JP3409742B2 - EPMA analysis method using Monte Carlo simulation - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electron probe microanalyzer for irradiating a sample with an electron beam and measuring the characteristic X-rays emitted from the sample to qualitatively or quantitatively analyze the elements in the sample. microanalys
er; hereinafter referred to as “EPMA”),
Especially EP using Monte Carlo simulation method
Regarding MA analysis method.

[0002]

2. Description of the Related Art The EPMA analysis method irradiates a sample surface with an electron beam (electron probe) that is extremely narrowed down, and the wavelength and intensity of characteristic X-rays emitted from the part are measured by an X-ray spectrometer or detector. It is possible to know which part of the sample is being measured because it measures and qualitatively or quantitatively determines the element contained in the minute part of the sample.
Since the sample can be analyzed non-destructively without being dissolved like chemical analysis, various minute substances such as minute foreign substances mixed in the sample and minute crystallized substances generated by melting of metal are included. It is applied to analysis of various samples in various fields such as measurement of shape and size.

However, the conventional EPMA analysis method is
Basically, it is established on the assumption that it is compared with a standard sample. If it is difficult to prepare or obtain a standard sample, it will be difficult to analyze the sample accurately, and about the sample that can be analyzed by this EPMA analysis method. Is an area where the sample size emits characteristic X-rays by irradiation with an electron beam, that is, an "X-ray generation area"
The size of the sample is limited to this X
If the area is smaller than the line generation area, the X-rays emitted from portions other than the sample are also measured, and accurate analysis of the sample cannot be performed.

For example, when the sample is a thin film and the depth direction of the X-ray generation region exceeds the depth direction of the thin film sample when the thin film sample is irradiated with an electron beam, the film thickness thereof Even if only one measurement is taken, the characteristic X-rays of the component elements emitted from the part other than the sample are measured, and the electrons that enter the sample again from the part other than the sample generate the characteristic X-rays of the sample. Analysis becomes difficult, and if the type of thin film is diverse, or if it is a film with several layers laminated, it will be difficult to create a standard sample for preparing the calibration curve, or a standard sample It takes a lot of time and effort to create a file.

Further, in the case of analyzing a minute object of about 1 μm found in an aluminum copy drum or an MD substrate, for example, even if elements such as Si, O and Al are detected from such minute object, the matrix Since Al is measured, it is impossible to determine whether the microscopic substance is SiO ₂ or another Al or Si oxide. The same applies to the case where elements such as Al, Mg, O, etc. are detected from the minute substances in the S3M alloy to which about 3% of Mg is added, or the heat exchanger parts made of aluminum. When elements such as Fe and Al are detected from the microscopic objects found around the hole that occurred in the automobile condenser tube,
This also occurs when elements such as Fe and Al are detected from minute substances existing in aluminum.

Therefore, recently, such a minute object is specified.
As a method of
There is a state analysis method that compares the states of the profile. This
The state analysis method currently has some size
Al₂O₃, MgO, spinel, SiO₂, FeO,
Fe₂O₃, Fe₃O_FourMetal oxides such as Al, Al
_FourC ₃, SiC and other metal carbides, AlN, Si₃N_Four
It is said that it is possible to identify such metal nitrides.

However, even in this state analysis method, it becomes difficult to accurately irradiate the minute object with the electron beam because it takes about 30 minutes or more to measure the minute object or the thin film having a size of about 1 μm or less. There is. In addition, Al ₃ Fe, Al ₆ Fe, AlFe, AlFe ₃ ,
In the case of metals and metal compounds such as Al ₂ Cu and AlCu, it is said that it is difficult to identify them by a state analysis because it is difficult for a unique satellite line to appear in oxides, carbides, nitrides and the like.

Further, in the case of thin-film measurement, the influence of the substrate, which cannot be corrected by the ZAF method, is taken into consideration, and the trajectory of electrons incident on the sample is simulated by the Monte Carlo method, and the amount of primary X-ray generation that can be generated by the trajectory of the electrons. And a generation function, and a method of analyzing a sample from the calculated value obtained by the above is also proposed (Japanese Patent Laid-Open Nos. 2-95,247 and
4-42,037, JP-A-5-26,826). However, even in this method, in order to perform an accurate analysis, it is usually 10,000 or more, and in some cases 30,000.
The trajectory of as many electrons as possible has to be simulated, which requires the use of a large computer, making it unsuitable for practical research, and has the problem that it cannot be applied to minute objects.

[0009]

Therefore, the inventor of the present invention
Not limited to bulk samples that are sufficiently larger than the X-ray generation region,
Accurate analysis is possible for thin film samples and minute sample smaller than the X-ray generation region in any one or more of the longitudinal direction, the lateral direction, and the depth direction.
As a result of earnestly studying an EPMA analysis method using a Monte Carlo simulation capable of performing an accurate analysis with a simulation of a small number of electrons of less than 00, a rectangular parallelepiped model is assumed as an X-ray absorption model, and the Monte Carlo simulation calculation formula is used. The inventors have found that the object can be achieved by adopting certain specific values as the constants of the ionization potential (J) and the screening parameter (β) used in the above, and have completed the present invention.

Therefore, the object of the present invention is not limited to a bulk sample larger than the X-ray generation region, and a thin film sample smaller than the X-ray generation region in any of the longitudinal direction, the horizontal direction, and the depth direction. EPM using Monte Carlo simulation that enables accurate analysis of minute samples
A. To provide an analytical method.

Another object of the present invention is to provide an EPMA analysis method using Monte Carlo simulation which enables accurate analysis by simulation with a small electron number of less than 1000.

[0012]

That is, the present invention provides X
A rectangular parallelepiped in a matrix that is sufficiently larger than the line generation area
X-ray absorption when a sample in the shape of a ring is exposed by exposing only its upper surface
Assuming a model, the vertical direction of the sample in this X-ray absorption model
Direction, width, and depth in terms of size and shape
It is set according to the situation and the Monte Carlo simulation
The following formulas (2) to (4) scattering in the formula
Calculation formula (2) for angle (ω) and rotation angle (φ) cos (ω, radian) = 1-2βR / (1 + β-R) φ (radian) = 2πR Calculation formula of electron energy loss (ΔE) (3) When E> 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ [ZC / A ・ ln (1.16
6 E / J)] / E When E ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ (ZC / A / J^1/2) /
1.26E^1/2 Calculation formula (4) of probability (P) that electron collides with element P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe^FourZ (Z + 1)] / [4E
_n ²β (β + 1)] [However, in the above formulas (2) to (4), E is an electron
Own energy (Kev), A is atomic weight, ρ is density (g /
cm³), Z is atomic number, J is ionization potential
(Kev), β is the screening parameter, R is uniform
Random number (0 to 1), π is circular constant (3.14), C is composition
, E is the electric charge of the electron (−4.8029 × 10 ^-Tenesu)
The E_nIs the kinetic energy of the electron (eE / 300 × 10
³) Respectively], J = 11.5Z × 10
^-3 [Kev] and β = {5.44Z^2/3/ E} × 10^-3 Simulation with less than 1000 incident electrons
Monte Carlo simulation characterized by
This is the EPMA analysis method used.

EPMA used in carrying out the method of the present invention
Is a wavelength dispersion type (Wavelength Dispersive X-ray An
alysis), but also energy dispersive (Energy D
ispersive X-ray Analysis), but wavelength dispersion type EPMA is preferable.

In the method of the present invention, there is no particular limitation on the sample to be measured, which is determined by EPMA X
Even a bulk sample that is sufficiently larger than the X-ray generation region, or a thin film sample or a microscopic sample that is smaller than the X-ray generation region in any of its longitudinal direction, horizontal direction, and depth direction. Good. And, regarding the thin film sample, it may be a single-layer thin film or a multi-layer thin film,
In addition, as for the sample of minute matter, even if it is a minute matter that is dispersed and present in the metal or metal compound of the matrix, it is fixed on a non-metallic carrier such as a PTFE membrane filter by a known method. Small objects, rubber,
It may be a minute foreign substance existing in an organic substance such as paper, cardboard, plastic or the like.

Regarding the sample to be measured,
These are Al, Fe, Cu, Au, Si, Ni, Cr, Ti
A sample composed of a single metal element such as
Al containing at least two sample metal elements₆Fe,
Al₃Fe, AlFe, AlFe₃Al-Fe system such as
Or Al-Fe-Mn system, Al-Fe-Si system, Al-
A of Fe-Mg-Si system, Al-Fe-Mn-Si system, etc.
l-Fe-X system, Al ₂Al-C such as Cu and AlCu
u-based, Al-Cu-Fe-based, Al-Cu-Mg-based, A
1-Cu-Mg-Si system, Al-Cu-Mg-Zn system, etc.
Al-Cu-X system and other intermetallic compounds in Al
It may be a metal or metal compound such as
Al containing one kind of sample metal element and sample non-metal element₂
O₃, SiO₂, Fe₂O₃, Metal oxides such as MgO,
Al_FourC₃, Metal carbide such as SiC, AlN, Si₃N
_FourMetal nitrides such as mullite (Al₂O₃・ 2SiO₂), Spinel
(Al₂O₃・ MgO), forsterite (2MgO ・ SiO₂), Jill
Con (ZrO₂..SiO₂) Metals such as ternary compounds, non-gold
It may be a genus compound. And, these measurement target
There is no particular limitation on the use of the sample.

In the method of the present invention, it is assumed that the sample to be measured has a rectangular parallelepiped shape, and the rectangular parallelepiped sample is embedded in a matrix sufficiently larger than the X-ray generation region by exposing only its upper surface. The X-ray absorption model is assumed, and the size of the sample in the vertical direction, the horizontal direction, and the depth direction in this X-ray absorption model is set according to the size and shape, and the trajectory of the electron is calculated by Monte Carlo simulation. To consider when.

That is, when the sample size is larger than the X-ray generation region in any of the vertical direction, the horizontal direction, and the depth direction, the sample is treated as a bulk sample, and the sample size is measured in the vertical direction and the vertical direction. If it is larger than the X-ray generation region in the horizontal direction and smaller than the X-ray generation region in the depth direction, it is treated as a thin film sample, and the size of the sample is any of the vertical direction, the horizontal direction, and the depth direction. If it is smaller than the X-ray generation region in the direction, it is treated as a minute sample.

The accelerating voltage for measuring the characteristic X-ray intensity by EPMA, the sample absorption current, the measuring time, and the electron beam irradiation conditions such as whether Kα rays or Lα rays are used depend on the sample to be measured. The form (that is, whether it is a bulk sample, thin film sample, or microscopic sample, the relationship between the sample thin film and the substrate, the relationship between the sample microscopic object and its carrier, etc.), its type, and the constituent metal elements, It is determined in consideration of the types of non-metallic elements, and the threshold values such as the relative X-ray intensity of the sample metal and the relative X-ray intensity ratio among a plurality of sample metals for the purpose of discriminating and determining the sample, and the film thickness Regarding the calibration curve of relative X-ray intensity-film thickness of the sample metal and sample non-metal for determining, electron beam trajectory simulation is performed according to the Monte Carlo method, and the determination is made based on the result, and the sample is manufactured.

In this Monte Carlo simulation, the trajectory of electrons is assumed to be a polygonal line, and one line segment of this polygonal line is defined as the mean free path, and the angle (scattering angle) between one line segment and the next line segment is defined. ) Is the probability corresponding to a certain random number, and the model is assumed to lose electron energy for each line segment, and the mean free path calculation formula (1), scattering angle (ω) and rotation angle (φ) Equation (2), electron energy loss (ΔE) equation (3), electron collision probability (P) equation (4), position after electron scattering (5), And the relative X-ray intensity is calculated based on the respective calculation formulas (6) of the generated X-ray quantum number.

Calculation formula of mean free path (λ) (1) λ [cm] = [(0.0554E × 10 ³ ) / ρ] × {ΣA
C / [Z ^1/3 (Z + 1)]} × 10 ⁻⁸ Scattering angle (ω) and rotation angle (φ) calculation formula (2) cos (ω, radian) = 1-2βR / (1 + β−R) φ (Radian) = 2πR Calculation formula of electron energy loss (ΔE) (3) When E> 6.338J ΔE [Kev / cm] = 7.85 × 10 ⁴ ρΣ [ZC / A · ln (1.16
6 E / J)] / EE When E ≦ 6.338 J ΔE [Kev / cm] = 7.85 × 10 ⁴ ρΣ (ZC / A / J ^1/2 ) /
1.26E ^1/2

[However, in the above calculation formulas (1) to (3), E is the electron owning energy (Kev), and ρ is the density (g / cm).
³ ), Z is atomic number, A is atomic weight, C is composition,
β is a screening parameter, R is a uniform random number (0 to 1)
, Π indicates the circular constant (3.14), and J indicates the ionization potential (Kev). ]

Here, the ionization potential (J)
In the literature, the following three values J = 11.5Z × 10 ⁻³ [Kev] J = 0.00976Z + 0.0588 / Z ^0.19 [Kev] J = {14.0 [1-exp ( −0.1Z)] + 75.5
/ Z ^{Z / 7.5} −Z / (100 + Z)} Z × 10 ⁻³ [Kev] has been proposed, and regarding the screening parameter (β), the following three values β = {5.44Z ^2/3 / E} × 10 ^-3 β = {3.4Z ^2/3 /E(1.13+3.76α ² )
^1/2 } × 10 ^-3 β = {3.4Z ^2/3 / E} × 10 ^-3 [where α = {3.69 (Z / E)} × 10 ^-3 ] has been proposed. In the method of the present invention, among these constants,
In particular, values of J = 11.5Z × 10 ⁻³ [Kev] and β = {5.44Z ^2/3 / E} × 10 ⁻³ are used. By adopting the combination of the constant of the ionization potential (J) and the constant of the screening parameter (β), the calculation result by Monte Carlo simulation agrees well with the measured value measured using the standard sample, and is input to the calculation. The number of incident electrons generated can be reduced as much as possible, and calculation can be performed without using a large computer.

Regarding the uniform random number (R) used in the calculation formula (2) of the scattering angle (ω), the literature has hitherto been known, for example, the central square method (x _{k + 1} = x _k ² ). A few digits), a multiplication type congruential method [x _{k + 1} = λ · x _k (mod, M)], a mixed congruential method [x _{k + 1} = λ · x _k + μ (mod, M)], etc. Although many have been proposed, in the method of the present invention, those incorporated in a normal personal computer can be used as they are, for example, random numbers incorporated in a commercially available NEC Personal Computer. Can be preferably used.

Here, which atom the electron incident on the multi-component compound collides with is determined by the probability (P) due to the collision cross section of the element, and is represented by the following calculation formula (4). Calculation formula of probability (P) of electron collision with element (4) P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe ⁴ Z (Z + 1)] / [4E
_n ² β (β + 1)] e: electron charge (−4.8029 × 10 ⁻¹⁰ esu) E _n : electron kinetic energy (eE / 300 × 10 ³ ) For example, in the case of a ternary compound, Do so. 0 <F ≦ P _a ... if collides with a elemental _{P a <F ≦ P a +} P b ... if collides with b element _{P a + P b <F ≦} P a + P b + P c ... if collides with c elements ( However, F is a uniform random number value.)

Further, the position after electron scattering is calculated by the following formula (5) for calculating the position after electron scattering. That is, the X-Y axis is taken on the surface of the sample, and Z in the depth direction.
Taking the axis, and letting the end point position of the nth electron of the electron incident on the origin be (x _n , y _n , z _n ), the position of the (n + 1) th electron is (x _{n + 1} , y _{n + 1} , Z _{n + 1} ) is first scattered by the collision in the direction (ω, φ) from the n-th position (ω: scattering angle from the incident direction due to collision, φ: rotation angle), and The position of the (n + 1) th electron is the direction (θ _{n + 1} , ψ _{n + 1} ) with respect to the (x, y, z) coordinate axis.
It can be expressed as follows.

Calculation formula of position after electron scattering (5) cos (θ _{n + 1} ) = cos (θ _n ) cos (ω) -sin (θ _n ) sin (ω) cos (φ) sin (ψ _{n + 1} ) = A sin (ψ _n ) + B cos (ψ _n ) cos (ψ _{n + 1} ) = A cos (ψ _n ) −B sin (ψ _n ) A = [cos (ω) -cos (θ _n ) cos (θ _{n + 1} )] / [sin (θ _n ) sin (θ _{n + 1} )] B = sin (φ) sin (ω) / sin (θ _{n + 1} ) x _{n + 1} = x _n + λ sin (θ _{n + 1} ) cos (ψ _{n + 1} ) × 10 ⁴ (μm) y _{n + 1} = y _n + λ sin (θ _{n + 1} ) sin (ψ _{n + 1} ) × 10 ⁴ (μm) z _{n + 1} = z _n + λ cos (θ _{n + 1} ) × 10 ⁴ (μm)

Then, the calculation of the generated X-ray quantum number I in which electrons of energy E are generated at the distance λ in the sample is calculated by the following calculation formula (6) of the generated X-ray quantum number, and this calculation is input. It is repeatedly performed until the energy of the electron becomes lower than the excitation voltage of the element, and the X-ray quantum number is calculated as an integration with that after scattering.

Calculation formula of the generated X-ray quantum number (6) I = N _A ρQ (E) W _K Cλ / AN _A : Avogadro's number (6.02 × 10 ²³ ) A: Atomic weight ρ: Density (g / cm ³ ) Q (E): Ionization cross section Q (E) · E _k ² = 7.92 × 10 ⁻²⁰ / U · ln
(U) U = E / E _k E _k : Excitation voltage of element [Kev] W _k : Fluorescence yield [W _k = α ⁴ / (1 + α ⁴ )] α = -0.0217 + 0.0332Z-1.14Z ³ ×
Calculation of X-ray quantum number after 10 ⁻⁶ X-ray absorption I ₁ = I exp (−μρd) μ: X-ray mass absorption coefficient d: X-ray passage distance (cm)

In the method of the present invention, as an X-ray absorption model, it is assumed that a rectangular parallelepiped sample is embedded with its upper surface exposed in a matrix sufficiently larger than the X-ray generation region. Since the size of the sample in the longitudinal direction, the lateral direction, and the depth direction is set, in the calculation formula (1) of the above mean free path (λ), when the incident electrons enter the matrix from the sample, Free path and handling of free path when entering the sample from the matrix were apportioned to the distance in the sample and the distance in the matrix using the mean free path in the sample or matrix, which is the starting point of electrons. The mean free path is used to calculate the X-ray quantum numbers generated from the sample and matrix. By handling in this way, the calibration curve produced especially for measuring the film thickness of a thin film becomes more accurate.

Further, in the method of the present invention, the X-ray generation position of the characteristic X-ray generated from the X-ray absorption model is determined by the EPM.
A region that is extracted by passing through only the matrix according to the X-ray extraction direction of A (that is, X-ray extraction angle: δ),
Areas that are taken out only through the sample, areas that are taken out from the matrix through the sample, areas that are taken out from the sample through the matrix, and areas that are taken out from the matrix through the sample and further through the matrix. The area is divided, and the distance from the X-ray generation position to the sample surface is calculated according to this divided area. In this way, by dividing into a plurality of regions according to the X-ray extraction direction of EPMA, it is possible to calculate the attenuation of the X-ray quantum number according to the absorption path of the generated X-rays.

Further, in the method of the present invention, when the sample is a fine substance sample fixed on a non-metallic carrier, X
The distance from the X-ray generation position of the characteristic X-ray generated from the X-ray absorption model to the sample surface is calculated assuming that all the X-ray generation positions are the regions taken out only through the sample. The calculation is performed on the assumption that the electrons reenter the sample from the non-metallic carrier at a low rate, and the sample is assumed to be “fixed in air” in the absence of a matrix.

In the present invention, the above formulas (1)-
The Monte Carlo simulation performed using (6) is usually sufficient for less than 1000 electrons, preferably about 100 to 500 electrons. From these calculation formulas (1) to (6),
The relative X-ray intensity of each element to be measured in each sample is 10 times the X-ray quantum number obtained from the sample with the same number of incident electrons.
It is calculated as a ratio with the X-ray quantum number obtained from a 0% sample, and if necessary, the relative X of each measured element obtained.
The relative X-ray intensity ratio of each element to be measured is calculated from the line intensity, and when the sample is a thin film sample, the relative X-ray intensity of the element to be measured when the film thickness is changed is calculated if necessary. Then, a calibration curve of the relative X-ray intensity-film thickness is created, and the relative X of the measurement target element thus calculated
The sample is analyzed using the line intensity or the relative X-ray intensity ratio as a threshold value or based on the prepared relative X-ray intensity-film thickness calibration curve.

For example, when the sample is a metal compound containing at least one metal element, the characteristic X-ray intensity of each metal element constituting this sample is measured, and then the measured characteristic X-ray of each metal element is measured. Strength and metal of the relevant metal element
The relative X-ray intensity of each metal element in the sample was calculated using 100% characteristic X-ray intensity, and the relative X-ray intensity of each metal element in this sample was determined by the Monte Carlo simulation method. The sample is analyzed by comparison with the relative X-ray intensity of each metal element in.

Further, for example, when the sample is a metal / metal compound containing at least two or more kinds of metal elements, the characteristic X-ray intensity of each of these two kinds of metal elements is measured, and then each of the measured metal elements is measured. The relative X-ray intensities of the two kinds of metal elements in the sample are calculated from the relative X-ray intensities and the 100% metal characteristic X-ray intensities of the metal elements, and the relative X-ray intensities of the two kinds of metal elements in the sample are calculated. The relative X-ray intensity ratio of the two metallic elements was determined, and the relative X-ray intensity ratio of the two metallic elements in this sample was determined by the Monte Carlo simulation method. Analyze the sample relative to the ratio.

Further, for example, when the sample is a metal / non-metal compound containing at least one kind of metal element and non-metal element, the metal characteristic X-ray intensity of the metal element is measured to determine the relative metal X-ray intensity. In addition, by using a bulk standard sample composed of a predetermined metal compound containing the same non-metal element as the above non-metal element, EPMA is used to measure the metal characteristic X-ray intensity of the metal element constituting the metal compound and the non-metal element The non-metal characteristic X-ray intensity is measured, and the 100% metal characteristic X-ray intensity is measured by EPMA from a pure metal bulk standard sample of the same metal as the above metal element. The relative metal X-ray intensity of the metal compound is calculated from the% characteristic X-ray intensity, and the calculated relative metal X-ray intensity and the non-metal characteristic X-ray intensity are used to calculate the relative X-ray intensity and the weight. The non-metal relative X-ray intensity in the metal compound when the weight composition percentage of the metal element and the non-metal element becomes 100% by weight is calculated by the ZAF conversion formula between the composition percentage and the calculated non-metal. Relative X
The non-metallic 100% characteristic X-ray intensity is calculated from the line intensity, and the non-metallic relative X-ray intensity in the sample is calculated using the non-metallic 100% characteristic X-ray intensity and the non-metallic characteristic X-ray intensity measured for the non-metallic element. The line intensity was determined, and the non-metal relative X-ray intensity and the metal relative X-ray intensity were compared with the non-metal relative X-ray intensity and the metal relative X-ray intensity for the classification determination obtained by the Monte Carlo simulation method. Perform an analysis.

When the sample is a metal / nonmetal compound containing at least one kind of metal element and nonmetal element and is a thin film sample, and the film thickness thereof is to be measured, the sample was obtained. The film thickness of the sample is measured from the non-metal relative X-ray intensity and the non-metal relative X-ray intensity-calibration curve of film thickness for classification determination obtained by the Monte Carlo simulation method.

According to the method of the present invention, a rectangular parallelepiped model is assumed as the X-ray absorption model, and certain specific values are adopted as the constants of the ionization potential (J) and the screening parameter (β) used in the Monte Carlo simulation calculation formula. However, the size is set in the vertical, horizontal, and depth directions according to the size and shape of the sample, and the simulation is performed. Therefore, the sample is not limited to a bulk sample larger than the X-ray generation region, and the vertical and horizontal directions , And an accurate EPMA analysis method is possible for a thin film sample or a minute sample smaller than the X-ray generation region in any of the depth direction.

[0038]

BEST MODE FOR CARRYING OUT THE INVENTION A wavelength dispersion type EPMA (EPMA-8705 manufactured by Shimadzu Corporation; X-ray extraction angle δ: 52.
5 °) and wavelength dispersion type EPMA (JSM-5 manufactured by JEOL Ltd.)
0A; X-ray extraction angle δ: 35 °), a preferred embodiment of the present invention will be specifically described based on an example.

[Assumption of X-ray Absorption Model and Area Division of X-ray Generation Position] Areas divided to specify the X-ray absorption model and X-ray generation location assumed in FIGS. 1A and 1B. It is shown. In this X-ray absorption model, the rectangular parallelepiped sample 1 having a predetermined size in the vertical direction (XX-XXX), the horizontal direction (YY-YYY), and the depth direction (ZZ) is more than the X-ray generation region. The upper surface 1a of the large matrix 1
It is assumed that only the exposed portion is embedded, and the X-ray extraction angle δ (52.5 °) is determined by the detector 3 and the dispersive crystal 4 of the EPMA used.

The assumed X-ray absorption model is, as shown in FIGS. 1 (a) and 1 (b), the longitudinal direction (XX-XXX) and the lateral direction (YY-YYY) of the sample 1. In addition, according to the size in the depth direction (ZZ) and the X-ray extraction angle δ (52.5 °) of the EPMA used, it is divided into regions A to N for indicating the X-ray generation position. ~ Depending on whether X-rays are generated from N, the X-rays are taken out only through the matrix, taken out only through the sample, taken out through the sample from the matrix, or passed through the matrix from the sample. Was taken out,
Further, it is determined whether the matrix is passed through the sample and further extracted through the matrix, and the handling of the free path of the incident electrons is determined, and the X-ray quantum number generated from the sample and the matrix is calculated. I am trying to do it.

Here, the electrons that have entered the sample 1 from the electron incident position 1b of the sample 1 are transferred from the sample 1 to the matrix 2.
The free path when entering the sample 1 and the free path when entering the sample 1 from the matrix 2 is handled by using the mean free path in the sample 1 or matrix 2 which is the starting point of the electron and the distance in the sample 1 and the matrix. The X-ray quantum number generated from the sample 1 and the matrix 2 is calculated by using the mean free path that is proportionally divided.

Therefore, in the X-ray absorption model shown in FIGS. 1A and 1B, the characteristic X generated from the regions A, B, L, M and N taken out through the matrix 2 only.
The X-ray quantum number of the X-ray is calculated assuming that the X-ray quantum number is generated only from the matrix 2, and the X-ray quantum number of the characteristic X-ray generated from the regions F and I taken out through only the sample 1 is calculated as occurring only from the sample 1. The X-ray quantum numbers of the characteristic X-rays generated from the regions G and H and the regions J and K which are extracted from the matrix 2 through the sample 1 are calculated by using the mean free path in the matrix 2 which is the starting point of electrons. The X-ray quantum number of the characteristic X-ray generated from the region C taken out from the sample 1 through the matrix 2 is the starting point of the electron, which is calculated by proportionally dividing the distance in the sample 1 and the distance in the matrix 2. The mean free path in the sample 1 is used to calculate proportionally to the distance in the sample 1 and the distance in the matrix 2, and it is taken out from the matrix 2 through the sample 1 and further through the matrix 2. The X-ray quantum numbers of the characteristic X-rays generated from the regions D and E are proportionally divided into three, that is, the distance in the sample 1 and the distance in the matrix 2 using the mean free path in the matrix 2 which is the starting point of the electron. Will be calculated.

Here, the calculation of the electron beam trajectory and the X-ray dose in the Monte Carlo simulation is executed according to the programs shown in FIGS. That is, first,
As shown in FIG. 2, constants such as atomic weight, atomic number, density, absorption coefficient, accelerating voltage, number of incident electrons, excitation voltage, composition, etc. are input to the computer. For the number of incident electrons,
Depending on the form and composition of the sample, the number is less than 1000, preferably about 100 to 500, and the above calculation formula (1) to
Using (6), collision with an element, calculation of electron position, calculation of electron energy, calculation of generated X-ray quantum number, absorption of X-ray quantum number, integration of X-ray quantum number are repeatedly calculated.

To specify the X-ray generation position, the electronic position is calculated in accordance with the program shown in FIG. 3 to specify from which area A to N the X-ray is generated, and the specified area A to N is selected. According to the calculation, the distance from the X-ray generation position to the sample surface is calculated, and the X-ray quantum number generated using the mean free path is calculated. From the result, the relative X-ray intensity of the metal element in the sample is obtained and analyzed. To use.

Example 1 (Verification by Al ₄ C ₃ standard sample) Assuming a sample size of 20 μm in the longitudinal direction × 20 μm in the lateral direction × 20 μm in the depth direction, a personal computer (PC) manufactured by NEC Corporation N88 BASIC) and the physical properties shown in Table 1 are used.
And 3 of accelerating voltage 5kV, 10kV, and 15kV
Perform electron beam trajectory simulation under standard measurement conditions,
The relative X-ray intensity of Al (Kα line) and C (Kα line) was obtained.

[0046]

[Table 1]

A powdery standard sample Al ₄ C ₃ was pressed into a solid sample, and platinum (Pt) was thinly vapor-deposited on the surface, and then a wavelength dispersion type EPMA (EPMA-87 manufactured by Shimadzu Corporation) was used.
05; X-ray extraction angle δ: 52.5 °), acceleration voltage 5 kV (sample absorption current 10 nA, measurement time 10 seconds),
10 kV (sample absorption current 10 nA, measurement time 10 seconds),
And 15 kV (sample absorption current 5 nA, measurement time 10 seconds)
The characteristic X-ray intensities of Al and C were measured under the conditions of
Characteristic X by EPMA for 00% sample and C-100% sample
The line strength was measured, and Al and C in the standard sample Al ₄ C ₃ were measured.
The relative X-ray intensity of was calculated (measured value) and compared with the calculation result (MC calculation value) by electron beam trajectory simulation. Furthermore, using the calculated MC values and measured values of the characteristic X-ray intensities of Al and C obtained above, the calculated MC values were converted into compound compositions by the ZAF method, and the calculated MC values and measured values were compared. The results are shown in Table 2.

[0048]

[Table 2]

Example 2 [Verification by solid solution 1.1% Zn in Al (Al-1.1% Zn) standard sample] Using the physical properties shown in Table 3, acceleration voltages of 15 kV and 25
Al (Kα ray) and Z were obtained in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at two levels of kV.
The relative X-ray intensity (MC calculation value) of n (Kα ray) was obtained. Further, using an Al-1.1% Zn standard sample, an Al-100% sample, and a Zn-100% sample as bulk samples, an acceleration voltage of 15 kV (sample absorption current 5 nA, measurement time 10
Second) and 25 kV (sample absorption current 5 nA, measurement time 10)
Under the condition of (sec), the relative X-ray intensities of Al and Zn in the standard sample Al-1.1% Zn were obtained (measured value) and compared with the calculation result (MC calculated value) by electron beam trajectory simulation.
In addition, MC of the characteristic X-ray intensity of Al and Zn obtained above
Using the calculated value and the actually measured value, the MC calculated value and the actually measured value were compared by converting the compound composition by the ZAF method. The results are shown in Table 4.

[0050]

[Table 3]

[0051]

[Table 4]

Example 3 [Verification by PbS standard sample] Using the physical properties shown in Table 5, accelerating voltages of 25 kV and 30
Pb (Lα ray) and S were performed in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at two levels of kV.
The relative X-ray intensity (MC calculation value) of (Kα ray) was obtained. In addition, PbS standard sample of bulk sample, Pb-100% sample, and
Using the S-100% sample, the accelerating voltage was 25 in the same manner as in Example 1.
kV (sample absorption current 10 nA, measurement time 10 seconds) and 3
Under the condition of 0 kV (sample absorption current 10 nA, measurement time 10 seconds), the relative X-ray intensities of Pb and S in the standard sample PbS were obtained (measured value) and compared with the calculation result (MC calculated value) by electron beam trajectory simulation. . Further, using the calculated MC values and measured values of the characteristic X-ray intensities of Pb and S obtained above, the calculated MC values were converted into compound compositions by the ZAF method, and the calculated MC values and measured values were compared. The results are shown in Table 6.

[0053]

[Table 5]

[0054]

[Table 6]

Example 4 [Verification with spinel (Al ₂ O ₃ .MgO) standard sample] Using the physical properties shown in Table 7, acceleration voltages of 10 kV and 15 were used.
Al (Lα ray), M were obtained in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at two levels of kV.
Relative X-ray intensities (MC calculation values) of g (Kα ray) and oxygen (O; Kα ray) were obtained.

Here, O-100% at an acceleration voltage of 10 kV
The characteristic X-ray intensity was determined as follows. That is, first, aluminum oxide (Al ₂ O ₃ ) and pure aluminum (A 2
l) Bulk standard samples are prepared, and the characteristic X-ray intensities of Al and oxygen are measured under the conditions of a sample absorption current of 5 nA and a measuring time of 10 seconds using each of the bulk standard samples. % Characteristic X-ray intensity was measured. As a result, the Al characteristic X-ray intensity was 67793, the O characteristic X-ray intensity was 855, and the Al-100% characteristic X-ray intensity was 142.
514 counts, and the Al relative X-ray intensity of Al in the bulk standard sample Al ₂ O ₃ is 0.4757 (= 6779).
3 ÷ 142514) was calculated.

A of the bulk standard sample thus obtained
Using the Al relative X-ray intensity in l ₂ O ₃ (0.4757), the O relative to oxygen when the weight percentage (% by weight) of Al and oxygen in Al ₂ O ₃ was 100% by weight from the ZAF method conversion formula. As a result of calculating the X-ray intensity, the O relative X-ray intensity was 0.3640. At this time, the weight percentage (% by weight) of aluminum (Al) and oxygen of Al ₂ O ₃ is
Al: 53.04 wt% and O: 46.98 wt% (total 100.02 wt%), theoretical composition (Al: 52.9
The relative error with respect to 4% by weight and O: 47.06% by weight is 10% or less, which is in good agreement. As a result, the O-100% characteristic X-ray intensity was 2350 counts (= 85
5 / 0.3640) was calculated. Also, the acceleration voltage 15
kV was calculated by the same method as in the case of 10 kV.

Next, a bulk sample spinel standard sample, Al
-100% sample and Mg-100% sample were used, and the O-100% characteristic X-ray intensity obtained above was used to perform acceleration voltage 10 kV (sample absorption current 5 nA, measurement time) in the same manner as in Example 1. 1
0 seconds and 15 kV (sample absorption current 5 nA, measurement time 1
0 seconds), Al, M in standard sample spinel
The relative X-ray intensities of g and oxygen were obtained (measured value) and compared with the calculation result (MC calculated value) by electron beam trajectory simulation. Further, the calculated MC values and the measured values of the characteristic X-ray intensities of Al, Mg, and oxygen obtained above were converted into the compound composition by the ZAF method, and the calculated MC values and the measured values were compared. The results are shown in Table 8.

[0059]

[Table 7]

[0060]

[Table 8]

Example 5 [Verification by assuming Al ₃ Fe sample] Using the physical property values shown in Table 9, acceleration voltage of 3 kV, 5 kV,
In the same manner as in Example 1 above, except that the electron beam trajectory simulation was performed at four levels of 10 kV and 15 kV,
Al (Kα line), Fe (Lα line), and Fe (Kα line)
The relative X-ray intensity (MC calculation value) of was calculated. The MC composition was used to compare the compound composition obtained by the ZAF method with the theoretical composition. The results are shown in Table 10.

[0062]

[Table 9]

[0063]

[Table 10]

Example 6 [Verification by Assuming Al ₂ Cu Sample] Using the physical property values shown in Table 11, accelerating voltage of 3 kV, 5 k
Al (Kα ray), Cu (Lα ray), and Cu (Kα) were performed in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV.
The relative X-ray intensity (MC calculation value) of the line) was obtained. The MC composition was used to compare the compound composition obtained by the ZAF method with the theoretical composition. The results are shown in Table 12.

[0065]

[Table 11]

[0066]

[Table 12]

Example 7 [Verification using an assumed sample of Mg ₂ Si] Using the physical property values shown in Table 13, an accelerating voltage of 3 kV and 5 k
Relative X-ray intensities of Mg (Kα rays) and Si (Kα rays) (calculated by MC) in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV. ) Was asked. ZA using this MC calculated value
The compound composition obtained by the F method was compared with the theoretical composition.
The results are shown in Table 14.

[0068]

[Table 13]

[0069]

[Table 14]

Example 8 [Verification by TiB ₂ assumed sample] Using the physical property values shown in Table 15, accelerating voltage of 3 kV, 5 k
Ti (Lα line), Ti (Kα line), and B (Kα) were performed in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV.
The relative X-ray intensity (MC calculation value) of the line) was obtained. The MC composition was used to compare the compound composition obtained by the ZAF method with the theoretical composition. The results are shown in Table 16.

[0071]

[Table 15]

[0072]

[Table 16]

Example 9 [Verification using Si ₃ N ₄ assumed sample] Using the physical properties shown in Table 17, accelerating voltage of 3 kV, 5 k
Relative X-ray intensities (MC calculated values) of Si (Kα rays) and N (Kα rays) were measured in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV. ) Was asked. ZAF using this MC calculated value
The compound composition obtained by the method was compared with the theoretical composition. The results are shown in Table 18.

[0074]

[Table 17]

[0075]

[Table 18]

Example 10 [Verification by assumed sample of α-AlFeSi] Using the physical properties shown in Table 19, accelerating voltage of 3 kV, 5 k
Al (Kα line), Fe (Lα line), and Si (Kα line) were performed in the same manner as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV.
The relative X-ray intensity (MC calculation value) of the line) was obtained. The MC composition was used to compare the compound composition obtained by the ZAF method with the theoretical composition. The results are shown in Table 20.

[0077]

[Table 19]

[0078]

[Table 20]

Example 11 [Verification by TiC Thin Film on Al Substrate] A TiC thin film was simultaneously formed on an Al substrate and a glass substrate by an ion plating apparatus to determine whether or not the TiC thin film was formed on the Al substrate. It was confirmed by X-ray diffraction, and the film thickness of the TiC thin film formed on the glass substrate was measured by a scanning electron microscope (SEM).
It was confirmed to be 45 μm.

Next, a wavelength dispersion type EPMA (JE manufactured by JEOL Ltd.)
SM-50A; X-ray extraction angle δ: 35 °)
About TiC thin film on Al substrate confirmed by line diffraction T
The characteristic X-ray intensity (Kα ray) of i, C, and Al is measured,
The relative X-ray intensities of Ti, C, and Al were obtained. The EPMA measurement conditions at this time were an acceleration voltage of 15 kV, a sample absorption current of 10 nA for Al, a measurement time of 20 seconds, and an electron beam diameter of 40 μm.

Also, using the physical property values shown in Table 21, electron beam trajectory simulation was carried out at the same acceleration voltage of 15 kV used in actual measurement, and Ti (Kα line), C (Kα line), and Al
The relative X-ray intensity (MC calculation value) of (Kα ray) was obtained and compared with the actual measurement value previously measured. The results are shown in Table 22.

[0082]

[Table 21]

[0083]

[Table 22]

Example 12 [Verification by Al thin film on propylene film] Al thin film was formed by vapor deposition of Al on a propylene film, embedded in resin, and polished to prepare a cross-section sample, and the Al film thickness was scanned. Thickness of 0.2μm measured with scanning electron microscope (SEM)
Was confirmed. Next, using a wavelength dispersion type EPMA (JSM-50A manufactured by JEOL Ltd .; X-ray extraction angle δ: 35 °), acceleration voltage 10 kV (sample absorption current 10 nA, measurement time 10 seconds) and 25 kV (sample absorption current 10 nA,
Characteristic X-ray intensity (Kα of Al under the condition of measurement time of 10 seconds)
Line) is measured, and the relative X of Al of the Al thin film on the propylene film is measured.
The line strength was calculated.

Further, using the physical property values shown in Table 23, electron beam trajectory simulation was carried out at the same acceleration voltages of 10 kV and 25 kV used in the actual measurement, and the relative X-ray intensity (MC calculation value) of Al (Kα ray) was obtained. The measured value was compared with the previously measured value.
The results are shown in Table 24.

[0086]

[Table 23]

[0087]

[Table 24]

Example 13 [Verification by Cr thin film on Ni substrate] A Cr thin film was formed on an Ni substrate by an ion plating device, a cross-section sample was prepared, and the thickness of the Cr thin film was measured by a scanning electron microscope (SEM). It was measured and it was confirmed that the film thickness was about 0.3 μm. Next, using a wavelength dispersion type EPMA (JSM-50A manufactured by JEOL Ltd .; X-ray extraction angle δ: 35 °), the characteristic X-ray intensities (Kα rays) of Ni and Cr of the Cr thin film on the Ni substrate were measured. , Relative X of Ni and Cr
The line strength was calculated. The EPMA measurement conditions at this time were an acceleration voltage of 15 kV, a sample absorption current with respect to Ni of 10 nA, a measurement time of 20 seconds, and an electron beam diameter of 40 μm.

Further, using the physical property values shown in Table 25, electron beam trajectory simulation was performed at the same acceleration voltage of 15 kV as in the actual measurement, and the relative X of Ni (Kα line) and Cr (Kα line) was measured.
The line strength (MC calculation value) was obtained and compared with the actual measurement value previously measured. The results are shown in Table 26.

[0090]

[Table 25]

[0091]

[Table 26]

Example 14 [Verification by Al ₂ O ₃ Coating on Al Substrate] An aluminum foil having a size of about 5 cm × 5 cm was annealed under the conditions shown in Table 27, and an oxide film ( Aluminum oxide: Al ₂ O ₃ ) was produced, and then cut into a size of 1 cm × 1 cm to prepare samples No. 1 to No. 5 under each annealing treatment condition. The film thickness of each of the samples No. 1 to No. 5 thus obtained was measured with an electron microscope. The results are shown in Table 27.

[0093]

[Table 27]

Next, for each of the samples No. 1 to No. 5 prepared above, a wavelength dispersion type EPMA (EPMA-8 manufactured by Shimadzu Corporation) was used.
705; X-ray extraction angle δ: 52.5 °), acceleration voltage 5 kV, sample absorption current 20 nA for Al-100%,
O characteristic X-ray intensity was measured and measured under conditions of a measurement time of 100 seconds, measurement points of each sample No. 1 to No. 5 at 100 μm intervals (A to E), and an electron beam diameter of 40 μm. The O relative X-ray intensity was calculated using the average value of the O characteristic X-ray intensity and the O-100% characteristic X-ray intensity 43890 count obtained by the same method as in Example 4. The results are shown in Table 28.

[0095]

[Table 28]

Assuming a sample in which an Al ₂ O ₃ oxide film is formed on an Al substrate, the film thickness is changed by 100 Å from 100 Å to 500 Å, and the density of the oxide film is set to 3.2 g / cm ³ and 3. .9g / cm ³ and the changing, the condition previously set the measurement conditions by EPMA, with physical properties shown in Table 29 is performed in accordance with the Monte Carlo method with an electron beam trajectory simulation in the sample, the film thickness and The O relative X-ray intensity of oxygen at each density was calculated.

[0097]

[Table 29]

The calculation results are shown in Table 30. A calibration curve was prepared by plotting the film thickness (Å) on the horizontal axis and the O relative X-ray intensity on the vertical axis. The calibration curve obtained is shown in FIG.

[Table 30]

From the value of the O relative X-ray intensity shown in Table 28, FIG.
The thickness of the oxide film of each sample No. 1 to No. 5 was estimated using the calibration curve shown in. The results are shown in Table 31 together with the measurement results by the electron microscope.

[Table 31]

Furthermore, the oxide film of sample No. 5 (annealing treatment:
550 ° C x 1 hr), and the acceleration voltage is 10
Calculations and actual measurements were made by electron beam trajectory simulation under the same conditions as above except that kV was used, and comparison was made. The results are shown in Table 32.

[Table 32]

Example 15 [Verification by Micro Al ₃ Fe] As a sample, high-purity aluminum in which only crystallized particles of Al ₃ Fe were confirmed as a result of X-ray diffraction analysis was used. Thirty
Charge a 0 ml flask with 120 ml of phenol and heat to 160 ° C. for about 1 minute to remove water, then 0.2
~ 0.3 g of sample aluminum is made into fine chips with a drill and put into a flask, and a reflux condenser is attached to
Heat the sample for about 3 minutes to dissolve the sample aluminum foil in phenol, then add 80 ml of benzyl alcohol and cool to room temperature. Transfer the resulting solution to a centrifuge tube and centrifuge (7000 rpm) to remove the supernatant. Then, benzyl alcohol was added to the centrifuge tube to re-disperse the precipitate, and then centrifugation (7000 rpm) was performed again to remove the supernatant liquid, and then methanol was added and filtered through a PTFE membrane filter (pore size 0.1 μm). Then, the sample was prepared by further washing with methanol to capture Al ₃ Fe particles on this filter.

Next, using a wavelength dispersion type EPMA (EPMA-8705 manufactured by Shimadzu Corporation; X-ray extraction angle δ: 52.5 °), an accelerating voltage of 15 kV and a sample absorption current of 5 for Al.
Under the conditions of nA and measurement time of 10 seconds, 5 Al ₃ Fe particles of different sizes captured on the filter were selected, and A
l and Fe characteristic X-ray intensities were measured, and
And the relative X-ray intensities of Fe were obtained, and then from these values
The Al / Fe relative X-ray intensity ratio (measured value) was determined. The result is N
o.1 particles are 0.9, No.2 particles are 0.9, No.3 particles are 0.
8, No. 4 particles are 1.0, and No. 5 particles are 0.8,
It was in the range of 0.8 to 1.0.

Further, the trapped Al ₃ Fe crystallized particles are assumed to be rectangular parallelepiped, and 0.2 to 10 μm in the vertical direction (X), the horizontal direction (Y), and the depth direction (Z) where electrons are incident. Electron beam trajectory simulation under the conditions of 150 incident electrons and acceleration voltage of 15 kV using the physical properties shown in Table 33 using a personal computer (PC N88 BASIC) manufactured by NEC Corporation. Done, Al (Kα ray)
And the relative X-ray intensities of Fe (Kα rays) are calculated, and then Al / Fe
The relative X-ray intensity ratio was calculated. The results are shown in Table 34.

[0104]

[Table 33]

[0105]

[Table 34]

[0106]

According to the method of the present invention, not only a bulk sample sufficiently larger than the X-ray generation region but also a vertical direction, a horizontal direction,
Also, it is possible to perform accurate analysis on thin film samples and minute object samples smaller than the X-ray generation region in any one or more of the depth directions, and moreover, accurate analysis by simulation with a small electron number of less than 1000. You can

[Brief description of drawings]

FIG. 1 is an explanatory view showing an X-ray absorption model assumed in the present invention and a region divided to specify an X-ray generation position, and FIG. 1A is a sectional explanatory view.
(B) is a plane explanatory view.

FIG. 2 is a flowchart showing a calculation flow of an electron trajectory simulation of the present invention.

FIG. 3 is a flowchart showing a procedure for specifying an X-ray generation position in the X-ray absorption model and the X-ray generation position division area of FIG. 1.

FIG. 4 shows the film thickness (Å) -obtained in Example 14
It is a graph which shows the calibration curve of O relative X-ray intensity.

Claims (13)

(57) [Claims] 1. A matrix sufficiently larger than the X-ray generation region.
A rectangular parallelepiped sample is buried in the chamber by exposing only its upper surface.
Assuming an embedded X-ray absorption model, this X-ray absorption model
Size of the sample in the vertical, horizontal and depth directions
According to the size and shape of the
The following formula in the Luro simulation formula
(2) to (4) Total of scattering angle (ω) and rotation angle (φ)
Formula (2) cos (ω, radian) = 1-2βR / (1 + β-R) φ (radian) = 2πR Calculation formula of electron energy loss (ΔE) (3) When E> 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ [ZC / A ・ ln (1.16
6 E / J)] / E When E ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ (ZC / A / J^1/2) /
1.26E^1/2 Calculation formula (4) of probability (P) that electron collides with element P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe^FourZ (Z + 1)] / [4E
_n ²β (β + 1)] [However, in the above formulas (2) to (4), E is an electron
Own energy (Kev), A is atomic weight, ρ is density (g /
cm³), Z is atomic number, J is ionization potential
(Kev), β is the screening parameter, R is uniform
Random number (0 to 1), π is circular constant (3.14), C is composition
, E is the electric charge of the electron (−4.8029 × 10 ^-Tenesu)
The E_nIs the kinetic energy of the electron (eE / 300 × 10
³) Respectively], J = 11.5Z × 10^-3 [Kev] and β = {5.44Z^2/3/ E} × 10^-3 Simulation with less than 1000 incident electrons
Monte Carlo simulation characterized by
EPMA analysis method used. 2. A calculation formula (1) for the mean free path (λ) in the simulation calculation formula: λ [cm] = [(0.0554E × 10 ³ ) / ρ] × {ΣA
C / [Z ^1/3 (Z + 1)]} × 10 ⁻⁸ [However, in the above calculation formula (1), E, ρ, Z, A,
And C are the same as in the case of the above calculation formulas (2) to (4). ], The free path when incident electrons enter the matrix from the sample and the free path when it enters the sample from the matrix are treated using the sample as the starting point of electrons or the mean free path in the matrix. The EPMA analysis method using Monte Carlo simulation according to claim 1, wherein the X-ray quantum numbers generated from the sample and the matrix are calculated by dividing the distances in the matrix and the distances in the matrix and using the proportionally divided mean free path. 3. The X-ray generation position of the characteristic X-ray generated from the X-ray absorption model is set according to the X-ray extraction direction of EPMA.
Areas that are taken out only through the matrix, areas that are taken out only through the sample, areas that are taken out through the sample from the matrix, areas that are taken out through the matrix from the sample, and areas that are taken out through the sample from the matrix. The EPMA analysis method using Monte Carlo simulation according to claim 1 or 2, further dividing into regions extracted through the matrix, and calculating the distance from the X-ray generation position to the sample surface in accordance with the divided regions. . 4. Kα depending on the type of element constituting the sample
EPMA using Monte Carlo simulation according to any one of claims 1 to 3, which uses X-rays and / or Lα rays.
Analytical method. 5. The sample size includes vertical and horizontal directions,
The EPMA analysis method using Monte Carlo simulation according to claim 1, wherein a bulk sample is measured by setting a size larger than the X-ray generation region in any of the depth direction and the depth direction. 6. The thin film sample is measured by setting the size of the sample to be larger than the X-ray generation region in the vertical and horizontal directions and smaller than the X-ray generation region in the depth direction. An EPMA analysis method using the Monte Carlo simulation according to any one of 4 above. 7. The sample size includes vertical and horizontal directions,
The EPMA analysis method using the Monte Carlo simulation according to any one of claims 1 to 4, wherein a size smaller than the X-ray generation region is set in any of the depth direction and the depth direction, and the minute object sample is measured. 8. The sample is a minute object sample fixed on a non-metallic carrier, and the distance from the X-ray generation position of the characteristic X-ray generated from the X-ray absorption model to the sample surface is the X-ray generation position. The EPMA analysis method using Monte Carlo simulation according to claim 7, which is calculated as an area in which all are taken out through only a sample. 9. The EP using Monte Carlo simulation according to claim 8, wherein the non-metallic carrier is a filter, and a microscopic sample is captured on the filter for analysis.
MA analysis method. 10. The sample is a metal compound containing at least one metal element, the characteristic X-ray intensity of each metal element constituting the sample is measured, and then the measured characteristic X-ray intensity of each metal element. And the metal 100% characteristic X-ray intensity of the metal element are used to calculate the relative X-ray intensity of each metal element in the sample, and the relative X-ray intensity of each metal element in this sample is determined by the Monte Carlo simulation method. EPMA using Monte Carlo simulation according to any one of claims 1 to 9, wherein the sample is analyzed by comparing it with the relative X-ray intensity of each metal element in the sample.
Analytical method. 11. A sample is a metal / metal compound containing at least two or more kinds of metal elements, the characteristic X-ray intensity of each of these two kinds of metal elements is measured, and then the relative X of each metal element is measured. The relative X-ray intensities of the two types of metal elements in the sample were calculated from the line intensities and the metal 100% characteristic X-ray intensities of the metal elements. Relative X of metallic elements
The line intensity ratio is obtained, and the relative X-ray intensity ratio of the two metal elements in this sample is compared with the relative X-ray intensity ratio of the two metal elements for the classification determination obtained by the Monte Carlo simulation method. The EPMA analysis method using the Monte Carlo simulation according to any one of claims 1 to 9. 12. The sample is a metal / nonmetal compound containing at least one kind of metal element and a nonmetal element, and the metal characteristic X-ray intensity of the metal element is measured to calculate a metal relative X-ray intensity. In addition, by using a bulk standard sample made of a predetermined metal compound containing the same non-metal element as the above non-metal element, the metal characteristic X-ray intensity of the metal element constituting the metal compound by EPMA and the non-metal characteristic of the non-metal element. In addition to measuring the X-ray intensity, 100% metal characteristic X-ray intensity was measured by EPMA from a pure metal bulk standard sample of the same metal as the above metal element, and these measured metal characteristic X-ray intensity and metal 100% characteristic X were measured. The metal relative X-ray intensity of the metal compound is calculated from the line intensity, and the calculated metal relative X-ray intensity and the non-metal characteristic X-ray intensity are used to calculate the relative X-ray intensity and the weight composition percentage. The non-metal relative X-ray intensity of the metal compound when the weight composition percentage of the metal element and the non-metal element becomes 100% by weight is calculated by the ZAF conversion formula of Non-metal
The 100% characteristic X-ray intensity is calculated, and the non-metal relative X-ray intensity of the sample is calculated using the non-metal 100% characteristic X-ray intensity and the non-metal characteristic X-ray intensity measured for the non-metal element, A sample is analyzed by comparing the non-metal relative X-ray intensity and the metal relative X-ray intensity with the non-metal relative X-ray intensity and the metal relative X-ray intensity for classification determination obtained by a Monte Carlo simulation method. An EPMA analysis method using the Monte Carlo simulation according to any one of 1 to 9. 13. The sample is a thin film sample, and the non-metal relative X-ray intensity obtained for the sample and the non-metal relative X-ray intensity-discrimination calibration curve for classification determination obtained by the Monte Carlo simulation method are used to obtain the sample. The thickness of the film is measured.
EP using the Monte Carlo simulation described in 2.
MA analysis method.