thin film sample.

Technical solution

The present invention provides a method for processing and analyzing data

from a synchrotron grazing incidence X-ray scattering apparatus, the method

including converting two-dimensional scattering data from a thin film sample that are

obtained from a signal detector of the synchrotron grazing incidence X-ray scattering

apparatus into one-dimensional scattering data for a specific scattering angle, and

acquiring quantitative information on internal structure of the thin film sample and the surface thereof with respect to a specific direction by comparing and analyzing

the one-dimensional scattering data.

The converting may include receiving the two-dimensional scattering data

from the signal detector, and converting the two-dimensional scattering data into the

one-dimensional scattering data by having experimental conditions for the sample as

variables.

The acquiring may include receiving the one-dimensional scattering data

obtained during the converting, assigning shapes or structures to a model sample that

is to be compared with the sample, calculating a form factor and a structure factor of

the model sample by inputting quantitative information on the shape or structure of

the model sample, calculating scattering intensity of the model sample from the form

factor and the structure factor, correcting the scattering intensity, and checking if the

corrected data of the model sample is the same as the one-dimensional scattering data

obtained during the converting, by comparing the two data.

If the scattering intensity from the model sample is the same as the scattering

intensity from the sample, the information on the shape and structure of the model

sample, characteristic information, and the calculated one-dimensional data as the

information on the sample may be saved.

If the scattering intensity from the model sample is not the same as the scattering intensity from the sample, the assigning may be returned and repeated until

the scattering intensity from the model sample matches the scattering intensity from

the sample.

The variables may include coordinates of a synchrotron X-ray beam that

transmits through the sample and is detected by the signal detector, an incident angle

of the synchrotron X-ray beam, a distance between the sample and the signal detector,

pixel size of the signal detector, and coordinates of the scattering angle.

The shape of the model sample may be selected from a sphere, a circular

cylinder, a circular cone, a pyramid, and a prism.

The structure of the model sample may be selected from a multi-layered

structure, a hexagonal packed structure, and a hexagonal perforated layer structure.

The correcting may include obtaining a transmittance and a reflectance of

the synchrotron X-ray beam from information on electron density of a thin film and

of a substrate, absorption coefficient, and thickness of the thin film, and correcting a

refraction and a reflection of the incident synchrotron X-ray beam.

Effect of the invention

According to the present invention, it is possible to accurately analyze the

internal structural shape of a thin film sample and the surface thereof.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a schematic diagram of a synchrotron grazing incidence X-ray scattering

apparatus according to the embodiment of the present invention.

Fig. 2 is a perspective view showing an incident X-ray being scattered from the

sample.

Fig. 3 is a flow chart showing procedures for processing and analyzing the data

of the synchrotron grazing incidence X-ray scattering apparatus according to the

embodiment of the present invention.

Fig. 4 is a flow chart schematically showing procedures for processing the data

embodiment of the present invention.

Fig. 5 is a flow chart schematically showing procedures for analyzing the data of

the synchrotron grazing incidence X-ray scattering apparatus according to the

embodiment of the present invention.

100 : sample mounting section 101 : sample chamber

102 : sample stage 103 : vacuum pump

104 : sample 110 : sample control section

111 : goniometer 112 : goniometer drive

113 : goniometer controller 114 : stepping motor 115 : stepping motor drive 116 : stepping motor controller

120 : temperature control section 121 : temperature adjuster

122 : temperature controller 123 : heating bar

124 : liquid nitrogen injector 125 : liquid nitrogen circulating tube

130 : main control section 140 : signal detector

150 : data processing and analyzing section

200 : goniometer driving section

210 : stepping motor driving section 301 : incident synchrotron X-ray beam

302 : scattering signal 303 : horizontal scattering angle

304 : vertical scattering angle

DETAILED DESCRIPTION OF THE EMBODIMENTS

Hereinafter, with reference to appended drawings, the embodiments of the

present invention will be described in detail for enabling those skilled in the art.

However, the present invention may have different forms and is not limited to these

embodiments.

Fig. 1 is a schematic diagram of a synchrotron grazing incidence X-ray

scattering apparatus according to an embodiment of the present invention.

Referring to Fig. 1, the synchrotron grazing incidence X-ray scattering

apparatus includes a sample mounting section 100 where a thin film sample to be analyzed is located and the thin film reacts with incident synchrotron X-ray beams to

be scattered so as to produce scattering signals; a sample control section 110 that

controls the incident angle of the synchrotron X-ray beam and the position of the

sample mounting section 100 with respect to the synchrotron X-ray beam so as to

control the scattering from the sample mounting section 100; a temperature control

section 120 that controls rise and drop in temperature of the sample mounting section

100; a main control section that conveys control commands to the sample control

section 110 and to the temperature control section 120, and restores and displays the

control commands and results thereof; a signal detector 140 that detects the

scattering signals from the sample mounting section 100; and a data

processing/analyzing section 150 that is connected with the signal detector 140 and

processes and analyzes the detected signals.

Hereinafter, the term "synchrotron grazing incidence" is defined such that a

synchrotron X-ray beam is incident on a thin film sample at the critical angle thereof

in order to graze the thin film sample.

Here, the synchrotron X-ray beam is generated by a synchrotron and is

preferably an X-ray that provides information on the molecular structure of the

sample by reacting with the sample and being scattered.

The sample mounting section 100 includes a sample chamber 101, a sample stage 102 that is placed inside the sample chamber 101 and where the sample is

mounted, and a vacuum pump 103 that keeps the sample chamber 101 under vacuum.

The sample chamber 101 is a device that generates scattering from the

surface of the sample by the incident synchrotron X-ray beam thereon. However,

since the scattering signal of the synchrotron X-ray beam weakens in intensity due to

the scattering with the air, the sample chamber 101 is kept under vacuum.

In addition, the window of the sample chamber 101 is preferably made of a

polymer film such that the sample chamber 101 is maintained under vacuum and the

synchrotron X-ray beam and the scattering signals are able to transmit to the sample

chamber 101.

The vacuum pump 103 is connected with the sample chamber 101 and

maintains the vacuum state of the sample chamber 101.

The sample stage 102 is a place where the sample from which the incident

synchrotron X-ray beam is scattered is located, and is placed inside the sample

chamber 101. The sample stage 102 is preferably made of aluminum for its

excellent heat transfer characteristics and non-deformability at high and low

temperature.

Fig. 2 is a perspective view showing that the incident X-ray is scattered from

the sample. Referring to Fig. 2, the incident synchrotron X-ray beam 301 that has passed

through the beam line enters the sample mounting section 100 and is scattered from

the surface of the sample 104. The scattering angle of the scattered synchrotron X-

ray beam is divided into a horizontal scattering angle 303 and a vertical scattering

angle 304.

The data processing/analyzing section 150 processes and analyzes the

scattering signals detected by the signal detector 140, and derives quantitative

information on the sample 104 such as the internal structure thereof.

The accurate scattering signals 302 may be produced because the inclination

(an inclining angle to the Y-Z plane of the drawing) of the sample stage 102 can be

corrected by operation of the sample control section 110 that is connected with the

sample mounting section 100.

The sample control section 110 includes a goniometer driving section 200

that adjusts an incident angle of the incident synchrotron X-ray beam 301 by

precisely rotating the sample mounting section 100 about the center axis (an axis

parallel to the Y direction of the drawing) of the goniometer 111, and a stepping

motor driving section 210 that moves the sample mounting section 100 up and down

(in the Z direction of the drawing).

The goniometer driving section 200 for precisely controlling the incident angle of the incident synchrotron X-ray beam 301 on the sample 104 includes the

goniometer 111 that is connected with and rotates the sample mounting section 100,

a goniometer drive 112 that drives the goniometer 111, and a goniometer controller

113 that is connected with the goniometer drive 112 and imposes control commands

thereon.

The goniometer 111 can be moved up and down (in the Z direction of the

drawing) by a stepping motor 111 that is directly connected thereto.

Fulfilling the control command of the angle adjustment on a scale as small as

0.001 degrees, the goniometer driving section 200 adjusts the incident angle of the

incident synchrotron X-ray beam 301 by rotating the sample mounting section 100

about the center axis of the goniometer 111.

The goniometer controller 113 serves to deliver control commands to the

goniometer 111 through the goniometer drive 112 and serves to display the control

results.

The stepping motor driving section 210 includes a stepping motor 114 that is

connected with the goniometer 111 and moves the sample mounting section 100 up

and down, a stepping motor drive 115 that drives the stepping motor 114, and a

stepping motor controller 116 that imposes control signals on the stepping motor

drive 115. The stepping motor controller 116 serves to deliver control commands to the

stepping motor 114 through the stepping motor drive 115 and serves to display the

control results.

The temperature control section 120 includes a temperature adjuster 121 that

adjusts the temperature of the sample stage 102, a temperature controller 122 that

controls the temperature adjuster 121, a heating bar 123 that supplies heat to the

sample stage 102 under the control of the temperature adjuster 121, a liquid nitrogen

injector 124 that supplies liquid nitrogen for cooling the sample stage 102, and a

liquid nitrogen circulating tube 125 that transports the liquid nitrogen to the sample

stage 102.

The temperature control section 120 for controlling the temperature of the

sample stage 102 is provided with the programmable temperature adjuster 121 and is

capable of maintaining the sample stage 102 at a constant temperature in the range of

room temperature to 450 ^°C or raising the temperature of the sample stage 102 at a

desired rate.

The heating bar 123 is a conventional device, having an electrical resistance

wire and an insulator, which is electrically connected to the temperature control

section 120 and is heated with a supplied electrical current.

The heating bar 123 is embedded in the sample stage 102. The temperature adjuster 121 is connected to the temperature controller 122 via an RS232 port and

receives the control command.

The liquid nitrogen injector 124 serves to cool down the sample stage using

liquid nitrogen. The liquid nitrogen circulating tube extends into the inside of the

sample stage 102 and circulates the liquid nitrogen through the sample stage 102,

lowering the temperature of the sample stage 102 to below -80 ^°C. Thus, the

temperature control section 120 is able to control the temperature of the sample stage

102 in the range of -80 to 1000 °C and to provide a circumstance suitable for

observing the change of the structure of a temperature-dependent sample.

In the present embodiment, the data processing/analyzing section 150 is

realized with a program installed in a computer, and Figs. 3 to 5 exemplify the

procedures for processing and analyzing data through the data processing and

analyzing section.

Here, the data processing/analyzing procedure consists of a series of the

programs that are programmed with computer-readable codes or commands, and

enables the computer to function as the data processing/analyzing section.

According to the embodiment of the present program, the embodiment for

the analyzing process by the aforementioned data processing/analyzing section is

easily realized in a way in which the program is read by the computer from recording media such as a ROM, CD-ROM, DVD-ROM, and hard disk, and is executed

thereby, or in which the program is executed after being down-loaded to the

computer through communicating means.

Referring to Fig. 3, the data processing/analyzing procedure for a thin film

sample includes converting two-dimensional scattering data from a thin film sample,

which are obtained from a signal detector of the synchrotron grazing incidence X-ray

scattering apparatus, into one-dimensional scattering data for a specific scattering

angle, and acquiring quantitative information on internal structure of the thin film

sample and the surface thereof with respect to a specific direction by comparing and

analyzing the one-dimensional scattering data.

The synchrotron X-ray beam that passed through the beam line generates a

specific scattering pattern by reacting with a thin film sample, the structure of which

is to be analyzed.

The signals are captured as two-dimensional scattering data by the two-

dimensional signal detector that is placed in the signal detecting section. Since the

two-dimensional scattering data include a distortion phenomenon that results from

the refraction and reflection of the incident synchrotron X-ray beam, the data

processing/analyzing section 150 obtains the one-dimensional scattering data at a

specific scattering angle by considering the scattering structure of the two- dimensional scattering data from the signal detector (SlOO).

The data processing/analyzing section 150 obtains quantitative information

on the internal and surface structures of the thin film sample by comparing and

analyzing the scattering data of the assigned model sample to the calculated

scattering data (S200).

Fig. 3 is a schematic flow chart showing procedures for processing the data

by the data processing and analyzing section, and one-dimensional scattering data at

a specific scattering angle is obtained from two-dimensional scattering data obtained

by the signal detector.

The data processing procedure includes receiving the two-dimensional

scattering data from the signal detector of the synchrotron grazing incidence X-ray

scattering apparatus, and calculating the two-dimensional scattering data into the

one-dimensional scattering data by having experimental conditions for the sample for

the synchrotron X-ray beam scattering experiment, and outputting and storing the

calculated one-dimensional scattering data.

The data processing/analyzing section 150 reads the file of the two-

dimensional scattering data acquired by the two-dimensional signal detector 140.

The data acquired by the signal detector 140 are accepted as a multi-dimensional

matrix that matches the number of data pixels (Sl 10). Next, a specific scattering angle at each coordinate is calculated from the

experimental variables for the thin film sample used in the scattering experiments,

and the scattering intensity at the specific angle is finally obtained (S 120).

The scattering angle is calculated from the experimental variables by the

following equations.

20, = atmι(sm(aicm(PX - CENTER)(I)) ÷ (SDDx PxSize)))

(i)

a _f = aoπ{sir.(<Aar.(-FY+ CHJFIR (2)) ÷ φϋD ;< hSize)² - J[PX - CEMER (I)) ^] )) - a_f

(2)

In the above equations, SDD, CENTER(1, 2), Q, PxSize, PX, and PY are the

variables for the experimental conditions of the thin film sample to be inputted to the

above equation, and respectively represent a distance between the thin film sample

and the signal detector (SDD), coordinates of the transmitted incident synchrotron X-

ray beam that is detected by the signal detector (CENTER(1, 2)), incident angle of the

synchrotron X-ray beam (Cj), the size of the pixel in the signal detector (PxSize), and

coordinates of the data for a specific scattering angle (PX, PY).

Therefore, if the experimental variables including the coordinates (PX or

PY) of the data for a specific scattering angle to be analyzed are inputted into

Equations (1) and (2), one-dimensional scattering data at the coordinate for the

scattering angle (2Cj) along the X or Y direction (horizontal direction) and the scattering angle (Q) along the Z direction (vertical direction) are obtained.

The one-dimensional scattering data obtained in the above procedure are

displayed on a computer screen and stored in the ASCII file format via the displaying

and storing, wherein X and Y coordinates of the stored file are the scattering angle

and the scattering intensity, respectively (S 130).

Thus, the scattering intensity for a specific angle can be calculated by

obtaining the one-dimensional scattering data for a specific angle from the two-

dimensional scattering data.

In the next procedure, the data processing/analyzing section 150 obtains the

quantitative information on the internal structure of the thin film sample and the

surface thereof by comparing and analyzing the scattering intensity obtained in the

data processing procedure (S200).

Referring to Fig. 5, the data analyzing procedure is explained as follows.

The data processing/analyzing section 150 reads, loads, and displays the

one-dimensional scattering data in the ASCII file format, which are obtained in the

data processing procedure (S210).

Further, the shape and structure of the model sample are assigned so as to be

compared with the thin film sample that is to be analyzed (S210).

The shape of the model sample can be selected from the predetermined various models such as a sphere, a circular cylinder, a circular cone, a pyramid, a

prism, etc. The structure of the model sample can be selected from the

predetermined various models such as a multi-layered structure, a hexagonal

perforated layer structure, a hexagonal packed structure, etc.

Once a shape and a structure of the model sample are determined through the

above procedure, quantitative information on the selected shape or structure, such as

diameter, length of a side, and a distance between the layers, are inputted. The form

factor (F(q)) of the thin film sample is calculated using the information on the shape,

and the structure factor (S(q)) is calculated using the information on the structure.

Then, the scattering intensity (Ij) is calculated from the form factor (F(q)) and the

structure factor (S(q)) with the following Equation (3) (S230 ~ S240).

Ii(q) = S(q)-F(q) (3)

Here, the scattering intensity (I₁) does not consider the distortion in the

scattering phenomenon due to the reflection and refraction of the synchrotron X-ray

beam in the multi-layered structure of the thin film and the substrate.

Therefore, there is a procedure for compensating for the refraction and

reflection of the synchrotron X-ray beam by the transmittance (T) and the reflectance

(R) of the synchrotron X-ray beam obtained using the characteristic information on

the multi-layered thin film such as electron density, absorption coefficient, and thickness of the thin film and the substrate (S250).

The scattering intensity obtained from the model sample is corrected by the

following Equation (4).

In Equation (4), Tj and Rj are the transmittance and the reflectance of the

incident synchrotron X-ray beam on the thin film, respectively, and T_f and R_f are the

transmittance and the reflectance of the synchrotron X-ray beam reflecting on the

substrate of the thin film, respectively.

Further, q n and q_z are the scattering vectors in which the wavelength of the

incident synchrotron X-ray beam is considered. The vector q_z can be distinguished

into four different scattering vectors with respect to the relative positions of the

incident synchrotron X-ray beam and the thin film and the substrate in the multi-

layered thin film, and can be represented by q_1>z, q₂,_z, q_3>z, and q_4jZ.

When the squared term in the right-hand side of the equation (4) is arranged

properly, the squared term can be represented by the summation (iGixs(independent)) of

each of small squared terms and the summation (I_GIXS(CΓOSS)) of each term multiplied by other small terms.

iGixs(independent) is always positive, but IGIXS(C_ΓOSS) may be positive or negative,

depending on the incident angle, the thickness of the sample, the internal structure of

the sample, the size of the structure, the divergence of the incident beam, etc.

However, IG_IXS_(CΓOSS) is a negligible amount or zero in a statistical view. Therefore,

when the contribution of I_GIXS(CTOSS) can be ignored, Equation (4) is in the following

mathematical form.

As stated above, when the scattering intensity of the model sample is

corrected, the data processing/analyzing section 150 displays the scattering intensity

obtained from Equations (3), (4), and (5), and checks by comparison if the scattering

intensity obtained in the data processing procedure for the thin film sample is the

same as the scattering intensity obtained in the data analyzing procedure for the

model sample (S270).

When the finally-obtained scattering intensity from the model sample

matches the scattering intensity from the thin film sample, it is determined that the shape and structure of the model sample correspond to the shape and structure of the

thin film sample. Thus the information on the shape and structure of the model

sample, characteristic information, and the calculated one-dimensional scattering

data are stored as information on the thin film sample (S280).

In the case that the scattering intensity from the model sample is not the

same as the scattering intensity from the thin film sample in the comparing and

confirming procedure, the procedure where the model sample is assigned is returned

to and repeated until the scattering intensity from the model sample is the same as the

scattering intensity from the thin film sample.

Although an embodiment of the present invention has been described in

detail hereinabove, it should be clearly understood that many variations and/or

modifications of the basic inventive concepts herein taught which may appear to

those skilled in the present art will still fall within the spirit and scope of the present

invention, as defined in the appended claims.

Claims

1. A method for processing and analyzing data from a synchrotron grazing incidence

X-ray scattering apparatus, the method comprising:

converting two-dimensional scattering data from a thin film sample, that are

apparatus, into one-dimensional scattering data for a specific scattering angle; and

acquiring quantitative information on internal structure of the thin film

analyzing the one-dimensional scattering data.

2. The method of claim 1, wherein the converting includes:

receiving the two-dimensional scattering data from the signal detector; and

calculating the two-dimensional scattering data into the one-dimensional

scattering data by having experimental conditions for the sample as variables.

3. The method of claim 1, wherein the acquiring includes:

receiving the one-dimensional scattering data obtained during the

converting;

assigning shapes or structures to a model sample that is to be compared with the sample;

calculating a form factor and a structure factor of the model sample by

inputting quantitative information on the shape or structure of the model sample;

calculating scattering intensity of the model sample from the form factor and

the structure factor;

correcting the scattering intensity; and

checking if the corrected data of the model sample is the same as the one-

dimensional scattering data obtained during the converting, by comparing the two

data.

4. The method of claim 3, further comprising:

saving the information on the shape and structure of the model sample,

characteristic information, and the calculated one-dimensional data as the

information on the sample if the scattering intensity from the model sample is the

same as the scattering intensity from the sample; and

returning to and repeating the assigning until the scattering intensity from the

model sample matches the scattering intensity from the sample if the scattering

intensity from the model sample is not the same as the scattering intensity from the

sample.

5. The method of claim 2, wherein the variables include coordinates of a synchrotron

X-ray beam that transmits through the sample and is detected by the signal detector,

an incident angle of the synchrotron X-ray beam, a distance between the sample and

the signal detector, pixel size of the signal detector, and coordinates of the scattering

angle.

6. The method of claim 3, wherein the shape of the model sample is selected from a

sphere, a circular cylinder, a circular cone, a pyramid, and a prism.

7. The method of claim 3, wherein the structure of the model sample is selected from

a multi-layered structure, a hexagonal packed structure, and a hexagonal perforated

layer structure.

8. The method of claim 3, wherein the compensating includes obtaining a

transmittance and a refractive index of the synchrotron X-ray beam from information

on electron density of a thin film and of a substrate, absorption coefficient, and

thickness of the thin film, and compensating for a refraction and a reflection of the

incident synchrotron X-ray beam.

9. The method of claim 2, wherein the calculating is carried out by the following

Equations (1) and (2):

Wf = aiωι(sin(aian(PX - CIM¹M)(I)) ÷ (SDDx PxSizejj)

(1)

ct _f = am{sir.{<tar.(-W + CENTER (2))÷(_λ/(5DDx ?xto)² - J[PX - CEMER (I))³)) - α_t (2)

wherein 2Q = scattering angle along X or Y direction,

Q- = scattering angle along Z direction,

SDD = distance between the thin film sample and the signal detector,

CENTER(1, 2) = coordinates of the transmitted synchrotron X-ray beam,

Q - incident angle of the synchrotron X-ray beam,

PxSize = pixel size of the signal detector, and

PX and PY = coordinates for a specific scattering angle.

10. The method of claim 3, wherein the compensating is carried out by the following

Equation (4):

wherein Tj = transmittance of the incident synchrotron X-ray beam in the

thin film,

Ri = reflectance of the incident synchrotron X-ray beam in the thin film,

T_f = transmittance of the synchrotron X-ray beam that is reflected on the

substrate of the thin film,

R_f = reflectance of the synchrotron X-ray beam that is reflected on the

substrate of the thin film, and

q Ii and q_z = scattering vectors, considering the wavelength of the incident

synchrotron X-ray beam, wherein

qi,_z, q₂,_z> q₃,z and q_4jZ = four different scattering vectors that are

distinguishable according to the incident synchrotron X-ray beam and positional

relationship between the thin film and the substrate in the multi-layered thin film.

11. The method of claim 3, wherein the compensating is carried out by the following

Equation (5): Iaxsfrf&fϊ ≡

wherein Tj = transmittance of the incident synchrotron X-ray beam in the

thin film,

Ri = reflectance of the incident synchrotron X-ray beam in the thin film,

T_f = transmittance of the synchrotron X-ray beam that is reflected on the

substrate of the thin film,

R_f = reflectance of the synchrotron X-ray beam that is reflected on the

substrate of the thin film, and

q ii and q_z = scattering vectors, considering the wavelength of the incident

synchrotron X-ray beam, wherein

qi,_z> q2,z, q3,z, and q₄,_z = four different scattering vectors that are

distinguishable according to the incident synchrotron X-ray beam and positional

relationship between the thin film and the substrate.