JPH0750044B2 - Method for creating calibration curve in X-ray spectroscopic analysis - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method for preparing a calibration curve when performing quantitative analysis by X-ray spectroscopy.

(Prior art) When performing quantitative analysis Usually, a calibration curve is prepared using several standard samples of known concentration of the element to be quantified, or X-ray intensity of pure element of the element to be quantified A method of performing a correction calculation on the ratio of the X-ray intensity of the target element in the sample to be measured is used.

(Problems to be Solved by the Invention) In the calibration curve method described above, some standard samples having different concentrations must be prepared, but it is often difficult to prepare standard samples. Further, in the thin layer sample, the transmission rate of the exciting electron beam increases and the X-ray generation amount decreases, so that a thin film standard sample has to be prepared, but this is more difficult than the case of forming a block standard sample. The method of performing a correction calculation on the X-ray intensity ratio with a pure substance is one in which the effect of coexisting elements is calculated by successive approximation, and the calculation is very troublesome.

The present invention intends to provide a method for preparing a calibration curve without using a standard sample, which solves the above-mentioned problems of the conventional method.

(Means for solving the problem) For a virtual sample whose concentration of the element to be quantified is known,
When an electron is injected, the process of the electron moving in the sample repeatedly repeating collisions with sample constituent atoms and losing energy is followed by a simulation method based on stochastic calculation for many electrons, and In the case of multiple concentrations of elements for which the probability that characteristic X-rays are radiated is calculated as a function of the depth from the sample surface and the function for integrating the function from the sample surface to a depth equal to the thickness of the sample to be measured is quantified Then, a calibration curve was created based on the above integration result and the corresponding target element concentration.

(Action) When an accelerated electron is incident on the sample, as shown in Fig. 4, the electron collides with the electron that constitutes the sample, repels it, and collides with another atom. It progresses while drawing an irregular trajectory, and gradually loses energy during that time. In this way, the trajectories of the electrons in the sample that proceed with repeated collisions are determined stochastically.
It can be simulated by a computer. Such a simulation method is called a Monte Carlo simulation method. When the above-mentioned simulation is performed a large number of times, the probability that electrons emit a characteristic X-ray of the target element to be quantified at a certain depth from the sample surface is obtained. The relationship between the X-ray emission probability Pi thus obtained and the depth from the sample surface is as shown in FIG. In this figure, the integral of the probability from the depth O to t is proportional to the characteristic X-ray emission intensity of the target element of the sample having the thickness t. On the other hand, since the concentration of the target element is assumed in advance, the relationship between the assumed concentration and the radiation intensity of the characteristic X-ray has been obtained, and the calibration curve can be created.

The above method is a theoretical calculation for a virtual sample and does not actually require samples of known concentrations with various concentrations of the target element.
Moreover, since the X-ray generation probability is calculated in the portion from the sample surface to an arbitrary depth, the result applicable to the thin film sample can be obtained.

(Embodiment) FIG. 1 is a flowchart of a calibration preparation operation in an embodiment of the present invention. The sample to be measured is a thin film having a thickness t, and the elements constituting the thin film are n kinds from 1 to n. Assuming K type samples having various combinations of the concentrations of these elements, the concentrations (% by weight) of the elements of each of these samples are Ck1, Ck2 ... Ckn
To start the simulation. Here, the subscript k is the sample number. Sample thickness t, scattering cross section for atoms of each element composing the sample, ionization cross section, concentration Cki of each element for each sample, initial energy Eo of electrons, final energy E ', and simulation Input the number of times into the computer (a). The simulation is performed on, for example, 1000 to 20000 electrons. Specifically, the tracking calculation of the trajectory of the electron when one electron is made incident on the sample is performed, and this is repeated No times. After inputting the data and parameters required for the simulation calculation in step (a), the sample number k = 1 (b), the number of calculations N = 1 (c), and the tracking calculation of the electrons injected into the sample is performed. Do (D). This calculation is a calculation of the process from the collision of the electron with the atom in the sample to the collision with the atom in the sample next. In the previous collision, the direction in which the electron is repulsed is stochastically determined. Then, which atom of the element to collide with is probabilistically determined by the formula (1) below in relation to the scattering cross section of each constituent element atom and the concentration of each element, and by the formula (2) below. It is assumed that the electrons travel only the mean free path in the sample and collide with the stochastically determined atoms, and the energy loss in this process is calculated by the following equation (3). Where Pi is the probability that an electron collides with an atom of element i, and pi is Here, Ai is the atomic weight of the element i, σi is the scattering cross section of the atom of the element i with respect to the electron, and the energy E of the colliding electron is
And the atomic number zi of each element that makes up the sample, Where βi is a screening parameter, Is.

The mean free path L is in units of Å The loss of energy as the electrons travel in the material is per unit flight distance, However, is the average value of the atomic number in consideration of the composition ratio (% by weight) of each element in the sample. Z = ΣCizi However, ΣCi = 1. Similarly, the average atomic weight of the element in the sample and ρ are the sample densities.

The unit of the above equation is KeV / Å and Ji is the ionization potential (eV) of element i.

When the tracking calculation is completed, the current depth of the electron from the sample surface is calculated by adding the depth-wise travel distance of the electron from the sample surface during the front-back collision in the calculation to the previous depth-direction travel distance. The position d is calculated (e). In this embodiment, in the next step (f), the characteristic X-ray emission probability of the element i in the later collision in the above process is calculated, and the result is input to the memory. The radiation probability of characteristic X-rays is the energy of the electron E,
Letting Ei be the excitation energy for the characteristic X-ray emission of the element i, it is related to vi = E / Ei and is proportional to φi given by the following equation.

As shown in the memory map of FIG. 2, this φi is added to the data in the address corresponding to the depth d from the sample surface in the area of the element i of the k-th sample in the memory and stored at the same address. . Next, it is checked whether the electron energy E is E <E '(G). E'is the terminal energy of the electron, and in this case, it should be set to the limit energy at which the atom of any element in the sample cannot be ionized. If this check is NO, it is checked whether the depth d of electrons from the sample surface is d <o (jumps out from the surface) (h), and then d> t
Check (re) whether it is (transmitting sample), if all are NO, the operation returns to (D), and the same operation is repeated until any step of (G), (H) and (D) becomes NO. Be done.

As described above, when any of the steps (g), (h), and (g) becomes YES, the tracking calculation for one electron ends there, N is set to N + 1 (l), and the new N is N> No. If it is No, the operation returns to the step (C), and the above-mentioned calculation is performed for the next electron. Thus, for example, when 1000 times of calculations are performed, N> No, the step (e) becomes YES, and the Monte Carlo simulation calculation for one sample is completed. Therefore, k + 1 is set in the next step (wa). New k
It is checked whether or not k is k> K (f), and if NO, the operation returns to the step (b), and the Monte Carlo simulation calculation is performed on the next sample. In this way
When k> K, the Monte Carlo simulation for all assumed samples ends. By the operations up to this point, the histogram of the characteristic X-ray emission intensity with respect to the depth from the sample surface is formed for each element in the memory in the memory, so it is formed in the memory in the last (Y) step. The characteristic X-ray emission intensity histogram of each element for each sample is subjected to X-ray absorption correction according to the depth from the sample surface and integrated. This is a relative value indicating the mutual ratio of the characteristic X-ray radiant intensities of each element of samples of various compositions with thickness t, and the relative intensity of one characteristic X-ray of one sample thus calculated and the above If the ratio to the actually measured intensity of the characteristic X-ray by one actual sample having the same composition as the sample is obtained, by multiplying the relative intensity of the respective characteristic X-rays of other samples and other elements by the above ratio, It is possible to convert each relative intensity into an actually measured intensity. For example, the concentration of the element i for quantitative determination is the intermediate concentration Ci ′ between the i-th and k-th concentrations Cji and Cki of the virtual sample described above.
Suppose that a sample such as is available as a standard. Since the calibration curve that gives the relationship between the concentration of the element i and the relative intensity of the characteristic X-ray in the above calculation is obtained by the calculation of the simulation described above, the relative calculation in the characteristic X-ray at the concentration Ci ′ is calculated. The intensity I (Ci ') is determined. On the other hand, if the measured intensity of the characteristic X-ray of the element i of the standard sample is Io (Ci '), the conversion ratio A between the calculated value and the measured value is determined.
The calibration curve to be obtained can be obtained by multiplying the relative intensity of the characteristic X-ray obtained by the above calculation by this conversion ratio and blotting for each concentration. As a standard sample, a sample with a concentration of 100% of the element to be quantified is used, and the above-mentioned simulation is performed for a sample with a concentration of 100% to calculate the relative intensity of the characteristic X-ray of the element. It is also convenient from the standpoint that the calculation of the simulation described above becomes simple. Depending on the element, it may be difficult to obtain a pure product, but the above-mentioned A is approximately applicable to other elements in the virtual sample used for the simulation calculation.
The element in the sample for obtaining the above A does not necessarily have to be the element to be quantified in the sample to be measured, and the standard sample may be one having a known concentration of other elements constituting the sample to be measured. Good. Also, in the above example, the characteristic X-ray emission intensity is calculated for all the elements that make up the sample, but the step (f) may be performed only for the element to be quantified (however, the simulation calculation itself All parameters of sample constituent elements are required.) FIG. 5 is a graph showing the degree of agreement between the calculated value and the measured value when the method of the present invention is applied to a gold-copper alloy, and the vertical axis is gold or copper. The calculated value and the measured value of the X-ray level at 100% are set to 1 respectively, and the calculated value and the measured value of the X-ray intensity at other concentrations are shown, and the agreement between them is good.

(Effect of the Invention) According to the present invention, a calibration curve can be prepared without preparing various standard samples of known concentrations, and a calibration curve corresponding to a sample having an arbitrary thickness can be prepared. A thin film sample can also be easily quantitatively analyzed by X-ray spectroscopy.

[Brief description of drawings]

FIG. 1 is a flow chart showing an embodiment of the present invention,
FIG. 4 is a memory map showing a partial structure of the memory in the same embodiment, FIG. 3 is a graph showing the relationship between the depth from the surface of the sample and the characteristic X-ray emission probability at that depth obtained by the method of the present invention, FIG. FIG. 5 is a diagram showing the trajectory of electrons incident on the sample, and FIG. 5 is a comparison diagram of calculated values and measured values by the method of the present invention.

Claims (1)

[Claims] 1. A process in which a virtual sample, in which the concentration of an element to be quantified is determined, moves when an electron is made incident on the virtual sample while repeatedly colliding with atoms constituting the sample to lose energy. A large number of electrons are traced by a simulation method based on a probability calculation, and a calculation for obtaining the probability that characteristic X-rays of an element to be quantified are emitted while the incident electrons progress from the sample surface to a specified depth A method for preparing a calibration curve in X-ray spectroscopic analysis, which is carried out for the case of concentration, and creates a calibration curve by the above probability and the corresponding concentration of the target element.