JP3889851B2

JP3889851B2 - Film thickness measurement method

Info

Publication number: JP3889851B2
Application number: JP12594797A
Authority: JP
Inventors: 慎一寺田
Original assignee: 日本政策投資銀行; 株式会社みなと銀行
Priority date: 1997-05-15
Filing date: 1997-05-15
Publication date: 2007-03-07
Anticipated expiration: 2017-05-15
Also published as: JPH10318737A

Description

【０００１】
【発明の属する技術分野】
本発明は、半導体ウエハ等の基板上に薄膜を形成した試料について、Ｘ線を用いて薄膜の膜厚を測定する膜厚測定方法に関する。
【０００２】
【従来の技術】
従来から知られている膜厚測定の手法として、１）薄膜に電極プローブを接触させてシート抵抗を計測し、膜厚に換算するシート抵抗計、２）基板と薄膜にマイクロメータ等のプローブを機械的に接触させて、段差を直接計測する段差計、３）薄膜での光干渉の様子を計測して、干渉条件から膜厚を算出するエリプソメータ、４）試料を極薄に加工して、断面の様子を観察する透過電子顕微鏡（ＴＥＭ）、５）試料にＸ線を照射して、蛍光Ｘ線の強度から膜厚と密度の積を計測する蛍光Ｘ線法、６）試料にＸ線を低角度で入射して、薄膜でのＸ線干渉の様子を計測するＸ線反射率法、などがある。
【０００３】
このうち１）シート抵抗計や２）段差計は接触測定であって、種々の要因による誤差が大きい。４）は透過電子顕微鏡は、試料加工が必要で破壊検査となる。
【０００４】
その他は非破壊検査であるが、３）エリプソメータは測定光に対して透明な材料に限定される。
【０００５】
【発明が解決しようとする課題】
上記５）の蛍光Ｘ線法は、膜を構成する元素の単位面積当たりの付着量に依存した蛍光Ｘ線の強度を計測するもので、長所として、ａ）測定範囲が１ｎｍ〜２０μｍ程度と広いこと、ｂ）表面や界面の粗さに対して大きな影響を受けないこと等が挙げられ、短所として、ｃ）標準試料を用いた相対測定であること、ｄ）膜厚と密度の積である付着量として測定され、密度の変化に対して大きな影響を受ける等が挙げられる。
【０００６】
上記６）のＸ線反射率法は、膜の表面反射と界面反射との干渉を利用して、Ｘ線の入射角度または波長を徐々に変化させて生ずる反射率曲線の振動構造から膜厚を算出するもので、長所として、ａ）標準試料無しの絶対測定であること、ｂ）密度が測定可能であること等が挙げられ、短所として、ｃ）測定範囲が１０ｎｍ〜３００ｎｍ程度と比較的狭いこと、ｄ）表面や界面が粗いと干渉が得られないこと等が挙げられる。
【０００７】
図４は、Ｘ線反射率法を用いて得られるＸ線反射率曲線の一例を示すグラフである。横軸は試料表面に対するＸ線入射角度で、縦軸はＸ線反射率（対数表示）である。試料はシリコンウエハ上に膜厚１００ｎｍのＷＳｉ（タングステンシリサイド）膜を形成したものである。
【０００８】
グラフを見ると、薄膜でのＸ線干渉によって振動構造が現われており、干渉条件を示す下記式（４）を用いて振動周期から膜厚ｔを測定することができる（ｔは膜厚、θは入射角度、θｒは全反射臨界角、ｎは整数、λは波長）。
【０００９】
２ｔ・ｓｉｎ（θ²−θｒ²）^1/2 ＝ｎ・λ …（４）
こうしたＸ線反射率法による膜厚測定は種々の分野で適用可能である。特に半導体製造分野では、ウエハ上の配線材料としてＡｌ膜、Ｔｉ膜、Ｃｏ膜等が使用され、集積度の高密度化によって配線パターンの形状を厳しく管理する必要性がある。
【００１０】
配線パターンの膜厚は場所に応じて種々に変化し、膜厚が１０ｎｍ〜３００ｎｍの範囲であれば上記のＸ線反射率法を用いて測定が可能である。しかし、電流が多く流れる配線パターンでは、膜厚１．５μｍのＡｌ膜といった厚い配線が使用されている。この厚さ程度になると、たとえばＣｕ陽極のＸ線管を使用したＸ線反射率法では、干渉の周期が極端に短くなり過ぎて測定不能となる。逆に、昨今では高密度配線として膜厚５ｎｍのＣｏ膜が検討されており、この膜厚では干渉の周期が極端に長くなって、振動構造が現われず、測定不能となる。
【００１１】
また、この程度まで薄くなると、薄膜の製造方法によっては、膜厚が面内で不均一になったり、表面や界面での粗さが大きくなって、振動構造がノイズに埋もれて不鮮明になる可能性がある。
【００１２】
本発明の目的は、Ｘ線反射率法と蛍光Ｘ線法との組合せによって、測定精度を維持しつつ、膜厚の測定範囲を大幅に拡大できる膜厚測定方法を提供することである。
【００１３】
【課題を解決するための手段】
本発明は、基板上に薄膜が形成され、薄膜の膜厚および密度が未知で、基板および薄膜の構成物質が既知である未知試料ｕの膜厚測定方法であって、
未知試料ｕと同種の物質で構成され、Ｘ線反射率法によって膜厚測定可能な標準試料ｃを用意する工程と、
Ｘ線反射率法を用いて、Ｘ線入射角度の変化に対する標準試料ｃのＸ線反射率曲線を計測し、該曲線の干渉周期から膜厚Ｔｃを、該曲線の全反射臨界角度から薄膜の密度ρｃをそれぞれ測定する工程と、
蛍光Ｘ線法を用いて、標準試料ｃの蛍光Ｘ線強度Ｆｃを測定する工程と、
標準試料ｃの感度係数αを次式（１）から算出する工程と、
α ＝Ｆｃ／（ρｃ・Ｔｃ） …（１）
Ｘ線反射率法を用いて、Ｘ線入射角度の変化に対する未知試料ｕのＸ線反射率曲線を計測し、該曲線の全反射臨界角度から薄膜の密度ρｕを測定する工程と、
蛍光Ｘ線法を用いて、未知試料ｕの蛍光Ｘ線強度Ｆｕを測定する工程と、
未知試料ｕの膜厚Ｔｕを次式（２）から算出する工程と、
Ｔｕ＝Ｆｕ／（α・ρｕ） …（２）
を含むことを特徴とする膜厚測定方法である。
【００１４】
本発明に従えば、未知試料ｕと同種の物質で構成され、Ｘ線反射率法によって膜厚測定可能な標準試料ｃを予め用意しておいて、この標準試料ｃに関してＸ線反射率法および蛍光Ｘ線法を適用して、膜厚Ｔｃ、密度ρｃおよび蛍光Ｘ線強度Ｆｃの各数値をそれぞれ測定する。蛍光Ｘ線法は、蛍光Ｘ線強度Ｆが、次式（３）のように、密度ρと膜厚Ｔの積に比例することを利用するものである。
【００１５】
Ｆ＝ α・ρ・Ｔ …（３）
比例係数である感度係数αは、上記の数値Ｔｃ、ρｃ、Ｆｃを式（３）に代入することによって決定できる。
【００１６】
次に、未知試料ｕに関してＸ線反射率法および蛍光Ｘ線法を適用して、密度ρｕおよび蛍光Ｘ線強度Ｆｕの各数値をそれぞれ測定する。感度係数αは同種の物質であれば一致するため、数値Ｆｕ、α、ρｕを式（３）に代入することによって、膜厚Ｔｕを決定できる。
【００１７】
このようにＸ線反射率法の測定範囲外にある膜厚を持つ試料に関しても、蛍光Ｘ線法との組合せによって高精度の膜厚測定が可能になる。
【００１８】
また本発明は、基板上に薄膜が形成され、薄膜の膜厚および密度が未知で、基板および薄膜の構成物質が既知である未知試料ｕの膜厚測定方法であって、
密度ρおよび膜厚Ｔの積（ρＴ）を変数とする理論Ｘ線強度Ｘ（ρＴ）を予め決定しておく工程と、
未知試料ｕと同種の物質で構成され、Ｘ線反射率法によって膜厚測定可能な標準試料ｃを用意する工程と、
Ｘ線反射率法を用いて、Ｘ線入射角度の変化に対する標準試料ｃのＸ線反射率曲線を計測し、該曲線の干渉周期から膜厚Ｔｃを、該曲線の全反射臨界角度から薄膜の密度ρｃをそれぞれ測定する工程と、
蛍光Ｘ線法を用いて、標準試料ｃの蛍光Ｘ線強度Ｆｃを測定する工程と、
該蛍光Ｘ線強度Ｆｃと、密度ρｃおよび膜厚Ｔｃの積（ρＴ）ｃを代入した理論Ｘ線強度Ｘ（ρＴ）ｃとの比である感度係数βを次式（１Ａ）から算出する工程と、
β ＝Ｆｃ／Ｘ（（ρＴ）ｃ） …（１Ａ）
Ｘ線反射率法を用いて、Ｘ線入射角度の変化に対する未知試料ｕのＸ線反射率曲線を計測し、該曲線の全反射臨界角度から薄膜の密度ρｕを測定する工程と、
蛍光Ｘ線法を用いて、未知試料ｕの蛍光Ｘ線強度Ｆｕを測定する工程と、
得られた蛍光Ｘ線強度Ｆｕが次式（２Ａ）を満足するように、逐次近似法を用いて未知試料ｕに関する密度ρｕおよび膜厚Ｔｕの積（ρＴ）ｕを求める工程と、
Ｆｕ＝ β・Ｘ（（ρＴ）ｕ） …（２Ａ）
得られた積（ρＴ）ｕを密度ρｕで除算して、膜厚Ｔｕを算出する工程とを含むことを特徴とする膜厚測定方法である。
【００１９】
本発明に従えば、密度ρおよび膜厚Ｔの積（ρＴ）を変数とする理論Ｘ線強度Ｘ（ρＴ）を予め決定している。前述した方法では、蛍光Ｘ線法における蛍光Ｘ線強度Ｆが密度ρと膜厚Ｔの積に比例することを前提した１次近似を用いた方法であるが、ここでは薄膜の自己吸収が無視できない比較的厚い膜に適用する場合や、膜を構成する元素の蛍光Ｘ線が検出困難な場合に、膜でのＸ線吸収等を考慮した理論Ｘ線強度法（ＦＰ法）を応用している（参考文献：“Handbook of
X-ray Spectrometry",MARCEL DEKKER,INC,1993等）。理論Ｘ線強度Ｘ（ρＴ）は、密度ρおよび膜厚Ｔの積（ρＴ）を変数とする関数であり、高次の近似式で表現可能である。
【００２０】
次に未知試料ｕと同種の物質で構成され、Ｘ線反射率法によって膜厚測定可能な標準試料ｃを予め用意しておいて、この標準試料ｃに関してＸ線反射率法および蛍光Ｘ線法を適用して、膜厚Ｔｃ、密度ρｃおよび蛍光Ｘ線強度Ｆｃの各数値をそれぞれ測定する。
【００２１】
そして、該蛍光Ｘ線強度Ｆｃと、密度ρｃおよび膜厚Ｔｃの積（ρＴ）ｃを代入した理論Ｘ線強度Ｘ（ρＴ）ｃとの比である感度係数βを式（１Ａ）によって算出し、実際の測定条件における蛍光Ｘ線強度Ｆと理論Ｘ線強度Ｘとの換算比率を求めておく。
【００２２】
次に、未知試料ｕに関してＸ線反射率法および蛍光Ｘ線法を適用して、密度ρｕおよび蛍光Ｘ線強度Ｆｕの各数値をそれぞれ測定する。このとき、未知試料ｕに関する積（ρＴ）ｕも理論Ｘ線強度Ｘに従う。
【００２３】
理論Ｘ線強度Ｘの逆関数が解析的に求めることが可能である場合は、蛍光Ｘ線強度Ｆｕを逆関数に代入すれば、直ちに積（ρＴ）ｕを算出でき、さらに積（ρＴ）ｕを密度ρｕで除算すれば簡単に膜厚Ｔｕを決定できる。
【００２４】
一方、理論Ｘ線強度Ｘの逆関数が解析的に求められない場合は、蛍光Ｘ線強度Ｆｕが式（２Ａ）を満足するように、逐次近似法を用いて未知試料ｕに関する密度ρｕおよび膜厚Ｔｕの積（ρＴ）ｕを求めることが可能である。そして、得られた積（ρＴ）ｕを密度ρｕで除算して、膜厚Ｔｕを決定できる。
【００２５】
なお、以上の説明では膜が単元素で構成される場合や膜の組成に変化がない場合を前提としているが、膜が複数元素で構成される場合には複数元素から発生する蛍光Ｘ線を検出することによって、同様な手順で膜厚を決定できる。
【００２６】
さらに、蛍光Ｘ線の代わりに入射Ｘ線の散乱を検出して、理論Ｘ線強度法（ＦＰ法）を用いて理論的に計算される散乱Ｘ線強度との換算比率を考慮する方法でも同様な手法で膜厚を決定できる。
【００２７】
このようにＸ線反射率法の測定範囲外にある膜厚を持つ試料に関しても、蛍光Ｘ線法との組合せによって高精度の膜厚測定が可能になる。
【００２８】
また本発明は、Ｘ線反射率法および蛍光Ｘ線法を同一のＸ線分析装置で行うことを特徴とする。
【００２９】
本発明に従えば、Ｘ線管、スリット、試料台などのＸ線光学系を共通に構成した同一のＸ線分析装置でＸ線反射率法および蛍光Ｘ線法を行うことによって、入射角度や波長、試料の配置などのＸ線照射条件を安定に維持できるため、測定誤差を低減化でき、しかも測定時間の短縮化に資する。
【００３０】
【発明の実施の形態】
図１は、本発明に係る膜厚測定方法が適用可能なＸ線分析装置の一例を示す構成図である。Ｘ線分析装置は、Ｘ線ビームＢ１を発生するためのＸ線管１と、Ｘ線ビームＢ１の中から単一の特性Ｘ線から成るＸ線ビームＢ２を分離するための分光結晶２と、他の特性Ｘ線を遮るためのスリット３ａと、半導体ウエハなどの被検物２０を支持するための試料テーブル４と、Ｘ線ビームＢ２のＸ線強度を検出する検出器１１と、試料テーブル４の３次元位置およびＸ線ビームＢ２に対する角度を設定するためのテーブル制御部５と、被検物２０から発生する蛍光Ｘ線Ｂ３を検出する検出器６などで構成される。検出器６は半導体検出器などで構成され、検出面側に受光角度を規定する絞り３ｃが配置される。
【００３１】
さらに、スリット３ｂが被検物２０と検出器１１との間に設けられ、検出器１１に入射するＸ線ビームＢ２の通過位置を規定する。このスリット３ｂは上下移動可能であり、データ処理部１０からの指令によってスリット制御部１２がスリット３ｂの位置を調整する。また、スリット３ｂは、検査点を中心とした円弧上を円運動するように移動しても構わない。
【００３２】
次に信号処理系に関して、検出器６からの信号を増幅する前置増幅器７と、前置増幅器７から出力される電荷パルスの立上がり幅に比例した波高を有するパルスに波形整形するための比例増幅器８と、比例増幅器８から出力される各波高値の計数率を測定する波高分析器９と、波高分析器９や検出器１１で測定されたデータを処理したり、テーブル制御部５へ指令を出すためのデータ処理器１０などが設けられる。
【００３３】
検出器１１は、１次Ｘ線と反射Ｘ線の強度を測定するもので、シンチレーションカウンタ、プロポーショナルカウンタ、イオンチェンバ、ＧＭカウンタ、半導体検出器などが使用できる。また、スリット３ｂは検出器１１に予め内蔵されているコリメータで代用することも可能であり、この場合はスリット制御部１２によって検出器１１全体の位置が制御される。
【００３４】
Ｘ線管１は固定陽極型や回転陽極型のものが使用できる。分光結晶２は、単一の結晶であっても、２つ以上の結晶の組合せでもよい。
【００３５】
また、検出器１１からの強度信号から被検物２０のＸ線反射率を測定することによって、被検物２０の表面粗さ、膜厚、密度等を検定できる。すなわち、試料テーブル４の傾斜角度を水平から徐々に増加させることによって、図４のようなＸ線反射率曲線が得られる。この曲線に現われる振動構造の周期を計測することによって膜厚の絶対測定が可能となる。
【００３６】
さらに、薄膜の密度については、全反射臨界角度が物質の密度に依存して変化することを利用する。すなわち、試料テーブル４の傾斜角度を水平から徐々に増加させると、全反射臨界角度でＸ線反射率が急激に小さくなるため、この全反射臨界角度の位置を計測することによって、薄膜の密度を算出できる。
【００３７】
次に膜厚測定方法について説明する。
【００３８】
まず被検物２０として、シリコンウエハ等の基板上に配線材料等の薄膜が形成された未知試料ｕおよび標準試料ｃを用意する。未知試料ｕは、薄膜の膜厚および密度が未知で、基板および薄膜の構成物質が既知であり、薄膜の膜厚がＸ線反射率法によって膜厚測定困難な範囲、たとえば１０ｎｍ〜３００ｎｍの範囲外のものである。標準試料ｃは、未知試料ｕと同種の物質で構成され、薄膜の膜厚がＸ線反射率法によって膜厚測定可能な範囲、たとえば１０ｎｍ〜３００ｎｍの範囲内のものである。
【００３９】
次にＸ線反射率法を用いて、標準試料ｃの膜厚Ｔｃ、薄膜の密度ρｃをそれぞれ測定する。その手順として、標準試料ｃを試料テーブル４にセットした後、単色のＸ線ビームＢ２を標準試料ｃに入射しながら、試料テーブル４を水平位置から徐々に傾斜させて、検出器１１の出力からＸ線入射角度の変化に対する標準試料ｃのＸ線反射率曲線を計測する。得られたＸ線反射率曲線の干渉周期から膜厚Ｔｃを、該曲線の全反射臨界角度から薄膜の密度ρｃをそれぞれ測定する。
【００４０】
次に蛍光Ｘ線法を用いて、標準試料ｃの蛍光Ｘ線強度Ｆｃを測定する。その手順として、単色のＸ線ビームＢ２を試料テーブル４にセットされた標準試料ｃに所定の入射角度、たとえば全反射角度で入射して、標準試料ｃから発生する蛍光Ｘ線の強度Ｆｃを検出器６で測定する。なお、Ｘ線入射角度は全反射角度より大きな角度を選び、試料間で測定条件の統一を図る。
【００４１】
図２は、蛍光Ｘ線法の測定原理の一例を示すグラフである。蛍光Ｘ線法は、蛍光Ｘ線強度Ｆが、次式（３）のように、密度ρと膜厚Ｔの積に比例することを利用するものである。
【００４２】
Ｆ＝ α・ρ・Ｔ …（３）
比例係数である感度係数αは同種の物質であれば一致し、上記の数値Ｔｃ、ρｃ、Ｆｃを式（３）に代入することによって決定でき、算出式は次式（１）となる。
【００４３】
α ＝Ｆｃ／（ρｃ・Ｔｃ） …（１）
次にＸ線反射率法を用いて、未知試料ｕの薄膜の密度ρｕを測定する。その手順として、未知試料ｕを試料テーブル４にセットした後、単色のＸ線ビームＢ２を未知試料ｕに入射しながら、試料テーブル４を水平位置から徐々に傾斜させて、検出器１１の出力からＸ線入射角度の変化に対する未知試料ｕのＸ線反射率曲線を計測する。得られたＸ線反射率曲線のうち急峻に変化する位置を全反射臨界角度θｒとして特定し、下記式（５）を用いて全反射臨界角度θｒから薄膜の密度ρｕを測定する。ここで、密度ρの単位はｋｇ／ｍ³ 、全反射臨界角度θｒはミリラジアン(mrad)、波長λはｎｍである。
【００４４】
ρ ＝３．８×（θｒ／λ）² …（５）
次に蛍光Ｘ線法を用いて、未知試料ｕの蛍光Ｘ線強度Ｆｕを測定する。その手順として、標準試料ｃの測定条件と一致するように、Ｘ線ビームＢ２の入射角度や波長などを調整した後、未知試料ｕから発生する蛍光Ｘ線の強度Ｆｕを検出器６で測定する。
【００４５】
次に上記測定によって得られた感度係数α、薄膜の密度ρｕおよび蛍光Ｘ線強度Ｆｕを次式（２）に代入して、未知試料ｕの膜厚Ｔｕを算出する。
【００４６】
Ｔｕ＝Ｆｕ／（α・ρｕ） …（２）
このようにＸ線反射率法の測定範囲外にある膜厚を持つ試料に関しても、蛍光Ｘ線法との組合せによって高精度の膜厚測定が可能になる。
【００４７】
また、上記のＸ線反射率法および蛍光Ｘ線法を行う際に、図１に示すように、Ｘ線管１、スリット３ａ〜３ｃ、試料テーブル４などのＸ線光学系を共通に構成した同一のＸ線分析装置を使用することによって、入射角度や波長、試料の配置などのＸ線照射条件を安定に維持できるため、測定誤差を低減化でき、しかも全体の測定時間を短縮できる。
【００４８】
図３は、蛍光Ｘ線法の測定原理の他の例を示すグラフである。図２では１次近似の手法を説明したが、ここでは非線形の場合も適用可能な理論Ｘ線強度法（ＦＰ法）を使用する例を説明する。
【００４９】
理論Ｘ線強度Ｘは、密度ρおよび膜厚Ｔの積（ρＴ）を変数とする関数として表現でき、図３中の一点鎖線で示すように、一般に積（ρＴ）の変化に対して曲線を示し、解析的には種々の近似式で表現可能である。
【００５０】
理論Ｘ線強度Ｘの一例として、Ｓｉ基板の上にアルミニウム薄膜が存在する例において、１）入射Ｘ線はＣｕ−Ｋα特性Ｘ線で単色化されていること、２）アルミニウム薄膜でのＸ線の吸収を考慮する、３）基板や薄膜内で発生した蛍光Ｘ線や散乱されたＸ線による二次的な蛍光Ｘ線励起は考慮しない、４）装置の機械的配置、検出器の感度設定、Ｘ線源のＸ線放射率等から計算される一次Ｘ線の強度に関連する比例項は感度係数βにて代表することが可能であるので省略する、という条件の下で、Ａｌ−Ｋα特性Ｘ線強度の近似式は次の式（６）で表すことができる。
【００５１】
【数１】

【００５２】
ここで、μａはアルミニウムにおけるＣｕ−Ｋα線の質量吸収係数、μｂはアルミニウムにおけるＡｌ−Ｋα線の質量吸収係数、Ψａは一次Ｘ線の入射角度、Ψｂは蛍光Ｘ線の取出し角度である。
【００５３】
図３中の実線は現実の測定条件下での蛍光Ｘ線強度Ｆであり、近似の精度が高い場合、理論Ｘ線強度Ｘのカーブと蛍光Ｘ線強度Ｆのカーブとは一定の比率βで相互に換算可能な相似形となり、両者の関係は予め決定しておく
。
【００５４】
次に上述と同様に、被検物２０として、未知試料ｕおよび標準試料ｃを用意する。未知試料ｕは、薄膜の膜厚および密度が未知で、基板および薄膜の構成物質が既知であり、薄膜の膜厚がＸ線反射率法によって膜厚測定困難な範囲、たとえば１０ｎｍ〜３００ｎｍの範囲外のものである。標準試料ｃは、未知試料ｕと同種の物質で構成され、薄膜の膜厚がＸ線反射率法によって膜厚測定可能な範囲、たとえば１０ｎｍ〜３００ｎｍの範囲内のものである。
【００５５】
次に上述と同様に、Ｘ線反射率法を用いて、標準試料ｃの膜厚Ｔｃ、薄膜の密度ρｃをそれぞれ測定する。次に蛍光Ｘ線法を用いて、標準試料ｃの蛍光Ｘ線強度Ｆｃを測定する。
【００５６】
次に密度ρｃおよび膜厚Ｔｃの積（ρＴ）ｃを理論Ｘ線強度Ｘの近似式に代入して、標準試料ｃの理論Ｘ線（ρＴ）ｃを算出し、蛍光Ｘ線強度Ｆｃと理論Ｘ線（ρＴ）ｃとの比、すなわち感度係数βを式（１Ａ）によって算出する。こうして実際の測定条件における蛍光Ｘ線強度Ｆと理論Ｘ線強度Ｘとの換算比率を求めておく。
【００５７】
次に上述と同様に、未知試料ｕに関してＸ線反射率法および蛍光Ｘ線法を適用して、密度ρｕおよび蛍光Ｘ線強度Ｆｕの各数値をそれぞれ測定する。
【００５８】
ここで理論Ｘ線強度Ｘの逆関数が解析的に求めることが可能である場合は、蛍光Ｘ線強度Ｆｕを逆関数に代入すれば、直ちに積（ρＴ）ｕを算出でき、さらに積（ρＴ）ｕを密度ρｕで除算すれば簡単に膜厚Ｔｕを決定できる。
【００５９】
一方、理論Ｘ線強度Ｘの逆関数が解析的に求められない場合は逐次近似法を用いる。具体的な手法として、理論Ｘ線強度Ｘのカーブにおいて、密度ρｕ、感度係数βの各変数を固定して膜厚Ｔを変化させ、蛍光Ｘ線強度Ｆが蛍光Ｘ線強度Ｆｕと一致するときの積（ρＴ）ｕを探索することになる。
【００６０】
こうして得られた積（ρＴ）ｕを密度ρｕで除算することによって、未知試料ｕの膜厚Ｔｕを決定できる。
【００６１】
このようにＸ線反射率法の測定範囲外にある膜厚を持つ試料に関しても、蛍光Ｘ線法との組合せによって高精度の膜厚測定が可能になる。
【００６２】
【発明の効果】
以上詳説したように本発明によれば、未知試料ｕと同種の物質から成る標準試料ｃを用意し、標準試料ｃに関してＸ線反射率法および蛍光Ｘ線法を適用して、膜厚Ｔｃ、密度ρｃおよび蛍光Ｘ線強度Ｆｃをそれぞれ測定して、感度係数αを求めた後、次に未知試料ｕに関してＸ線反射率法および蛍光Ｘ線法を適用して、密度ρｕおよび蛍光Ｘ線強度Ｆｕをそれぞれ測定することによって、未知試料ｕの薄膜の膜厚Ｔｕを決定できる。こうしてＸ線反射率法の測定範囲外にある膜厚を持つ試料に関しても、蛍光Ｘ線法との組合せによって高精度の膜厚測定が可能になる。
【００６３】
また、蛍光Ｘ線法において高次近似による理論Ｘ線強度法を適用することによって、より高精度の膜厚測定が可能になる。
【００６４】
また、Ｘ線反射率法および蛍光Ｘ線法を同一のＸ線分析装置で行うことによって、Ｘ線照射条件を安定に維持できるため、測定誤差を低減化でき、しかも測定時間の短縮化に資する。
【図面の簡単な説明】
【図１】本発明に係る膜厚測定方法が適用可能なＸ線分析装置の一例を示す構成図である。
【図２】蛍光Ｘ線法の測定原理の一例を示すグラフである。
【図３】蛍光Ｘ線法の測定原理の他の例を示すグラフである。
【図４】Ｘ線反射率法を用いて得られるＸ線反射率曲線の一例を示すグラフである。
【符号の説明】
１Ｘ線管
２分光結晶
３ａ，３ｂ，３ｃスリット
４試料テーブル
５テーブル制御部
６，１１検出器
７前置増幅器
８比例増幅器
９波高分析器
１０データ処理器
２０被検物[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a film thickness measuring method for measuring a film thickness of a thin film using X-rays on a sample in which a thin film is formed on a substrate such as a semiconductor wafer.
[0002]
[Prior art]
Conventionally known methods for measuring film thickness are as follows: 1) A sheet resistance meter that measures the sheet resistance by bringing an electrode probe into contact with the thin film, and 2) a probe such as a micrometer on the substrate and the thin film. Step meter that directly measures the step by mechanical contact, 3) Measures the state of optical interference in the thin film, calculates the film thickness from the interference condition, 4) Processes the sample extremely thinly, Transmission electron microscope (TEM) for observing the state of the cross section, 5) X-ray fluorescence method of irradiating the sample with X-rays and measuring the product of film thickness and density from the intensity of the fluorescent X-rays, 6) X-rays on the sample Are incident at a low angle, and there is an X-ray reflectivity method for measuring the state of X-ray interference in a thin film.
[0003]
Of these, 1) sheet resistance meter and 2) level difference meter are contact measurements, and errors due to various factors are large. 4) The transmission electron microscope requires sample processing and is a destructive inspection.
[0004]
Others are non-destructive inspections. 3) Ellipsometers are limited to materials that are transparent to measurement light.
[0005]
[Problems to be solved by the invention]
The fluorescent X-ray method of 5) measures the intensity of fluorescent X-rays depending on the amount of the elements constituting the film depending on the amount of adhesion per unit area. As an advantage, a) the measurement range is as wide as about 1 nm to 20 μm. B) not being greatly affected by the roughness of the surface or interface, and the disadvantages are c) relative measurement using a standard sample, d) product of film thickness and density. It is measured as the amount of adhesion, and is greatly affected by changes in density.
[0006]
The above 6) X-ray reflectivity method uses the interference between the surface reflection and the interface reflection of the film to change the film thickness from the vibration structure of the reflectivity curve generated by gradually changing the incident angle or wavelength of the X-ray. The advantages include a) absolute measurement without a standard sample, b) the density is measurable, and the disadvantage is c) the measurement range is relatively narrow, about 10 nm to 300 nm. D) If the surface or interface is rough, interference cannot be obtained.
[0007]
FIG. 4 is a graph showing an example of an X-ray reflectivity curve obtained using the X-ray reflectivity method. The horizontal axis represents the X-ray incident angle with respect to the sample surface, and the vertical axis represents the X-ray reflectivity (logarithmic display). The sample is obtained by forming a WSi (tungsten silicide) film having a thickness of 100 nm on a silicon wafer.
[0008]
From the graph, the vibration structure appears due to the X-ray interference in the thin film, and the film thickness t can be measured from the vibration period using the following equation (4) indicating the interference condition (t is the film thickness, θ Is the incident angle, θr is the total reflection critical angle, n is an integer, and λ is the wavelength).
[0009]
2t · sin (θ ² −θr ² ) ^1/2 = n · λ (4)
Such film thickness measurement by the X-ray reflectivity method can be applied in various fields. In particular, in the semiconductor manufacturing field, Al films, Ti films, Co films, and the like are used as wiring materials on wafers, and it is necessary to strictly manage the shape of wiring patterns by increasing the density of integration.
[0010]
The thickness of the wiring pattern varies depending on the location, and can be measured using the X-ray reflectivity method as long as the thickness is in the range of 10 nm to 300 nm. However, in a wiring pattern in which a large amount of current flows, a thick wiring such as an Al film with a thickness of 1.5 μm is used. At this thickness, for example, in the X-ray reflectivity method using an X-ray tube with a Cu anode, the period of interference becomes extremely short and measurement becomes impossible. Conversely, a Co film having a film thickness of 5 nm has been studied recently as a high-density wiring, and at this film thickness, the period of interference becomes extremely long, the vibration structure does not appear, and measurement is impossible.
[0011]
Also, if the thickness is reduced to this level, the film thickness may become uneven in the surface, or the roughness at the surface or interface may become large depending on the thin film manufacturing method, and the vibration structure may be buried in noise and become unclear. There is sex.
[0012]
An object of the present invention is to provide a film thickness measuring method capable of greatly expanding a film thickness measurement range while maintaining measurement accuracy by a combination of an X-ray reflectance method and a fluorescent X-ray method.
[0013]
[Means for Solving the Problems]
The present invention is a method for measuring the thickness of an unknown sample u in which a thin film is formed on a substrate, the thickness and density of the thin film are unknown, and the constituent materials of the substrate and the thin film are known,
Preparing a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectivity method;
Using the X-ray reflectivity method, the X-ray reflectivity curve of the standard sample c with respect to the change in the X-ray incident angle is measured, and the film thickness Tc is determined from the interference period of the curve, and the total reflection critical angle of the curve is used. Measuring each density ρc;
Measuring the fluorescent X-ray intensity Fc of the standard sample c using a fluorescent X-ray method;
Calculating the sensitivity coefficient α of the standard sample c from the following equation (1);
α = Fc / (ρc · Tc) (1)
Measuring an X-ray reflectivity curve of an unknown sample u with respect to a change in an X-ray incident angle using an X-ray reflectivity method, and measuring a density ρu of the thin film from a total reflection critical angle of the curve;
Measuring the fluorescent X-ray intensity Fu of the unknown sample u using the fluorescent X-ray method;
Calculating the film thickness Tu of the unknown sample u from the following equation (2);
Tu = Fu / (α · ρu) (2)
It is the film thickness measuring method characterized by including.
[0014]
According to the present invention, a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectance method is prepared in advance, and the X-ray reflectance method and the standard sample c are prepared. Each value of the film thickness Tc, the density ρc, and the fluorescent X-ray intensity Fc is measured by applying the fluorescent X-ray method. The fluorescent X-ray method utilizes the fact that the fluorescent X-ray intensity F is proportional to the product of the density ρ and the film thickness T as shown in the following equation (3).
[0015]
F = α · ρ · T (3)
The sensitivity coefficient α, which is a proportional coefficient, can be determined by substituting the above numerical values Tc, ρc, and Fc into Equation (3).
[0016]
Next, the X-ray reflectivity method and the fluorescent X-ray method are applied to the unknown sample u, and the numerical values of the density ρu and the fluorescent X-ray intensity Fu are measured. Since the sensitivity coefficient α is the same for the same kind of substances, the film thickness Tu can be determined by substituting the numerical values Fu, α, and ρu into the equation (3).
[0017]
As described above, even for a sample having a film thickness outside the measurement range of the X-ray reflectivity method, the film thickness can be measured with high accuracy by combination with the fluorescent X-ray method.
[0018]
Further, the present invention is a method for measuring the thickness of an unknown sample u in which a thin film is formed on a substrate, the thickness and density of the thin film are unknown, and the constituent materials of the substrate and the thin film are known,
A step of preliminarily determining a theoretical X-ray intensity X (ρT) having a product of density ρ and film thickness T (ρT) as variables;
Preparing a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectivity method;
Using the X-ray reflectivity method, the X-ray reflectivity curve of the standard sample c with respect to the change in the X-ray incident angle is measured, and the film thickness Tc is determined from the interference period of the curve, and the total reflection critical angle of the curve is used. Measuring each density ρc;
Measuring the fluorescent X-ray intensity Fc of the standard sample c using a fluorescent X-ray method;
A step of calculating a sensitivity coefficient β, which is a ratio between the fluorescent X-ray intensity Fc and the theoretical X-ray intensity X (ρT) c into which the product (ρT) c of density ρc and film thickness Tc is substituted, from the following equation (1A) When,
β = Fc / X ((ρT) c) (1A)
Measuring an X-ray reflectivity curve of an unknown sample u with respect to a change in an X-ray incident angle using an X-ray reflectivity method, and measuring a density ρu of the thin film from a total reflection critical angle of the curve;
Measuring the fluorescent X-ray intensity Fu of the unknown sample u using the fluorescent X-ray method;
Obtaining the product (ρT) u of the density ρu and the film thickness Tu for the unknown sample u using the successive approximation method so that the obtained fluorescent X-ray intensity Fu satisfies the following formula (2A):
Fu = β · X ((ρT) u) (2A)
And dividing the obtained product (ρT) u by the density ρu to calculate the film thickness Tu.
[0019]
According to the present invention, the theoretical X-ray intensity X (ρT) having the product of the density ρ and the film thickness T (ρT) as variables is determined in advance. In the above-described method, the first-order approximation is premised on the assumption that the fluorescent X-ray intensity F in the fluorescent X-ray method is proportional to the product of the density ρ and the film thickness T. Here, the self-absorption of the thin film is ignored. Applying the theoretical X-ray intensity method (FP method) considering X-ray absorption in the film when it is difficult to detect the fluorescent X-rays of the elements constituting the film when it is applied to a relatively thick film that cannot. (Reference: “Handbook of
X-ray Spectrometry ", MARCEL DEKKER, INC, 1993, etc.) The theoretical X-ray intensity X (ρT) is a function with the product of density ρ and film thickness T (ρT) as variables, and is a high-order approximation. It can be expressed.
[0020]
Next, a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectivity method is prepared in advance, and the X-ray reflectivity method and the fluorescent X-ray method are used for this standard sample c. Are applied to measure the numerical values of the film thickness Tc, the density ρc, and the fluorescent X-ray intensity Fc.
[0021]
Then, a sensitivity coefficient β, which is a ratio between the fluorescent X-ray intensity Fc and the theoretical X-ray intensity X (ρT) c obtained by substituting the product (ρT) c of the density ρc and the film thickness Tc, is calculated by the equation (1A). A conversion ratio between the fluorescent X-ray intensity F and the theoretical X-ray intensity X under actual measurement conditions is obtained.
[0022]
Next, the X-ray reflectivity method and the fluorescent X-ray method are applied to the unknown sample u, and the numerical values of the density ρu and the fluorescent X-ray intensity Fu are measured. At this time, the product (ρT) u related to the unknown sample u also follows the theoretical X-ray intensity X.
[0023]
If the inverse function of the theoretical X-ray intensity X can be obtained analytically, the product (ρT) u can be immediately calculated by substituting the fluorescent X-ray intensity Fu into the inverse function, and further the product (ρT) u. Is divided by the density ρu to easily determine the film thickness Tu.
[0024]
On the other hand, when the inverse function of the theoretical X-ray intensity X is not analytically determined, the density ρu and the film relating to the unknown sample u are determined using the successive approximation method so that the fluorescent X-ray intensity Fu satisfies the equation (2A). It is possible to determine the product (ρT) u of the thickness Tu. Then, the film thickness Tu can be determined by dividing the obtained product (ρT) u by the density ρu.
[0025]
In the above explanation, it is assumed that the film is composed of a single element or the composition of the film is not changed. However, when the film is composed of a plurality of elements, fluorescent X-rays generated from the plurality of elements are detected. By detecting, the film thickness can be determined in the same procedure.
[0026]
Further, the same applies to a method that detects scattering of incident X-rays instead of fluorescent X-rays and considers a conversion ratio with the scattered X-ray intensity theoretically calculated using the theoretical X-ray intensity method (FP method). The film thickness can be determined by various methods.
[0027]
As described above, even for a sample having a film thickness outside the measurement range of the X-ray reflectivity method, the film thickness can be measured with high accuracy by combination with the fluorescent X-ray method.
[0028]
Further, the present invention is characterized in that the X-ray reflectivity method and the fluorescent X-ray method are performed with the same X-ray analyzer.
[0029]
According to the present invention, by performing the X-ray reflectivity method and the fluorescent X-ray method with the same X-ray analyzer having a common X-ray optical system such as an X-ray tube, a slit, and a sample stage, Since X-ray irradiation conditions such as wavelength and sample arrangement can be stably maintained, measurement errors can be reduced and measurement time can be shortened.
[0030]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a configuration diagram showing an example of an X-ray analyzer to which the film thickness measuring method according to the present invention can be applied. The X-ray analyzer includes an X-ray tube 1 for generating an X-ray beam B1, a spectroscopic crystal 2 for separating an X-ray beam B2 comprising a single characteristic X-ray from the X-ray beam B1, A slit 3a for blocking other characteristic X-rays, a sample table 4 for supporting an object 20 such as a semiconductor wafer, a detector 11 for detecting the X-ray intensity of the X-ray beam B2, and a sample table 4 The table control unit 5 for setting the three-dimensional position and the angle with respect to the X-ray beam B2, the detector 6 for detecting the fluorescent X-ray B3 generated from the test object 20, and the like. The detector 6 is composed of a semiconductor detector or the like, and a diaphragm 3c that defines a light receiving angle is disposed on the detection surface side.
[0031]
Furthermore, the slit 3b is provided between the test object 20 and the detector 11, and defines the passage position of the X-ray beam B2 incident on the detector 11. The slit 3b can be moved up and down, and the slit controller 12 adjusts the position of the slit 3b in response to a command from the data processor 10. The slit 3b may move so as to make a circular motion on an arc centered on the inspection point.
[0032]
Next, with respect to the signal processing system, a preamplifier 7 for amplifying the signal from the detector 6 and a proportional amplifier for waveform shaping into a pulse having a wave height proportional to the rising width of the charge pulse output from the preamplifier 7. 8, a pulse height analyzer 9 that measures the count rate of each peak value output from the proportional amplifier 8, data measured by the peak height analyzer 9 and the detector 11, and a command to the table control unit 5 For example, a data processor 10 is provided.
[0033]
The detector 11 measures the intensity of the primary X-ray and the reflected X-ray, and a scintillation counter, a proportional counter, an ion chamber, a GM counter, a semiconductor detector, or the like can be used. The slit 3b can be replaced by a collimator built in the detector 11 in advance. In this case, the position of the entire detector 11 is controlled by the slit controller 12.
[0034]
The X-ray tube 1 can be a fixed anode type or a rotary anode type. The spectroscopic crystal 2 may be a single crystal or a combination of two or more crystals.
[0035]
Further, by measuring the X-ray reflectance of the test object 20 from the intensity signal from the detector 11, the surface roughness, film thickness, density, etc. of the test object 20 can be verified. That is, by gradually increasing the tilt angle of the sample table 4 from the horizontal, an X-ray reflectivity curve as shown in FIG. 4 is obtained. By measuring the period of the vibration structure appearing in this curve, the absolute measurement of the film thickness becomes possible.
[0036]
Further, as for the density of the thin film, it is used that the total reflection critical angle changes depending on the density of the material. That is, when the tilt angle of the sample table 4 is gradually increased from the horizontal, the X-ray reflectivity rapidly decreases at the total reflection critical angle. Therefore, by measuring the position of the total reflection critical angle, the density of the thin film can be reduced. It can be calculated.
[0037]
Next, the film thickness measuring method will be described.
[0038]
First, as the test object 20, an unknown sample u and a standard sample c in which a thin film such as a wiring material is formed on a substrate such as a silicon wafer are prepared. In the unknown sample u, the thickness and density of the thin film are unknown, the substrate and the constituent materials of the thin film are known, and the thickness of the thin film is difficult to measure by the X-ray reflectivity method, for example, the range of 10 nm to 300 nm. Is outside. The standard sample c is made of the same kind of material as the unknown sample u, and has a thin film thickness within a range in which the film thickness can be measured by the X-ray reflectivity method, for example, in the range of 10 nm to 300 nm.
[0039]
Next, the film thickness Tc of the standard sample c and the density ρc of the thin film are measured using the X-ray reflectivity method. As the procedure, after setting the standard sample c on the sample table 4, the sample table 4 is gradually inclined from the horizontal position while the monochromatic X-ray beam B2 is incident on the standard sample c, and the output of the detector 11 is used. The X-ray reflectivity curve of the standard sample c with respect to the change in the X-ray incident angle is measured. The film thickness Tc is measured from the interference period of the obtained X-ray reflectivity curve, and the density ρc of the thin film is measured from the total reflection critical angle of the curve.
[0040]
Next, the fluorescent X-ray intensity Fc of the standard sample c is measured using the fluorescent X-ray method. As the procedure, a monochromatic X-ray beam B2 is incident on a standard sample c set on the sample table 4 at a predetermined incident angle, for example, a total reflection angle, and the intensity Fc of fluorescent X-rays generated from the standard sample c is detected. Measure with instrument 6. The X-ray incident angle is selected to be larger than the total reflection angle, and the measurement conditions are unified among the samples.
[0041]
FIG. 2 is a graph showing an example of the measurement principle of the fluorescent X-ray method. The fluorescent X-ray method utilizes the fact that the fluorescent X-ray intensity F is proportional to the product of the density ρ and the film thickness T as shown in the following equation (3).
[0042]
F = α · ρ · T (3)
The sensitivity coefficient α, which is a proportional coefficient, is the same for the same type of substance, and can be determined by substituting the numerical values Tc, ρc, and Fc into the expression (3), and the calculation expression is the following expression (1).
[0043]
α = Fc / (ρc · Tc) (1)
Next, the density ρu of the thin film of the unknown sample u is measured using the X-ray reflectivity method. As the procedure, after setting the unknown sample u on the sample table 4, the sample table 4 is gradually inclined from the horizontal position while the monochromatic X-ray beam B2 is incident on the unknown sample u, and the output of the detector 11 is used. The X-ray reflectance curve of the unknown sample u with respect to the change in the X-ray incident angle is measured. The sharply changing position of the obtained X-ray reflectivity curve is specified as the total reflection critical angle θr, and the density ρu of the thin film is measured from the total reflection critical angle θr using the following formula (5). Here, the unit of density ρ is kg / m ³ , the total reflection critical angle θr is milliradians (mrad), and the wavelength λ is nm.
[0044]
ρ = 3.8 × (θr / λ) ² (5)
Next, the fluorescent X-ray intensity Fu of the unknown sample u is measured using the fluorescent X-ray method. As the procedure, after adjusting the incident angle and wavelength of the X-ray beam B2 so as to coincide with the measurement conditions of the standard sample c, the intensity Fu of fluorescent X-rays generated from the unknown sample u is measured by the detector 6. .
[0045]
Next, the film thickness Tu of the unknown sample u is calculated by substituting the sensitivity coefficient α, the thin film density ρu, and the fluorescent X-ray intensity Fu obtained by the above measurement into the following equation (2).
[0046]
Tu = Fu / (α · ρu) (2)
As described above, even for a sample having a film thickness outside the measurement range of the X-ray reflectivity method, the film thickness can be measured with high accuracy by combination with the fluorescent X-ray method.
[0047]
Further, when performing the X-ray reflectance method and the fluorescent X-ray method, the X-ray optical system such as the X-ray tube 1, the slits 3a to 3c, and the sample table 4 is configured in common as shown in FIG. By using the same X-ray analyzer, the X-ray irradiation conditions such as the incident angle, wavelength, and sample arrangement can be stably maintained, so that measurement errors can be reduced and overall measurement time can be shortened.
[0048]
FIG. 3 is a graph showing another example of the measurement principle of the fluorescent X-ray method. Although the first-order approximation method has been described with reference to FIG. 2, an example in which a theoretical X-ray intensity method (FP method) that can also be applied to a non-linear case will be described.
[0049]
The theoretical X-ray intensity X can be expressed as a function having the product of the density ρ and the film thickness T (ρT) as variables, and generally shows a curve with respect to the change of the product (ρT), as shown by a one-dot chain line in FIG. It can be expressed analytically by various approximate expressions.
[0050]
As an example of the theoretical X-ray intensity X, in an example in which an aluminum thin film is present on a Si substrate, 1) the incident X-ray is monochromatized with Cu-Kα characteristic X-ray, and 2) the X-ray in the aluminum thin film 3) Does not consider secondary fluorescent X-ray excitation by fluorescent X-rays or scattered X-rays generated in the substrate or thin film 4) Mechanical arrangement of the device, sensitivity setting of the detector Under the condition that the proportional term related to the intensity of the primary X-ray calculated from the X-ray emissivity of the X-ray source can be represented by the sensitivity coefficient β, it is omitted. An approximate expression of the characteristic X-ray intensity can be expressed by the following expression (6).
[0051]
[Expression 1]

[0052]
Here, μa is a mass absorption coefficient of Cu—Kα rays in aluminum, μb is a mass absorption coefficient of Al—Kα rays in aluminum, ψa is an incident angle of primary X-rays, and ψb is an extraction angle of fluorescent X-rays.
[0053]
The solid line in FIG. 3 is the fluorescent X-ray intensity F under actual measurement conditions. When the approximation accuracy is high, the curve of the theoretical X-ray intensity X and the curve of the fluorescent X-ray intensity F are at a constant ratio β. Similar shapes that can be converted to each other are obtained, and the relationship between the two is determined in advance.
[0054]
Next, an unknown sample u and a standard sample c are prepared as the test object 20 in the same manner as described above. In the unknown sample u, the thickness and density of the thin film are unknown, the substrate and the constituent materials of the thin film are known, and the thickness of the thin film is difficult to measure by the X-ray reflectivity method, for example, the range of 10 nm to 300 nm. Is outside. The standard sample c is made of the same kind of material as the unknown sample u, and has a thin film thickness within a range in which the film thickness can be measured by the X-ray reflectivity method, for example, in the range of 10 nm to 300 nm.
[0055]
Next, similarly to the above, the thickness Tc of the standard sample c and the density ρc of the thin film are measured using the X-ray reflectivity method. Next, the fluorescent X-ray intensity Fc of the standard sample c is measured using the fluorescent X-ray method.
[0056]
Next, the product (ρT) c of the density ρc and the film thickness Tc is substituted into the approximate expression of the theoretical X-ray intensity X to calculate the theoretical X-ray (ρT) c of the standard sample c, and the fluorescent X-ray intensity Fc and the theory The ratio to the X-ray (ρT) c, that is, the sensitivity coefficient β is calculated by the equation (1A). Thus, a conversion ratio between the fluorescent X-ray intensity F and the theoretical X-ray intensity X under actual measurement conditions is obtained.
[0057]
Next, similarly to the above, the X-ray reflectivity method and the fluorescent X-ray method are applied to the unknown sample u, and the numerical values of the density ρu and the fluorescent X-ray intensity Fu are measured.
[0058]
If the inverse function of the theoretical X-ray intensity X can be obtained analytically, the product (ρT) u can be immediately calculated by substituting the fluorescent X-ray intensity Fu into the inverse function, and the product (ρT ) The thickness Tu can be easily determined by dividing u by the density ρu.
[0059]
On the other hand, when the inverse function of the theoretical X-ray intensity X cannot be obtained analytically, a successive approximation method is used. As a specific method, in the curve of the theoretical X-ray intensity X, when the film thickness T is changed by fixing the variables of density ρu and sensitivity coefficient β, and the fluorescent X-ray intensity F matches the fluorescent X-ray intensity Fu Will be searched for (ρT) u.
[0060]
By dividing the product (ρT) u thus obtained by the density ρu, the film thickness Tu of the unknown sample u can be determined.
[0061]
As described above, even for a sample having a film thickness outside the measurement range of the X-ray reflectivity method, the film thickness can be measured with high accuracy by combination with the fluorescent X-ray method.
[0062]
【The invention's effect】
As described in detail above, according to the present invention, the standard sample c made of the same kind of material as the unknown sample u is prepared, and the X-ray reflectivity method and the fluorescent X-ray method are applied to the standard sample c to obtain the film thickness Tc, After measuring the density ρc and the fluorescent X-ray intensity Fc to obtain the sensitivity coefficient α, the density ρu and the fluorescent X-ray intensity are then applied to the unknown sample u by applying the X-ray reflectance method and the fluorescent X-ray method. The film thickness Tu of the thin film of the unknown sample u can be determined by measuring each Fu. Thus, even for a sample having a film thickness outside the measurement range of the X-ray reflectance method, the film thickness can be measured with high accuracy by combination with the fluorescent X-ray method.
[0063]
Further, by applying the theoretical X-ray intensity method based on the higher-order approximation in the fluorescent X-ray method, the film thickness can be measured with higher accuracy.
[0064]
In addition, by performing the X-ray reflectivity method and the fluorescent X-ray method with the same X-ray analyzer, the X-ray irradiation conditions can be stably maintained, so that measurement errors can be reduced and the measurement time can be shortened. .
[Brief description of the drawings]
FIG. 1 is a configuration diagram showing an example of an X-ray analysis apparatus to which a film thickness measuring method according to the present invention can be applied.
FIG. 2 is a graph showing an example of the measurement principle of the fluorescent X-ray method.
FIG. 3 is a graph showing another example of the measurement principle of the fluorescent X-ray method.
FIG. 4 is a graph showing an example of an X-ray reflectivity curve obtained by using an X-ray reflectivity method.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 X-ray tube 2 Spectral crystal 3a, 3b, 3c Slit 4 Sample table 5

Table control part

6, 11 Detector 7 Preamplifier 8 Proportional amplifier 9 Wave height analyzer 10 Data processor 20 Test object

Claims

A method for measuring the thickness of an unknown sample u in which a thin film is formed on a substrate, the thickness and density of the thin film are unknown, and the constituent materials of the substrate and the thin film are known,
Preparing a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectivity method;
Using the X-ray reflectivity method, the X-ray reflectivity curve of the standard sample c with respect to the change in the X-ray incident angle is measured, and the film thickness Tc is determined from the interference period of the curve, and the total reflection critical angle of the curve is used. Measuring each density ρc;
Measuring the fluorescent X-ray intensity Fc of the standard sample c using a fluorescent X-ray method;
Calculating the sensitivity coefficient α of the standard sample c from the following equation (1);
α = Fc / (ρc · Tc) (1)
Measuring an X-ray reflectivity curve of an unknown sample u with respect to a change in an X-ray incident angle using an X-ray reflectivity method, and measuring a density ρu of the thin film from a total reflection critical angle of the curve;
Measuring the fluorescent X-ray intensity Fu of the unknown sample u using the fluorescent X-ray method;
Calculating the film thickness Tu of the unknown sample u from the following equation (2);
Tu = Fu / (α · ρu) (2)
The film thickness measuring method characterized by including.

A method for measuring the thickness of an unknown sample u in which a thin film is formed on a substrate, the thickness and density of the thin film are unknown, and the constituent materials of the substrate and the thin film are known,
A step of preliminarily determining a theoretical X-ray intensity X (ρT) having a product of density ρ and film thickness T (ρT) as variables;
Preparing a standard sample c composed of the same kind of material as the unknown sample u and capable of measuring the film thickness by the X-ray reflectivity method;
Using the X-ray reflectivity method, the X-ray reflectivity curve of the standard sample c with respect to the change in the X-ray incident angle is measured, and the film thickness Tc is determined from the interference period of the curve, and the total reflection critical angle of the curve is used. Measuring each density ρc;
Measuring the fluorescent X-ray intensity Fc of the standard sample c using a fluorescent X-ray method;
A step of calculating a sensitivity coefficient β, which is a ratio between the fluorescent X-ray intensity Fc and the theoretical X-ray intensity X (ρT) c into which the product (ρT) c of density ρc and film thickness Tc is substituted, from the following equation (1A) When,
β = Fc / X ((ρT) c) (1A)
Measuring an X-ray reflectivity curve of an unknown sample u with respect to a change in an X-ray incident angle using an X-ray reflectivity method, and measuring a density ρu of the thin film from a total reflection critical angle of the curve;
Measuring the fluorescent X-ray intensity Fu of the unknown sample u using the fluorescent X-ray method;
Obtaining a product (ρT) u of the density ρu and the film thickness Tu for the unknown sample u using a successive approximation method so that the obtained fluorescent X-ray intensity Fu satisfies the following formula (2A):
Fu = β · X ((ρT) u) (2A)
Dividing the obtained product (ρT) u by the density ρu to calculate the film thickness Tu.

2. The film thickness measuring method according to claim 1, wherein the X-ray reflectivity method and the fluorescent X-ray method are performed with the same X-ray analyzer.