JP2004253673A - Prediction method, evaluation method, adjustment method, exposure method, device manufacturing method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for predicting the transfer characteristic of a pattern via a projection optical system in a short time. <P>SOLUTION: A change in the imaged state of the transfer image of a pattern according to a defocus is regarded as a change in the wave front aberration of the projection optical system. In a step 108, respective focus dependency aberration components (Z<SB>4</SB>, Z<SB>9</SB>, Z<SB>16</SB>, Z<SB>25</SB>, Z<SB>36</SB>) are corrected. In a step 112, the value of linear coupling of aberration components (Z<SB>1</SB>-Z<SB>37</SB>) including the corrected focus dependency aberration components (Z<SB>4</SB>, Z<SB>9</SB>, Z<SB>16</SB>, Z<SB>25</SB>, Z<SB>36</SB>) are calculated, and a change ΔCD in the line width of an image of the pattern is predicted. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【００９９】
スポット位置のみでしか与えられていない波面の傾きをそのまま積分するのは容易ではないため、面形状を級数に展開して、これにフィットするものとする。この場合、級数は直交系を選ぶものとする。ツェルニケ多項式は軸対称な面の展開に適した級数で、円周方向は三角級数に展開する。すなわち、波面Ｗを極座標系（ρ，θ）で表すと、次式（３）のように展開できる。
【０１００】
【数２】

【０１０１】
直交系であるから各項の係数Ｚ_ｉを独立に決定することができる。ｉを適当な値で切ることはある種のフィルタリングを行うことに対応する。なお、一例として第１項〜第３７項までのｆ_ｉをＺ_ｉとともに例示すると、次の表１のようになる。但し、表１中の第３７項は、実際のツェルニケ多項式では、第４９項に相当するが、本明細書では、ｉ＝３７の項（第３７項）として取り扱うものとする。すなわち、本発明において、ツェルニケ多項式の項の数は、特に限定されるものではない。
【０１０２】
【表１】

【０１０３】
実際には、その微分が上記の位置ずれとして検出されるので、フィッティングは微係数について行う必要がある。極座標系（ｘ＝ρｃｏｓθ，ｙ＝ρｓｉｎθ）では、次式（４）、（５）のように表される。
【０１０４】
【数３】

【０１０５】
ツェルニケ多項式の微分形は直交系ではないので、フィッティングは最小自乗法で行う必要がある。１つのスポット像の結像点の情報（ずれ量）はＸとＹ方向につき与えられるので、ピンホールの数をｎ（ｎは、投影光学系ＰＬの有効視野内の計測点（評価点）の数に対応しており、本実施形態では、説明の簡略化のためにｎは例えば３３とする）とすると、上記式（１）〜（５）で与えられる観測方程式の数は２ｎ（＝６６）となる。
【０１０６】
ツェルニケ多項式のそれぞれの項は光学収差に対応する。しかも低次の項（ｉの小さい項）は、ザイデル収差にほぼ対応する。ツェルニケ多項式を用いることにより、投影光学系ＰＬの波面収差を求めることができる。
【０１０７】
上述のような原理に従って、変換プログラムの演算手順が決められており、この変換プログラムに従った演算処理により、投影光学系ＰＬの視野内の第１計測点〜第ｎ計測点に対応する波面の情報（波面収差）、ここでは、ツェルニケ多項式の各項の係数、例えば第１項の係数Ｚ_１〜第３７項の係数Ｚ_３７が求められる。
【０１０８】
前記記憶装置４２内には、投影光学系ＰＬの波面収差変化表のデータベースが記憶されている。ここで、波面収差変化表とは、投影光学系ＰＬと実質的に等価なモデルを用いて、シミュレーションを行い、このシミュレーション結果として得られた、パターンの投影像のウエハ上での形成状態を最適化するのに使用できる調整パラメータの単位調整量の変化と、投影光学系ＰＬの視野内の複数の計測点それぞれに対応する結像性能、具体的には波面のデータ、例えばツェルニケ多項式の第１項〜第３７項の係数の変動量との関係を示すデータを所定の規則に従って並べたデータ群から成る変化表である。
【０１０９】
本実施形態では、上記の調整パラメータとしては、可動レンズ１３_１，１３_２，１３_３，１３_４、１３_５の各自由度方向（駆動可能な方向）の駆動量ｚ_１、θｘ_１、θｙ_１、ｚ_２、θｘ_２、θｙ_２、ｚ_３、θｘ_３、θｙ_３、ｚ_４、θｘ_４、θｙ_４、ｚ_５、θｘ_５、θｙ_５と、ウエハＷ表面（ウエハステージＷＳＴ）の３自由度方向の駆動量Ｗｚ、Ｗθｘ、Ｗθｙ、及び照明光ＥＬの波長のシフト量Δλの合計１９のパラメータが用いられる。
【０１１０】
ここで、上記の波面収差変化表のデータベースの作成手順について、簡単に説明する。まず、特定の光学ソフトがインストールされているシミュレーション用コンピュータ４６に、露光装置１００の光学条件（例えば、投影光学系ＰＬの設計値（開口数Ｎ．Ａ．や各レンズのデータなど）、コヒーレンスファクタσ値又は照明光学系の開口数Ｎ．Ａ．、照明光ＥＬの波長λ等）を入力する。次に、シミュレーション用コンピュータ４６に、投影光学系ＰＬの視野内の任意の第１計測点（計測点１）のデータを入力する。
【０１１１】
次いで、可動レンズ１３_１〜１３_５の各自由度方向（可動方向）、ウエハＷ表面の上記各自由度方向、照明光の波長のシフト量のそれぞれについての単位量のデータを入力する。例えば可動レンズ１３_１をＺ方向シフトの＋方向に関して単位量だけ駆動するという指令を入力すると、シミュレーション用コンピュータ４６により、投影光学系ＰＬの視野内の予め定めた第１計測点についての第１波面の理想波面からの変化量のデータ、例えばツェルニケ多項式の各項（例えば第１項〜第３７項）の係数の変化量が算出され、その変化量のデータがシミュレーション用コンピュータ４６のディスプレイの画面上に表示されるとともに、その変化量がパラメータＰＡＲＡ１Ｐ１としてメモリに記憶される。
【０１１２】
次いで、可動レンズ１３_１をＹ方向チルト（ｘ軸回りの回転θｘ）の＋方向に関して単位量だけ駆動するという指令を入力すると、シミュレーション用コンピュータ４６により、第１計測点についての第２波面のデータ、例えばツェルニケ多項式の上記各項の係数の変化量が算出され、その変化量のデータが上記ディスプレイの画面上に表示されるとともに、その変化量がパラメータＰＡＲＡ２Ｐ１としてメモリに記憶される。
【０１１３】
次いで、可動レンズ１３_１をＸ方向チルト（ｙ軸回りの回転θｙ）の＋方向に関して単位量だけ駆動するという指令を入力すると、シミュレーション用コンピュータ４６により、第１計測点についての第３波面のデータ、例えばツェルニケ多項式の上記各項の係数の変化量が算出され、その変化量のデータが上記ディスプレイの画面上に表示されるとともに、その変化量がパラメータＰＡＲＡ３Ｐ１としてメモリに記憶される。
【０１１４】
以後、上記と同様の手順で、第２計測点〜第ｎ計測点までの各計測点の入力が行われ、可動レンズ１３_１のＺ方向シフト、Ｙ方向チルト，Ｘ方向チルトの指令入力がそれぞれ行われる度毎に、シミュレーション用コンピュータ４６によって各計測点における第１波面、第２波面、第３波面のデータ、例えばツェルニケ多項式の上記各項の係数の変化量が算出され、各変化量のデータがディスプレイの画面上に表示されるとともに、パラメータＰＡＲＡ１Ｐ２，ＰＡＲＡ２Ｐ２，ＰＡＲＡ３Ｐ２、……、ＰＡＲＡ１Ｐｎ，ＰＡＲＡ２Ｐｎ，ＰＡＲＡ３Ｐｎとしてメモリに記憶される。
【０１１５】
他の可動レンズ１３_２，１３_３，１３_４，１３_５についても、上記と同様の手順で、各計測点の入力と、各自由度方向に関してそれぞれ単位量だけ＋方向に駆動する旨の指令入力が行われ、これに応答してシミュレーション用コンピュータ４６により、可動レンズ１３_２，１３_３，１３_４，１３_５を各自由度方向に単位量だけ駆動した際の第１〜第ｎ計測点のそれぞれについての波面のデータ、例えばツェルニケ多項式の各項の変化量が算出され、パラメータ（ＰＡＲＡ４Ｐ１，ＰＡＲＡ５Ｐ１，ＰＡＲＡ６Ｐ１，……，ＰＡＲＡ１５Ｐ１）、パラメータ（ＰＡＲＡ４Ｐ２，ＰＡＲＡ５Ｐ２，ＰＡＲＡ６Ｐ２，……，ＰＡＲＡ１５Ｐ２）、……、パラメータ（ＰＡＲＡ４Ｐｎ，ＰＡＲＡ５Ｐｎ，ＰＡＲＡ６Ｐｎ，……，ＰＡＲＡ１５Ｐｎ）がメモリ内に記憶される。
【０１１６】
また、ウエハＷについても、上記と同様の手順で、各計測点の入力と、各自由度方向に関してそれぞれ単位量だけ＋方向に駆動する旨の指令入力が行われ、これに応答してシミュレーション用コンピュータ４６により、ウエハＷをＺ、θｘ、θｙの各自由度方向に単位量だけ駆動した際の第１〜第ｎ計測点のそれぞれについての波面のデータ、例えばツェルニケ多項式の各項の変化量が算出され、パラメータ（ＰＡＲＡ１６Ｐ１，ＰＡＲＡ１７Ｐ１，ＰＡＲＡ１８Ｐ１）、パラメータ（ＰＡＲＡ１６Ｐ２，ＰＡＲＡ１７Ｐ２，ＰＡＲＡ１８Ｐ２）、……、パラメータ（ＰＡＲＡ１６Ｐｎ，ＰＡＲＡ１７Ｐｎ，ＰＡＲＡ１８Ｐｎ）がメモリ内に記憶される。
【０１１７】
さらに、波長シフトに関しても、上記と同様の手順で、各計測点の入力と、単位量だけ＋方向に波長をシフトする旨の指令入力が行われ、これに応答してシミュレーション用コンピュータ４６により、波長を＋方向に単位量だけシフトした際の第１〜第ｎ計測点のそれぞれについての波面のデータ、例えばツェルニケ多項式の各項の変化量が算出され、ＰＡＲＡ１９Ｐ１、ＰＡＲＡ１９Ｐ２、……、ＰＡＲＡ１９Ｐｎがメモリ内に記憶される。
【０１１８】
ここで、上記パラメータＰＡＲＡｉＰｊ（ｉ＝１〜１９、ｊ＝１〜ｎ）のそれぞれは、３７行１列の列マトリックス（縦ベクトル）である。すなわち、ｎ＝３３とすると、調整パラメータＰＡＲＡ１について、次式（６）のようになる。なお、パラメータＰＡＲＡｉＰｊは、いずれも列マトリックスであるが、次式（６）以下の式では、便宜上、行マトリックスであるかのような表現形式を採用している。
【０１１９】
【数４】

【０１２０】
また、調整パラメータＰＡＲＡ２について、次式（７）のようになる。
【０１２１】
【数５】

【０１２２】
同様に、他の調整パラメータＰＡＲＡ３〜ＰＡＲＡ１９についても、次式（８）のようになる。
【０１２３】
【数６】

【０１２４】
そして、このようにしてメモリ内に記憶されたツェルニケ多項式の各項の係数の変化量から成る列マトリックス（縦ベクトル）ＰＡＲＡ１Ｐ１〜ＰＡＲＡ１９Ｐｎは、調整パラメータ毎に纏められ、１９個の調整パラメータ毎の波面収差変化表として並べ替えが行われる。その結果、列マトリックス（縦ベクトル）ＰＡＲＡ１Ｐ１〜ＰＡＲＡ１９Ｐｎを要素とする次式（９）で示されるマトリックス（行列）Ｏが作成される。なお、式（９）では、ｍ＝１９である。
【０１２５】
【数７】

【０１２６】
そして、このようにして作成された、投影光学系ＰＬの波面収差変化表から成るデータベースが、記憶装置４２の内部に格納されている。
【０１２７】
次に、本実施形態の露光装置１００のメンテナンス時などにおいて行われる、投影光学系ＰＬによるパターン像の結像状態を調整するための、可動レンズ１３_１〜１３_５などの前述の１９個の調整パラメータの設定方法、すなわち投影光学系ＰＬの通常の調整方法について、その原理説明を含めて詳述する。
【０１２８】
まず、前述した手順で投影光学系ＰＬの波面収差を、波面収差計測装置８０を用いて計測する。その計測結果、すなわち投影光学系ＰＬの視野内の第１計測点（評価点）〜第ｎ計測点（評価点）に対応する波面（波面収差）のデータ、すなわちツェルニケ多項式の各項、例えば第１項の係数Ｚ_１〜第３７項の係数Ｚ_３７（以下、計測点ｎの第ｉ項の係数をＺ_ｎ，ｉと表記する）が求められ、主制御装置５０のＲＡＭなどのメモリ内に記憶される。
【０１２９】
以下の説明においては、第１計測点〜第ｎ計測点に対応する波面（波面収差）のデータを、次式（１０）のような列マトリックスＱで表現する。
【０１３０】
【数８】

【０１３１】
なお、上式（１０）において、マトリックスＱの要素Ｐ_１〜Ｐ_ｎは、それぞれがツェルニケ多項式の第１項〜第３７項の係数（Ｚ_１〜Ｚ_３７）から成る列マトリックス（縦ベクトル）である。
【０１３２】
次に、主制御装置５０により、次のようにして前述した可動レンズ１３_１〜１３_５の各自由度方向の調整量、ウエハＷの各自由度方向の調整量、照明光ＥＬの波長シフト量が演算される。
【０１３３】
すなわち、第１計測点〜第ｎ計測点に対応する波面（波面収差）のデータＱと、前述したデータベース（マトリックスＯ）と、前述の１９個の調整量Ｐとの間には、次式（１１）のような関係が成立する。
【０１３４】
Ｑ＝Ｏ・Ｐ ……（１１）
【０１３５】
上式（１１）において、Ｐは、次式（１２）で表されるｍ個、すなわち１９個の要素から成る列マトリックス（すなわち縦ベクトル）である。
【０１３６】
【数９】

【０１３７】
従って、上式（１２）より、次式（１３）の演算を行うことにより、すなわち最小自乗法により、Ｐの各要素ＡＤＪ１〜ＡＤＪｍ、すなわち可動レンズ１３_１〜１３_５の各自由度方向の調整量（目標調整量）、ウエハＷの各自由度方向の調整量（目標調整量）、及び照明光ＥＬの波長シフト量（目標シフト量）を求めることができる。
【０１３８】
Ｐ＝（Ｏ^Ｔ・Ｏ）^−１・Ｏ^Ｔ・Ｑ ……（１３）
【０１３９】
上式（１３）において、Ｏ^Ｔは、行列Ｏの転置マトリックスであり、（Ｏ^Ｔ・Ｏ）^−１は、（Ｏ^Ｔ・Ｏ）の逆マトリックスである。
【０１４０】
従って、主制御装置５０は、記憶装置４２内のデータベースをＲＡＭ内に順次読み込みつつ、調整量ＡＤＪ１〜ＡＤＪｍを算出する。
【０１４１】
次に、主制御装置５０では、記憶装置４２に記憶された調整量ＡＤＪ１〜ＡＤＪ１５に従って、可動レンズ１３_１〜１３_５を各自由度方向に駆動すべき旨の指令値を、結像性能補正コントローラ４８に与える。これにより、結像性能補正コントローラ４８により、可動レンズ１３_１〜１３_５をそれぞれの自由度方向に駆動する各駆動素子に対する印加電圧が制御され、可動レンズ１３_１〜１３_５の位置及び姿勢の少なくとも一方がほぼ同時に調整される。これと同時に、主制御装置５０は、実際の走査露光時には、露光領域ＩＡ内でウエハＷが、常に調整量ＡＤＪ１６〜ＡＤＪ１８によって調整されたのと等価な姿勢に保たれるように、ウエハＷをＺ、θｘ、θｙの各自由度方向に駆動するための指令値を、ウエハステージ駆動部（不図示）に与えて、ウエハステージＷＳＴを駆動する。さらに、上記の各動作と同時に、主制御装置５０は、調整量ＡＤＪ１９に従って光源１６に指令を与え、照明光ＥＬの波長をシフトする。これにより、投影光学系ＰＬの光学特性、例えばディストーション、像面湾曲、コマ収差、球面収差、及び非点収差等が補正される。なお、コマ収差、球面収差、及び非点収差については、低次のみならず高次の収差をも補正可能である。
【０１４２】
次に、本実施形態の予測方法、評価方法でサイズ（線幅）の予測又は評価の対象となるパターンが形成されたレチクルＲ_Ｔについて、図４に基づいて説明する。この図４は、レチクルＲ_Ｔを、パターン面側から見た平面図である。この図４に示されるように、レチクルＲ_Ｔは、正方形のガラス基板から成り、そのパターン面の中央部に、遮光帯ＳＢで囲まれる、照明領域ＩＡＲとほぼ同様の形状を有する長方形のパターン領域ＰＡが形成されている。パターン領域ＰＡの内部には、合計３３個の計測用パターンＭＰ_１〜ＭＰ_３３が形成されている。各計測用パターンＭＰ_ｊ（ｊ＝１〜３３）は、例えばレチクルＲ_Ｔ（パターン領域ＰＡ）の中心が投影光学系ＰＬの光軸ＡＸと一致するときに、前述の波面収差が計測される投影光学系ＰＬの有効視野内の各計測点（評価点）に対応する位置に配置されるようにその位置関係が設定されている。
【０１４３】
各計測用パターンＭＰ_ｊは、図４に示されるように、Ｙ軸方向に延びる設計上の線幅が例えば６００ｎｍの第１ラインパターンと、Ｘ軸方向に延びる設計上の線幅が例えば６００ｎｍの第２ラインパターンとを含む。投影光学系ＰＬの投影倍率を１／４として、これら第１ラインパターンと第２ラインパターンとをウエハ上に転写すると、投影光学系ＰＬに球面収差、非点収差などの諸収差が存在しない理想的な状態では、第１ラインパターンと第２ラインパターンの像として、線幅１５０ｎｍのラインパターン像がそれぞれ得られることとなる。
【０１４４】
また、パターン領域ＰＡの中心（レチクルセンタに一致）を通るＸ軸上のパターン領域ＰＡの両外側には、レチクルアライメントマークＭ１、Ｍ２が形成されている。このレチクルＲ_Ｔは、レチクルステージＲＳＴ上にロードされた状態では、パターン面（図４における紙面手前側の面）が、投影光学系ＰＬに対向する側の面となる。
【０１４５】
本実施形態の予測方法では、レチクルステージＲＳＴ上にロードされたレチクルＲ_Ｔ上に形成された計測用パターンＭＰ_ｊが、ウエハステージＷＳＴ上にロードされたウエハＷに転写されたときの第１ラインパターン及び第２ラインパターンの像の線幅を予測する。
【０１４６】
ところで、第１ラインパターン及び第２ラインパターンの像の線幅のばらつきΔＣＤは、従来のツェルニケ感度法（Ｚｅｒｎｉｋｅ Ｓｅｎｓｉｔｉｖｉｔｙ法：以下、適宜「ＺＳ法」又は「ＺＳＭ」と呼ぶ）では、次式（１４）で表されるようなＺｅｒｎｉｋｅ Ｓｅｎｓｉｔｉｖｉｔｙ（以下、適宜「ツェルニケ感度」と記述する）Ｓ_ｉ（ｉ＝１〜３７）と、計測点ｎにおけるツェルニケ項の大きさＺ_ｎ，ｉ（計測点ｎにおける係数Ｚ_ｉ）との線形結合で表現することができる。なお、以下では、Ｚ_ｎ，ｉを各計測点のツェルニケ項の成分（ツェルニケ項成分）と略述する。
【０１４７】
【数１０】

【０１４８】
しかしながら、上式（１４）を用いたＺＳ法を用いた計算結果と、適当な波面収差を与えて直接空間像を計算する手法との間には、図５のグラフに示されるような乖離が見られる。すなわち、上式（１４）を用いたＺＳ法による計算では誤差が大きすぎる。
【０１４９】
このため、発明者等は、従来のＺＳ法に代わり、本実施形態の予測方法、すなわち新たなＺＳ法によって線幅を予測する予測方法を考えた。以下に、その新たなＺＳ法の原理を説明するとともに、本実施形態の予測方法、評価方法、調整方法、及び露光方法について説明する。
【０１５０】
まず、新たなＺＳ法の原理について説明する。各計測点ｎ（ｎ＝１〜３３）におけるデフォーカス量による波面収差の変化量、すなわち波面の乱れ量Ｗｄ’は、厳密には、次式で表される。
【数１１】

【０１５１】
ここで、Ｄｅｆは、波面収差参照点、すなわち計測点ｎにおけるデフォーカス量であり、ｒは、投影光学系ＰＬの瞳座標における半径である。なお、ｒの最大値は、投影光学系ＰＬのＮ．Ａ．（最大開口数、又は開口絞り１５にて設定される開口数）となる。
【０１５２】
波面の乱れ量を、ツェルニケ多項式で記述するには、上述の式（１５）で示されるＷｄ’を用いるよりも、次式に示されるＷｄを用いた方が、都合が良い。
【０１５３】
【数１２】

【０１５４】
ここで、λは、露光装置１００における照明光ＥＬの波長である。さらに、式（１６）をベキ級数展開すると次式のようになる。
【０１５５】
【数１３】

【０１５６】
デフォーカス量Ｄｅｆによる波面の乱れ量Ｗｄを記述するのに用いられるツェルニケ多項式は、上述の表１に示される項のうち、次式に示される回転対称成分の項となる。
【０１５７】
【数１４】

【０１５８】
ここで、ρは、投影光学系Ｎ．Ａ．（以下、「ＮＡ」と略述する）で正規化した瞳座標半径方向の値であるから、ρ×ＮＡ＝ｒの関係がある。そこで、上述の式（１７）を、次式に書き換えることができる。
【０１５９】
【数１５】

【０１６０】
一方、デフォーカス量Ｄｅｆによる波面収差の変化量Ｗｄは、前述したデフォーカス量に対して感度があるツェルニケ項の成分、すなわちフォーカス依存収差成分の線形結合によって次式のように表すことができる。
【０１６１】
【数１６】

【０１６２】
ここで、Ｂ_１、Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６は、デフォーカス量Ｄｅｆによるツェルニケ多項式の第１項、第４項、第９項、第１６項、第２５項、第３６項の変化量である。なお、上述した式（１８−１）〜式（１８−６）、式（１９）、式（２０）より、次式が導き出される。
【０１６３】
【数１７】

【０１６４】
計算を簡略化するために、式（２１−１）〜式（２１−６）の右辺を、次式（２２）のように置き、その連立方程式を解くと、次式（２３）が得られる。
【０１６５】
【数１８】

【０１６６】
【数１９】

【０１６７】
上述の式（２０）に示されるように、デフォーカス量による波面の乱れ量Ｗｄは、デフォーカス量の各フォーカス依存収差成分の変化量Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６の線形結合で表すことができる。この変化量Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６が、デフォーカスＤｅｆに対するそれぞれのフォーカス依存収差成分の補正量となる。したがって、デフォーカスにより補正された各フォーカス依存収差成分は、それぞれ次式に示されるように補正される。
【０１６８】
【数２０】

【０１６９】
次に、以上のような原理に基づく、本実施形態の予測方法、評価方法、調整方法、露光方法について、主制御装置５０内のＣＰＵの処理アルゴリズムを簡略化して示す図６のフローチャートに基づいて説明する。まず、ステップ１０２において、表示装置４４に、実際の露光時の光学条件（例えば、照明光ＥＬの波長λ、即ち露光波長（及び露光光源１６の種類など）、投影光学系ＰＬの最大Ｎ．Ａ．、使用Ｎ．Ａ．（本実施形態では、露光時に開口絞り１５にて設定される開口数）、コヒーレンスファクタσ値又は照明Ｎ．Ａ．（照明光学系の開口数）、及びレチクルの照明条件（照明光学系の瞳面上での照明光ＥＬの光量分布、即ち２次光源の形状や大きさ）などの少なくとも１つ）等を含む露光条件の設定画面を表示する。この設定画面を見て、オペレータは、入力装置４５を介して、実際の露光に用いられる光学条件などを設定する。なお、この露光条件の設定時には、各計測点ｎ（ｎ＝１〜３３）にそれぞれ転写されるレチクルＲ上のパターンの形状、寸法などのパターンに関する情報も併せて設定できるようになっている。パターンに関する情報としては、例えば、孤立ラインパターン、ライン・アンド・スペース（Ｌ／Ｓ）パターン、ラインパターンが直交している直交パターンなどのパターン種別（位相シフトパターンであるか否か及びその種類なども含む）、ラインパターンの線幅、長さ、ピッチなどのパターンサイズ情報などがある。パターンの選択は、評価すべき評価項目に応じて決定される。例えば、上述の動作と同様に縦横の線幅差を評価項目とするならば、図４に示されるような、互いに直交する直交ラインパターンを設定する必要がある。ここでは、図４のレチクルＲ_Ｔを用いるとして、直交ラインパターン（すなわち、第１ラインパターン及び第２ラインパターン）に関する情報を設定するものとする。
【０１７０】
次に、ステップ１０４において、デフォーカス量Ｄｅｆ、露光装置１００の投影光学系ＰＬのＮ．Ａ．の値（ＮＡ）と、照明光ＥＬの波長λとに基づいて、上述の式（２２）を用いて、Ｃ_２、Ｃ_４、Ｃ_６、Ｃ_８、Ｃ_１０を求める。そして、ステップ１０６では、求められたＣ_２〜Ｃ_１０に基づいて、上述の式（２３）を用いて、各フォーカス依存収差成分の補正量Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６を求める。そして、ステップ１０８では、求められた補正量Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６に基づいて、上述の式（２４）を用いて各フォーカス依存収差成分Ｚ_４、Ｚ_９、Ｚ_１６、Ｚ_２５、Ｚ_３６を補正する。
【０１７１】
次に、そのデフォーカス量における計測用パターンＭＰ_ｊの第１ラインパターン及び第２ラインパターンの像の線幅を求めるが、その前に、ツェルニケ係数とパターンの線幅の相関関係について説明する。
【０１７２】
図７には、露光装置１００におけるＣＤ（クリティカルディメンジョン；Ｃｒｉｔｉｃａｌ Ｄｉｍｅｎｓｉｏｎ）−フォーカス曲線の一例が示されている。ＣＤ−フォーカス曲線は、通常、デフォーカス量に対するラインパターンの像の線幅の変動を示すものとなっている。この図７の例では、最良フォーカス位置（デフォーカス量Ｄｅｆが０であるところ）近傍では、ラインパターンの像の線幅が大きくなっており、デフォーカスするにつれて、その像の線幅は小さくなっている。また、図７からわかるように、デフォーカス量Ｄｅｆに対する線幅の変化ΔＣＤに関しては、Ｄｅｆ∝ΔＣＤの関係とはなっておらず、Ｄｅｆ^２∝ΔＣＤの関係となっている。
【０１７３】
図８には、ツェルニケ項毎（Ｚ_６、Ｚ_７、Ｚ_９）に−５０ｍλ〜５０ｍλまで１０ｍλピッチで１１点の収差をシミュレーション用コンピュータ４６に入力して、空間像計算を行って求められたラインパターン像の線幅と収差の関係が示されている。これらの関係については、収差の量がプラスであってもマイナスであってもその線幅に対する影響が同じであることや、収差が増えると比例関係以上に像の劣化が観察されることから、ラインパターンの像の線幅の変化は、各ツェルニケ項成分の二乗等の線形結合で表されるものと仮定することができる。シミュレーション用コンピュータ４６により、像計算で得た１１点の線幅変化量の計算に２次関数を仮定し、最小二乗法によって近似をしてみると、図８に示されるように、ｙ＝ｓｘ^２という関数に乗っていることが観察される。なお、この図８には、第６項（Ｚ．６）、第７項（Ｚ．７）、第９項（Ｚ．９）の３種類だけが代表的に示されているが、他のツェルニケ項についても二次関数で表現できることが確認されている。
【０１７４】
また、最近では、互いに異なるツェルニケ項同士の積、すなわちクロスターム（クロス項）についても、ラインパターン像の線幅の変化に感度があることを発見した。すなわち、ラインパターンの像の線幅の変化は、以下の式に示されるように、各ツェルニケ項成分の二乗及びクロス項の線形結合によって表すことができる。なお、式中のＳ_ｉ，ｊは、ラインパターンの像の線幅変化に対するその項（Ｚ_ｎ，ｉＺ_ｎ，ｊ）の感度を示す。
【０１７５】
【数２１】

【０１７６】
また、図９（Ａ）、図９（Ｂ）のグラフに示されるように、収差の組み合わせによっては、線幅分布が傾いた楕円上に分布していることがある（図９（Ａ）では、Ｚ．６とＺ．１３との関係が示されており、図９（Ｂ）ではＺ．９とＺ．１２との関係が示されている）。この場合には、それらの収差の組み合わせのクロスタームは、ラインパターンの線幅変化に対して感度を有することとなる。なお、式（２５）の中から、２項だけ取り出すと、例えば次式のような形となる。
【０１７７】
【数２２】

【０１７８】
これより、図９（Ａ）、図９（Ｂ）のグラフに示されるような傾いた楕円分布の表現が可能であることがわかる。実際にクロスタームの計算をしてみると、かなり多くの項の間でクロスタームが存在することを確認できる。
【０１７９】
図６に戻り、ステップ１１０において、シミュレーション用コンピュータ４６の空間像計算により求められた、設定された露光条件下での、第１ラインパターン及び第２ラインパターンの線幅に対する、各ツェルニケ項成分の二乗のツェルニケ感度Ｓ_ｉ，ｊ（ｉ＝ｊ）及びクロス項のツェルニケ感度Ｓ_ｉ，ｊ（ｉ≠ｊ）を、読み込む。なお、各ツェルニケ項成分の二乗のツェルニケ感度Ｓ_ｉ，ｊ（ｉ＝ｊ）については、像計算で得た１１点の線幅変化量の計算に２次関数を仮定し、最小二乗法によって近似をしてみると、前述したように、ｙ＝ｓｘ^２という関数に乗っていることが観察されるため、その関数の係数からツェルニケ感度Ｓ_ｉ，ｊ（ｉ＝ｊ）を求めることができる。
【０１８０】
図６のステップ１１２において、前述した波面収差の計測により計測され主制御装置５０のメモリ内に記憶されている投影光学系ＰＬの収差成分Ｚ_ｎ，ｉ（又はＺ_ｎ，ｊ）、及びステップ１１０で求められた各ツェルニケ感度Ｓ_ｉ，ｊに基づいて式（２５）を計算して、第１〜第ｎ計測点の各々における第１ラインパターン及び第２ラインパターンについてのΔＣＤ（それぞれΔＣＤ（Ｖ）、ΔＣＤ（Ｈ）とする）を求める。
【０１８１】
図１０には、この線幅のばらつきΔＣＤに関して、上で説明した新たなＺＳ法を用いた計算結果と、適当な波面収差を与えて直接空間像を計算する手法との関係が示されている。この図１０と前述の図５とを比較すると明らかなように、新たなＺＳ法によると、誤差が格段に低減されていることがわかる。
【０１８２】
すなわち、図１０からも明らかなように、結像シミュレーションによる空間像計算を行なわなくても、ＺＳ法を拡張することで線幅を正確に計算（予測）できることがわかる。
【０１８３】
図６に戻り、次のステップ１１４において、投影光学系ＰＬの物体面側で、第１〜第ｎ計測点に対応する位置にそれぞれ配置される第１ラインパターン、第２ラインパターンに関して、ステップ１１２で予測されたそれぞれの線幅の変化ΔＣＤ（Ｖ）、ΔＣＤ（Ｈ）に基づいて、第１〜第ｎ計測点における線幅差（ＶＨ差）を、ＶＨ差＝ΔＣＤ（Ｖ）−ΔＣＤ（Ｈ）として求める。
【０１８４】
次に、ステップ１１６において、算出された第１〜第ｎ計測点のＶＨ差と、上述しした式（１３）等で表されるような投影光学系ＰＬの波面収差と調整量ＡＤＪ１〜ＡＤＪ１９などとの関係を利用して、それらのＶＨ差が小さくなるようなツェルニケ調整量ＡＤＪ１〜調整量ＡＤＪ１９を、算出し、記憶装置４２に記憶する。
【０１８５】
次に、ステップ１１８において、記憶装置４２に記憶された調整量ＡＤＪ１〜ＡＤＪ１５に従って、前述と同様に、結像性能補正コントローラ４８により、可動レンズ１３_１〜１３_５の位置及び姿勢の少なくとも一方を調整し、上記の各動作と同時に、主制御装置５０は、調整量ＡＤＪ１９に従って光源１６に指令を与え、照明光ＥＬの波長をシフトする。
【０１８６】
なお、本実施形態では、投影光学系ＰＬ等の調整後の状態で、さらに、上述したステップ１０２〜ステップ１１８を実行して、調整後の第１〜第ｎ計測点における縦横パターンの線幅の変化ΔＣＤ（Ｖ）、ΔＣＤ（Ｈ）の予測、線幅差（ＶＨ差）の評価、調整量ＡＤＪ１〜ＡＤＪ１９による調整を繰り返し行うようにしても良い。
【０１８７】
そして、半導体デバイスの製造時における露光工程では、デバイス製造用のレチクルＲがレチクルステージＲＳＴ上に装填され、その後、レチクルアライメント及びいわゆるベースライン計測、並びにＥＧＡ（エンハンスト・グローバル・アライメント）等のウエハアライメントなどの準備作業が行われる。なお、上記のレチクルアライメント、ベースライン計測等の準備作業については、例えば特開平７−１７６４６８号公報などに詳細に開示され、また、これに続くＥＧＡについては、特開昭６１−４４４２９号公報などに詳細に開示されている。
【０１８８】
その後、ウエハアライメント結果に基づいて、ステップ・アンド・スキャン式の露光が行われる。なお、露光時の動作等は通常の走査型露光装置と異なることがないので、詳細説明については省略する。但し、本実施形態の露光装置１００では、上記のステップ・アンド・スキャン方式の露光に際し、前述の露光領域ＩＡ内におけるウエハＷの位置及び姿勢を、算出された調整量ＡＤＪ１６〜ＡＤＪ１８に基づいて制御することは、前述した通りである。
【０１８９】
また、本実施形態では、露光条件の設定や、レチクルＲの交換により、実際に転写する回路パターンが変更された場合には、上述したステップ１０２〜ステップ１１８を再実行する必要があることはいうまでもない。
【０１９０】
以上詳細に述べたように、本実施形態の予測方法によれば、ステップ１０２〜ステップ１０８において、デフォーカス量Ｄｅｆに応じた波面収差の乱れ量Ｗｄに基づいて、フォーカス依存収差成分（Ｚ_４、Ｚ_９、Ｚ_１６、Ｚ_２５、Ｚ_３６）の変化量（Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６）を算出し、フォーカス依存収差成分（Ｚ_４、Ｚ_９、Ｚ_１６、Ｚ_２５、Ｚ_３６）を、その変化量（Ｂ_４、Ｂ_９、Ｂ_１６、Ｂ_２５、Ｂ_３６）を加算することによって補正する。このようにすれば、ステップ１１２において、補正されたフォーカス依存収差成分（Ｚ_４、Ｚ_９、Ｚ_１６、Ｚ_２５、Ｚ_３６）を含む収差成分（Ｚ_ｉ、ｉ＝１〜３６）の線形結合を計算することによって、本来のツェルニケ感度法では予測困難であった、所定パターンの像のサイズとデフォーカス量との対応関係を、結像シミュレーションを動作させることなく、短時間に予測することができるようになる。
【０１９１】
また、本実施形態の予測方法によれば、像のサイズの変化は、各収差成分の二乗及び互いに異なる収差成分同士のクロス項に感度があり、それらの項の線形結合（式（２５））を考慮すれば、そのデフォーカス量に対する像のサイズの変化を算出することができる。
【０１９２】
また、本実施形態の評価方法によれば、上述の予測方法を用いて、所定パターンの像のサイズの変化（ΔＣＤ（Ｖ）、ΔＣＤ（Ｈ））とデフォーカス量Ｄｅｆとの対応関係を短時間に予測することができるようになるので、結果的に、その対応関係に基づいて、投影光学系ＰＬの有効視野内における所定パターンの像の均一性（ここでは縦横線幅差（ＶＨ差））を短時間に評価することが可能となる。
【０１９３】
また、本実施形態の調整方法によれば、上述した評価方法を用いて、投影光学系ＰＬの有効視野内における所定パターンの像の転写状態の均一性が短時間で評価されるので、結果的に、その評価結果に基づいて、投影光学系ＰＬを介した所定パターンの転写状態を、所定パターンの像の転写状態の均一性が改善されるように調整することができる。
【０１９４】
また、本実施形態の露光方法によれば、上述した調整方法を実行して、前記パターンの転写状態が短時間に調整され、調整された転写状態でパターンがウエハＷ上に転写されるので、露光工程のスループットを向上させることが可能となる。
【０１９５】
また、本実施形態の予測方法によるラインパターンの線幅の予測を、一定間隔の異なるデフォーカス量で実行すれば、図７で示したようなＣＤ−フォーカス曲線を求めることができるようになる。例えば、Ｚ_４及びＺ_９の収差量に対するラインパターンの線幅の変化の様子が図１１（Ａ）に示されるような状態であったとし、シミュレーション用コンピュータ４６による空間像計算により求められた式（２５）におけるＺ_４及びＺ_９に関するツェルニケ感度がそれぞれＳ_４，４＝−９３８、Ｓ_４，９＝４２３７、Ｓ_９，９＝−３２５７であったとする。さらに、他のツェルニケ項についても同様にツェルニケ感度を求め、デフォーカス量を一定間隔で逐次変更しながら、式（２５）の値を計算し、各デフォーカス量におけるラインパターンの線幅を示す点を図１１（Ｂ）の◆で示されるようにプロットし、それらの点を補間していくと、図１１（Ｂ）に示されるようなツェルニケ感度法（ＺＳＭ）によるＣＤ−フォーカス曲線（太線）を作成することができる。図１１（Ｂ）においては、空間像シミュレーションにより求められたＣＤ−フォーカス曲線（細線）もあわせて示されている。
【０１９６】
図１１（Ｂ）に示されるように、最良フォーカス位置近傍では、式（２５）の計算により求められたＣＤ−フォーカス曲線と、結像シミュレーションにより求められたＣＤ−フォーカス曲線とは良く一致しているが、デフォーカス量が大きくなるに連れて、式（２５）の計算により求められたＣＤ−フォーカス曲線と、結像シミュレーションによるＣＤ−フォーカス曲線との間には、若干のずれが生じているのがわかる。
【０１９７】
本発明者の鋭意検討により、このずれは、フォーカス依存収差成分の中の第４項、すなわちＺ_４に起因するものであることが判明した。そこで、Ｚ_４に関してのみ、その大きさに対するラインパターン像の線幅の変動を示すデータテーブルを予め記憶装置４２に記憶させておき、主制御装置５０では、Ｚ_４の値から得られる線幅変化量をそのデータテーブルを参照して求め、さらに、Ｚ_４を除く、他のツェルニケ項だけの項に基づいて、式（２５）を計算したときの計算結果から得られる線幅変化量と、データテーブルより求まる線幅変化量とを加算した値を、そのデフォーカス量における線幅変化量とするようにしても良い。図１２に示されるように、このデータテーブルを参照する方法（ＺＳＭ）で求めた各デフォーカス量におけるラインパターン像の線幅と、空間像シミュレーションによるＣＤ−フォーカス曲線におけるその像の線幅とは、デフォーカス量が大きいところでも、良く一致しているのがわかる。なお、図１２では、計測点１（Ｐ１）、１７（Ｐ１７）、３３（Ｐ３３）におけるデータしか図示していないが、その他の計測点においても、本発明により予測されたラインパターン像の線幅及び空間像シミュレーションによるＣＤ−フォーカス曲線については、同様に良く一致していることが確認されている。
【０１９８】
なお、上記実施形態では、ツェルニケ多項式級数の第３７項までを対象としたが、本発明はこれに限定されるものではなく、第３７項以上のツェルニケ項、例えば第１２１項までをＺＳ法の対象とするようにしても良い。この場合、フォーカス依存収差成分となるのは、第４９項、第６４項、第８１項、第１００項、第１２１項である。
【０１９９】
また、上記実施形態は、互いに交差するラインパターンの線幅差を評価する場合について説明したが、本発明はこれに限定されるものではなく、互いに平行なラインパターン（例えばＬ／Ｓパターン）に関し、それらの線幅差、すなわち線幅異常値を評価するようにしても良く、計測点間における孤立パターンを各計測点に配置して均一性を評価するようにしても良い。この場合には、第１〜第ｎ計測点において、主に非点収差による縦横線幅差の均一性の評価だけでなく、主にコマ収差による線幅異常値の均一性なども評価することができるようになる。
【０２００】
また、サイズの予測対象となるパターンは、ラインパターンには限られず、例えば菱形パターンなどであっても良い。また、上記実施形態では１９個の調整パラメータを用いるものとしたが、その数や種類は任意で良く、例えばウエハ表面（ウエハステージＷＳＴ）の駆動量や照明光ＥＬの波長シフトなどを含まなくても良い。
【０２０１】
さらに、上記実施形態では、波面収差計測装置８０を用いて投影光学系ＰＬの波面収差を計測するものとしたが、例えば試し焼きなどによって波面収差を求めても良い。例えば、米国特許第５，９７８，０８５号などに開示されている特殊な構造の計測用マスクを用い、そのマスク上の複数の計測用パターンのそれぞれを、個別に設けられたピンホール及び投影光学系を順次介して基板上に焼き付けるとともに、マスク上の基準パターンを集光レンズ及びピンホールを介することなく、投影光学系を介して基板上に焼き付けて、それぞれの焼き付けの結果得られる複数の計測用パターンのレジスト像それぞれの基準パターンのレジスト像に対する位置ずれを計測して所定の演算により、波面収差を算出することとしても良い。
【０２０２】
また、上記実施形態の調整方法では、上述の式（１３）などを用いて算出された最適な調整量に基づいて、主制御装置５０の制御の下、結像性能補正コントローラ４８等による調整を自動的に行うものとしたが、これに限らず、前記調整量に基づいて、投影光学系の結像性能などを手動で調整しても良い。
【０２０３】
また、上記実施形態では、予測方法、その予測方法によって予測されたＣＤ−フォーカス曲線に基づいて縦横線幅差などを評価する評価方法、その評価結果に応じてパターンの転写状態を調整する調整方法などを、一連の処理によって説明したが、すべての方法を一連の処理で行う必要はなく、本発明の予測方法、評価方法、調整方法は、それぞれ単独で、あるいは任意に組み合わせて実行しうるものである。
【０２０４】
さらに、上記実施形態では、投影光学系ＰＬの光学素子を移動して結像性能を調整するものとしたが、これに限らず、その駆動機構に加えて、あるいはその代わりに、例えば投影光学系ＰＬの光学素子間での気体の圧力を変更する、レチクルＲを投影光学系の光軸方向に移動又は傾斜させる、あるいはレチクルとウエハとの間に配置される平行平面板の光学的な厚さを変更する機構などを用いても良い。但し、この場合には上記実施形態又は変形例における自由度の数が変更され得る。
【０２０５】
なお、上記実施形態では、露光装置として走査型露光装置を用いる場合について説明したが、これに限らず、例えばステップ・アンド・リピート型の露光装置を用いても良い。
【０２０６】
この場合の露光装置の用途としては半導体製造用の露光装置に限定されることなく、例えば、角型のガラスプレートに液晶表示素子パターンを転写する液晶用の露光装置、プラズマディスプレイ又は有機ＥＬなどの表示装置、撮像素子（ＣＣＤなど）、薄膜磁気へッド、マイクロマシーン及びＤＮＡチップなどを製造するための露光装置にも広く適用できる。また、半導体素子などのマイクロデバイスだけでなく、光露光装置、ＥＵＶ露光装置、Ｘ線露光装置、及び電子線露光装置などで使用されるレチクル又はマスクを製造するために、ガラス基板又はシリコンウエハなどに回路パターンを転写する露光装置にも本発明を適用できる。
【０２０７】
また、上記実施形態の露光装置の光源は、Ｆ_２レーザ、ＡｒＦエキシマレーザ、ＫｒＦエキシマレーザなどの紫外パルス光源に限らず、連続光源、例えばｇ線（波長４３６ｎｍ）、ｉ線（波長３６５ｎｍ）などの輝線を発する超高圧水銀ランプを用いることも可能である。さらに、照明光ＥＬとして、Ｘ線、特にＥＵＶ光などを用いても良い。
【０２０８】
また、ＤＦＢ半導体レーザ又はファイバーレーザから発振される赤外域、又は可視域の単一波長レーザ光を、例えばエルビウム（又はエルビウムとイッテルビウムの両方）がドープされたファイバーアンプで増幅し、非線形光学結晶を用いて紫外光に波長変換した高調波を用いても良い。また、投影光学系の倍率は縮小系のみならず等倍及び拡大系のいずれでも良い。また、投影光学系としては、屈折系に限らず、反射光学素子と屈折光学素子とを有する反射屈折系（カタッディオプトリック系）あるいは反射光学素子のみを用いる反射系を用いても良い。なお、投影光学系ＰＬとして反射屈折系又は反射系を用いるときは、前述した可動の光学素子として反射光学素子（凹面鏡や反射鏡など）の位置などを変更して投影光学系の結像性能を調整する。また、照明光ＥＬとして、特にＡｒ_２レーザ光、又はＥＵＶ光などを用いる場合には、投影光学系ＰＬを反射光学素子のみから成るオール反射系とすることもできる。但し、Ａｒ_２レーザ光やＥＵＶ光などを用いる場合にはレチクルＲも反射型とする。さらに、例えば国際公開ＷＯ９９／４９５０４号などに開示される、投影光学系ＰＬとウエハとの間に液体が満たされる液浸型露光装置に本発明を適用しても良い。
【０２０９】
《デバイス製造方法》
次に上述した露光装置をリソグラフィ工程で使用したデバイスの製造方法の実施形態について説明する。
【０２１０】
図１３には、デバイス（ＩＣやＬＳＩ等の半導体チップ、液晶パネル、ＣＣＤ、薄膜磁気ヘッド、マイクロマシーン等）の製造例のフローチャートが示されている。図１３に示されるように、まず、ステップ３０１（設計ステップ）において、デバイスの機能・性能設計（例えば、半導体デバイスの回路設計等）を行い、その機能を実現するためのパターン設計を行う。引き続き、ステップ３０２（マスク製作ステップ）において、設計した回路パターンを形成したマスクを製作する。一方、ステップ３０３（ウエハ製造ステップ）において、シリコン等の材料を用いてウエハを製造する。
【０２１１】
次に、ステップ３０４（ウエハ処理ステップ）において、ステップ２０１〜ステップ３０３で用意したマスクとウエハを使用して、後述するように、リソグラフィ技術等によってウエハ上に実際の回路等を形成する。次いで、ステップ３０５（デバイス組立てステップ）において、ステップ３０４で処理されたウエハを用いてデバイス組立てを行う。このステップ３０５には、ダイシング工程、ボンディング工程、及びパッケージング工程（チップ封入）等の工程が必要に応じて含まれる。
【０２１２】
最後に、ステップ３０６（検査ステップ）において、ステップ３０５で作成されたデバイスの動作確認テスト、耐久テスト等の検査を行う。こうした工程を経た後にデバイスが完成し、これが出荷される。
【０２１３】
図１４には、半導体デバイスにおける、上記ステップ３０４の詳細なフロー例が示されている。図１４において、ステップ３１１（酸化ステップ）においてはウエハの表面を酸化させる。ステップ３１２（ＣＶＤステップ）においてはウエハ表面に絶縁膜を形成する。ステップ３１３（電極形成ステップ）においてはウエハ上に電極を蒸着によって形成する。ステップ３１４（イオン打ち込みステップ）においてはウエハにイオンを打ち込む。以上のステップ３１１〜ステップ３１４それぞれは、ウエハ処理の各段階の前処理工程を構成しており、各段階において必要な処理に応じて選択されて実行される。
【０２１４】
ウエハプロセスの各段階において、上述の前処理工程が終了すると、以下のようにして後処理工程が実行される。この後処理工程では、まず、ステップ３１５（レジスト形成ステップ）において、ウエハに感光剤を塗布する。引き続き、ステップ３１６（露光ステップ）において、上で説明した露光装置及び露光方法によってマスクの回路パターンをウエハに転写する。次に、ステップ３１７（現像ステップ）においては露光されたウエハを現像し、ステップ３１８（エッチングステップ）において、レジストが残存している部分以外の部分の露出部材をエッチングにより取り去る。そして、ステップ３１９（レジスト除去ステップ）において、エッチングが済んで不要となったレジストを取り除く。
【０２１５】
これらの前処理工程と後処理工程とを繰り返し行うことによって、ウエハ上に多重に回路パターンが形成される。
【０２１６】
以上説明した本実施形態のデバイス製造方法を用いれば、露光工程（ステップ３１６）において上記実施形態の予測方法、評価方法、露光方法が用いられるので、縦線パターンと横線パターンの転写像同士の線幅差が効果的に低減された良好かつ短時間な露光を実現することができる。従って、最終製品であるデバイスの歩留まりが向上し、その生産性の向上が可能となる。
【０２１７】
【発明の効果】
以上説明したように、本発明の予測方法によれば、投影光学系を介したパターンの転写特性を短時間に予測することが可能となる。
【０２１８】
本発明の評価方法によれば、投影光学系を介したパターンの転写状態を短時間に評価することができる。
【０２１９】
本発明の調整方法によれば、投影光学系を介したパターンの転写状態を短時間に調整することができる。
【０２２０】
本発明の露光方法によれば、露光工程のスループットを向上させることができる。
【０２２１】
本発明のデバイス製造方法によれば、デバイスの生産性（歩留まりを含む）の向上に寄与することができるという効果がある。
【０２２２】
本発明のプログラムによれば、コンピュータに投影光学系を介したパターンの転写特性を短時間に予測させる手順を実行させることができる。
【図面の簡単な説明】
【図１】本発明の一実施形態に係る露光装置の構成を概略的に示す図である。
【図２】図１の波面収差計測装置を示す断面図である。
【図３】図３（Ａ）は、光学系に収差が存在しない場合においてマイクロレンズアレイから射出される光束を示す図であり、図３（Ｂ）は、光学系に収差が存在する場合においてマイクロレンズアレイから射出される光束を示す図である。
【図４】図４は、計測用レチクルを、パターン面側から見た平面図である。
【図５】線幅ばらつきΔＣＤに関して、従来のＺＳ法を用いた計算結果と、空間像による計算結果との関係を示す図である。
【図６】本発明の一実施形態の予測方法等を示すフローチャートである。
【図７】ＣＤ−フォーカス曲線の一例を示す図である。
【図８】１１点の線幅変化量の計算結果に二次関数を仮定して、最小自乗法による近似をした結果の一例を示す図である。
【図９】図９（Ａ）は、Ｚ_６とＺ_１３のクロストークを示す図であり、図９（Ｂ）は、Ｚ_９とＺ_１２のクロストークを示す図である。
【図１０】線幅ばらつきΔＣＤに関して、本発明の一実施形態の予測方法の予測結果と、空間像の計算結果との関係を示す図である。
【図１１】図１１（Ａ）は、第４項及び第９項の収差量に対するラインパターンの線幅の変化の様子を示す図であり、図１１（Ｂ）は、本発明の予測方法によって求められるＣＤ−フォーカス曲線の一例を示す図である。
【図１２】第４項の成分の大きさに対するラインパターン像の線幅のデータをデータテーブルから求めるＺＳＭ法を用いたときのその線幅の予測結果と、空間像シミュレーションによって求められたＣＤ−フォーカス曲線とを比較するための図である。
【図１３】本発明に係るデバイス製造方法の実施形態を説明するためのフローチャートである。
【図１４】図１３のステップ３０４の詳細を示すフローチャートである。
【符号の説明】
１３_１〜１３_５…可動レンズ、１６…光源、４８…結像性能補正コントローラ、５０…主制御装置、８０…波面収差計測装置、ＥＬ…照明光、ＰＬ…投影光学系、Ｗ…ウエハ（物体）、１００…露光装置、ＡＬＧ…アライメント系。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a prediction method, an evaluation method, an adjustment method, an exposure method, a device manufacturing method, and a program. More specifically, the present invention relates to a prediction method for predicting a pattern transfer characteristic via a projection optical system, and a method using the projection optical system. Evaluation method for evaluating the transfer state of the pattern, adjustment method for adjusting the transfer state of the pattern via the projection optical system, exposure method for transferring the pattern to an object via the projection optical system, device manufacturing method using the exposure method, The present invention also relates to a program for causing a computer to predict a transfer characteristic of a pattern via a projection optical system.
[0002]
[Prior art]
2. Description of the Related Art Generally, in a lithography process for manufacturing a micro device such as a semiconductor device, a display device, a thin film magnetic head, and a micro machine, a pattern formed on a mask or a reticle (hereinafter collectively referred to as a “reticle”) is projected onto a projection optical system. A projection exposure apparatus such as a so-called stepper or a so-called scanner (also referred to as a scanning stepper) for transferring a wafer or a glass plate onto a sensitive object (hereinafter, collectively referred to as a “wafer”) via the substrate is used.
[0003]
In this type of exposure apparatus, it is desirable that a transfer image that is as faithful as possible to a pattern (has good reproducibility) can be formed on a wafer.
[0004]
One of the factors hindering the formation of a transfer image faithful to the pattern is the aberration of the projection optical system. Due to the influence of the aberration of the projection optical system, the image formation state at different transfer positions within the effective visual field (that is, within the exposure field) of the projection optical system becomes different, and the uniformity of the size of the transferred image of the pattern (eg, In the case of a circuit pattern including a fine line pattern extending vertically and horizontally, the uniformity of the line width of the line pattern mainly deteriorates.
[0005]
Therefore, it is essential to minimize the wavefront aberration of the projection optical system for high-accuracy transfer. However, it is very difficult to completely reduce the wavefront aberration to 0 from the viewpoint of technology, cost, etc. Therefore, focusing on the imaging performance for a specific pattern, the wavefront aberration is adjusted so that the imaging performance is not deteriorated. Adjusting the overall balance of aberrations is the next best measure against wavefront aberrations.
[0006]
Recently, in order to measure the imaging performance for a specific pattern, for example, a Zernike polynomial series obtained by developing a wavefront aberration of a projection optical system is used, and the sensitivity of an exposure apparatus is determined based on the sensitivity of each term (Zernike term). A so-called Zernike sensitivity method for predicting the imaging performance has been used. By using this Zernike sensitivity method, it is not necessary to actually print a pattern on a substrate, and it is not necessary to operate an imaging simulation that requires complicated calculations and requires a considerable amount of time for the calculation. Image performance can be evaluated in a short time.
[0007]
On the other hand, the transfer state of the pattern largely depends on the focus of the projection optical system that projects the transferred image. That is, if the pattern and the transferred image transferred onto the wafer are completely in an image-forming relationship (that is, the position of the wafer in the optical axis direction of the projection optical system is the best focus position), The pattern is transferred in the best condition, and the transfer state of the pattern deteriorates as the position shifts (defocuses), and the size of the transferred image fluctuates according to the defocus amount.
[0008]
[Problems to be solved by the invention]
However, the imaging performance that can be evaluated by the above-described Zernike sensitivity method is limited to only the imaging performance in an image plane, such as an abnormal line width value or an in-plane displacement of an image. This is because, for example, a change in the size of the transferred image with respect to the defocus amount includes a high-order even function component, and it is very difficult to express the change by the Zernike sensitivity method, that is, a linear combination of Zernike terms. Because. For this reason, when evaluating the imaging performance of the projection optical system in the focus direction, it is the current situation that the calculation by the above-described imaging simulation is performed for a long time.
[0009]
The present invention has been made under such circumstances, and a first object of the present invention is to provide a prediction method capable of predicting a transfer characteristic of a pattern via a projection optical system in a short time.
[0010]
A second object of the present invention is to provide an evaluation method capable of evaluating the transfer state of a pattern via a projection optical system in a short time.
[0011]
A third object of the present invention is to provide an adjustment method capable of adjusting a transfer state of a pattern via a projection optical system in a short time.
[0012]
A fourth object of the present invention is to provide an exposure method that can improve the throughput.
[0013]
A fifth object of the present invention is to provide a device manufacturing method that contributes to improvement in device productivity.
[0014]
A sixth object of the present invention is to provide a program for causing a computer to execute prediction of transfer characteristics of a pattern via a projection optical system in a short time.
[0015]
[Means for Solving the Problems]
The invention according to claim 1 is a prediction method for predicting a transfer characteristic of a pattern via a projection optical system (PL), wherein a plurality of aberration components obtained by expanding a wavefront aberration of the projection optical system are provided. A plurality of focus-dependent aberration components that vary depending on the defocus amount from the best focus position with respect to an image of a predetermined pattern projected through the projection optical system under predetermined exposure conditions, according to the defocus amount. A first step of correcting based on a change amount of the wavefront aberration, and a size of the image and the defocus amount based on a value of a linear combination of the plurality of aberration components including the corrected focus-dependent aberration component. And a second step of predicting the correspondence between the two.
[0016]
If there is a wavefront aberration in the projection optical system, even if the transfer of the pattern via the projection optical system is performed at the best focus position, the diffracted light contributing to the formation of the transferred image will have a wavefront aberration. An optical path difference occurs, and the optical path difference of the diffracted light increases as the defocusing proceeds from the best focus position.
[0017]
According to the knowledge obtained by the inventor, the change in the optical path difference of the diffracted light according to the defocus changes depending on the focus among the aberration components obtained by developing the wavefront aberration of the projection optical system. It can be considered as a change in a plurality of focus-dependent aberration components. In other words, the change in the imaging state of the transferred image of the pattern according to the defocus amount can be regarded as the change in the wavefront aberration of the projection optical system.
[0018]
Therefore, in the present invention, in the first step, each focus-dependent aberration component is corrected based on the change amount of the wavefront aberration according to the defocus amount, and in the second step, the aberration component including the corrected focus-dependent aberration component is corrected. Calculate the value of the linear combination of. In this way, the correspondence between the size of the image of the predetermined pattern and the defocus amount, which is difficult to predict with the conventional Zernike sensitivity method, can be predicted in a short time without using an imaging simulation or the like. become.
[0019]
In this case, each of the focus-dependent aberration components may be a rotationally symmetric component about the optical axis of the projection optical system.
[0020]
In the predicting method according to claim 1 or 2, as in the predicting method according to claim 3, in the first step, the wavefront aberration of the power series expanded with respect to a radius on the pupil coordinates of the projection optical system is calculated. The change amount of each focus-dependent aberration component is calculated based on the change amount, and the focus-dependent aberration component can be corrected by adding the calculated change amount to the focus-dependent aberration component. .
[0021]
The change amount of the wavefront aberration according to the defocus amount can be represented by a linear combination of the focus-dependent aberration components. Therefore, if the change amount of the wavefront aberration calculated based on the defocus amount is expanded in a power series and is made to correspond to each focus-dependent aberration component, the change amount of each focus-dependent aberration component according to the defocus amount can be obtained. The amounts of these changes become the amounts of correction of the respective focus-dependent aberration components.
[0022]
In the prediction method according to any one of claims 1 to 3, as in the prediction method according to claim 4, in the second step, each of the aberrations with respect to the size of the image under the predetermined exposure condition. Each coefficient is a linear combination of the squares of the aberration components with the sensitivity of the square of the component as a coefficient, and the sensitivity of the cross term of the different aberration components with respect to the size of the image under the predetermined exposure condition is a coefficient. Based on the linear combination of the cross terms, a value of a linear combination corresponding to a change caused by the wavefront aberration in the size of the image can be calculated.
[0023]
According to this, the change in the size of the image is sensitive to the square of each aberration component and the cross term between the different aberration components, and taking into account the linear combination of those terms, the image is not sensitive to the defocus amount. The size change amount can be calculated.
[0024]
In the prediction method according to any one of claims 1 to 4, as in the prediction method according to claim 5, each of the aberration components is a coefficient of each Zernike term in a Zernike polynomial series. Can be. A typical fringe Zernike polynomial series is a typical aberration component obtained by developing the wavefront aberration of the projection optical system. In the present invention, this Zernike polynomial series can naturally be applied as each aberration component. In this case, the focus-dependent aberration component typically includes, for example, the fourth, ninth, sixteenth, twenty-fifth, and thirty-second terms of the Zernike polynomial series.
[0025]
In this case, as in the prediction method according to claim 6, the second step is based on a data table indicating the relationship between the value of the aberration component of the fourth term in the Zernike polynomial series created in advance and the size of the image. The amount of change in the size of the image, based on the amount of change in the size of the image obtained by the above method and the amount of change in the size of the image obtained based on the linear combination of the aberration components of the respective items except the fourth item Can be obtained.
[0026]
The invention according to claim 7 is an evaluation method for evaluating a transfer state of a pattern via a projection optical system, wherein a predetermined pattern is set at each of a plurality of measurement points in an effective visual field of the projection optical system. And performing the prediction method according to any one of claims 1 to 6 for each measurement point to predict a correspondence relationship between an image size of the predetermined pattern and the defocus amount; Evaluating the uniformity of the image of the predetermined pattern within the effective field of view of the projection optical system based on the result.
[0027]
According to this, the correspondence between the size of the image of the predetermined pattern and the defocus amount can be predicted in a short time using the prediction method according to any one of claims 1 to 6. Therefore, the uniformity of the image of the predetermined pattern in the effective visual field of the projection optical system can be evaluated in a short time based on the correspondence.
[0028]
In this case, as in the evaluation method according to claim 8, the predetermined pattern includes two line patterns orthogonal to each other provided on a plane orthogonal to the optical axis direction of the projection optical system. Alternatively, the predetermined pattern may include two parallel line patterns provided on a plane orthogonal to the optical axis direction of the projection optical system. it can. In these cases, the correspondence can be predicted for each of the line patterns as in the evaluation method of the tenth aspect. In such a case, at each measurement point, for example, the uniformity of the vertical and horizontal line width difference mainly due to astigmatism and the uniformity of the line width abnormal value mainly due to coma aberration can be evaluated.
[0029]
According to an eleventh aspect of the present invention, there is provided an adjusting method for adjusting a transfer state of a pattern via a projection optical system, wherein the evaluation method according to any one of the seventh to tenth aspects is performed to execute the projection method. Evaluating the uniformity of the transfer state of the image of the predetermined pattern within the effective visual field of the optical system; adjusting the transfer state of the predetermined pattern via the projection optical system based on the evaluation result; The adjustment method includes:
[0030]
According to this, the uniformity of the transfer state of the image of the predetermined pattern within the effective visual field of the projection optical system is evaluated in a short time by using the evaluation method according to any one of claims 7 to 10. Based on the evaluation result, the transfer state of the predetermined pattern via the projection optical system can be adjusted in a short time so that the uniformity of the transfer state of the image of the predetermined pattern is improved.
[0031]
According to a twelfth aspect of the present invention, there is provided an exposure method for transferring a pattern to an object via a projection optical system, wherein the adjusting method according to the eleventh aspect is performed every time an exposure condition is set. Adjusting the transfer state of the pattern via the projection optical system; and, under the set exposure condition, the pattern formed on the mask in the adjusted transfer state via the projection optical system. Transferring to the object by using an exposure method.
[0032]
According to this, the transfer state of the pattern is adjusted in a short time by executing the adjustment method according to claim 11, and the pattern is transferred onto the object in the adjusted transfer state. Can be improved.
[0033]
According to a thirteenth aspect of the present invention, there is provided a device manufacturing method including a lithography step, wherein in the lithography step, the exposure method according to the twelfth aspect is performed to perform exposure.
[0034]
According to this, since the exposure can be accurately performed in a short time by using the exposure method according to the twelfth aspect, the productivity of the device can be improved.
[0035]
According to a fourteenth aspect of the present invention, there is provided a program for causing a computer to predict a transfer characteristic of a pattern via a projection optical system, wherein the plurality of aberration components are obtained by developing a wavefront aberration of the projection optical system. A plurality of focus-dependent aberration components that vary depending on the defocus amount from the best focus position with respect to an image of a predetermined pattern projected through the projection optical system under predetermined exposure conditions, according to the defocus amount. A first procedure of correcting based on the change amount of the wavefront aberration; and a size of the image and the defocus amount based on a value of a linear combination of the plurality of aberration components including the corrected focus-dependent aberration component. And a second procedure for estimating the correspondence between the two.
[0036]
When this program is installed in the computer, the computer executes each of the above procedures. Thereby, the prediction method according to claim 1 is executed by the control computer. Therefore, the transfer characteristic of the pattern via the projection optical system can be predicted in a short time as in the first aspect.
[0037]
In this case, as in a program according to a fifteenth aspect, each of the focus-dependent aberration components may be a rotationally symmetric component about the optical axis of the projection optical system.
[0038]
In the program according to claim 14 or 15, as in the program according to claim 16, in the first procedure, a change amount of the wavefront aberration that is power series expanded with respect to a radius on a pupil coordinate of the projection optical system. Calculating a change amount of each of the focus-dependent aberration components based on the above, and causing the computer to execute a procedure of correcting each of the focus-dependent aberration components by adding the calculated change amount to the focus-dependent aberration component. can do.
[0039]
The program according to any one of claims 14 to 16, wherein, in the second step, each of the aberrations with respect to a change in the size of the image under the predetermined exposure condition. The linear combination of the squares of the respective aberration components with the sensitivity of the square of the component as the respective coefficient, and the sensitivity of the cross term between the different aberration components with respect to the change in the size of the image under the predetermined exposure condition, respectively. And calculating a linear combination value corresponding to a change in the size of the image caused by the wavefront aberration based on the linear combination of the cross terms.
[0040]
In the program according to any one of the fourteenth to seventeenth aspects, as in the program according to the eighteenth aspect, each of the aberration components may be a coefficient of each term in a Zernike polynomial series.
[0041]
In this case, as in the program according to claim 19, in the second procedure, based on a data table indicating a relationship between the size of the aberration component of the fourth term in the Zernike polynomial series created in advance and the size of the image. The amount of change in the size of the image is calculated based on the amount of change in the size of the obtained image and the amount of change in the size of the image obtained based on the linear combination of the aberration components of the respective items except the fourth term. The computer may execute the required procedure.
[0042]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, an embodiment of the present invention will be described with reference to FIGS.
[0043]
FIG. 1 shows a schematic configuration of an exposure apparatus 100 according to an embodiment to which the adjustment method and the exposure method of the present invention are applied. The exposure apparatus 100 is a step-and-scan projection exposure apparatus (a so-called scanner).
[0044]
Exposure apparatus 100 includes an illumination system including light source 16 and illumination optical system 12, and a reticle stage RST as a mask stage for holding reticle R as a mask illuminated by exposure illumination light EL as an energy beam from the illumination system. , A projection optical system PL that projects the exposure illumination light EL emitted from the reticle R onto a wafer W (on an image plane) as an object, a wafer stage WST that holds the wafer W, and a control system therefor. I have.
[0045]
Here, a KrF excimer laser (output wavelength: 248 nm) is used as the light source 16. In addition, as the light source 16, F ₂ A pulsed ultraviolet light source that outputs pulsed light in a vacuum ultraviolet region such as a laser (output wavelength 157 nm) or an ArF excimer laser (output wavelength 193 nm) may be used.
[0046]
The light source 16 is actually a clean room in which the chamber 11 in which the components of the illumination optical system 12 and the exposure apparatus body including the reticle stage RST, the projection optical system PL, and the wafer stage WST are housed is installed. It is installed in another service room with low cleanliness, and is connected to the chamber 11 via a light transmission optical system (not shown) including at least a part of an optical axis adjustment optical system called a beam matching unit. In the light source 16, based on control information TS from the main controller 50, an internal controller turns on / off the output of the laser beam LB, energy per pulse of the laser beam LB, oscillation frequency (repetition frequency), The center wavelength and the spectrum half width (wavelength width) are controlled.
[0047]
The illumination optical system 12 includes a cylinder lens, a beam expander (both not shown), an optical integrator (homogenizer) 22, a beam shaping / illumination uniforming optical system 20, a first relay lens 28A, and a second relay lens 28B. , Fixed reticle blind 30A, movable reticle blind 30B, mirror M for bending the optical path, condenser lens 32, and the like. As the optical integrator, a fly-eye lens, a rod integrator (internal reflection type integrator), a diffractive optical element, or the like can be used. In the present embodiment, since a fly-eye lens is used as the optical integrator 22, it is also referred to as a fly-eye lens 22 below.
[0048]
The beam shaping / illuminance uniforming optical system 20 is connected to a light transmitting optical system (not shown) via a light transmission window 17 provided in the chamber 11. The beam shaping / illuminance uniforming optical system 20 shapes the cross-sectional shape of the laser beam LB that is pulsed by the light source 16 and enters through the light transmission window 17 using, for example, a cylinder lens or a beam expander. Further, in the beam shaping / illuminance uniforming optical system 20, the laser beam is provided with an energy rough adjuster (not shown) having an ND filter capable of changing the transmittance in a geometric series in a plurality of steps or continuously. An optical unit (not shown) including at least one of a plurality of exchangeable diffractive optical elements, a prism (cone prism, polyhedral prism, etc.) movable along the optical axis of the illumination optical system, and a zoom optical system; Through the optical integrator 22. When the optical integrator 22 is a fly-eye lens, the optical unit has an intensity distribution of illumination light on its incident surface, and when the optical integrator 22 is an internal reflection type integrator, an incident angle range of the illumination light on the incident surface. By changing the parameters, the light amount distribution of the illumination light on the pupil plane of the illumination optical system (the size and shape of the secondary light source), that is, the illumination condition of the reticle R is changed. In addition, this optical unit is designed to minimize the loss of light quantity when the illumination conditions are changed.
[0049]
The fly-eye lens 22 located on the exit end side inside the beam shaping / illumination uniforming optical system 20 illuminates the reticle R with a uniform illuminance distribution by the above-described incidence of the laser beam LB. A surface light source (secondary light source) composed of a number of point light sources (light source images) is formed on the exit-side focal plane that is arranged so as to substantially coincide with the pupil plane of No. 12. Hereinafter, the laser beam emitted from the secondary light source is referred to as “illumination light EL”. When the optical integrator 22 is an internal reflection type integrator, a plurality of light source images (virtual images) formed by the internal reflection type integrator are also called secondary light sources.
[0050]
A relay optical system including a first relay lens 28A and a second relay lens 28B is disposed on the optical path of the illumination light EL emitted from the optical integrator 22 with a fixed reticle blind 30A and a movable reticle blind 30B interposed therebetween. The fixed reticle blind 30A is arranged on a plane slightly defocused from a conjugate plane with respect to the pattern plane of the reticle R, and has a rectangular opening defining a rectangular illumination area IAR on the reticle R. A movable reticle blind 30B having an opening whose position and width in the direction corresponding to the scanning direction (the Y-axis direction, which is the horizontal direction in the drawing of FIG. 1) is arranged near the fixed reticle blind 30A. By further restricting the illumination area via the movable reticle blind 30B at the start and end of the exposure, unnecessary portions are prevented from being exposed. Further, the width of the opening of the movable reticle blind 30B is variable also in a direction corresponding to a non-scanning direction orthogonal to the scanning direction (an X-axis direction which is a direction orthogonal to the plane of FIG. The width of the illumination area in the non-scanning direction can be adjusted according to the pattern of the reticle R.
[0051]
On the optical path of the illumination light EL behind the second relay lens 28B constituting the relay optical system, a bending mirror M for reflecting the illumination light EL passing through the second relay lens 28B toward the reticle R is arranged. A condenser lens 32 is arranged on the optical path of the illumination light EL behind the mirror M.
[0052]
In the above configuration, the entrance surface of the fly-eye lens 22, the arrangement surface of the movable reticle blind 30B, and the pattern surface of the reticle R are optically set to be conjugate with each other and formed on the exit-side focal plane of the fly-eye lens 22. The light source plane (pupil plane of the illumination optical system) and the Fourier transform plane (exit pupil plane) of the projection optical system PL are optically set to be conjugate to each other, forming a Koehler illumination system.
[0053]
To briefly explain the operation of the illumination system configured as described above, the laser beam LB pulsed from the light source 16 is incident on the beam shaping / illuminance uniforming optical system 20 and the cross-sectional shape is shaped. Thereafter, the light enters the fly-eye lens 22. Thus, the above-described secondary light source is formed on the emission-side focal plane of the fly-eye lens 22.
[0054]
The illumination light EL emitted from the secondary light source reaches the fixed reticle blind 30A via the first relay lens 28A, passes through the opening of the fixed reticle blind 30A, the movable reticle blind 30B, and further passes through the second relay lens 28B. After the optical path is bent vertically downward by the mirror M, the rectangular illumination area IAR on the reticle R held on the reticle stage RST is illuminated with a uniform illuminance distribution via the condenser lens 32.
[0055]
A reticle R is loaded on the reticle stage RST, and is held by suction via an electrostatic chuck (or vacuum chuck) (not shown). The reticle stage RST is configured to be capable of fine driving (including rotation) in a horizontal plane (XY plane) by a driving system (not shown). The reticle stage RST can be finely driven in an XY plane perpendicular to an optical axis IX of an illumination system (coincident with an optical axis AX of a projection optical system PL described later) by a reticle stage drive unit (not shown) including, for example, a linear motor. (Including rotation about the Z axis), and can be driven at a scanning speed specified in a predetermined scanning direction (here, the Y axis direction).
[0056]
The position of the reticle stage RST in the XY plane is, for example, 0.5 to 1 nm by a reticle laser interferometer (hereinafter, referred to as a “reticle interferometer”) 54R via a reflection surface provided or formed on the reticle stage RST. It is always detected with a resolution of the order. The position information of reticle stage RST from reticle interferometer 54R is supplied to main controller 50 installed outside main body chamber 11. Main controller 50 drives and controls reticle stage RST via a reticle stage driving unit (not shown) based on the position information of reticle stage RST.
[0057]
Note that the material used for the reticle R needs to be properly used depending on the light source used. That is, when a KrF excimer laser or an ArF excimer laser is used as a light source, synthetic quartz, fluoride crystal such as fluorite, or fluorine-doped quartz can be used. ₂ When a laser is used, it is necessary to use a fluoride crystal such as fluorite or fluorine-doped quartz.
[0058]
As the projection optical system PL, for example, a both-side telecentric reduction system is used. The projection magnification of the projection optical system PL is, for example, 1/4, 1/5 or 1/6. Therefore, as described above, when the illumination area IAR on the reticle R is illuminated by the illumination light EL, a reduced image of the circuit pattern or the like of the reticle R in the illumination area IAR is projected via the projection optical system PL. It is formed in an irradiation area (exposure area) IA of the illumination light EL on the wafer W conjugate to the illumination area IAR.
[0059]
As the projection optical system PL, a refraction system including only a plurality of, for example, about 10 to 20 refraction optical elements (lens elements) 13 is used. Of the plurality of lens elements 13 constituting the projection optical system PL, a plurality of lens elements 13 on the object plane side (the reticle R side) (here, five are used for simplicity of description). ₁ , 13 ₂ , 13 ₃ , 13 ₄ , 13 ₅ Is a movable lens that can be driven externally by the imaging performance correction controller 48. Lens element 13 ₁ ~ 13 ₅ Are held in the lens barrel via respective lens holders having a double structure (not shown). These lens elements 13 ₁ ~ 13 ₅ Are held by inner lens holders, respectively, and these inner lens holders are supported by the drive lens (not shown), for example, a piezo element, at three points in the direction of gravity with respect to the outer lens holder. By independently adjusting the voltages applied to these drive elements, the lens element 13 ₁ ~ 13 ₅ Are driven in the Z-axis direction, which is the optical axis direction of the projection optical system PL, and are tilted with respect to the XY plane (that is, the rotation direction around the X-axis (θx direction) and the rotation direction around the Y-axis (θy direction)). It has a drivable (tiltable) configuration.
[0060]
Other lens elements 13 are held in a lens barrel via a normal lens holder. Note that the lens element 13 ₁ ~ 13 ₅ Not only that, but a lens disposed near the pupil plane of the projection optical system PL or on the image plane side, or an aberration correction plate (optical plate) for correcting aberrations of the projection optical system PL, particularly non-rotationally symmetric components thereof, is driven. You may comprise so that it is possible. Further, the degrees of freedom (movable directions) of these drivable optical elements are not limited to three, but may be one, two, or four or more.
[0061]
In the vicinity of the pupil plane of the projection optical system PL, a pupil aperture stop 15 capable of continuously changing the numerical aperture (NA) within a predetermined range is provided. As the pupil aperture stop 15, for example, a so-called iris stop is used. The pupil aperture stop 15 is controlled by the main controller 50.
[0062]
When KrF excimer laser light or ArF excimer laser light is used as the illumination light EL, each lens element constituting the projection optical system PL may be made of a fluoride crystal such as fluorite or the above-mentioned fluorine-doped quartz, Quartz can also be used, but F ₂ When a laser beam is used, the material of the lens used for the projection optical system PL is a fluoride crystal such as fluorite or fluorine-doped quartz.
[0063]
The wafer W is held on the wafer stage WST via a wafer holder (not shown) by electrostatic suction (or vacuum suction) or the like.
[0064]
Wafer stage WST is arranged below projection optical system PL, and can be moved in the XY plane direction and the Z-axis direction by a wafer stage drive unit (not shown) including a linear motor, a voice coil motor (VCM), and the like. It can be finely driven also in an inclination direction with respect to the XY plane (a rotation direction around the X axis (θx direction) and a rotation direction around the Y axis (θy direction)). In other words, the wafer stage WST is not only moved in the scanning direction (Y-axis direction), but also moved so that a plurality of shot areas on the wafer W can be moved relative to the exposure area to perform scanning exposure. It is also configured to be movable in a non-scanning direction (X-axis direction) orthogonal to the direction, thereby performing scanning (scanning) exposure of each shot area on the wafer W and acceleration for exposure of the next shot A step-and-scan operation that repeats the operation of moving (stepping) to the start position can be performed.
[0065]
The position of the wafer stage WST in the XY plane (including rotation about the Z axis (θz rotation)) is determined via a reflection surface provided or formed on the wafer stage WST via a wafer laser interferometer (hereinafter, referred to as “wafer interference”). 54 W), which is always detected with a resolution of, for example, about 0.5 to 1 nm. Wafer interferometer 54W includes a plurality of multi-axis interferometers having a plurality of length measurement axes, and these interferometers rotate wafer stage WST (θz rotation (yaw), θy rotation (pitching) rotation around Y axis). , And θx rotation (rolling), which is rotation about the X axis, can be measured.
[0066]
Position information (or speed information) of wafer stage WST detected by wafer interferometer 54W is supplied to main controller 50. Main controller 50 controls the position of wafer stage WST via a wafer stage driving unit (not shown) based on the position information (or speed information) of wafer stage WST.
[0067]
On wafer stage WST, reference mark plate FM on which a reference mark such as a so-called baseline measurement reference mark of alignment system ALG described later is formed, the surface of which is substantially at the same height as the surface of wafer W. So that it is fixed.
[0068]
Further, a wavefront aberration measuring device 80 as a detachable portable optical characteristic measuring device is attached to a side surface on the + Y side (right side in the paper surface of FIG. 1) of wafer stage WST.
[0069]
As shown in FIG. 2, the wavefront aberration measuring apparatus 80 includes a hollow housing 82, a light receiving optical system 84 including a plurality of optical elements arranged in a predetermined positional relationship inside the housing 82, A light-receiving unit 86 disposed at an end portion on the −X side inside the housing 82.
[0070]
The housing 82 is made of a member having an L-shaped YZ cross section and having a space formed therein, and the uppermost portion (the end in the + Z direction) receives light from above the housing 82 in the internal space of the housing 82. The opening 82a is formed in a circular shape in plan view (as viewed from above) so as to be incident toward. A cover glass 88 is provided to cover the opening 82a from the inside of the housing 82. On the upper surface of the cover glass 88, a light-shielding film having a circular opening in the center is formed by vapor deposition of a metal such as chrome, and the light-shielding film eliminates unnecessary light from the surroundings when measuring the wavefront aberration of the projection optical system PL. Light is blocked from entering the light receiving optical system 84.
[0071]
The light receiving optical system 84 includes an objective lens 84a, a relay lens 84b, a bending mirror 84c, and a −X side of the bending mirror 84c, which are sequentially arranged from top to bottom below the cover glass 88 inside the housing 82. , And a collimator lens 84d and a microlens array 84e which are sequentially arranged. The bending mirror 84c is inclined at 45 °, and the bending mirror 84c bends the optical path of the light incident on the objective lens 84a vertically downward from the top toward the collimator lens 84d. . Each optical member constituting the light receiving optical system 84 is fixed to the inside of the wall of the housing 82 via a holding member (not shown). The micro lens array 84e is configured by arranging a plurality of small convex lenses (lens elements) in an array in a plane orthogonal to the optical path.
[0072]
The light receiving section 86 includes a light receiving element composed of a two-dimensional CCD or the like, and an electric circuit such as a charge transfer control circuit. The light receiving element has an area sufficient to receive all of the light beams that enter the objective lens 84a and exit from the micro lens array 84e. The measurement data from the light receiving section 86 is output to the main controller 50 via a signal line (not shown) or by wireless transmission.
[0073]
By using the above-described wavefront aberration measuring device 80, the wavefront aberration of the projection optical system PL can be measured on-body. A method for measuring the wavefront aberration of the projection optical system PL using the wavefront aberration measurement device 80 will be described later.
[0074]
Returning to FIG. 1, the exposure apparatus 100 of the present embodiment has a light source whose on / off is controlled by the main controller 50, and has a large number of pinholes or slits directed toward the imaging plane of the projection optical system PL. An irradiation system 60a for irradiating an image forming light beam for forming an image obliquely with respect to the optical axis AX, and a light receiving system 60b for receiving the reflected light beam of the image forming light beam on the surface of the wafer W. A multi-point focal position detection system (hereinafter simply referred to as a “focus position detection system”) is provided. The detailed configuration of the multipoint focal position detection system similar to the focal position detection systems (60a, 60b) of the present embodiment is disclosed in, for example, Japanese Patent Application Laid-Open No. Hei 6-283403. The multipoint focal position detection system described in the publication has a function of prefetching not only the exposure area IA on the wafer W but also the undulation of the wafer W in the scanning direction. The shape of the light beam irradiated by the irradiation system 60a may be a parallelogram or another shape.
[0075]
The main controller 50 controls the Z of the wafer W such that the defocus is zero or within the depth of focus based on a defocus signal (defocus signal) from the light receiving system 60b, for example, an S-curve signal during scanning exposure or the like. By controlling the position and the inclination with respect to the XY plane via a wafer stage drive unit (not shown), auto focus (auto focus) and auto leveling are executed. The main controller 50 also measures and aligns the Z position of the wavefront aberration measurement device 80 using the focal position detection system (60a, 60b) when measuring the wavefront aberration described below. At this time, the inclination of the wavefront aberration measurement device 80 may be measured as needed.
[0076]
Further, exposure apparatus 100 employs an off-axis method used for position measurement of an alignment mark on wafer W held on wafer stage WST and a reference mark formed on reference mark plate FM. An alignment system ALG is provided. As the alignment system ALG, for example, a target band is irradiated with a broadband detection light beam that does not expose the resist on the wafer, and an image of the target mark formed on the light receiving surface by reflected light from the target mark and an index (not shown) An image processing type FIA (Field Image Alignment) sensor that captures an image of the image using an image sensor (CCD or the like) and outputs an image signal of the image is used. In addition to the FIA system, a target mark is irradiated with coherent detection light to detect scattered light or diffracted light generated from the target mark, or two diffracted lights (for example, the same order) generated from the target mark. Of course, it is possible to use an alignment sensor for detecting by causing interference with each other alone or in an appropriate combination.
[0077]
Further, in the exposure apparatus 100 of the present embodiment, although not shown, a reticle mark on the reticle R and a reference mark on a reference mark plate corresponding to the reticle R are projected above the reticle R via the projection optical system PL. A pair of reticle alignment detection systems including a TTR (Through The Reticle) alignment optical system using an exposure wavelength for simultaneous observation are provided. As these reticle alignment detection systems, those having the same configuration as that disclosed in, for example, JP-A-7-176468 are used.
[0078]
The control system is mainly configured by the main controller 50 in FIG. The main controller 50 includes a so-called workstation (or microcomputer) including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. In addition to performing the control operation described above, the entire apparatus is generally controlled. Main controller 50 generally controls, for example, shot-to-shot stepping, exposure timing, and the like of wafer stage WST so that the exposure operation is appropriately performed.
[0079]
Further, the main controller 50 is connected to a storage device 42 composed of, for example, a hard disk, an input device 45 including a pointing device such as a keyboard and a mouse, and a display device 44 such as a CRT display (or a liquid crystal display). ing. Further, a simulation computer 46 such as a workstation or a personal computer is connected to the main controller 50 via a communication network such as a LAN. In the simulation computer 46, imaging simulation software in which an optical model of the exposure apparatus 100 is set, that is, an imaging simulator is installed.
[0080]
Next, a method of measuring wavefront aberration in exposure apparatus 100 performed at the time of maintenance or the like will be described. In the following description, for simplification of the description, it is assumed that the aberration of the light receiving optical system 84 in the wavefront aberration measuring device 80 is so small as to be negligible.
[0081]
During normal exposure, the wavefront aberration measurement device 80 is detached from the wafer stage WST. Therefore, when measuring the wavefront, first, an operator or a service engineer (hereinafter, appropriately referred to as an “operator”) or the like (hereinafter, appropriately referred to as “operator etc.”) An operation of attaching the wavefront aberration measurement device 80 to the is performed. In this mounting, the wavefront aberration measurement device 80 is fixed to a predetermined reference surface (here, the surface on the + Y side) via a bolt or a magnet so that the wavefront aberration measurement device 80 is within the movement stroke of the wafer stage WST during wavefront measurement. .
[0082]
After the completion of the mounting, in response to the input of a measurement start command by an operator or the like, main controller 50 sets a wafer stage driving unit (not shown) so that wavefront aberration measuring device 80 is positioned below alignment system ALG. ) To move the wafer stage WST. Then, main controller 50 detects an alignment mark (not shown) provided in wavefront aberration measuring device 80 by alignment system ALG, and determines the position based on the detection result and the measured value of wafer interferometer 54W at that time. The position coordinates of the alignment mark are calculated, and the accurate position of the wavefront aberration measuring device 80 is obtained. After the position of the wavefront aberration measuring device 80 is measured, the main controller 50 executes the measurement of the wavefront aberration as follows.
[0083]
First, main controller 50 loads a not-shown measurement reticle (hereinafter, referred to as a “pinhole reticle”) on which a pinhole pattern has been formed by a not-shown reticle loader onto reticle stage RST. This pinhole reticle is a reticle in which pinholes (pinholes which become almost ideal point light sources and generate spherical waves) are formed at a plurality of points in the same area as the illumination area IAR on the pattern surface.
[0084]
Note that the pinhole reticle used here is provided with a diffusing surface on the upper surface, for example, to distribute light from the pinhole pattern over substantially the entire pupil plane of the projection optical system PL, so that the projection optical system PL It is assumed that the wavefront aberration is measured over the entire pupil plane. In this embodiment, since the aperture stop 15 is provided near the pupil plane of the projection optical system PL, the wavefront aberration is substantially measured at the pupil plane defined by the aperture stop 15.
[0085]
After loading the pinhole reticle, main controller 50 detects a reticle alignment mark formed on the pinhole reticle using the above-described reticle alignment detection system, and sets the pinhole reticle to a predetermined position based on the detection result. Align to position. Thereby, the center of the pinhole reticle and the optical axis of the projection optical system PL substantially match.
[0086]
Thereafter, the main controller 50 gives the light source 16 the control information TS to emit the laser beam LB. Thereby, the illumination light EL from the illumination optical system 12 is applied to the pinhole reticle. Then, light emitted from the plurality of pinholes of the pinhole reticle is condensed on the image plane via the projection optical system PL, and an image of the pinhole is formed on the image plane.
[0087]
Next, main controller 50 sets the aperture 82a of wavefront aberration measurement device 80 at the image formation point where an image of any pinhole (hereinafter referred to as a pinhole of interest) on the pinhole reticle is formed. The wafer stage WST is moved via a wafer stage driving unit (not shown) while monitoring the measured value of the wafer interferometer 54W such that the centers substantially coincide. At this time, the main controller 50 matches the upper surface of the cover glass 88 of the wavefront aberration measuring device 80 with the image plane on which the pinhole image is formed based on the detection result of the focus position detection system (60a, 60b). To this end, wafer stage WST is minutely driven in the Z-axis direction via a wafer stage driving unit (not shown). At this time, the inclination angle of wafer stage WST is adjusted as needed. As a result, the image light flux of the pinhole of interest enters the light receiving optical system 84 through the central opening of the cover glass 88 and is received by the light receiving element constituting the light receiving section 86.
[0088]
More specifically, a spherical wave is generated from the pinhole of interest on the pinhole reticle, and this spherical wave is used as an objective lens constituting the projection optical system PL and the light receiving optical system 84 of the wavefront aberration measuring device 80. A collimated light beam passes through a microlens array 84e via a relay lens 84a, a relay lens 84b, a mirror 84c, and a collimator lens 84d. Thereby, the pupil plane of the projection optical system PL is relayed to the microlens array 84e and is divided. Then, each light is condensed on the light receiving surface of the light receiving element by each lens element of the micro lens array 84e, and the image of the pinhole is formed on the light receiving surface.
[0089]
At this time, if the projection optical system PL is an ideal optical system having no wavefront aberration, the wavefront on the pupil plane of the projection optical system PL becomes an ideal wavefront (here, a plane), and as a result, the microlens array The parallel light beam incident on 84e becomes a plane wave, and its wavefront should be an ideal wavefront. In this case, as shown in FIG. 3A, a spot image (hereinafter, also referred to as “spot”) is formed at a position on the optical axis of each lens element constituting the microlens array 84e.
[0090]
However, since the projection optical system PL usually has a wavefront aberration, the wavefront of the parallel light beam incident on the microlens array 84e is shifted from the ideal wavefront, and the shift, that is, the inclination of the wavefront with respect to the ideal wavefront, As shown in FIG. 3B, the image forming position of each spot is shifted from the position on the optical axis of each lens element of the microlens array 84e. In this case, the displacement of each spot from the reference point (the position of each lens element on the optical axis) corresponds to the inclination of the wavefront.
[0091]
The light (light flux of the spot image) incident on each light condensing point on the light receiving element constituting the light receiving section 86 is photoelectrically converted by the light receiving element, and the photoelectric conversion signal is sent to the main controller 50 via an electric circuit. Sent. The main controller 50 calculates the imaging position of each spot on the basis of the photoelectric conversion signal, and further calculates the displacement (Δξ, Δη) using the calculation result and the position data of the known reference point. And store it in the RAM. At this time, main controller 50 stores the measured value (X) of wafer interferometer 54W at that time. _i , Y _i ) Is supplied.
[0092]
As described above, when the measurement of the positional shift of the spot image by the wavefront aberration measuring device 80 at the focus point of one pinhole image of interest is completed, the main control device 50 forms the next pinhole image. Wafer stage WST is moved such that the center of aperture 82a of wavefront aberration measuring device 80 substantially coincides with the point. When this movement is completed, the main controller 50 emits the laser beam LB from the light source 16 in the same manner as described above, and similarly, the main controller 50 calculates the imaging position of each spot. Thereafter, the same measurement is sequentially performed at the other imaging points of the pinhole image.
[0093]
When the necessary measurement is completed in this manner, the RAM of main controller 50 stores the above-described positional deviation data (Δξ, Δη) at the imaging point of each pinhole image and the coordinates of each imaging point. Data (measured value (X) of wafer interferometer 54W when measurement was performed at the imaging point of each pinhole image _i , Y _i )) Are stored. Note that, at the time of the above measurement, the movable reticle blind 30B is used to illuminate only the pinhole of interest on the reticle, or at least a partial area including the pinhole of interest, with the illumination light EL. Alternatively, the position and size of the illumination area on the reticle may be changed.
[0094]
Next, main controller 50 will be described below based on the positional deviation data (Δξ, Δη) at the imaging point of each pinhole image stored in the RAM and the coordinate data of each imaging point. The wavefront (wavefront aberration) corresponding to the imaging point of the pinhole image in accordance with the principle of the following, ie, the first measurement point (evaluation point) to the n-th measurement point (evaluation point) in the field of view of the projection optical system PL, Then, the coefficient of each term of the fringe Zernike polynomial (hereinafter abbreviated as “Zernike polynomial” as appropriate) of equation (3) described later, for example, the coefficient Z of the first term ₁ ~ Coefficient Z of the 37th term ₃₇ Is calculated according to the conversion program.
[0095]
In the present embodiment, the wavefront of the projection optical system PL is obtained by an operation according to the conversion program based on the above-described positional deviation (Δξ, Δη). That is, the displacement (Δξ, Δη) is a value that directly reflects the inclination of the wavefront with respect to the ideal wavefront, and conversely, the wavefront can be restored based on the displacement (Δξ, Δη). Note that, as is clear from the physical relationship between the above-described positional deviation (Δξ, Δη) and the wavefront, the principle of calculating the wavefront in the present embodiment is the well-known Shack-Hartmann wavefront calculation principle itself.
[0096]
Next, a brief description will be given of a method of calculating a wavefront based on the above-described positional deviation.
[0097]
As described above, the positional deviation (Δξ, Δη) corresponds to the inclination of the wavefront, and the shape of the wavefront (strictly speaking, deviation from the reference plane (ideal wavefront)) is obtained by integrating this. Assuming that the equation of the wavefront (the deviation of the wavefront from the reference plane) is W (x, y) and the proportional coefficient is k, the following relational expressions (1) and (2) are established.
[0098]
(Equation 1)

[0099]
Since it is not easy to integrate the inclination of the wavefront given only by the spot position as it is, it is assumed that the surface shape is developed into a series to fit this. In this case, the series should be orthogonal. The Zernike polynomial is a series suitable for developing axisymmetric surfaces, and expands in the circumferential direction into a triangular series. That is, if the wavefront W is represented by a polar coordinate system (ρ, θ), it can be expanded as in the following expression (3).
[0100]
(Equation 2)

[0101]
Since it is an orthogonal system, the coefficient Z of each term _i Can be determined independently. Cutting i by an appropriate value corresponds to performing some sort of filtering. In addition, as an example, f of the first to 37th items _i To Z _i Table 1 below shows an example. However, the 37th term in Table 1 corresponds to the 49th term in an actual Zernike polynomial, but is treated as a term of i = 37 (the 37th term) in this specification. That is, in the present invention, the number of terms of the Zernike polynomial is not particularly limited.
[0102]
[Table 1]

[0103]
In practice, the derivative is detected as the above-mentioned positional deviation, so that the fitting needs to be performed on the derivative. In the polar coordinate system (x = ρcosθ, y = ρsinθ), it is expressed as in the following equations (4) and (5).
[0104]
[Equation 3]

[0105]
Since the differential form of the Zernike polynomial is not an orthogonal system, fitting must be performed by the least square method. Since information (shift amount) of the image forming point of one spot image is given in the X and Y directions, the number of pinholes is set to n (n is the number of measurement points (evaluation points) in the effective visual field of the projection optical system PL). In this embodiment, n is assumed to be, for example, 33 for the sake of simplicity of the description, and the number of observation equations given by the above equations (1) to (5) is 2n (= 66) ).
[0106]
Each term in the Zernike polynomial corresponds to an optical aberration. Moreover, the low-order term (the term with a small i) substantially corresponds to Seidel aberration. By using the Zernike polynomial, the wavefront aberration of the projection optical system PL can be obtained.
[0107]
The calculation procedure of the conversion program is determined according to the above-described principle, and the calculation process according to the conversion program determines the wavefronts corresponding to the first to n-th measurement points in the field of view of the projection optical system PL. Information (wavefront aberration), here, the coefficient of each term of the Zernike polynomial, for example, the coefficient Z of the first term ₁ ~ Coefficient Z of the 37th term ₃₇ Is required.
[0108]
In the storage device 42, a database of a wavefront aberration change table of the projection optical system PL is stored. Here, the wavefront aberration change table is obtained by performing a simulation using a model substantially equivalent to the projection optical system PL, and optimizing a state of formation of a projected image of the pattern on the wafer obtained as a result of the simulation. Of the unit adjustment amount of the adjustment parameter that can be used for conversion, and the imaging performance corresponding to each of a plurality of measurement points in the field of view of the projection optical system PL, specifically, wavefront data, for example, the first of Zernike polynomials 39 is a change table including a data group in which data indicating the relationship between the coefficients of the items to the 37th item and the amount of change is arranged according to a predetermined rule.
[0109]
In the present embodiment, the movable lens 13 is used as the adjustment parameter. ₁ , 13 ₂ , 13 ₃ , 13 ₄ , 13 ₅ Drive amount z in each of the degrees of freedom (drivable direction) ₁ , Θx ₁ , Θy ₁ , Z ₂ , Θx ₂ , Θy ₂ , Z ₃ , Θx ₃ , Θy ₃ , Z ₄ , Θx ₄ , Θy ₄ , Z ₅ , Θx ₅ , Θy ₅ And a total of 19 parameters of the drive amounts Wz, Wθx, Wθy of the surface of the wafer W (wafer stage WST) in three degrees of freedom and the shift amount Δλ of the wavelength of the illumination light EL.
[0110]
Here, a procedure for creating the database of the wavefront aberration change table will be briefly described. First, optical conditions of the exposure apparatus 100 (for example, design values of the projection optical system PL (numerical aperture NA, data of each lens, etc.), coherence factor, etc.) are stored in a simulation computer 46 in which specific optical software is installed. σ value, numerical aperture NA of illumination optical system, wavelength λ of illumination light EL, etc.). Next, data of an arbitrary first measurement point (measurement point 1) in the field of view of the projection optical system PL is input to the simulation computer 46.
[0111]
Next, the movable lens 13 ₁ ~ 13 ₅ In each of the degrees of freedom (movable direction), the directions of the degrees of freedom on the surface of the wafer W, and the shift amount of the wavelength of the illumination light, data of a unit amount is input. For example, the movable lens 13 ₁ Is input by a unit amount with respect to the + direction of the Z-direction shift, the computer 46 for simulation uses the simulation computer 46 to set the first wavefront at a predetermined first measurement point in the field of view of the projection optical system PL from the ideal wavefront. The data of the change amount, for example, the change amount of the coefficient of each term (for example, the first to 37th terms) of the Zernike polynomial is calculated, and the data of the change amount is displayed on the screen of the display of the simulation computer 46. Are stored in the memory as a parameter PARA1P1.
[0112]
Next, the movable lens 13 ₁ Is input in the + direction of the Y-direction tilt (rotation θx about the x-axis) by a unit amount, the simulation computer 46 inputs data of the second wavefront at the first measurement point, for example, the Zernike polynomial The amount of change in the coefficient of each term is calculated, the data of the amount of change is displayed on the screen of the display, and the amount of change is stored in the memory as a parameter PARA2P1.
[0113]
Next, the movable lens 13 ₁ Is input in the + direction of the X-direction tilt (rotation θy around the y-axis) by a unit amount, the simulation computer 46 outputs data of the third wavefront at the first measurement point, for example, the Zernike polynomial The amount of change of the coefficient of each term is calculated, the data of the amount of change is displayed on the screen of the display, and the amount of change is stored in the memory as a parameter PARA3P1.
[0114]
Thereafter, in the same procedure as above, input of each measurement point from the second measurement point to the n-th measurement point is performed, and the movable lens 13 ₁ Each time the Z-direction shift, the Y-direction tilt, and the X-direction tilt are input, the simulation computer 46 uses the simulation computer 46 to generate data on the first wavefront, the second wavefront, and the third wavefront, for example, the Zernike polynomial. The amount of change in the coefficient of each term is calculated, and the data of each amount of change is displayed on the screen of the display and stored in the memory as parameters PARA1P2, PARA2P2, PARA3P2,..., PARA1Pn, PARA2Pn, PARA3Pn.
[0115]
Other movable lens 13 ₂ , 13 ₃ , 13 ₄ , 13 ₅ In the same manner as above, the input of each measurement point and the command input to drive in the + direction by a unit amount in each of the degrees of freedom are performed in the same procedure as described above. Movable lens 13 ₂ , 13 ₃ , 13 ₄ , 13 ₅ Is driven by a unit amount in each direction of degree of freedom, the wavefront data for each of the first to n-th measurement points, for example, the amount of change in each term of the Zernike polynomial is calculated, and the parameters (PARA4P1, PARA5P1, PARA6P1,...) Are calculated. , PARA15P1), parameters (PARA4P2, PARA5P2, PARA6P2,..., PARA15P2),..., Parameters (PARA4Pn, PARA5Pn, PARA6Pn,..., PARA15Pn) are stored in the memory.
[0116]
In the same manner as described above, the input of each measurement point and the input of a command to drive the wafer W in the + direction by a unit amount in each of the degrees of freedom are performed in the same manner as described above. When the computer 46 drives the wafer W by a unit amount in each of the degrees of freedom in the directions of Z, θx, and θy, the wavefront data for each of the first to n-th measurement points, for example, the amount of change in each term of the Zernike polynomial is The parameters (PARA16P1, PARA17P1, PARA18P1), parameters (PARA16P2, PARA17P2, PARA18P2),..., And parameters (PARA16Pn, PARA17Pn, PARA18Pn) are stored in the memory.
[0117]
Further, regarding the wavelength shift, the input of each measurement point and the input of the command to shift the wavelength in the + direction by a unit amount are performed in the same procedure as described above, and in response, the simulation computer 46 Wavefront data for each of the first to n-th measurement points when the wavelength is shifted by a unit amount in the + direction, for example, the amount of change in each term of the Zernike polynomial is calculated, and PARA19P1, PARA19P2,. Is stored within.
[0118]
Here, each of the parameters PARAiPj (i = 1 to 19, j = 1 to n) is a column matrix (vertical vector) of 37 rows and 1 column. That is, when n = 33, the following equation (6) is obtained for the adjustment parameter PARA1. Each of the parameters PARAiPj is a column matrix, but in the following equation (6), for convenience, an expression form as if it were a row matrix is adopted.
[0119]
(Equation 4)

[0120]
Further, the adjustment parameter PARA2 is represented by the following equation (7).
[0121]
(Equation 5)

[0122]
Similarly, the other adjustment parameters PARA3 to PARA19 are represented by the following equation (8).
[0123]
(Equation 6)

[0124]
The column matrices (vertical vectors) PARA1P1 to PARA19Pn composed of the amounts of change in the coefficients of each term of the Zernike polynomial stored in the memory in this way are grouped for each adjustment parameter, and the wavefront for each of the 19 adjustment parameters is obtained. Rearrangement is performed as an aberration change table. As a result, a matrix (matrix) O represented by the following equation (9) having column elements (vertical vectors) PARA1P1 to PARA19Pn as elements is created. Note that in Expression (9), m = 19.
[0125]
(Equation 7)

[0126]
Then, the database made up of the wavefront aberration change table of the projection optical system PL created in this way is stored in the storage device 42.
[0127]
Next, the movable lens 13 for adjusting the image forming state of the pattern image by the projection optical system PL, which is performed at the time of maintenance of the exposure apparatus 100 of the present embodiment or the like. ₁ ~ 13 ₅ The setting method of the above-described 19 adjustment parameters, that is, the normal adjustment method of the projection optical system PL will be described in detail including a description of its principle.
[0128]
First, the wavefront aberration of the projection optical system PL is measured using the wavefront aberration measurement device 80 in the above-described procedure. The measurement result, that is, data of the wavefront (wavefront aberration) corresponding to the first measurement point (evaluation point) to the nth measurement point (evaluation point) in the field of view of the projection optical system PL, that is, each term of the Zernike polynomial, for example, One term coefficient Z ₁ ~ Coefficient Z of the 37th term ₃₇ (Hereinafter, the coefficient of the i-th term at the measurement point n is Z _{n, i} ) Is obtained and stored in a memory such as a RAM of main controller 50.
[0129]
In the following description, the data of the wavefront (wavefront aberration) corresponding to the first to n-th measurement points is represented by a column matrix Q as shown in the following equation (10).
[0130]
(Equation 8)

[0131]
In the above equation (10), the element P of the matrix Q ₁ ~ P _n Are the coefficients of the first to 37th terms of the Zernike polynomial (Z ₁ ~ Z ₃₇ ) Is a column matrix (vertical vector).
[0132]
Next, the main controller 50 controls the movable lens 13 as described above as follows. ₁ ~ 13 ₅ , The amount of adjustment of the wafer W in each direction of freedom, and the amount of wavelength shift of the illumination light EL are calculated.
[0133]
That is, between the data Q of the wavefront (wavefront aberration) corresponding to the first measurement point to the n-th measurement point, the database (matrix O) described above, and the nineteen adjustment amounts P described above, The relationship shown in 11) is established.
[0134]
Q = OP (11)
[0135]
In the above equation (11), P is a column matrix (that is, a vertical vector) composed of m elements, that is, 19 elements, represented by the following equation (12).
[0136]
(Equation 9)

[0137]
Therefore, from the above equation (12), the respective elements ADJ1 to ADJm of P, that is, the movable lens 13 are calculated by calculating the following equation (13), that is, by the least square method. ₁ ~ 13 ₅ , The adjustment amount in each direction of freedom (target adjustment amount) of the wafer W, and the wavelength shift amount (target shift amount) of the illumination light EL.
[0138]
P = (O ^T ・ O) ^-1 ・ O ^T ・ Q …… (13)
[0139]
In the above equation (13), O ^T Is the transpose of the matrix O, and (O ^T ・ O) ^-1 Is (O ^T -O) is the inverse matrix.
[0140]
Therefore, the main controller 50 calculates the adjustment amounts ADJ1 to ADJm while sequentially reading the database in the storage device 42 into the RAM.
[0141]
Next, the main controller 50 sets the movable lens 13 in accordance with the adjustment amounts ADJ1 to ADJ15 stored in the storage device 42. ₁ ~ 13 ₅ Is given to the imaging performance correction controller 48 to drive the camera in each direction of freedom. Accordingly, the movable lens 13 is controlled by the imaging performance correction controller 48. ₁ ~ 13 ₅ Is applied to each driving element for driving the movable lens 13 in the direction of each degree of freedom. ₁ ~ 13 ₅ At least one of the position and the posture is adjusted almost simultaneously. At the same time, main controller 50 holds wafer W in an exposure area IA so that wafer W is always maintained in an attitude equivalent to that adjusted by adjustment amounts ADJ16 to ADJ18 during actual scanning exposure. A command value for driving in each of Z, θx, and θy degrees of freedom is given to a wafer stage drive unit (not shown) to drive wafer stage WST. Further, at the same time as the above operations, main controller 50 gives a command to light source 16 in accordance with adjustment amount ADJ19 to shift the wavelength of illumination light EL. Thereby, optical characteristics of the projection optical system PL, such as distortion, curvature of field, coma, spherical aberration, and astigmatism, are corrected. As for coma, spherical aberration, and astigmatism, not only low-order aberrations but also high-order aberrations can be corrected.
[0142]
Next, the reticle R on which a pattern to be predicted or evaluated in size (line width) by the prediction method and evaluation method of the present embodiment is formed _T Will be described with reference to FIG. FIG. 4 shows a reticle R _T Is a plan view as seen from the pattern surface side. As shown in FIG. 4, reticle R _T Is formed of a square glass substrate, and a rectangular pattern area PA having substantially the same shape as the illumination area IAR, which is surrounded by a light-shielding band SB, is formed at the center of the pattern surface. Inside the pattern area PA, a total of 33 measurement patterns MP ₁ ~ MP ₃₃ Is formed. Each measurement pattern MP _j (J = 1 to 33) is, for example, a reticle R _T When the center of the (pattern area PA) coincides with the optical axis AX of the projection optical system PL, a position corresponding to each measurement point (evaluation point) in the effective visual field of the projection optical system PL where the above-mentioned wavefront aberration is measured. The positional relationship is set so as to be arranged in the.
[0143]
Each measurement pattern MP _j As shown in FIG. 4, a first line pattern having a designed line width extending in the Y-axis direction is, for example, 600 nm, and a second line pattern having a designed line width extending in the X-axis direction is, for example, 600 nm. Including. When the first line pattern and the second line pattern are transferred onto a wafer with the projection magnification of the projection optical system PL set to ４, an ideal in which various aberrations such as spherical aberration and astigmatism do not exist in the projection optical system PL. In a typical state, a line pattern image having a line width of 150 nm is obtained as an image of the first line pattern and the second line pattern.
[0144]
Further, reticle alignment marks M1 and M2 are formed on both outer sides of the pattern area PA on the X-axis passing through the center of the pattern area PA (coincident with the reticle center). This reticle R _T In the state loaded on the reticle stage RST, the pattern surface (the surface on the near side in FIG. 4) is the surface facing the projection optical system PL.
[0145]
In the prediction method of the present embodiment, the reticle R loaded on the reticle stage RST _T Measurement pattern MP formed on top _j Predicts the line width of the image of the first line pattern and the second line pattern when transferred to the wafer W loaded on the wafer stage WST.
[0146]
By the way, the variation ΔCD of the line width of the image of the first line pattern and the second line pattern is calculated by the following formula (Zernike Sensitivity method: hereinafter, appropriately referred to as “ZS method” or “ZSM”) in the following Zernike sensitivity method. Zernike Sensitivity (hereinafter referred to as “Zernike sensitivity” as appropriate) 14) _i (I = 1 to 37) and the size Z of the Zernike term at the measurement point n _{n, i} (Coefficient Z at measurement point n _i ) Can be expressed by a linear combination with In the following, Z _{n, i} Is simply referred to as a Zernike term component (Zernike term component) at each measurement point.
[0147]
(Equation 10)

[0148]
However, there is a difference as shown in the graph of FIG. 5 between the calculation result using the ZS method using the above equation (14) and the method of directly calculating an aerial image by giving an appropriate wavefront aberration. Can be seen. That is, the error is too large in the calculation by the ZS method using the above equation (14).
[0149]
For this reason, the inventors considered a prediction method of the present embodiment, that is, a prediction method of predicting a line width by a new ZS method, instead of the conventional ZS method. Hereinafter, the principle of the new ZS method will be described, and the prediction method, the evaluation method, the adjustment method, and the exposure method of the present embodiment will be described.
[0150]
First, the principle of the new ZS method will be described. Strictly speaking, the change amount of the wavefront aberration due to the defocus amount at each measurement point n (n = 1 to 33), that is, the wavefront disturbance amount Wd ′ is expressed by the following equation.
[Equation 11]

[0151]
Here, Def is the defocus amount at the wavefront aberration reference point, that is, the measurement point n, and r is the radius of the projection optical system PL at the pupil coordinates. Note that the maximum value of r is equal to N.V. of projection optical system PL. A. (The maximum numerical aperture or the numerical aperture set by the aperture stop 15).
[0152]
In order to describe the wavefront turbulence amount by a Zernike polynomial, it is more convenient to use Wd shown by the following equation than to use Wd 'shown by the above equation (15).
[0153]
(Equation 12)

[0154]
Here, λ is the wavelength of the illumination light EL in the exposure apparatus 100. Further, the following equation is obtained by expanding the equation (16) into a power series.
[0155]
(Equation 13)

[0156]
The Zernike polynomial used to describe the wavefront turbulence amount Wd due to the defocus amount Def is a rotationally symmetric component term shown in the following equation among the terms shown in Table 1 described above.
[0157]
[Equation 14]

[0158]
Here, ρ is the projection optical system N. A. (Hereinafter abbreviated as “NA”), the values in the pupil coordinate radial direction are normalized, so that there is a relationship of ρ × NA = r. Therefore, the above equation (17) can be rewritten into the following equation.
[0159]
(Equation 15)

[0160]
On the other hand, the change amount Wd of the wavefront aberration due to the defocus amount Def can be expressed by the following equation by the linear combination of the Zernike term component sensitive to the above-described defocus amount, that is, the focus-dependent aberration component.
[0161]
(Equation 16)

[0162]
Where B ₁ , B ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ Is the amount of change in the first, fourth, ninth, sixteenth, twenty-fifth, and thirty-second terms of the Zernike polynomial due to the defocus amount Def. Note that the following equation is derived from Equations (18-1) to (18-6), Equation (19), and Equation (20) described above.
[0163]
[Equation 17]

[0164]
In order to simplify the calculation, the right-hand sides of the equations (21-1) to (21-6) are placed as shown in the following equation (22), and the simultaneous equations are solved to obtain the following equation (23). .
[0165]
(Equation 18)

[0166]
[Equation 19]

[0167]
As shown in the above equation (20), the wavefront turbulence amount Wd due to the defocus amount is the change amount B of each focus-dependent aberration component of the defocus amount. ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ Can be represented by a linear combination of This variation B ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ Are the correction amounts of the respective focus-dependent aberration components with respect to the defocus Def. Therefore, each focus-dependent aberration component corrected by defocus is corrected as shown by the following equation.
[0168]
(Equation 20)

[0169]
Next, a prediction method, an evaluation method, an adjustment method, and an exposure method of the present embodiment based on the above principle will be described based on a flowchart of FIG. 6 which shows a simplified processing algorithm of the CPU in the main control device 50. explain. First, in step 102, the display device 44 displays the optical conditions at the time of actual exposure (for example, the wavelength λ of the illumination light EL, ie, the exposure wavelength (and the type of the exposure light source 16), and the maximum NA of the projection optical system PL. , The NA used (in this embodiment, the numerical aperture set by the aperture stop 15 at the time of exposure), the coherence factor σ value or the illumination NA (numerical aperture of the illumination optical system), and the illumination of the reticle An exposure condition setting screen including conditions (at least one of the light amount distribution of the illumination light EL on the pupil plane of the illumination optical system, ie, the shape and size of the secondary light source) and the like is displayed. Looking at this setting screen, the operator sets, via the input device 45, optical conditions and the like used for actual exposure. When setting the exposure conditions, information on the pattern such as the shape and size of the pattern on the reticle R transferred to each of the measurement points n (n = 1 to 33) can be set together. The information on the pattern includes, for example, a pattern type such as an isolated line pattern, a line-and-space (L / S) pattern, and an orthogonal pattern in which the line pattern is orthogonal (whether or not it is a phase shift pattern and the type thereof). And pattern size information such as the line width, length, and pitch of the line pattern. The selection of the pattern is determined according to the evaluation item to be evaluated. For example, if the vertical and horizontal line width differences are used as evaluation items as in the above-described operation, it is necessary to set orthogonal line patterns orthogonal to each other as shown in FIG. Here, reticle R in FIG. _T Is used, information on the orthogonal line pattern (that is, the first line pattern and the second line pattern) is set.
[0170]
Next, in step 104, the defocus amount Def and the N.V. A. Of the illumination light EL based on the value (NA) of the illumination light EL and ₂ , C ₄ , C ₆ , C ₈ , C ₁₀ Ask for. Then, in step 106, the obtained C ₂ ~ C ₁₀ The correction amount B of each focus-dependent aberration component is calculated based on ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ Ask for. Then, in step 108, the obtained correction amount B ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ Based on the above, each focus-dependent aberration component Z is calculated using the above equation (24). ₄ , Z ₉ , Z ₁₆ , Z ₂₅ , Z ₃₆ Is corrected.
[0171]
Next, the measurement pattern MP at that defocus amount _j Before obtaining the line widths of the images of the first line pattern and the second line pattern, the correlation between the Zernike coefficient and the line width of the pattern will be described.
[0172]
FIG. 7 shows an example of a CD (Critical Dimension) -focus curve in the exposure apparatus 100. The CD-focus curve usually indicates a change in the line width of the line pattern image with respect to the defocus amount. In the example of FIG. 7, the line width of the image of the line pattern is large near the best focus position (where the defocus amount Def is 0), and the line width of the image becomes smaller as the image is defocused. ing. Further, as can be seen from FIG. 7, the relationship ΔCD of the line width with respect to the defocus amount Def does not have the relationship of Def∝ΔCD. ² ＣＤΔCD.
[0173]
FIG. 8 shows each Zernike term (Z ₆ , Z ₇ , Z ₉ 11) shows the relationship between the line width of the line pattern image and the aberration obtained by inputting 11 aberrations at a 10 mλ pitch from -50 mλ to 50 mλ to the simulation computer 46 and performing aerial image calculation. Regarding these relationships, whether the amount of aberration is positive or negative, the effect on the line width is the same, and when the aberration increases, the deterioration of the image is observed more than the proportional relationship, It can be assumed that the change in the line width of the image of the line pattern is represented by a linear combination such as the square of each Zernike term component. Assuming a quadratic function in the calculation of the line width change amount of the 11 points obtained by the image calculation by the simulation computer 46 and approximation by the least square method, as shown in FIG. 8, y = sx ² It is observed that it is riding on the function. Note that FIG. 8 representatively shows only three types of the sixth term (Z.6), the seventh term (Z.7), and the ninth term (Z.9). It has been confirmed that the Zernike term can be expressed by a quadratic function.
[0174]
Also, recently, it has been discovered that a product of different Zernike terms, that is, a cross term (cross term) is sensitive to a change in the line width of the line pattern image. That is, the change in the line width of the image of the line pattern can be expressed by a linear combination of the square of each Zernike term component and the cross term as shown in the following equation. Note that S in the equation _{i, j} Is the term (Z) for the line width change of the line pattern image. _{n, i} Z _{n, j} ) Indicates the sensitivity.
[0175]
(Equation 21)

[0176]
Further, as shown in the graphs of FIGS. 9A and 9B, the line width distribution may be distributed on an inclined ellipse depending on the combination of aberrations (in FIG. 9A, , Z.6 and Z.13 are shown, and FIG. 9 (B) shows the relationship between Z.9 and Z.12). In this case, the cross term of the combination of these aberrations has sensitivity to a change in the line width of the line pattern. When only two terms are extracted from the equation (25), the following equation is obtained, for example.
[0177]
(Equation 22)

[0178]
From this, it can be seen that the expression of the inclined elliptical distribution as shown in the graphs of FIGS. 9A and 9B is possible. When we actually calculate the cross terms, we can see that there are cross terms between quite a lot of terms.
[0179]
Returning to FIG. 6, in step 110, the Zernike term components of the first line pattern and the second line pattern with respect to the line widths under the set exposure conditions obtained by the aerial image calculation of the simulation computer 46. Zernike sensitivity S of the square _{i, j} (I = j) and the Zernike sensitivity S of the cross term _{i, j} (I ≠ j) is read. The square Zernike sensitivity S of each Zernike term component _{i, j} As for (i = j), assuming a quadratic function in the calculation of the line width variation at 11 points obtained by the image calculation and approximating by the least square method, as described above, y = sx ² It is observed that the Zernike sensitivity S _{i, j} (I = j) can be obtained.
[0180]
In step 112 of FIG. 6, the aberration component Z of the projection optical system PL measured by the above-described measurement of the wavefront aberration and stored in the memory of the main control device 50 _{n, i} (Or Z _{n, j} ), And each Zernike sensitivity S determined in step 110 _{i, j} Equation (25) is calculated based on the above equation, and ΔCD (referred to as ΔCD (V) and ΔCD (H), respectively) for the first line pattern and the second line pattern at each of the first to n-th measurement points is obtained. .
[0181]
FIG. 10 shows the relationship between the line width variation ΔCD and the calculation result using the new ZS method described above, and the method of directly calculating an aerial image by giving an appropriate wavefront aberration. . As is apparent from a comparison between FIG. 10 and FIG. 5 described above, according to the new ZS method, it is understood that the error is significantly reduced.
[0182]
That is, as is apparent from FIG. 10, it is understood that the line width can be accurately calculated (predicted) by extending the ZS method without performing the aerial image calculation by the imaging simulation.
[0183]
Returning to FIG. 6, in the next step 114, the first line pattern and the second line pattern arranged at positions corresponding to the first to n-th measurement points on the object plane side of the projection optical system PL, respectively, in step 112. The line width difference (VH difference) at the first to n-th measurement points is calculated based on the change ΔCD (V) and ΔCD (H) of the line width predicted by the following equation: VH difference = ΔCD (V) −ΔCD ( H).
[0184]
Next, in step 116, the calculated VH difference between the first to n-th measurement points, the wavefront aberration of the projection optical system PL and the adjustment amounts ADJ1 to ADJ19 represented by the above-described equation (13) and the like. The Zernike adjustment amounts ADJ <b> 1 to ADJ <b> 19 that reduce the VH difference therebetween are calculated by using the relationship with and are stored in the storage device 42.
[0185]
Next, in step 118, according to the adjustment amounts ADJ1 to ADJ15 stored in the storage device 42, the imaging performance correction controller 48 controls the movable lens 13 in the same manner as described above. ₁ ~ 13 ₅ At the same time as the above operations, main controller 50 gives a command to light source 16 in accordance with adjustment amount ADJ19 to shift the wavelength of illumination light EL.
[0186]
In the present embodiment, in the state after the adjustment of the projection optical system PL and the like, the above-described steps 102 to 118 are further executed, and the line widths of the vertical and horizontal patterns at the first to n-th measurement points after the adjustment are obtained. The prediction of the changes ΔCD (V) and ΔCD (H), the evaluation of the line width difference (VH difference), and the adjustment using the adjustment amounts ADJ1 to ADJ19 may be repeatedly performed.
[0187]
In an exposure step at the time of manufacturing a semiconductor device, a reticle R for manufacturing a device is loaded on a reticle stage RST, and thereafter, reticle alignment and so-called baseline measurement, and wafer alignment such as EGA (enhanced global alignment) are performed. Preparation work such as is performed. The above-mentioned preparation work for reticle alignment and baseline measurement is disclosed in detail in, for example, JP-A-7-176468, and the subsequent EGA is described in JP-A-61-44429. Is disclosed in detail.
[0188]
After that, a step-and-scan exposure is performed based on the wafer alignment result. Since the operation at the time of exposure and the like are not different from those of a normal scanning type exposure apparatus, detailed description will be omitted. However, in the exposure apparatus 100 of the present embodiment, the position and orientation of the wafer W in the above-described exposure area IA are controlled based on the calculated adjustment amounts ADJ16 to ADJ18 during the above-described step-and-scan exposure. What is done is as described above.
[0189]
Further, in the present embodiment, when the circuit pattern to be actually transferred is changed by setting the exposure condition or exchanging the reticle R, it is necessary to re-execute the steps 102 to 118 described above. Not even.
[0190]
As described in detail above, according to the prediction method of the present embodiment, in steps 102 to 108, the focus-dependent aberration component (Z) is determined based on the wavefront aberration turbulence Wd corresponding to the defocus amount Def. ₄ , Z ₉ , Z ₁₆ , Z ₂₅ , Z ₃₆ ) (B) ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ ) Is calculated, and the focus-dependent aberration component (Z ₄ , Z ₉ , Z ₁₆ , Z ₂₅ , Z ₃₆ ) And the change amount (B ₄ , B ₉ , B ₁₆ , B ₂₅ , B ₃₆ ) Is corrected. By doing so, in step 112, the corrected focus-dependent aberration component (Z ₄ , Z ₉ , Z ₁₆ , Z ₂₅ , Z ₃₆ Aberration component (Z) _i , I = 1 to 36), an image formation simulation is performed to determine the correspondence between the image size of the predetermined pattern and the defocus amount, which is difficult to predict with the original Zernike sensitivity method. Without making any predictions.
[0191]
Further, according to the prediction method of the present embodiment, the change in the size of the image is sensitive to the square of each aberration component and the cross term between the different aberration components, and a linear combination of those terms (Equation (25)) Is considered, the change in the image size with respect to the defocus amount can be calculated.
[0192]
Further, according to the evaluation method of the present embodiment, the correspondence between the change in the size of the image of the predetermined pattern (ΔCD (V), ΔCD (H)) and the defocus amount Def is shortened by using the above-described prediction method. As a result, the uniformity of the image of the predetermined pattern within the effective visual field of the projection optical system PL (here, the difference between the vertical and horizontal line widths (VH difference)) can be predicted based on the correspondence. ) Can be evaluated in a short time.
[0193]
According to the adjustment method of the present embodiment, the uniformity of the transfer state of the image of the predetermined pattern within the effective visual field of the projection optical system PL is evaluated in a short time by using the above-described evaluation method. Further, based on the evaluation result, the transfer state of the predetermined pattern via the projection optical system PL can be adjusted so that the uniformity of the transfer state of the image of the predetermined pattern is improved.
[0194]
Further, according to the exposure method of the present embodiment, the transfer method of the pattern is adjusted in a short time by executing the adjustment method described above, and the pattern is transferred onto the wafer W in the adjusted transfer state. It is possible to improve the throughput of the exposure process.
[0195]
Further, if the line width of the line pattern is predicted by the prediction method of the present embodiment with different defocus amounts at fixed intervals, a CD-focus curve as shown in FIG. 7 can be obtained. For example, Z ₄ And Z ₉ It is assumed that the state of change of the line width of the line pattern with respect to the aberration amount is as shown in FIG. 11A, and Z in the equation (25) obtained by the aerial image calculation by the simulation computer 46. ₄ And Z ₉ Zernike sensitivity is S _4,4 = -938, S _4,9 = 4237, S _9,9 = -3257. Further, the Zernike sensitivity is similarly obtained for other Zernike terms, and the value of Expression (25) is calculated while sequentially changing the defocus amount at regular intervals, to indicate the line width of the line pattern at each defocus amount. Is plotted as indicated by ◆ in FIG. 11 (B), and the points are interpolated to obtain a CD-focus curve (thick line) by the Zernike sensitivity method (ZSM) as shown in FIG. 11 (B). Can be created. FIG. 11B also shows a CD-focus curve (thin line) obtained by the aerial image simulation.
[0196]
As shown in FIG. 11B, in the vicinity of the best focus position, the CD-focus curve obtained by the calculation of Expression (25) and the CD-focus curve obtained by the imaging simulation match well. However, as the defocus amount increases, a slight shift occurs between the CD-focus curve obtained by the calculation of Expression (25) and the CD-focus curve obtained by the imaging simulation. I understand.
[0197]
According to the inventor's earnest studies, this displacement is the fourth term in the focus-dependent aberration component, that is, Z ₄ It was found to be due to. So, Z ₄ Is stored in the storage device 42 in advance, indicating a variation in the line width of the line pattern image with respect to the size, and the main controller 50 ₄ Is obtained by referring to the data table, and the line width change amount obtained from the value of ₄ The value obtained by adding the line width variation obtained from the calculation result when Equation (25) is calculated and the line width variation obtained from the data table based on the other Zernike terms only, The line width change amount in the defocus amount may be used. As shown in FIG. 12, the line width of the line pattern image at each defocus amount obtained by the method (ZSM) referring to the data table and the line width of the image in the CD-focus curve by the aerial image simulation are as follows. It can be seen that they match well even where the defocus amount is large. Although FIG. 12 shows only data at measurement points 1 (P1), 17 (P17), and 33 (P33), the line width of the line pattern image predicted according to the present invention at other measurement points is also shown. Also, it has been confirmed that the CD-focus curves obtained by the aerial image simulation match well.
[0198]
In the above embodiment, the Zernike polynomial series up to the 37th term is targeted. However, the present invention is not limited to this, and Zernike terms of the 37th term or more, for example, the 121st term of the ZS method are used. You may make it a target. In this case, the focus-dependent aberration components are the 49th, 64th, 81st, 100th, and 121st terms.
[0199]
In the above-described embodiment, the case where the line width difference between the line patterns intersecting with each other is evaluated has been described. However, the present invention is not limited to this, and relates to line patterns parallel to each other (for example, L / S patterns). The difference between the line widths, that is, the line width abnormal value may be evaluated, or the uniformity may be evaluated by arranging an isolated pattern between the measurement points at each measurement point. In this case, at the first to n-th measurement points, not only the evaluation of the uniformity of the vertical and horizontal line width difference mainly due to astigmatism, but also the uniformity of the line width abnormal value mainly due to coma aberration, etc. Will be able to
[0200]
The pattern whose size is to be predicted is not limited to a line pattern, and may be, for example, a rhombus pattern. In the above embodiment, 19 adjustment parameters are used. However, the number and type of the adjustment parameters may be arbitrary, and may include, for example, the driving amount of the wafer surface (wafer stage WST) and the wavelength shift of the illumination light EL. Is also good.
[0201]
Furthermore, in the above-described embodiment, the wavefront aberration of the projection optical system PL is measured using the wavefront aberration measurement device 80. However, the wavefront aberration may be obtained by, for example, trial printing. For example, a measurement mask having a special structure disclosed in U.S. Pat. No. 5,978,085 or the like is used, and a plurality of measurement patterns on the mask are individually provided with individually provided pinholes and projection optics. In addition to printing on the substrate sequentially through the system, the reference pattern on the mask is printed on the substrate via the projection optical system without passing through the condenser lens and pinhole, and a plurality of measurements obtained as a result of each printing The wavefront aberration may be calculated by measuring the positional shift of each reference pattern of the resist image of the use pattern with respect to the resist image and performing a predetermined calculation.
[0202]
In the adjustment method of the above embodiment, the adjustment by the imaging performance correction controller 48 and the like under the control of the main control device 50 is performed based on the optimum adjustment amount calculated using the above-described equation (13). Although the adjustment is performed automatically, the invention is not limited thereto, and the imaging performance of the projection optical system may be manually adjusted based on the adjustment amount.
[0203]
Further, in the above embodiment, a prediction method, an evaluation method for evaluating a vertical and horizontal line width difference and the like based on a CD-focus curve predicted by the prediction method, and an adjustment method for adjusting a pattern transfer state according to the evaluation result And the like are described in a series of processes, but it is not necessary to perform all the methods in a series of processes, and the prediction method, the evaluation method, and the adjustment method of the present invention can be executed alone or in any combination. It is.
[0204]
Further, in the above embodiment, the imaging element is adjusted by moving the optical element of the projection optical system PL. However, the present invention is not limited to this. For example, in addition to or instead of the driving mechanism, the projection optical system PL Change the pressure of gas between the optical elements of the PL, move or tilt the reticle R in the direction of the optical axis of the projection optical system, or the optical thickness of a plane parallel plate disposed between the reticle and the wafer May be used. However, in this case, the number of degrees of freedom in the above embodiment or the modification may be changed.
[0205]
In the above embodiment, the case where the scanning exposure apparatus is used as the exposure apparatus has been described. However, the present invention is not limited to this. For example, a step-and-repeat exposure apparatus may be used.
[0206]
The application of the exposure apparatus in this case is not limited to an exposure apparatus for manufacturing a semiconductor, and is, for example, an exposure apparatus for a liquid crystal that transfers a liquid crystal display element pattern to a square glass plate, a plasma display or an organic EL. The present invention can be widely applied to an exposure apparatus for manufacturing a display device, an image pickup device (such as a CCD), a thin film magnetic head, a micro machine, a DNA chip, and the like. In addition to micro devices such as semiconductor elements, glass substrates or silicon wafers for manufacturing reticles or masks used in light exposure equipment, EUV exposure equipment, X-ray exposure equipment, electron beam exposure equipment, etc. The present invention can also be applied to an exposure apparatus that transfers a circuit pattern to a substrate.
[0207]
Further, the light source of the exposure apparatus of the above embodiment is F ₂ Not only an ultraviolet pulse light source such as a laser, an ArF excimer laser, and a KrF excimer laser, but also a continuous light source, for example, an ultra-high pressure mercury lamp that emits a bright line such as a g-line (wavelength 436 nm) or an i-line (wavelength 365 nm) can be used. is there. Further, X-rays, particularly EUV light, etc. may be used as the illumination light EL.
[0208]
In addition, a single-wavelength laser beam in the infrared or visible region oscillated from a DFB semiconductor laser or a fiber laser is amplified by, for example, a fiber amplifier doped with erbium (or both erbium and ytterbium) to form a nonlinear optical crystal. Alternatively, a harmonic converted to ultraviolet light may be used. Further, the magnification of the projection optical system may be not only a reduction system but also any one of an equal magnification and an enlargement system. Further, the projection optical system is not limited to the refractive system, and a catadioptric system (catadioptric system) having a reflective optical element and a refractive optical element or a reflective system using only a reflective optical element may be used. When a catadioptric system or a catoptric system is used as the projection optical system PL, the position of a reflective optical element (such as a concave mirror or a reflective mirror) is changed as the above-mentioned movable optical element to improve the imaging performance of the projection optical system. adjust. Further, as the illumination light EL, in particular, Ar ₂ When laser light, EUV light, or the like is used, the projection optical system PL may be an all-reflection system including only reflection optical elements. Where Ar ₂ When laser light or EUV light is used, the reticle R is also of a reflection type. Further, the present invention may be applied to an immersion type exposure apparatus disclosed in, for example, International Publication WO99 / 49504, in which a liquid is filled between a projection optical system PL and a wafer.
[0209]
《Device manufacturing method》
Next, an embodiment of a device manufacturing method using the above-described exposure apparatus in a lithography process will be described.
[0210]
FIG. 13 shows a flowchart of an example of manufacturing devices (semiconductor chips such as ICs and LSIs, liquid crystal panels, CCDs, thin-film magnetic heads, micro machines, and the like). As shown in FIG. 13, first, in step 301 (design step), a function / performance design of a device (for example, a circuit design of a semiconductor device) is performed, and a pattern design for realizing the function is performed. Subsequently, in step 302 (mask manufacturing step), a mask on which the designed circuit pattern is formed is manufactured. On the other hand, in step 303 (wafer manufacturing step), a wafer is manufactured using a material such as silicon.
[0211]
Next, in step 304 (wafer processing step), using the mask and the wafer prepared in steps 201 to 303, an actual circuit or the like is formed on the wafer by a lithography technique or the like, as described later. Next, in step 305 (device assembly step), device assembly is performed using the wafer processed in step 304. Step 305 includes processes such as a dicing process, a bonding process, and a packaging process (chip encapsulation) as necessary.
[0212]
Finally, in step 306 (inspection step), inspections such as an operation confirmation test and a durability test of the device created in step 305 are performed. After these steps, the device is completed and shipped.
[0213]
FIG. 14 shows a detailed flow example of step 304 in the semiconductor device. In FIG. 14, in step 311 (oxidation step), the surface of the wafer is oxidized. In step 312 (CVD step), an insulating film is formed on the wafer surface. In step 313 (electrode forming step), electrodes are formed on the wafer by vapor deposition. In step 314 (ion implantation step), ions are implanted into the wafer. Each of the above steps 311 to 314 constitutes a pre-processing step in each stage of wafer processing, and is selected and executed according to a necessary process in each stage.
[0214]
In each stage of the wafer process, when the above-described pre-processing step is completed, the post-processing step is executed as follows. In this post-processing step, first, in step 315 (resist forming step), a photosensitive agent is applied to the wafer. Subsequently, in step 316 (exposure step), the circuit pattern of the mask is transferred to the wafer by the exposure apparatus and the exposure method described above. Next, in step 317 (development step), the exposed wafer is developed, and in step 318 (etching step), the exposed members other than the portion where the resist remains are removed by etching. Then, in step 319 (resist removing step), unnecessary resist after etching is removed.
[0215]
By repeating these pre-processing and post-processing steps, multiple circuit patterns are formed on the wafer.
[0216]
If the device manufacturing method of the present embodiment described above is used, the prediction method, the evaluation method, and the exposure method of the above embodiment are used in the exposure step (step 316). Good and short-time exposure in which the width difference is effectively reduced can be realized. Therefore, the yield of the device as the final product is improved, and the productivity can be improved.
[0219]
【The invention's effect】
As described above, according to the prediction method of the present invention, it is possible to predict the transfer characteristics of a pattern via a projection optical system in a short time.
[0218]
According to the evaluation method of the present invention, the transfer state of the pattern via the projection optical system can be evaluated in a short time.
[0219]
According to the adjustment method of the present invention, the transfer state of the pattern via the projection optical system can be adjusted in a short time.
[0220]
According to the exposure method of the present invention, the throughput of the exposure step can be improved.
[0221]
ADVANTAGE OF THE INVENTION According to the device manufacturing method of this invention, there exists an effect which can contribute to the improvement of the productivity (including a yield) of a device.
[0222]
According to the program of the present invention, it is possible to cause a computer to execute a procedure for predicting a transfer characteristic of a pattern via a projection optical system in a short time.
[Brief description of the drawings]
FIG. 1 is a view schematically showing a configuration of an exposure apparatus according to an embodiment of the present invention.
FIG. 2 is a cross-sectional view showing the wavefront aberration measuring device of FIG.
FIG. 3A is a diagram illustrating a light beam emitted from a microlens array when aberration is not present in the optical system, and FIG. 3B is a diagram illustrating a light beam when aberration is present in the optical system. FIG. 3 is a diagram illustrating a light beam emitted from a microlens array.
FIG. 4 is a plan view of a measurement reticle as viewed from a pattern surface side.
FIG. 5 is a diagram showing a relationship between a calculation result using a conventional ZS method and a calculation result based on an aerial image with respect to a line width variation ΔCD.
FIG. 6 is a flowchart illustrating a prediction method and the like according to an embodiment of the present invention.
FIG. 7 is a diagram illustrating an example of a CD-focus curve.
FIG. 8 is a diagram showing an example of a result of approximation by a least squares method assuming a quadratic function as a calculation result of a line width change amount at 11 points.
FIG. 9 (A) ₆ And Z _Thirteen FIG. 9B is a diagram showing the crosstalk of FIG. ₉ And Z ₁₂ FIG. 4 is a diagram showing crosstalk of FIG.
FIG. 10 is a diagram showing a relationship between a prediction result of a prediction method according to an embodiment of the present invention and a calculation result of an aerial image with respect to a line width variation ΔCD.
FIG. 11A is a diagram showing a change in the line width of a line pattern with respect to the aberration amounts of the fourth and ninth terms. FIG. It is a figure showing an example of a CD-focus curve calculated.
FIG. 12 shows a result of predicting the line width of the line pattern image with respect to the size of the component of the fourth term using the ZSM method for obtaining the line width data from the data table, and the CD-width obtained by the aerial image simulation. It is a figure for comparing with a focus curve.
FIG. 13 is a flowchart illustrating an embodiment of a device manufacturing method according to the present invention.
FIG. 14 is a flowchart showing details of step 304 in FIG.
[Explanation of symbols]
13 ₁ ~ 13 ₅ .. Movable lens, 16 light source, 48 imaging performance correction controller, 50 main control device, 80 wavefront aberration measuring device, EL illumination light, PL projection optical system, W wafer (object), 100 exposure Equipment, ALG: Alignment system.

Claims (19)

A prediction method for predicting a transfer characteristic of a pattern via a projection optical system,
Of a plurality of aberration components obtained by developing the wavefront aberration of the projection optical system, a defocus amount from a best focus position on an image of a predetermined pattern projected through the projection optical system under predetermined exposure conditions A first step of correcting a plurality of focus-dependent aberration components that fluctuate depending on a change amount of the wavefront aberration according to the defocus amount;
A second step of predicting a correspondence between the size of the image and the defocus amount based on a value of a linear combination of the plurality of aberration components including the corrected focus-dependent aberration component. The prediction method according to claim 1, wherein each of the focus-dependent aberration components is a rotationally symmetric component about an optical axis of the projection optical system. In the first step,
A change amount of each focus-dependent aberration component is calculated based on a change amount of the wavefront aberration developed by a power series with respect to a radius on a pupil coordinate of the projection optical system, and the calculated change amount is determined by the focus-dependent aberration component. The prediction method according to claim 1, wherein the focus-dependent aberration components are corrected by adding the focus-dependent aberration components. In the second step,
A linear combination of squares of the aberration components, each having a sensitivity of a square of the aberration component to a change in the size of the image under the predetermined exposure condition, and a size of the image under the predetermined exposure condition The linear combination of the cross terms with the sensitivity of the cross terms of the different aberration components to the change in the respective coefficients being the respective coefficients, and the value of the linear combination corresponding to the change in the size of the image caused by the wavefront aberration. The prediction method according to claim 1, wherein is calculated. The prediction method according to claim 1, wherein each aberration component is a coefficient of each term in a Zernike polynomial series. In the second step,
The amount of change in the size of the image obtained based on a data table indicating the relationship between the value of the aberration component of the fourth term in the Zernike polynomial series created in advance and the size of the image, and each term excluding the fourth term 6. The prediction method according to claim 5, wherein the amount of change in the size of the image is obtained based on the amount of change in the size of the image obtained based on a linear combination of the aberration components. An evaluation method for evaluating a transfer state of a pattern via a projection optical system,
The method according to claim 1, wherein a predetermined pattern is set at each of a plurality of measurement points in an effective visual field of the projection optical system, and the prediction method according to claim 1 is executed for each measurement point. Estimating the correspondence between the size of the pattern image and the defocus amount;
Evaluating the uniformity of the image of the predetermined pattern within the effective visual field of the projection optical system based on the prediction result. The evaluation method according to claim 7, wherein the predetermined pattern includes two line patterns orthogonal to each other provided on a plane orthogonal to the optical axis direction of the projection optical system. The evaluation method according to claim 7, wherein the predetermined pattern includes two parallel line patterns provided on a plane orthogonal to an optical axis direction of the projection optical system. The evaluation method according to claim 8, wherein the correspondence is predicted for each of the line patterns. An adjustment method for adjusting a transfer state of a pattern via a projection optical system,
A step of performing the evaluation method according to any one of claims 7 to 10 to evaluate uniformity of a transfer state of an image of a predetermined pattern within an effective visual field of the projection optical system;
An adjusting step of adjusting a transfer state of the predetermined pattern via the projection optical system based on the evaluation result. An exposure method for transferring a pattern to an object via a projection optical system,
Adjusting the transfer state of the pattern via the projection optical system by executing the adjustment method according to claim 11 each time an exposure condition is set;
Transferring a pattern formed on the mask to the object via the projection optical system in the adjusted transfer state under the set exposure conditions. A device manufacturing method including a lithography step,
13. A device manufacturing method for performing exposure by performing the exposure method according to claim 12 in the lithography step. A program that causes a computer to execute a prediction of a pattern transfer characteristic through a projection optical system,
Of a plurality of aberration components obtained by developing the wavefront aberration of the projection optical system, a defocus amount from a best focus position on an image of a predetermined pattern projected through the projection optical system under predetermined exposure conditions A first procedure for correcting a plurality of focus-dependent aberration components that fluctuate depending on the change amount of the wavefront aberration according to the defocus amount;
A second procedure of predicting a correspondence between the size of the image and the defocus amount based on a value of a linear combination of the plurality of aberration components including the corrected focus-dependent aberration component. program. 15. The program according to claim 14, wherein each of the focus-dependent aberration components is a rotationally symmetric component about an optical axis of the projection optical system. In the first procedure,
A change amount of each of the focus-dependent aberration components is calculated based on a change amount of the wavefront aberration developed by a power series with respect to a radius on a pupil coordinate of the projection optical system, and the calculated change amount is determined by the focus-dependent aberration component. 16. The program according to claim 14, wherein the program causes a computer to execute a procedure of correcting each of the focus-dependent aberration components by adding the program to a computer. In the second procedure,
A linear combination of squares of the aberration components, each having a coefficient of a sensitivity of a square of the aberration component to a change in the size of the image under the predetermined exposure condition, and a size of the image under the predetermined exposure condition. Based on the linear combination of the cross terms with respective coefficients representing the sensitivity of the cross terms of the different aberration components to changes in the value of the linear combination corresponding to the change in the size of the image caused by the wavefront aberration. The program according to any one of claims 14 to 16, wherein the program causes a computer to execute a procedure for calculating. 18. The program according to claim 14, wherein each aberration component is a coefficient of each term in a Zernike polynomial series. In the second procedure,
A change amount of the image size obtained based on a data table indicating a relationship between the magnitude of the aberration component of the fourth term and the size of the image in the Zernike polynomial series created in advance, and each item except the fourth term 19. The program according to claim 18, wherein the program causes the computer to execute a procedure for obtaining the amount of change in the size of the image based on the amount of change in the size of the image obtained based on a linear combination of the aberration components of .

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