【発明の詳細な説明】 （産業上の利用分野） 本発明は試料を電子線照射によって励起し、試料から
放射される試料成分元素の特性Ｘ線を測定するＸ線分光
分析にけるお蛍光励起補正方法に関する。DETAILED DESCRIPTION OF THE INVENTION (Industrial application field) The present invention excites a sample by irradiating the sample with an electron beam, and performs fluorescence excitation in X-ray spectroscopic analysis for measuring characteristic X-rays of sample constituent elements emitted from the sample. It relates to a correction method.
（従来の技術） 試料を電子線によって励起するＸ線分光分析では試料
の電子線照射によって発生した１次Ｘ線によって試料が
励起されて蛍光Ｘ線が放射され、試料成分元素の特性Ｘ
線検出強度はこの１次Ｘ線と蛍光Ｘ線との和となってい
る。このうち試料成分元素の濃度に直接関係しているの
は１次Ｘ線中のその元素の特性Ｘ線強度であって、それ
と重なっている蛍光Ｘ線強度は試料中の他成分元素の影
響を受け、蛍光Ｘ線の影響は試料の成分構成によって異
なったものとなる。例えば成分元素をA,B,Cとすると
き、元素Ｂの特性Ｘ線波長が元素Ａの特性Ｘ線波長より
短いとき、元素Ｂの特性Ｘ線は元素Ａを励起して蛍光を
発生させるから、元素Ａの濃度が同じでもＢ元素が多い
試料と少い試料とでは直接測定される元素Ａの特性Ｘ強
度は前者の方が強くなる。従って共存他元素の１次Ｘ線
により励起された蛍光Ｘ線に対する補正が必要となる。
これが試料を電子線で励起するＸ線分光分析における蛍
光補正があるが、従来この蛍光補正は試料の厚さが充分
に厚い塊状試料については方法が提案されているが、薄
膜試料の場合に適用できる補正方法は提案されていな
い。(Prior Art) In X-ray spectroscopy in which a sample is excited by an electron beam, the sample is excited by primary X-rays generated by irradiating the sample with an electron beam, and fluorescent X-rays are emitted.
The line detection intensity is the sum of the primary X-ray and the fluorescent X-ray. Of these, the characteristic X-ray intensity of the element in the primary X-ray is directly related to the concentration of the element in the sample, and the intensity of the fluorescent X-ray that overlaps that element is the influence of the other element in the sample. Thus, the influence of the fluorescent X-rays differs depending on the composition of the sample. For example, when the component elements are A, B, and C, when the characteristic X-ray wavelength of the element B is shorter than the characteristic X-ray wavelength of the element A, the characteristic X-ray of the element B excites the element A and generates fluorescence. Even when the concentration of the element A is the same, the characteristic X intensity of the element A, which is directly measured between the sample having a large amount of the element B and the sample having a small amount of the element B, is higher in the former case. Therefore, it is necessary to correct for fluorescent X-rays excited by primary X-rays of other coexisting elements.
There is fluorescence correction in X-ray spectroscopy, which excites the sample with an electron beam.However, this fluorescence correction has been proposed for bulk samples with a sufficiently large sample thickness, but is applied to thin film samples. A possible correction method has not been proposed.
即ち試料に電子線を照射して、試料から放射されるＸ
線を分光するＸ線分光分析において、一つの成分元素の
特性Ｘ線強度に対する補正には次の３種がある。（１）
電子線の試料中への進入深さ，後方散乱電子の割合等の
影響を受け、電子線の進入深さ、後方散乱電子の割合等
は試料を構成している元素の種類，平均原子番号に依存
しているため、この影響に対する補正は原子番号補正と
呼ばれる。（２）また試料内で発生した目的元素の特性
Ｘ線は他共存元素の原子により吸収されるので、吸収に
対する補正が必要で、これは吸収補正と呼ばれる。
（３）更に共存他元素の特性Ｘ線とか連続Ｘ線によって
目的元素が励起され、見掛上目的元素の特性Ｘ線強度を
強めるので、これに対する補正が必要で、この補正は蛍
光補正と呼ばれる。これら三種の補正を合わせてZAF補
正と呼ぶ。これらの補正は試料の元素組成が分っておれ
ば計算可能であるが、当初試料の成分組成は不明である
から、各成分元素の特性Ｘ線強度から、第１近似の組成
を仮定してZAF補正を計算して第２近似組成を求め、第
２近似に基いて再びZAF補正の計算を行うと云う手順を
繰返す遂次近似法により正しい元素組成に到達する。試
料厚さが充分大きな試料に対しては上記補正を実行する
具体的な手法が提案されているが薄膜試料については具
体的な補正手法が提案されていない。That is, the sample is irradiated with an electron beam, and X
In the X-ray spectroscopy for analyzing the rays, there are the following three types of correction for the characteristic X-ray intensity of one component element. (1)
The penetration depth of the electron beam into the sample, the ratio of backscattered electrons, etc. are affected by the penetration depth of the electron beam, the ratio of backscattered electrons, etc., depending on the types of elements constituting the sample and the average atomic number. Because of this, the correction for this effect is called atomic number correction. (2) Since the characteristic X-rays of the target element generated in the sample are absorbed by atoms of other coexisting elements, it is necessary to correct the absorption, which is called absorption correction.
(3) Further, the target element is excited by the characteristic X-rays of the coexisting other elements or continuous X-rays, and apparently the characteristic X-ray intensity of the target element is increased. Therefore, a correction for this is necessary, and this correction is called a fluorescence correction. . These three types of correction are collectively called ZAF correction. These corrections can be calculated if the element composition of the sample is known, but since the component composition of the sample is initially unknown, the first approximate composition is assumed from the characteristic X-ray intensity of each component element. The second approximate composition is obtained by calculating the ZAF correction, and the correct element composition is reached by the successive approximation method which repeats the procedure of calculating the ZAF correction again based on the second approximation. A specific method for performing the above-described correction has been proposed for a sample having a sufficiently large sample thickness, but no specific correction method has been proposed for a thin-film sample.
（発明が解決しようとする課題） 薄膜試料の場合、吸収補正は小さく、薄膜支持体から
放射されるＸ線による蛍光Ｘ線の影響が大きい。本発明
は薄膜試料に適する蛍光補正の方法を提供するものであ
る。(Problems to be Solved by the Invention) In the case of a thin film sample, 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 a thin film sample.
（課題を解決するための手段） 電子線照射による試料および試料保持体の成分元素の
１次特性Ｘ線発生強度分布を試料およびその支持体を含
めて計算し、この計算された１次特性Ｘ線発生強度分布
により、試料および試料保持体の各部からの１次特性Ｘ
線による試料各成分元素の２次特性Ｘ線発生強度を試料
表面からの深さの関数として計算し、この計算結果を試
料表面から試料の厚さだけ積分した計算上の２次特性Ｘ
線強度の上記１次特性Ｘ線発生強度分布から求めた計算
上の１次特性Ｘ線強度との比率により試料成分元素の実
測特性Ｘ線強度に対する蛍光励起補正を行うようにし
た。(Means for Solving the Problems) The primary characteristic X-ray generation intensity distribution of the component elements of the sample and the sample holder by electron beam irradiation is calculated including the sample and its support, and the calculated primary characteristic X is calculated. The primary characteristic X from each part of the sample and the sample holder is obtained by the line generation intensity distribution.
The secondary characteristic X-ray generation intensity of each component element by the X-ray is calculated as a function of the depth from the sample surface, and the calculated result is integrated by the thickness of the sample from the sample surface to calculate a secondary characteristic X.
The fluorescence excitation correction was performed on the measured characteristic X-ray intensity of the sample component element by the ratio of the linear intensity to the calculated primary characteristic X-ray intensity obtained from the above-mentioned primary characteristic X-ray generation intensity distribution.
（作用） 試料を電子ビームで照射すると試料からＸ線が放射さ
れる。電子は試料内に進入し、試料内原子と衝突してＸ
線を放出させるので、試料の組成が分っているときは試
料内から発生する成分元素の特性Ｘ線の発生強度分布を
計算することができる。この分布を試料面からの深さを
x1、試料面の電子ビーム照射点から試料面に沿う距離を
r1としてφ（x1,r1）とする。試料内の原子はこの１次
特性Ｘ線（以後単に１次Ｘ線と云う）の照射を受けて励
起され、２次特性Ｘ線（蛍光Ｘ線、以後単に２次Ｘ線と
云う）を放射する。試料内の一点における上記１次Ｘ線
の効果は計算可能であり、従って試料内各点の２次Ｘ線
放射強度も計算できる。この試料内各点の２次Ｘ線放射
強度を試料表面から深さx2の層面についても積分する
と、２次Ｘ線発生強度の試料面からの深さ分布を求める
ことができ、これを試料の厚さだけ積分すると２次Ｘ線
強度I2が求められる。前記した１次Ｘ線発生強度分布φ
（x1,r1）をx1,r1について０から無限大まで積分すれ
ば、１次Ｘ線強度I1が求められる。試料について実測さ
れる成分元素の特性Ｘ線強度は１次Ｘ線と２次Ｘ線の強
度の和であるが、その１次Ｘ線と２次Ｘ線との強度の比
は上記計算上のI1とI2との比と同じであるから、上記計
算上のI1,I2によって蛍光励起補正が可能である。この
方法によると、１次Ｘ線は試料および試料膜保持体も含
めて計算され、その１次Ｘ線が試料膜に及ぼす影響を計
算しているので、任意厚さの試料について蛍光励起補正
ができるのである。(Operation) When a sample is irradiated with an electron beam, X-rays are emitted from the sample. The electrons enter the sample, collide with atoms in the sample, and X
Since the line is emitted, when the composition of the sample is known, it is possible to calculate the intensity distribution of the characteristic X-rays of the component elements generated from within the sample. This distribution is calculated as the depth from the sample surface.
x1, the distance along the sample surface from the electron beam irradiation point on the sample surface
Let r (x1, r1) be r1. The atoms in the sample are excited by irradiation with the primary characteristic X-rays (hereinafter simply referred to as primary X-rays) and emit secondary characteristic X-rays (fluorescent X-rays, hereinafter simply referred to as secondary X-rays). I do. The effect of the primary X-ray at one point in the sample can be calculated, and therefore the secondary X-ray emission intensity at each point in the sample can also be calculated. When the secondary X-ray emission intensity at each point in the sample is integrated with respect to the layer surface having a depth x2 from the sample surface, the depth distribution of the secondary X-ray generation intensity from the sample surface can be obtained. By integrating by the thickness, the secondary X-ray intensity I2 is obtained. The above-mentioned primary X-ray generation intensity distribution φ
By integrating (x1, r1) for x1, r1 from 0 to infinity, the primary X-ray intensity I1 is obtained. The characteristic X-ray intensity of the component element actually measured for the sample is the sum of the intensity of the primary X-ray and the intensity of the secondary X-ray. Since the ratio is the same as I1 and I2, the fluorescence excitation can be corrected by I1 and I2 in the above calculation. According to this method, the primary X-ray is calculated including the sample and the sample film holder, and the effect of the primary X-ray on the sample film is calculated. You can.
上記計算は試料の組成が分っていなければできない
が、試料を電子線で照射したとき試料から放射される特
性Ｘ線強度の実測値から、試料成分の特性と第１近似の
各成分濃度を決定し、これを用いて上記計算を行って、
上記実測特性Ｘ線強度に蛍光補正を行い、補正された各
成分元素の特性Ｘ線強度から第２近似の各成分濃度を決
め、それに基いて前記計算を行って実測特性Ｘ線強度に
補正を行い、第３近似の各成分濃度を決める。以下この
ような手順を繰返すと、第ｎ近似と第ｎ＋１近似の成分
濃度の差が目標値以下になる。そこで第ｎ＋１近似の成
分濃度を以って試料の定量分析値とすればよい。The above calculation cannot be performed unless the composition of the sample is known, but from the measured values of the characteristic X-ray intensity emitted from the sample when the sample is irradiated with an electron beam, the characteristics of the sample components and the first approximate component concentrations can be calculated. Is determined, and the above calculation is performed using this.
Fluorescence correction is performed on the measured characteristic X-ray intensity, a second approximate component concentration is determined from the corrected characteristic X-ray intensity of each component element, and the calculation is performed based on the concentration to correct the measured characteristic X-ray intensity. Then, the third approximate component concentrations are determined. Hereinafter, when such a procedure is repeated, the difference between the component densities of the n-th approximation and the (n + 1) -th approximation becomes equal to or smaller than the target value. Therefore, the quantitative analysis value of the sample may be determined using the component concentration of the (n + 1) th approximation.
（実施例） まずこの実施例で蛍光Ｘ線強度を求める計算式につい
て説明する。第２図でＦは試料表面で、試料上の一点０
を照射している電子のうち一つが図ｆのような軌跡を画
いて試料面から深さx1における一点ａに到達し、そこで
試料構成原子から１次線を放射させたとする。この１次
Ｘ線の方向および強度は個々の電子によって異り確率的
に決まるものであるが、多数の電子について平均すれ
ば、全ての方向に均一で、試料の組成および密度によっ
て決まり、深x1と図示r1の関数として表わされる。ａ点
を含む微小体積dVから放射される元素ｊの１次Ｘ線量を
φｊ（x1,r1）dVとする。(Example) First, a calculation formula for obtaining the fluorescent X-ray intensity in this example will be described. In FIG. 2, F is the surface of the sample, and one point 0
It is assumed that one of the electrons irradiating the laser beam reaches a point a at a depth x1 from the sample surface along a locus as shown in FIG. F, and emits a primary line from atoms constituting the sample there. The direction and intensity of the primary X-ray are differently and stochastically determined by individual electrons. However, when a large number of electrons are averaged, they are uniform in all directions, are determined by the composition and density of the sample, and have a depth x1. And shown as a function of r1. The primary X-ray dose of the element j emitted from the minute volume dV including the point a is defined as φj (x1, r1) dV.
計算の目的は試料を電子線で照射したとき試料から任
意の一方向に放射される１次Ｘ線と、蛍光Ｘ線の強度比
を求めることである。今試料面の垂線に対しΨの方向を
観測方向としてこの方向で微小角範囲ｄω内に放射され
る１次Ｘ線の量I1jdwを求める。ａ点を含む微小体積dV
から立体角ｄω内に放射される１次Ｘ線量は φｊ（χ1,r1）dVdw で、このＸ線が試料内をx1/cosΨだけ進んで試料面から
出るので、その間の吸収を考慮して表面から放射される
量は exp（−ρμx1/cosΨ）φjdVdw こゝでρは試料の密度、μは１次Ｘ線波長に対する試料
の平均的な質量吸収係数で、各元素の原子の質量吸収係
数をμｉとし、各元素の試料中濃度をCiとすると、 μ＝Σμｉ×Ci である。The purpose of the calculation is to determine the intensity ratio between the primary X-ray emitted from the sample in one arbitrary direction and the fluorescent X-ray when the sample is irradiated with an electron beam. Now, with the direction of 線 with respect to the perpendicular of the sample surface as the observation direction, the amount I1jdw of the primary X-ray radiated within the small angle range dω in this direction is determined. Small volume dV including point a
The primary X-ray dose radiated from within the solid angle dω is φj ({1, r1) dVdw. Since this X-ray travels through the sample by x1 / cosΨ and exits from the sample surface, it takes into account the absorption between The amount emitted from exp is exp (-ρμx1 / cosΨ) φjdVdw where ρ is the density of the sample, μ is the average mass absorption coefficient of the sample for the primary X-ray wavelength, and the mass absorption coefficient of the atoms of each element. Assuming that μi and the concentration of each element in the sample are Ci, μ = Σμi × Ci.
試料面からの深さx1なる層面で発生し、試料面からΨ
の方向に放射される１次Ｘ線の総量は上式をx1の層面全
体について積分して得られる。この積分で指数関数の項
は定数として扱えるから上式でｒの定積分は試料面からの深さx1の層面における
１次Ｘ線の総量で深さx1の関数であり、後述する方法に
より計算される。これをDj（x1）とすると、試料からΨ
の方向に放射される１次Ｘ線強度I1jは上式をx1につい
て積分し、で与えられる。It occurs on the layer surface with a depth x1 from the sample surface, and
Is obtained by integrating the above equation with respect to the entire layer surface of x1. In this integration, the exponential function term can be treated as a constant In the above equation, the definite integral of r is the total amount of primary X-rays on the layer surface having a depth x1 from the sample surface and is a function of the depth x1, and is calculated by a method described later. If this is Dj (x1), Ψ
The primary X-ray intensity I1j emitted in the direction of Given by
次に上述した１次Ｘ線により励起されて放射される２
次Ｘ線の量を求める。試料面からの深さx1なる層面上の
一点ａから放射される１次Ｘ線の深さx2なる層面上のｂ
点に到達する量は幾何学的な関係量を第２図に示すよう
に決め、x2面上でｂ点を含む微小面積をdsとするとｂ点を含む微小体積dsdx2から発生する２次Ｘ線量は、
元素ｊの１次Ｘ線がＲ方向に単位距離進行する間の元素
ｉに対する２次Ｘ線発生効率をQijとすると、１次Ｘ線
が厚さdx2の層を通過する距離はｄ×2/cosθであるか
ら、（２）式にQijdx2/cosθを掛けて得られる。（２）
式でＲ＝（x1−x2）/cosθ、またx2面内にｃ点を原点と
する極座標（r,α）を考えると、 dS＝rdrdα ｒ＝（x1−x2）tanθであるから、ａ点からの１次Ｘ線によって深さx2におけ
る厚さdx2なる層から発生する２次Ｘ線の量ｗはこのｗはａ点における１次Ｘ線の発生強度φｊ（x1r1）
に比例し、深さx1およびx2の２層間の距離（x1−x2）の
関数とφｊ（x1r1）dVとの積であるから、この関数をＦ
（x1−x2）とすると、深さx1厚さdx1厚さdx1の層全体か
ら発生する１次Ｘ線によって深さx2厚さdx2の層全体か
ら放出される２対Ｘ線の総量Δ（x2）dx2は（３）式を
深さx1の面に沿って放射される１次Ｘ線について積分し
て得られる。この積分に当り（３）式の定積分が上記Ｆ
（x1−x2）であるから（４）式で定積分の項は前述したDj（x1）である。そこ
で試料内で発生する全１次Ｘ線によってx2の層面から発
生する２次Ｘ線の総量をD2（x2）dx2とすると（４）式
をx1について積分して試料面からΨの方向に放射される２次Ｘ線強度I2ijは前
述（１）式と同様にして次にＦ（x1−x2）を計算する。（３）式の２重定積分は
αについて積分してであるから、上記定積分はとなる。ここでなる置換を行うと、上の積分は（７）式の積分はなる公式により第３項までとってＦ（x1−x2）は Ｆ（x1−x2）＝−log｛ρμ（x1−x2）｝＋γ−ρμ（x
1−x2） こゝでγ＝0.577…。Next, it is excited and radiated by the above-mentioned primary X-ray 2
The amount of the next X-ray is obtained. The depth x of the primary X-ray radiated from a point a on the layer surface having a depth x1 from the sample surface b on the layer surface having a depth x2
Assuming that the amount to reach the point is determined by the geometric relational amount as shown in FIG. 2, and the small area including the point b on the x2 plane is ds. The secondary X-ray dose generated from the small volume dsdx2 including the point b is
Assuming that the secondary X-ray generation efficiency with respect to the element i while the primary X-ray of the element j travels a unit distance in the R direction is Qij, the distance that the primary X-ray passes through the layer having a thickness of dx2 is d × 2 / Since it is cos θ, it is obtained by multiplying equation (2) by Qijdx2 / cos θ. (2)
Considering R = (x1−x2) / cos θ and polar coordinates (r, α) with the origin at point c in the x2 plane, dS = rdrdα r = (x1−x2) tan θ Therefore, the amount w of the secondary X-ray generated from the layer having the thickness dx2 at the depth x2 by the primary X-ray from the point a is This w is the generation intensity φj (x1r1) of the primary X-ray at the point a.
Is the product of the function of the distance (x1−x2) between the two layers at the depths x1 and x2 and φj (x1r1) dV.
Assuming that (x1−x2), the total amount Δ (x2) of two pairs of X-rays emitted from the entire layer having the depth x2 and the thickness dx2 by the primary X-ray generated from the entire layer having the depth x1 and the thickness dx1 Dx2 is obtained by integrating the equation (3) with respect to the primary X-rays emitted along the plane of the depth x1. In this integration, the definite integration of the equation (3) is obtained by the above F
(X1-x2) In the equation (4), the term of the definite integral is Dj (x1) described above. Therefore, assuming that the total amount of secondary X-rays generated from the x2 layer surface by all the primary X-rays generated in the sample is D2 (x2) dx2, the equation (4) is integrated with respect to x1. The secondary X-ray intensity I2ij emitted from the sample surface in the direction of Ψ is calculated in the same manner as in the above equation (1). Next, F (x1−x2) is calculated. The double definite integral of equation (3) is obtained by integrating α. Therefore, the definite integral is Becomes here With the permutation The integral of equation (7) is According to the following formula, F (x1−x2) is calculated as F (x1−x2) = − log {ρμ (x1−x2)} + γ−ρμ (x
1−x2) where γ = 0.577….
元素ｉは元素ｊだけでなくｉも含めて元素ｉより短波
長の特性Ｘ線を放出する他の全元素の１次Ｘ線により励
起されるので、２次Ｘ線の全強度I2iは 以上のようにしてI1i（式（１）により求められる元
素ｉの１次Ｘ線強度）およびI2iが計算されると、実測
Ｘ線強度はI1i＋I2iに比例する。そこで元素ｉの特性Ｘ
線の実測Ｘ線強度をIi、２次Ｘ線による補正量をΔｉと
すると、補正された１次Ｘ線強度Iicは上式最右辺のIiは実測値、I1i,I2iは前式によって計算
される値である。Element i is excited not only by element j but also by primary X-rays of all other elements that emit characteristic X-rays having a shorter wavelength than element i, including i, so that the total intensity I2i of secondary X-rays is When I1i (the primary X-ray intensity of element i obtained by equation (1)) and I2i are calculated as described above, the measured X-ray intensity is proportional to I1i + I2i. Therefore, the characteristic X of element i
Assuming that the measured X-ray intensity of the line is Ii and the correction amount by the secondary X-ray is Δi, The corrected primary X-ray intensity Iic is Ii on the rightmost side of the above equation is an actually measured value, and I1i and I2i are values calculated by the above equation.
次に１次Ｘ線強度φｊ（X1,r1）の求め方の一例を説
明する。これは試料内に入射した電子が試料を構成して
いる原子と衝突を繰返しながら次第にエネルギーを失い
つゝ不規則な軌跡を画いて試料内を進行して行く仮定を
モンテカルロシミュレーション法によって追跡し、この
電子の進行過程の各点で試料の組成と電子のエネルギー
によって決まるＸ線放射確率を掛ける。このような計算
を多数の電子について行うと、試料内の各点における１
次Ｘ線の強度が求まる。第３図にシミュレーション演算
のフローチャートを示す。被測定試料は厚さｔとし、そ
れを構成している元素は１からｎまでのｎ種である。こ
れらの元素の濃度の組合せを想定しこれらの元素の濃度
（重量％）をC1,C2…Ci…Cnとしてシミュレーションを
開始するこゝで添字のｉは成分番号である。試料厚さt,
試料を構成している各元素の電子に対する散乱断面積，
イオン化断面積，各元素の濃度Ci,電子の初期エネルギ
ーEo,終末エネルギーＥ′，シミュレーションを行う回
数No等をコンピュータに入力する（イ）。シミュレーシ
ョンは例えば1000から20000個の電子について行う。具
体的には一個の電子を試料に入射させたときの電子の軌
跡の追跡演算を行い、これをNo回繰返すのである。
（イ）のステップでシミュレーション演算に必要なデー
タおよびパラメータの入力を終ったら、演算回数Ｎ＝１
とし（ハ）、試料に入射させた電子の追跡演算を行う
（ニ）。この演算は電子が先の試料内原子との衝突から
次の試料内の原子と衝突するまでの過程の計算で、先の
衝突において、電子がどの方向に反撥されるかその方向
を確率的にきめ、次にどの元素の原子と衝突をするかを
下記（８）式により各構成元素の原子の散乱断面積およ
び各元素の濃度に関係させて確率的に決定し、下記
（９）式により電子の試料内での平均自由行程だけ電子
が進行して、上記確率的に決定された原子に衝突するも
のとし、この過程におけるエネルギーの損耗を下記（1
0）式によって算定すると云う演算で但し、Piは電子が元素のｉの原子に衝突する確率で、Pi
はこゝにAiは元素ｉの原子量、σｉは元素ｉの原子の電子
に対する散乱断面積で、衝突する電子のエネルギーＥ
と、試料を構成している各元素の原子番号ziによって決
まり、但しβｉはスクリーニングパラメータで、である。Next, an example of a method of obtaining the primary X-ray intensity φj (X1, r1) will be described. This means that the electrons incident on the sample repeatedly lose their energy while repeatedly colliding with the atoms that make up the sample. At each point in the electron advancing process, an X-ray emission probability determined by the composition of the sample and the energy of the electron is multiplied. When such a calculation is performed for a large number of electrons, one point at each point in the sample is obtained.
The intensity of the next X-ray is obtained. FIG. 3 shows a flowchart of the simulation calculation. The sample to be measured has a thickness t, and the constituent elements are n types from 1 to n. Assuming a combination of the concentrations of these elements and starting the simulation with the concentrations (% by weight) of these elements as C1, C2... Ci... Cn, the subscript i is the component number. Sample thickness t,
Scattering cross section for electrons of each element constituting the sample,
The ionization cross section, the concentration Ci of each element, the initial energy Eo of the electron, the terminal energy E ', the number of times of performing the simulation, and the like are input to the computer (A). The simulation is performed for, for example, 1000 to 20,000 electrons. Specifically, the tracing calculation of the electron trajectory when one electron is made incident on the sample is performed, and this operation is repeated No times.
After inputting data and parameters required for the simulation calculation in step (a), the number of calculations N = 1
(C), the tracking calculation of the electrons made incident on the sample is performed (d). This calculation is a calculation of the process from the collision of an electron with an atom in the sample to the atom in the next sample, and stochastically determines the direction in which the electron is repelled in the previous collision. Then, which element atom to collide with is determined stochastically according to the scattering cross section of each constituent element atom and the concentration of each element according to the following equation (8), and is determined according to the following equation (9). It is assumed that the electrons travel by the mean free path in the sample and collide with the stochastically determined atoms.
0) is calculated by the formula Here, Pi is the probability that an electron collides with the atom of element i.
Is Here, Ai is the atomic weight of element i, σi is the scattering cross section of the atoms of element i for the electrons, and the energy E of the colliding electrons is
And the atomic number zi of each element constituting the sample, Where βi is a screening parameter, It is.
平均自由行程ＬはÅ単位で 電子物質内を進行して行くときのエネルギーの損耗は
単位飛距離当り、 但し は試料内の各元素の組成比（重量％）を加味し
た原子番号の平均値で ＝ΣCizi 但しΣCi＝１ で表わされる。同様にしてＡは試料内元素の平均原子
量、ρは試料密度である。上式の単位はKeV/ÅでJiは元
素ｉのイオン化ポテンシャル（eV）である。The mean free path L is in units of Å The energy loss when traveling in electronic matter is per unit flight distance, Where is the average value of atomic numbers taking into account the composition ratio (% by weight) of each element in the sample, and is represented by = Cizi where ΣCi = 1. Similarly, A is the average atomic weight of the elements in the sample, and ρ is the sample density. The unit of the above equation is KeV / Å, and Ji is the ionization potential (eV) of element i.
追跡計算が終わったら、その演算における前後の衝突
の間の電子の試料表面からの深さ方向の進行距離および
電子入射点からの試料面に平行方向の進行距離を前回ま
での深さ方向および試料面と平行方向の進行距離に加算
して現在の電子の試料面からの深さ位置x1を積算（ホ）
する。この実施例では次の（ヘ）のステップで、上記過
程で後の衝突における元素ｉの特性Ｘ線放射確率を計算
し、その結果をメモリに入力する。特性Ｘ線の放射確率
は電子エネルギーをＥ、元素ｉの特性Ｘ線放射のための
励起エネルギーをEiとすると、vi＝E/Eiに関係し、次式
で与えられるφ′ｉに比例する。When the tracking calculation is completed, the travel distance in the depth direction of the electron from the sample surface and the travel distance in the direction parallel to the sample surface from the electron incident point during the previous and subsequent collisions in the calculation are the depth direction and the sample Adds to the travel distance in the direction parallel to the surface and integrates the current electron depth position x1 from the sample surface (e)
I do. In this embodiment, in the next step (f), the characteristic X-ray emission probability of the element i in the subsequent collision in the above process is calculated, and the result is input to the memory. Assuming that electron energy is E and excitation energy for characteristic X-ray emission of element i is Ei, the characteristic X-ray emission probability is related to vi = E / Ei and is proportional to φ′i given by the following equation.
このφｉをx1なる座標データをアドレス指定データと
するメモリにおいてアドレス内のデータに加算して同ア
ドレスに格納する。次に電子エネルギーＥがE/E′か否
かチェックされる（ト）。Ｅ′は電子の終末エネルギー
で今の場合試料中の何れの元素の原子もイオン化できな
い限界エネルギーに設定しておけばよい。このチェック
がNOの場合、電子の試料面からの深さx1が＜０（表面か
ら飛び出す）か否かチェック（チ）、次にx1＞ｔ（試料
を透過）か否かチェック（リ）、全てNOであれば動作は
（ニ）に戻り、（ト）（チ）（リ）の何れかのステップ
がNOになる迄同じ動作が繰返される。 This φi is added to the data in the address in the memory using the coordinate data x1 as the address designation data 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, may be set to a limit energy at which atoms of any element in the sample cannot be ionized. If this check is NO, check whether the depth x1 of the electrons from the sample surface is <0 (protruding from the surface) (h), and then check if x1> t (transmit through the sample) (h), If all are NO, the operation returns to (D), and the same operation is repeated until any of the steps (G), (H), and (R) becomes NO.
以上のようにして（ト）（チ）（リ）の何れかのステ
ップがYESになるとそこで一個の電子について追跡演算
が終わり、ＮをＮ＋１とし（ル）、新しいＮがＮ＞NOか
否かチェック（オ）し、NOなら動作は（ハ）のステップ
に戻って次の電子について上述した演算が行われる。か
くして例えば10000回の演算が行われるとＮ＞NOとなっ
て（オ）のステップがYESとなり一つの試料についての
モンテカルロシミュレーション演算が完了したことにな
る。こゝまでの動作でメモリ内には各元素毎に試料内の
深さ位置x1に対する特性Ｘ線放射度数のヒストグラムが
形成されている。これが先の計算で用いられるDi（x1）
に他ならない。As described above, when any of the steps (g), (h), and (li) becomes YES, the tracking operation is completed for one electron, and N is set to N + 1 (L), and whether or not the new N is N> NO is determined. Check (e), and if NO, the operation returns to step (c) and the above-described calculation is performed for the next electron. Thus, for example, when 10,000 calculations are performed, N> NO, and the step (e) becomes YES, which means that the Monte Carlo simulation calculation for one sample is completed. By the above operation, a histogram of the characteristic X-ray radiant power for the depth position x1 in the sample is formed for each element in the memory. This is Di (x1) used in the previous calculation
Nothing else.
第１図は本発明方法をコンピュータを用いて実行する
場合の動作のフローチャートである。コンピュータには
予め計算に用いられる各元素の特性値例えば原子番号，
質量吸収系数等が入力してある。分析に先立ち、試料薄
膜の厚さ、保持体の成分組成等のデータを入力（イ）
し、試料の各成分の特性Ｘ線強度Iiを測定（ロ）する。
今の場合試料成分元素は既知（定性分析ずみ）であり、
従って各成分元素の特性Ｘ線強度測定は予め指定された
波長でのＸ線測定動作である。この測定結果から各成分
元素の第１近似濃度Ciを決める（ハ）。この第１近似濃
度はこの実施例では各成分元素の純品試料の特性Ｘ線強
度との比として決定する。次いで演算回数ｎを１とおき
（ニ）、各成分の第ｎ近似濃度▲Ｃni▼の所に上記Ｃ′
ｉを設定（ホ）して、前記Di（x1）および（７）式のI2
ijの演算（ヘ）（ト）を行い、前記計算上の各成分特性
Ｘ線の１次Ｘ線強度I1iおよび蛍光Ｘ線強度（２次Ｘ線
強度）I2iを算（チ）し、を算出（リ）、この▲Ｉic▼により第ｎ＋１近似（今の
場合第２近似）濃度▲Ｃn+1i▼を決定（ヌ）、全成分に
つきか否か検定（ル）し、YESであれば▲Ｃn+1i▼を以って
分析値として、動作は終了し、NOであればｎ＋１をｎと
して動作は（ホ）に戻る。FIG. 1 is a flowchart of the operation when the method of the present invention is executed using a computer. The computer stores in advance the characteristic values of each element used in the calculation, such as atomic numbers,
The mass absorption number and the like are entered. Prior to analysis, input data such as the thickness of the sample thin film and the component composition of the holder (b)
Then, the characteristic X-ray intensity Ii of each component of the sample is measured (b).
In this case, the sample constituent elements are known (qualitatively analyzed),
Therefore, the characteristic X-ray intensity measurement of each component element is an X-ray measurement operation at a wavelength designated in advance. From this measurement result, the first approximate concentration Ci of each component element is determined (C). In this embodiment, the first approximate concentration is determined as a ratio of each component element to the characteristic X-ray intensity of a pure sample. Next, the number of operations n is set to 1 (d), and the above-mentioned C ′ is placed at the n-th approximate concentration {Cni } of each component.
i is set (e), and Di (x1) and I2 of the equation (7) are set.
The calculation (f) and (g) of ij are performed, and the primary X-ray intensity I1i and the fluorescent X-ray intensity (secondary X-ray intensity) I2i of each component characteristic X-ray in the calculation are calculated (h). Is calculated, and the (n + 1) th (in this case, the second approximation) concentration ΔCn + 1i ▼ is determined from this (Iic ) (nu). Whether test and (le), if YES ▲ the Cn + 1i ▼ as an analytical value I or more, the operation is terminated, if NO operated n + 1 as n returns to (e).
実測された各成分の特性Ｘ線強度Ii或は補正されたＩ
から各成分濃度を決める方法としては例えば本願出願
人によって提案された「特願昭63−186492号Ｘ線分光分
析法」を用いることとができる。The characteristic X-ray intensity Ii or the corrected I
As a method of determining the concentration of each component from the above, for example, "X-ray spectroscopy of Japanese Patent Application No. 63-186492" proposed by the present applicant can be used.
（発明の効果） 本発明によれば薄膜試料で保持体からの１次Ｘ線の照
射効果がある場合でも、計算によって蛍光励起補正が可
能であり、特殊な標準試料を用意しなくてもよく、精度
の良い分析ができる。(Effect of the Invention) According to the present invention, even when the thin film sample has an irradiation effect of primary X-rays from the holder, the fluorescence excitation can be corrected by calculation, and a special standard sample need not be prepared. , Accurate analysis is possible.
第１図は本発明方法の一実施例における動作のフローチ
ャート、第２図は試料内における２次Ｘ線発生のメカニ
ズムを説明するモデル図、第３図は１次Ｘ線強度を計算
する動作の一例フローチャートである。FIG. 1 is a flowchart of an operation in an embodiment of the method of the present invention, FIG. 2 is a model diagram for explaining a mechanism of secondary X-ray generation in a sample, and FIG. 3 is an operation for calculating a primary X-ray intensity. It is an example flowchart.
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63248429AJP2595686B2 (en) | 1988-09-30 | 1988-09-30 | X-ray spectroscopy by electron beam excitation |
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63248429AJP2595686B2 (en) | 1988-09-30 | 1988-09-30 | X-ray spectroscopy by electron beam excitation |
| Publication Number | Publication Date |
|---|---|
| JPH0295247A JPH0295247A (en) | 1990-04-06 |
| JP2595686B2true JP2595686B2 (en) | 1997-04-02 |
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP63248429AExpired - LifetimeJP2595686B2 (en) | 1988-09-30 | 1988-09-30 | X-ray spectroscopy by electron beam excitation |
| Country | Link |
|---|---|
| JP (1) | JP2595686B2 (en) |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002062270A (en)* | 2000-08-21 | 2002-02-28 | Jeol Ltd | Surface analysis data display method in surface analyzer using electron beam |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2015011018A (en)* | 2013-07-02 | 2015-01-19 | 株式会社東芝 | Sample analysis method, program, and sample analyzer |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002062270A (en)* | 2000-08-21 | 2002-02-28 | Jeol Ltd | Surface analysis data display method in surface analyzer using electron beam |
| Publication number | Publication date |
|---|---|
| JPH0295247A (en) | 1990-04-06 |
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