JPH0295247A - X-ray spectrochemical analysis by electron beam excitation - Google Patents

Abstract

PURPOSE:To allow the correction of fluorescent excitation by calculation by irradiating the atoms in a sample with primary characteristic X-rays (primary X-rays) by which the atoms are excited to radiate secondary characteristic X-rays (secondary X-rays). CONSTITUTION:The atoms in the sample are irradiated with the primary X-rays and are thereby excited to radiate the secondary X-rays. The effect of the primary X-ray at one point in the sample can be calculated and, therefore, the intensity of the secondary X-rays at the respective points in the sample can be calculated as well. The depth distribution from the sample surface of the secondary X-ray generating intensity can be determined when the radiation intensities of the secondary X-rays at the respective points in the sample are integrated with the layer surface of depth x2 from the sample surface. The intensity of the secondary X-rays is determined if these intensities are integrated by as much as the thickness of the sample. Further, the intensity of the primary X-rays is determined if the intensity distributions phi of the primary X-rays (x1, r1) are integrated form 0 to infinity with x1, r1. The correction of the fluorescent excitation is executed by calculating the intensity ratio of the primary and secondary X-rays.

Description

Detailed Description of the Invention (Industrial Application Field) The present invention is directed to fluorescence excitation in X-ray spectroscopy in which a sample is excited by electron beam irradiation and characteristic X-rays of sample component elements emitted from the sample are measured. Regarding the correction method.

(Prior art) In X-ray spectroscopy, in which a sample is excited by an electron beam, the sample is excited by the primary X-rays generated by irradiating the sample with an electron beam, and fluorescent X-rays are emitted, allowing characteristic X-ray detection of sample component elements. The intensity is the sum of this primary X-ray and fluorescent X-ray. Of these, what is directly related to the concentration of a sample component element is the characteristic X-ray intensity of that element in the primary X-rays, and the fluorescent X-ray intensity that overlaps with it is influenced by other component elements in the sample. Therefore, the influence of fluorescent X-rays differs depending on the component composition of the sample. For example, the component elements are A and B.

C, the characteristic X-ray wavelength of element B is
When shorter than the line wavelength, the property X* of element B excites the element $A and generates fluorescence, so even if the concentration of element f: is the same, it can be directly measured in samples with more and less element B. The characteristic X-ray intensity to the element is stronger in the former case. Therefore, it is necessary to correct the fluorescent X-rays excited by the primary X-rays of other coexisting elements. This is the fluorescence correction in X-ray spectroscopy in which the sample is excited with an electron beam. Conventionally, this fluorescence correction method has been proposed for bulk samples with a sufficiently thick sample thickness, but it has been applied to thin film samples. No possible correction method has been proposed.

That is, by irradiating the sample with an electron beam, the Xl emitted from the sample
In X49 spectroscopic analysis of S, there are three types of corrections for the characteristic X-ray intensity of one component element: (
1) The penetration depth of the electron beam and the proportion of backscattered electrons are affected by the penetration depth of the electron beam into the sample, the proportion of backscattered electrons, etc. Because it is number dependent, correction for this effect is called atomic number correction. (2) Also, since the characteristic X-rays of the target element generated in test 1 are absorbed by atoms of other coexisting elements,
Correction for absorption is required and is called absorption correction. (3) Furthermore, the target element is excited by characteristic X-rays or continuous X-rays of other coexisting elements, apparently increasing the characteristic X-ray intensity of the target element, so correction for this is necessary, and this correction is called fluorescence correction. . Combined with these three types of correction, Z
AF'? I call it ili positive. These corrections can be calculated if the elemental composition of the sample is known, but since the elemental composition of the sample is initially unknown, a first approximation of the composition is assumed based on the characteristic X-ray intensity of each component element. A correct elemental composition is reached by a successive approximation method that repeats the procedure of calculating the ZAF correction to obtain a second approximate composition, and calculating the ZΔF correction again based on the second approximation. A specific method of performing the above correction has been proposed for a sample with a sufficiently large sample thickness, but no specific correction method has been proposed for thin film sample 11.

(Problems to be Solved by the Invention) In the case of a thin film sample, the absorption correction is small and the influence of fluorescent X-rays due to X-rays emitted from the thin film support is large. The present invention provides a fluorescence correction method suitable for thin film samples.

(Means for solving the problem) 1 of the component elements of the sample and sample holder by electron beam irradiation
The secondary characteristic X-ray generation intensity distribution is calculated including the sample and its support, and based on this calculated primary characteristic X-ray generation intensity distribution, each sample is The secondary characteristic X-ray intensity of the component elements is calculated as a function of the depth from the sample surface, and the calculated secondary characteristic Fluorescence excitation correction was performed on the actually measured characteristic X-ray intensity of the sample component element based on the ratio of the calculated primary characteristic X-ray intensity obtained from the characteristic X-ray generation intensity distribution.

(Effect) When a sample is irradiated with an electron beam, X-rays are emitted from the sample.The electrons enter the sample and collide with the atoms coming out of the sample, emitting X-rays, so when the composition of the sample is known. can calculate the intensity distribution of characteristic X-rays of component elements generated from within the sample.This distribution can be calculated by dividing the depth from the sample surface into
l, the distance along the sample surface from the electron beam irradiation point on the sample surface! - Assume φ(xl, rl) as 1. Atoms in the sample are excited by being irradiated with this primary characteristic X-ray (hereinafter simply referred to as primary
It emits radiation (called X-rays). The effect of the primary X-rays at a point in the sample can be calculated, and therefore the intensity of the secondary XfI radiation at each point on the sample can also be calculated. 2 of each sample point
If the secondary X-ray radiation intensity is integrated over the layer plane at depth X2 from the sample surface, the depth distribution of the secondary X-ray generation intensity from the sample surface can be obtained, and if this is integrated by the sample thickness, the secondary The intensity I2 is determined. The above-mentioned primary X&Ii! The occurrence intensity distribution φ(xi, rl) is xl, rl
If we integrate from O to infinity for 1 & X-ray intensity 1
1 is required. The characteristic X-ray intensity of a component element actually measured for a sample is the sum of the primary and secondary X-ray intensities,
The intensity ratio between the primary X-ray and the secondary X full is calculated as above! ■And! Since the ratio is the same as that of 2, it is possible to correct the fluorescence excitation using the above calculated ratio of 11.12. According to this method, the primary X-ray is calculated including the sample and the sample membrane holder, and the influence of the primary X-ray does not reach the sample membrane is calculated, so fluorescence excitation correction is performed for a sample of arbitrary thickness. This is possible.

The above calculation cannot be performed unless the composition of the sample is known.
Characteristics X emitted from a sample when the sample is irradiated with an electron beam
Determine the qualitative characteristics of the sample components and the first approximate concentration of each component from the measured value of the line intensity, perform the above calculation using this, perform fluorescence correction on the above measured characteristic X-ray intensity, and calculate the corrected each component. Determine the concentration of each component in the second approximation from the characteristic X-ray intensity of the element,
Based on this, the calculation is performed to correct the actually measured characteristic X-ray intensity, and the third approximation of each component concentration is determined. If such a procedure is repeated thereafter, the difference in component concentration between the n-th approximation and the (n+1)-th approximation becomes equal to or less than the target value. Therefore, the n+1th approximate component concentration may be used as the quantitative analysis value of the sample.

(Example) First, a calculation formula for determining fluorescent X-ray intensity in this example will be explained. In Fig. 2, F is the sample surface, and one of the electrons irradiating a point O on the sample traces a trajectory as shown in Fig. f and reaches a point a at a depth Xl from the sample surface, where the sample structure changes. Suppose that an atom emits primary X-rays. This one
The direction and intensity of the secondary X-rays vary depending on the individual electrons and are determined stochastically, but when averaged over many electrons, they are uniform in all directions and are determined by the composition and density of the sample, and are determined by the depth x 1. It is expressed as a function of r1 shown in the figure.

Let φj(xl, rl)dV be the primary X &'il ffi of element j emitted from the microscopic bond dV including point a.

The purpose of the calculation is to calculate the primary X! radiation emitted from the sample in one arbitrary direction when the sample is irradiated with an electron beam. The purpose is to find the intensity ratio of IIi+ and fluorescent X-rays. With the direction of the city as the observation direction with respect to the perpendicular to the entire sample surface, Mlljdw of the primary X-rays emitted within the small angle range dω in this direction is determined. The first-order X radiated within a solid angle [1ω
49 M is (17, i”t)dVclω, and since this X-ray travels through the sample by Xl/cosqr and exits from the sample surface, taking into account the absorption during that time, the amount emitted from the surface is In \, ρ is the density of the sample, μ is the average mass absorption coefficient of the sample for the primary X-ray wavelength, the mass absorption coefficient of the atoms of each element is μi, and the concentration of each element in the sample is Ci, then μ =Σμ1xci.

It occurs at a layer plane with a depth xl from the sample surface, and 1 from the sample surface.
1illffi of the primary X-rays emitted in the direction 11 is obtained by integrating the above equation over the entire layer plane xl.

Since this integral and the exponential function term can be treated as a constant, the definite integral of r in the above formula is the total amount of primary be done. If this is Dj (Xl), the primary X-ray intensity 11j emitted from the sample in the direction of 1V is expressed by the above equation
It is given by integral with respect to l.

Next, 2 is excited and emitted by the above-mentioned primary X-ray
Find the quantity of the next X49. The amount of primary X-rays emitted from a point a on the layer surface at depth Xl from the sample surface and reaching point b on the layer surface at depth X2 is a geometrically related quantity as shown in Figure 2. Determine,
Let ds be the microbody Wt d s d x containing point b
Secondary X1 generated from 2! The amount of A is the secondary X-ray for element i while the primary X-ray of element j travels a unit distance in the R direction.
Taking the ray generation efficiency as Q ij, the primary X-ray has a thickness of d
The distance that X2 passes through the layer is dx2/cosQ, so in formula c2), Q I J CI X 2 / co! I
Get it by multiplying by θ. In formula (2), R = (xi-x2)
/cost, and polar coordinates with the origin at the 0 point in the X2 plane (
Considering r, α), since dS = td, dpe, the quadratic X generated from a layer with thickness dx2 at depth X2 due to the primary X-ray from point a is The term is Dj (xi) mentioned above. Therefore, if the total amount of secondary X-rays generated from the layer surface of x2 due to all the primary X-rays generated within the sample is D2 (x2) dx2, (4)
The equation is integrated with respect to xl, and this W is the generated intensity of primary X-rays at point a φj(xlr
l), and the distance m (
Since it is the product of the function x l −x 2 ) and φj(xlrl)dV, if this function is F(xix2),
The secondary X-rays emitted from the entire layer of depth X2 and thickness dx2 by the primary X-rays generated from the entire layer of depth X1 and thickness dxl.
The total amount of lines Δ(X2)dx2 is obtained by integrating equation (3) with respect to the first-order XI emitted along the plane of depth xi.

For this integral, the definite integral of equation (3) is the above F (xl-x
2) is the secondary X-ray intensity emitted from the sample surface in a flat direction!
'R-(x-7-λ2)/, θ, so the above definite integral becomes. When the above integral (first-order X-ray intensity of element i) and 12i are calculated, the actual measured X-ray intensity is proportional to I l i +12 i.

Therefore, the actually measured X-ray intensity of the characteristic X-ray of element i is taken up to the third term using the formula I (7) where the integral is Since i is excited by the primary X-rays of not only element j but also all other elements, including i, which emit characteristic xm with a shorter wavelength than the element "Xi," the total intensity of secondary X-rays ■21 is as follows. In this way, l1i (calculated by equation (1), !i on the right-most side of the above equation is an actual measured value, and Ili and 12i are values calculated by both equations.

Next, an example of how to obtain the primary X-ray intensity φj (XI, rl) will be explained. This method uses the Monte Carlo simulation method to track the process in which electrons that enter a sample repeatedly collide with the atoms that make up the sample, gradually losing energy, and progress through the sample in an irregular trajectory. At each point in the electron's progress, it is multiplied by the X-ray emission probability determined by the composition of the sample and the energy of the electron. When such calculations are performed for a large number of electrons, the intensity of the first-order XI at each point within the sample is determined. FIG. 3 shows a flowchart of simulation calculations. The sample to be measured has a thickness t,
The elements constituting it are nf]T[ from 1 to n. Assuming the combination of concentrations of these elements, the concentrations (wt%) of these elements are C1, C2...Ci...Cn
Start the simulation as Here, the subscript i is the component number. The sample thickness t, the scattering cross section for electrons of each element constituting the sample, the ionization cross section, the concentration C1 of each element, the initial energy Eo of the electron, the terminal energy E', the number of simulations NO, etc. are entered into the computer. Enter (a). For example, the simulation is 10
This is done for 00 to 20,000 electrons. Specifically, a calculation is performed to trace the trajectory of an electron when it is incident on a sample, and this is repeated no number of times. After inputting the data and parameters necessary for the simulation calculation in step (a), set the number of calculations N = 1 (c)
, Perform tracking calculations for the electrons incident on the sample (d). This calculation calculates the process from the collision of the electron with the previous sample atom to the collision with the next sample atom, and calculates in which direction the electron will be repelled in the previous collision, based on probability. Then, the atom of the element to collide with is determined probabilistically using the following equation (8) in relation to the scattering cross section of the atom of each constituent element and the concentration of each element, and then using the following equation (9). Assume that the electron travels along its mean free path within the sample and collides with the atom determined probabilistically above, and the loss of energy in this process is calculated as follows (10).
i is the atomic weight of element i, Ci is the scattering cross section of the atom of element i for electrons, the energy E of the colliding electrons, and the source of each element constituting the sample.

The mean free path is the energy when an electron moves through a substance in units of λ. However, it is the average value of the atomic number taking into account the composition ratio (wt%) of each element in the sample. 2 = ΣC3・2. It is expressed as LL;l(:□'=/.Similarly, A is the average atomic weight of the elements in the sample, ρ
is the sample density. The unit in the above equation is K eVl8, and Ji is the ionization potential of element i (eVl).

After the tracking calculation is completed, calculate the distance traveled by the electron in the depth direction from the sample surface and the distance traveled parallel to the sample surface from the electron incident point between the previous and subsequent strikes in the previous depth direction and the distance traveled parallel to the sample surface from the electron incident point. The current depth position X1 of the electron from the sample surface is fanned by adding it to the traveling distance in the direction parallel to the sample surface. In this embodiment, in the next step, the characteristic X-ray emission probability of the element 'Mi in the subsequent collision is calculated in the above process, and the result is input into the memory. The emission probability of characteristic X-rays is related to vi=E/Ei, where the electron energy is E1 and the excitation energy for characteristic X-ray emission of an element element is Ei, and is proportional to φ′i given by the following equation is added to the data in the address in a memory that uses coordinate data xl as addressing data, and is stored at the same address. Next, it is checked whether the electron energy E is E/E' (T).

E' is the terminal energy of the electron, and in this case it may be set to a limit energy at which atoms of any element in the sample cannot be ionized. This check is N.

In the case of , check whether the electron depth xl from the sample surface is <0 (jumps out from the surface), then check whether Xl>t (transmits through the sample), and all answers are No. Then, the operation returns to step 2), and the same operation is repeated until any of steps (g), (ch), and (su) becomes No.

As described above, when any of steps (G), (C), and (S) becomes YES, the tracking calculation for one electron ends, and the new N becomes N> A check is made to determine whether or not the result is NO. If NO, the operation returns to step (C) and the above-mentioned calculation is performed for the next electron. (For example, if 10,000 calculations are performed, N>No, and step (e) becomes YES, meaning that the Monte Carlo simulation calculation for one sample is completed. For each element, a histodrum of the characteristic X-ray radiance with respect to the depth position xi within the sample is formed.
This is nothing but Di (xi) used in 1 arithmetic.

FIG. 1 is a flowchart of operations when the method of the present invention is executed using a computer. Characteristic values of each element used in calculations, such as atomic number and mass absorption coefficient, are input into the computer in advance. Prior to analysis, input data such as the thickness of the sample thin film and the component composition of the support (A).
Measure the characteristic X-ray intensity 1i of each component of the sample (b). In this case, the sample component elements are known (qualitatively analyzed), and therefore the characteristic X-ray intensity measurement of each component element is an X-ray measurement operation at a predetermined wavelength. From this measurement result, the first approximate concentration Ci of each component element is determined (c). In this embodiment, this first approximate concentration is determined as a ratio of the characteristic X-ray intensity of a pure sample of each component element. Next, set the number of calculations n to 1 (D), set the above Ci at the n-th approximate concentration C4: of each component (E), and calculate the above Di (xi) and 12ij of equation ('7) ( Go to) (g) and calculate the primary X-ray intensity 11i and fluorescent X-ray intensity (secondary X-ray intensity) 121 of each component characteristic X-ray in the calculation (h).
If so, the operation returns to (E) with n+1 set to n.

The characteristic X-ray intensity 1i of each component was actually measured or corrected!
As a method for determining the concentration of each component from
Line spectroscopy" can be used.

(Effects of the Invention) According to the present invention, even if there is an irradiation effect of primary X-rays from the holder on a thin film sample, it is possible to correct the fluorescence excitation by calculation, and there is no need to prepare a special standard sample. (Able to perform accurate analysis.

[Brief explanation of the drawing]

Fig. 1 is a flowchart of the operation in one embodiment of the method of the present invention, Fig. 2 is a model diagram explaining the mechanism of secondary X-ray generation within the sample, and Fig. 3 is a flowchart of the operation for calculating the primary X-ray intensity. This is a flowchart. Figure 1 Agent: Patent Attorney Kosuke Agata

Claims (1)

[Claims] The primary characteristic X-ray intensity distribution of the component elements of the sample and sample holder by electron beam irradiation is calculated, including the sample and its support, and from this calculated primary characteristic X-ray intensity distribution,
The secondary characteristic X-ray intensity of each component element of the sample due to the primary characteristic X-rays from each part of the sample and sample holder is calculated as a function of the depth from the sample surface, and this calculation result is calculated as a function of the depth from the sample surface to the thickness of the sample. The ratio of the calculated secondary characteristic X-ray intensity integrated by An X-ray spectroscopic analysis method using electron beam excitation, characterized by performing fluorescence excitation correction.