JP2004046200A - Photomask design method - Google Patents

Abstract

A shifter arrangement with high resolution can be realized in a Levenson-type phase shift mask, which can determine a degree of resolution suitable for exposure conditions by a simple method.
A method of designing a Levenson-type photomask in which a plurality of opening patterns that transmit incident light are formed in a part of a light-shielding film that blocks incident light, and a phase shifter is provided in a part of these patterns, For each line segment obtained by decomposing the pattern into line segments, a line segment pair of a different pattern adjacent within a distance R is extracted, and a line segment pair is drawn from the intermediate point 13 of the facing region 12 where the line segment pair 11 of interest faces. And a pattern that intersects within a distance S in the vertical direction, a process simulation is performed on the obtained pattern, a resolution easiness that is the ease of resolution of the adjacent pattern is obtained, The phase shifters are arranged so as to give a phase difference preferentially in the order of resolution difficulty based on the ease of resolution obtained for the pair.
[Selection diagram] Fig. 4

Description

【００８０】
次に、抽出した線分ペア毎、距離Ｓを用いて近傍のパターンを取り出し、プロセスシミュレーションにより解像容易度を求める（ステップ３〜ステップ５）。プロセスシミュレーションにおいては、前記（１２）に基づき露光シミュレーションを行うか、現像までをシミュレーションするか、エッチングまでをシミュレーションかを選択することができる。
【００８１】
本実施形態では露光シミュレーションを適用する。勿論シミュレーションではなく実際に実験を行っても良いし、実験とシミュレーションを組み合わせても良い。
【００８２】
シミュレータに入力するパターンの抽出方法はいくつか考えられる。最も基本的な方法としては図４に示すように、設計パターンから着目線分ペアと垂直方向に距離Ｓ以内で交わるパターンを１次元的に抽出し、１次元プロセスシミュレーションを行う。即ち、着目線分ペア１１の対向領域１２の中間ポイント１３より線分と垂直方向に距離Ｓ以内で交わるパターンを得、得られたパターンに対し１次元プロセスシミュレーションを行う。
【００８３】
なお、図４中の１４は取り出されるエッジポイント、１５はパターン１次元配置取得領域、２０はマスク、２１は透明基板、２２は遮光部、２３は透過部、３０はウェハを示している。また、マスク２０への入射光は部分的にコヒーレントな光である。
【００８４】
前記（５）に基づけば図５に示すように、着目隣接ペアのパターンのみを１次元的に抽出し、プロセスシミュレーションを行う。或いは前記（６）によれば図６に示すように、１辺２×Ｓの矩形領域と重なるパターンを２次元的に抽出し、２次元プロセスシミュレーションを行うこともできる。ここで、図中の１６，１７はパターン抽出幅（２Ｓ）、１８はパターン取り出し領域を示している。
【００８５】
なお、２次元シミュレーションは１次元シミュレーションと比較して計算時間が長くなるため、２次元シミュレーションを行う箇所をなるべく少なくした方が好ましい。そこで前記（１０）によれば、対向領域長さがＴ以下であるときに２次元シミュレーションを行い、それ以外は１次元シミュレーションを適用する。
【００８６】
続いて、露光シミュレーション結果から解像性を求める。解像性の評価方法も幾つか考えられる。
【００８７】
前記（１３）に基づく方法を図７（ａ）に示す。抽出したパターンに対し露光シミュレーションを行い、対向領域の中心位置での光強度Ｃと着目線分が属するそれぞれのパターンの中心位置での光強度Ａ，Ｂを求め、光強度Ａと光強度Ｂの小さい方の値から光強度Ｃを引く。対向領域間の中心位置の光強度が光強度の極小値と一致しない場合は、中心位置での光強度の代わりに光強度の極小値を使用してもよい。同じく、パターン中心位置での光強度が光強度の極大値と一致しない場合は、極大値を使用してもよい。この求めた差の値が大きいほど解像性が良いことを意味する。
【００８８】
前記（１４）に基づく方法を図７（ｂ）に示す。抽出したパターンに対し露光シミュレーションを行い、対向領域の中心位置での光強度Ｃと着目線分が属するそれぞれのパターンの中心位置での光強度Ａ，Ｂを求め、光強度Ａと光強度Ｂの平均値から光強度Ｃを引く。この値が大きいほど解像性が良いことを意味する。
【００８９】
前記（１５）に基づく方法を図７（ｃ）に示す。抽出したパターンに対し露光シミュレーションを行い、対向領域の中心位置での光強度Ｃを求め、レジストを解像させる光強度値であるスライスレベルより光強度Ｃを引く。この値が大きいほど解像性が良いことを意味する。また、場合により、着目線分が属するそれぞれのパターン中心位置での光強度Ａか光強度Ｂがスライスレベルよりも小さい場合は、その小さい値から光強度Ｃを引くか、或いはスライスレベル、光強度Ａ，Ｂの内の小さい方から２つ若しくは３つの値を対象に平均値を求め、その平均値から光強度Ｃを引く場合などが考えられる。
【００９０】
前記（１６）に基づく方法を図７（ｄ）に示す。抽出したパターンに対し露光シミュレーションを行い、光強度分布より対向領域の中心位置と着目線分が属するパターン中心位置との中心位置での接線の傾き角α１とα２を求め、αが大きいほど解像性が良いものとし、どちらか解像性の低いもの或いはα１，α２の平均値を解像容易度とする。
【００９１】
前記（１７）に基づく方法を図８に示す。抽出したパターンに対し、例えばデフォーカス値を変えて幾つか露光シミュレーションを行い、パターン間の寸法を測定しＥＤ−ｔｒｅｅを作成する。この場合、所望寸法±１０％でのＥＤ−ｔｒｅｅである。そして、ＥＤ−ｔｒｅｅから図に示すＦＯＣＵＳ裕度又はＤＯＳＥ裕度を求め、その値を解像容易度とする。この値は大きいほど解像し易いものとする。また、図８に示すウインドウの大きさを解像容易度とすることもできる。この場合、ウインドウサイズが大きいほど解像し易いものとする。
【００９２】
前記（１８）では、露光時間やエッチングなどの様々な要因を考慮し、裕度をウインドウ化し、そのウインドウサイズが大きいほど解像しやすいものとする。前記（１９）では、複数の条件で裕度をウインドウ化されたものが共通するウインドウサイズを求め、そのサイズが大きいものほど解像し易いものとする。また、前記（２１）に示すように、以上の解像容易度の求める方法を組み合わせて行うことも考えられる。
【００９３】
次に、図１のステップ３〜ステップ５までについて詳しく説明する。パターンを抽出するステップに関しては基本的な方法及び前記（１０）、解像性を求める方法としては前記（１５）を用いることにする。ステップ３〜５の詳しいフローを図９に示す。また、本実施形態では処理高速化のため、前記（１１）に記載されている参照テーブルを用いて同一のパターンのプロセスシミュレーションを繰り返し行わない処理方法を適用する。
【００９４】
その詳しい方法は、最初にパターンを抽出し、プロセスシミュレーション又は実験により解像容易度を求め、テーブルに追加する。それ以降は、パターンを抽出した後テーブルを参照し、そのパターン情報と一致する解像容易度を得る。もし一致しなかった場合は、最初と同様プロセスシミュレーションにより解像容易度を求め、テーブルに追加する。
【００９５】
１次元的に行う場合のテーブル格納方法の例として、図１０（ａ）に示すように、パターンエッジの並びを対向領域の中心位置からの相対的な位置で表現したものを索引部とし、そのときの解像容易度を対応させる。また、１次元配置が左右逆の場合も同様の評価結果になるため、逆の並びも追加しておく。テーブルを参照する場合は、図１０（ｂ）に示すように、索引部と一致する解像容易度を取り出す。
【００９６】
また、２次元的に行う場合のテーブルへの格納方法の例として、図１１に示すように抽出されたパターンを線分化して、それらを第１キーとして対向領域長さ方向と垂直方向に昇順、第２キーとして平行方向に昇順としてソートし、その線分情報列の並びをテーブルの索引部として、求めた解像容易度を格納する。パターン情報の形式以外は、テーブル格納方法及び参照方法共に１次元の場合と同様である。また、対向領域長さ方向を軸に関してミラー反転した場合も同様の解像容易度のため、その場合のパターンについてもテーブルに追加しておく。
【００９７】
次に、パターンを抽出しプロセスシミュレーションを行い、解像性を評価するステップについて詳しく説明する。前記（表１）には図１中の線分ペアと対向領域の長さが示してある。
【００９８】
本実施形態では距離Ｔは０．２μｍとし、距離Ｓを０．６μｍ（これは、光学的に影響の及ぶ範囲の距離を指定することが望ましい）とする。また、露光条件は光源を通常照明、λ＝０．２４８μｍ、σ＝０．３、ＮＡ＝０．５５、デフォーカス値０．３μｍ、そしてスライスレベルは０．３とした。
【００９９】
線分ペアを抽出した後、抽出された線分ペアを露光シミュレーションする。まず、着目線分ペアが２−１５のときは対向領域長さが０．２で距離Ｔ以下であるので、図１２（ａ）のように、対向領域中心位置より矩形領域２Ｓ×２Ｓ＝１．２μｍ×１．２μｍで重なるパターンを２次元的に抽出する。続いて、その抽出されたパターンに対し２次元露光シミュレーションを行い、図１２（ｂ）に示すように、着目線分の対向領域の中心から垂直方向（ラインＡ）の光強度分布を得る。その結果を、図１２（ｃ）に示す。
【０１００】
このときの対向領域の中心位置の光強度は　０．０９１７３７　である。従って、解像容易度の値は　０．３−０．０９１７３７＝０．２０８２６３となる。そして、２次元用テーブルに抽出されたパターンと解像容易度を追加する。ここで、前記（２０）のように、パターン間の中心付近の光強度が小さいほど解像容易として解像容易度を決定するようにしてもよい。
【０１０１】
次に、着目線分ペアが３−５のときでは、対向領域長さは０．６μｍとなる。これは距離Ｔ以上となるため、図１３（ａ）に示すように距離Ｓ以内で重なるパターンを１次元的に取り出し、１次元露光シミュレーションを行う。その結果を、図１３（ｂ）に示す。
【０１０２】
対向領域の中心位置の光強度は　０．１９０９７０　で、解像容易度は　０．３−０．１９０９７０＝０．１０９０３　となる。そして、今回抽出されたパターン（（−０．３　−０．１）（０．１　０．３））及びそれのパターン配置を左右反転したもの（（−０．３　０．１）（０．１　０．３）　）を１次元用テーブルに解像容易度と対応させて追加する。但し、この場合はパターンを反転しても同じパターンになるため、反転したパターンを追加しない。現時点での１次元用テーブルを（表２）に示す。
【０１０３】
【表２】

【０１０４】
次に、着目線分ペアが４−１８のときは、対向領域長さが０．５となる。これは距離Ｔ以上となるため、図１４に示すように、距離Ｓ以内で重なるパターンを１次元的に取り出す。抽出されたパターン情報は（（−０．３　−０．１）（０．１　０．３））である。そして、（表２）に示す１次元用テーブルを参照し、既に同様のパターンをシミュレーションしたかをチェックする。この場合、テーブル検索部に（（−０．３　−０．１）（０．１　０．３））が見つかるため、その解像容易度　０．１０９０３を得る。
【０１０５】
以上のような手順に従って、同様に全ての隣接線分ペアについて行うと、（表３）に示す結果となる。また、参考までに強度Ａ及び強度Ｂについても記載している。
【０１０６】
【表３】

【０１０７】
（表３）は線分のペアであるが、これを下記の（表４）に示すように隣接パターンペアに置き換える。
【０１０８】
【表４】

【０１０９】
１つの隣接パターンペアに複数の隣接線分ペアが含まれる場合（表４、隣接パターンペアＦ−Ｇ）、解像容易度が難しい順にソートしておく。次いで、隣接パターンペアを線分ペアの先頭から比較して、解像容易度値が小さい順でソースする。但しこの場合、（表３）に示すＦ−ＧとＧ−Ｈとの比較の場合は、第１隣接線分ペアの解像容易度が同じであるがＦ−Ｇではもう一つ要素が多くある。これは、隣接線分ペアの多い方のＦ−Ｇを優先する。また、隣接線分ペア数と解像容易度が同じ場合、隣接する面の長さなどの要素で順序付けすることも考えられるが、本実施形態では省く。ソート結果を下記の（表５）に示す。
【０１１０】
【表５】

【０１１１】
続いて、（表５）に示す順で優先的に位相差を与える（ステップ６）。順位付けされた隣接ペア順から優先的に位相差を与える方法は様々あるが、ここでは本発明者らが既に提案した方法（特開平８−３２８２３７号公報）に記載してある方法で位相を決定した。その位相決定結果を図１５に示す。但しこの図は、位相差が与えられたペアの片方に位相差を与えるシフタを貼って示してある（ステップ７）。
【０１１２】
このように本実施形態によれば、露光条件に合った解像容易度をシンプルな方法で求めることができ、レベンソン型位相シフトマスクにおいて解像性の高いシフタ配置を実現することができる。このため、半導体の設計作業が効率化され生産コストを低減させることが可能となる。
【０１１３】
なお、線分の分割方法としては、次のような方法を採用することもできる。図２９は、前記（３）に基づいた線分の分割方法を示す図である。即ち、線分を分割する工程として、着目線分から垂直方向にある特定の距離以内を見て、該着目線分を含むパターンに対向する隣接パターンの頂点から着目線分に下ろした垂線の交点又はその近傍を目安に、分割後の線分の長さが指定の長さよりも短くならないように着目線分を分割する。具体的に、図形Ｂ上の線分の分割について説明する。即ち、Ｂから垂直方向に距離Ｒ内で対向している隣接パターンＡ，Ｃの線分の配置環境が変わる点において線分を分割する。このような線分の分割方法を取ることにより配置環境に柔軟に対応できる。
【０１１４】
図３０は前記（４）に基づいた線分の分割方法を示す図である。即ち、線分を分割する工程として、着目線分から垂直方向に特定の距離Ｒ以内にあるパターンを見て、パターンの頂点から着目線分に下ろした垂線の交点又はその近傍を目安に、分割後の線分の長さが指定の長さよりも短くならないように着目線分を分割する。具体的には、Ｂから垂直方向に距離Ｒ内で、対向辺に限らず、パターンの配置環境が変わる点において線分を分割する。このような線分の分割方法を取ることにより、複雑な配置環境に柔軟に対応できる。
【０１１５】
また、分割線分の配置が１次元的ルールで近似できないと判定する条件としては、次のような方法を採用することもできる。図３１は、前記（７）に基づいて解像容易度を求める図形を示す図である。図３１（ａ）に示すパターンでは、前記（７）に基づいて線分＜２＞　が１次元に近似できないと判定する。このとき、図３１（ｂ）に示すように、線分＜２＞　の左右両側及び両端から上下にそれぞれ距離Ｓ１，Ｓ２，Ｓ３，Ｓ４にわたる矩形領域を像計算領域として取出す。そして、図１（ｃ）に示すように、この矩形領域を２次元プロセスシミュレーションにかける。
【０１１６】
図３２は、前記（８）に基づいて解像容易度を求める図形を示す図である。図３２（ａ）に示すレイアウトにおける対象線分　＜１＞〜＜８＞　のうち、マスク座標軸に垂直でも平行でもない方向に配置されている線分は＜５＞，＜６＞　である。ここでは特に、線分＜６＞　について説明する。図３２（ａ）のレイアウトより図３２（ｂ）に示すように、線分＜６＞　の両端を含み距離Ｓの範囲のパターンを抽出する。この領域に関して２次元プロセスシミュレーションを行い、解像容易度を求める。プロセスシミュレーションを行う範囲として、図形抽出の利便性を鑑みて、図３２（ｃ）のように対象線分を含む矩形から距離Ｓ内の範囲としてもよい。
【０１１７】
なお、図１のフローチャートにおける各ステップを、各々のステップを行う機能ブロックに置き換え、これらの機能ブロックを接続することにより、フォトマスク設計装置を構成することができる。実際にはこの装置は、例えば磁気ディスク等の記録媒体に記録されたプラグラムを読み込み、このプログラムによって動作が制御されるコンピュータによって実現される。
【０１１８】
（第２の実施形態）
次に、前記（２）に基づく実施形態を説明する。その処理フローを、図１６に示す。
【０１１９】
本実施形態は基本的に第１の実施形態と同様であるが、第１の実施形態と異なる点は、ステップ１から３において、パターン間で最も解像しにくい線分のみを抽出することである。また、パターン間で最も解像し難い線分ペアを判別する方法としては、前記（２２）に示すように距離Ｖ以内で隣接する領域が最も長い隣接線分ペアが最も解像しにくいものとする。
【０１２０】
図２に示すパターンでは隣接パターンペアＦ−Ｇのみが線分ペア３２−３６及び３３−３９の２箇所のエッジで隣接している。これらの線分ペアのうちで距離Ｖ、Ｖ＝０．２μｍで隣接するエッジが最も長い線分ペア３２−３６が解像容易度を求める対象となる。実パターンでは、隣接ペア間で隣接するエッジが複数存在するのは当然のことで、この方法を適用することにより高速処理につながる。本実施形態に基づき、図２に示すパターンに対して抽出した隣接線分ペア（隣接パターンペア）を、下記の（表６）に示す。
【０１２１】
【表６】

【０１２２】
以下ソート、位相決定を行う部分は第１の実施形態と同様であり、たまたま結果も同じである（表は省く）。従って、シフタ配置結果は前記図１５に示すのと同様になる。
【０１２３】
なお、図１６のフローチャートにおける各ステップを、各々のステップを行う機能ブロックに置き換え、これらの機能ブロックを接続することにより、フォトマスク設計装置を構成することができる。実際にはこの装置は、例えば磁気ディスク等の記録媒体に記録されたプラグラムを読み込み、このプログラムによって動作が制御されるコンピュータによって実現される。
【０１２４】
（第３の実施形態）
図１７は、本発明の第３の実施形態に係わるフォトマスクの設計方法を示すフローチャートであり、これは前記〈１〉に基づく実施形態である。まず、図１８の設計データを入力する。図中のＡ〜Ｔはクロムの開口部に相当し、以下これをパターンと呼ぶ。また、Ｃ，Ｆ，Ｉ，及びＫには固定位相が与えられている。
【０１２５】
まず、距離０．２μｍ（しきい値）以内で隣接するパターンのペアを抽出し、それぞれ図１９に示すように隣接パターンペア間の隣接する面の長さ（以下、隣接面長さと称する）を求める。その結果を、下記の（表７）に示す。
【０１２６】
【表７】

【０１２７】
そして、隣接面長さが長い順にソートを行う。その結果を、下記の（表８）に示す。
【０１２８】
【表８】

【０１２９】
ここでは、隣接面長さの長い順にソートを行ったが、先の第１の実施形態のように解像容易度の低い順にソートしても良いし、その他の重み付けの条件を用いても良い。
【０１３０】
次に、図２０（ａ）に示すように、パターンをノード化し予め位相が与えられているノードＣ，Ｆ，Ｋ，Ｉに固定位相を位相情報として与え、ソートされた隣接パターンペア順に以下のルールで、位相決定と位相が決まっていない反転グラフの作成を行う。
【０１３１】
１．互いのノードに位相情報が存在しない場合は、閉ループにならないようにノードを繋ぐ。
【０１３２】
２．片方のみに位相情報が存在する場合は、その位相情報と逆の位相値を初期位相とし、もう片方のノードの繋がりに対し位相を決定する。
【０１３３】
３．互いに位相情報が存在する場合には、位相決定もノードの接続も行わない。
【０１３４】
以下、実際に隣接ペア毎にノードを繋いでみる。まず、隣接ペアＭ−Ｑでは、両方のノード共に位相情報が与えられておらず、かつ繋いだ場合にループが発生しないため図２０（ｂ）に示すように、そのペアを繋ぎ、グループ番号を与える。ここで、グループ番号を与える理由について説明すると、ノードを繋ごうとする際にループが発生するか否かを判定するためである。ループの判定の方法は、隣接パターンペアのノードの属するグループ番号が同じ番号であればループとなり、両方が違うグループ若しくは片方がグループに割り当てられていない場合はループを形成しない。
【０１３５】
次にＩ−Ｊでは、ノードＩのみに位相情報が与えられているため、もう片方のＪが繋がるグループに対して位相を決定する。この場合では、Ｊが繋がるグループが無いため、図２０（ｃ）のようにＩの位相と逆位相をＪに与える。
【０１３６】
続いてＥ−Ｊでは、Ｊのみに位相情報があるため、Ｅとその繋がるグループに対し位相を与える。これもＥと繋がるノードが無いため、図２１（ｄ）に示すようにＥに対してのみＪの逆位相を与える。
【０１３７】
Ｃ−Ｅでは両方に位相情報があるため、図２１（ｅ）に示すように、ルール３に従ってノードパターンを接続しない。勿論、得られる結果は変わらないため、繋いでも構わない。Ｆ−ＩもＣ−Ｅのときと同様、両方に位相情報があるため、図２１（ｆ）に示すように、ルール３に従い繋がない。
【０１３８】
Ｄ−Ｈでは、両方とも位相情報を持っておらず、かつ繋いだ場合にループを形成しないため、図２２（ｇ）に示すようにＤ−Ｈを繋ぎ、グループ番号２を与える。
【０１３９】
Ｆ−Ｈでは、Ｆのみ位相情報が与えられている。従って、Ｈとそれに繋がるグループに対し位相を決定する。この場合、Ｈに繋がるグループ２があるため、図２２（ｈ）のようにＨの位相情報にＦの逆位相（初期位相）を与え、Ｈと繋がるＤに対し、Ｈの逆位相を与える。本方法では、位相決定がなされたグループの繋がりを解除している。これは得られる結果は変わらないため、解除しなくても構わないが、これを行うことで、コンピュータ処理を行う上でメモリを削除することができる。
【０１４０】
以下同様に、全ての隣接パターンペアを処理すると、最終的に図２３（ｉ）に示すグラフ（反転グラフ）が得られる。そして、未だ位相の決まっていないグループ１とグループ３に対し、初期図形（ノード）をそれぞれＬとＭとし、位相を決定する。その結果を図２３（ｊ）に示し、対応する設計パターンを図２４に示す。以上の方法によれば、固定位相を保持し、かつ優先度を考慮した位相決定が可能となる。
【０１４１】
なお、図１７のフローチャートにおける各ステップを、各々のステップを行う機能ブロックに置き換え、これらの機能ブロックを接続することにより、フォトマスク設計装置を構成することができる。実際にはこの装置は、例えば磁気ディスク等の記録媒体に記録されたプラグラムを読み込み、このプログラムによって動作が制御されるコンピュータによって実現される。
【０１４２】
（第４の実施形態）
図２５は、本発明の第４の実施形態に係わるフォトマスク設計方法を示すフローチャートであり、これは前記〈２〉に基づく実施形態である。第３の実施形態と同様に図１８のレイアウトデータを例に説明する。固定位相も第３の実施形態と同様、Ｃ，Ｆ，Ｉ，及びＫに与えられている。
【０１４３】
まず、距離０．２μｍ以内で隣接するパターンペアを抽出する。その際、隣接ペアの両方に固定位相が付いているものは抽出しない。そして、抽出した隣接ペアそれぞれの隣接面長さを求める。その結果を、下記の（表９）に示す。
【０１４４】
【表９】

【０１４５】
ここで、第３の実施形態では隣接パターンペア数は２９個得られたが、本実施形態では固定位相を両方に持つ隣接パターンペア４つが減り、２５個となった。そして、隣接する面の長さが長い順になるようにソートを行う。その結果を、下記の（表１０）に示す。
【０１４６】
【表１０】

【０１４７】
続いて、第３の実施形態のときと同様のルールで、ソートされた順に反転グラフを作成し、位相決定を行う。反転グラフ、位相決定結果、そしてシフタ配置結果は第３の実施形態の図２３、図２４と全く同じになる。
【０１４８】
本実施形態の方法では、隣接パターンペアを抽出する数が減るため、その分だけ隣接面長さを求める作業、及び反転グラフ作成の対象データが減り、処理の高速化が図れる。
【０１４９】
（第５の実施形態）
図２６は、本発明の第５の実施形態に係わるフォトマスクの設計方法を示すフローチャートであり、これは前記〈３〉に基づく実施形態である。第３及び第４の実施形態と同様に、図１８のレイアウトを例に説明する。これもまた、Ｃ，Ｆ，Ｉ，及びＫに固定位相が与えられている。
【０１５０】
まず、距離０．２μｍ以内で隣接するパターンペアを抽出する。第３の実施形態と同様に全てのパターンペアを抽出してもかまわないが、本実施形態では前記〈２〉に基づいて固定位相を互いに持つ隣接パターンペアを抽出しないこととする。そして、抽出された隣接ペア毎に隣接面長さを求める。その結果が、下記の（表１１）となる。
【０１５１】
【表１１】

【０１５２】
続いて、第１ソートキーにペアの片方に固定位相を持つもの、第２ソートキーに隣接面長さが長い順としてソートを行う。その結果を、下記の（表１２）に示す。
【０１５３】
【表１２】

【０１５４】
続いて、第３の実施形態のときと同様のルールでソートされた順に反転グラフを作成すると、図２７（ａ）に示す結果となり、それに対し位相を決定すると図２７（ｂ）となる。対応する設計パターンのシフタ配置結果は図２８に示す通りとなる。
【０１５５】
本実施形態におけるシフタ配置結果を、第３及び第４の実施形態の配置結果と比較すると余り差が見られないが（実際のパターンに固定位相が存在する位相決定においては、この差が大きくなる）、図形Ａの位相が違っている。これは、固定位相と隣接するパターンが特に優先的に位相差を与えられたからである。従って本実施形態方法により、固定位相と隣接するパターンペアの位相決定の優先度を上げることができ、固定位相端部の解像性を向上させることが可能となる。
【０１５６】
以上説明した第３〜第５の実施形態では、隣接ペアを求める際のしきい値を０．２μｍとしたが、この値は何等限定されるものではない。通常は、対象デバイスのパターンの特徴を反映した値に設定される。また、これらの実施形態では、ノードを繋ぐ際に閉ループが生じないようにしたが、これは奇数の閉ループが生じると位相決定の際に矛盾が生じるためである。偶数の閉ループが生じても任意の一つを選択して位相決定することができるので、偶数の閉ループが生じるのは許容してもよい。つまり、奇数の閉ループが生じないようにノードを繋ぐようにすればよい。
【０１５７】
なお、本発明は上述した各実施形態に限定されるものではなく、その要旨を逸脱しない範囲で、種々変形して実施することができる。
【０１５８】
また、上述した各実施形態において記載した手法は、コンピュータに実行させることのできるプログラムとして、例えば磁気ディスク（フロッピーディスク，ハードディスク等）、光ディスク（ＣＤ−ＲＯＭ，ＤＶＤ等）、半導体メモリなどの記録媒体に書き込んで各種装置に適用したり、通信媒体により伝送して各種装置に適用することも可能である。本装置を実現するコンピュータは、記録媒体に記録されたプログラムを読み込み、このプログラムによって動作が制御されることにより、上述した処理を実行する。
【０１５９】
【発明の効果】
以上述べたように本発明によれば、設計パターンに対して、しきい値Ｒ以内で隣接する線分（又はパターン）の組み合わせを抽出した後、それぞれの線分ペア（パターンペア）毎に着目パターンを得、得られたパターンに対してプロセスシミュレーション，実験，又はこれらの組み合わせのいずれかを行い、隣り合うパターンの解像の容易さを求めることによって、露光条件に合った解像容易度をシンプルな方法で求めることができる。従って解像のし難い隣接パターンから優先的に位相差を与えることが可能となり、より解像性の高いシフタ配置結果を得ることができ、半導体の設計作業が効率化され生産コストを低減させることが可能となる。
【０１６０】
また本発明によれば、固定位相が存在する設計パターンのシフタ配置において、固定位相を変更させることなく優先度を保った位相決定が可能となる。例えばＤＲＡＭのレベンソン型位相シフトマスク設計のように、特に解像が厳しい周期性をもつメモリセル部では人手で位相決定することが望ましく、残りの周辺パターンに対し本発明の方法を用いて位相を自動決定することで、メモリセル部の人手で配置した位相情報をそのまま保持して周辺パターンへシフタを配置することができる。また固定位相が与えられたパターンは、特に寸法精度が厳しかったり要求される解像度が高い場合が多いと想定されるため、それと隣接するパターンを優先的に逆位相とすることにより、固定位相端部の解像性を向上させることが可能となる。このように、人手の配置と自動は位置の組合わせにより、高品位なレベンソンタイプのフォトマスク設計が効率的に行うことができる。
【図面の簡単な説明】
【図１】第１の実施形態に係わるフォトマスク設計方法の処理フローを示す図。
【図２】第１の実施形態で用いたパターンデータを示す図。
【図３】図２に示すパターンデータを線分に分解した図。
【図４】第１の実施形態におけるパターン抽出方法の例を示す図。
【図５】第１の実施形態におけるパターン抽出方法の別の例を示す図。
【図６】第１の実施形態におけるパターン抽出方法の更に別の例を示す図。
【図７】第１の実施形態における解像容易度を求める方法を示す図。
【図８】第１の実施形態における解像容易度を求める別の方法を示す図。
【図９】図１のステップ３からステップ５までの詳細な処理フローを示す図。
【図１０】１次元用テーブルの追加及び参照方法を示す図。
【図１１】２次元用テーブル検索部の作成方法を示す図。
【図１２】隣接線分ペア２−１５におけるパターン抽出とシミュレーションを示す図。
【図１３】隣接線分ペア３−５におけるパターン抽出とシミュレーションを示す図。
【図１４】隣接線分ペア３−１８におけるパターン抽出を示す図。
【図１５】位相シフタ配置結果を示す図。
【図１６】第２の実施形態に係わるフォトマスク設計方法の処理フローを示す図。
【図１７】第３の実施形態に係わるフォトマスク設計方法の処理フローを示す図。
【図１８】第３の実施形態における入力設計データと固定位相を示す図。
【図１９】隣接面長さを説明するための図。
【図２０】初期段階のノード及び位相情報と、着目隣接パターンペアＭ−Ｑ，Ｉ−Ｊの時のグラフを示す図。
【図２１】着目隣接パターンペアＥ−Ｊ，Ｃ−Ｅ，Ｆ−Ｉの時のグラフを示す図。
【図２２】着目隣接パターンペアＤ−Ｈ，Ｆ−Ｈの時のグラフを示す図。
【図２３】第３の実施形態における位相情報及び反転グラフと、反転グラフに対する位相決定結果を示す図。
【図２４】第３の実施形態における設計パターンから見た位相決定結果を示す図。
【図２５】第４の実施形態に係わるフォトマスク設計方法の処理フローを示す図。
【図２６】第５の実施形態に係わるフォトマスク設計方法の処理フローを示す図。
【図２７】第５の実施形態における位相情報及び反転グラフと、反転グラフに対する位相決定結果を示す図。
【図２８】第５の実施形態における設計パターンから見た位相決定結果を示す図。
【図２９】線分の分割方法の一例を示す図。
【図３０】線分の分割方法の他の例を示す図。
【図３１】解像容易度を求める図形の一例を示す図。
【図３２】解像容易度を求める図形の他の例を示す図。
【符号の説明】
１１…着目線分ペア
１２…対向領域
１３…中間ポイント
１４…エッジポイント
１５…パターン１次元配置取得領域
１６，１７…パターン抽出幅
１８…パターン取り出し領域
２０…マスク
２１…透明基板
２２…遮光部
２３…透過部
３０…ウェハ[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for designing a photomask for manufacturing a semiconductor, and more particularly to a method for designing a photomask in which a phase shifter is arranged on one of adjacent patterns, such as a Levenson-type phase shift mask. The present invention also relates to a photomask designing apparatus for designing the above photomask and a recording medium storing a program for realizing the photomask designing by a computer.
[0002]
[Prior art]
As a method of designing a Levenson-type phase shift mask, the following techniques are conventionally known.
[0003]
As a first prior art, (Automatic Pattern Generation System for Phase Shifting is a phase-based DRAM in (Symposium on VLSI Technology, pp. 95-96, JSAPCAT, No. AP9111210 (1991)). It is designed using an automatic shift mask design device. Then, when automatically determining the phase of light passing through a figure, an arbitrary figure is first selected and its phase is set to 0 °, and the phase of any subsequent figure is set around the figure. Of the figures for which a phase has been determined, the figure whose phase is to be determined is the opposite of the one whose longest side is facing, and there are multiple figures that face the longest side. A shifter automatic arrangement method in which a warning is issued and the processing is interrupted when the two are different is discussed.
[0004]
As a second conventional technique, (Investigating Phase-Shifting Mask Layout, a paper given in (IEDM Tech. Digest, pp. 705-708, 1991) by (Andrew. R. Neureuser) et al. It discusses a device in which a designer determines a reduction ratio for a pattern, performs automatic placement of shifters on the reduced pattern, and displays a portion where there is a contradiction in the automatic shifter placement. .
[0005]
As a third related art, Japanese Patent Laid-Open Publication No. Hei 5-341498 discloses that, when the distance between transparent regions is less than a threshold value, a shifter is arranged on one side of the transparent region, and a position where a contradiction occurs in the shifter arrangement. Describes a method of presenting the location to a designer. Further, the document describes a device having a function of automatic shifter placement, shifter verification, and shifter placement / verification for a layout in which some shifters are already placed.
[0006]
As a fourth prior art, in Japanese Patent Application Laid-Open No. Hei 7-13326, sides forming a closed loop are weighted under various conditions, and ends of one or more sides of each closed loop are sequentially arranged in order from the side having the largest weight. A technique for correcting a graphic pattern corresponding to a node is described.
[0007]
As a fifth conventional technique, (Jpn. J. Phys. Vol. 32 (1993) pp. 5874-5879), an article entitled (Algorithm for Phase Shift Shift Design with Priority on Shifter Placement) and Japanese Patent Application Laid-Open No. 308-314, pp. 308-1994. In the publication, a combination of two patterns arranged closer than a specified value is extracted from an input layout, and a combination having a longer side length adjacent to another pattern in this combination has a higher phase. A method and apparatus for increasing the priority of the shifter arrangement and alternately arranging the phase shifters in the shifter arrangement priority order are described.
[0008]
As a sixth related art, in Japanese Patent Application Laid-Open No. 8-328237, an adjacency relationship between adjacent patterns within a threshold value S2 is determined in design data composed of a pattern that is a transparent region, and 1 A method of extracting all combinations of adjacent patterns for each adjacent group as a group, sorting the combinations in the order in which correction is difficult, creating an inversion relationship based on the sorting, and determining a phase based on the created inversion relationship Has been described.
[0009]
As a seventh prior art, JPN. J. Appl. Phys. Vol. 32 (1993) pp. A paper titled “Computer Aided Design Software for Design Phase-Shifting Masks” in US Pat. No. 5,887-5891, describes a method of determining a phase by following an adjacency relationship from a pattern that has been previously determined by a designer.
[0010]
[Problems to be solved by the invention]
However, this kind of prior art has the following problems. That is, the first to third prior arts merely describe the phase determination result when a specific figure is used as an initial figure when a phase inconsistency occurs. No arrangement can be found. Therefore, these prior arts cannot realize a shifter arrangement with high resolution.
[0011]
Further, in the fourth to sixth related arts, the phase is determined by weighting in consideration of the length of the adjacent surface, the distance between the adjacent surfaces, and the like, and contradictory portions that can be easily corrected can be obtained. However, since the resolution viewpoint is not included, for example, in order to repair a pattern pair having inferior resolution, a pattern pair having the same ease of correction but having clearly superior or inferior resolution is used. It cannot be considered that the phase is reversed. Furthermore, the resolution scale is not clear. Therefore, even with these conventional techniques, a shifter arrangement with high resolution cannot be realized.
[0012]
In addition, for example, in a DRAM, the phase of the memory cell section is manually determined in some cases. Therefore, without changing the phase information, the phase of the pattern in which the phase of the sense amplifier section or the row decoder section is not yet determined is determined. There is a need. Considering that the phase is determined based on a figure (fixed phase) for which the phase has already been determined, the first to third conventional techniques describe a phase determination method when a specific figure is used as an initial figure. And the phase cannot be determined in consideration of the fixed phase.
[0013]
In the fourth conventional technique, it is not possible to determine a phase in consideration of a fixed phase by a method for minimizing a contradictory portion. In the fifth and sixth prior arts, the phase can be determined by giving priority to the resolution or easiness of correction, but the phase difference cannot be given in consideration of the fixed phase. Further, in the seventh conventional technique, a fixed phase is considered. However, since the phase is determined by tracing the adjacent relationship, it is not possible to determine the phase in consideration of the resolution, the ease of correcting the phase inconsistency, and the like.
[0014]
The present invention has been made in consideration of the above circumstances, and an object of the present invention is to provide a simple method for determining the degree of resolution suitable for exposure conditions, and in a Levenson-type phase shift mask or the like. An object of the present invention is to provide a method for designing a photomask that can realize a shifter arrangement with high resolution.
[0015]
Another object of the present invention is to provide a method for designing a photomask capable of determining a phase of a portion where a phase is not determined in consideration of a prioritized adjacent pattern pair without changing a fixed phase at all. Is to do.
[0016]
Still another object of the present invention is to provide a photomask designing apparatus for realizing the above method, and a recording medium storing a program for realizing the above method.
[0017]
[Means for Solving the Problems]
(Constitution)
In order to solve the above problems, the present invention employs the following configuration.
[0018]
(1) A plurality of aperture patterns that transmit incident light are formed in a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to incident light that transmits through the pattern is formed in a part of these patterns. In the method of designing the provided photomask, a pair with a line segment belonging to a different pattern adjacent within a distance R is extracted for each line segment obtained by decomposing the pattern into line segments, and a line segment is divided for each line segment pair. Obtains a pattern that intersects with a line segment within a distance S in the vertical direction from the intermediate position of the opposing region, and uses a process simulation, an experiment, or a combination thereof to resolve the adjacent pattern. A phase shifter is arranged to determine the ease of resolution, which is the ease, and to give a phase difference preferentially to a pair of adjacent patterns in the order of resolution difficulty based on the ease of resolution determined for the line segment pair. Characterized in that it.
[0019]
(2) A plurality of aperture patterns for transmitting the incident light are formed in a part of the light-shielding film that blocks the incident light, and a phase shifter for giving a phase difference to the incident light transmitting the pattern is formed in a part of these patterns. In the method of designing the provided photomask, a pair of patterns adjacent to each other within a distance R is extracted, and after decomposing each pattern into line segments, an intermediate position of a facing region where resolution is expected to be the least difficult between the patterns. A pattern that intersects the stranded line segment within a distance S in the vertical direction is obtained, and the obtained pattern is subjected to a process simulation, an experiment, or a combination thereof to determine the degree of ease of resolution, which is the ease of resolving adjacent patterns. A phase shifter is arranged so as to preferentially give a phase difference to a pair having difficulty in resolution based on the degree of resolution obtained for a pair of adjacent patterns within the distance R. To.
[0020]
(3) In the above (1) or (2), as a step of decomposing a line segment, a predetermined distance in the vertical direction from the line segment of interest is observed, and a point is reached from a vertex of an adjacent pattern facing the pattern including the line segment of interest. The line segment of interest is divided so that the length of the line segment after division is not shorter than the designated length, using the intersection of the perpendicular line drawn down to the line segment or its vicinity as a guide.
[0021]
(4) In the above (1) or (2), as a step of decomposing a line segment, a pattern which is within a predetermined distance in the vertical direction from the line segment of interest is observed, and an intersection of a perpendicular line lowered from the vertex of the pattern to the line segment of interest is obtained. Alternatively, the line segment of interest is divided such that the length of the line segment after division is not shorter than the designated length using the vicinity thereof as a guide.
[0022]
(5) In (1) or (2) above, when extracting a pattern that intersects with a line segment within a distance S in the vertical direction from the intermediate position of the opposing region, only the pattern pair to which the line segment of interest belongs is extracted as a target. It is characterized by doing.
[0023]
(6) In the above (1) or (2), a pattern overlapping a rectangular area formed by a vertical direction and a parallel direction at a distance S from an intermediate position of the facing area is two-dimensionally extracted, and the extracted pattern is defined as 2 It is characterized in that the degree of resolution is obtained by using a dimensional process simulation, an experiment, or a combination thereof.
[0024]
(7) In the above (1) or (2), when an adjacent line segment within a predetermined distance in the vertical direction from the line of interest is arranged in a direction that is neither perpendicular nor parallel to the line of interest, the pattern including the line of interest Is extracted two-dimensionally, and the degree of resolution is obtained from the extracted pattern using two-dimensional process simulation, experiment, or a combination thereof.
[0025]
(8) In the above (1) or (2), when the line of interest is arranged in a direction that is neither perpendicular nor parallel to the mask data design coordinate axis, a pattern including the line of interest is extracted two-dimensionally. The method is characterized in that the degree of resolution of the extracted pattern is obtained by using a two-dimensional process simulation, an experiment, or a combination thereof.
[0026]
(9) In the above (6) to (8), after performing the two-dimensional process simulation, the solution is performed at a place where the pattern arrangement environment changes in the direction parallel to the line of interest at the intermediate position of the facing area and in the vertical direction. It is characterized in that image ease is obtained. (10) In the above (1) or (2), if the length of the region facing the line segment pair of interest is less than or equal to a predetermined distance T, the degree of resolution is obtained by the methods (6) to (8). It is characterized by the following.
[0027]
(11) In the above (1) or (2), each time the process simulation is performed, the pattern information used at that time and the value of the ease of resolution obtained by the process simulation, experiment, or a combination thereof are stored in a table. Each time a pattern is extracted, the table is referred to, and if the pattern matches, the resolvability value stored in the table is obtained. If the pattern does not match, the process simulation, experiment, or Is obtained by obtaining the degree of resolution easiness by performing the combination of.
[0028]
(12) In the above (1) or (2), the process simulation is one or a combination of an exposure simulation, a development simulation, and an etching simulation.
[0029]
(13) In the above (1) or (2), as a method of obtaining the degree of ease of resolution, a region where a line segment pair of interest is opposed from a smaller light intensity value at an intermediate position of each pattern portion. A value obtained by subtracting the light intensity value at the intermediate position is determined, and the phase is determined on the assumption that the larger the difference is, the easier the resolution is.
[0030]
(14) In the above (1) or (2), as a method of obtaining the degree of ease of resolution, the average value of the light intensity values at the intermediate positions of the respective pattern portions is calculated based on the average of the light intensity values at the intermediate position of the line segment pair of interest. A value is obtained by subtracting the light intensity value at the position, and the phase is determined on the assumption that the larger the difference is, the easier the resolution is.
[0031]
(15) In the above (1) or (2), as a method of obtaining the degree of resolution, the light intensity for resolving the resist is set as a slice level, and the area of the line segment pair of interest is determined from the slice level value. A value obtained by subtracting the light intensity value at the intermediate position is determined, and the phase is determined on the assumption that the larger the difference is, the easier the resolution is.
[0032]
(16) In the above (1) or (2), as a method of obtaining the degree of ease of resolution in a one-dimensional intensity distribution, a middle position between an intermediate position of each pattern portion and a center position of a facing area, or a pattern edge position The phase is determined based on the assumption that the larger the inclination angle of the tangent of the light intensity distribution is, the easier the resolution is.
[0033]
(17) In the above (1) or (2), as a method of obtaining the degree of resolution, the dependence of the combination of the focus and the exposure amount at the point of interest and the dimensional difference from the desired dimension is determined by process simulation, experiment, or the like. The size of the window composed of the exposure margin and the defocus margin is determined by taking into account the exposure margin, defocus margin, or both, and the margin or window size is large. The phase is determined on the assumption that the resolution is easier.
[0034]
(18) In the above (1) or (2), as a method of obtaining the degree of ease of resolution, a process simulation, an experiment, or a combination thereof is used to obtain a window of a process margin at a position of interest, and a window size is obtained. It is characterized that the phase is determined on the assumption that the larger the value of, the easier the resolution is.
[0035]
(19) In the above (1) or (2), as a method of obtaining the degree of resolution, using a process simulation, an experiment, or a combination thereof, a window of process latitude at a plurality of target positions is common. The method is characterized in that a window size is determined and a phase is determined on the assumption that the larger the common window size is, the easier the resolution is.
(20) In the above (1) or (2), as a method of obtaining the degree of resolution, the phase is determined on the assumption that the lower the light intensity at the middle position of the facing region of the line pair of interest, the easier the resolution is. It is characterized by doing.
[0036]
(21) In (1) or (2), when determining the degree of resolution, the methods of (13) to (20) are used in combination of two or more.
[0037]
(22) In the above (2), in the pattern pair of interest, a line segment pair having the longest region facing within a distance V is defined as the least resolvable portion in the pattern pair of interest, and that portion is evaluated for resolution. It is characterized by the following.
[0038]
Further, the present invention employs the following configuration.
[0039]
<1> A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to incident light that transmits through the pattern is formed on a part of these patterns. In the method for designing a photomask to be provided, a step of extracting a pair of adjacent patterns within a predetermined range with respect to a design pattern in which a fixed phase pattern whose phase is already determined, Prioritizing, a step of converting the design pattern into a node, and giving a phase value corresponding to the phase information of the pattern to a node of the pattern having a fixed phase; If the phase information does not exist in both of the nodes of the pair, the nodes of the adjacent pattern pair are connected so as not to form an odd closed loop. (A) When phase information exists only in one of the nodes, a phase value opposite to the one phase information is set as an initial phase, and a phase is determined by following the connection of the node whose phase has not been determined. And determining an initial figure for the connection for which the phase of the adjacent pattern pair has not been determined and obtained by connecting the nodes of the adjacent pattern pair, and determining the phase by following the connection of the nodes from the initial figure.
[0040]
<2> In the step of extracting an adjacent pattern pair, an adjacent pattern pair in which both adjacent patterns have a fixed phase is not extracted.
[0041]
<3> In the step of assigning priorities, the priority of an adjacent pattern pair in which one of adjacent patterns has a fixed phase is set higher than the priority of an adjacent pattern pair having no fixed phase. Features.
[0042]
Further, the present invention employs the following configuration.
[0043]
[1] A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to incident light that transmits through the pattern is formed on a part of these patterns. In a photomask designing apparatus for designing a provided photomask, means for extracting a line segment pair with a line segment belonging to a different pattern adjacent within a distance R for each line segment obtained by dividing a pattern into line segments. Means for obtaining, for each of the extracted line segment pairs, a pattern that intersects with the line segment within a distance S in the vertical direction from an intermediate position of the opposing region in which the line segment opposes; Means for determining the ease of resolution, which is the ease of resolving adjacent patterns, using an experiment or a combination thereof, and means for determining the degree of ease of resolution between adjacent line patterns based on the ease of resolution determined for the line pair. Characterized by comprising and means for arranging the phase shifter to give priority to the phase difference from the hard order resolution against over down pair.
[0044]
[2] A plurality of aperture patterns that transmit incident light are formed in a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to the incident light that transmits through the pattern is formed in a part of these patterns. In a photomask designing apparatus for designing a provided photomask, means for extracting a pair of adjacent patterns within a distance R, decomposing each of the extracted patterns into line segments, and solving Means for obtaining a pattern that intersects with a line segment within a distance S in the vertical direction from an intermediate position of the facing region where image formation is expected to be difficult, and using a process simulation, an experiment, or a combination thereof to obtain the obtained pattern Means for determining the ease of resolution, which is the ease of resolving the matching pattern, and the difficulty of resolution based on the ease of resolution determined for a pair of adjacent patterns within the distance R. Characterized by comprising and means for arranging the phase shifter to give priority to the phase difference from the stomach pair.
[0045]
[3] A plurality of opening patterns for transmitting incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter for giving a phase difference to incident light transmitting through the pattern is formed on a part of these patterns. In a photomask designing apparatus to be provided, a means for extracting a pair of patterns adjacent to each other within a predetermined range with respect to a design pattern having a fixed phase pattern whose phase is already determined, and Means for assigning priorities, means for converting the design pattern into a node, means for giving a phase value corresponding to the phase information of the pattern to a node of a pattern having a fixed phase, and priority of the adjacent pattern pair, If the phase information does not exist in both nodes of the adjacent pattern pair, the nodes of the adjacent pattern pair are connected so as not to form an odd closed loop, and the adjacent pattern is connected. Means for determining the phase by tracing the connection of the node whose phase has not been determined, when the phase information exists in only one of the nodes of the pair, and the phase value opposite to the phase information of the one node is used as the initial phase. Means for determining an initial figure for the connection for which the phase of the adjacent pattern pair has not been determined and obtained by connecting the nodes of the adjacent pattern pair, and tracing the connection of the nodes from the initial figure to determine the phase. And
[0046]
[4] A plurality of aperture patterns that transmit incident light are formed in a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to incident light that transmits through the pattern is formed in a part of these patterns. A computer-readable recording medium storing a program for designing a photomask provided, wherein each line segment obtained by decomposing a pattern into line segments is a line between adjacent line segments belonging to different patterns within a distance R. A step of extracting a segment pair, a step of obtaining a pattern that intersects a line segment within a distance S in a vertical direction from a middle position of an opposing region where the line segment faces each line segment pair, and a process for the obtained pattern. Using a simulation, an experiment, or a combination of these procedures, based on the procedure for determining the resolution easiness, which is the easiness of resolving adjacent patterns, and the resolution easiness determined for a line segment pair, And controls a computer to carry out the steps of placing a phase shifter as a difficult order resolution against contact pattern pairs give priority to the phase difference.
[0047]
[5] A plurality of aperture patterns for transmitting incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter for giving a phase difference to incident light transmitting through the pattern is formed on a part of these patterns. A computer-readable recording medium storing a program for designing a photomask provided therein, the procedure of extracting a pair of adjacent patterns within a distance R, and decomposing each pattern into line segments; Of obtaining a pattern that intersects with a line segment within a distance S in the vertical direction from an intermediate position of an opposing region, which is expected to be most difficult to resolve by using a process simulation, an experiment, or a combination thereof. A procedure for determining the degree of resolution, which is the ease of resolution of adjacent patterns, and a degree of resolution obtained for a pair of adjacent patterns within the distance R. And controls a computer to carry out the steps of placing a phase shifter to give priority to the phase difference a difficult pair resolution.
[0048]
[6] A plurality of aperture patterns that transmit incident light are formed in a part of a light-shielding film that blocks incident light, and a phase shifter that gives a phase difference to incident light that transmits through the pattern is formed in a part of these patterns. A computer-readable recording medium storing a program for designing a photomask provided therein, wherein a predetermined pattern of a pattern adjacent to a design pattern having a fixed-phase pattern having a predetermined phase exists. A procedure for extracting a pair, a procedure for prioritizing the extracted adjacent pattern pairs, and converting the design pattern into a node, and giving a phase value corresponding to the phase information of the pattern to a node of the pattern having a fixed phase. In the order of the procedure and the priority of the adjacent pattern pair, if there is no phase information in both the nodes of the adjacent pattern pair, If the phase information is present only in one node of the adjacent pattern pair so that the phase information is present only in one node of the adjacent pattern pair, the phase value opposite to the phase information of one of the adjacent pattern pairs is set as the initial phase, and the phase is determined. Determining the phase by tracing the connection of the node that does not exist, and determining the initial figure for the undetermined connection obtained by connecting the nodes of the adjacent pattern pair, and tracing the connection of the node from the initial figure And controlling the computer to perform the steps of determining the phase.
[0049]
(Action)
In the above (1), after extracting a combination of adjacent line segments within the threshold value R with respect to the design pattern, the line segment of interest is determined for each line segment pair from the intermediate position of the opposing region of the line segment. Is obtained in a one-dimensional manner, and a process simulation, an experiment, or a combination thereof is performed on the obtained pattern to determine the ease of resolution of the adjacent pattern. . Accordingly, a phase difference can be preferentially given to an adjacent pattern that is difficult to resolve, and a shifter arrangement with higher resolution can be realized.
[0050]
In the above (2), after extracting a combination of patterns adjacent to the design pattern within a threshold value R, an opposing area which is considered to be the most difficult to resolve is selected for each pattern pair, One-dimensionally obtains a pattern that intersects with the line of interest within the distance S in the vertical direction from the intermediate position of, and performs any one of process simulation, experiment, or a combination thereof on the obtained pattern, Determine the degree of ease of resolution. As a result, similarly to (1), a phase difference can be preferentially given to an adjacent pattern that is difficult to resolve, and a shifter arrangement with higher resolution can be realized.
[0051]
In the above (3), the line segment of interest is divided at the intersection of a perpendicular drawn down from the vertex of an adjacent pattern facing the pattern including the line segment of interest to the line segment of interest by looking at a predetermined distance in the vertical direction from the line segment of interest. As a result, a more accurate facing region can be extracted.
[0052]
In the above (4), a pattern that is within a predetermined distance in the vertical direction from the line of interest is viewed, and the line of interest is divided at the intersection of a perpendicular line that is lowered from the vertex of the pattern to the line of interest, thereby providing more accurate opposition. Regions can be extracted.
[0053]
In (5), when extracting a pattern overlapping within the distance S in (1) or (2), a pattern used for a simulation or an experiment is extracted only for a pattern pair to which a line segment of interest belongs. By limiting the pattern in this way, the processing can be speeded up.
[0054]
In the above (6), in the pattern extraction of (1) or (2), a two-dimensional pattern is extracted two-dimensionally in a rectangular area whose one side is twice the distance S, and a two-dimensional process simulation or experiment is performed. Or a combination thereof. Thereby, more strict evaluation of resolution can be performed.
[0055]
In the above (7), as a condition for determining that the arrangement of the divided line segments cannot be approximated by the one-dimensional rule, a direction in which an adjacent line segment within a predetermined distance in the vertical direction from the line of interest is neither perpendicular nor parallel to the line of interest. , A two-dimensional simulation can be performed in the case of a non-one-dimensional pattern arrangement, and a more rigorous evaluation of resolution can be performed.
[0056]
In the above (8), the conditions for determining that the arrangement of the divided line segments cannot be approximated by the one-dimensional rule include a case where the line of interest is arranged in a direction that is neither perpendicular nor parallel when viewed from the mask data design coordinate axis. By doing so, a two-dimensional simulation can be performed in the case of a non-one-dimensional pattern arrangement, and more precise evaluation of the resolution can be performed.
[0057]
In (9), two-dimensional process simulation, experiments, or a combination thereof are performed in (6) to (8), and the degree of ease of resolution is obtained at a position where the pattern environment changes when obtaining the resolution. This is to increase the number of locations for which the degree of resolution is to be checked and perform a more strict evaluation.
[0058]
In the above (10), when the pattern extraction and the resolution easiness of the (1) and (2) are obtained, the two-dimensional method of (4) is used when the length of the facing region is T or less, When it is larger than T, a one-dimensional method is applied, so that strict evaluation can be performed while maintaining high-speed processing.
[0059]
In (11), a so-called learning function using a reference table in (1) and (2) is provided, and a process simulation, an experiment of the same pattern, or a combination thereof is omitted. This also performs high-speed processing.
[0060]
In (12), the process simulation in (1) and (2) is performed by an exposure simulation, a development simulation, an etching simulation, or a combination thereof.
[0061]
In the above (13) to (20), a method of obtaining the degree of resolution is provided, and the calculation of the degree of resolution suitable for the process and the experimental conditions can be easily performed. It is intended to speed up.
[0062]
In the above (21), since two or more combinations of (13) to (20) are used, a method for obtaining the degree of ease of resolution is selected depending on conditions. Further, by applying a method of obtaining a plurality of resolution easiness at one point of interest, a more strict resolution easiness can be obtained.
[0063]
The method (22) provides a method of finding the most difficult-to-resolve opposing area in the pattern pair of interest in (2). The area of a part adjacent to the edge line segment between the pattern pairs within a distance V is provided. Is determined as a portion where resolution is difficult.
[0064]
In the above <1>, an adjacent pattern pair adjacent within a predetermined range is extracted, priorities are assigned to the adjacent pattern pairs, and after replacing the pattern with a node, the phase value of the fixed phase is changed to the node value. The information is stored in the phase information, the nodes of adjacent patterns are connected in the order of the priority of the adjacent pattern pair according to the following rules, and a phase-determined and phase-undetermined group (inversion graph) is created. The conditions are the following three types.
[0065]
1. If there is no phase information at both nodes of the adjacent pattern pair, the nodes of the adjacent pattern pair are connected so as not to form a closed loop. When forming a closed loop, there is no connection. Here, if an odd number of closed loops occurs, inconsistency occurs in phase determination, but even if an even number of closed loops occur, any one can be selected and the phase can be determined. May be.
[0066]
2. If phase information exists only in one of the nodes of the adjacent pattern pair, the phase value opposite to the phase information of the one is set as the initial phase, and the phase is determined by following the connection of the node whose phase has not been determined.
[0067]
3. If the phase information of the nodes of the adjacent pattern pair exists, the phase determination and the operation of connecting the nodes are not performed.
[0068]
However, a method in which the third rule is not applied is also possible. In that case, a similar result is obtained, but it is not efficient.
[0069]
Finally, an initial figure is selected for the inverted graph whose phase has not been determined, and the phase is determined by tracing the inverted graph from the figure.
[0070]
As a result, the phase can be determined by prioritization without changing the fixed phase.
[0071]
In the step <2>, in the step of extracting the adjacent pattern pair of the above <1>, the one having a fixed phase in both of the adjacent pattern pairs is excluded. This eliminates the need for a wasteful operation of processing the adjacent pattern pair for which the phase has been determined at the time of creating the inversion graph, so that the phase can be determined efficiently.
[0072]
In the above <3>, when the prioritization of the above <1> is performed, one of the adjacent pattern pairs has the priority of the adjacent pattern pair to which the fixed phase is given, and the priority of the adjacent pattern pair having no fixed phase. Higher than the degree. Thereby, the phase of the pattern adjacent to the fixed phase can be preferentially inverted.
[0073]
In the above [1] and [4], similarly to the above (1), a phase difference can be preferentially given to an adjacent pattern that is difficult to resolve, and a shifter arrangement with higher resolution can be realized. It becomes.
[0074]
In the above [2] and [5], similarly to the above (2), a phase difference can be preferentially given to an adjacent pattern which is difficult to resolve, and a shifter arrangement with higher resolution can be realized. It becomes possible.
[0075]
In the above [3] and [6], similarly to the above <1>, the phase can be determined by prioritizing without changing the fixed phase.
[0076]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the present invention will be described in detail with reference to the illustrated embodiments.
[0077]
(1st Embodiment)
FIG. 1 is a flowchart showing a method for designing a photomask according to the first embodiment of the present invention, which is an embodiment based on the above (1). According to this flowchart, the layout of FIG. 2 will be described as an example.
[0078]
First, the design pattern in which the patterns A to I shown in FIG. 2 are laid out is decomposed into line segments as shown in FIG. At this time, line segment numbers (1 to 47) are assigned to all the line segments, and information on a pattern to which each line segment belongs is given to the attribute (step 1). Subsequently, the threshold value R for determining whether or not the line segments are adjacent is set to 0.2 μm, and all line segment pairs that are adjacent and belong to different patterns are extracted (step 2). The results are shown in the following (Table 1).
[0079]
[Table 1]

[0080]
Next, for each extracted line segment pair, a nearby pattern is extracted using the distance S, and the degree of resolution is determined by process simulation (steps 3 to 5). In the process simulation, it is possible to select whether to perform an exposure simulation, a simulation up to development, or a simulation up to etching based on the above (12).
[0081]
In the present embodiment, an exposure simulation is applied. Of course, the experiment may be actually performed instead of the simulation, or the experiment and the simulation may be combined.
[0082]
There are several methods for extracting a pattern to be input to the simulator. As a most basic method, as shown in FIG. 4, a pattern that intersects a line segment of interest within a distance S in the vertical direction from a design pattern is one-dimensionally extracted, and a one-dimensional process simulation is performed. That is, a pattern that intersects with a line segment within a distance S in the vertical direction from the intermediate point 13 of the facing region 12 of the line segment pair 11 of interest is obtained, and a one-dimensional process simulation is performed on the obtained pattern.
[0083]
In FIG. 4, reference numeral 14 denotes an edge point to be taken out, reference numeral 15 denotes a pattern one-dimensional arrangement acquisition area, reference numeral 20 denotes a mask, reference numeral 21 denotes a transparent substrate, reference numeral 22 denotes a light shielding portion, reference numeral 23 denotes a transmission portion, and reference numeral 30 denotes a wafer. The light incident on the mask 20 is partially coherent light.
[0084]
Based on the above (5), as shown in FIG. 5, only the pattern of the adjacent pair of interest is one-dimensionally extracted and a process simulation is performed. Alternatively, according to the above (6), as shown in FIG. 6, it is also possible to two-dimensionally extract a pattern overlapping a rectangular area of 2 × S on one side and perform a two-dimensional process simulation. Here, 16 and 17 in the figure indicate the pattern extraction width (2S), and 18 indicates the pattern extraction area.
[0085]
Since the calculation time of the two-dimensional simulation is longer than that of the one-dimensional simulation, it is preferable to reduce the number of places where the two-dimensional simulation is performed as much as possible. Therefore, according to the above (10), a two-dimensional simulation is performed when the length of the facing region is equal to or less than T, and a one-dimensional simulation is applied to the other cases.
[0086]
Subsequently, the resolution is obtained from the exposure simulation result. There are several methods for evaluating the resolution.
[0087]
FIG. 7A shows a method based on the above (13). Exposure simulation is performed on the extracted pattern to determine the light intensity C at the center position of the opposing region and the light intensity A and B at the center position of each pattern to which the line of interest belongs. The light intensity C is subtracted from the smaller value. When the light intensity at the center position between the opposing regions does not match the minimum value of the light intensity, the minimum value of the light intensity may be used instead of the light intensity at the center position. Similarly, when the light intensity at the pattern center position does not match the maximum value of the light intensity, the maximum value may be used. The larger the value of the obtained difference is, the better the resolution is.
[0088]
FIG. 7B shows a method based on the above (14). Exposure simulation is performed on the extracted pattern to determine the light intensity C at the center position of the opposing region and the light intensity A and B at the center position of each pattern to which the line of interest belongs. The light intensity C is subtracted from the average value. The larger the value, the better the resolution.
[0089]
FIG. 7C shows a method based on the above (15). Exposure simulation is performed on the extracted pattern to determine the light intensity C at the center position of the facing region, and the light intensity C is subtracted from the slice level, which is the light intensity value for resolving the resist. The larger the value, the better the resolution. If the light intensity A or the light intensity B at the center position of each pattern to which the line of interest belongs is smaller than the slice level, the light intensity C may be subtracted from the smaller value, or the slice level and the light intensity may be reduced. A case is conceivable in which an average value is calculated for two or three values from the smaller one of A and B, and the light intensity C is subtracted from the average value.
[0090]
FIG. 7D shows a method based on the above (16). Exposure simulation is performed on the extracted pattern, and the inclination angles α1 and α2 of the tangent at the center position between the center position of the opposing region and the center position of the pattern to which the line segment of interest belongs are obtained from the light intensity distribution. And the average value of α1 and α2 is defined as the ease of resolution.
[0091]
FIG. 8 shows a method based on the above (17). For example, several exposure simulations are performed on the extracted patterns while changing the defocus value, and dimensions between the patterns are measured to create an ED-tree. In this case, the ED-tree is at the desired size ± 10%. Then, the FOCUS allowance or DOSE allowance shown in the figure is obtained from the ED-tree, and the obtained value is defined as the ease of resolution. It is assumed that the larger this value is, the easier it is to resolve. Further, the size of the window shown in FIG. 8 can be used as the resolution ease. In this case, it is assumed that the larger the window size is, the easier the resolution is.
[0092]
In the above (18), in consideration of various factors such as the exposure time and the etching, the tolerance is windowed, and the larger the window size is, the easier the resolution is. In the above (19), a window size whose window is set under a plurality of conditions is found to have a common window size, and the larger the size, the easier the resolution is. Further, as shown in the above (21), it is also conceivable to combine the above-described methods of obtaining the degree of resolution.
[0093]
Next, steps 3 to 5 in FIG. 1 will be described in detail. The basic method and the method (10) are used for extracting the pattern, and the method (15) is used as the method for obtaining the resolution. FIG. 9 shows a detailed flow of steps 3 to 5. Further, in this embodiment, in order to speed up the processing, a processing method in which the process simulation of the same pattern is not repeatedly performed using the reference table described in (11) is applied.
[0094]
The detailed method is to first extract a pattern, obtain the degree of resolution by process simulation or experiment, and add it to a table. After that, after extracting the pattern, the table is referred to, and the degree of resolution that matches the pattern information is obtained. If they do not match, the degree of resolution is determined by process simulation as in the first case, and is added to the table.
[0095]
As an example of a table storage method in the case of performing one-dimensionally, as shown in FIG. 10A, an index portion is a pattern edge sequence expressed by a relative position from the center position of the opposing region. The resolution ease at the time is made to correspond. In addition, since the same evaluation result is obtained when the one-dimensional arrangement is reversed left and right, the reverse arrangement is also added. When referring to the table, as shown in FIG. 10B, the degree of resolution that matches the index part is extracted.
[0096]
In addition, as an example of a method of storing data in a table in the case of performing two-dimensionally, as shown in FIG. 11, an extracted pattern is divided into lines, and they are used as a first key in ascending order in the length direction of the facing area and in the vertical direction. Are sorted in ascending order in the parallel direction as the second key, and the arrangement of the line segment information strings is used as an index part of the table to store the obtained resolution easiness. Except for the format of the pattern information, the table storage method and the reference method are the same as those in the one-dimensional case. Also, when mirror inversion in the longitudinal direction of the opposing region is performed with respect to the axis, the same resolution is easily achieved. Therefore, the pattern in that case is also added to the table.
[0097]
Next, steps for extracting a pattern, performing a process simulation, and evaluating the resolution will be described in detail. Table 1 above shows the line segment pairs in FIG. 1 and the lengths of the facing regions.
[0098]
In the present embodiment, the distance T is set to 0.2 μm, and the distance S is set to 0.6 μm (this is preferably specified as a distance within a range that has an optical influence). The exposure conditions were as follows: light source was normally illuminated, λ = 0.248 μm, σ = 0.3, NA = 0.55, defocus value 0.3 μm, and slice level 0.3.
[0099]
After extracting the line segment pair, the extracted line segment pair is subjected to exposure simulation. First, when the line segment pair of interest is 2-15, the opposing area length is 0.2 and is equal to or less than the distance T, so that the rectangular area 2S × 2S = 1 from the opposing area center position as shown in FIG. 2. Two-dimensionally extract overlapping patterns of 2 μm × 1.2 μm. Subsequently, a two-dimensional exposure simulation is performed on the extracted pattern to obtain a light intensity distribution in the vertical direction (line A) from the center of the region of interest corresponding to the line of interest, as shown in FIG. The result is shown in FIG.
[0100]
At this time, the light intensity at the center position of the facing region is 0.091737. Therefore, the value of the ease of resolution is 0.3-0.091737 = 0.08263. Then, the extracted pattern and the ease of resolution are added to the two-dimensional table. Here, as in (20) above, the degree of ease of resolution may be determined such that the lower the light intensity near the center between the patterns, the easier the resolution.
[0101]
Next, when the line segment pair of interest is 3-5, the opposing region length is 0.6 μm. Since this is longer than the distance T, a pattern overlapping within the distance S is one-dimensionally extracted and a one-dimensional exposure simulation is performed as shown in FIG. The result is shown in FIG.
[0102]
The light intensity at the center position of the opposing region is 0.190970, and the degree of resolution is 0.3-0.190970 = 0.10903. Then, the pattern ((−0.3−0.1) (0.1 0.3)) extracted this time and a pattern obtained by inverting the pattern arrangement ((−0.3 0.1) (0. 10.3)) is added to the one-dimensional table in correspondence with the degree of resolution. However, in this case, since the same pattern is obtained even if the pattern is inverted, the inverted pattern is not added. The current one-dimensional table is shown in (Table 2).
[0103]
[Table 2]

[0104]
Next, when the line segment pair of interest is 4-18, the facing region length is 0.5. Since this is longer than the distance T, a pattern overlapping within the distance S is one-dimensionally extracted as shown in FIG. The extracted pattern information is ((−0.3−0.1) (0.10.3)). Then, by referring to the one-dimensional table shown in (Table 2), it is checked whether the same pattern has been simulated. In this case, since ((−0.3−0.1) (0.1 0.3)) is found in the table search unit, the resolution ease 0.10903 is obtained.
[0105]
When the same procedure is performed for all adjacent line segment pairs in accordance with the above procedure, the results shown in (Table 3) are obtained. The strength A and the strength B are also described for reference.
[0106]
[Table 3]

[0107]
(Table 3) is a line segment pair, which is replaced with an adjacent pattern pair as shown in (Table 4) below.
[0108]
[Table 4]

[0109]
When one adjacent pattern pair includes a plurality of adjacent line segment pairs (Table 4, adjacent pattern pairs FG), the adjacent line segment pairs are sorted in order of difficulty in resolution. Next, adjacent pattern pairs are compared from the head of the line segment pair, and the source is sourced in the order of smaller resolution ease value. However, in this case, in the case of comparing FG and GH shown in (Table 3), the resolution easiness of the first adjacent line segment pair is the same, but in FG there is one more element. is there. This gives priority to the FG with the greater number of adjacent line segment pairs. In the case where the number of adjacent line segment pairs and the degree of resolution are the same, it is conceivable to order by factors such as the length of adjacent surfaces, but this is omitted in the present embodiment. The sorting result is shown in the following (Table 5).
[0110]
[Table 5]

[0111]
Subsequently, a phase difference is given preferentially in the order shown in (Table 5) (Step 6). There are various methods for giving a phase difference preferentially from the ordered adjacent pair order. Here, the phase is determined by the method described in the method already proposed by the present inventors (JP-A-8-328237). Were determined. FIG. 15 shows the result of the phase determination. However, in this figure, a shifter for giving a phase difference is attached to one of the pair to which a phase difference is given (step 7).
[0112]
As described above, according to the present embodiment, it is possible to obtain the ease of resolution suitable for exposure conditions by a simple method, and to realize a shifter arrangement with high resolution in a Levenson-type phase shift mask. For this reason, the efficiency of semiconductor design work can be increased, and production costs can be reduced.
[0113]
Note that the following method can also be adopted as a line segment dividing method. FIG. 29 is a diagram showing a line segment dividing method based on the above (3). That is, as a step of dividing a line segment, an intersection point of a perpendicular line drawn from the vertex of an adjacent pattern facing the pattern including the line segment of interest to the line segment of interest, within a certain distance in the vertical direction from the line segment of interest or The target line segment is divided such that the length of the line segment after division is not shorter than the designated length using the vicinity as a guide. Specifically, division of a line segment on the graphic B will be described. That is, the line segment is divided at a point where the arrangement environment of the line segments of the adjacent patterns A and C facing each other within the distance R in the vertical direction from B changes. By adopting such a line segment dividing method, it is possible to flexibly cope with the arrangement environment.
[0114]
FIG. 30 is a diagram illustrating a line segment dividing method based on the above (4). That is, as a step of dividing the line segment, a pattern that is within a specific distance R in the vertical direction from the line of interest is looked at, and the intersection of a perpendicular line lowered from the vertex of the pattern to the line of interest or its vicinity is used as a guide, The target line segment is divided so that the length of the line segment is not shorter than the designated length. Specifically, the line segment is divided not only at the opposite side but also at a point where the pattern arrangement environment changes within a distance R in the vertical direction from B. By adopting such a line segment dividing method, it is possible to flexibly cope with a complicated arrangement environment.
[0115]
Further, as a condition for determining that the arrangement of the dividing line segments cannot be approximated by the one-dimensional rule, the following method can be adopted. FIG. 31 is a diagram showing a figure for obtaining the degree of ease of resolution based on (7). In the pattern shown in FIG. 31A, it is determined based on the above (7) that the line segment <2> cannot be approximated one-dimensionally. At this time, as shown in FIG. 31 (b), a rectangular area extending over distances S1, S2, S3, and S4 up and down from both left and right sides and both ends of the line segment <2> is extracted as an image calculation area. Then, as shown in FIG. 1C, this rectangular area is subjected to a two-dimensional process simulation.
[0116]
FIG. 32 is a diagram showing a graphic for obtaining the degree of ease of resolution based on the above (8). Of the target line segments <1> to <8> in the layout shown in FIG. 32A, the line segments arranged in a direction that is neither perpendicular nor parallel to the mask coordinate axes are <5> and <6>. Here, the line segment <6> will be particularly described. As shown in FIG. 32B, a pattern including both ends of the line segment <6> and having a range of the distance S is extracted from the layout of FIG. A two-dimensional process simulation is performed on this area to determine the degree of resolution. The range in which the process simulation is performed may be a range within a distance S from the rectangle including the target line segment as shown in FIG.
[0117]
Note that each step in the flowchart of FIG. 1 is replaced with a functional block for performing each step, and a photomask designing apparatus can be configured by connecting these functional blocks. In practice, this apparatus is realized by a computer which reads a program recorded on a recording medium such as a magnetic disk and whose operation is controlled by the program.
[0118]
(Second embodiment)
Next, an embodiment based on the above (2) will be described. FIG. 16 shows the processing flow.
[0119]
This embodiment is basically the same as the first embodiment, but differs from the first embodiment in that, in steps 1 to 3, only the lines which are the least resolvable among the patterns are extracted. is there. In addition, as a method of determining the line segment pair that is most difficult to resolve between patterns, as shown in the above (22), an adjacent line segment pair whose region adjacent within the distance V is the longest is most difficult to resolve. I do.
[0120]
In the pattern shown in FIG. 2, only the adjacent pattern pair FG is adjacent at two edges of line segment pairs 32-36 and 33-39. Among these line segment pairs, the line segment pair 32-36 having the longest adjacent edge at the distance V, V = 0.2 μm is the target of obtaining the degree of ease of resolution. In an actual pattern, it is natural that there are a plurality of adjacent edges between adjacent pairs. Applying this method leads to high-speed processing. Based on the present embodiment, adjacent line segment pairs (adjacent pattern pairs) extracted for the pattern shown in FIG. 2 are shown in (Table 6) below.
[0121]
[Table 6]

[0122]
The steps for performing the sorting and phase determination are the same as those in the first embodiment, and the results are also the same (the table is omitted). Therefore, the shifter arrangement result is the same as that shown in FIG.
[0123]
Note that each step in the flowchart of FIG. 16 is replaced with a functional block for performing each step, and a photomask designing apparatus can be configured by connecting these functional blocks. In practice, this apparatus is realized by a computer which reads a program recorded on a recording medium such as a magnetic disk and whose operation is controlled by the program.
[0124]
(Third embodiment)
FIG. 17 is a flowchart showing a method for designing a photomask according to the third embodiment of the present invention, which is an embodiment based on the above <1>. First, the design data of FIG. 18 is input. A to T in the figure correspond to chromium openings, which are hereinafter referred to as patterns. C, F, I, and K are given fixed phases.
[0125]
First, a pair of adjacent patterns within a distance of 0.2 μm (threshold value) is extracted, and the length of an adjacent surface between adjacent pattern pairs (hereinafter, referred to as an adjacent surface length) as shown in FIG. Ask. The results are shown in the following (Table 7).
[0126]
[Table 7]

[0127]
Then, sorting is performed in descending order of the adjacent surface length. The results are shown in Table 8 below.
[0128]
[Table 8]

[0129]
Here, sorting is performed in descending order of the length of the adjacent surface. However, sorting may be performed in the order of low resolution like the first embodiment, or another weighting condition may be used. .
[0130]
Next, as shown in FIG. 20 (a), a fixed phase is given as phase information to nodes C, F, K, and I to which a phase is given in advance as a node, and the following adjacent pattern pairs are sorted in the following order. The rule is used to determine the phase and create an inverted graph whose phase is not determined.
[0131]
1. If there is no phase information at each node, the nodes are connected so as not to form a closed loop.
[0132]
2. If the phase information exists in only one of the nodes, the phase value opposite to the phase information is used as the initial phase, and the phase is determined for the connection of the other node.
[0133]
3. If phase information exists for each other, neither phase determination nor node connection is performed.
[0134]
Hereinafter, nodes are actually connected for each adjacent pair. First, in the adjacent pair MQ, no phase information is given to both nodes, and no loop occurs when the nodes are connected. Therefore, as shown in FIG. 20B, the pairs are connected and the group number is changed. give. Here, the reason why the group number is given is to determine whether or not a loop occurs when trying to connect nodes. In the method of determining a loop, a loop is formed if the group numbers to which the nodes of the adjacent pattern pair belong are the same, and a loop is not formed if both groups are different or one of them is not assigned to a group.
[0135]
Next, in IJ, since the phase information is given only to the node I, the phase is determined for the group to which the other J is connected. In this case, since there is no group to which J is connected, J is given a phase opposite to the phase of I as shown in FIG.
[0136]
Subsequently, in EJ, since only J has phase information, a phase is given to E and a group connected to E. Since there is no node connected to E, the opposite phase of J is given only to E as shown in FIG.
[0137]
In CE, since both have phase information, the node patterns are not connected according to rule 3 as shown in FIG. Of course, the results obtained do not change and may be connected. As in the case of CE, FI also has phase information in both, and therefore is not connected according to rule 3 as shown in FIG.
[0138]
Since both DHs do not have phase information and do not form a loop when they are connected, DHs are connected as shown in FIG.
[0139]
In FH, only F is given phase information. Therefore, the phase is determined for H and the group connected to it. In this case, since there is a group 2 connected to H, an opposite phase (initial phase) of F is given to the phase information of H and an opposite phase of H is given to D connected to H as shown in FIG. In this method, the connection of the group for which the phase has been determined is released. Since this does not change the obtained result, it does not have to be canceled, but by doing so, the memory can be deleted in performing the computer processing.
[0140]
Similarly, when all adjacent pattern pairs are processed, a graph (inverted graph) shown in FIG. 23 (i) is finally obtained. Then, for groups 1 and 3 whose phases have not yet been determined, the initial figures (nodes) are L and M, respectively, and the phase is determined. The result is shown in FIG. 23 (j), and the corresponding design pattern is shown in FIG. According to the above method, it is possible to maintain a fixed phase and determine a phase in consideration of priority.
[0141]
Note that each step in the flowchart in FIG. 17 is replaced with a functional block that performs each step, and a photomask designing apparatus can be configured by connecting these functional blocks. In practice, this apparatus is realized by a computer which reads a program recorded on a recording medium such as a magnetic disk and whose operation is controlled by the program.
[0142]
(Fourth embodiment)
FIG. 25 is a flowchart showing a photomask designing method according to the fourth embodiment of the present invention, which is an embodiment based on <2>. Similar to the third embodiment, the layout data of FIG. 18 will be described as an example. The fixed phase is also given to C, F, I, and K as in the third embodiment.
[0143]
First, pattern pairs adjacent within a distance of 0.2 μm are extracted. At this time, those having a fixed phase in both adjacent pairs are not extracted. Then, an adjacent surface length of each of the extracted adjacent pairs is obtained. The results are shown in Table 9 below.
[0144]
[Table 9]

[0145]
Here, in the third embodiment, the number of adjacent pattern pairs is 29, but in the present embodiment, four adjacent pattern pairs having both fixed phases are reduced to 25. Then, sorting is performed so that the lengths of the adjacent surfaces are in descending order. The results are shown in the following (Table 10).
[0146]
[Table 10]

[0147]
Subsequently, according to the same rule as in the third embodiment, an inverted graph is created in the sorted order, and the phase is determined. The inverted graph, the phase determination result, and the shifter arrangement result are exactly the same as those in FIGS. 23 and 24 of the third embodiment.
[0148]
In the method of the present embodiment, the number of adjacent pattern pairs to be extracted is reduced, so that the operation of determining the length of the adjacent surface and the data to be inverted for creating the inverse graph are reduced by that amount, and the processing speed can be increased.
[0149]
(Fifth embodiment)
FIG. 26 is a flowchart showing a method of designing a photomask according to the fifth embodiment of the present invention, which is an embodiment based on the above <3>. Similar to the third and fourth embodiments, the layout of FIG. 18 will be described as an example. Again, C, F, I, and K are given fixed phases.
[0150]
First, pattern pairs adjacent within a distance of 0.2 μm are extracted. As in the third embodiment, all pattern pairs may be extracted, but in the present embodiment, adjacent pattern pairs having a fixed phase are not extracted based on <2>. Then, an adjacent surface length is obtained for each extracted adjacent pair. The result is shown in the following (Table 11).
[0151]
[Table 11]

[0152]
Subsequently, sorting is performed in such a manner that the first sort key has a fixed phase on one side of the pair, and the second sort key has a longer adjacent surface length. The results are shown in Table 12 below.
[0153]
[Table 12]

[0154]
Subsequently, when an inversion graph is created in the order of sorting according to the same rule as in the third embodiment, the result shown in FIG. 27A is obtained, and when the phase is determined, the result is shown in FIG. 27B. The shifter arrangement result of the corresponding design pattern is as shown in FIG.
[0155]
When comparing the shifter arrangement result of the present embodiment with the arrangement results of the third and fourth embodiments, there is not much difference (in the phase determination where the fixed phase exists in the actual pattern, the difference becomes large). ), The phase of FIG. A is different. This is because the pattern adjacent to the fixed phase is given a phase difference with special priority. Therefore, according to the method of the present embodiment, the priority of determining the phase of the pattern pair adjacent to the fixed phase can be increased, and the resolution of the fixed phase end can be improved.
[0156]
In the third to fifth embodiments described above, the threshold value for obtaining an adjacent pair is 0.2 μm, but this value is not limited at all. Usually, the value is set to a value reflecting the characteristic of the pattern of the target device. In these embodiments, a closed loop is not generated when connecting nodes. This is because an odd number of closed loops causes inconsistency in phase determination. Even if an even number of closed loops occurs, any one of them can be selected and the phase can be determined, so that the occurrence of an even number of closed loops may be allowed. That is, the nodes may be connected so that an odd closed loop does not occur.
[0157]
The present invention is not limited to the above-described embodiments, and can be implemented with various modifications without departing from the scope of the invention.
[0158]
In addition, the method described in each of the above-described embodiments includes, as a program that can be executed by a computer, a recording medium such as a magnetic disk (floppy disk, hard disk, etc.), an optical disk (CD-ROM, DVD, etc.), and a semiconductor memory. And can be applied to various devices, or transmitted by a communication medium and applied to various devices. A computer that realizes the present apparatus reads a program recorded on a recording medium, and executes the above-described processing by controlling the operation of the program.
[0159]
【The invention's effect】
As described above, according to the present invention, after extracting a combination of adjacent line segments (or patterns) within a threshold value R with respect to a design pattern, attention is paid to each line segment pair (pattern pair). A pattern is obtained, and a process simulation, an experiment, or a combination thereof is performed on the obtained pattern, and the ease of resolution of an adjacent pattern is obtained. It can be determined in a simple way. Therefore, it is possible to give a phase difference preferentially from an adjacent pattern that is difficult to resolve, to obtain a shifter arrangement result with higher resolution, to make semiconductor design work more efficient and to reduce production cost. Becomes possible.
[0160]
Further, according to the present invention, in the shifter arrangement of a design pattern having a fixed phase, it is possible to determine the phase while maintaining the priority without changing the fixed phase. For example, it is desirable to manually determine the phase in a memory cell portion having a periodicity whose resolution is severe, such as in the design of a Levenson type phase shift mask for a DRAM, and the phase of the remaining peripheral patterns is determined using the method of the present invention. With the automatic determination, the shifter can be arranged in the peripheral pattern while retaining the phase information manually arranged in the memory cell section as it is. In addition, it is assumed that a pattern given a fixed phase often has particularly strict dimensional accuracy or a high required resolution. Can be improved. As described above, a high-quality Levenson-type photomask can be efficiently designed by combining the positions of manual placement and automatic placement.
[Brief description of the drawings]
FIG. 1 is a view showing a processing flow of a photomask designing method according to a first embodiment.
FIG. 2 is a view showing pattern data used in the first embodiment.
FIG. 3 is a diagram in which the pattern data shown in FIG. 2 is decomposed into line segments.
FIG. 4 is a diagram showing an example of a pattern extraction method according to the first embodiment.
FIG. 5 is a diagram showing another example of the pattern extraction method according to the first embodiment.
FIG. 6 is a view showing still another example of the pattern extraction method according to the first embodiment.
FIG. 7 is a view showing a method for obtaining the degree of ease of resolution in the first embodiment.
FIG. 8 is a view showing another method for obtaining the degree of ease of resolution in the first embodiment.
FIG. 9 is a diagram showing a detailed processing flow from step 3 to step 5 in FIG. 1;
FIG. 10 is a diagram showing a method for adding and referencing a one-dimensional table.
FIG. 11 is a diagram showing a method of creating a two-dimensional table search unit.
FIG. 12 is a diagram showing pattern extraction and simulation in an adjacent line segment pair 2-15.
FIG. 13 is a diagram showing pattern extraction and simulation in the adjacent line segment pair 3-5.
FIG. 14 is a view showing pattern extraction in an adjacent line segment pair 3-18.
FIG. 15 is a diagram showing a phase shifter arrangement result.
FIG. 16 is a view showing a processing flow of a photomask designing method according to the second embodiment;
FIG. 17 is a view showing a processing flow of a photomask designing method according to the third embodiment;
FIG. 18 is a diagram showing input design data and a fixed phase according to the third embodiment.
FIG. 19 is a view for explaining adjacent surface lengths.
FIG. 20 is a diagram showing node and phase information in an initial stage, and a graph for the adjacent pattern pair of interest MQ, IJ.
FIG. 21 is a diagram showing a graph at the time of a focused adjacent pattern pair EJ, CE, and FI.
FIG. 22 is a view showing a graph for a focused adjacent pattern pair DH and FH.
FIG. 23 is a diagram illustrating phase information, an inverted graph, and a phase determination result for the inverted graph according to the third embodiment.
FIG. 24 is a diagram showing a phase determination result as viewed from a design pattern in the third embodiment.
FIG. 25 is a view showing a processing flow of a photomask designing method according to the fourth embodiment;
FIG. 26 is a view showing a processing flow of a photomask designing method according to the fifth embodiment;
FIG. 27 is a diagram illustrating phase information, an inverted graph, and a phase determination result for the inverted graph according to the fifth embodiment.
FIG. 28 is a diagram showing a phase determination result as viewed from a design pattern according to the fifth embodiment.
FIG. 29 is a diagram showing an example of a line segment dividing method.
FIG. 30 is a diagram showing another example of a line segment dividing method.
FIG. 31 is a diagram illustrating an example of a figure for which the degree of ease of resolution is obtained.
FIG. 32 is a diagram showing another example of a figure for which the degree of ease of resolution is obtained.
[Explanation of symbols]
11 ... line segment pair of interest
12 ... facing area
13 ... Intermediate point
14 ... Edge point
15 Pattern one-dimensional arrangement acquisition area
16, 17 ... pattern extraction width
18… Pattern extraction area
20 ... Mask
21 ... Transparent substrate
22 ... Shading part
23 ... Transmissive part
30 ... wafer

Claims (24)

A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that provides a phase difference to incident light that transmits through the pattern is provided on a part of these patterns. In the method of designing a mask,
For each line segment obtained by decomposing the pattern into line segments, a line segment pair with a line segment belonging to a different pattern adjacent within a distance R is extracted, and an intermediate position of an opposing region where the line segment is opposed for each line segment pair A pattern that intersects the stranded line within a distance S in the vertical direction is obtained, and the obtained pattern is subjected to a process simulation, an experiment, or a combination thereof to provide a resolution easiness that is the easiness of resolving adjacent patterns. ,
Based on the resolution easiness obtained for the line segment pair, a phase shifter is arranged so as to preferentially give a phase difference to a pair of adjacent patterns in the order of difficulty in resolution. Design method. A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that provides a phase difference to incident light that transmits through the pattern is provided on a part of these patterns. In the method of designing a mask,
A pair of adjacent patterns within a distance R is extracted, and after decomposing each pattern into line segments, a pair of adjacent line segments which is expected to be most difficult to resolve between patterns is extracted and extracted for each adjacent pattern pair. For a pair of adjacent line segments, a process simulation, an experiment, or a combination thereof is used to determine a resolution ease, which is the ease of resolution of an adjacent pattern,
A method for designing a photomask, comprising: arranging a phase shifter so as to give a phase difference preferentially to a pair having difficulty in resolution based on the ease of resolution determined for a pair of patterns adjacent within a distance R. . Upon decomposing the pattern into line segments, look at a predetermined distance in the vertical direction from the line segment of interest, and at or near the intersection of perpendiculars drawn down to the line segment of interest from the vertices of adjacent patterns facing the pattern containing the line segment of interest. 3. The method according to claim 1, wherein the line segment of interest is divided such that the length of the line segment after division is not shorter than the designated length. When decomposing the pattern into line segments, look at patterns that are within a predetermined distance in the vertical direction from the line segment of interest, and use the intersection point of a perpendicular line lowered from the vertex of the pattern to the line segment of interest or its vicinity as a guide to the segment after division. 3. The method for designing a photomask according to claim 1, wherein the line segment of interest is divided so that the length of the line segment does not become shorter than the designated length. 3. The method according to claim 1, wherein when extracting a pattern that intersects with a line segment within a distance S in a vertical direction from an intermediate position of the facing region, only a pattern pair to which the line segment of interest belongs is extracted as a target. Photomask design method. A pattern overlapping a 2S × 2S rectangular area centered on the middle position of the facing area is extracted two-dimensionally, and the extracted pattern is subjected to two-dimensional process simulation, experiment, or a combination thereof to determine the degree of resolution. 3. The method for designing a photomask according to claim 1, wherein the photomask is determined. When an adjacent line segment within a predetermined distance in the vertical direction from the line of interest is arranged in a direction that is neither perpendicular nor parallel to the line of interest, a pattern including the line of interest is extracted two-dimensionally, and the extracted pattern is extracted. 3. The method for designing a photomask according to claim 1, wherein the degree of ease of resolution is obtained using two-dimensional process simulation, experiment, or a combination thereof. When the line of interest is arranged in a direction that is neither perpendicular nor parallel to the mask data design coordinate axis, a pattern including the line of interest is extracted two-dimensionally, and the extracted pattern is subjected to two-dimensional process simulation, experiment, 3. The method of designing a photomask according to claim 1, wherein the degree of resolution is determined by using a combination of these. After the two-dimensional process simulation is performed, in the direction parallel to the line segment of interest at the intermediate position of the facing area, the resolution ease is obtained on both sides of the boundary where the pattern arrangement environment changes in the vertical direction. A method for designing a photomask according to claim 6. In the method of designing a photomask according to claim 1 or 2, when the length of a region opposed to the line segment pair of interest is a predetermined distance T or less, the degree of resolution is determined by the method according to claim 6. A photomask design method characterized by the following. Each time a process simulation is performed, the pattern information used at that time and the value of the ease of resolution obtained by the process simulation, experiment, or a combination thereof are stored in a table, and each time a pattern is extracted. Referring to the table, if the pattern matches, the resolution ease value stored in the table is obtained. If the pattern does not match, the process simulation, experiment, or a combination thereof is performed to obtain the resolution ease. The method for designing a photomask according to claim 1 or 2, wherein: As a method of obtaining the degree of resolution, a value obtained by subtracting the light intensity value at the intermediate position of the opposing region of the line segment pair of interest from the smaller value of the light intensity value at the intermediate position of each pattern portion is obtained. 3. The method for designing a photomask according to claim 1, wherein the larger the difference is, the easier the resolution is. As a method of obtaining the ease of resolution, from the average value of the light intensity value at the intermediate position of each pattern portion, find a value obtained by subtracting the light intensity value at the intermediate position of the opposed region of the line pair of interest, 3. The method for designing a photomask according to claim 1, wherein the larger the difference is, the easier the resolution is determined. As a method of obtaining the degree of resolution, a reference light intensity is set as a slice level, and a value obtained by subtracting a light intensity value at an intermediate position between opposed regions of the line pair of interest from the slice level value is obtained. 3. The method for designing a photomask according to claim 1, wherein the larger the difference is, the easier the resolution is determined. As a method of calculating the degree of resolution in the one-dimensional intensity distribution, the larger the inclination angle of the tangent line of the light intensity distribution at the intermediate position between the intermediate position of each pattern portion and the center position of the opposing area or at the pattern edge position. 3. The method for designing a photomask according to claim 1, wherein it is determined that resolution is easy. As a method of obtaining the degree of ease of resolution, the dependence of the combination of focus and exposure amount at the target position and the dimensional difference from the desired size is obtained using process simulation, experiment, or a combination of these, and the exposure latitude, The window size composed of the exposure latitude and the defocus latitude is examined in consideration of the focus latitude or both, and it is determined that the larger the latitude or the window size is, the easier the resolution is. The method for designing a photomask according to claim 1. 3. The photomask according to claim 1, wherein the degree of resolution is determined by determining that the lower the light intensity at an intermediate position between the opposing regions of the line segment pair of interest, the easier the resolution is. Design method. The step of arranging the phase shifter preferentially in the order of resolution difficulty for the pair of adjacent patterns,
Turning the design pattern into a node, and giving a node of the pattern having a fixed phase a phase value corresponding to the phase information of the pattern;
Based on the degree of resolution of the adjacent pattern pair, if there is no phase information at both nodes of the adjacent pattern pair, connect the nodes of the adjacent pattern pair so as not to form an odd closed loop, and connect one of the adjacent pattern pairs. When the phase information is present only in the node of, the phase value opposite to the one phase information as the initial phase, the step of determining the phase by following the connection of the node whose phase has not been determined,
2. A step of determining an initial figure for the connection for which the phase of the adjacent pattern pair has not been determined and obtained by connecting the nodes of the adjacent pattern pair, and determining the phase by following the connection of the nodes from the initial figure. Or the method of designing a photomask according to 2. A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that provides a phase difference to incident light that transmits through the pattern is provided on a part of these patterns. In a photomask designing apparatus for designing a mask,
Means for extracting, for each line segment obtained by decomposing the pattern into line segments, a line segment pair with a line segment belonging to a different pattern adjacent within a distance R, the line segment being opposed to each of the extracted line segment pairs Means for obtaining a pattern that intersects with a line segment within a distance S in the vertical direction from the intermediate position of the opposing region, and resolution of an adjacent pattern by using a process simulation, an experiment, or a combination thereof for the obtained pattern. Means for determining the degree of resolvability which is the ease of resolving, and, based on the resolvability obtained for the line segment pair, a phase difference is preferentially given to pairs of adjacent patterns in the order of difficulty in resolving. Means for arranging a phase shifter as described above. A plurality of aperture patterns that transmit incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter that provides a phase difference to incident light that transmits through the pattern is provided on a part of these patterns. In a photomask designing apparatus for designing a mask,
Means for extracting a pair of adjacent patterns within a distance R, and decomposing each of the extracted patterns into line segments, and for each adjacent pattern pair, an adjacent line segment pair which is expected to be least likely to be resolved between patterns Means for extracting the adjacent line segment pair, using a process simulation, an experiment, or a combination thereof to obtain a resolution ease, which is the ease of resolution of an adjacent pattern, Means for arranging a phase shifter so as to give a phase difference preferentially from a pair that is difficult to resolve based on the degree of resolution obtained for a pair of adjacent patterns within R. Photomask design equipment. Means for arranging the phase shifter preferentially in the order of resolution difficulty for the pair of adjacent patterns,
Means for converting the design pattern into a node, a means for giving a phase value corresponding to the phase information of the pattern to a node of the pattern having a fixed phase, and a node of the adjacent pattern pair based on the resolution ease of the adjacent pattern pair. When phase information does not exist in both, the nodes of the adjacent pattern pair are connected so as not to form an odd closed loop, and when phase information exists only in one node of the adjacent pattern pair, the phase information of the one The reverse phase value as the initial phase, means for determining the phase by following the connection of the node whose phase has not been determined, and for the connection for which the phase has not been determined obtained by connecting the nodes of the adjacent pattern pair 21. The photomask according to claim 19, further comprising: means for determining an initial figure, tracing a connection of nodes from the initial figure, and determining a phase. The design of equipment. A plurality of aperture patterns for transmitting incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter for providing a phase difference to the incident light transmitting through the pattern is provided on a part of these patterns. A recording medium storing a program for designing a mask,
A procedure for extracting a line segment pair with a line segment belonging to a different pattern adjacent within a distance R for each line segment obtained by decomposing a pattern into line segments, and a procedure for extracting an opposing region in which the line segment faces each line segment pair. A procedure for obtaining a pattern that intersects a line segment within a distance S in the vertical direction from the intermediate position, and the ease of resolving an adjacent pattern by using a process simulation, an experiment, or a combination thereof for the obtained pattern. Based on the procedure for determining the degree of resolution and the degree of resolution obtained for the line segment pairs, a phase shifter is arranged to give a phase difference preferentially to adjacent pairs of patterns in the order of resolution difficulty. And a computer-readable recording medium storing a program for controlling a computer to perform the following steps. A plurality of aperture patterns for transmitting incident light are formed on a part of a light-shielding film that blocks incident light, and a phase shifter for providing a phase difference to the incident light transmitting through the pattern is provided on a part of these patterns. A recording medium storing a program for designing a mask,
A procedure of extracting pairs of adjacent patterns within the distance R, and a procedure of decomposing each pattern into line segments, and extracting a pair of adjacent line segments expected to be most difficult to resolve among the patterns for each adjacent pattern pair And a procedure for obtaining the resolution easiness, which is the easiness of resolution of the adjacent pattern, using a process simulation, an experiment, or a combination thereof for the extracted adjacent line segment pairs. Based on the degree of resolution obtained for the pattern pair, a program for controlling the computer to perform the procedure of arranging the phase shifter so as to give a phase difference preferentially from the difficult-to-resolve pair is stored. Computer readable recording medium. The procedure for arranging the phase shifter so as to give a phase difference preferentially to the pair of adjacent patterns in the order of resolution difficulty is as follows:
A procedure for converting a design pattern into a node and giving a phase value corresponding to the phase information of the pattern to a node of the pattern having a fixed phase, and both the nodes of the adjacent pattern pair based on the resolution ease of the adjacent pattern pair If there is no phase information in the adjacent pattern pair, the nodes of the adjacent pattern pair are connected so as not to form an odd closed loop. The phase value of the adjacent pattern pair is determined as the initial phase, the phase is determined by tracing the connection of the node whose phase has not been determined. 24. The recording medium according to claim 22, further comprising a step of determining a figure, tracing a connection of nodes from the initial figure, and determining a phase.

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