JP2000338065A - Epma analysis method using monte carlo simulation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an EPMA analysis method using Monte Carlo simulation that can accurately analyze thin-film and minute-object samples that are smaller than an X-ray generation region, and can accurately carry out analysis by simulation with a small number of electrons. SOLUTION: An X-ray absorption model where a sample in a rectangular parallelepiped shape is buried into a matrix that is sufficiently larger than an X-ray generation region while merely the upper surface is being exposed is supposed, size in the vertical, horizontal, and depth directions of the sample in the X-ray absorption model is set according to the size and shape, at the same time, J=11.5Z×10-3 [Kev] and Β= 5.44Z2/3/E)×10-3 are used as ionized potential (Kev) and the constant of a screening parameter in each calculation expression of a scattering angle and the angle of rotation in the calculation expression, the energy loss of an electron, and a probability where the electron collides with an element, and the number of incident electrons is set to less than 1,000 for simulating.

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 characteristic X-rays emitted from the sample to qualitatively or quantitatively determine elements in the sample. microanalys
er; hereinafter referred to as “EPMA”).
In particular, EP using Monte Carlo simulation technique
It relates to the MA analysis method.

[0002]

2. Description of the Related Art EPMA analysis involves irradiating a sample surface with an electron beam (Electron probe) that is extremely finely squeezed, and measuring the wavelength and intensity of characteristic X-rays emitted from that portion using an X-ray spectrometer or detector. Measuring, thereby qualitatively or quantitatively determining the elements contained in the minute part of the sample, it is possible to know which part of the sample is being measured,
Since the sample can be analyzed nondestructively without dissolving it as in chemical analysis, it is possible to analyze various minute substances such as micro foreign substances mixed in the sample, microcrystals generated by melting metal, etc. It is applied to the analysis of various samples in various fields such as measurement of shape and size.

[0003] However, the conventional EPMA analysis method,
Basically, it is established based on the premise of comparison with a standard sample. If it is difficult to prepare or obtain a standard sample, it will be difficult to accurately analyze the sample. Is the region where the size of the sample emits characteristic X-rays when irradiated with an electron beam, that is, the "X-ray generation region"
Only when the sample size is sufficiently larger,
If it is smaller than the line generation area, X-rays radiated from parts other than the sample will also be measured, and accurate analysis of the sample will not be possible.

For example, when the sample is a thin film, and when the thin film sample is irradiated with an electron beam, the depth direction of the X-ray generation region exceeds the depth direction of the thin film sample, Even if one measurement is taken, the characteristic X-ray of the component element radiated from the part other than the sample is measured, and the electrons re-entering the sample from the part other than the sample generate the characteristic X-ray of the sample. Analysis becomes difficult, and when the types of thin films are diverse, or when several layers are stacked, it becomes difficult to prepare a standard sample for preparing a calibration curve. In such a case, it takes a lot of time and effort to create the file.

For example, when analyzing a minute object of about 1 μm found on an aluminum copy drum or an MD substrate, even if an element such as Si, O, or Al is detected from such a minute object, a matrix is required. Of Al is measured, so it cannot be determined whether the minute substance is SiO ₂ or another oxide of Al or Si. The same applies to a case where an element such as Al, Mg, O, etc. is detected from a minute substance in an S3M alloy to which about 3% of Mg is added, or an aluminum heat exchanger part. When elements such as Fe and Al are detected from minute objects found around the hole generated in the automobile condenser tube,
It also occurs when an element such as Fe or Al is detected from a minute substance present in aluminum.

Therefore, recently, such a minute object is specified.
As a method, a unique satellite line from characteristic X-ray
There is a state analysis method that compares the state of profiles. This
Of the state analysis method of
Al_TwoO_Three, MgO, spinel, SiO_Two, FeO,
Fe_TwoO_Three, Fe_ThreeO_FourMetal oxides such as Al
_FourC _Three, SiC and other metal carbides, AlN, Si_ThreeN_Four
It is said that it is possible to specify a metal nitride or the like.

However, even in this state analysis method, when a minute object or a thin film having a thickness of about 1 μm or less is used, the measurement requires about 30 minutes or more, so that it is difficult to continuously irradiate the electron beam accurately to the minute object. There is. 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 specify a specific satellite line such as oxides, carbides, nitrides, and the like by state analysis, so that it is difficult to specify them.

Further, in the case of thin film measurement, the trajectory of electrons incident on the sample is simulated by the Monte Carlo method in consideration of the influence of the substrate which cannot be corrected by the ZAF method, and the amount of primary X-rays that can be generated by the trajectory of the electrons is measured. And a method of analyzing a sample from a calculated value obtained by calculating the generated function and the generated function (Japanese Patent Application 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, usually 10,000 or more, and sometimes 30,000
The trajectory of many electrons must be simulated, which requires the use of a large computer, which is unsuitable for practical research, and has the problem that it cannot be applied to minute objects.

[0009]

Therefore, the present inventor has proposed:
Not only bulk samples that are sufficiently larger than the X-ray generation area,
Accurate analysis is possible even for a thin film sample or a minute sample that is smaller than the X-ray generation region in one or more of the vertical, horizontal, and depth directions.
As a result of intensive studies on an EPMA analysis method using Monte Carlo simulation that can perform accurate analysis with a small number of electrons less than 00, a rectangular parallelepiped model is assumed as an X-ray absorption model. It has been found that the object can be achieved by adopting certain values as constants of the ionization potential (J) and the screening parameter (β) used in the above, and completed the present invention.

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

Another object of the present invention is to provide an EPMA analysis method using Monte Carlo simulation, which can perform accurate analysis with a small number of electrons less than 1,000.

[0012]

That is, the present invention provides an X
A rectangular parallelepiped in a matrix sufficiently larger than the line generation area
X-ray absorption in which a sample in the shape of a sample is embedded with only its upper surface exposed
Assuming a model, the vertical length of the sample in this X-ray absorption model
The size in the direction, lateral direction, and depth direction
Settings and Monte Carlo simulation
The following calculation formulas (2) to (4) in the calculation formula
Equation (2) for calculating angle (ω) and rotation angle (φ) cos (ω, radian) = 1−2βR / (1 + β−R) φ (radian) = 2πR Equation (3) for calculating electron energy loss (ΔE) ) When E> 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ [ZC / A · ln (1.16
6E / J)] / E When E ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ (ZC / A / J^1/2) /
1.26E^1/2 Formula (4) for calculating the probability (P) that an electron collides with an element P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe^FourZ (Z + 1)] / [4E
_n ^Twoβ (β + 1)] [However, in the above formulas (2) to (4), E is an electron
Is the owned energy (Kev), A is the atomic weight, ρ is the density (g /
cm^Three), Z is the atomic number, J is the ionization potential
(Kev), β is the screening parameter, R is uniform
Random number (0 to 1), π is pi (3.14), C is composition
And e is the electron charge (−4.8029 × 10 ^-Tenesu)
To E_nIs the kinetic energy of the electron (eE / 300 × 10
^Three)], J = 11.5Z × 10
^-3 [Kev] and β = ｛5.44Z^2/3/ E｝ × 10^-3 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
Wavelength Dispersive X-ray An
alysis) or energy dispersive (Energy D
It may be ispersive X-ray Analysis, but is preferably a wavelength dispersion type EPMA.

In the method of the present invention, there is no particular limitation on the sample to be measured.
Even a bulk sample sufficiently larger than the X-ray generation region, a thin film sample or a minute sample smaller than the X-ray generation region in any of the longitudinal direction, the horizontal direction, and the depth direction. Good. And as for the thin film sample, it may be a single layer thin film or a multilayer thin film,
Regarding the micro sample, even if it is a micro sample dispersed in the metal or metal compound of the matrix, it is also fixed on a non-metal carrier such as a PTFE membrane filter by a known method. Small objects, rubber,
Fine foreign substances or the like existing in organic substances such as paper, cardboard, and plastic may be used.

For the sample to be measured,
These are Al, Fe, Cu, Au, Si, Ni, Cr, Ti
May be a sample composed of a single metal element such as
Al containing at least two or more sample metal elements₆Fe,
Al_ThreeFe, AlFe, AlFe_ThreeAl-Fe system such as
Al-Fe-Mn-based, Al-Fe-Si-based, Al-
A such as Fe-Mg-Si system, Al-Fe-Mn-Si system
l-Fe-X system, Al _TwoAl-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 based intermetallic compounds in Al
Metal and metal compounds such as
Al including one kind of sample metal element and sample non-metal element_Two
O_Three, SiO_Two, Fe_TwoO_Three, Metal oxides such as MgO,
Al_FourC_Three, Metal carbides such as SiC, AlN, Si_ThreeN
_FourMetal nitride, mullite (Al_TwoO_Three・ 2SiO_Two), Spinel
(Al_TwoO_Three・ MgO), Forsterite (2MgO ・ SiO_Two), Jill
Con (ZrO_Two..SiO_TwoMetals and non-gold such as ternary compounds such as
It may be a genus compound. And these measurement targets
The use of the sample is not particularly limited.

In the method of the present invention, it is assumed that such a sample to be measured has a rectangular parallelepiped shape, and the rectangular parallelepiped sample is embedded in a matrix having a size sufficiently larger than the X-ray generation area with only its upper surface exposed. Assuming the obtained X-ray absorption model, the size of the sample in the vertical, horizontal, and depth directions in this X-ray absorption model is set according to the size and shape, and the electron trajectory is calculated by Monte Carlo simulation. To take into account.

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

The acceleration voltage, the sample absorption current, the measurement time, and the electron beam irradiation conditions, such as whether to use Kα or Lα rays, for measuring the characteristic X-ray intensity by EPMA are determined according to the sample to be measured. The form (that is, whether it is a bulk sample, a thin film sample, or a minute sample, the relationship between the sample thin film and the substrate, the relationship between the sample minute object and its carrier, etc.), the type thereof, and the constituent metal elements and It is determined in consideration of the type of the non-metallic element, etc., and the threshold such as the relative X-ray intensity of the sample metal and the relative X-ray intensity ratio between a plurality of sample metals for separating and judging the sample, and further, the film thickness An electron beam trajectory simulation is performed according to the Monte Carlo method for the calibration curve of the relative X-ray intensity-film thickness of the sample metal or the sample nonmetal for the determination, and the determination is made based on the result.

In this Monte Carlo simulation, the trajectory of the electron is assumed to be a broken line, and one of the broken lines is defined as the mean free path, and the angle (scattering angle) between one line and the next line is assumed. ) Is a probability corresponding to a certain random number, further assumes a model assuming that electron energy is lost for each line segment, and calculates a mean free path equation (1), a scattering angle (ω), and a rotation angle (φ). Equation (2), Equation (3) for calculating electron energy loss (ΔE), Equation (4) for calculating the probability (P) that an electron collides with an element, Equation (5) for calculating the position after electron scattering, Then, the relative X-ray intensity is calculated based on each calculation formula (6) of the generated X-ray quantum number.

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

In the above formulas (1) to (3), E is the possessed energy (Kev) of the electron, and ρ is the density (g / cm).
³ ), Z is the atomic number, A is the atomic weight, C is the composition,
β is a screening parameter, R is a uniform random number (0 to 1)
, Π indicates the pi (3.14), and J indicates the ionization potential (Kev). ]

Here, the above ionization potential (J)
Has been described in the literature, the following three values J = 11.5Z × 10 ⁻³ [Kev] J = 0.9776Z + 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. 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 a combination of the constant of the ionization potential (J) and the constant of the screening parameter (β), the calculation result by the Monte Carlo simulation matches well with the actually measured value measured using the standard sample, and is input to the calculation. As a result, the number of incident electrons can be reduced as much as possible, and calculation can be performed without a large computer.

The uniform random number (R) used in the equation (2) for calculating the scattering angle (ω) has also been described in the literature, for example, in the central square method (x _{k + 1} = x _k ² Several digits), multiplication type combination method [x _{k + 1} = λ · x _k (mod, M)], mixed type congruential method [x _{k + 1} = λ · x _k + μ (mod, M)], etc. Although many methods have been proposed, in the method of the present invention, those incorporated in an ordinary personal computer can be used as they are, for example, a random number incorporated in a commercially available personal computer manufactured by NEC Corporation. Can be suitably used.

Here, which atom the electron incident on the multi-component compound collides with is determined by the probability (P) based on the collision cross section of the element, and is expressed by the following equation (4). Formula (4) for calculating the probability (P) that an electron collides with an element: 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 following the case of ternary compound Do as follows. 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 ( Here, F is a uniform random value.)

Further, the position after electron scattering is calculated by the following equation (5) for calculating the position after electron scattering. That is, the XY axis is set on the sample surface, and the Z direction is set in the depth direction.
Taking the axis, the electron of the n-th electron of the end position which is incident at the origin (x _n, y _n, z _n) When, (n + 1) -th position of the electron _{(x n + 1, y n} + 1 , Z _{n + 1} ) are first scattered from the n-th position by the collision in the direction (ω, φ) (ω: scattering angle from the incident direction due to the collision, φ: rotation angle). The position of the (n + 1) th electron in the direction (θ _{n + 1} , ψ _{n + 1} ) with respect to the (x, y, z) coordinate axis
When expressed as follows,

Formula for calculating 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) = Asin (ψ n)} + Bcos (ψ n) cos (ψ n + 1) = Acos (ψ n) -Bsin (ψ n) A = [cos (ω) -cos (θ n) cos (θ n + ₁ )] / [sin ([theta] _n ) sin ([theta] _{n + 1} )] B = sin ([phi]) sin ([omega]) / sin ([theta] _{n + 1} ) _{xn + 1} = _xn + [lambda] sin ([theta] _{n + 1} ) _{cos (ψ n + 1) ×} 10 4 (μm) y n + 1 = y n + λsin (θ n + 1) sin (ψ n + 1) × 10 4 (μm) z n + 1 = z n + λcos (θ _{n + 1} ) × 10 ⁴ (μm)

Then, the calculation of the generated X-ray quantum number I in which an electron having the energy E is generated at the distance λ in the sample is calculated by the following equation (6) for calculating the generated X-ray quantum number. The process is repeated until the energy of the electrons becomes lower than the excitation voltage of the element, and the X-ray quantum number is calculated as an integrated value after scattering.

Formula for calculating the generated X-ray quantum number (6) I = N _A ρQ (E) W _K Cλ / A N _A : Avogadro 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 ×
10 ^-6 Calculation of X-ray quantum number after 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 a X-ray absorption model, it is assumed that a rectangular parallelepiped sample is embedded in a matrix sufficiently larger than the X-ray generation region with only its upper surface exposed. Since the size of the sample in the vertical direction, the horizontal direction, and the depth direction is set, in the equation (1) for calculating the mean free path (λ), when the incident electrons enter the matrix from the sample. The handling of the free path when the sample enters the sample from the free path and the matrix is apportioned to the distance in the sample and the distance in the matrix using the average free path in the sample or matrix, which is the starting point of the electrons, and is apportioned. The mean free path is used to calculate the number of X-ray quanta generated from the sample and the matrix. By handling in this way, a calibration curve prepared especially for measuring the thickness of a thin film becomes more accurate.

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 extracted through only the matrix according to the X-ray extraction direction of A (that is, X-ray extraction angle: δ),
A region that is removed only through the sample, a region that is removed through the sample from the matrix, a region that is removed through the matrix from the sample, and a region that is removed from the matrix through the sample and further through the matrix Then, the distance from the X-ray generation position to the sample surface is calculated according to the divided area. By dividing the region into a plurality of regions according to the X-ray extraction direction of the EPMA, the attenuation of the X-ray quantum number according to the absorption path of the generated X-ray can be calculated.

Further, in the method of the present invention, when the sample is a minute sample fixed on a nonmetallic 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 of the X-ray generation positions are regions that are extracted through only the sample. The calculation is performed assuming in this manner because the sample is assumed to be "in the air" without a matrix because the rate at which electrons re-enter the sample from the nonmetallic carrier is small.

In the present invention, the above formulas (1) to (1)
The Monte Carlo simulation performed using (6) is usually sufficient for less than 1000 electrons, and is preferably performed for about 100 to 500 electrons. According to these calculation formulas (1) to (6),
The relative X-ray intensity of each element to be measured in each sample is equal to the X-ray quantum number obtained from the sample by making the number of incident electrons the same.
Calculated as the ratio to the X-ray quantum number obtained from the 0% sample, and if necessary, the relative X
The relative X-ray intensity ratio of each element to be measured is calculated from the line intensity. If 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 prepared, and the relative X of the element to be measured thus calculated is calculated.
The sample is analyzed based on the line intensity or the relative X-ray intensity ratio as a threshold or based on the prepared calibration curve of relative X-ray intensity-film thickness.

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 the sample is measured, and then the measured characteristic X-ray of each metal element is measured. Strength and metal of the metal element
Using the 100% characteristic X-ray intensity, the relative X-ray intensity of each metal element in the sample was calculated, 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 comparing with the relative X-ray intensity of each metal element in.

For example, when the sample is a metal / metal compound containing at least two or more metal elements, the characteristic X-ray intensity of each of these two metal elements is measured, and then the measured metal element The relative X-ray intensity of the two metal elements in the sample is calculated from the relative X-ray intensity of the sample and the metal 100% characteristic X-ray intensity of the metal element, and the relative X-ray intensity of the two metal elements in the sample is calculated in the sample. The relative X-ray intensity ratio of the two metal elements was determined, and the relative X-ray intensity ratio of the two metal elements in this sample was determined by the Monte Carlo simulation method. The sample is analyzed in comparison with the ratio.

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

In the case where the sample is a metal / nonmetal compound containing at least one metal element and a nonmetal element and is a thin film sample, and the thickness of the sample is measured, it is determined for the sample. The film thickness of the sample is measured from the non-metal relative X-ray intensity and the calibration curve of the non-metal relative X-ray intensity-film thickness for classification judgment 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 specific values are employed as constants of the ionization potential (J) and the screening parameter (β) used in the Monte Carlo simulation calculation formula. The simulation is performed by setting the size in the vertical, horizontal, and depth directions according to the size and shape of the sample. Therefore, the simulation is not limited to the bulk sample larger than the X-ray generation area. And an accurate EPMA analysis method can be performed on a thin film sample or a minute sample that is smaller than the X-ray generation region in any direction of the depth direction.

[0038]

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, a wavelength dispersion type EPMA (EPMA-8705 manufactured by Shimadzu Corporation; X-ray extraction angle δ: 52.
5 °) and wavelength dispersive 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.

[Assumption of X-ray Absorption Model and Region Division of X-ray Generation Position] The X-ray absorption model assumed in FIGS. 1A and 1B and the region divided for specifying the X-ray generation position 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 sufficiently larger than the X-ray generation region. In a large matrix 1, its upper surface 1a
The X-ray extraction angle δ (52.5 °) is assumed by the EPMA detector 3 and the dispersing crystal 4 to be used.

The assumed X-ray absorption model, as shown in FIGS. 1A and 1B, shows the sample 1 in the vertical direction (XX-XXX) and the horizontal direction (YY-YYY). And X-ray extraction angle δ (52.5 °) of EPMA used in the depth direction (ZZ), and is divided into regions A to N for indicating X-ray generation positions. ~ X, the X-rays were extracted only through the matrix, extracted only through the sample, extracted through the matrix, extracted through the sample, or passed through the matrix from the sample, depending on whether X-rays were generated from N. Was taken out
Furthermore, it is distinguished whether the matrix passes through the sample and is further extracted through the matrix, thereby determining the handling of the free path of the incident electrons, and calculating the X-ray quantum number generated from the sample and the matrix. I am trying to do it.

Here, electrons incident on the sample 1 from the electron incident position 1b of the sample 1
The handling of the free path when entering the sample 1 and the free path when entering the sample 1 from the matrix 2 is performed by using the mean free path in the sample 1 or the matrix 2 which is the starting point of the electrons and the distance in the sample 1 and the matrix. The X-ray quantum numbers generated from the sample 1 and the matrix 2 are calculated using the proportionally divided mean free path.

Therefore, in the X-ray absorption models shown in FIGS. 1A and 1B, the characteristic X generated from the regions A, B, L, M, and N that are extracted through only the matrix 2 is obtained.
The X-ray quantum number of the line is calculated as being generated only from the matrix 2, and the X-ray quantum number of the characteristic X-ray generated from the regions F and I extracted through only the sample 1 is calculated as being generated only from the sample 1. The X-ray quantum numbers of characteristic X-rays generated from the regions G and H and the regions J and K extracted from the matrix 2 through the sample 1 are calculated using the mean free path in the matrix 2 which is the starting point of the electrons. The X-ray quantum number of characteristic X-rays calculated from the distance in the sample 1 and the distance in the matrix 2 from the region C extracted from the sample 1 through the matrix 2 is the starting point of electrons. The distance in the sample 1 and the distance in the matrix 2 are calculated proportionally using the mean free path in the sample 1, and are extracted 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 distributed to 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 electrons. Will be calculated.

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

The X-ray generation position is specified by calculating the electron position according to the program shown in FIG. 3 and specifying from which area A to N the X-ray is generated, and determining the X-ray generation position in the specified area A to N. The distance from the X-ray generation position to the sample surface is calculated accordingly, the X-ray quantum number generated using the mean free path is calculated, and the relative X-ray intensity of the metal element in the sample is obtained from the result and analyzed. Use for

Example 1 (Verification with Al ₄ C ₃ standard sample) A personal computer (PC) manufactured by NEC Corporation was assumed to have a size of 20 μm in the vertical direction × 20 μm in the horizontal direction × 20 μm in the depth direction. N88 BASIC) and the physical properties shown in Table 1 were used.
And acceleration voltage of 5 kV, 10 kV, and 15 kV
Perform electron beam trajectory simulation under the standard measurement conditions,
The relative X-ray intensity of Al (Kα ray) and C (Kα ray) was determined.

[0046]

[Table 1]

Further, a powdery standard sample Al ₄ C ₃ is formed into a solid sample by pressing, and platinum (Pt) is vapor-deposited on the surface, and then a wavelength dispersion type EPMA (EPMA-87 manufactured by Shimadzu Corporation) is 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 intensity of Al and C was measured under the conditions of
Characteristic X by EPMA for 00% sample and C-100% sample
The linear intensity was measured, and Al and C in the standard sample Al ₄ C ₃ were measured.
Was obtained (actual measurement value) and compared with the calculation result (MC calculation value) by the electron beam locus simulation. Further, using the calculated and measured values of the characteristic X-ray intensities of Al and C obtained above and converted to the compound composition by the ZAF method, the calculated values of MC and the measured values were compared. Table 2 shows the results.

[0048]

[Table 2]

Example 2 [Verification using 1.1% Zn in Al (Al-1.1% Zn) as a solid solution in Al] Using the physical properties shown in Table 3, an acceleration voltage of 15 kV and 25 kV were used.
Except that the electron beam locus simulation was performed at two levels of kV, Al (Kα ray) and Z
The relative X-ray intensity (MC calculated value) of n (Kα ray) was determined. 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)
(Seconds), the relative X-ray intensity of Al and Zn in the standard sample Al-1.1% Zn was determined (actually measured value), and compared with the calculation result by electron beam trajectory simulation (MC calculated value).
Furthermore, MC of the characteristic X-ray intensity of Al and Zn obtained above
Using the calculated value and the actually measured value, the value was converted into the compound composition by the ZAF method, and the calculated MC value and the actually measured value were compared. Table 4 shows the results.

[0050]

[Table 3]

[0051]

[Table 4]

Example 3 [Verification with PbS standard sample] Using the physical properties shown in Table 5, an acceleration voltage of 25 kV and an acceleration voltage of 30 kV were used.
Except that the electron beam trajectory simulation was performed at two levels of kV, Pb (Lα ray) and S
(Kα ray) relative X-ray intensity (MC calculated value) was determined. In addition, PbS standard sample of bulk sample, Pb-100% sample, and
Using an S-100% sample, the acceleration voltage was 25 as in Example 1.
kV (sample absorption current 10 nA, measurement time 10 seconds) and 3
Under the conditions 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 (actually measured values) and compared with the calculation results by electron beam trajectory simulation (MC calculated values). . Further, using the calculated and measured values of the characteristic X-ray intensities of Pb and S obtained above and converted to the compound composition by the ZAF method, the calculated values of MC and the measured values were compared. Table 6 shows the results.

[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, an acceleration voltage of 10 kV and a voltage of 15 kV were used.
Except that the electron beam trajectory simulation was performed at two levels of kV, Al (Lα ray), M
g (Kα ray) and the relative X-ray intensity (MC calculated value) of oxygen (O; Kα ray) were determined.

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
l) Bulk standard samples were prepared, and characteristic X-ray intensities of Al and oxygen were measured under the conditions of a sample absorption current of 5 nA and a measurement time of 10 seconds using each of these bulk standard samples. % Characteristic X-ray intensity was measured. As a result, the Al characteristic X-ray intensity was 67793 counts, the O characteristic X-ray intensity was 855 counts, and the Al-100% characteristic X-ray intensity was 142 counts.
514 counts, and the Al relative X-ray intensity of Al in the bulk standard sample Al ₂ O ₃ was 0.4575 (= 6779).
3 ÷ 142514).

The A of the bulk standard sample thus determined
Using the relative X-ray intensity of Al at ₂ O ₃ (0.4757), the O relative to oxygen when the weight percentage (% by weight) of Al and oxygen of Al ₂ O ₃ is 100% by weight according to the ZAF method conversion formula. As a result of calculating the X-ray intensity, the O relative X-ray intensity was 0.3640. The weight percentage (% by weight) of aluminum (Al) and oxygen of Al ₂ O ₃ at this time was
Al: 53.04% by weight and O: 46.98% by weight (100.02% by weight in total), and the theoretical composition (Al: 52.9)
(4% by weight and O: 47.06% by weight) is less than 10%, which is relatively good agreement. As a result, the O-100% characteristic X-ray intensity was 2350 counts (= 85
5 ÷ 0.3640). In addition, acceleration voltage 15
kV was calculated in the same manner as in the case of 10 kV.

Next, a spinel standard sample of bulk sample, Al
Using the -100% sample and the Mg-100% sample, and using the O-100% characteristic X-ray intensity determined above, the acceleration voltage was 10 kV (sample absorption current 5 nA, measurement time 1
0 sec) and 15 kV (sample absorption current 5 nA, measurement time 1)
0 seconds), Al, M in the standard sample spinel.
The relative X-ray intensities of g and oxygen were obtained (actually measured values) and compared with the results of calculation by electron beam trajectory simulation (MC calculated values). Furthermore, using the calculated and measured values of the characteristic X-ray intensities of Al, Mg, and oxygen obtained above and converted to the compound composition by the ZAF method, the calculated values of MC and the measured values were compared. Table 8 shows the results.

[0059]

[Table 7]

[0060]

[Table 8]

Example 5 [Verification by Assumed Sample of Al ₃ Fe] Using the physical property values shown in Table 9, the acceleration voltage was 3 kV, 5 kV,
Except that the electron beam trajectory simulation was performed at four levels of 10 kV and 15 kV, in the same manner as in Example 1 above,
Al (Kα ray), Fe (Lα ray), and Fe (Kα ray)
Was calculated for the relative X-ray intensity (MC calculated value). The compound composition obtained by the ZAF method and the theoretical composition were compared using the calculated MC value. Table 10 shows the results.

[0062]

[Table 9]

[0063]

[Table 10]

Example 6 [Verification by Assumed Sample of Al ₂ Cu] Using the physical properties shown in Table 11, the acceleration voltage was 3 kV, 5 k
Al (Kα ray), Cu (Lα ray), and Cu (Kα) 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 calculated. The compound composition obtained by the ZAF method and the theoretical composition were compared using the calculated MC value. Table 12 shows the results.

[0065]

[Table 11]

[0066]

[Table 12]

Example 7 [Validation by Assumed Sample of Mg ₂ Si] Using the physical properties shown in Table 13, an acceleration voltage of 3 kV and 5 k
The relative X-ray intensities of Mg (Kα ray) and Si (Kα ray) (MC calculated values) were the same as in Example 1 except that the electron beam trajectory simulation was performed at four levels of V, 10 kV, and 15 kV. ). Using this MC calculation value, ZA
The compound composition obtained by the method F and the theoretical composition were compared.
Table 14 shows the results.

[0068]

[Table 13]

[0069]

[Table 14]

Example 8 [Verification by Assumed Sample of TiB ₂ ] Using the physical properties shown in Table 15, the acceleration voltage was 3 kV, 5 k
Ti (Lα line), Ti (Kα line), and B (Kα) in the same manner as in Example 1 except that the electron beam locus simulation was performed at four levels of V, 10 kV, and 15 kV.
) Was calculated. The compound composition obtained by the ZAF method and the theoretical composition were compared using the calculated MC value. Table 16 shows the results.

[0071]

[Table 15]

[0072]

[Table 16]

Example 9 [Verification by Assumed Sample of Si ₃ N ₄ ] Using the physical properties shown in Table 17, the acceleration voltage was 3 kV, 5 k
V, 10 kV, and 15 kV, in the same manner as in Example 1 except that the electron beam locus simulation was performed at four levels, the relative X-ray intensities of Si (Kα ray) and N (Kα ray) (MC calculated values). ). Using this MC calculation value, ZAF
The compound composition obtained by the method and the theoretical composition were compared. 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, an acceleration voltage of 3 kV and 5 k
Al (Kα ray), Fe (Lα ray), and Si (Kα) in the same manner as in Example 1 except that the electron beam locus simulation was performed at four levels of V, 10 kV, and 15 kV.
) Was calculated. The compound composition obtained by the ZAF method and the theoretical composition were compared using the calculated MC value. The results are shown in Table 20.

[0077]

[Table 19]

[0078]

[Table 20]

Example 11 [Verification Using 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, and it was determined whether the TiC thin film was formed on the Al substrate. Confirmed by X-ray diffraction, the thickness of the TiC thin film formed on the glass substrate was measured by a scanning electron microscope (SEM).
It was confirmed that the thickness was 45 μm.

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

Using the physical properties shown in Table 21, an electron beam trajectory simulation was performed at the same acceleration voltage of 15 kV as in the actual measurement, and Ti (Kα ray), C (Kα ray), and Al
The relative X-ray intensity (MC calculated value) of (Kα ray) was obtained and compared with the actually measured value measured earlier. The results are shown in Table 22.

[0082]

[Table 21]

[0083]

[Table 22]

Example 12 [Verification with Al Thin Film on Propylene Film] Al thin film was formed by vapor deposition of Al on a propylene film, embedded in resin, polished to prepare a cross section sample, and scanned for Al film thickness. Measured with a scanning electron microscope (SEM).
Was confirmed. Next, using a wavelength dispersive 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,
The characteristic X-ray intensity of Al (Kα
Line) and the relative X of Al of the Al thin film on the propylene film
The line intensity was determined.

Using the physical properties shown in Table 23, electron beam trajectory simulation was performed at the same accelerating voltage of 10 kV and 25 kV as in the actual measurement, and the relative X-ray intensity (MC calculated value) of Al (Kα ray) was obtained. This was compared with the actually measured value previously measured.
The results are shown in Table 24.

[0086]

[Table 23]

[0087]

[Table 24]

Example 13 [Verification Using Cr Thin Film on Ni Substrate] A Cr thin film was formed on an Ni substrate by an ion plating apparatus, a cross-sectional sample was prepared, and the thickness of the Cr thin film was measured with a scanning electron microscope (SEM). The thickness 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 intensity (Kα ray) of Ni and Cr was measured for the Cr thin film on the Ni substrate. , Ni and Cr relative X
The line intensity was determined. The EPMA measurement conditions at this time were an acceleration voltage of 15 kV, a sample absorption current for Ni of 10 nA, a measurement time of 20 seconds, and an electron beam diameter of 40 μm.

Using the physical properties shown in Table 25, an 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 ray) and Cr (Kα ray) was measured.
The line intensity (calculated value of MC) was determined and compared with the actually measured value previously measured. The results are shown in Table 26.

[0090]

[Table 25]

[0091]

[Table 26]

Example 14 [Verification with Al ₂ O ₃ Coating on Al Substrate] An aluminum foil substrate 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 thus obtained samples No. 1 to No. 5 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 °), accelerating voltage 5 kV, sample absorption current 20 nA with respect to Al-100%,
The measurement was performed by measuring the O-characteristic X-ray intensity under the conditions of a measurement time of 100 seconds, five locations (A to E) at measurement locations of 100 μm at each sample No. 1 to No. 5, 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 counts obtained in the same manner 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 ° from 100 ° to 500 Å, and the density of the oxide film is set to 3.2 g / cm ³ to 3 g / cm 3. 9.9 g / cm ³ , the EPMA measurement conditions were set to the conditions previously set, and the electron beam trajectory simulation in the sample was performed according to the Monte Carlo method using the physical properties shown in Table 29. The O relative X-ray intensity of oxygen at each density was calculated.

[0097]

[Table 29]

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

[Table 30]

From the values of 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 FIG. The results are shown in Table 31 together with the measurement results by an electron microscope.

[Table 31]

Further, the oxide film of sample No. 5 (annealing treatment:
550 ° C x 1 hr), and set the accelerating voltage to 10 as the measurement condition.
The calculation and the actual measurement by the electron beam locus simulation were performed under the same conditions as above except that kV was used, and the comparison was made. The results are shown in Table 32.

[Table 32]

Example 15 [Verification with minute Al ₃ Fe] As a sample, high-purity aluminum in which only crystallized particles of Al ₃ Fe were confirmed by X-ray diffraction analysis was used. 30
A 0 ml flask is charged with 120 ml of phenol and heated to 160 ° C. for about 1 minute to remove water, then 0.2 ml
~ 0.3g of sample aluminum was drilled into fine chips and charged into the flask, and a reflux condenser was attached to
Heat 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 disperse the precipitate again, and then centrifuged again (7000 rpm) to remove the supernatant. Thereafter, methanol was added, and the mixture was filtered through a PTFE membrane filter (pore size: 0.1 μm). After further washing with methanol, Al ₃ Fe particles were captured on the filter to prepare a sample.

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 with respect to Al.
Under the conditions of nA and measurement time of 10 seconds, five Al ₃ Fe particles of different sizes captured on the filter were selected, and A
and the characteristic X-ray intensity of Fe and
And the relative X-ray intensities of Fe and
The Al / Fe relative X-ray intensity ratio (actually measured value) was determined. The result is N
o.1 particles were 0.9, No.2 particles were 0.9, and No.3 particles were 0.9.
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, assuming that the captured Al ₃ Fe crystallized particles are rectangular parallelepiped, the vertical direction (X), the horizontal direction (Y), and the depth direction (Z) into which electrons are incident are 0.2 to 10 μm. Using a personal computer (PC N88 BASIC) manufactured by NEC Corporation and using the physical properties shown in Table 33, an electron beam trajectory simulation was performed under the conditions of 150 incident electrons and an acceleration voltage of 15 kV. Performed, Al (Kα ray)
And the relative X-ray intensity of Fe (Kα ray), 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 bulk samples sufficiently larger than the X-ray generation region but also vertical,
Accurate analysis is possible for thin film samples and minute sample samples smaller than the X-ray generation region in any one or two or more of the depth directions, and accurate analysis is possible with a small number of electrons less than 1,000. Can be.

[Brief description of the drawings]

FIG. 1 is an explanatory view showing an X-ray absorption model assumed in the present invention and an area divided for specifying an X-ray generation position; FIG. 1 (a) is a sectional explanatory view;
(B) is an explanatory plan view.

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

FIG. 3 is a flowchart illustrating a procedure for specifying an X-ray generation position in a divided region of the X-ray absorption model and the X-ray generation position in FIG. 1;

FIG. 4 shows the film thickness (膜厚) obtained in Example 14.
FIG. 3 is a graph showing a calibration curve of O relative X-ray intensity.

 ──────────────────────────────────────────────────続 き Continued on front page F term (reference) 2G001 AA03 BA05 BA07 BA28 CA01 CA03 EA02 FA02 FA08 FA12 FA14 FA29 FA30 KA01 KA11 LA02 MA04 MA05 MA10 NA03 NA06 NA07 NA08 NA10 NA11 NA13 NA15 NA17 NA18 NA20 RA01 RA03 RA08 RA10

Claims (13)

[Claims] A matrix sufficiently larger than an X-ray generation region.
A rectangular parallelepiped sample is exposed in the box
Assuming the embedded X-ray absorption model, this X-ray absorption model
Vertical, horizontal and depth size of the sample at
Is set according to its size and shape, and
The following formula in the LURO simulation formula
(2) to (4) Measurement of scattering angle (ω) and rotation angle (φ)
Formula (2) cos (ω, radian) = 1-2βR / (1 + β−R) φ (radian) = 2πR Formula (3) for electron energy loss (ΔE) When E> 6.338J ΔE [Kev / cm] = 7.85 x 10^FourρΣ [ZC / A · ln (1.16
6E / J)] / E When E ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ (ZC / A / J^1/2) /
1.26E^1/2 Formula (4) for calculating the probability (P) that an electron collides with an element P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe^FourZ (Z + 1)] / [4E
_n ^Twoβ (β + 1)] [However, in the above formulas (2) to (4), E is an electron
Is the owned energy (Kev), A is the atomic weight, ρ is the density (g /
cm^Three), Z is the atomic number, J is the ionization potential
(Kev), β is the screening parameter, R is uniform
Random number (0 to 1), π is pi (3.14), C is composition
And e is the electron charge (−4.8029 × 10 ^-Tenesu)
To E_nIs the kinetic energy of the electron (eE / 300 × 10
^Three) Respectively], J = 11.5Z × 10^-3 [Kev] and β = ｛5.44Z^2/3/ E｝ × 10^-3 With less than 1000 incident electrons
Monte Carlo simulation characterized by
EPMA analysis method used. 2. Formula (1) for calculating mean free path (λ) in the simulation formula: λ [cm] = [(0.0554E × 10 ³ ) / ρ] × ｛ΣA
C / [Z ^1/3 (Z + 1)]｝ × 10 ^-8 [where E, ρ, Z, A,
And C are the same as in the above equations (2) to (4). ], The handling of the free path when the incident electrons enter the matrix from the sample and the free path when the electrons enter the sample from the matrix is performed using the sample or the mean free path in the matrix, which is the starting point of the electrons. 2. 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 using the proportionally divided mean free path, which is proportional to the distance in the matrix and the distance in the matrix. 3. An X-ray generation position of a characteristic X-ray generated from an X-ray absorption model is determined according to an X-ray extraction direction of EPMA.
The area taken out only through the matrix, the area taken out only through the sample, the area taken out through the sample from the matrix, the area taken out from the sample through the matrix, and the area taken out from the matrix through the sample 3. An EPMA analysis method using Monte Carlo simulation according to claim 1 or 2, wherein the area is further divided into regions extracted through the matrix, and the distance from the X-ray generation position to the sample surface is calculated according to the divided regions. . 4. Kα according to the kind of element constituting the sample
EPMA using Monte Carlo simulation according to any one of claims 1 to 3, wherein a line and / or an Lα line is used.
Analytical method. 5. The size of the sample may be vertical, horizontal,
The EPMA analysis method using Monte Carlo simulation according to any one of claims 1 to 4, wherein a size larger than the X-ray generation region is set in any of the depth direction and the bulk sample is measured. 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. 4. An EPMA analysis method using the Monte Carlo simulation according to any one of 4. 7. The size of the sample may be vertical, horizontal,
The EPMA analysis method using 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 small sample is measured. 8. The sample is a minute 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 equal to the X-ray generation position. The EPMA analysis method using Monte Carlo simulation according to claim 7, wherein all are calculated as regions which are taken out only through the sample. 9. The EP using Monte Carlo simulation according to claim 8, wherein the non-metallic carrier is a filter, and a minute sample is captured on the filter for analysis.
MA analysis method. 10. A sample is a metal compound containing at least one metal element, a 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 is measured. And the 100% characteristic X-ray intensity of the metal 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 Monte Carlo simulation. EPMA using Monte Carlo simulation according to any one of claims 1 to 9, wherein the analysis of the sample is performed by comparing the relative X-ray intensity of each metal element in the sample for the analysis.
Analytical method. 11. A sample is a metal / metal compound containing at least two metal elements, the characteristic X-ray intensity of each of these two metal elements is measured, and the relative X-ray intensity of each metal element is measured. The relative X-ray intensities of the two metal elements in the sample are calculated from the line intensity and the 100% characteristic X-ray intensity of the metal of the metal element, and the relative X-ray intensities of the two metal elements in the sample are calculated. Relative X of metal element
X-ray intensity ratio is determined, and the sample is analyzed by comparing the relative X-ray intensity ratio of the two metal elements in the sample with the relative X-ray intensity ratio of the two metal elements for classification determination determined by Monte Carlo simulation. An EPMA analysis method using the Monte Carlo simulation according to any one of claims 1 to 9. 12. The sample is a metal / non-metal compound containing at least one metal element and a non-metal element, and the metal characteristic X-ray intensity of the metal element is measured to calculate a metal relative X-ray intensity. Further, using a bulk standard sample made of a predetermined metal compound containing the same non-metal element as the above-mentioned non-metal element, the metal characteristic X-ray intensity of the metal element constituting the metal compound and the non-metal characteristic of the non-metal element are determined by EPMA. In addition to measuring the X-ray intensity, a 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 the measured metal characteristic X-ray intensity and metal 100% characteristic X were measured. The metal relative X-ray intensity in the metal compound is calculated from the X-ray intensity and the calculated relative metal X-ray intensity and the above-mentioned 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 is 100% by weight is calculated by the ZAF method conversion formula, and from the calculated non-metal relative X-ray intensity, Non-metal
Calculate 100% characteristic X-ray intensity, determine the non-metal relative X-ray intensity in the sample 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 a non-metal relative X-ray intensity and a metal relative X-ray intensity for classification determination obtained by Monte Carlo simulation. 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 sample is obtained from a nonmetal relative X-ray intensity obtained for the sample and a nonmetal relative X-ray intensity-film thickness calibration curve for classification judgment obtained by Monte Carlo simulation. 2. The method according to claim 1, wherein the film thickness is measured.
EP using the Monte Carlo simulation described in 2
MA analysis method.