JP3555833B2 - Method and apparatus for evaluating optical constants - Google Patents

Description

を各々満たすような実部ｎ、虚部ｋの値（曲線）が求められる。
【０００４】
（１）式の場合、図１９に示すように、これらの３つの曲線Ｒ_ｃａｌ ，Ｔ_ｃａｌ ，Ｒｍ_ｃａｌ の交点が記録材料層の複素屈折率の実部ｎ、虚部ｋとなる。
【０００５】
他の方法として、垂直入射反射率から複素屈折率を求める方法があり、これは、一般に、垂直入射反射法（クラマース・クローニッヒ法）と称されている。
【０００６】
まず、垂直入射光に対する平面研磨面試料のエネルギー反射率をＲ（ω）、反射による位相とび（位相遅れ）をφ（ω）とすると、複素屈折率ｒ（ω）は（２）式で与えられる。
【０００７】
【数１】

【０００８】
これを変形すると、（３）式のようになる。
【０００９】
【数２】

【００１０】
この関係をクラマース・クローニッヒ関係式に代入すると、（４）式が得られる。
【００１１】
【数３】

【００１２】
この結果から、垂直入射光に対する強度反射率を理想的にはω＝０からω＝∞まで測定できれば、（４）式によって反射による位相とびφ（ω）を計算することで、（５）式によって複素屈折率を求めることができる。
【００１３】
【数４】

【００１４】
【発明が解決しようとする課題】
ところが、前者のＲ‐Ｔ法による場合、複素屈折率を知りたい物質の膜厚を正確に知る必要があるため、膜厚測定精度で複素屈折率の評価精度が決まってしまう。また、複素屈折率と膜厚とを未知とすることも可能であるが、収束する解が複数存在する可能性が非常に大きいために、評価結果の信頼性が低下する。また、解が複数存在した場合には、意味のある解を選択させることがプログラム上では困難である。さらに、反射率や透過率のデータを複数用いるため、各々の測定精度の影響を受けやすい。
【００１５】
一方、後者の垂直入射反射率法（クラマース・クローニッヒ法）は、基本的には、薄膜の測定・評価には不向きである。また、薄膜の場合には、多重反射の効果を取り入れなければならないため、正確な膜厚を知る必要がある。さらには、膜厚をも未知とした場合には、Ｒ‐Ｔ法の場合と同様に収束する解の信用性が低下してしまう。
【００１６】
そこで、本発明は、Ｒ‐Ｔ法とクラマース・クローニッヒ法との利点を活かすことで、理論的に正しい複素屈折率等の光学定数を容易にプログラミング可能な方法で得ることができる光学定数の評価方法及び評価装置を提供することを目的とする。
【００１７】
【課題を解決するための手段】
＜発明の構成＞
請求項１記載の発明の光学定数の判定方法は、透明基板上に成膜した光透過性物質に対して、任意に仮定した膜厚を用いてＲ‐Ｔ法により複素屈折率の実部と虚部とを求め、求められた実部と虚部との内で虚部データからクラマース・クローニッヒ関係式を用いて複素屈折率の実部を計算し、Ｒ‐Ｔ法により求められた複素屈折率の実部とクラマース・クローニッヒ関係式から計算された複素屈折率の実部とを比較することで、Ｒ‐Ｔ法により求められた複素屈折率の実部と虚部との解の正当性を判定するようにした。
【００１８】
請求項２記載の発明の光学定数の判定方法は、透明基板上に成膜した光透過性物質に対して、膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の虚部を求め、求められた複素屈折率の複数波長における虚部データに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部を求めるようにした。
【００１９】
請求項３記載の発明の光学定数の判定方法は、透明基板上に成膜した光透過性物質に対して、
▲１▼ 膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により、任意に仮定した光透過性物質の膜厚ｄ_ＲＴを用いて光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
▲２▼ ▲１▼のプロセスで求められた複数波長における複素屈折率の虚部ｋ_ＲＴのデータに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部ｎ_ＫＫと光透過性物質の膜厚ｄ_ＫＫを計算するプロセス
▲３▼ ▲１▼のプロセスで求められた複素屈折率の実部ｎ_ＲＴのデータと、▲２▼のプロセスで計算された複素屈折率の実部ｎ_ＫＫのデータとを比較するプロセス
▲４▼ ▲２▼のプロセスで計算された光透過性物質の膜厚ｄ_ＫＫを膜厚ｄ_ＲＴと見做し、見做されたこの膜厚ｄ_ＲＴを用いて再度▲１▼のプロセスのＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
を有し、これらの▲１▼〜▲４▼のプロセスを、▲３▼のプロセスにおいて実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなるまで繰返し、これらの実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなったときに得られる複素屈折率を当該光透過性物質の複素屈折率とするようにした。
【００２０】
請求項４記載の発明の光学定数の判定方法は、透明基板上に成膜した光透過性物質に対して、
▲１▼ 膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により、任意に仮定した光透過性物質の膜厚ｄ_ＲＴを用いて光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
▲２▼ ▲１▼のプロセスで求められた複数波長における複素屈折率の虚部ｋ_ＲＴのデータに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部ｎ_ＫＫと光透過性物質の膜厚ｄ_ＫＫを計算するプロセス
▲３▼ ▲１▼のプロセスで求められた複素屈折率の実部ｎ_ＲＴのデータと、▲２▼のプロセスで計算された複素屈折率の実部ｎ_ＫＫのデータとを比較するプロセス
▲４▼ ▲２▼のプロセスで計算された光透過性物質の膜厚ｄ_ＫＫを膜厚ｄ_ＲＴと見做し、見做されたこの膜厚ｄ_ＲＴを用いて再度▲１▼のプロセスのＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
を有し、これらの▲１▼〜▲４▼のプロセスを、▲３▼のプロセスにおいて実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなるまで繰返し、これらの実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなったときに得られる膜厚値を当該光透過性物質の膜厚とするようにした。
【００２１】
請求項５記載の発明は、請求項２，３又は４記載の光学定数の評価方法であって、複素屈折率の虚部データに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部を求めるプロセスは、Ｒ‐Ｔ法により求められた複数波長における複素屈折率の虚部データの定数倍データからクラマース・クローニッヒ関係式により求められた複数波長における複素屈折率の実部に、これらの複数波長における複素屈折率の虚部データの非測定波長範囲のデータからのクラマース・クローニッヒ関係式中の積分寄与分を定数加算により補償し、この定数加算により複数波長における複素屈折率の実部を求め、複数波長において測定された膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の何れか１つ以上の測定値と、その測定値に対応する複数波長における複素屈折率の虚部の定数倍値と複素屈折率の実部に適用される吸収スペクトルの非測定波長範囲のデータを補償する定数加算値を任意に仮定することで計算される膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の何れかとの誤差が最小となる複数波長における複素屈折率の虚部データの定数倍値と複素屈折率の実部に適用される吸収スペクトルの非測定波長範囲のデータを補償する定数加算値を求めることで、光透過性物質の複素屈折率の実部を計算する。
【００２２】
請求項６記載の発明は、請求項２，３又は４記載の光学定数の評価方法において、Ｒ‐Ｔ法により複数波長での複素屈折率の実部と虚部とを求める際、複素屈折率の虚部を求めるために少なくとも透過率データを用いる。
【００２３】
請求項７記載の発明の光学定数の評価装置は、少なくとも透明基板上に成膜した光透過性物質に対して或る波長範囲で反射率と透過率とを測定する測定手段と、透明基板上に成膜した光透過性物質に対して、膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の虚部を求め、求められた複素屈折率の複数波長における虚部データに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部を求める演算処理手段とを備える。
【００２４】
請求項８記載の発明の光学定数の評価装置は、少なくとも透明基板上に成膜した光透過性物質に対して或る波長範囲で反射率と透過率とを測定する測定手段と、
透明基板上に成膜した光透過性物質に対して、
▲１▼ 膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により、任意に仮定した光透過性物質の膜厚ｄ_ＲＴを用いて光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
▲２▼ ▲１▼のプロセスで求められた複数波長における複素屈折率の虚部ｋ_ＲＴのデータに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部ｎ_ＫＫと光透過性物質の膜厚ｄ_ＫＫを計算するプロセス
▲３▼ ▲１▼のプロセスで求められた複素屈折率の実部ｎ_ＲＴのデータと、▲２▼のプロセスで計算された複素屈折率の実部ｎ_ＫＫのデータとを比較するプロセス
▲４▼ ▲２▼のプロセスで計算された光透過性物質の膜厚ｄ_ＫＫを膜厚ｄ_ＲＴと見做し、見做されたこの膜厚ｄ_ＲＴを用いて再度▲１▼のプロセスのＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
を順次実行し、これらの▲１▼〜▲４▼のプロセスを、▲３▼のプロセスにおいて実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなるまで繰返し、これらの実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなったときに得られる複素屈折率を当該光透過性物質の複素屈折率とする演算処理手段とを備える。
【００２５】
請求項９記載の発明の光学定数の評価装置は、少なくとも透明基板上に成膜した光透過性物質に対して或る波長範囲で反射率と透過率とを測定する測定手段と、
透明基板上に成膜した光透過性物質に対して、
▲１▼ 膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の内の２つ以上の複数波長での測定値と、膜厚を任意に仮定した場合のこれらの測定値に対応する計算値との二乗誤差の和が最小となる解の組合せを決定することで複素屈折率を求めるＲ‐Ｔ法により、任意に仮定した光透過性物質の膜厚ｄ_ＲＴを用いて光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
▲２▼ ▲１▼のプロセスで求められた複数波長における複素屈折率の虚部ｋ_ＲＴのデータに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部ｎ_ＫＫと光透過性物質の膜厚ｄ_ＫＫを計算するプロセス
▲３▼ ▲１▼のプロセスで求められた複素屈折率の実部ｎ_ＲＴのデータと、▲２▼のプロセスで計算された複素屈折率の実部ｎ_ＫＫのデータとを比較するプロセス
▲４▼ ▲２▼のプロセスで計算された光透過性物質の膜厚ｄ_ＫＫを膜厚ｄ_ＲＴと見做し、見做されたこの膜厚ｄ_ＲＴを用いて再度▲１▼のプロセスのＲ‐Ｔ法により光透過性物質の複数波長における複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴを求めるプロセス
を順次実行し、これらの▲１▼〜▲４▼のプロセスを、▲３▼のプロセスにおいて実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなるまで繰返し、これらの実部ｎ_ＫＫのデータと実部ｎ_ＲＴのデータとの波長依存性が略等しくなったときに得られる膜厚値を当該光透過性物質の膜厚とする演算処理手段とを備える。
【００２６】
請求項１０記載の発明は、請求項７，８又は９記載の光学定数の評価装置におて、演算処理手段において複素屈折率の虚部データに対してクラマース・クローニッヒ関係式を適用して複数波長における複素屈折率の実部を求めるプロセスは、Ｒ‐Ｔ法により求められた複数波長における複素屈折率の虚部データの定数倍データからクラマース・クローニッヒ関係式により求められた複数波長における複素屈折率の実部に、これらの複数波長における複素屈折率の虚部データの非測定波長範囲のデータからのクラマース・クローニッヒ関係式中の積分寄与分を定数加算により補償し、この定数加算により複数波長における複素屈折率の実部を求め、複数波長において測定された膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の何れか１つ以上の測定値と、その測定値に対応する複数波長における複素屈折率の虚部の定数倍値と複素屈折率の実部に適用される吸収スペクトルの非測定波長範囲のデータを補償する定数加算値を任意に仮定することで計算される膜面入射反射率、基板面入射反射率、透過率、光透過性物質上に反射層を設けた構造での基板面入射反射率の何れかとの誤差が最小となる複数波長における複素屈折率の虚部データの定数倍値と複素屈折率の実部に適用される吸収スペクトルの非測定波長範囲のデータを補償する定数加算値を求めることで、光透過性物質の複素屈折率の実部を計算するプロセスである。
【００２７】
請求項１１記載の発明は、請求項７，８又は９記載の光学定数の評価装置において、演算処理手段においてＲ‐Ｔ法により複数波長での複素屈折率の実部と虚部とを求める際、複素屈折率の虚部を求めるために少なくとも透過率データを用いる。
【００２８】
＜発明の原理＞
基本的には、任意に仮定した膜厚を用いてＲ‐Ｔ法により複素屈折率の実部と虚部とを求め、求められたこれらの実部と虚部との解の正当性をクラマース・クローニッヒ関係式を用いて判定する。
【００２９】
より具体的には、請求項１記載の発明のように、任意に仮定した膜厚を用いてＲ‐Ｔ法により複素屈折率の実部と虚部とを求め、求められたこれらの実部と虚部との内で虚部データからクラマース・クローニッヒ関係式を用いて複素屈折率の実部を計算し、Ｒ‐Ｔ法により求められた複素屈折率の実部とクラマース・クローニッヒ関係式から計算された複素屈折率の実部とを比較することで、Ｒ‐Ｔ法により求められた複素屈折率の解の正当性、つまり、任意に仮定した膜厚値や、複数存在した解から選択された解の正当性を判定する。
【００３０】
ここに、Ｒ‐Ｔ法により求められた複素屈折率の虚部を基盤として処理するようにしているが、Ｒ‐Ｔ法による場合には、複素屈折率の虚部データが膜厚にあまり依存せず（絶対値は変動してもその形は膜厚によって大きく変化しない）、かつ、複数存在する最適解間での値の差が小さく、一定した値が得られることを見出し、これを積極的に利用するためである。
【００３１】
反面、Ｒ‐Ｔ法では、複素屈折率の実部は膜厚依存性が大きく、また、複数存在する最適解間での値の差が大きいため、大きくばらつきやすく、膜厚や各測定データの正確さが非常に要求されるが、現実には、膜厚は特に基板の平行度や成膜方法、条件によりかなりのばらつきが生じていると考えられ、正確な値を求めることは非常に困難である。このため、Ｒ‐Ｔ法は複素屈折率の実部を決定するために用いるには不向きと考えられる。但し、Ｒ‐Ｔ法でも正確な膜厚値が得られれば、正確に複素屈折率（実部、虚部ともに）を求めることができる。
【００３２】
即ち、Ｒ‐Ｔ法においては、本来の膜厚値に対して異なる膜厚値を用いると、複素屈折率の虚部ｋと実部ｎとの関係が理論からずれを生ずる（一般的には、複素屈折率の虚部の波長依存曲線は膜厚依存性が少ないことから、複素屈折率の虚部ｋの波長依存性に対する複素屈折率の実部ｎの波長依存性が理論からずれるといってもよい）。従って、膜厚を変化させて或る波長範囲で複素屈折率を求めれば（複素屈折率の波長依存性）、正確な膜厚時にのみ複素屈折率の虚部に対して理論的に正しい複素屈折率の実部解が得られることになる。
【００３３】
このように複素屈折率の虚部に対して理論的に正しい複素屈折率の実部解が得られたときが、正しい膜厚値と複素屈折率値とが得られたことになる。
【００３４】
ところが、膜厚を変化させて各膜厚値毎に複素屈折率の波長依存性を計算することは、前述したように、解が複数存在するために非常に手間がかかり面倒であり、プログラム化しにくい事項である。
【００３５】
一方、クラマース・クローニッヒ関係式を利用して複素屈折率を決定するクラマース・クローニッヒ法の場合、理論的に正確であり、複素屈折率の実部或いは虚部が既知であれば、他方の値（虚部或いは実部）は一義的に正確に求め得る利点がある。もっとも、クラマース・クローニッヒ関係式を用いる場合、通常は、有限波長範囲の測定データを利用するため、測定データの測定波長両端近傍ではその精度が低下するという問題を有する。
【００３６】
これらの点を総合的に考察すると、理想的には、Ｒ‐Ｔ法により複素屈折率の計算ができればよく、このとき、必要なのが正確な膜厚値であるといえる。そこで、本発明では、効率よくＲ‐Ｔ法により複素屈折率を決定させるため、複素屈折率の実部評価と虚部評価とを独立させ、Ｒ‐Ｔ法により複素屈折率の虚部を求め、求められた虚部データを用いてクラマース・クローニッヒ関係式から複素屈折率や膜厚を求めるようにした。クラマース・クローニッヒ関係式を用いる方法は容易にプログラム化できる。このとき、Ｒ‐Ｔ法で求められた複素屈折率の実部とクラマース・クローニッヒ関係式により計算された複素屈折率の実部との波長依存性が略一致すれば、正確な解がＲ‐Ｔ法により得られている、と考えることができる。
【００３７】
ところで、クラマース・クローニッヒ関係式を利用する場合、前述したように理論的に正確であり、複素屈折率の実部或いは虚部が既知であれば、他方の値は一義的に正確に求め得る利点があるが、反面、既知でなければならない複素屈折率の実部又は虚部に関して測定波長範囲として０〜∞が要求され、その測定波長範囲が限定されてしまうと、計算される値の精度も低下してしまう欠点がある。本発明では、この点も考慮して、限られた波長範囲の複素屈折率の虚部データから比較的正確な複素屈折率の実部を求める補償方法も請求項３記載の発明として提供している。
【００３８】
即ち、本発明によれば、Ｒ‐Ｔ法では正確な複素屈折率の実部が計算できず、クラマース・クローニッヒ関係式を利用する方法では複素屈折率の実部か虚部かの何れか一方がわからなければ他方の値も計算できない、という欠点が補われる。
【００３９】
さらに、本発明によれば、Ｒ‐Ｔ法で複素屈折率の虚部を求めるために用いた任意に仮定した膜厚値と、クラマース・クローニッヒ関係式を用いて複素屈折率の実部を決定するために得られた膜厚値とが同一となるときに正確な複素屈折率が計算される、と仮定しているため、請求項４記載の発明のように、評価する光学定数を膜厚とする場合にも応用できる。このように、Ｒ‐Ｔ法で複素屈折率の虚部を求めるために用いた任意に仮定した膜厚値と、クラマース・クローニッヒ関係式を用いて複素屈折率の実部を決定するために得られた膜厚値とが同一となるときに正確な複素屈折率が計算される、と仮定できる根拠は、本発明の方法により計算された複素屈折率と膜厚値とを用いることで、膜面入射反射率等の実測値と計算値とが殆ど一致すること、クラマース・クローニッヒ関係式を用いて複素屈折率の実部を決定する方法で取り入れた近似が精度的に信用できる検証結果が得られているためであり、さらには、最終的に得られた膜厚値でのみＲ‐Ｔ法により得られた複素屈折率とクラマース・クローニッヒ関係式を用いて計算された複素屈折率の値とが、実部、虚部ともにほぼ一致するためである。
【００４０】
【発明の実施の形態】
本発明の一実施の形態を図１ないし図６に基づいて説明する。本実施の形態は、図１に示すように透明基板１上に成膜した光透過性物質２に関する複素屈折率や膜厚を評価するためのものであり、少なくとも光透過性物質２に対して或る波長範囲でその反射率や透過率を測定し得る測定装置３（測定手段）と、この測定装置３から得られた測定値や予めプログラミングされているクラマース・クローニッヒ関係式等を用いて所定の演算処理を行うコンピュータ４（演算処理手段）とを備えた装置構成により処理される。
【００４１】
本実施の形態の複素屈折率の評価方法では、以下のような仮定Ａ，近似Ｂを用いる。
【００４２】
Ａ．Ｒ‐Ｔ法により複素屈折率の虚部を求める。
このとき、測定物質（光透過性物質２）の膜厚を知る必要があるが、或る程度任意に設定しても構わない。
【００４３】
Ｂ．限られた波長領域の複素屈折率の虚部データから複素屈折率の実部を精度よく評価するために、波長領域を以下のように３分割し、
領域１．∞ 〜λ_ａ （非測定領域、測定不能領域）
領域２．λ_ａ 〜λ_ｂ （測定領域）
領域３．λ_ｂ 〜０ （非測定領域、測定不能領域）
領域１，３の積分寄与を（６）式に示すように定数を置き換える。
【００４４】
【数５】

【００４５】
仮定Ａは、本実施の形態上、最も重要な事項の一つであり、Ｒ‐Ｔ法により求められる複素屈折率の内、実部は膜厚値の影響を大きく受けるが、虚部はその影響を非常に小さくし得る点を利用したものである。つまり、最適解が複数存在した場合でも、実部は広範囲な値をとりやすいが、虚部は殆ど一定値とすることができる。
【００４６】
このような複素屈折率の虚部を得るためには、Ｒ‐Ｔ法において透過率データを用いることが好ましい。なぜなら、透過率は反射の影響もあるが、基本的に膜の吸収、即ち、複素屈折率の虚部の大きさで決まってしまうためである。このため、或る膜厚を仮定したとき、測定透過率データと一致するような複素屈折率の実部と虚部との解の組を計算すると、測定データと一致する解の虚部依存性が非常に小さいからである。
【００４７】
具体的に、Ｒ‐Ｔ法により求められた複素屈折率の虚部の解を見ると、図２に示すようになる。これは、光透過性物質２の膜材料をＯｘｏ〔５，１０，１５，２０‐ｔｅｔｒａ（４‐ｐｙｒｉｄｙｌ）ｐｏｒｐｈｉｎａｔｏ〕ｔｉｔａｎｉｕｍ（ＩＶ）の膜厚を８７ｎｍと仮定したときの計算結果（測定データと一致する膜面入射反射率の解曲線、基板面入射反射率の解曲線、及び、透過率の解曲線）を示し、図２（ａ）は波長５００ｎｍ、図２（ｂ）は波長６００ｎｍの場合を示している。図中、横軸は複素屈折率の実部、縦軸は複素屈折率の虚部である。
【００４８】
図２からも明らかなように、実測透過率データと一致するための複素屈折率の解曲線は複素屈折率の虚部にあまり依存していない。例えば、図２（ａ）に示す波長５００ｎｍの場合で、この膜材料の複素屈折率は０．５‐ｉ＊０と３．２‐ｉ＊０との近傍の解が得られているが、何れの解を選択しても虚部はあまり影響を受けないことがわかる。ちなみに、膜面入射反射率と基板面入射反射率とを用いても同じように複数得られる解は、虚部が殆ど同じような値となるが、上記のような透過率データを用いることで、より一層、虚部の膜厚依存性、複数解の虚部値間の差を低減させることが可能となる（膜面入射反射率と基板面入射反射率とだけを用いると、その誤差は虚部に大きく影響し得るが、透過率データを併用することで誤差が虚部に与える影響を低減させることができる）。
【００４９】
近似Ｂにおいては、領域３の長波長領域では、ほぼ吸収が０となるため無視できるので、領域１の吸収の取扱いを検討する必要がある。そこで、測定波長領域以外からの吸収による積分の寄与を定数化することの妥当性を検討した結果を図３に示す。なお、波長２００〜９００ｎｍ領域は実測データであり、波長０〜２００ｎｍ領域は任意に仮定したデータである。なお、波長０〜２００ｎｍ領域に関して任意に仮定したデータは、倍数ａ（定数）により可変とし、波長２００〜９００ｎｍ領域の実測データに連続させるようにしたものである。図３（ａ）は倍数ａ＝１．０の場合、図３（ｂ）は倍数ａ＝２．０の場合を示す。
【００５０】
このようなアブソーバンスデータを用いて実部ｎを求めるが、波長０〜２００ｎｍ領域のデータ欠損が計算される実部ｎに与える影響の検討結果を図４に示す。図４（ａ）は倍数ａ＝１．０なる条件下に波長０〜２００ｎｍ領域のアブソーバンスデータを計算に取り入れた場合、図４（ｂ）は波長０〜２００ｎｍ領域のアブソーバンスデータを無視した場合の各々の複素屈折率の実部ｎの計算結果を示しており、図４（ｃ）はこれらを同時に図示したものである。図５はこれらの２つの計算結果の差Δｎを示すものである。
【００５１】
このような検討結果によれば、短波長側の方が波長０〜２００ｎｍ領域のアブソーバンスデータを無視することの影響が大きく出ることがわかるが、波長４００ｎｍと波長８００ｎｍとの場合の差Δｎ＝０．１程度であり、定数加算と近似してもそれほど大きな影響がないと思われる。また、図４（ｃ）からも波長０〜２００ｎｍ領域の吸収帯の影響は、複素屈折率の実部の形には殆ど影響を与えないことがわかる。
【００５２】
次に、波長０〜２００ｎｍ領域の吸収の大きさの影響の検討結果を図６に示す。ここでは、波長０〜２００ｎｍ領域の吸収の大きさに関わらず限られた波長域のデータから計算される実部ｎの値に定数加算する妥当性があるか否かを検討したものである。図６（ａ）は、波長０〜２００ｎｍ領域の吸収の大きさａに対する波長４５１ｎｍにおける波長０〜２００ｎｍ領域のアブソーバンスデータを無視した場合と取り入れた場合に計算される実部ｎの値の差をプロットしたものであり、図６（ｂ）は、波長０〜２００ｎｍ領域の吸収の大きさａに対する波長８００ｎｍにおける波長０〜２００ｎｍ領域のアブソーバンスデータを無視した場合と取り入れた場合に計算される実部ｎの値の差をプロットしたものであり、図６（ｃ）はこれらを同時に図示したものである。
【００５３】
この結果、波長０〜２００ｎｍなる吸収帯の大きさの如何に関わらず、限られた波長域から得られたアブソーバンスデータで計算される実部ｎの値に、各波長均一に定数を加算することで、或る程度正確な複素屈折率が得られることがわかる。
【００５４】
具体的な計算方法を示すと、以下のようになる。
▲１▼ 任意に仮定した膜厚ｄ_ＲＴを用いてＲ‐Ｔ法により、複素屈折率の実部ｎ_ＲＴと虚部ｋ_ＲＴとを求める。
▲２▼ 求められた虚部ｋ_ＲＴのデータに対して定数ａ倍した値ｋ_ＲＴ（ａ）を用いて、クラマース・クローニッヒの分散関係式中の積分を実行することで、複素屈折率の実部ｎ_ＫＫ（ａ）′を計算する（Ｋ‐Ｋ変換法）。
▲３▼ 計算された実部ｎ_ＫＫ（ａ）′に対して非測定波長領域からの積分寄与分として定数ｎ_ａｄｄ を加算し、定数ａと定数ｎ_ａｄｄ と膜厚とを任意に設定して計算される膜面入射反射率と膜面入射反射率の測定値との差が最小となる値ｎ_ａｄｄ 及び値ａ，膜厚ｄ_ＫＫを決定し、これらの値ｎ_ａｄｄ ，ａにより最終的にクラマース・クローニッヒ関係式からの補正された複素屈折率の実部ｎ_ＫＫ（ａ）を得る。ここに、実部ｎ_ＲＴとこの実部ｎ_ＫＫとがほぼ同じ波長依存性と値であれば、これにより、膜の複素屈折率ｎ（λ）‐ｉ＊ｋ（λ）を得る。このとき、膜の複素屈折率ｎ（λ）‐ｉ＊ｋ（λ）の実部は、Ｒ‐Ｔ法の結果を用いても、Ｋ‐Ｋ変換による値を用いてもよい。
▲４▼ 実部ｎ_ＲＴと実部ｎ_ＫＫとが大きく異なる場合は、膜厚ｄ_ＫＫを用いてＲ‐Ｔ法により複素屈折率の虚部を求め、これらの実部ｎ_ＲＴと実部ｎ_ＫＫとがほぼ同じになるまで、▲２▼のプロセスと▲３▼のプロセスとを繰返し、最終的に膜の複素屈折率ｎ（λ）‐ｉ＊ｋ（λ）を得る。このときも、膜の複素屈折率ｎ（λ）‐ｉ＊ｋ（λ）の実部は、Ｒ‐Ｔ法の結果を用いても、Ｋ‐Ｋ変換による値を用いてもよい。
【００５５】
なお、非測定波長領域からの積分寄与分として定数ｎ_ａｄｄ を波長の１次関数として補償する方法を用いてもよい。この方法（仮定）は、図５や図６（ｃ）に示したように、短波長側の非測定波長領域からの積分寄与分は複素屈折率を知りたい波長域での短波長ほど大きく、波長が長くなるにつれてほぼリニアに減少すること、また、短波長側の非測定波長領域の吸収成分が大きくなるほどこの短波長側の非測定波長領域からの積分寄与分は複素屈折率を知りたい波長域での短波長ほど大きく、波長が長くなるにつれてほぼリニアに減少することにより、その妥当性が保証されることになる。
【００５６】
【実施例】
上記実施の形態に基づく、本発明の実施例を図７ないし図１８に基づいて説明する。本実施例では、ポルフィラジン誘導体をクロロホルムに溶解させ、スピンコーティング法により石英基板上に薄膜を形成してサンプルとした。このようなサンプルに対して、吸光度、膜面入射垂直反射率、基板面入射反射率及び透過率を測定し、これらの膜面入射垂直反射率、基板面入射反射率及び透過率の測定値を用いてＲ‐Ｔ法により膜厚を２７ｎｍと仮定して複素屈折率を計算した。図７（ａ）は吸光度、図７（ｂ）は膜面入射垂直反射率、図７（ｃ）は基板面入射反射率、図７（ｄ）は透過率の各々の測定値を示す図であり、横軸は波長を示している。なお、Ｒ‐Ｔ法の計算プログラム中、膜面入射垂直反射率、基板面入射反射率及び透過率に関するデータは基板の影響を補正してあり、図７（ｂ）〜（ｄ）中には、補正前のデータと補正後のデータとが図示されている。
【００５７】
図８（ａ）はＲ‐Ｔ法による複素屈折率の計算結果を示す図である。即ち、膜厚を任意に２７ｎｍと仮定して得られた複素屈折率を示すが、複素屈折率の虚部は図７（ａ）に示す吸光度データの波長依存性とが類似しており、任意に仮定した膜厚から得られた複素屈折率の虚部の信頼性を示している。図８（ｂ）は図８（ａ）の縦軸を拡大して示す図である。図８（ａ）では２００〜３００ｎｍ近傍の波長領域で、複素屈折率の虚部に対する複素屈折率の実部が理論的に異常な関係を示していることがわかる。これは、Ｒ‐Ｔ法で用いた膜厚２７ｎｍが適切でないことを示唆するものである。
【００５８】
次に、図８（ａ）で示された複素屈折率の虚部のデータを元に、クラマース・クローニッヒ関係式を用いて複素屈折率の実部を計算した。この計算時には、図８（ａ）で示された複素屈折率の虚部に全波長一律に掛けられる定数倍値ａと、複素屈折率の虚部のデータの非測定波長（具体的には、２００ｎｍ以下の波長であり、８００ｎｍ以上の波長データは欠損しているがポルフィラジン誘導体なる化合物は８００ｎｍ以上の波長に対して吸収帯を有しないので考慮する必要はない）からの積分寄与分を全波長一律に補正するために、複素屈折率の実部へ加えられる定数倍加算値ｎ_ａｄｄ 、さらに、膜厚値をパラメータとして、このパラメータを任意に仮定したときに計算される膜面垂直入射反射率と、実際に測定された膜面垂直入射反射率との各波長での二乗誤差の和が最小となるような複素屈折率の虚部に全波長一律に掛けられる定数倍値ａと、複素屈折率の虚部のデータの非測定波長領域からの積分寄与分を全波長一律に補正するために複素屈折率の実部に加えられる定数加算値ｎ_ａｄｄ 、及び、膜厚値を計算させたものである。
【００５９】
このとき、複素屈折率の虚部に全波長一律に掛けられる定数倍値ａは０．５、複素屈折率の虚部のデータの非測定波長領域からの積分寄与分を全波長一律に補正するために複素屈折率の実部に加えられる定数加算値ｎ_ａｄｄ は１．５、膜厚は４８ｎｍとなったものである。このようなクラマース・クローニッヒ関係式を用いた計算で得られた複素屈折率を示すと図９のようになる。
【００６０】
クラマース・クローニッヒ関係式を用いて複素屈折率の虚部から実部を求める場合、虚部のデータの波長範囲が２００〜８００ｎｍと限られた波長域での値であるため、複素屈折率の虚部のデータの非測定波長領域からの積分寄与分を補正しているにも関わらず、波長２００ｎｍ近傍は正しい値を示さない。これは、波長２００ｎｍ近傍の複素屈折率の実部は、波長２００ｎｍ近傍の複素屈折率の虚部の値（値変化）に強く影響されるからであり、本実施例では、波長２００ｎｍ以下の複素屈折率のデータが欠損するためである（波長８００ｎｍの複素屈折率の実部は、波長８００ｎｍ以上の複素屈折率の虚部が０である考えられるため正しい結果が得られる）。従って、クラマース・クローニッヒ関係式から複素屈折率の実部を計算する波長範囲としては３５０〜８００ｎｍの範囲としている。
【００６１】
前述した本発明の計算ルーチンの手順のように、図８に示すようにＲ‐Ｔ法による複素屈折率の実部と図９に示すようにクラマース・クローニッヒ関係式から得られる複素屈折率の実部とを比較すると、若干の違いが見られる。これは、両者を同時に示す図１０（ａ）及びその内の実部だけを拡大して示す図１０（ｂ）により明らかであり、２００〜８００ｎｍなる波長領域で１０ｎｍ毎のＲ‐Ｔ法による複素屈折率の実部とクラマース・クローニッヒ関係式から得られる複素屈折率の実部との二乗誤差の和は１．７１０となったものである（表１参照）。この結果、図８に示したＲ‐Ｔ法による複素屈折率の解は収束解ではなく、正しい値でないと判断できる。
【００６２】
【表１】

【００６３】
つづいて、上記のようにクラマース・クローニッヒ関係式を用いて得られた膜厚値４８ｎｍを用いて、再度、Ｒ‐Ｔ法により複素屈折率を計算した。この結果を図１１（ａ）に示し、その拡大図を図１１（ｂ）に示す。この結果によれば、図８では異常な関係となっていた２００〜３００ｎｍ波長領域の複素屈折率の実部と虚部との関係が正しくなっていることがわかる。
【００６４】
この後、図１１に示すような結果となった複素屈折率の虚部のデータを元にして、再度、クラマース・クローニッヒ関係式を用いて複素屈折率の実部を計算し直した。この計算時には、図１１に示したような複素屈折率の虚部のデータに対して全波長一律に掛けられる定数倍値ａと、複素屈折率の虚部データの非測定波長領域（具体的には、２００ｎｍ以下の波長であり、８００ｎｍ以上の波長データは欠損しているがポルフィラジン誘導体なる化合物は８００ｎｍ以上の波長に対して吸収帯を有しないので考慮する必要はない）からの積分寄与分を全波長一律に補正するために複素屈折率の実部へ加えられる定数倍加算値ｎ_ａｄｄ 、さらに、膜厚値をパラメータとして、このパラメータを任意に仮定したときに計算される膜面垂直入射反射率と、実際に測定された膜面垂直入射反射率との各波長での二乗誤差の和が最小となるような複素屈折率の虚部に全波長一律に掛けられる定数倍値ａと、複素屈折率の虚部のデータの非測定波長領域からの積分寄与分を全波長一律に補正するために複素屈折率の実部に加えられる定数加算値ｎ_ａｄｄ 、及び、膜厚値を計算させたものである。
【００６５】
このとき、複素屈折率の虚部に全波長一律に掛けられる定数倍値ａは０．５、複素屈折率の虚部のデータの非測定波長領域からの積分寄与分を全波長一律に補正するために複素屈折率の実部に加えられる定数加算値ｎ_ａｄｄ は１．５、膜厚は４８ｎｍとなったものである。このようなクラマース・クローニッヒ関係式を用いた計算で得られた複素屈折率を示すと図１２のようになる。
【００６６】
前述した本発明の計算ルーチンの手順のように、図１１に示すようにＲ‐Ｔ法による複素屈折率の実部と図１２に示すようにクラマース・クローニッヒ関係式から得られる複素屈折率の実部とを比較すると、ほぼ波長依存性と絶対値とが一致していることがわかる。これは、両者を同時に示す図１３（ａ）及びその内の実部だけを拡大して示す図１３（ｂ）により明らかであり、２００〜８００ｎｍなる波長領域で１０ｎｍ毎のＲ‐Ｔ法による複素屈折率の実部とクラマース・クローニッヒ関係式から得られる複素屈折率の実部との二乗誤差の和は８．５９５×１０￣^３となったものである（表２参照）。この結果、図１１に示したＲ‐Ｔ法による複素屈折率の解は収束解であり、正しい値が算出されていると判断できる。
【００６７】
【表２】

【００６８】
また、Ｒ‐Ｔ法で複素屈折率を求めたときの膜厚値と、その膜厚値で得られた複素屈折率の虚部のデータからクラマース・クローニッヒ関係式により計算された最適膜厚値とが一致していることからも、図１１で得られた複素屈折率は信頼性が高いと考えられる。
【００６９】
さらに、膜面垂直入射反射率の実測値と、図１１で得られた複素屈折率と膜厚値４８ｎｍとを用いて計算した膜面入射反射率は、図１４に示すように、ほぼ完全に一致し、本実施の形態によって得られた複素屈折率と膜厚値との信頼性が高いことを示す結果となっている。
【００７０】
ここで、初期に膜厚を２７ｎｍと仮定してＲ‐Ｔ法により求められた各波長２００，３００，４００，５００，６００，７００ｎｍ毎の膜面垂直入射反射率、基板面垂直入射反射率及び膜面垂直入射透過率の解曲線を図１５に示す（図１５中、（ａ）は波長２００ｎｍの場合、（ｂ）は波長３００ｎｍの場合、（ｃ）は波長４００ｎｍの場合、（ｄ）は波長５００ｎｍの場合、（ｅ）は波長６００ｎｍの場合、（ｆ）は波長７００ｎｍの場合を示す）。
【００７１】
同様に、初期に膜厚を４８ｎｍと仮定してＲ‐Ｔ法により求められた各波長２００，３００，４００，５００，６００，７００ｎｍ毎の膜面垂直入射反射率、基板面垂直入射反射率及び膜面垂直入射透過率の解曲線を図１６に示す（図１６中、（ａ）は波長２００ｎｍの場合、（ｂ）は波長３００ｎｍの場合、（ｃ）は波長４００ｎｍの場合、（ｄ）は波長５００ｎｍの場合、（ｅ）は波長６００ｎｍの場合、（ｆ）は波長７００ｎｍの場合を示す）。
【００７２】
この結果から、初期に任意に仮定した膜厚では、膜面垂直入射反射率と基板面垂直入射反射率と膜面垂直入射透過率とが交わる交点（即ち、解）がはっきりせず、解の信頼性が低いことがうかがえるが、クラマース・クローニッヒ関係式を用いて得られた膜厚値４８ｎｍを用いた場合には膜面垂直入射反射率と基板面垂直入射反射率と膜面垂直入射透過率とが交わる交点がはっきりしており、解の信頼性が非常に高いことが保証されたと考えられる。
【００７３】
このように、Ｒ‐Ｔ法によっても膜面垂直入射反射率と基板面垂直入射反射率と膜面垂直入射透過率とが交わる交点の様子によって、仮定した膜厚値の判定を行えるが、Ｒ‐Ｔ法のみを用いた場合には、闇雲に膜厚値を変化させなければならず、非常に計算効率が悪いが、本発明ないしは実施例のように、クラマース・クローニッヒ関係式を併用することにより、最適膜厚を容易に求めることができ、非常に計算効率が上がることになる。即ち、本実施例からも明らかなように、Ｒ‐Ｔ法のみで最適膜厚を探す場合には、或る膜厚値で得られた複素屈折率から本当の膜厚値に対する情報が全く得られないため、闇雲に膜厚値を変化させて複素屈折率を評価するか、数ｎｍ置きに膜厚を変化させて地道に複素屈折率を評価するしかなかったが、クラマース・クローニッヒ関係式を併用することにより容易に最適膜厚を探し出すことが可能となる。従って、非常に効率よく、かつ、信頼性の高い光学定数（複素屈折率と膜厚）を決定することができる。
【００７４】
ところで、上記のような本発明の実施の形態ないしは実施例を踏まえて、本発明の重要な２つの仮定
・ Ｒ‐Ｔ法によって得られる複素屈折率の虚部は膜厚や複数存在する解の中からの最適解の選択方法によって、あまり変化しない
・ Ｒ‐Ｔ法によって得られる複素屈折率の実部は膜厚や複数存在する解の中からの最適解の選択方法によって、大きく変化するため、Ｒ‐Ｔ法のみによる複素屈折率の評価方法は不確定さを伴う
が事実であることを検証した。
【００７５】
図１７（ａ）〜（ｆ）はその検証結果を示すもので、図１７中、（ａ）は膜厚９２ｎｍ、（ｂ）は膜厚８７ｎｍ、（ｃ）は膜厚８２ｎｍ、（ｄ）は膜厚８１ｎｍ、（ｅ）は膜厚７７ｎｍ、（ｆ）は膜厚７０ｎｍの場合の複素屈折率の実部ｎ、虚部ｋの波長依存性を示している。図１７によれば、膜厚が変化しても複素屈折率の虚部ｋは殆ど変化せず、一定な解が得られていることがわかる。図１８はわかりやすくするため、図１７（ａ）〜（ｆ）に示した各膜厚時においてＲ‐Ｔ法により得られた複素屈折率の虚部を同時に図示したものであり、特性的に殆ど重なっており、膜厚が変化しても虚部のデータは殆ど変わらないことがよくわかる。
【００７６】
つまり、任意に仮定した膜厚値を用いても、Ｒ‐Ｔ法から得られる複素屈折率の虚部は信頼性がある程度補償されるため、この値を用いたクラマース・クローニッヒ関係式から得られる複素屈折率と膜厚値とはともに同様に高い信頼性が確保されることとなり、本発明で提示した計算ルーチンで解が容易に収束することになる。
【００７７】
一方、複素屈折率の実部は膜厚或いは複数存在する解の中からの最適解の選択方法によって大きく左右されており、Ｒ‐Ｔ法は複素屈折率の実部の評価には適さないことがわかる。換言すれば、Ｒ‐Ｔ法から求められた複素屈折率の実部はＲ‐Ｔ法の計算信頼度を示しているともいえる。
【００７８】
【発明の効果】
本発明は、上述したように複素屈折率の虚部が膜厚にあまり依存せず複数存在する最適解間での値の差が小さくほぼ一定した値が得られる特性を持つＲ‐Ｔ法と、複素屈折率の虚部が既知であれば実部は一義的に理論的に正確に得られる特性を持つクラマース・クローニッヒ関係式を利用する方法とを併用することで、任意に仮定した膜厚を用いてＲ‐Ｔ法により複素屈折率の実部と虚部とを求め、求められた実部と虚部との解の正当性をクラマース・クローニッヒ関係式を用いて判定する複素屈折率、膜厚等の光学定数の判定方法ないしは判定装置を提供したので、クラマース・クローニッヒ関係式におけるＫ‐Ｋ変換に用いられる複素屈折率の虚部の信頼性をある程度保証できるため、計算ルーチンの収束を早めることができ、また、クラマース・クローニッヒ関係式を併用することで複素屈折率の実部はＲ‐Ｔ法のように各波長毎に独立して実部、虚部を決める必要がなく、波長分散性を正しく評価でき、Ｒ‐Ｔ法のように複素屈折率の実部が異常値をとることがないため、最適膜厚に関しても容易に求めることができ、さらには、解の収束判定を定量的な行えるため、プログラム作成が容易であり、動作の信頼性を高めることができ、また、限られた波長範囲の複素屈折率の虚部データから比較的正確な複素屈折率の実部を求める計算補償方法も提供されており、所定の定数を決定させればよいので、プログラム構成も簡単化できる等の効果を有する。
【図面の簡単な説明】
【図１】本発明の一実施の形態の光学定数の評価装置の概要を示すブロック図である。
【図２】Ｒ‐Ｔ法により求められた各種解曲線を示す特性図である。
【図３】定数ａの可変に伴う複素屈折率の実部の測定値を示す特性図である。
【図４】アブソーバンスデータの有無に応じたデータ欠損の影響を示す特性図である。
【図５】２つの計算結果の差を示す特性図である。
【図６】定数加算する妥当性を示す特性図である。
【図７】本発明の一実施例のサンプルに対する吸光度、反射率、透過率等の測定結果を示す特性図である。
【図８】測定値に対してＲ‐Ｔ法を用いた計算結果を示す特性図である。
【図９】クラマース・クローニッヒ関係式により計算された複素屈折率を示す特性図である。
【図１０】Ｒ‐Ｔ法とクラマース・クローニッヒ関係式による方法との計算結果同士を対比させて示す特性図である。
【図１１】計算値に対して再度Ｒ‐Ｔ法を用いた計算結果を示す特性図である。
【図１２】再度クラマース・クローニッヒ関係式により計算された複素屈折率を示す特性図である。
【図１３】再度のＲ‐Ｔ法と再度のクラマース・クローニッヒ関係式による方法との計算結果同士を対比させて示す特性図である。
【図１４】膜面垂直入射反射率の実測値と計算値との一致性を示す特性図である。
【図１５】膜厚を２７ｎｍと仮定して波長を種々変化させた場合にＲ‐Ｔ法により計算された各種解曲線を示す特性図である。
【図１６】膜厚を４８ｎｍと仮定して波長を種々変化させた場合にＲ‐Ｔ法により計算された各種解曲線を示す特性図である。
【図１７】膜厚を種々変化させた場合の複素屈折率の変化の様子を示す特性図である。
【図１８】複素屈折率の虚部が膜厚に依存しないことを示す特性図である。
【図１９】従来のＲ‐Ｔ法のみにより複素屈折率と計算値との関係を示す特性図である。
【符号の説明】
１ 透明基板
２ 光透過性物質
３ 測定手段
４ 演算処理手段[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method and an apparatus for evaluating optical constants such as a complex refractive index and a film thickness at a plurality of wavelengths of a light transmitting substance formed on a transparent substrate.
[0002]
[Prior art]
Conventionally, methods for evaluating the complex refractive index and wavelength dispersibility of a dye include, for example, film surface reflectance, substrate surface reflectance, transmittance, and the reflectance and transmittance of a dye thin film prepared on a substrate. Is measured, and there is a method of calculating by calculation from the substrate surface reflectance in the case where a metal reflection film such as gold is provided on the dye thin film (for example, “Unique reflection properties of films of organic soluble naphalineases.”). Chem. Soc., Perkin Trans. 2, 1996, p. 1219), which is generally referred to as the RT method.
[0003]
For example, the complex refractive index of a recording material containing a dye is n-ik, and the complex refractive index of a substrate is n-ik. _s -Ik _s , The complex index of refraction of air to n _air -Ik _air Where d is the film thickness of the recording material containing the dye, λ is the wavelength, and the reflectance measured from the air side of the constituent sample of the substrate / recording material layer is R. _exp , The transmittance measured from the air side is T _exp The reflectance measured from the substrate side of a sample composed of a substrate, a recording material layer, and a metal (Au) reflection layer is represented by Rm. _exp , The calculated value of the reflectance from the air side for the constituent sample of _cal , The calculated value of the transmittance from the air side is T _cal , The calculated value of the reflectance from the substrate side is Rm _cal Then, for each measured value, the following equation (1)

Are satisfied, the values (curves) of the real part n and the imaginary part k are obtained.
[0004]
In the case of equation (1), as shown in FIG. _cal , T _cal , Rm _cal Are the real part n and the imaginary part k of the complex refractive index of the recording material layer.
[0005]
As another method, there is a method of obtaining a complex refractive index from the normal incidence reflectance, which is generally called a normal incidence reflection method (Kramers-Kronig method).
[0006]
First, assuming that the energy reflectivity of the flat polished surface sample with respect to normal incident light is R (ω) and the phase jump (phase delay) due to reflection is φ (ω), the complex refractive index r (ω) is given by equation (2). Can be
[0007]
(Equation 1)

[0008]
When this is modified, it becomes as shown in equation (3).
[0009]
(Equation 2)

[0010]
Substituting this relation into the Kramers-Kronig relational equation gives equation (4).
[0011]
(Equation 3)

[0012]
From this result, if the intensity reflectance for vertically incident light can be ideally measured from ω = 0 to ω = ∞, the phase jump φ (ω) due to reflection can be calculated by the equation (4) to obtain the equation (5). Can determine the complex refractive index.
[0013]
(Equation 4)

[0014]
[Problems to be solved by the invention]
However, in the case of the former RT method, since it is necessary to accurately know the film thickness of the substance whose complex refractive index is to be known, the evaluation accuracy of the complex refractive index is determined by the film thickness measurement accuracy. Although it is possible to make the complex refractive index and the film thickness unknown, it is highly probable that there are a plurality of converging solutions, so that the reliability of the evaluation result decreases. When there are a plurality of solutions, it is difficult to select a meaningful solution in a program. Furthermore, since a plurality of data of the reflectance and the transmittance are used, each measurement accuracy is easily affected.
[0015]
On the other hand, the latter normal incidence reflectance method (Kramers-Kronig method) is basically unsuitable for measurement and evaluation of thin films. Further, in the case of a thin film, it is necessary to take the effect of multiple reflection, so it is necessary to know an accurate film thickness. Further, when the film thickness is also unknown, the reliability of the converged solution is reduced as in the case of the RT method.
[0016]
Therefore, the present invention makes use of the advantages of the RT method and the Kramers-Kronig method to evaluate the optical constants that can obtain theoretically correct optical constants, such as complex refractive index, by an easily programmable method. It is an object to provide a method and an evaluation device.
[0017]
[Means for Solving the Problems]
<Structure of the Invention>
The method for determining an optical constant according to the first aspect of the present invention is a method for determining a real part of a complex refractive index by an RT method using an arbitrarily assumed film thickness for a light-transmitting substance formed on a transparent substrate. The imaginary part is calculated, the real part of the complex refractive index is calculated from the imaginary part data using the Kramers-Kronig relational expression, and the complex refraction obtained by the RT method is calculated. By comparing the real part of the refractive index with the real part of the complex refractive index calculated from the Kramers-Kronig relation, the validity of the solution of the real part and the imaginary part of the complex refractive index obtained by the RT method Was determined.
[0018]
The method for determining an optical constant according to the second aspect of the present invention is directed to a method for determining an optical constant formed on a transparent substrate with respect to a film surface incident reflectance, a substrate surface incident reflectance, a transmittance and a light transmitting material. The square error between the measured values at two or more wavelengths of the substrate surface incident reflectance in the structure provided with the reflective layer and the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed The imaginary part of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is determined by the RT method, which determines the complex refractive index by determining the combination of solutions that minimize the sum of The real part of the complex refractive index at a plurality of wavelengths is obtained by applying the Kramers-Kronig relation to the imaginary part data at.
[0019]
The method for determining an optical constant according to the third aspect of the present invention comprises:
{Circle around (1)} Measured values at two or more wavelengths out of the substrate surface incident reflectivity, the substrate surface incident reflectivity, the transmittance, and the substrate surface incident reflectivity in a structure in which a reflective layer is provided on a light transmitting material. And an RT method for determining a complex refractive index by determining a combination of solutions that minimize the sum of square errors with calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The thickness d of the light transmissive substance assumed in _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance using _RT And the imaginary part k _RT The process of seeking
(2) The imaginary part k of the complex refractive index at a plurality of wavelengths obtained in the process of (1) _RT Applying the Kramers-Kronig relation to the data of _KK And the thickness d of the light transmitting material _KK The process of calculating
(3) Real part n of the complex refractive index obtained in the process of (1) _RT And the real part n of the complex refractive index calculated in the process of (2) _KK Process of comparing data with
(4) The film thickness d of the light transmitting material calculated in the process of (2) _KK Is the film thickness d _RT This film thickness d regarded as _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is again obtained by the RT method in the process (1) using _RT And the imaginary part k _RT The process of seeking
These processes (1) to (4) are performed by the real part n in the process (3). _KK Data and real part n _RT This is repeated until the wavelength dependence with the data of _KK Data and real part n _RT The complex refractive index obtained when the wavelength dependence with the above data becomes substantially equal is used as the complex refractive index of the light transmitting material.
[0020]
The method for determining an optical constant according to the invention according to claim 4 is directed to a light-transmitting substance formed on a transparent substrate.
{Circle around (1)} Measured values at two or more wavelengths out of the substrate surface incident reflectivity, the substrate surface incident reflectivity, the transmittance, and the substrate surface incident reflectivity in a structure in which a reflective layer is provided on a light transmitting material. And an RT method for determining a complex refractive index by determining a combination of solutions that minimize the sum of square errors with calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The thickness d of the light transmissive substance assumed in _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance using _RT And the imaginary part k _RT The process of seeking
(2) The imaginary part k of the complex refractive index at a plurality of wavelengths obtained in the process of (1) _RT Applying the Kramers-Kronig relation to the data of _KK And the thickness d of the light transmitting material _KK The process of calculating
(3) Real part n of the complex refractive index obtained in the process of (1) _RT And the real part n of the complex refractive index calculated in the process of (2) _KK Process of comparing data with
(4) The film thickness d of the light transmitting material calculated in the process of (2) _KK Is the film thickness d _RT This film thickness d regarded as _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is again obtained by the RT method in the process (1) using _RT And the imaginary part k _RT The process of seeking
These processes (1) to (4) are performed by the real part n in the process (3). _KK Data and real part n _RT This is repeated until the wavelength dependence with the data of _KK Data and real part n _RT The film thickness value obtained when the wavelength dependence with the data of the above was substantially equal was set as the film thickness of the light transmitting substance.
[0021]
According to a fifth aspect of the present invention, there is provided the method for evaluating an optical constant according to the second, third or fourth aspect, wherein the complex refractive index at a plurality of wavelengths is obtained by applying the Kramers-Kronig relational expression to the imaginary part data of the complex refractive index. The process of obtaining the real part of the refractive index is performed by the real part of the complex refractive index at a plurality of wavelengths obtained by the Kramers-Kronig relation from data obtained by multiplying the imaginary part data of the imaginary part of the complex refractive index at a plurality of wavelengths by the RT method. In addition, the integral contribution in the Kramers-Kronig relation from the data in the non-measured wavelength range of the imaginary part data of the complex refractive index at these multiple wavelengths is compensated by a constant addition, and the complex refractive index at the multiple wavelengths is compensated by this constant addition. Of the film surface incident reflectance measured at multiple wavelengths, the substrate surface incident reflectance, the transmittance, and the structure in which a reflective layer is provided on a light-transmitting substance. Any one or more measured values of the plate surface incident reflectivity, a constant multiple of the imaginary part of the complex refractive index at a plurality of wavelengths corresponding to the measured value, and the non-absorption spectrum applied to the real part of the complex refractive index. Film surface incident reflectance, substrate surface incident reflectivity, calculated by assuming arbitrarily a constant addition value that compensates for data in the measurement wavelength range, a structure with a reflective layer provided on a light-transmitting material Compensates for the data of the non-measured wavelength range of the absorption spectrum applied to the real part of the complex refractive index and the constant multiple of the imaginary part data of the complex refractive index at multiple wavelengths where the error with any of the substrate surface incident reflectance is minimized. The real part of the complex refractive index of the light transmissive substance is calculated by calculating a constant addition value.
[0022]
According to a sixth aspect of the present invention, in the method for evaluating an optical constant according to the second, third or fourth aspect, when the real part and the imaginary part of the complex refractive index at a plurality of wavelengths are determined by the RT method, At least transmittance data is used to determine the imaginary part of.
[0023]
An apparatus for evaluating an optical constant according to the invention according to claim 7, comprising: a measuring means for measuring a reflectance and a transmittance in a certain wavelength range with respect to at least a light transmitting substance formed on the transparent substrate; Of the film surface incident reflectance, the substrate surface incident reflectance, the transmittance, and 2 of the substrate surface incident reflectance in the structure in which the reflective layer is provided on the light transmitting material. The complex index of refraction is determined by determining the solution that minimizes the sum of the squared errors between the measured values at one or more wavelengths and the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The imaginary part of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is determined by the RT method, and the Kramers-Kronig relational expression is applied to the imaginary part data of the determined complex refractive index at a plurality of wavelengths. Arithmetic processing means for obtaining the real part of the complex refractive index at the wavelength; Provided.
[0024]
The optical constant evaluation apparatus according to claim 8 is a measuring means for measuring reflectance and transmittance in a certain wavelength range with respect to at least a light transmitting substance formed on a transparent substrate,
For light-transmitting substances formed on transparent substrates,
{Circle around (1)} Measured values at two or more wavelengths out of the substrate surface incident reflectivity, the substrate surface incident reflectivity, the transmittance, and the substrate surface incident reflectivity in a structure in which a reflective layer is provided on a light transmitting material. And an RT method for determining a complex refractive index by determining a combination of solutions that minimize the sum of square errors with calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The thickness d of the light transmissive substance assumed in _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance using _RT And the imaginary part k _RT The process of seeking
(2) The imaginary part k of the complex refractive index at a plurality of wavelengths obtained in the process of (1) _RT Applying the Kramers-Kronig relation to the data of _KK And the thickness d of the light transmitting material _KK The process of calculating
(3) Real part n of the complex refractive index obtained in the process of (1) _RT And the real part n of the complex refractive index calculated in the process of (2) _KK Process of comparing data with
(4) The film thickness d of the light transmitting material calculated in the process of (2) _KK Is the film thickness d _RT This film thickness d regarded as _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is again obtained by the RT method in the process (1) using _RT And the imaginary part k _RT The process of seeking
Are sequentially executed, and the processes of (1) to (4) are executed in the process of (3). _KK Data and real part n _RT This is repeated until the wavelength dependence with the data of _KK Data and real part n _RT And a processing means for setting a complex refractive index obtained when the wavelength dependence with the data of the optical transmission material becomes substantially equal to the complex refractive index of the light transmitting material.
[0025]
The optical constant evaluation apparatus according to the ninth aspect of the present invention is a measuring unit that measures reflectance and transmittance in a certain wavelength range with respect to at least a light-transmitting substance formed on a transparent substrate,
For light-transmitting substances formed on transparent substrates,
{Circle around (1)} Measured values at two or more wavelengths out of the substrate surface incident reflectivity, the substrate surface incident reflectivity, the transmittance, and the substrate surface incident reflectivity in a structure in which a reflective layer is provided on a light transmitting material. And an RT method for determining a complex refractive index by determining a combination of solutions that minimize the sum of square errors with calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The thickness d of the light transmissive substance assumed in _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance using _RT And the imaginary part k _RT The process of seeking
(2) The imaginary part k of the complex refractive index at a plurality of wavelengths obtained in the process of (1) _RT Applying the Kramers-Kronig relation to the data of _KK And the thickness d of the light transmitting material _KK The process of calculating
(3) Real part n of the complex refractive index obtained in the process of (1) _RT And the real part n of the complex refractive index calculated in the process of (2) _KK Process of comparing data with
(4) The film thickness d of the light transmitting material calculated in the process of (2) _KK Is the film thickness d _RT This film thickness d regarded as _RT The real part n of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is again obtained by the RT method in the process (1) using _RT And the imaginary part k _RT The process of seeking
Are sequentially executed, and the processes of (1) to (4) are executed in the process of (3). _KK Data and real part n _RT This is repeated until the wavelength dependence with the data of _KK Data and real part n _RT And an arithmetic processing means for setting a film thickness value obtained when the wavelength dependence with the data of the light transmission material becomes substantially equal to the film thickness of the light transmitting substance.
[0026]
According to a tenth aspect of the present invention, in the optical constant evaluation apparatus according to the seventh, eighth or ninth aspect, the arithmetic processing means applies a Kramers-Kronig relational expression to the imaginary part data of the complex refractive index. The process of obtaining the real part of the complex refractive index at a wavelength is a complex refraction at a plurality of wavelengths obtained by the Kramers-Kronig relation from data obtained by multiplying the imaginary part data of the complex refractive index at a plurality of wavelengths by the RT method. In the real part of the index, the integral contribution in the Kramers-Kronig relation from the data of the unmeasured wavelength range of the imaginary part data of the complex refractive index at these multiple wavelengths is compensated for by constant addition. The real part of the complex index of refraction is determined at the film surface incident reflectivity, substrate surface incident reflectivity, transmittance, The measured value of any one or more of the substrate surface incident reflectance in the structure having the layer, the constant multiple of the imaginary part of the complex refractive index and the real part of the complex refractive index at a plurality of wavelengths corresponding to the measured value. Reflection on film-surface incident reflectance, substrate incident reflectance, transmittance, light-transmitting material calculated by arbitrarily assuming a constant addition value that compensates for data in the non-measureable wavelength range of the absorption spectrum to be applied The constant multiple of the imaginary part data of the complex refractive index and the absorption spectrum applied to the real part of the complex refractive index at a plurality of wavelengths where the error with any of the substrate surface incident reflectances in the structure having the layer is minimized. This is a process of calculating the real part of the complex refractive index of the light-transmitting substance by obtaining a constant addition value for compensating the data in the measurement wavelength range.
[0027]
According to an eleventh aspect of the present invention, in the optical constant evaluation apparatus according to the seventh, eighth or ninth aspect, the real-time part and the imaginary part of the complex refractive index at a plurality of wavelengths are obtained by the arithmetic processing means by the RT method. , At least the transmittance data is used to determine the imaginary part of the complex refractive index.
[0028]
<Principle of the invention>
Basically, the real part and the imaginary part of the complex refractive index are obtained by the RT method using an arbitrarily assumed film thickness, and the correctness of the obtained solution of the real part and the imaginary part is determined by Krammers. -Judgment is made using the Kronig equation.
[0029]
More specifically, the real part and the imaginary part of the complex refractive index are obtained by the RT method using an arbitrarily assumed film thickness, and the obtained real parts are determined. The real part of the complex refractive index is calculated from the imaginary part data using the Kramers-Kronig relation between the imaginary part and the imaginary part, and from the real part of the complex refractive index obtained by the RT method and the Kramers-Kronig relation By comparing the calculated real part of the complex refractive index with the real part, the validity of the solution of the complex refractive index obtained by the RT method can be selected. Determine the validity of the solution obtained.
[0030]
Here, processing is performed on the basis of the imaginary part of the complex refractive index obtained by the RT method. However, in the case of the RT method, the imaginary part data of the complex refractive index greatly depends on the film thickness. No change (the absolute value fluctuates but the shape does not change significantly with the film thickness), and the difference between the multiple optimal solutions is small and a constant value is obtained. This is for the purpose of use.
[0031]
On the other hand, in the RT method, the real part of the complex refractive index has a large film thickness dependence, and the value difference between a plurality of optimal solutions is large. Accuracy is extremely required, but in reality, the film thickness is considered to vary considerably depending on the parallelism of the substrate, the deposition method, and conditions, and it is very difficult to obtain an accurate value. It is. For this reason, the RT method is considered unsuitable for use in determining the real part of the complex refractive index. However, if an accurate film thickness value can be obtained by the RT method, the complex refractive index (both real and imaginary parts) can be accurately obtained.
[0032]
That is, in the RT method, if a different film thickness value is used for the original film thickness value, the relationship between the imaginary part k and the real part n of the complex refractive index deviates from the theory (generally, Since the wavelength dependence curve of the imaginary part of the complex refractive index has little film thickness dependence, the wavelength dependence of the real part n of the complex refractive index with respect to the wavelength dependence of the imaginary part k of the complex refractive index deviates from the theory. May be). Therefore, if the complex refractive index is obtained in a certain wavelength range by changing the film thickness (wavelength dependence of the complex refractive index), the complex refractive index is theoretically correct for the imaginary part of the complex refractive index only when the film thickness is accurate. The real part solution of the rate will be obtained.
[0033]
Thus, when the real part solution of the complex refractive index is theoretically correct for the imaginary part of the complex refractive index, it means that the correct film thickness value and the complex refractive index value are obtained.
[0034]
However, as described above, calculating the wavelength dependence of the complex refractive index by changing the film thickness for each film thickness value is extremely troublesome and troublesome due to the existence of a plurality of solutions. It is a difficult matter.
[0035]
On the other hand, in the case of the Kramers-Kronig method of determining the complex refractive index using the Kramers-Kronig relational expression, if the real part or the imaginary part of the complex refractive index is known, the other value ( The imaginary part or the real part) has an advantage that it can be uniquely and accurately obtained. However, when the Kramers-Kronig relational expression is used, usually, measurement data in a finite wavelength range is used, and therefore, there is a problem that the accuracy of the measurement data decreases near both ends of the measurement wavelength.
[0036]
Considering these points comprehensively, ideally, it is sufficient if the complex refractive index can be calculated by the RT method. At this time, it can be said that what is required is an accurate film thickness value. Therefore, in the present invention, in order to efficiently determine the complex refractive index by the RT method, the real part evaluation and the imaginary part evaluation of the complex refractive index are made independent, and the imaginary part of the complex refractive index is obtained by the RT method. Using the obtained imaginary part data, the complex refractive index and the film thickness were determined from the Kramers-Kronig relational expression. The method of using the Kramers-Kronig relation is easily programmable. At this time, if the wavelength dependence of the real part of the complex refractive index obtained by the RT method and the real part of the complex refractive index calculated by the Kramers-Kronig relation substantially match, an accurate solution is given by R- It can be considered that it is obtained by the T method.
[0037]
By the way, when the Kramers-Kronig relation is used, it is theoretically accurate as described above, and if the real part or the imaginary part of the complex refractive index is known, the other value can be uniquely and accurately obtained. However, on the other hand, a measurement wavelength range of 0 to 要求 is required for the real or imaginary part of the complex refractive index, which must be known, and if the measurement wavelength range is limited, the accuracy of the calculated value also increases. There is a disadvantage that it is reduced. In the present invention, taking this point into consideration, a compensation method for obtaining a relatively accurate real part of the complex refractive index from the imaginary part data of the complex refractive index in a limited wavelength range is also provided as the invention according to claim 3. I have.
[0038]
That is, according to the present invention, the RT method cannot accurately calculate the real part of the complex refractive index, and the method using the Kramers-Kronig relational expression is one of the real part and the imaginary part of the complex refractive index. The disadvantage is that the other value cannot be calculated without knowing it.
[0039]
Furthermore, according to the present invention, the real part of the complex refractive index is determined using the arbitrarily assumed film thickness value used for obtaining the imaginary part of the complex refractive index by the RT method and the Kramers-Kronig relational expression. Since it is assumed that an accurate complex refractive index is calculated when the obtained film thickness value is the same as the calculated value, the optical constant to be evaluated is set to be equal to the film thickness. It can also be applied to Thus, the arbitrarily assumed film thickness value used for obtaining the imaginary part of the complex refractive index by the RT method and the real part of the complex refractive index obtained by using the Kramers-Kronig relational expression are obtained. The basis that can be assumed that an accurate complex refractive index is calculated when the calculated film thickness value is the same is that by using the complex refractive index and the film thickness value calculated by the method of the present invention, The measured values such as the surface incident reflectivity are almost the same as the calculated values, and the approximation adopted by the method of determining the real part of the complex refractive index using the Kramers-Kronig relational expression gives a highly reliable verification result. Furthermore, the complex refractive index obtained by the RT method only with the finally obtained film thickness value and the complex refractive index value calculated using the Kramers-Kronig relational expression But the real part and the imaginary part are almost the same. That.
[0040]
BEST MODE FOR CARRYING OUT THE INVENTION
An embodiment of the present invention will be described with reference to FIGS. This embodiment is for evaluating the complex refractive index and the film thickness of the light transmitting substance 2 formed on the transparent substrate 1 as shown in FIG. A measuring device 3 (measuring means) capable of measuring the reflectance and transmittance in a certain wavelength range, and a predetermined value obtained by using a measured value obtained from the measuring device 3 or a pre-programmed Kramers-Kronig equation. And a computer 4 (arithmetic processing means) for performing the arithmetic processing.
[0041]
In the method for evaluating a complex refractive index according to the present embodiment, the following assumption A and approximation B are used.
[0042]
A. The imaginary part of the complex refractive index is obtained by the RT method.
At this time, it is necessary to know the thickness of the measurement substance (light-transmitting substance 2), but it may be set arbitrarily to some extent.
[0043]
B. In order to accurately evaluate the real part of the complex refractive index from the imaginary part data of the complex refractive index in the limited wavelength region, the wavelength region is divided into three as follows,
Region 1. ∞ to λ _a (Non-measurable area, unmeasurable area)
Region 2. λ _a ~ Λ _b (Measurement area)
Region 3. λ _b ０0 (non-measurable area, unmeasurable area)
The integral contribution of the areas 1 and 3 is replaced with a constant as shown in the equation (6).
[0044]
(Equation 5)

[0045]
Assumption A is one of the most important items in the present embodiment, and among the complex refractive indices obtained by the RT method, the real part is greatly affected by the film thickness value, while the imaginary part is the This is based on the fact that the influence can be made very small. In other words, even when there are a plurality of optimal solutions, the real part can easily take a wide range of values, but the imaginary part can be almost constant.
[0046]
In order to obtain such an imaginary part of the complex refractive index, it is preferable to use transmittance data in the RT method. This is because the transmittance is affected by reflection but is basically determined by the absorption of the film, that is, the size of the imaginary part of the complex refractive index. For this reason, assuming a certain film thickness, when a set of solutions of the real part and the imaginary part of the complex refractive index that matches the measured transmittance data is calculated, the imaginary part dependence of the solution that matches the measured data is obtained. Is very small.
[0047]
Specifically, the solution of the imaginary part of the complex refractive index obtained by the RT method is as shown in FIG. This is due to the calculation results (measurement data and data) when assuming that the film material of the light transmitting substance 2 is 87 nm in thickness of Oxo [5,10,15,20-tetra (4-pyridyl) porphinato] titanium (IV). FIG. 2 (a) shows a case where the wavelength is 500 nm, and FIG. 2 (b) shows a case where the wavelength is 600 nm. Is shown. In the figure, the horizontal axis represents the real part of the complex refractive index, and the vertical axis represents the imaginary part of the complex refractive index.
[0048]
As is clear from FIG. 2, the solution curve of the complex refractive index for matching the measured transmittance data does not depend much on the imaginary part of the complex refractive index. For example, in the case of a wavelength of 500 nm shown in FIG. 2A, the complex refractive index of this film material is a solution near 0.5-i * 0 and 3.2-i * 0. It can be seen that the imaginary part is not significantly affected by which solution is selected. By the way, even if a plurality of solutions are obtained in the same way using the film surface incident reflectance and the substrate surface incident reflectance, the imaginary part has almost the same value, but by using the transmittance data as described above, It is possible to further reduce the dependence of the imaginary part on the film thickness and the difference between the imaginary part values of a plurality of solutions. (Using only the film-surface incident reflectance and the substrate-surface incident reflectance, the error becomes Although it can greatly affect the imaginary part, using the transmittance data together can reduce the effect of the error on the imaginary part.)
[0049]
In the approximation B, in the long wavelength region of the region 3, the absorption becomes almost zero and can be ignored. Therefore, it is necessary to consider the treatment of the absorption in the region 1. Thus, FIG. 3 shows the results of examining the validity of converting the contribution of integration from absorption outside the measurement wavelength region into a constant. The wavelength range of 200 to 900 nm is actually measured data, and the wavelength range of 0 to 200 nm is data arbitrarily assumed. The data arbitrarily assumed for the wavelength range of 0 to 200 nm is made variable by a multiple a (constant) and is made continuous with the actually measured data of the wavelength range of 200 to 900 nm. FIG. 3A shows a case where the multiple a = 1.0, and FIG. 3B shows a case where the multiple a = 2.0.
[0050]
The real part n is obtained using such absorption data. FIG. 4 shows the result of studying the effect of the data loss in the wavelength range of 0 to 200 nm on the calculated real part n. FIG. 4A shows the case where the absorption data in the wavelength range of 0 to 200 nm is included in the calculation under the condition that the multiple a = 1.0, and FIG. 4B ignores the absorption data in the wavelength range of 0 to 200 nm. The calculation results of the real part n of the complex refractive index in each case are shown, and FIG. 4C shows these at the same time. FIG. 5 shows the difference Δn between these two calculation results.
[0051]
According to such examination results, it can be seen that the influence of ignoring the absorption data in the wavelength range of 0 to 200 nm is greater on the short wavelength side, but the difference Δn = 400 between the wavelengths of 400 nm and 800 nm. It is about 0.1, and it seems that there is not much effect even when approximation with constant addition is performed. FIG. 4C also shows that the influence of the absorption band in the wavelength range of 0 to 200 nm hardly affects the shape of the real part of the complex refractive index.
[0052]
Next, FIG. 6 shows the result of study of the influence of the magnitude of absorption in the wavelength range of 0 to 200 nm. Here, whether or not it is appropriate to add a constant to the value of the real part n calculated from data in a limited wavelength range regardless of the magnitude of absorption in the wavelength range of 0 to 200 nm is examined. FIG. 6A shows the difference between the value of the real part n calculated when the absorption data at the wavelength 451 nm and the absorption data at the wavelength 0 to 200 nm are ignored and the absorption magnitude a at the wavelength 0 to 200 nm is calculated. FIG. 6B is calculated when the absorption data in the wavelength range of 0 to 200 nm at the wavelength of 800 nm with respect to the absorption magnitude a in the wavelength range of 0 to 200 nm is ignored and when the absorption data is incorporated. FIG. 6C is a diagram in which the difference between the values of the real part n is plotted, and FIG.
[0053]
As a result, regardless of the size of the absorption band having a wavelength of 0 to 200 nm, a constant is uniformly added to the value of the real part n calculated from the absorption data obtained from the limited wavelength range. This shows that a somewhat accurate complex refractive index can be obtained.
[0054]
The specific calculation method is as follows.
(1) Arbitrarily assumed film thickness d _RT The real part n of the complex refractive index is obtained by the RT method using _RT And the imaginary part k _RT And ask.
(2) The calculated imaginary part k _RT Value k multiplied by a constant a _RT By using (a) to perform the integration in the Kramers-Kronig dispersion relation, the real part n of the complex refractive index is obtained. _KK (A) 'is calculated (KK conversion method).
(3) Calculated real part n _KK (A) 'is a constant n as an integral contribution from the non-measurement wavelength region. _add Are added, and a constant a and a constant n _add N that minimizes the difference between the film-surface incident reflectance and the measured value of the film-surface incident reflectance calculated by arbitrarily setting the thickness and the film thickness. _add And value a, film thickness d _KK And determine these values n _add , A finally the real part n of the corrected complex refractive index from the Kramers-Kronig relation _KK (A) is obtained. Where the real part n _RT And this real part n _KK Is approximately the same wavelength dependence and value, this gives the complex refractive index n (λ) -i * k (λ) of the film. At this time, the real part of the complex refractive index n (λ) -i * k (λ) of the film may use the result of the RT method or a value obtained by KK conversion.
▲ 4 ▼ Real part n _RT And real part n _KK Is significantly different from the film thickness d _KK The imaginary part of the complex refractive index is obtained by the RT method using _RT And real part n _KK The processes (2) and (3) are repeated until is substantially the same to finally obtain the complex refractive index n (λ) -i * k (λ) of the film. Also in this case, the real part of the complex refractive index n (λ) -i * k (λ) of the film may use the result of the RT method or a value obtained by the KK conversion.
[0055]
Note that the constant n is used as an integral contribution from the non-measurement wavelength region. _add May be used as a linear function of wavelength. In this method (assumed), as shown in FIGS. 5 and 6 (c), the integral contribution from the non-measurement wavelength region on the short wavelength side increases as the wavelength becomes shorter in the wavelength region where the complex refractive index is to be known. As the wavelength increases, it decreases almost linearly, and as the absorption component in the non-measurement wavelength region on the short wavelength side increases, the integral contribution from the non-measurement wavelength region on the short wavelength side is the wavelength at which one wants to know the complex refractive index. Shorter wavelengths in the region are larger and decrease almost linearly with longer wavelengths, thereby ensuring their validity.
[0056]
【Example】
An example of the present invention based on the above embodiment will be described with reference to FIGS. In this example, a sample was prepared by dissolving a porphyrazine derivative in chloroform and forming a thin film on a quartz substrate by spin coating. For such a sample, the absorbance, the film surface incident vertical reflectance, the substrate surface incident reflectance and the transmittance are measured, and the measured values of the film surface incident perpendicular reflectance, the substrate surface incident reflectance and the transmittance are measured. The complex refractive index was calculated by the RT method assuming a film thickness of 27 nm. FIG. 7A shows the measured values of the absorbance, FIG. 7B shows the measured values of the vertical reflectance on the film surface, FIG. 7C shows the measured values of the reflectance on the substrate surface, and FIG. Yes, and the horizontal axis shows the wavelength. In the calculation program of the RT method, the data on the film surface incident vertical reflectance, the substrate surface incident reflectance, and the transmittance are corrected for the influence of the substrate, and are shown in FIGS. 7B to 7D. , The data before correction and the data after correction are shown.
[0057]
FIG. 8A is a diagram showing a calculation result of a complex refractive index by the RT method. That is, although the complex refractive index is shown assuming that the film thickness is arbitrarily set to 27 nm, the imaginary part of the complex refractive index is similar to the wavelength dependence of the absorbance data shown in FIG. 2 shows the reliability of the imaginary part of the complex refractive index obtained from the assumed film thickness. FIG. 8B is an enlarged view of the vertical axis of FIG. In FIG. 8A, it can be seen that the real part of the complex refractive index with respect to the imaginary part of the complex refractive index shows a theoretically abnormal relationship in the wavelength region around 200 to 300 nm. This suggests that the film thickness of 27 nm used in the RT method is not appropriate.
[0058]
Next, based on the data of the imaginary part of the complex refractive index shown in FIG. 8A, the real part of the complex refractive index was calculated using the Kramers-Kronig relational expression. At the time of this calculation, a constant multiple value a that is uniformly applied to the imaginary part of the complex refractive index shown in FIG. 8A over all wavelengths and a non-measured wavelength of the data of the imaginary part of the complex refractive index (specifically, It is a wavelength of 200 nm or less, and wavelength data of 800 nm or more is missing, but it is not necessary to consider the porphyrazine derivative compound since it does not have an absorption band for wavelengths of 800 nm or more.) A constant multiplication value n added to the real part of the complex refractive index to uniformly correct the wavelength _add Further, with the film thickness value as a parameter, the square error at each wavelength between the film surface normal incidence reflectance calculated when this parameter is arbitrarily assumed and the actually measured film surface normal incidence reflectance is calculated. The imaginary part of the complex refractive index that minimizes the sum is uniformly multiplied by a constant value a that is multiplied by all wavelengths, and the integral contribution of the imaginary part of complex refractive index from the unmeasured wavelength region is uniformly corrected by all wavelengths. Constant n added to the real part of the complex index of refraction _add , And a film thickness value.
[0059]
At this time, the constant multiple value a for uniformly multiplying the imaginary part of the complex refractive index over the entire wavelength is 0.5, and the integral contribution from the non-measurement wavelength region of the imaginary part of the complex refractive index is uniformly corrected over the entire wavelength. Added constant n to the real part of the complex index of refraction _add Is 1.5 and the film thickness is 48 nm. FIG. 9 shows a complex refractive index obtained by calculation using such a Kramers-Kronig relational expression.
[0060]
When the real part is obtained from the imaginary part of the complex refractive index using the Kramers-Kronig relational expression, the imaginary part data has a limited wavelength range of 200 to 800 nm. Despite correcting the integral contribution from the non-measurement wavelength region of the data of the portion, a value near 200 nm does not show a correct value. This is because the real part of the complex refractive index near the wavelength of 200 nm is strongly influenced by the value (value change) of the imaginary part of the complex refractive index near the wavelength of 200 nm. This is because the data of the refractive index is lost (the real result of the complex refractive index at a wavelength of 800 nm is considered to be 0 because the imaginary part of the complex refractive index at a wavelength of 800 nm or more is 0). Therefore, the wavelength range in which the real part of the complex refractive index is calculated from the Kramers-Kronig relation is in the range of 350 to 800 nm.
[0061]
As in the above-described procedure of the calculation routine of the present invention, the real part of the complex refractive index by the RT method as shown in FIG. 8 and the real part of the complex refractive index obtained from the Kramers-Kronig relation as shown in FIG. There are some differences when compared to parts. This is evident from FIG. 10 (a), which shows both of them, and FIG. 10 (b), which shows only the real part thereof in an enlarged scale. The sum of the square errors of the real part of the refractive index and the real part of the complex refractive index obtained from the Kramers-Kronig relation is 1.710 (see Table 1). As a result, it can be determined that the solution of the complex refractive index by the RT method shown in FIG. 8 is not a convergent solution and is not a correct value.
[0062]
[Table 1]

[0063]
Subsequently, the complex refractive index was calculated again by the RT method using the film thickness value of 48 nm obtained by using the Kramers-Kronig relational expression as described above. The result is shown in FIG. 11A, and an enlarged view thereof is shown in FIG. According to this result, it can be seen that the relationship between the real part and the imaginary part of the complex refractive index in the 200 to 300 nm wavelength region, which was abnormal in FIG. 8, is correct.
[0064]
Thereafter, based on the data of the imaginary part of the complex refractive index as shown in FIG. 11, the real part of the complex refractive index was calculated again using the Kramers-Kronig relational expression. At the time of this calculation, a constant multiple value a that is uniformly applied to the data of the imaginary part of the complex refractive index as shown in FIG. 11 over the entire wavelength and the non-measurement wavelength region of the imaginary part data of the complex refractive index (specifically, Is the wavelength of 200 nm or less, and the wavelength data of 800 nm or more is missing, but it is not necessary to consider the compound of the porphyrazine derivative since it does not have an absorption band for the wavelength of 800 nm or more.) Is added to the real part of the complex index of refraction in order to uniformly compensate for all wavelengths. _add Further, with the film thickness value as a parameter, the square error at each wavelength between the film surface normal incidence reflectance calculated when this parameter is arbitrarily assumed and the actually measured film surface normal incidence reflectance is calculated. The imaginary part of the complex refractive index that minimizes the sum is uniformly multiplied by a constant value a that is multiplied by all wavelengths, and the integral contribution of the imaginary part of complex refractive index from the unmeasured wavelength region is uniformly corrected by all wavelengths. Constant n added to the real part of the complex index of refraction _add , And a film thickness value.
[0065]
At this time, the constant multiple value a for uniformly multiplying the imaginary part of the complex refractive index over the entire wavelength is 0.5, and the integral contribution from the non-measurement wavelength region of the imaginary part of the complex refractive index is uniformly corrected over the entire wavelength. Added constant n to the real part of the complex index of refraction _add Is 1.5 and the film thickness is 48 nm. FIG. 12 shows a complex refractive index obtained by calculation using such a Kramers-Kronig relational expression.
[0066]
As in the procedure of the calculation routine of the present invention described above, the real part of the complex refractive index by the RT method as shown in FIG. 11 and the real part of the complex refractive index obtained from the Kramers-Kronig relation as shown in FIG. Comparing with the section, it can be seen that the wavelength dependence substantially coincides with the absolute value. This is evident from FIG. 13 (a) which shows both of them simultaneously and FIG. 13 (b) which shows only the real part thereof in an enlarged manner. In the wavelength region of 200 to 800 nm, the complex method by the RT method for every 10 nm is used. The sum of the square errors of the real part of the refractive index and the real part of the complex refractive index obtained from the Kramers-Kronig relation is 8.595 × 10 ° ³ (See Table 2). As a result, the solution of the complex refractive index by the RT method shown in FIG. 11 is a convergent solution, and it can be determined that a correct value has been calculated.
[0067]
[Table 2]

[0068]
Further, an optimum film thickness value calculated by the Kramers-Kronig relational expression from a film thickness value when the complex refractive index is obtained by the RT method and data of an imaginary part of the complex refractive index obtained by the film thickness value. Also, it is considered that the complex refractive index obtained in FIG. 11 has high reliability.
[0069]
Further, the measured values of the film surface normal incidence reflectance and the film surface incidence reflectance calculated using the complex refractive index and the film thickness value of 48 nm obtained in FIG. 11 are almost completely as shown in FIG. This is consistent with the result showing that the reliability of the complex refractive index and the film thickness value obtained by the present embodiment is high.
[0070]
Here, assuming that the film thickness is initially 27 nm, the film surface normal incidence reflectance, the substrate surface normal incidence reflectance, and the substrate surface normal incidence reflectance for each of the wavelengths 200, 300, 400, 500, 600, and 700 nm obtained by the RT method. The solution curve of the film surface normal incidence transmittance is shown in FIG. 15 (in FIG. 15, (a) is for a wavelength of 200 nm, (b) is for a wavelength of 300 nm, (c) is for a wavelength of 400 nm, and (d) is (E) shows a case of a wavelength of 600 nm, and (f) shows a case of a wavelength of 700 nm.
[0071]
Similarly, the film-surface normal incidence reflectance, substrate-surface normal incidence reflectance, and substrate surface normal incidence reflectance for each of the wavelengths 200, 300, 400, 500, 600, and 700 nm obtained by the RT method assuming that the film thickness is initially 48 nm. FIG. 16 shows a solution curve of the normal incidence transmittance of the film surface. In FIG. 16, (a) is a wavelength of 200 nm, (b) is a wavelength of 300 nm, (c) is a wavelength of 400 nm, and (d) is (E) shows a case of a wavelength of 600 nm, and (f) shows a case of a wavelength of 700 nm.
[0072]
From these results, it is not clear at the initial arbitrarily assumed film thickness that the intersection (that is, the solution) where the film surface normal incidence reflectance, the substrate surface normal incidence reflectance, and the film surface normal incidence transmittance intersect is not clear. It can be seen that the reliability is low, but when the film thickness value of 48 nm obtained using the Kramers-Kronig relation is used, the film surface normal incidence reflectance, the substrate surface normal incidence reflectance, and the film surface normal incidence transmittance It is supposed that the intersection of and was clear, and that the reliability of the solution was very high.
[0073]
As described above, even by the RT method, the assumed film thickness value can be determined based on the state of the intersection of the film surface normal incidence reflectance, the substrate surface normal incidence reflectance, and the film surface normal incidence transmittance. -When only the T method is used, the film thickness value must be changed in a dark cloud, and the calculation efficiency is extremely low. However, as in the present invention or the embodiment, the combined use of the Kramers-Kronig relational expression is required. As a result, the optimum film thickness can be easily obtained, and the calculation efficiency is greatly increased. That is, as is apparent from the present embodiment, when searching for the optimum film thickness only by the RT method, no information on the true film thickness value can be obtained at all from the complex refractive index obtained at a certain film thickness value. Because it is not possible to evaluate the complex refractive index by changing the film thickness value in dark clouds, or to evaluate the complex refractive index steadily by changing the film thickness every few nm, the Kramers-Kronig relational expression By using them together, the optimum film thickness can be easily found. Therefore, highly efficient and highly reliable optical constants (complex refractive index and film thickness) can be determined.
[0074]
By the way, based on the above-described embodiments or examples of the present invention, two important assumptions of the present invention are given.
-The imaginary part of the complex refractive index obtained by the RT method does not change much depending on the film thickness and the method of selecting the optimum solution from a plurality of existing solutions.
-Since the real part of the complex refractive index obtained by the RT method varies greatly depending on the film thickness and the method of selecting the optimal solution from among a plurality of existing solutions, the method of evaluating the complex refractive index using only the RT method Involves uncertainty
Verified that this is the case.
[0075]
17 (a) to 17 (f) show the results of the verification. In FIG. 17, (a) is 92 nm thick, (b) is 87 nm thick, (c) is 82 nm thick, and (d) is (E) shows the wavelength dependence of the real part n and the imaginary part k of the complex refractive index when the film thickness is 81 nm, (e) shows the film thickness of 77 nm, and (f) shows the film thickness of 70 nm. According to FIG. 17, it can be seen that even when the film thickness changes, the imaginary part k of the complex refractive index hardly changes, and a constant solution is obtained. FIG. 18 simultaneously shows the imaginary part of the complex refractive index obtained by the RT method at each film thickness shown in FIGS. 17A to 17F for the sake of clarity. It can be clearly seen that the data of the imaginary part hardly changes even if the film thickness changes.
[0076]
In other words, even if an arbitrarily assumed film thickness value is used, the imaginary part of the complex refractive index obtained from the RT method is compensated to some extent, so that it can be obtained from the Kramers-Kronig relational expression using this value. Both the complex refractive index and the film thickness value ensure high reliability, and the solution easily converges in the calculation routine presented in the present invention.
[0077]
On the other hand, the real part of the complex refractive index is greatly influenced by the film thickness or the method of selecting an optimal solution from a plurality of existing solutions, and the RT method is not suitable for evaluating the real part of the complex refractive index. I understand. In other words, it can be said that the real part of the complex refractive index obtained from the RT method indicates the calculation reliability of the RT method.
[0078]
【The invention's effect】
The present invention relates to an RT method having a characteristic that an imaginary part of a complex refractive index does not depend much on the film thickness and a difference between values of a plurality of optimal solutions is small and an almost constant value is obtained as described above. If the imaginary part of the complex refractive index is known, the real part is unambiguously assumed to be the film thickness by using a method that uses the Kramers-Kronig relation that has characteristics that can be theoretically accurately obtained. Is used to determine the real part and the imaginary part of the complex refractive index by the RT method, and the validity of the solution of the determined real part and the imaginary part is determined using the Kramers-Kronig relational expression. Since a method or apparatus for determining an optical constant such as a film thickness is provided, the reliability of the imaginary part of the complex refractive index used for the KK conversion in the Kramers-Kronig relation can be guaranteed to some extent. Can be accelerated, and By using the Maas-Kronig relation in combination, the real part of the complex refractive index does not need to determine the real part and the imaginary part independently for each wavelength as in the RT method, and the chromatic dispersion can be evaluated correctly. Since the real part of the complex refractive index does not take an abnormal value unlike the RT method, the optimum film thickness can be easily obtained. Further, since the convergence of the solution can be quantitatively determined, the program A calculation compensation method that is easy to create, can increase the reliability of operation, and provides a relatively accurate real part of the complex refractive index from the imaginary part data of the complex refractive index in a limited wavelength range is also provided. Since it is sufficient to determine a predetermined constant, there is an effect that the program configuration can be simplified.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating an outline of an optical constant evaluation apparatus according to an embodiment of the present invention.
FIG. 2 is a characteristic diagram showing various solution curves obtained by the RT method.
FIG. 3 is a characteristic diagram showing measured values of a real part of a complex refractive index with a change in a constant a.
FIG. 4 is a characteristic diagram showing the effect of data loss depending on the presence or absence of absorption data.
FIG. 5 is a characteristic diagram showing a difference between two calculation results.
FIG. 6 is a characteristic diagram showing validity of adding a constant.
FIG. 7 is a characteristic diagram showing measurement results such as absorbance, reflectance, and transmittance of a sample according to an example of the present invention.
FIG. 8 is a characteristic diagram showing a calculation result using an RT method for a measured value.
FIG. 9 is a characteristic diagram showing a complex refractive index calculated by the Kramers-Kronig relational expression.
FIG. 10 is a characteristic diagram showing a comparison between calculation results of the RT method and a method based on the Kramers-Kronig relational expression.
FIG. 11 is a characteristic diagram showing a calculation result obtained by using the RT method again for the calculated value.
FIG. 12 is a characteristic diagram showing a complex refractive index calculated again by the Kramers-Kronig relational expression.
FIG. 13 is a characteristic diagram showing the results of comparison between the RT method again and the method using the Kramers-Kronig relation again, in comparison with each other.
FIG. 14 is a characteristic diagram showing the coincidence between the measured value and the calculated value of the film surface normal incidence reflectance.
FIG. 15 is a characteristic diagram showing various solution curves calculated by the RT method when the wavelength is variously changed assuming a film thickness of 27 nm.
FIG. 16 is a characteristic diagram showing various solution curves calculated by the RT method when the wavelength is variously changed assuming a film thickness of 48 nm.
FIG. 17 is a characteristic diagram showing how the complex refractive index changes when the film thickness is variously changed.
FIG. 18 is a characteristic diagram showing that the imaginary part of the complex refractive index does not depend on the film thickness.
FIG. 19 is a characteristic diagram showing a relationship between a complex refractive index and a calculated value only by a conventional RT method.
[Explanation of symbols]
1 Transparent substrate
2 Light transmitting material
3 Measurement means
4 Arithmetic processing means

Claims (11)

The real part and the imaginary part of the complex refractive index are obtained by the RT method using an arbitrarily assumed film thickness for the light-transmitting substance formed on the transparent substrate. The real part of the complex refractive index was calculated from the imaginary part data using the Kramers-Kronig relation, and the real part of the complex refractive index and the Kramers-Kronig relation calculated by the RT method were calculated. A method for determining an optical constant by comparing the real part of the complex refractive index with the real part to determine the validity of the solution of the real part and the imaginary part of the complex refractive index obtained by the RT method. For a light-transmitting substance formed on a transparent substrate, the film-surface incident reflectance, the substrate-surface incident reflectance, the transmittance, the substrate-surface incident reflectance in a structure in which a reflective layer is provided on the light-transmitting substance Determining a solution combination that minimizes the sum of squared errors between measured values at two or more of the wavelengths and calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The imaginary part of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is obtained by the RT method, and the Kramers-Kronig relational expression is calculated with respect to the imaginary part data at the plurality of wavelengths of the complex refractive index. An evaluation method of an optical constant which is applied to obtain a real part of a complex refractive index at a plurality of wavelengths. For light-transmitting substances formed on transparent substrates,
(1) Measurement at two or more wavelengths among two or more of the film surface incident reflectance, the substrate surface incident reflectance, the transmittance, and the substrate surface incident reflectance in a structure in which a reflective layer is provided on the light transmitting material. By the RT method of determining the complex refractive index by determining the combination of the solution and the solution that minimizes the sum of the square errors of the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed, The process of obtaining the real part n _RT and the imaginary part k _RT of the complex refractive index at a plurality of wavelengths of the light transmitting substance using the film thickness d _RT of the light transmitting substance arbitrarily assumed is as follows: The real part n _KK of the complex refractive index at a plurality of wavelengths and the film thickness d _{KK of the} light transmissive material are obtained by applying the Kramers-Kronig relation to the data of the imaginary part k _RT of the complex refractive index at the plurality of wavelengths. Is calculated by the process of (3) and (1). And data of the real part n _RT of the complex refractive index that was calculated by the ▲ 2 ▼ process ▲ 4 compares the data of the calculated real part n _KK of the complex refractive index in the process of ▼ ▲ 2 ▼ Process The film thickness d _KK of the light transmitting material is regarded as the film thickness d _RT, and the film thickness d _{RT of the} light transmitting material is used again by the _RT method in the process (1) using the film thickness d _RT considered. a process for obtaining the real part n _RT and the imaginary part k _RT of the complex refractive index at a plurality of wavelengths, these ▲ 1 ▼ ~ ▲ 4 ▼ processes, ▲ 3 ▼ real part n _KK data and real in the process of Repeat until the wavelength dependence of the parts n _RT data are substantially equal, the complex refractive index obtained when the wavelength dependency was substantially equal with those of the real part n _KK data and the real part n _RT data Evaluation of optical constants to be used as the complex refractive index of the light transmitting material Method. For light-transmitting substances formed on transparent substrates,
(1) Measurement at two or more wavelengths among two or more of the film surface incident reflectance, the substrate surface incident reflectance, the transmittance, and the substrate surface incident reflectance in a structure in which a reflective layer is provided on the light transmitting material. By the RT method of determining the complex refractive index by determining the combination of the solution and the solution that minimizes the sum of the square errors of the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed, Process of obtaining a real part n _RT and an imaginary part k _RT of a complex refractive index at a plurality of wavelengths of the light transmitting material using the film thickness d _RT of the light transmitting material arbitrarily assumed. Applying the Kramers-Kronig relation to the data of the imaginary part k _RT of the complex refractive index at a plurality of wavelengths obtained in the above, the real part n _KK of the complex refractive index at a plurality of wavelengths and the film thickness d of the light transmitting material in the process ▲ 3 ▼ ▲ 1 ▼ process of calculating the _KK And data of the real part n _RT eyes was complex refractive index is calculated by ▲ 2 ▼ process ▲ 4 compares the data of the calculated real part n _KK of the complex refractive index in the process of ▼ ▲ 2 ▼ Process The thickness d _KK of the light transmissive material thus determined is regarded as a film thickness d _RT, and the light transmissive material is again used by the _RT method in the process (1) using the film thickness d _RT considered. _Has a process of calculating the real part n _RT and the imaginary part k _RT of the complex refractive index at a plurality of wavelengths. The processes of (1) to (4) are _{replaced with} the data of the real part n _KK in the process of (3). Repeat until the wavelength dependence of the real part n _RT data are substantially equal, the film thickness value wavelength dependency of these real part n _KK data and the real part n _RT data obtained when substantially equal Method for evaluating optical constants such that is set to the thickness of the light-transmitting substance The process of applying the Kramers-Kronig relation to the imaginary part data of the complex refractive index to obtain the real part of the complex refractive index at multiple wavelengths is as follows.
From the constant multiple data of the imaginary part data of the complex refractive index at a plurality of wavelengths obtained by the RT method, the real part of the complex refractive index at a plurality of wavelengths obtained by the Kramers-Kronig relational expression is converted into the complex refraction at the plurality of wavelengths. Compensate the integral contribution in the Kramers-Kronig relation from the data of the non-measurement wavelength range of the imaginary part data of the index by adding a constant, and obtain the real part of the complex refractive index at a plurality of wavelengths by adding the constant,
Measured value of at least one of film-surface incident reflectance, substrate-surface incident reflectance, transmittance, and substrate-surface incident reflectance in a structure in which a reflective layer is provided on the light-transmitting material, measured at a plurality of wavelengths. And a constant addition value for compensating for the data of the non-measurement wavelength range of the absorption spectrum applied to the real part of the complex refractive index and the imaginary part of the complex refractive index at a plurality of wavelengths corresponding to the measured value. The error with any of the film surface incident reflectance calculated by assuming, the substrate surface incident reflectance, the transmittance, and the substrate surface incident reflectance in the structure in which the reflective layer is provided on the light transmitting material is minimized. By obtaining a constant multiplication value of the imaginary part data of the complex refractive index at a plurality of wavelengths and a constant addition value that compensates for data in a non-measureable wavelength range of the absorption spectrum applied to the real part of the complex refractive index,
5. The method for evaluating an optical constant according to claim 2, wherein the real part of the complex refractive index of the light transmitting material is calculated. 5. The optical constant according to claim 2, wherein at least the transmittance data is used for obtaining the imaginary part of the complex refractive index when obtaining the real part and the imaginary part of the complex refractive index at a plurality of wavelengths by the RT method. Evaluation method. Measuring means for measuring the reflectance and transmittance in a certain wavelength range for the light-transmitting substance formed on at least the transparent substrate,
For the light-transmitting substance formed on the transparent substrate, the film-surface incident reflectance, the substrate-surface incident reflectance, the transmittance, the substrate-surface incidence in a structure in which a reflective layer is provided on the light-transmitting material Determine the combination of solutions that minimize the sum of squared errors between the measured values at two or more wavelengths of the reflectance and the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed. The imaginary part of the complex refractive index at a plurality of wavelengths of the light-transmitting substance is obtained by the RT method to obtain the complex refractive index, and the Kramers-Kronig relation is obtained for the obtained imaginary part data at the plurality of wavelengths of the complex refractive index. Arithmetic processing means for obtaining the real part of the complex refractive index at a plurality of wavelengths by applying the equation;
An optical constant evaluation device comprising: Measuring means for measuring the reflectance and transmittance in a certain wavelength range for the light-transmitting substance formed on at least the transparent substrate,
For the light-transmitting substance formed on the transparent substrate,
(1) Measurement at two or more wavelengths among two or more of the film surface incident reflectance, the substrate surface incident reflectance, the transmittance, and the substrate surface incident reflectance in a structure in which a reflective layer is provided on the light transmitting material. By the RT method of determining the complex refractive index by determining the combination of the solution and the solution that minimizes the sum of the square errors of the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed, Process of obtaining a real part n _RT and an imaginary part k _RT of a complex refractive index at a plurality of wavelengths of the light transmitting material using the film thickness d _RT of the light transmitting material arbitrarily assumed. Applying the Kramers-Kronig relation to the data of the imaginary part k _RT of the complex refractive index at a plurality of wavelengths obtained in the above, the real part n _KK of the complex refractive index at a plurality of wavelengths and the film thickness d of the light transmitting material in the process ▲ 3 ▼ ▲ 1 ▼ process of calculating the _KK And data of the real part n _RT eyes was complex refractive index is calculated by ▲ 2 ▼ process ▲ 4 compares the data of the calculated real part n _KK of the complex refractive index in the process of ▼ ▲ 2 ▼ Process The thickness d _KK of the light transmissive material thus determined is regarded as a film thickness d _RT, and the light transmissive material is again used by the _RT method in the process (1) using the film thickness d _RT considered. the process for obtaining the real part n _RT and the imaginary part k _RT of the complex refractive index are sequentially performed at a plurality of wavelengths, these ▲ 1 ▼ ~ ▲ 4 ▼ processes, ▲ 3 ▼ real part n _KK data in the process of Is repeated until the wavelength dependence of the data of the real part n _RT becomes substantially equal to that of the real part n _RT , and the complex refraction obtained when the wavelength dependence of the data of the real part n _{KK and} the data of the real part n _RT becomes substantially equal. Processing means for setting the refractive index to the complex refractive index of the light transmitting substance ,
An optical constant evaluation device comprising: Measuring means for measuring the reflectance and transmittance in a certain wavelength range for the light-transmitting substance formed on at least the transparent substrate,
For the light-transmitting substance formed on the transparent substrate,
(1) Measurement at two or more wavelengths among two or more of the film surface incident reflectance, the substrate surface incident reflectance, the transmittance, and the substrate surface incident reflectance in a structure in which a reflective layer is provided on the light transmitting material. By the RT method of determining the complex refractive index by determining the combination of the solution and the solution that minimizes the sum of the square errors of the calculated values corresponding to these measured values when the film thickness is arbitrarily assumed, Process of obtaining a real part n _RT and an imaginary part k _RT of a complex refractive index at a plurality of wavelengths of the light transmitting material using the film thickness d _RT of the light transmitting material arbitrarily assumed. Applying the Kramers-Kronig relation to the data of the imaginary part k _RT of the complex refractive index at a plurality of wavelengths obtained in the above, the real part n _KK of the complex refractive index at a plurality of wavelengths and the film thickness d of the light transmitting material in the process ▲ 3 ▼ ▲ 1 ▼ process of calculating the _KK And data of the real part n _RT eyes was complex refractive index is calculated by ▲ 2 ▼ process ▲ 4 compares the data of the calculated real part n _KK of the complex refractive index in the process of ▼ ▲ 2 ▼ Process The thickness d _KK of the light transmissive material thus determined is regarded as a film thickness d _RT, and the light transmissive material is again used by the _RT method in the process (1) using the film thickness d _RT considered. the process for obtaining the real part n _RT and the imaginary part k _RT of the complex refractive index are sequentially performed at a plurality of wavelengths, these ▲ 1 ▼ ~ ▲ 4 ▼ processes, ▲ 3 ▼ real part n _KK data in the process of film thickness and repeated until the wavelength dependence of the real part n _RT data are substantially equal, the wavelength dependence of these real part n _KK data and the real part n _RT data obtained when substantially equal Arithmetic processing means for setting the value to the thickness of the light-transmitting substance,
An optical constant evaluation device comprising: The process of obtaining the real part of the complex refractive index at a plurality of wavelengths by applying the Kramers-Kronig relational expression to the imaginary part data of the complex refractive index in the arithmetic processing means is the complex refractive index at a plurality of wavelengths obtained by the RT method. The real part of the complex refractive index at multiple wavelengths determined by the Kramers-Kronig relational equation from the constant multiple data of the imaginary part data of the index is calculated from the data of the unmeasured wavelength range of the imaginary part data of the complex refractive index at these multiple wavelengths. The integral contribution in the Kramers-Kronig relation is compensated by adding a constant, the real part of the complex refractive index at a plurality of wavelengths is obtained by the addition of the constant, and the film surface incidence reflectance and the substrate surface incidence reflection measured at a plurality of wavelengths are calculated. And at least one of measured values of transmittance, transmittance, and substrate surface incident reflectance in a structure in which a reflective layer is provided on the light-transmitting substance. By arbitrarily assuming a constant multiplication value of the imaginary part of the complex refractive index at a plurality of wavelengths corresponding to the value and a constant addition value that compensates for data in a non-measured wavelength range of the absorption spectrum applied to the real part of the complex refractive index. The calculated film surface incident reflectance, substrate surface incident reflectance, transmittance, at a plurality of wavelengths at which an error with any one of the substrate surface incident reflectance in the structure in which the reflective layer is provided on the light transmitting material is minimized. The complex refractive index of the light-transmitting material is obtained by calculating a constant addition value of the imaginary part data of the complex refractive index and a constant addition value for compensating the data in the non-measureable wavelength range of the absorption spectrum applied to the real part of the complex refractive index. The optical constant evaluation apparatus according to claim 7, 8 or 9, which is a process of calculating the real part of. 10. The arithmetic processing means for determining the real part and the imaginary part of the complex refractive index at a plurality of wavelengths by the RT method, wherein at least transmittance data is used to determine the imaginary part of the complex refractive index. Apparatus for evaluating optical constants described.

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