JPH0894551A - Method for analyzing rutherford backscattering spectroscopic analysis data - Google Patents

Abstract

PURPOSE: To provide a data analysis method for analyzing, using Rutherford backscattering spectroscopic analysis method, the in-depth distribution of element concentrations in a solid sample with higher reliability and in a shorter time than with conventional methods. CONSTITUTION: To set an assumed distribution as to the in-depth distribution of element concentrations, an equation consisting of parameters having physical meaning is used and simulation is carried out by setting an initial value in accordance with known information about a sample. To compare a theoretical spectrum obtained through the simulation with a measured spectrum, fitting is performed by employing not gradient method but Powell method.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing the concentration distribution of elements in a solid sample in the depth direction in Rutherford backscattering spectroscopy with higher reliability and in a shorter time than conventional methods.

[0002]

2. Description of the Related Art Rutherford backscattering spectroscopy is known as a means for qualitatively or quantitatively analyzing the depthwise distribution of element concentration in the surface region of a solid sample. This method is performed by irradiating the sample surface with an ion beam, capturing the ions scattered by the atoms in the sample, and measuring the energy spectrum thereof. However, the actually measured spectrum is as shown in FIG. 1, for example, and the element concentration distribution of the sample cannot be immediately obtained from this.

Therefore, in Rutherford backscattering spectroscopy, as shown in FIG. 2, the actual concentration distribution 3 in the depth direction from the sample surface is determined from the measured spectrum 1 for the element to be analyzed of the sample 5. In doing so, first, based on known information about the sample 5 and the like, a provisional distribution in the depth direction (this is referred to as assumed distribution 4 in this specification) is set on a trial basis with respect to the concentration of the element to be analyzed. Figure 2
In the example, “Sample 5 has coating 7 and coating 8 on the surface of substrate 6, and the element to be analyzed is present in coating 7, not in coating 8, and diffuses into substrate 6.” The hypothetical distribution 4 is set based on the information.

Then, the theoretical spectrum 2 based on the set hypothetical distribution 4 is obtained by simulation, and the theoretical spectrum 2 and the measured spectrum 1 are compared. If the data of both spectra do not match, the assumed distribution 4 is corrected and the simulation is performed again. By repeating this, the assumed distribution when the theoretical spectrum 2 matches the measured spectrum 1 is determined as the actual concentration distribution 3. The fitting method was used. That is, the analysis was performed according to the procedure of the flowchart shown in FIG.

In such a conventional method, the theoretical spectrum 2 and the measured spectrum 1 in FIG. 2 are compared, or in FIG.
In determining d in, the χ ² (chi-square) value of the equation (3) is calculated, cd-e of FIG. 3 is repeated, and the fitting method in which χ ² is the minimum value is the optimal solution. Was being done. χ ² = Σ {(measured spectrum)-(theoretical spectrum)} ² …………… (3)

As a simulation method widely used in conventional Rutherford backscattering spectroscopy, Doolit
tle method (LRDoolittle, Nuclear Instruments and Met
hodsin Physics Research, B15 (1986), p.227) and RUMP software package (MOThomson and L.
R. Doolittle, Cornell University and the Computer G
raphics Service Ltd. 52 Genung Circle, Ithica, New
York, USA). In this method, the stopping power (the energy that an ion loses while traveling a unit length in a substance)
Using the interpolation method in the calculation of, the simulation is done quickly.

Further, there is a Tanaka method proposed in Japanese Patent Laid-Open No. 157710/1993, in which a sample is subdivided into layers of about 100 to 1000 to set a hypothetical distribution and the stopping power is calculated in each layer. , High-precision simulation can be performed without using the interpolation method. In this Tanaka method, if the scattering formula of Rutherford is not applied, the scattering cross section can be calculated from the database of the relation between the scattering cross section and the incident ion energy.

Next, regarding the fitting method in the conventional Rutherford backscattering spectroscopy, it takes a huge amount of time to manually carry out the repetition of cd of FIG. 3 above, and in particular, χ ² becomes the minimum value. It is almost impossible to manually determine whether or not it has been reached. Therefore, as a fitting method for automatic analysis, the Toray method using the Gauss-Newton automatic optimization algorithm (Morita and Sasayama, Toray Resea
rch, The TRC News No.40, July 1992) has been proposed. The Toray method, upon comparing the data of the data and the theoretical spectrum of the measured spectrum by the difference functions such as chi ^2, is intended to obtain the minimum value of the gradient calculation (dχ ² / dx) from chi ^2.

[0009]

In the above-mentioned conventional simulation method, the Doolittle method calculates the ion scattering cross section by Rutherford's scattering formula. Therefore, in the case of combinations of irradiated ions and analytical elements that do not follow the formula, Has the problem that it cannot be simulated. The Tanaka method can be simulated even if it does not follow the above formula and is highly accurate, but it requires more time for simulation than the Doolittle method, so automatic analysis is difficult. In carrying out the Doolittle method, there are 5 to 6 types of models in the RUMP software package, and it was necessary to select the optimum model based on the expertise and experience of the operator. Furthermore, when setting the hypothetical distribution, the operator's specialized knowledge and experience were required to input the initial values.

Further, in the conventional fitting method, the gradient calculation like the Toray method may be affected by the variation and error of the data, resulting in an incorrect calculation result. If the gradient calculation is not correct, not only will it take a long time to perform the fitting for obtaining the optimum solution, but also incorrect simulation results will be introduced.

Further, in a computer-based simulation and fitting method, the parameter determined to be the best fit may become a physically meaningless solution. For example, the depth of an interface becomes negative,
That is, there is a case where it is determined that the interface exists outside the actual sample. Since the computer does not understand the sample with a set of numbers and does not grasp the physically realistic contents, it may be such a physically meaningless solution.

According to the present invention, in the Rutherford backscattering spectroscopy, when a computer simulates a theoretical spectrum based on a tentative distribution in the depth direction (hypothetical distribution) which is tentatively determined for the concentration of the element to be analyzed,
A first object of the present invention is to provide a simulation method which is highly reliable and can be analyzed in a short time, and which can analyze even a sample which is difficult to analyze by the conventional method, without relying on the operator's high specialized knowledge and experience. A second object of the present invention is to provide a method for obtaining an optimal solution in a short time without error when fitting the theoretical spectrum and the measured spectrum obtained by the simulation, without relying on the conventional gradient calculation. To do.

[0013]

A first aspect of the present invention for achieving the above first object is to use Rutherford backscattering spectroscopy to obtain a hypothetical distribution of element concentration in a solid sample in the depth direction. In the method of analyzing the actual concentration distribution of the element in the sample, by setting, obtain a theoretical spectrum based on the assumed distribution by simulation, and perform fitting by comparing with the measured spectrum,
The Rutherford backscattering spectrometry data analysis method is characterized in that a hypothetical distribution of the concentration ratio of the element to be analyzed with respect to the substrate element is set by the equations (1) and (2) to perform the simulation.

[0014]

[Equation 2] Where P _{i is} the atomic concentration ratio of the element to be analyzed to the substrate element x is the depth from the sample surface A is the maximum value of the atomic concentration ratio of the element to be analyzed to the substrate element D is the depth when the element to be analyzed appears W1 Width of concentration increasing range of analysis target element W2 Width of maximum concentration range of analysis target element W3 Width of concentration decreasing range of analysis target element a ₁ , b ₁ ... Shape parameter of incomplete β function in concentration increasing range a ₂ , b ₂ … Shape parameter of incomplete β function in the concentration falling region

The second invention of the present invention for achieving the above second object is the Rutherford backscattering spectrometry, wherein an assumed distribution is set for the depthwise distribution of the element concentration in the solid sample, and Obtaining a theoretical spectrum based on a hypothetical distribution by simulation, by performing fitting by comparing with the measured spectrum, in the method of analyzing the actual concentration distribution of the element in the sample, characterized by performing the fitting by Powell method Rutherford backscattering spectroscopy data analysis method.

In the method of the present invention, it is preferable that a hypothetical distribution of the concentration ratio of the element to be analyzed with respect to the substrate element is set by the equations (1) and (2) to perform the simulation, and the fitting is performed by the Powell method. further,
It is preferable to prevent unnecessary repetition of simulation by providing a step to judge that any solution obtained in the simulation is a solution that corresponds to a physically realistic concentration distribution. It is preferable to perform a simulation for each layer of the prepared sample.

[0017]

The first aspect of the present invention is to set the hypothetical distribution 4 of the concentration of the element to be analyzed in the Rutherford backscattering spectroscopy as shown in FIGS. In this document, this is referred to as the substrate element) and the assumed distribution of the atomic concentration ratio of the element to be analyzed is set by the equations (1) and (2). In equation (1), P
_i atomic concentration ratio with respect to the substrate element for the i-th analyzed element, x is the depth from the sample surface, nine parameters A, D, W1, W2, W3, a 1, a 2,
Both b ₁ and b ₂ have the above-mentioned physical meanings.

[0018] That is, as shown in FIG. 4, the assumptions distribution, increase in concentration range where P _i is increased, the maximum density area where P _i is the maximum value, divided into three regions of concentration falling range P _i is lowered The width of each region in the depth direction is W1, W2,
It is W3. The depth of the starting point of the concentration increasing region is D, and the concentration ratio of the maximum concentration region is A. Further, in the equation (1), β is an incomplete β function represented by the equation (2), and the distribution shape in the concentration increasing region is a ₁ and b ₁ , and the distribution shape in the concentration decreasing region is a ₂ and b. Determined by ₂ respectively.

At each depth position from the surface of the sample, the atomic concentration ratio P _i of the element to be analyzed to the substrate element is the ratio of the substrate element to the atomic concentration at that position. Therefore, a sample with a coating that does not contain substrate elements,
For example, when a Si substrate is coated with Au, the film does not contain Si, and therefore the parameter A is set to ∞ in the concentration distribution of the film-constituting element Au. When a compound with a substrate element is formed on the sample surface, for example, when a SiO ₂ film is formed on a Si substrate, the parameter A is set to 2 in the O (oxygen) concentration distribution.

In performing the simulation in the first invention, by using the equations (1) and (2) composed of the nine parameters having the physical meanings as described above, various types of samples can be obtained. On the other hand, a hypothetical distribution can be set by theoretically determining each parameter based on known information about the sample. For example, when the distribution of the element concentration in the depth direction exhibits an ion implantation type profile as shown in FIG. 5, a diffusion type profile as shown in FIG. 6, or a block type profile in which elements do not diffuse at the boundary between layers. In this case, the above nine parameters can be theoretically determined, and any of them can be simulated by using the equations (1) and (2).

When inputting the initial values of the nine parameters in equations (1) and (2), classify each parameter into a variable parameter, a related parameter and a fixed parameter based on known information about the sample. so,
The simulation can be performed more efficiently. The variable parameter is initially input independently of other parameters and is corrected as appropriate to perform fitting. Related parameters are determined as a function of other parameters. For example, assuming that a certain layer of the sample is SiO ₂ , the parameter A in the analysis of the O concentration is twice the parameter A in the analysis of the Si concentration, and thus is a related parameter. The fixed parameter is determined as a constant regardless of other parameters. For example, when the sample was deposited Au Au is assumed constant concentration to the outermost surface, the parameters W1 in the analysis of Au concentration is 0, since a ₁ and b ₁ is a waste, these parameters are fixed parameters.

FIG. 5 shows a (100) single crystal silicon substrate.
The distribution of the H / Si atomic concentration ratio in the depth direction is shown for the sample when hydrogen ions are implanted into the surface at 100 keV.
The mark is the actual distribution in the sample measured by secondary ion mass spectrometry. The ◯ mark is a hypothetical distribution obtained by the simulation of the method of the present invention, where the parameters of the equations (1) and (2) are A = 0.001, D = 7 nm, W1 = 223.
8 nm, W2 = 13.6 nm, W3 = 61.5n
m, a ₁ = 3.27, b ₁ = 1.0, a ₂ =
By setting 2.3 and b ₂ = 2.3, the result is in good agreement with the actual distribution. Therefore, it is understood that the simulation of the first invention method can be applied to the sample exhibiting the ion implantation type profile and the accurate analysis can be performed. Each parameter in this example is a variable parameter.

FIG. 6 shows the depthwise distribution of the atomic concentration ratio of the element of the surface layer to the substrate element in the sample in the case where the element of the surface layer diffused into the substrate. It is the actual distribution obtained by the method. A circle indicates an assumed distribution obtained by the simulation of the method of the present invention,
The parameters of equations (1) and (2) are set as follows. That is, at the depth at which the element of the surface layer starts to diffuse, the element maintains a constant maximum concentration, and there is no concentration increasing region. Therefore, W1 = 0, D = 0
, A ₁ and b ₁ are both unnecessary, and the required parameters are 5. And A = 1.0, W2 = 200 nm, W3 = 150
By setting nm, a ₂ = 5.0 and b ₂ = 0.5, the result is in good agreement with the actual distribution. Therefore, it can be understood that the simulation of the first invention method can be applied to a sample exhibiting a diffusion type profile and can be accurately analyzed. In this example W1, D, a ₁ and b1 are fixed parameters, others are variable parameters.

Further, in the sample in which the element of the surface layer does not diffuse into the substrate, the distribution of the atomic concentration ratio of the element with respect to the substrate element in the depth direction becomes a block type profile. In this case, since there are both the increase in concentration range and concentration lowering zone, W1 = 0, W3 = 0 , D = 0, a 1, b 1, a 2, b 2 are both a waste, is required parameters A and W2 There will be only two. Even for a sample exhibiting such a type of profile, it is possible to accurately analyze it by applying the simulation of the first invention method. In this example, A and W2 are variable parameters and the others are fixed parameters.

As an example of the related parameters, Si
There is a parameter A for Si and a parameter A for O in the O ₂ layer. That is, the parameter A
Since (O) = 2A (Si), when one is a variable or fixed parameter, the other is a related parameter.

In the first invention, since the incomplete β function shown in the equation (2) is adopted, the shape parameters a ₁ ,
By appropriately inputting initial values to b ₁ , a ₂ and b ₂ , the shape of the distribution curve in the concentration rising region and the concentration falling region can be changed to a parabola as shown in FIG. 4, a double hyperbola as shown in FIG. A hypothetical distribution can be set by theoretically assuming a straight line or the like.

Next, the second aspect process of this invention, the Rutherford backscattering spectroscopy as shown in FIGS. 2 and 3, by comparing the data of the theoretical spectrum and the measured spectrum, (3) the chi ² The Powell method is applied to the fitting for obtaining the hypothetical distribution with the minimum value of. The Powell method is a means to find the minimum point at which the slope of the curve changes from negative to positive.
It is a method known in the field of mathematics (WHPress, S.
A. Teukolsky, WTVetterling and BPFlannery, Nume
rical Recipes in Fortran-second edition, Cambrid
ge University Press). The fitting by the Powell method of the second invention will be described below with reference to FIG. 7 in comparison with the fitting by the conventional gradient method.

In FIG. 7, a certain parameter, for example, D is changed in a relatively wide range, and cd to e of FIG. 3 are repeated,
It is the figure which plotted the (chi) < ² > value of Formula (3). Three local minimum values of χ ² are seen, but 9 and 11 are not the minimum values, but 1
0 is the minimum value and is the optimum solution. In the gradient method used in the conventional Rutherford backscattering spectroscopy, the gradient χ ² / dD of the initial value P point is obtained, and if this is negative, the minimum value 10 is on the right side of the P point, and if it is positive, it is determined to be on the left side. Was. However, due to simulation errors, etc.
As shown in the enlarged view near the point, the χ ² value fluctuates in a sawtooth shape with respect to the change in D, and therefore the gradient may be reversed depending on how dD is taken. That is, χ ² / dD becomes negative when P _{1 to} P ₂ is dD, but becomes positive when P _{2 to} P ₃ is dD. Therefore, it takes a long time to find the minimum value 10 of χ ² , or the minimum value 9 may be mistaken for the optimum solution.

On the other hand, fitting by the Powell method of the second invention is performed as follows. For example, when determining the optimum value of the parameter D, first, the χ ² value is calculated for at least 5 points within the range that D can take. Figure 7
In this example, the range minimum value D ₁ of the to be taken, a maximum value D _2, an intermediate value somewhat more off value D _3, D ₁ and the intermediate value D ₄ of D _3, D ₃ and the intermediate value D ₅ of D ₂ The χ ² value is calculated for the 5 points to determine points Q ₁ , Q ₂ , Q ₃ , Q ₄ , and Q ₅ . Then, comparing the χ ² values at each Q point, it can be seen that there is a minimum value between Q ₄ and Q ₃ , so next, set 3 points in the same way, calculate the χ ₂ value, and compare. The minimum value 10 is determined by gradually narrowing the range. D1 and D2 are
Instead of the maximum value and the minimum value, any value in the vicinity of both ends in the possible range may be used. Further, D ₃ is (D ₂ −
Although D ₁ ) × 0.6 is set, it can be appropriately set according to the target. Optimal values are similarly determined for parameters other than D.

According to the method of the second invention, the number of iterations of the simulation can be significantly reduced, and accurate fitting can be performed without leading to an erroneous conclusion. The simulation is not limited to the method according to the first invention method, but can be applied to the case where the conventional Doolittle method or the Tanaka method is used. However, by combining the first invention and the second invention,
Since the number of parameters can be limited to a minimum and the number of iterations can be reduced, highly efficient simulation and fitting is achieved. This is because when the number of repetitions in one parameter is K and the number of parameters is M, the total number of repetitions is generally KM ² .

Next, a preferred embodiment of the present invention will be described. When performing a computer simulation, there is a possibility that a physically meaningless solution may be produced, so that when the hypothetical distribution is set in the first invention or when the hypothetical distribution is modified after the simulation, they are physically realistic. There is a step to determine whether or not. For example, since the parameters D, W1, W2, and W3 cannot be negative, in such a case, χ ² is set to ∞ and the simulation is restarted from the beginning. Also, by subdividing the sample into multiple layers and performing simulation for each layer, even when a complex sample, for example, many layers are provided on the substrate and there are a plurality of peaks as shown in FIG. 4 for one element to be analyzed. Can respond.

The most preferable embodiment of the method of the present invention is shown in the flow chart of FIG. Determine the substrate element based on known information about the sample. For example, S used in general IC circuit boards
For i semiconductor, the substrate material is Si and the substrate element is Si
Set and enter. Then, determine the type and number of elements to be analyzed. For example, in the case of the above example, O, B, etc. are considered, and these are input as analysis elements. Then nine parameters A for each element, D, W1, W2, W3 , a 1,
Input the initial values of b ₁ , a ₂ and b ₂ , classify each parameter into variable parameters, related parameters and fixed parameters and input.

Then, simulation and fitting are performed by a preset program. First of all, it is judged whether the input hypothetical distribution of the initial value is physically realistic, and when it is judged as realistic (YES), a simulation is performed, the theoretical spectrum is obtained, fitting by the Powell method is performed, and the measured spectrum is obtained. The χ ² value is calculated by comparing with the data of, and if it is equal to or less than the preset limit value, it is determined that the assumed distribution based on each input parameter is the actual concentration distribution. If the χ ² value is larger than the limit value, modify the parameters and perform simulation and fitting again.

At this time, the variable parameters are corrected,
The related parameter is modified based on the modification of the related variable parameter. Fixed parameters are not modified. Then, it is determined whether or not the hypothetical distribution of the modified variable parameter and the related parameter and the fixed parameter that is not modified is physically realistic, and the same processing is performed thereafter. When it is determined that the assumed distribution is physically unrealistic for the initial value and the modified value of each parameter, the χ ² value is set to ∞ and the simulation is repeated.

In the above-described method of the present invention, the distribution of the element concentration is output as the atomic concentration ratio with respect to the substrate element, so that it is possible to display not only the qualitative analysis but also the quantitative analysis by the atomic% or the weight%.

[0036]

[Examples] Concentrations of Ti, N, O, and Si from the sample surface for samples in which a SiO ₂ layer and a TiN layer were formed on a (100) plane of a Si single crystal by a CVD method (chemical vapor deposition method) The distribution was analyzed by the method of the invention. The cross-sectional structure of the sample is, as shown in FIG.
80 nm thick SiO ₂ layer and 100 nm thick TiN
The presence of layers was estimated by the CVD conditions. The surface of this sample was irradiated with a He ⁺ ion beam having an energy of 2275 keV, and He scattered by atoms in the sample was scattered.
The intensity of the ⁺ energy spectrum was measured at a scattering angle of 160 °. The measured spectrum is as shown in FIG.

The simulation and fitting of the present invention were performed by the flow of FIG. First, Si was input as a substrate element, and Ti, N, and O were input as analysis elements. Known information about the sample, in addition to the thickness of each layer above,
The Ti and N does not diffuse into the SiO ₂ layer, SiO ₂
The O of the layer is to diffuse into the Si substrate. Therefore,
Initial values of parameters were set and input as shown in FIG. 11A for each analysis element. Then, each parameter is divided into a variable parameter marked with a circle, a related parameter marked with a triangle, and other fixed parameters. Here, the related parameter W2 (N) =
W2 (Ti) and D (O) = W2 (N) = W2 (Ti).

Next, the limit value of the fitting is χ ² ≤
It was determined to be 10 ⁻⁴ and input, and computer simulation and fitting were performed. As a result, the theoretical spectrum was as shown by the solid line in FIG. 10 (b), which was in good agreement with the data of the measured spectrum marked with a circle. The value of each parameter of the hypothetical distribution at this time was the value shown in FIG. Based on this value, when the atomic abundances of all elements in the material for each element were normalized, the atomic ratio distributions were as shown in FIGS. 9 (b), 9 (c) and 9 (d). That is, there is a TiN layer having a thickness of 135nm on further its a SiO ₂ layer having a thickness of 85nm on a Si substrate, SiO ₂
The layer has a region in which O is reduced to 70 nm from the SiO ₂ —Si interface, and the O concentration is continuously changing. The TiN layer has constant Ti and N concentrations, and no diffusion is observed at the interface with SiO ₂ . The concentration distribution can be displayed as atomic% or weight% by calculation from the atomic ratio.

The time required for the analysis by the method of the present invention described above (the flow of FIG. 8) is about one hour, and the same is true when the operator inputs numerical values one by one and performs fitting by the conventional Tanaka method. It took about 10 hours to get accuracy. Therefore, according to the method of the present invention, about 1/10 of the conventional method is obtained.
High-precision analysis was possible in the time of.

[0040]

INDUSTRIAL APPLICABILITY According to the method of the present invention, in Rutherford backscattering spectroscopy, a hypothetical distribution is set for the depthwise distribution of the element concentration in a sample, and a theoretical spectrum based on the hypothetical distribution is obtained by simulation. Since the initial value of the parameter is set based on the known information about the sample by using the equation consisting of the parameter with, reliable data analysis can be performed without relying on the advanced expertise and experience of the operator like the conventional method. It can be performed.

In the Rutherford backscattering spectrometry, the Powell method is used for the fitting by comparing the theoretical spectrum based on the hypothetical distribution of the element concentration in the sample with the measured spectrum in Rutherford backscattering spectroscopy. Therefore, the minimum value of χ ² can be obtained without mistake and with a small number of simulations, and data analysis can be performed in a short time.

Furthermore, by the method combining the simulation method of the present invention and the fitting method of the present invention, highly reliable and short-time data analysis can be performed without relying on the operator's high expertise and experience. . Also,
According to the preferred embodiment of the present invention, it is possible to analyze in a shorter time by eliminating an unrealistic solution. Furthermore, by performing a simulation by subdividing a sample into multiple layers, it seems that the conventional method cannot analyze. It is possible to analyze even complex samples.

Therefore, in the qualitative analysis and the quantitative analysis near the surface of the solid sample, the Rutherford backscattering spectroscopic method, which has been difficult to adopt due to various problems in the related art, can be reliably realized by the method of the present invention by using a computer. It will be possible.

[Brief description of drawings]

FIG. 1 is an example of a general measured spectrum in Rutherford backscattering spectroscopy, and is a spectrum diagram when a TiN film is provided on a Si substrate.

FIG. 2 is an explanatory diagram of data analysis in conventional Rutherford backscattering spectroscopy.

FIG. 3 is a flowchart showing a procedure of data analysis in conventional Rutherford backscattering spectroscopy.

FIG. 4 is an explanatory diagram of the physical meaning of each parameter in the simulation method of the present invention.

FIG. 5 is a diagram showing an example of a concentration distribution forming an ion implantation type profile.

FIG. 6 is a diagram showing an example of a concentration distribution forming a diffusion type profile.

FIG. 7 is an explanatory diagram showing the Powell method in the fitting of the present invention in comparison with the conventional gradient method.

FIG. 8 is a flow chart showing a preferred embodiment of the method of the present invention.

9A is a cross-sectional view showing a structure of a sample initialized in an example of the present invention, and FIGS. 9B to 9D are concentration distributions of respective elements obtained in the example of the present invention. It is a graph shown.

FIG. 10 is a spectrum diagram in an example of the present invention, in which (a) is a measured spectrum and (b) is a graph showing the obtained theoretical spectrum in comparison with the measured spectrum.

FIG. 11 is an explanatory diagram showing values of each parameter in the example of the present invention, in which (a) is an initial setting value and (b) is a value of the obtained optimum solution.

[Explanation of symbols]

1 ... Measured spectrum 2 ... Theoretical spectrum 3 ... Actual concentration distribution 4 ... Assumed distribution 5 ... Sample 6 ... Substrate 7,8 ... Coating 9,11 ... Minimum value 10 ... Minimum value A ... Atomic concentration of element to be analyzed with respect to substrate element Maximum value of ratio D ... Depth when the element to be analyzed appears W1 ... Width of concentration increasing range of element to be analyzed W2 ... Width of maximum concentration range of element to be analyzed W3 ... Width of concentration decreasing range of element to be analyzed a ₁ , b ₁ ... Shape parameter of incomplete β function in the concentration increasing region a ₂ , b ₂ ... Shape parameter of incomplete β function in the concentration decreasing region

Claims (5)

[Claims] 1. A rutherford backscattering spectroscopic method is used to set a hypothetical distribution of the elemental concentration distribution in a solid sample in the depth direction, a theoretical spectrum based on the hypothetical distribution is obtained by simulation, and fitting is performed by comparison with the measured spectrum. In the method of analyzing the actual concentration distribution of the element in the sample, the assumed distribution of the concentration ratio of the element to be analyzed with respect to the substrate element is set by the equations (1) and (2) to perform the simulation. Rutherford backscattering spectroscopy data analysis method characterized by carrying out. [Equation 1] Where P _{i is} the atomic concentration ratio of the element to be analyzed to the substrate element x is the depth from the sample surface A is the maximum value of the atomic concentration ratio of the element to be analyzed to the substrate element D is the depth when the element to be analyzed appears W1 Width of concentration increasing range of analysis target element W2 Width of maximum concentration range of analysis target element W3 Width of concentration decreasing range of analysis target element a ₁ , b ₁ ... Shape parameter of incomplete β function in concentration increasing range a ₂ , b ₂ … Shape parameter of incomplete β function in the concentration falling region 2. A rutherford backscattering spectroscopy method is used to set a hypothetical distribution for the depthwise distribution of element concentrations in a solid sample, obtain a theoretical spectrum based on the hypothetical distribution by simulation, and compare the measured spectrum with the measured spectrum to perform fitting. In the method for analyzing the actual concentration distribution of the element in the sample by performing, the fitting is performed by the Powell method, and the Rutherford backscattering spectrometry data analysis method. 3. A Rutherford backscattering spectrometry data analysis method, characterized in that a theoretical spectrum is obtained by performing simulation by the method of claim 1 and fitting is performed by the method of claim 2. 4. An unnecessary repetition of the simulation is prevented by providing a step of determining that an arbitrary solution obtained in the simulation is a solution corresponding to a physically realistic concentration distribution. Claim 1
Alternatively, the Rutherford backscattering spectrometry data analysis method described in 3 above. 5. The simulation is performed for each layer of a sample subdivided into multiple layers.
Alternatively, the Rutherford backscattering spectrometry data analysis method described in 4.