JPH0395446A - Apparatus and method for measuring lattice constant - Google Patents

Abstract

PURPOSE:To exclude a crystallographic restriction in an optical system and to enable highly-precise measurement of the lattice constant of any single crystals by a method wherein a monochromator constituting an apparatus is constructed of a plurality of crystals of which the crystal faces in a plurality are disposed in parallel. CONSTITUTION:An X-ray beam 1 generated from an X-ray source 2 is made monochrome by a monochromator 4 and applied to a sample crystal 10 and a standard crystal 11 fixed on a rotary sample stage 9, and a diffracted beam obtained at this time is measured by a counter tube 7. On the occasion, the monochromator 4 is formed of spectral crystals 5 and 6, which are cut out of the same crystal so that they are disposed in complete parallel in terms of crystallography, respectively. By using Si or the like, these crystal faces can take out the beam 1 made monochrome. By making the beam 1 enter the crystals 5 and 6 from directions reverse to each other before and after the rotation of the sample stage 9, besides, various errors due to measurement are offset and thus highly precise measurement can be conducted.

Description

【発明の詳細な説明】 ［産業上の利用分野］ 本発明は格子定数測定装置及び格子定数測定方法、更に
詳しく言えば、モノクロメータにより単色化されたＸ線
ビームを標準結晶及び測定すへき試料結晶に同時照射し
、両結晶の回折ビームの角度差から試料結晶の格子定数
の変化（相対値）を高精度に測定する方法及び装置に関
する。[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a lattice constant measuring device and a lattice constant measuring method, and more specifically, to a standard crystal and a sample to be measured using an X-ray beam made monochromatic by a monochromator. The present invention relates to a method and apparatus for simultaneously irradiating a crystal and measuring changes in the lattice constant (relative value) of a sample crystal with high precision from the angular difference between the diffraction beams of both crystals.

［従来の技術］ 半導体の技術分野において、半導体素子の電気的特性を
改善するため、半導体結晶の格子定数を正確に測定する
技術が重要になる。格子定数ａ。の測定は通常Ｘ線回折
法を用いて行われる。単結晶にＸ線を照射すると、特定
の方向に強いＸ線が散乱される。単結晶に入射されるＸ
線ビー、ムとその強い散乱ビーム（回折ビーム）の間の
角度を２０　（０をブラッグ角という）とすると、結晶
の格子面間隔ｄと、ブラック角θ及び回折ビームの波長
λとの間には、よく知られたブラッグの法則２　ｄ　ｓ
ｉｎθ＝λ　がなりたつ。格子定数ａ。は格子面間隔ｄ
に一定の定数を乗したものとしてあたえられる。従って
、ブラッグ角θを測定することによって、格子定数ａ。[Background Art] In the technical field of semiconductors, a technique for accurately measuring the lattice constant of a semiconductor crystal is important in order to improve the electrical characteristics of a semiconductor element. Lattice constant a. The measurement is usually carried out using an X-ray diffraction method. When a single crystal is irradiated with X-rays, strong X-rays are scattered in a specific direction. X incident on a single crystal
Assuming that the angle between the linear beam, M and its strongly scattered beam (diffraction beam) is 20 (0 is called the Bragg angle), there is a relationship between the lattice spacing d of the crystal, the Black angle θ, and the wavelength λ of the diffracted beam. is the well-known Bragg's law 2 d s
inθ=λ. Lattice constant a. is the lattice spacing d
It is given as the product of , multiplied by a certain constant. Therefore, by measuring the Bragg angle θ, the lattice constant a.

を求めることができる。can be found.

格子定数をＸ線回折法によって高精度に求める測定装置
として、第５図に示す装置が知られている（特開昭４．
　９　−　３　６　７　７号公報参照）。この公知の測
定装置は，Ｘ線源２０から発生したＸ線ビームを２方向
に分割するスリット１２、１３を有し、上記スリッ１−
によって２方向に分割されたＸ線ビームそれぞれを反射
させるモノクロメータ１４、１５を設け、モノクロメー
タ１４、１５によって反射されたそれぞれのＸ線ビーム
１６、１７が同一の回転台に固定された標準結晶１８と
試料結晶工９に照射し、両結晶による回折条件を満たし
うる方向に計数管２１、２２を配置させた単結晶の格子
定数測定装置である。As a measuring device for determining lattice constants with high precision using the X-ray diffraction method, the device shown in FIG.
(See Publication No. 9-3677). This known measuring device has slits 12 and 13 that divide an X-ray beam generated from an X-ray source 20 into two directions.
Monochromators 14 and 15 are provided to reflect the X-ray beams split into two directions by the monochromators 14 and 15. This is a single-crystal lattice constant measuring device in which counter tubes 21 and 22 are arranged in a direction that can irradiate the sample crystal 18 and the sample crystal 9 and satisfy the diffraction conditions for both crystals.

［発明が解決しようとする課題］ 上記公知の格子定数測定装置は二結品法の並行配置を応
用したもの、即ち、モノクロメータを構成する分光結晶
の結晶面と測定すへき試料結晶の結晶面を並行とするこ
とによってＸ線ビームの分散を少なくし、測定精度を高
精度にするものであり、測定すべき試料結晶の種類、あ
るいは測定回折面の条件によっては高精度に格子定数の
変化（相対値）を測定できる。しかし、Ｘ線ビームに対
するモノクロメータｌ４、１５と試料結品１９、或は標
準結晶１８には一定のＸ線結晶学的拘束がある。　例え
ば、試料結晶１９とモノクロメータ１４或は１５の格子
定数、回折格子面がほぼ等しいこと、モノクロメータ］
４による回折Ｘ線ビー−３− ムｌ６とモノクロメータ１５による回折Ｘ線ビーム７は
試料結晶１９上の回転中心で交差する必要がある。[Problems to be Solved by the Invention] The above-mentioned known lattice constant measuring device applies the parallel arrangement of the two-piece method, that is, the crystal plane of the spectroscopic crystal constituting the monochromator and the crystal plane of the sample crystal to be measured. By making the lattice constants parallel, the dispersion of the X-ray beam is reduced and the measurement accuracy is increased. Depending on the type of sample crystal to be measured or the conditions of the measurement diffraction surface, changes in the lattice constant ( relative value) can be measured. However, there are certain X-ray crystallographic constraints on the monochromators 14, 15 and the sample sample 19 or standard crystal 18 for the X-ray beam. For example, the lattice constants and diffraction grating planes of the sample crystal 19 and the monochromator 14 or 15 are approximately the same, and the monochromator]
It is necessary that the diffracted X-ray beam 16 by the monochromator 4 and the diffracted X-ray beam 7 by the monochromator 15 intersect at the center of rotation on the sample crystal 19.

上記Ｘ線結晶学的拘束から、上記公知の格子定数測定装
置は試料結晶の種類、或は結晶の測定回折面に大きな制
約を受ける。結晶によっては測定できないものも有り、
格子定数測定装置としての汎用性に欠ける。Due to the above-mentioned X-ray crystallographic constraints, the above-mentioned known lattice constant measuring apparatus is greatly restricted by the type of sample crystal or the measurement diffraction plane of the crystal. Some crystals cannot be measured,
It lacks versatility as a lattice constant measuring device.

本発明の目的は従来装置の欠点である光学系における結
晶学的拘束を排除し、あらゆる結晶（結晶面）の単結晶
の格子定数を相対値（Δｄ／ｄ）で１０−゜〜１０−７
の高精度で測定しうる格子定数測定装置および格子定数
の測定方法を提供することである。The purpose of the present invention is to eliminate the crystallographic constraints in the optical system, which are the drawbacks of conventional devices, and to adjust the lattice constant of a single crystal of any crystal (crystal plane) from 10-° to 10-7 in relative value (Δd/d).
An object of the present invention is to provide a lattice constant measuring device and a lattice constant measuring method capable of measuring lattice constants with high accuracy.

［課題を解決するための手段］ 本発明は上記目的を達戊するために、格子定数の測定装
置を測定すべき試料結晶と標準結晶を搭載する回転試料
台と、上記試料結晶と標準結晶に同時にＸ線ビームを照
射する並行配置の複数結晶からなるモノクロメータと、
上記試料結晶と標準４ 結晶からの回折ビームを割数する計数管とを持つように
構威した。なお、回転試料台とＸ線ビームの関係はＸ線
ビームが上記標準結晶および試料結晶に回転試料台の回
転前後によって互いに逆方向から入射できるようにする
。[Means for Solving the Problems] In order to achieve the above object, the present invention provides a rotary sample stage on which a lattice constant measuring device is mounted with a sample crystal to be measured and a standard crystal, and a rotary sample stage on which a lattice constant measuring device is mounted. A monochromator consisting of multiple crystals arranged in parallel that simultaneously irradiates an X-ray beam,
It was constructed to have a counter that divides the diffracted beams from the sample crystal and the standard 4 crystal. The relationship between the rotating sample stage and the X-ray beam is such that the X-ray beam is incident on the standard crystal and the sample crystal from opposite directions depending on whether the rotating sample stage is rotated or not.

［作用］ 本発明の格子定数測定装置を構戊するモノクロメータは
複数の結晶面が並行配置された複数の結晶で構成された
ものであるので、波長による分散効果が除かれ、上記試
料結晶と標準結晶を照射するｘｌビーム自体の波長分散
（Δλ／λ、λはＸ線ビームの中心波長、△λ半値幅の
槽域）を１０−６程度に小さくすることができる。また
、モノクロメータ自体によってＸ線ビームの波長分散を
小さくしているので、試料結晶の穐類、結晶面の位置に
よらず、得られる回折強度曲線のピークの半値幅は１〜
２秒程度と或り、高精度の格子定数測定精度（１０’〜
１０−７）が可能となる。また、本発明の測定装置では
回転試料台の回転前後において同一のＸ線ビームが利用
されるため、前記公知技術における結晶学的拘束が除か
れる。[Function] Since the monochromator constituting the lattice constant measuring device of the present invention is composed of a plurality of crystals in which a plurality of crystal planes are arranged in parallel, the dispersion effect due to wavelength is removed, and the monochromator can be used to measure the lattice constant of the sample crystal. The wavelength dispersion (Δλ/λ, where λ is the center wavelength of the X-ray beam and the tank region of the half-value width of Δλ) of the xl beam itself that irradiates the standard crystal can be reduced to about 10 −6 . In addition, since the wavelength dispersion of the X-ray beam is reduced by the monochromator itself, the half-width of the peak of the obtained diffraction intensity curve is 1 to 1, regardless of the position of the sample crystal or crystal plane.
High precision lattice constant measurement accuracy (10'~2 seconds)
10-7) becomes possible. Furthermore, in the measurement apparatus of the present invention, the same X-ray beam is used before and after the rotation of the rotating sample stage, so the crystallographic constraints in the known techniques are removed.

［実施例］ 第１図及び第２図に本発明による格子定数測定装置の一
実施例の要部（光学系）構戊を示す。なお、第１図及び
第２図は同一装置において、回転試料台１．９の回転前
後における様子を分けて示したものである。ＸｌｔＸ２
から発生したｘＰＩＡはスリット３により制限され、モ
ノクロメータ４に入則する。モノクロメータ４は第１結
晶５と第２結晶６とから或り、それぞれの結晶は結晶工
学的適に完全に並行になるような配置（並行配置の二結
品法）がとられるよう、同一結晶から切り出した結晶を
用いている。[Embodiment] FIGS. 1 and 2 show the structure of a main part (optical system) of an embodiment of a lattice constant measuring device according to the present invention. Note that FIGS. 1 and 2 separately show the same apparatus before and after rotation of the rotating sample stage 1.9. XltX2
The xPIA generated from the slit 3 is restricted by the slit 3 and enters the monochromator 4. The monochromator 4 consists of a first crystal 5 and a second crystal 6, and the crystals are identical so that they are arranged completely parallel to each other (parallel arrangement two-piece method) suitable for crystal engineering. It uses crystals cut from crystals.

第１結品５、第２結品６の結晶面はＳｉ（４４０）など
を使用することにより、Ｘ線ビームの波長の広がりはΔ
λ／λが１０″″６となり、単色化（Ｋα、）されたＸ
線ビーム７を取り出すことができる。また、第１結晶５
などに非対称反射の結晶面を用いれば、波長の分散は極
めてよくなり、かつ、ｘｌのビーム幅を広くすることが
でき？。By using Si (440) etc. as the crystal planes of the first crystal 5 and the second crystal 6, the wavelength spread of the X-ray beam is Δ
λ/λ becomes 10″″6, and X becomes monochromatic (Kα,)
The line beam 7 can be taken out. In addition, the first crystal 5
If we use crystal planes with asymmetric reflection for example, the wavelength dispersion will be extremely good and the xl beam width can be widened. .

モノクロメータ４によって単色化されたＸ線ビーム７は
スリッ１・８によりビーム径が制限され、ゴニオメータ
の回転試料台９上に固定された試料結晶１０および標準
結晶１１を同時照射し、それぞれから回折されたＸ線ビ
ームは計数管７によって検出される。以下の説明では第
１図に示した光学系での測定をＡ側測定と呼ぶことにす
る。The X-ray beam 7 made monochromatic by the monochromator 4 has its beam diameter limited by the slits 1 and 8, and simultaneously irradiates the sample crystal 10 and standard crystal 11 fixed on the rotating sample stage 9 of the goniometer, and diffracts from each. The generated X-ray beam is detected by a counter tube 7. In the following explanation, the measurement using the optical system shown in FIG. 1 will be referred to as A-side measurement.

次に、入射Ｘ線側の光学系は第上図と同しで、回転試料
台９の回転によって試料結晶１０および標準結晶１１の
向きをωだけ回転し、第２図に示した位置での測定（Ｂ
側ｄ１リ定と呼ぶ）を行う。回転試料台９の回転ωによ
り、第１図と第２図の結晶に対するＸ線ビーム１の入射
方向が互いに逆になる。Next, the optical system on the incident X-ray side is the same as that shown in the upper figure, and the orientation of the sample crystal 10 and standard crystal 11 is rotated by ω by the rotation of the rotating sample stage 9, and the positions shown in FIG. Measurement (B
(referred to as side d1 determination). Due to the rotation ω of the rotating sample stage 9, the directions of incidence of the X-ray beam 1 on the crystals in FIGS. 1 and 2 are reversed.

第３図（ａ）及び（ｂ）はそれぞれ第１図及び第２図の
試料結晶１０近傍を拡大した図である。FIGS. 3(a) and 3(b) are enlarged views of the vicinity of the sample crystal 10 in FIGS. 1 and 2, respectively.

Ａ側測定における試料結晶１０からの回折線をＯ■Ｓ、
標準結晶１１からの回折線をｆｌｘｒ＋とする。The diffraction line from the sample crystal 10 in the A-side measurement is O■S,
Let the diffraction line from the standard crystal 11 be flxr+.

また、Ｂ側測定においても、試料結晶１０からの−７− ？折線をｏ２ｓ．標準結晶１１からの回折線をＯ，Ｒと
する。これらの回折強度曲線の様子を第５図に示す。以
上の測定結果から、上記０１ｓ、Ｏ■Ｒ、０，ｓ、及び
θ２Ｒが回折角度も表すとすると、（コ）及び（２）式
が得られる。Also, in the B-side measurement, -7-? from sample crystal 10? The broken line is o2s. Let the diffraction lines from the standard crystal 11 be O and R. The appearance of these diffraction intensity curves is shown in FIG. From the above measurement results, if the above-mentioned 01s, O■R, 0,s, and θ2R also represent the diffraction angle, equations (c) and (2) can be obtained.

ΔＳ　１　＝　ＦＢ，ｓ−０１Ｒ＝　ｃｔ−ΔＯ　　　
　　（上）ΔＳ２＝Ｑ，ｓ−０，ｎ＝ａ＋ΔＯ　　　　
（２）但し、αは試料結晶１０と標準結晶１１の回折面
における両者の並行からの角度ずれ、Δθは試料結晶１
０と標準結晶１工の格子定数の差によるブラッグ角の角
度差である。従って、（コ）と（２）式の差を求めるこ
とにより（３），（４．）式を求めることができる。ΔS 1 = FB, s-01R = ct-ΔO
(Top) ΔS2=Q, s-0, n=a+ΔO
(2) However, α is the angular deviation of the diffraction planes of the sample crystal 10 and the standard crystal 11 from parallelism, and Δθ is the angle deviation of the sample crystal 10 and the standard crystal 11 from parallel.
This is the difference in Bragg angle due to the difference in lattice constant between 0 and standard crystal. Therefore, equations (3) and (4.) can be obtained by finding the difference between equations (e) and (2).

Δθ＝（ΔＳ１−Δ８２）／２　　　　　（３）Δｄ／
ｄｏ＝−ｃｏｔ６１ｏ・Δ０　　　　（４）ここで、Δ
ｄ＝ｄ１−ｄｏ，ｄｏは標準結晶の格子面間隔、ｄ１は
試料結晶の格子面間隔、ＯｏはＸ線の波長λに対する標
準結晶のブラッグ角である。Δθ=(ΔS1−Δ82)/2 (3) Δd/
do=-cot61o・Δ0 (4) Here, Δ
d=d1-do, do is the lattice spacing of the standard crystal, d1 is the lattice spacing of the sample crystal, and Oo is the Bragg angle of the standard crystal with respect to the wavelength λ of the X-ray.

即ち、第１図、第２図に示した光学系において、Ａ側、
Ｂ側の測定データθ．Ｓ、（Ｊ１Ｒ、および０，ｓ、−
８− θ２Ｒのピーク間隔を求めることにより、（３），（４
）式から試料結晶の標準結晶に対する相対格子定数（Δ
ｄ／ｄｏ）を高精度に求めることができる。That is, in the optical system shown in FIGS. 1 and 2, the A side,
B side measurement data θ. S, (J1R, and 0,s,-
8- By finding the peak interval of θ2R, (3), (4
), the relative lattice constant (Δ
d/do) can be determined with high precision.

上記実施例においてはモノクロメータは２個の結晶を並
行配置した場合を示したが、結晶の個数は更に増やして
よい。しかし結晶の個数を増やすことはビームの強度を
弱めること、結晶面の調整のための複雑さが伴う。In the above embodiment, the monochromator has two crystals arranged in parallel, but the number of crystals may be further increased. However, increasing the number of crystals involves weakening the beam intensity and complicating the adjustment of crystal planes.

［発明の効果コ 本発明によれば、複数個の結晶からなるモノクロメータ
により、波長幅の狭い（〜１０−６）入射Ｘ線ビームを
得ることができ、それによる回折強度曲線の半値幅は秒
オーダとなる。また、本発明による測定方法は標準結晶
と試料結晶に対し、Ａ側、Ｂ側の逆方向入射を採用して
いるため、測定による各種誤差は相殺され、高精度（Δ
ｄ／ｄｏで１０−６〜１０−７）な測定ができる。[Effects of the Invention] According to the present invention, an incident X-ray beam with a narrow wavelength width (~10-6) can be obtained by using a monochromator made of a plurality of crystals, and the half-width of the diffraction intensity curve is It is on the order of seconds. In addition, since the measurement method according to the present invention adopts opposite directions of incidence on the A side and B side for the standard crystal and sample crystal, various errors caused by measurement are canceled out, resulting in high accuracy (Δ
10-6 to 10-7) can be measured in d/do.

更に、本発明の特徴は」二述のように、入射Ｘ線に並行
配置の二結晶法を光学系の基本とするため、１０ 測定すべき試料（結晶）の結晶の種類が変わるとき、モ
ノクロメータの交換など、光学系の変更は全く必要がな
く、実験の効率を大幅に向上することができる。Furthermore, as mentioned in Section 2, the present invention is characterized by the fact that the optical system is based on the two-crystal method in which the two crystals are arranged parallel to the incident X-rays. There is no need to change the optical system, such as replacing meters, and the efficiency of experiments can be greatly improved.

【図面の簡単な説明】[Brief explanation of drawings]

第１図及び第２図はいずれも本発明による格子定数測定
装置の１実施例の要部構成図、第３図（ａ）及び（ｂ）
はそれぞれ第↓図及び第２図の試料結晶１０近傍を拡大
した図、第４図は本発明で得られる回折強度曲線の模式
図、第５図は従来の格子定数測定装置の概略図である。 工：Ｘ線ビーム、２：Ｘ線源、３：スリット、５：モノ
クロメータの第１結晶、６：モノクロメータの第２結晶
、７：計数管、９：回転試料台、１０：試料結晶、１１
：標準結晶、。1 and 2 are main part configuration diagrams of one embodiment of the lattice constant measuring device according to the present invention, and FIGS. 3(a) and (b)
are enlarged views of the vicinity of the sample crystal 10 in Figures ↓ and 2, respectively, Figure 4 is a schematic diagram of the diffraction intensity curve obtained by the present invention, and Figure 5 is a schematic diagram of a conventional lattice constant measuring device. . Engineering: X-ray beam, 2: X-ray source, 3: slit, 5: first crystal of monochromator, 6: second crystal of monochromator, 7: counter tube, 9: rotating sample stage, 10: sample crystal, 11
: Standard crystal.

Claims (1)

【特許請求の範囲】 １、Ｘ線源から発生するＸ線ビームを単色化するモノク
ロメータと、回転試料台を有し、上記モノクロメータに
よって単色化されたＸ線ビームを上記回転試料台に固定
された複数個の単結晶に対し照射したときの回折ビーム
を計測する手段とを有する格子定数測定装置において、
上記モノクロメータが複数個の結晶を反射結晶面が並行
になるように配置して構成されたことを特徴とする格子
定数測定装置。 ２、請求項第１記載の格子定数測定装置を用いて試料結
晶の格子定数の変化を測定する方法において、 上記回転試料台に固定された複数個の単結晶のうち、少
なくとも１つを標準結晶とし、上記試料結晶の近くに配
置し、第１の方向から上記単色化されたＸ線ビームを上
記標準結晶及び試料結晶に照射し、その時の標準結晶及
び試料結晶の回折ビームの第１の角度差、及び上記第１
の方向に上記回折ビームが生じるような第２の方向から
上記単色化されたＸ線ビームを上記標準結晶及び試料結
晶に照射し、その時の標準結晶及び試料結晶の回折ビー
ムの第２の角度差を計測し、上記第１及び第２の角度差
をもちいて試料結晶の格子定数の変化を測定することを
特徴とする格子定数の測定方法。[Claims] 1. A monochromator that monochromates an X-ray beam generated from an X-ray source and a rotating sample stage, and the X-ray beam monochromated by the monochromator is fixed to the rotating sample stage. A lattice constant measuring device having a means for measuring a diffracted beam when irradiating a plurality of single crystals,
A lattice constant measuring device characterized in that the monochromator is constructed by arranging a plurality of crystals so that their reflective crystal planes are parallel. 2. A method for measuring a change in the lattice constant of a sample crystal using the lattice constant measuring device according to claim 1, wherein at least one of the plurality of single crystals fixed to the rotating sample stage is a standard crystal. is placed near the sample crystal, and the monochromated X-ray beam is irradiated to the standard crystal and sample crystal from a first direction, and the first angle of the diffracted beams of the standard crystal and sample crystal at that time is difference, and the first
The standard crystal and the sample crystal are irradiated with the monochromatic X-ray beam from a second direction such that the diffracted beam is generated in the direction of the second angular difference between the diffracted beams of the standard crystal and the sample crystal. A method for measuring a lattice constant, characterized in that the change in the lattice constant of a sample crystal is measured using the first and second angular differences.