JP2004140311A - Exposure method and aligner - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an exposure method and an aligner, capable of correcting the influence due to fogging exposure, in addition to the influence of proximity effect with high precision. <P>SOLUTION: A sample resist is exposed to light by applying a command signal to an exposure means from a control means, so that the exposure amount due to an exposure beam from the exposure means will be a corrected exposure amount computed by an computing means. With respect to the positions of the sample, a fogging exposure energy component and a back-scattering exposure energy component are computed, including the influence from the peripheral part of respective positions by using provisional exposure amounts, having different values according to these respective positions. Based on these fogging exposure energy component and back scattering exposure energy component, corrected exposure amounts for respective positions are computed. Final corrected exposure amounts with respect to the positions are computed by iterative computation, using the corrected exposure amounts for respective positions as the provisional exposure amounts. <P>COPYRIGHT: (C)2004,JPO

Description

【００３２】
ここで、Ｅ_ｆ（ｘ，ｙ）は、電子線のレジスト膜２３０中での前方散乱によるエネルギー分布を表わす前方散乱関数であり、Ｅ_ｂ（ｘ，ｙ）は、遮光膜２２０からの電子線の反射によるエネルギー分布を表わす後方散乱関数であり、ともに正規化されている場合、記号ηは後方散乱係数として前方散乱と後方散乱の比を表わす。Ｆｏｇ（ｘ，ｙ）は、かぶり露光によるエネルギー分布を表わすかぶり露光関数である。
関数Ｅ_ｆ（ｘ，ｙ），Ｅ_ｂ（ｘ，ｙ），Ｆｏｇ（ｘ，ｙ）の具体的な形は、ブランクス２００の種類や描画手法に応じて種々提案されており、Ｅｆ（ｘ，ｙ）、Ｅｂ（ｘ，ｙ）には主としてガウス分布関数が用いられているが、Ｆｏｇ（ｘ，ｙ）については任意作成関数が使用されることが多い。
【００３３】
電子線の加速電圧を高くすると前方散乱は小さくなり、後方散乱は大きくなる。後方散乱の及ぶ範囲は、レジストの種類等の条件にもよるが、一例として、加速電圧が５０ｋＶのときには電子線の照射中心位置からの後方散乱半径Ｒ_Ｂの大きさが２５μｍ程度の円内である。
一方、かぶり露光の及ぶ範囲は、一例として、加速電圧５０ｋＶの場合、照射中心位置から半径Ｒ_Ａの大きさが５０ｍｍ程度の円内であり、後方散乱の及ぶ範囲よりも大幅に広い。
【００３４】
単位露光量の電子線入射に対する感光現象がレジスト膜２３０の面内で不変に再現され、感光現象の重ね合わせが成り立つとする。このとき、露光によりパターンを形成する描画領域を、露光量分布Ｄ（ｘ，ｙ）で描画した場合に、任意座標（ｘ，ｙ）におけるレジスト膜２３０に蓄積されるエネルギーを表わすエネルギー分布Ｅ（ｘ，ｙ）は、畳み込み積分を用いて下記式で表わすことができる。
【００３５】
【数１２】

【００３６】
式（１２）における積分の領域は、描画領域である。
パターンの太りや細りはパターンエッジ地点において顕著である。従って、パターンエッジ地点において蓄積エネルギーＥ（ｘ，ｙ）がレジスト感度Ｅｔｈと精度良く一致するような露光量分布Ｄ（ｘ，ｙ）の算出が望まれる。
【００３７】
露光量分布Ｄ（ｘ，ｙ）を算出する場合、本第１実施形態においては、まず、描画領域全体を、かぶり露光半径よりも十分に小さい第１の領域に分割する。第１の領域Ｃｌ（ｘｌ，ｙｌ）の面積はＳｌとするが、一例としては１ｍｍ□程度である。以後、第１の領域は、ラージセルと呼称する。なお、以後ではこのような矩形を単位として計算を行なうため、たとえば記号Ｃｌの（　）内の記号ｘｌ，ｙｌは、座標ではなく各ラージセルの番号を表わすものとする。
【００３８】
次に、各ラージセルＣｌ（ｘｌ，ｙｌ）に対する、かぶり露光によるエネルギーの蓄積の寄与を表わすかぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）を求める。あるラージセルへのかぶり露光エネルギーを、かぶり露光の及ぶ範囲内にあるパターン面積率を畳み込むことで近似した場合、かぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）は、下記式で表わすことができる。
【００３９】
【数１３】

【００４０】
式（３）においては、計算の単位が各ラージセルＣｌ（ｘｌ，ｙｌ）であるため、畳み込みは積分ではなく、記号Σを用いた和分により計算している。式（３）における和分の範囲は、あるラージセルＣｌ（ｘｌ，ｙｌ）を中心とした、かぶり露光が及ぶ範囲であるかぶり露光範囲ＦＧである。また、記号ｐ，ｑは、ラージセルを対象とした計算に用いる変数である。
これ以降でも同様に、矩形の領域を単位とした計算においては、積分ではなく和分を用いる。
なお、式（１３）における記号Ｐｌ（ｘｌ，ｙｌ）は、（ｘｌ，ｙｌ）という番号のラージセルにおけるパターン面積率である。
【００４１】
次に、描画領域全面を、ラージセルおよび図７に示す後方散乱半径Ｒ_Ｂよりも十分に小さい第２の領域に分割する。第２の領域Ｃｓ（ｘｓ，ｙｓ）の面積はＳｓとするが、たとえば１μｍ□程度である。以後、第２の領域はスモールセルと呼称する。スモールセルを表わす記号Ｃｓの（　）内の記号ｘｓ，ｙｓも、座標ではなく各スモールセルの番号を表わす。
このスモールセルＣｓ（ｘｓ，ｙｓ）ごとに、露光量分布Ｄ（ｘ，ｙ）に対する後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）を求める。
後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）は、（ｘｓ，ｙｓ）という番号のスモールセルにおけるパターン面積率Ｐｓ（ｘｓ，ｙｓ）を用いて、下記式で与えられる。
【００４２】
【数１４】

【００４３】
式（１４）も、対象とするスモールセルＣｓ（ｘｓ，ｙｓ）の周辺部のスモールセルでのショットによる後方散乱の影響も考慮したものであり、畳み込みは、スモールセルＣｓ（ｘｓ，ｙｓ）を中心とした、後方散乱が及ぶ範囲である後方散乱範囲ＢＳにおいて計算している。記号ｒ，ｓは、スモールセルを対象とした計算に用いる変数である。
【００４４】
前述のように、試料に対する露光量は、後方散乱の影響やかぶり露光の影響を考慮して補正する必要がある。
本実施形態においては、かぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）および後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）を用いて、補正露光量をスモールセルごとに算出する。この場合に、各スモールセルＣｓ（ｘｓ，ｙｓ）に対するかぶり露光エネルギー成分としては、そのスモールセルＣｓ（ｘｓ，ｙｓ）が含まれるラージセルＣｌ（ｘｌ，ｙｌ）に対するかぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）を用いるものとする。
第１実施形態における補正露光量Ｄ_{ｃｏｎｖ．}（ｘｓ，ｙｓ）は、式（１３）、式（１４）を用いて、以下のように算出することができる。
【００４５】
【数１５】

【００４６】
ここで、記号Ｄ_０は、予め規定してある一定の設定露光量である。また、式（１５）におけるＣｓ（ｘｓ，ｙｓ）⊂Ｃｌ（ｘｌ，ｙｌ）は、各スモールセルＣｓ（ｘｓ，ｙｓ）に関する演算を行なう場合は、それぞれのスモールセルＣｓ（ｘｓ，ｙｓ）が含まれている各ラージセルＣｌ（ｘｌ，ｙｌ）の領域内を対象としていることを意味している。
なお、式（１６）における記号Ｃは任意定数である。
この補正露光量Ｄ_{ｃｏｎｖ．}（ｘｓ，ｙｓ）が、露光量分布Ｄ（ｘ，ｙ）に相当する。
ＥＢ描画装置１０を用いて実際に露光する場合には、式（１５）のように、補正露光量Ｄ_{ｃｏｎｖ．}（ｘｓ，ｙｓ）を、設定露光量Ｄ_０と、この設定露光量Ｄ_０の大きさを変化させる露光量変調率ｍ（ｘｓ，ｙｓ）の積として表わす。露光量変調率ｍ（ｘｓ，ｙｓ）がスモールセルごとに変化することにより、結果的に各スモールセルを露光する各ショットの露光量が補正される。
【００４７】
ただし、本第１実施形態においては、式（１３）のかぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）および式（１４）の後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）をそれぞれ求める際に、各セルの面積率をもとにした和分を用いている。しかし、結果的に得られる補正露光量Ｄ_{ｃｏｎｖ．}（ｘｓ，ｙｓ）はスモールセルごとに異なるため、周辺パターンからの実際のかぶり露光エネルギーは、式（１６）中で見られる、式（１３）と定数Ｃとの積とは異なる量となる。第１実施形態においては、この差を考慮していない分、得られた補正露光量Ｄ_{ｃｏｎｖ．}（ｘｓ，ｙｓ）による露光量の補正精度は低くなる。
【００４８】
たとえば１つのレジスト膜にロジック領域とメモリ領域の両方をパターンニングする場合、ロジック領域におけるショットとメモリ領域におけるショットでは、１ショットあたりの露光量が異なる。１ショットあたりの露光量は、パターンが低密度に形成されるロジック領域においては大きくなり、パターンが高密度に形成されるメモリ領域においては小さくなる。
従って、特にロジック領域とメモリ領域が混在しているパターンを露光する場合には、このような領域による露光量の違いを考慮して補正露光量を算出しなければ、露光量を高精度に補正することはできない。
また、後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）におけるパターン面積率Ｐｓ（ｘｓ，ｙｓ）に掛け合わせる係数を定数２でおいているために、現像やエッチング等の描画後の工程で発生する寸法ばらつきを十分に補正することができない。
以下の実施形態においては、かぶり露光エネルギー成分および後方散乱エネルギー成分を求める際に、各セルの面積率分布ではなく暫定的な露光量変調率を用いることによって補正精度を高めた補正露光量算出手法について述べる。
【００４９】
第２実施形態
本発明の第２実施形態に係る露光方法を、図２に示すフローチャートの各ステップに沿って述べる。なお、以下では、第１実施形態において現われた記号は、第１実施形態と同じ意味を表わすものとして、説明を省略して用いる。
ステップＳＴ１：第２実施形態においては、繰り返し計算により補正露光量を計算し直し、露光量の補正精度を向上させる。このステップにおいては、その繰り返し計算の回数ｎを、０から無限大までの整数により設定する。
ステップＳＴ２：ここでは、ステップＳＴ１において設定した繰り返し計算の回数ｎをカウントするカウンタｉの初期値を、ｉ＝０と設定する。
【００５０】
ステップＳＴ３：ここでは繰り返し計算に先立ち、暫定露光量変調率を算出するが、第２実施形態においては、かぶり露光エネルギー成分と後方散乱エネルギー成分を、ともにスモールセルを単位として算出する。従って、描画領域全面をスモールセルに分割しておく。
単位露光量に対する感光現象が第１実施形態と同様に式（１１）で表されるとして、後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）および、かぶり露光エネルギー成分ＦＥ_０（ｘｓ，ｙｓ）を、スモールセルごとに和分をとって下記式で算出する。
【００５１】
【数１６】

【００５２】
式（１７）、式（１８）を用いて、スモールセルごとに値が異なる変数として規定した、以下の暫定露光量変調率ｍ_ｐ０（ｘｓ，ｙｓ）を算出する。
【００５３】
【数１７】

【００５４】
記号Ａ（ｘｓ，ｙｓ）は、現像やエッチング等の描画後の工程で発生するパターン寸法ばらつきを考慮した変数である。通常は定数２で置き換えて構わない。現像、エッチング等で寸法が細る地点については２より大きな値、逆に寸法が太る地点については２より小さな値を設定すると効果的である。
式（１９）は、スモールセルを単位として計算した結果得られた暫定露光量変調率の式である。式（１９）を、座標（０，０）で表わされる定点を中心とした（ｘ，ｙ）座標系を用いて一般化すると、式（２），（４），（７），（９）が得られる。最終的な描画露光量が得られるまでは、暫定露光量変調率ｍ_ｐ０（ｘｓ，ｙｓ）が暫定露光量を意味しているものとみなす。
【００５５】
ステップＳＴ４：カウンタｉが繰り返し回数ｎと一致しているかどうかを判断する。カウンタｉと繰り返し回数ｎとが一致しており、繰り返し計算を行なわない場合にはステップＳＴ９へ進む。
【００５６】
カウンタｉと繰り返し回数ｎとが一致しておらず、繰り返し計算を行なう場合にはステップＳＴ５へ進み、繰り返し計算のルーチンに入る。
【００５７】
ステップＳＴ５：カウンタｉの数を１つ増加させる。
【００５８】
ステップＳＴ６：ｉ＝１の場合は暫定露光量変調率ｍ_Ｐ０（ｘｓ，ｙｓ）、ｉ≧２の場合は補正露光量変調率ｍ_{Ｐ（ｉ−１）}（ｘｓ，ｙｓ）を用いて、下記式によりかぶり露光エネルギー成分ＦＥ　_Ｐｉ（ｘｓ，ｙｓ）を算出する。
【００５９】
【数１８】

【００６０】
ステップＳＴ７：次に、同様にして、下記式により後方散乱エネルギー成分ＢＥ_Ｐｉ（ｘｓ，ｙｓ）を算出する。
【００６１】
【数１９】

【００６２】
ステップＳＴ８：かぶり露光エネルギー成分ＦＥ_Ｐｉ（ｘｓ，ｙｓ）と後方散乱エネルギー成分ＢＥ_Ｐｉ（ｘｓ，ｙｓ）とを用いて、下記式によりｉ番目（ｉ≧１）の補正露光量変調率ｍ_Ｐｉ（ｘｓ，ｙｓ）を算出する。
【００６３】
【数２０】

【００６４】
ステップＳＴ４へ戻る。
【００６５】
ステップＳＴ９：繰り返し回数ｎの値に応じて、描画露光量Ｄ_Ｅ２ｎ（ｘｓ，ｙｓ）を、Ｄ_Ｅ２ｎ（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_ｐｎ（ｘｓ，ｙｓ）と定義する。繰り返し回数ｎ＝０の場合は、描画露光量Ｄ_Ｅ２０（ｘｓ，ｙｓ）を、Ｄ_Ｅ２０（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_Ｐ０（ｘｓ，ｙｓ）とする。
【００６６】
ステップＳＴ１０：描画露光量Ｄ_Ｅ２ｎ（ｘｓ，ｙｓ）を用いて実際に露光を行う。
【００６７】
本実施形態で用いた逐次代入計算は、後方散乱係数ηとかぶり露光エネルギー成分との和が、パターンエッジ地点に蓄積される前方散乱関数Ｅ_ｆ（ｘ，ｙ）に係る前方散乱エネルギーよりも大きい場合には、必ずしも収束することが保証されているわけではない。ただし、５〜６回も計算を繰り返せば、半導体プロセスとしては十分な精度が得られるものと考えられる。
【００６８】
第３実施形態
第２実施形態で示した一般的な逐次代入計算のほかに、近接効果を補正するための繰り返し計算が公知となっている。本実施形態は、このような繰り返し計算式を用いて、かぶり露光と近接効果とを同時に補正する方法である。
【００６９】
本実施形態では、第２実施形態のステップＳＴ６〜ステップＳＴ８の代わりに、繰り返し途中の各回の補正露光量で露光した際に発生する、後方散乱エネルギー成分の誤差分、およびかぶり露光エネルギー成分の誤差分に着目して新たな補正露光量を算出するステップを用いる。
ステップＳＴ１〜ステップＳＴ５は第２実施形態と同一のため省略し（ただし、ステップＳＴ３の暫定露光量変調率はｍ_０（ｘｓ，ｙｓ）とする。）、以下にステップＳＴ６〜ステップＳＴ１０に代わるステップＳＴ１６〜ステップＳＴ２１を記す。
【００７０】
ステップＳＴ１６：かぶり露光エネルギー成分の誤差分を、以下の式（２３）で算出する。
【００７１】
【数２１】

【００７２】
ステップＳＴ１７：後方散乱エネルギー成分の誤差分を、以下の式（２４）で算出する。
【００７３】
【数２２】

【００７４】
ステップＳＴ１８：後方散乱エネルギー成分の誤差分ＤＢＥ_ｉ（ｘｓ，ｙｓ）およびかぶり露光エネルギー成分の誤差分ＤＦＥ_ｉ（ｘｓ，ｙｓ）を用いて、ｉ番目（ｉ≧１）の露光量変調率誤差ｍ_ｉ（ｘｓ，ｙｓ）を算出する。
【００７５】
【数２３】

【００７６】
ステップＳＴ４へ戻る。
【００７７】
ステップＳＴ１９：補正露光量変調率ｍ_ｐｎ（ｘｓ，ｙｓ）を、各回の繰り返しステップで算出された変調率誤差の総和として、下記式で表す。
【００７８】
【数２４】

【００７９】
ステップＳＴ２０：繰り返し回数ｎの値に応じて、描画露光量Ｄ_Ｅ３ｎ（ｘｓ，ｙｓ）を、Ｄ_{Ｅ ３ｎ}（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_ｐｎ（ｘｓ，ｙｓ）と定義する。繰り返し回数ｎ＝０の場合は、描画露光量Ｄ_Ｅ３０（ｘｓ，ｙｓ）を、Ｄ_Ｅ３０（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_Ｐ０（ｘｓ，ｙｓ）とする。
【００８０】
ステップＳＴ２１：描画露光量Ｄ_Ｅ３ｎ（ｘｓ，ｙｓ）を用いて実際に露光を行う。
【００８１】
本実施形態は第２実施形態よりも少ない計算回数で、実用的な露光量の補正精度が得られると考えられる。また、かぶり露光と近接効果とを同時に補正するため、高精度な補正が可能である。
なお、第２〜第３実施形態のステップＳＴ３で算出される暫定露光量変調率の求め方には任意性がある。
【００８２】
以上のように、第２〜第３実施形態では露光領域をセルに分割し、各位置のショット露光量の違いを考慮したうえで、かぶり露光エネルギーを算出している。また、繰り返し計算によりこの各ショットの露光量の違いを繰り返し補正する。したがって、最初の段階では各ショットの露光量の違いを考慮しておらず、また繰り返し計算も行なっていない第１実施形態よりも高精度に各ショットの補正露光量を算出することができる。各ショットの露光量の違いを考慮して補正露光量を算出することは、特に、ロジック領域とメモリ領域のように、パターン面積率が大きく異なる領域が混在しているデバイスを露光する場合に効果的である。
また、第２〜第３実施形態においては、かぶり露光エネルギー成分も、ＦＥ（ｘｓ，ｙｓ）のようにスモールセルＣｓ（ｘｓ，ｙｓ）を単位として算出している。したがって、この点からも、第１実施形態よりも高精度に露光量を補正することができる。パターン面積率に掛け合わせる係数についても、記号Ａ（ｘ，ｙ）＞０により変数化しているため、描画後の工程で発生する寸法ばらつきにも対応可能である。
レジスト寸法のばらつきは、第２、第３実施形態では１ｎｍ以内におさめられると考えられる。また、描画後の工程で発生する寸法ばらつきも、第２、第３実施形態においては３ｎｍ以内におさめられると考えられる。
【００８３】
しかしながら、かぶり露光の及ぶ範囲は、前述のように、露光地点から一例として半径５０ｍｍ程度の範囲までと広い。したがって、たとえば１０ｃｍ□のブランクス２００を１μｍ□のスモールセルに分割して、スモールセルごとにかぶり露光の影響を補正する場合を考えると、補正すべきセルの数が１００億個となり、実用的な時間内で補正計算を実行することには困難を伴う。
第４実施形態以降では、この不利益を解消し、かつ、十分な補正精度を得ることができるような補正露光量の算出手法について述べる。
【００８４】
第４実施形態
本発明の第４実施形態に係る露光方法を、図５に示すフローチャートの各ステップに沿いながら、図４も併用して述べる。図４において、図４（ａ）は描画領域をラージセルに分割した様子を示し、図４（ｂ）は１つのラージセルにおいて、後方散乱の及ぶ領域をさらにスモールセルに分割した様子を示している。
第４実施形態に係る補正露光量の算出方法は、簡潔には、まずラージセルを単位としてかぶり露光エネルギー成分を算出し、このかぶり露光エネルギー成分を用いて、スモールセル単位で後方散乱の影響を、繰り返し計算により補正するものである。
【００８５】
ステップＳＴ３１：まず、図４（ａ）に示すように、描画領域全面を、たとえば１ｍｍ□のラージセルに分割する。以下では、任意の１つのラージセルを記号Ｃｌ（ｘｌ，ｙｌ）で表わすことにする。各ラージセルＣｌ（ｘｌ，ｙｌ）に対する第１暫定露光量Ｄ_ｐｒｏｖ（ｘｌ，ｙｌ）を規定する。本第４実施形態においては、一例として、各ラージセルＣｌ（ｘｌ，ｙｌ）の中心地点を露光する場合に、後方散乱による近接効果が生じないように補正したショット露光量を、第１暫定露光量Ｄ_ｐｒｏｖ（ｘｌ，ｙｌ）として用いる。
【００８６】
そのために、図４（ｂ）に示すように、各ラージセルＣｌ（ｘｌ，ｙｌ）の領域のうち、その中心のスモールセルＣｓ（ｘｌｃ，ｙｌｃ）およびその周辺で後方散乱が及ぶ範囲を、たとえば１μｍ□のスモールセルに分割する。後方散乱が及ぶ範囲ＢＳは、前述のように、図７における半径Ｒ_Ａの大きさたとえば２５μｍの円内である。
なお、図４（ｂ）において、ラージセルＣｌ（ｘｌ，ｙｌ）とスモールセルＣｓ（ｘｓ，ｙｓ）の縮尺は実際の通りではない。
【００８７】
図４（ｂ）に示すように、ラージセルＣｌ（ｘｌ，ｙｌ）とスモールセルＣｓ（ｘｓ，ｙｓ）の各領域には、露光によりパターンを形成するべきパターン領域Ｐａが存在する。各ラージセルＣｌ（ｘｌ，ｙｌ）およびスモールセルＣｓ（ｘｓ，ｙｓ）におけるパターン領域Ｐａが占める割合を、それぞれラージセルＣｌ（ｘｌ，ｙｌ）内のパターン面積率Ｐｌ（ｘｌ，ｙｌ）およびスモールセルＣｓ（ｘｓ，ｙｓ）内のパターン面積率Ｐｓ（ｘｓ，ｙｓ）とする。このとき、近接効果を補正するための第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）は、設定露光量をＤ_０、後方散乱エネルギー成分を式（２７）により表わすものとして、周知のように、式（２８）で与えることができる。
【００８８】
【数２５】

【００８９】
ここで、記号Ｐｓ（ｘｌｃ＋ｒ，ｙｌｃ＋ｓ）は、スモールセルＣｓ（ｘｌｃ，ｙｌｃ）からｘ軸方向にｒ番目、ｙ軸方向にｓ番目のスモールセルのパターン面積率を表わす。また、変数Ａ（ｘｌ，ｙｌ）は通常２としてよい。
式（２８）は、スモールセルを単位として計算した結果得られた暫定露光量変調率の式である。式（２８）を、座標（０，０）で表わされる定点を中心とした（ｘ，ｙ）座標系を用いて一般化すると、式（１），（３），（６），（８）が得られる。最終的な描画露光量が得られるまでは、暫定露光量変調率が露光量を意味しているとみなせるため、第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）を、第１暫定露光量Ｄ_ｐｒｏｖ（ｘｌ，ｙｌ）とみなす。
【００９０】
ステップＳＴ３２：算出した第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）を用いて、ラージセルＣｌ（ｘｌ，ｙｌ）ごとに、第１〜第３実施形態の場合と同様にかぶり露光エネルギー成分を算出する。本第４実施形態においては、かぶり露光エネルギー成分を、暫定かぶり露光エネルギー成分と呼ぶ。
算出した暫定かぶり露光エネルギー成分ＦＥ_ｐｒｏｖ（ｘｌ，ｙｌ）は、下記式のようになる。
【００９１】
【数２６】

【００９２】
ステップＳＴ３３：算出した暫定かぶり露光エネルギー成分ＦＥ_ｐｒｏｖ（ｘｌ，ｙｌ）、レジスト閾値感度Ｅｔｈ、設定露光量Ｄ_０を用いて、第１の領域ごとに暫定ビーム散乱エネルギーＥ_ｐｒｏｖ（ｘｌ，ｙｌ）を、下記式で定義して求める。
【００９３】
【数２７】

【００９４】
ステップＳＴ３４：以下、近接効果を補正するための繰り返し計算を行なう。まず、繰り返し計算の回数ｎを、０から無限大までの整数により設定する。
【００９５】
ステップＳＴ３５：ここでは、ステップＳＴ３４において設定した繰り返し計算の回数ｎをカウントするカウンタｉの初期値を、ｉ＝０と設定する。
【００９６】
ステップＳＴ３６：描画領域全面をスモールセルに分割し、これまでと同様に後方散乱エネルギー成分ＢＥ_０（ｘｓ，ｙｓ）を下記式により算出する。
【００９７】
【数２８】

【００９８】
ステップＳＴ３７：式（３０）の暫定ビーム散乱エネルギーおよび式（３１）の後方散乱エネルギー成分を用いて、下記式で表される第２暫定露光量変調率ｍ_ｐ０（ｘｓ，ｙｓ）を算出する。この第２暫定露光量変調率ｍ_ｐ０（ｘｓ，ｙｓ）、第２実施形態のレジスト閾値感度を、スモールセルを含有するラージセルごとに設定された暫定電子散乱エネルギーＥ_ｐｒｏｖ（ｘｌ，ｙｌ）で置き換えて、計算式からかぶり露光に関する項を取り除くことにより算出される。
【００９９】
【数２９】

【０１００】
記号Ａ（ｘｓ，ｙｓ）は現像やエッチング等の描画後の工程で発生するパターン寸法ばらつきを考慮した変数であり、通常は定数２で置き換えて構わない。
【０１０１】
ステップＳＴ３８：カウンタｉが繰り返し回数ｎと一致しているかどうかを判断する。カウンタｉと繰り返し回数ｎとが一致しており、繰り返し計算を行なわない場合にはステップＳＴ４２へ進む。
【０１０２】
カウンタｉと繰り返し回数ｎとが一致しておらず、繰り返し計算を行なう場合にはステップＳＴ３９へ進み、繰り返し計算のルーチンに入る。
【０１０３】
ステップＳＴ３９：カウンタｉの数を１つ増加させる。
【０１０４】
ステップＳＴ４０：ｉ＝１の場合は第２暫定露光量変調率ｍ_Ｐ０（ｘｓ，ｙｓ）、ｉ≧２の場合は補正露光量変調率ｍ_{ｐ（ｉ−１）}（ｘｓ，ｙｓ）を用いて、後方散乱エネルギー成分ＢＥ_ｐｉ（ｘｓ，ｙｓ）を算出する。
【０１０５】
【数３０】

【０１０６】
ステップＳＴ４１：暫定ビーム散乱エネルギーＥ_ｐｒｏｖ（ｘｌ，ｙｌ）と後方散乱エネルギー成分ＢＥ_ｐｉ（ｘｓ，ｙｓ）とを用いて、ｉ番目（ｉ≧１）の補正露光量変調率ｍ_ｐｉ（ｘｓ，ｙｓ）を算出する。
【０１０７】
【数３１】

【０１０８】
ステップＳＴ３８へ戻る。
【０１０９】
ステップＳＴ４２：繰り返し回数ｎの値に応じて、描画露光量Ｄ_Ｅ４ｎ（ｘｓ，ｙｓ）を、Ｄ_{Ｅ ４ｎ}（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_ｐｎ（ｘｓ，ｙｓ）と定義する。繰り返し回数ｎ＝０の場合は、描画露光量Ｄ_Ｅ４０（ｘｓ，ｙｓ）を、Ｄ_Ｅ４０（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_Ｐ０（ｘｓ，ｙｓ）とする。
【０１１０】
ステップＳＴ４３：描画露光量Ｄ_Ｅ４ｎ（ｘｓ，ｙｓ）を用いて実際に露光を行なう。
本第４実施形態によれば、暫定かぶり露光エネルギー成分ＦＥ_ｐｒｏｖ（ｘｌ，ｙｌ）をラージセルＣｌ（ｘｌ，ｙｌ）単位で算出しているため、かぶり露光補正のセルの数が第２、第３実施形態の場合に較べて大幅に少なくなり、計算時間も短くなる。
詳細には、たとえば１０ｃｍ□の描画領域を１ｍｍ□のラージセルに分割する場合には、かぶり露光の影響を補正すべきラージセルの数は１万個となり、第２、第３実施形態の場合の１００億個に較べて大幅に少ない。
【０１１１】
第５実施形態
本実施形態では第４実施形態と全く同様にして暫定ビーム散乱エネルギーＥ_ｐｒｏｖ（ｘｌ，ｙｌ）を算出した後、第３実施形態と同様の繰り返し計算によってスモールセルごとに近接効果補正の計算を行なう。
本第５実施形態における計算手順を、図６に示すフローチャートに従って述べるが、図６におけるステップＳＴ３１〜ステップＳＴ３９は第４実施形態と同一のため省略する。
【０１１２】
ステップＳＴ５０：下記式によって後方散乱エネルギー成分の誤差分を求める。
【０１１３】
【数３２】

【０１１４】
ステップＳＴ５１：式（３５）の後方散乱エネルギー誤差ＤＢＥ_ｉ（ｘｓ，ｙｓ）を用いて、ｉ番目（ｉ≧１）の補正露光量変調率ｍ_ｉ（ｘｓ，ｙｓ）を、下記式から算出する。
【０１１５】
【数３３】

【０１１６】
ステップＳＴ３８へ戻る。
【０１１７】
ステップＳＴ５２：補正露光量変調率ｍ_ｐｎ（ｘｓ，ｙｓ）を、各回の繰り返しステップで算出された露光量変調率誤差の総和として、下記式で表す。
【０１１８】
【数３４】

【０１１９】
ステップＳＴ５３：繰り返し回数ｎの値に応じて、描画露光量Ｄ_Ｅ５ｎ（ｘｓ，ｙｓ）を、Ｄ_Ｅ５ｎ（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_ｐｎ（ｘｓ，ｙｓ）と定義する。繰り返し回数ｎ＝０の場合は、描画露光量Ｄ_Ｅ５０（ｘｓ，ｙｓ）を、Ｄ_Ｅ５０（ｘｓ，ｙｓ）＝Ｄ_０×ｍ_Ｐ０（ｘｓ，ｙｓ）とする。
【０１２０】
ステップＳＴ５４：描画露光量Ｄ_Ｅ５ｎ（ｘｓ，ｙｓ）を用いて実際に露光を行う。
【０１２１】
第５実施形態においても、暫定かぶり露光エネルギー成分ＦＥ_ｐｒｏｖ（ｘｌ，ｙｌ）をラージセルＣｌ（ｘｌ，ｙｌ）単位で算出しているため、第４実施形態の場合と同様に計算時間が短くなる。
また、かぶり露光と近接効果とを同時に補正するため、高精度な補正が可能である。
【０１２２】
第４、第５実施形態の補正精度は、ラージセルごとに設定した第１暫定露光量Ｄ_ｐｒｏｖ（ｘ，ｙ）に係る第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）が、スモールセルごとに算出された最終的な補正露光量変調率ｍ_Ｐｎ（ｘｓ，ｙｓ）との間で下記式の関係を満たすか否かによっている。
なお、第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）と第１暫定露光量Ｄ_ｐｒｏｖ（ｘ，ｙ）との間、および、最終的な補正露光量変調率ｍ_Ｐｎ（ｘｓ，ｙｓ）と最終的な補正露光量をＤ_ｃｏｒ（ｘｓ，ｙｓ）との間には直接的な相関関係存在する。このため、下記式（３８）は式（５）および式（１０）を意味しているとみなせる。
【０１２３】
【数３５】

【０１２４】
各ラージセル内において、第１暫定露光量変調率が最終的な補正露光量変調率の平均値となっていればよいのであるが、第４、第５実施形態のステップＳＴ３１において与えた第１暫定露光量変調率が式（３８）の関係を満たすかどうかは、パターン分布に依存する。よって、ステップＳＴ３１の第１暫定露光量変調率の与え方と、ステップＳＴ４０またはステップＳＴ５０以降での繰り返し計算の方法とを組み合わせれば、第４、第５実施形態の派生形態が幾つも考えられる。
第６実施形態では、第１暫定露光量を与える際に、かぶり露光エネルギー成分も考慮した例を示す。
【０１２５】
第６実施形態
本実施形態は、式（３８）の関係をより精度よく満たすために、ラージセルごとに算出したかぶり露光エネルギーと、ラージセルの中心地点ごとに算出した後方散乱エネルギー成分とを用いて、第２実施形態および第３実施形態と同様の暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）をラージセルごとに算出する形態である。
基本的な流れは第５実施形態と同じであるため、以下、図６に示すフローチャートを流用して述べる。
【０１２６】
ステップＳＴ３１：第６実施形態のステップＳＴ３１においては、描画領域全面をラージセルＣｌ（ｘｌ，ｙｌ）に分割し、このラージセルの中央地点周辺をスモールセルに分割する。中央地点のスモールセルをＣｓ（ｘｌｃ，ｙｌｃ）として、中央地点を含むラージセルごとに後方散乱エネルギー成分ＢＥ_０（ｘｌｃ，ｙｌｃ）およびかぶり露光エネルギー成分ＦＥ_０（ｘｌ，ｙｌ）を下記式により算出する。
【０１２７】
【数３６】

【０１２８】
式（３９）および式（４０）を用いて、ラージセルごとに第１暫定露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）を下記式によって算出する。
【０１２９】
【数３７】

【０１３０】
以下、ステップＳＴ３２以降は繰り返し計算の方法を選択することで、第４実施形態または第５実施形態と同じとなるため、記述は省略する。
【０１３１】
計算時間の増大を抑制するために、ラージセルごとにかぶり露光を補正するための露光量変調率ｍ_ｐｒｏｖ（ｘｌ，ｙｌ）を算出した後に、かぶり露光エネルギー成分の影響を取り除いた上で、スモールセルごとに近接効果補正を実施すればよい。近接効果補正の計算前に仮定した暫定かぶり露光エネルギー成分ＦＥ_ｐｒｏｖ（ｘｌ，ｙｌ）が、最終的な補正露光量で露光した時の実際のかぶり露光エネルギー成分と同じならば、補正計算の精度が高くなると考えてよい。
【０１３２】
第４〜６実施形態においては、レジスト寸法のばらつきを３ｎｍ以内にできると考えられる。また、エッチング等の描画後の工程で発生する寸法ばらつきにも対応することが可能であり、第４〜６実施形態では後工程における寸法ばらつきを５ｎｍ以内にできると考えられる。さらに、第４〜６実施形態によれば、従来と同等の時間内において露光量を算出することが可能である。
【０１３３】
以上、本発明の内容について種々の実施形態を参照して述べたが、本発明は上記の実施形態ならびに図面に記載の事項に限定されない。
たとえば、各フローチャートにおける各エネルギー成分を算出するステップ、繰り返しの回数ｎを規定するステップやカウンタを増加させるステップ等のそれぞれのステップの順番は、特許請求の範囲に記載した本願発明の内容を実現可能であれば、任意である。また、繰り返し計算のフローについても、最終的に目的とする描画露光量が得られれば、どのようなフローであってもよい。
また、式（１１）で示した単位露光量照射に対する感光関数の係数等の変更可能部分を適宜変更すれば、請求項や実施形態中の関数の記述も変更されることは自明である。
その他、本発明は、露光ビームによりパターン描画が可能なものであれば、シリコン基板等のフォトマスク以外に対しても適用することができる。
【０１３４】
【発明の効果】
以上のように、本発明によれば、かぶり露光の影響も考慮して各ショットの露光量を算出することによって、近接効果の影響に加えてかぶり露光の影響をも高精度に補正可能であり、その補正計算時間が従来の場合と同等な露光方法を提供することができる。
また、本発明によれば、近接効果の影響に加えてかぶり露光の影響をも高精度に補正可能であり、その補正計算時間が従来の場合と同等な露光装置を提供することもできる。
【図面の簡単な説明】
【図１】図１は、本発明の第１実施形態に係るＥＢ描画装置の要部の概略構成図である。
【図２】図２は、本発明の第２実施形態に係る露光方法を述べるためのフローチャートである。
【図３】図３は、本発明の第３実施形態に係る露光方法を述べるためのフローチャートである。
【図４】図４は描画領域を分割した状態を示す図であり、図４（ａ）は描画領域をラージセルに分割した状態を示しており、図４（ｂ）は、図４（ａ）に示すラージセルのうちのあるラージセルにおいて、後方散乱の及ぶ領域をさらにスモールセルに分割した様子を示している。
【図５】図５は、本発明の第４実施形態に係る露光方法を述べるためのフローチャートである。
【図６】図６は、本発明の第５実施形態に係る露光方法を述べるためのフローチャートである。
【図７】図７は、ＥＢ描画装置を用いたレジストの露光において発生するかぶり露光の状態を示した図である。
【符号の説明】
１０…ＥＢ描画装置、２０…ＥＢ描画装置本体、５０…制御装置、１００…鏡筒、１２０…電子銃、２００…ブランクス、２１０…基板、２２０…遮光膜、２３０…レジスト膜[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an exposure method and an exposure apparatus for manufacturing, for example, a photomask. Specifically, the present invention is directed to an exposure which determines an exposure amount in consideration of the influence of fog exposure in addition to the influence of back scattering at the time of exposure, and the dimensional variation occurring in a post-drawing process such as development and etching. The present invention relates to a method and an exposure apparatus.
[0002]
[Prior art]
As an example of the exposure step, exposure of photomask blanks using an electron beam lithography apparatus (hereinafter, abbreviated as EB (Electron Beam) lithography apparatus) is known.
FIG. 7 is a view schematically showing this blank exposure method.
As illustrated in FIG. 7, the lens barrel 100 of the EB lithography apparatus having the electron gun 120 therein and the blanks 200 are arranged to face each other.
The blanks 200 are formed by, for example, applying a light shielding film 220 to a glass substrate 210 and further applying a resist film 230 on the light shielding film 220.
[0003]
An emission electron beam Bi indicated by a downward arrow in the figure is emitted from the electron gun 120 toward the blanks 200. When viewed from the blanks 200, the emitted electron beam Bi becomes an incident electron beam Bi with respect to the resist film 230 of the blanks 200. The incident electron beam Bi that has exposed the resist film 230 is reflected at the boundary between the resist film 230 and the light-shielding film 220, and returns to the lens barrel 100 as a reflected electron beam Br indicated by an upward arrow in the drawing.
The reflection of the electron beam from the light-shielding film 220 is called back scattering, and due to the back scattering by the reflected electron beam Br, a proximity effect that causes the pattern of the resist film 230 to be exposed to become thicker or thinner occurs.
[0004]
Further, the reflected electron beam Br that has passed through the resist film 230 is further reflected by the lens barrel 100 and is again irradiated to a wide range of the blanks 200, and becomes an effective irradiation electron beam Bf for exposing the resist film 230 again. In FIG. 7, the effective irradiation electron beam Bf is indicated by a dotted arrow. The effective irradiation exposure by the effective irradiation electron beam Bf causes the pattern to become thick.
As shown in FIG. 7, the effective irradiation electron beam Bf is applied so as to cover a wide area of the blank 200, and hence the effective irradiation electron beam Bf is hereinafter referred to as a fogging electron beam Bf, and the effective irradiation electron beam Bf is used. Is called fog exposure.
[0005]
When the beam acceleration voltage of the electron beam lithography apparatus is accelerated to 50 kV or more, the problem of pattern thickening due to fog exposure becomes significant. As a countermeasure, a method of physically reducing the fogging electron beam Bf by attaching a carbon film, an antireflection plate, or the like to the lower surface of the objective lens (not shown) in the lens barrel 100 has been adopted. Has not been reached.
[0006]
Therefore, as in the case of the proximity effect correction, a method of correcting fog exposure by exposure amount modulation for adjusting the exposure amount has been devised (for example, see Patent Document 1). However, the conventional method is not always an accurate correction method. This is because, in the conventional fogging exposure correction based on the exposure amount modulation, the exposure amount due to the fogging exposure is calculated and corrected based on the pattern area distribution at each position in the exposure area of the blank 200. I do.
[0007]
[Patent Document 1]
JP-A-9-289164
[0008]
[Problems to be solved by the invention]
It is considered that the fogging exposure energy from the peripheral region at each position of the exposure region can be calculated by convoluting the exposure amount distribution of the peripheral region.
Therefore, when correcting the fog exposure by the exposure amount modulation, the correction amount should be calculated by calculating the exposure amount by the fog exposure using the exposure amount distribution, not the pattern area distribution at each position in the exposure region. If the exposure amount is corrected based on the pattern area distribution of the drawing area, it cannot be said that the influence of fog exposure has been corrected with high accuracy.
In addition, in order to perform highly accurate exposure amount modulation, it is necessary to consider proximity effect correction at the same time when performing fog exposure correction calculation.
Further, unless the calculation of the correction exposure amount by the exposure amount modulation is completed within a practical time, it cannot be implemented as a semiconductor process.
[0009]
An object of the present invention is that it is possible to accurately correct not only the proximity effect but also the influence of fog exposure, dimensional variation occurring in a post-drawing process such as development and etching, and the correction calculation time is equivalent to the conventional case. It is an object of the present invention to provide an exposure method which is within a practical time.
Another object of the present invention is to be able to accurately correct not only the proximity effect but also the influence of fogging exposure, and dimensional variations that occur in a post-drawing process such as development and etching, and the correction calculation time is conventionally reduced. The purpose of the present invention is to provide an exposure apparatus which is within a practical time equivalent to the case of (1).
[0010]
[Means for Solving the Problems]
The exposure method according to the present invention, for each position of the sample on which the resist is applied, using a provisional exposure amount having a different value depending on each position, the influence of the peripheral portion of each position to each position. A first step of calculating a backscattering energy component and a fog exposure energy component, and a second step of calculating a correction exposure amount for each position based on the fog exposure energy component and the backscattering energy component. And the first and second steps are repeated a predetermined number of times using the corrected exposure amount at each position as the provisional exposure amount to calculate a final corrected exposure amount for each position. And exposing the resist at each of the positions using an exposure beam of the final corrected exposure amount.
[0011]
The exposure method according to the present invention divides the resist-coated sample into a plurality of first regions that are sufficiently smaller than a fog exposure radius, and a first provisional region having a different value for each of the first regions. A first step of defining an exposure amount, and for each of the first regions, using the first provisional exposure amount, including an influence from the first region around the first region, A second step of calculating a provisional fog exposure energy component, a third step of calculating a provisional beam scattering energy for each of the first regions based on the provisional fog exposure energy component, Dividing the first region and a plurality of second regions that are sufficiently smaller than the backscattering diameter, based on the provisional beam scattering energy in the first region including the second region; Per area A fourth step of calculating a second provisional exposure amount, and using the calculated second provisional exposure amount, for each of the second regions, from the second region around the second region. A fifth step of calculating a backscattering energy component including the effect of the above, the provisional beam scattering energy in the first region including the second region, and the backscattering energy component for each of the second regions. A sixth step of calculating a correction exposure amount for each of the second regions based on the above, and the fifth and sixth steps are performed a predetermined number of times using the correction exposure amount as the second provisional exposure amount Repeatedly calculating a final corrected exposure amount for each of the second regions, and exposing the resist for each of the second regions using an exposure beam having the final corrected exposure amount. Exposure method That it is also possible to take.
[0012]
An exposure apparatus according to the present invention includes an exposure unit that irradiates an exposure beam on a sample on which a resist is applied, an arithmetic unit that calculates an exposure amount by the exposure beam for each position of the sample, Control means for giving to the exposure means a command signal for irradiating the exposure beam, the exposure amount being the calculated exposure amount, wherein the calculating means uses a temporary exposure amount having a different value depending on each position. Including the influence of the peripheral portion of each position on each position, including the backscattering energy component, and calculating the fog exposure energy component, based on the fog exposure energy component and the backscattering energy component, A correction exposure amount for each position is calculated, and a new correction exposure amount is calculated by using the correction exposure amount at each position as the provisional exposure amount. Number of iterations to calculate the final corrected exposure dose to said each position, an exposure apparatus according to the exposure the final corrected exposure dose.
[0013]
An exposure apparatus according to the present invention includes an exposure unit that irradiates an exposure beam on a sample on which a resist is applied, an arithmetic unit that calculates an exposure amount by the exposure beam for each position of the sample, Control means for giving to the exposure means a command signal for irradiating the exposure beam at which the exposure amount is the calculated exposure amount, wherein the calculation means sets the plurality of samples to be sufficiently smaller than a fogging exposure radius. The first provisional exposure amount having a different value for each first region is defined, and the first provisional exposure amount is defined for each first region using the first provisional exposure amount. Calculating a provisional fog exposure energy component including the influence from the first region around the first region; and providing a provisional beam scattering energy for each of the first regions based on the provisional fog exposure energy component. Calculating, dividing the entire surface of the sample into the first region and a plurality of second regions that are sufficiently smaller than the backscattering diameter, and providing the provisional beam in the first region including the second region. Based on the scattering energy, a second provisional exposure is calculated for each of the second regions, and the calculated second provisional exposure is used to calculate the second provisional exposure for each of the second regions. A backscattering energy component including an influence from the surrounding second region is calculated, and the provisional beam scattering energy in the first region including the second region and the backscattering energy component in each of the second regions are calculated. Based on the scattered energy component, a correction exposure amount is calculated for each of the second regions, and a new correction exposure amount calculation using the correction exposure amount as the second provisional exposure amount is repeated a predetermined number of times. The second area Preparative to calculate the final corrected exposure dose, it is also possible to the final corrected exposure dose a configuration of an exposure apparatus according to the exposure amount.
[0014]
In the present invention, the resist applied to the sample is exposed by irradiating an exposure beam from exposure means. The amount of exposure by the exposure beam is corrected and changed for each position on the sample based on the shape of the drawing pattern, which is an exposure area for the resist. As an initial value of the exposure amount for calculating the correction exposure amount, a provisional exposure amount that differs for each exposure position is defined.
When the effects of the backscattering of the exposure beam and the effects of fogging exposure are corrected in the same area as a unit, the backscattering energy component and the fogging exposure, including the effects from surrounding areas, are corrected for each area. Calculate the energy component.
Based on these two energy components, a correction exposure amount for each area is calculated. The final corrected exposure amount is calculated by iterative calculation for further correcting the corrected exposure amount using the calculated corrected exposure amount in each region as a provisional exposure amount for each region.
For the repetitive calculation for calculating the final corrected exposure amount from the provisional exposure amount, general sequential substitution calculation may be used.
[0015]
In order to reduce the time required for the correction calculation, the effect of fogging exposure and the effect of backscattering of the exposure beam are corrected in different regions as a unit, the drawing region of the sample is divided into a plurality of first regions. The first area is divided into a plurality of second areas.
In this case, the provisional exposure amount is defined for each first area.
The fogging exposure energy component also uses the provisional exposure amount defined for each first area, and includes not only the influence of the exposure in the target first area but also the influence of the exposure in the surrounding first area. The calculation is performed for each first area.
Similarly, the backscattering energy component is calculated for each second region, including the influence from the surrounding second region.
The correction exposure amount is calculated for each second region based on the fog exposure energy component calculated for each first region and the backscattering energy component calculated for each second region.
The iterative calculation for improving the correction accuracy of the correction exposure amount is performed on the backscattered energy component for each second region, and the final correction exposure amount is calculated.
[0016]
The correction exposure amount is calculated by the arithmetic unit, and the control unit gives a command signal to the exposure unit so that the exposure beam at each irradiation position emits an exposure beam having the calculated correction exposure amount.
[0017]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings, taking EB drawing as an example.
[0018]
First embodiment
FIG. 1 shows a schematic configuration diagram of a main part of an EB drawing apparatus according to a first embodiment of the present invention. The EB lithography apparatus 10 as an exposure apparatus shown in FIG. 1 is roughly divided into an EB lithography apparatus main body 20 and a control device 50 for controlling the EB lithography apparatus main body 20.
[0019]
[EB drawing device body]
The EB writing apparatus main body 20 includes a lens barrel 100, a sample chamber 21 connected to the lens barrel 100, and a gantry 30 on which the connected lens barrel 100 and the sample chamber 21 are mounted.
An electron gun 120 is provided in the lens barrel 100. The electron gun 120 is one embodiment of the exposure means in the present invention. An electron beam of the electron beam Bi emitted from the electron gun 120 at an acceleration voltage of, for example, 50 kV passes through the lens barrel 100 and reaches a sample arranged in the sample chamber 21. The electron beam forms an image on the drawing surface of the sample by an optical system constituted by the lenses 24a to 24d installed in the lens barrel 100. The electron beam can be deflected by deflectors 25a and 25b installed in the lens barrel 100. Thus, the irradiation position of the electron beam can be changed even when the sample is stopped.
[0020]
Although not shown, the beam shape of the electron beam Bi can be changed by a beam shaping aperture provided in the lens barrel 100. The beam shape includes a figure beam including a triangular beam and a rectangular beam, and the size of one side is, for example, about 2 μm at the maximum.
A drawing pattern, which is an exposure area for a resist, is divided into figures and rectangles and exposed. Beam irradiation on each divided figure is called one shot.
The irradiation time of the electron beam can be changed by a blanking unit (not shown). This makes it possible to adjust the amount of exposure to the sample for each shot.
[0021]
The sample chamber 21 is provided with a loader 22 for storing a sample to be exposed and a stage 23 for mounting the sample taken out of the loader 22. The stage 23 moves continuously during writing or stops during writing, and moves by a predetermined amount when a predetermined area of the sample is drawn.
[0022]
As an example of the sample, the blanks 200 illustrated in FIG. 7 are handled. As the substrate 210 of the blanks 200, for example, a glass substrate such as a synthetic quartz glass is used.
As the light shielding film 220 applied to the surface of the substrate 210, for example, a chromium thin film is used. The thickness of the chromium thin film is, for example, about 50 to 100 nm.
If a halftone material that transmits light by about 5% to 16%, for example, is used instead of the chromium thin film that blocks a beam (light), the pattern resolution at the time of exposure can be improved. This is because the light leaking from the light shielding portion and the light passing through the pattern opening have inverted phases, and at the boundary of the pattern, the light intensity decreases due to the phase inversion and the spread of the skirt of the light intensity distribution is suppressed. This is because it can be done.
As the material of the halftone light-shielding film, for example, a chromium-based material such as CrON, a molybdenum-based material such as MoSiON, a tungsten-based material such as WSiON, or a silicon-based material such as SiN can be used.
As the resist film 230 formed on the light shielding film 220, for example, a film made of a phenol resin, a novolak resin, a diazonaphthoquinone (DNQ) compound, or the like is used.
[0023]
The gantry 30 is provided with an evacuation system for evacuating the lens barrel 100 and the sample chamber 21 and a filter for preventing the exposure position from shifting due to blurring of components such as the lens barrel 100, the sample chamber 21 and the stage 23 during exposure. It has a gantry.
[0024]
[Control device]
The control device 50 includes a calculation unit 51, a control command unit 52, an electron gun control unit 53, an electron optical system control unit 54, a memory control unit 55, a deflection control unit 56, a stage control unit 57, and a temperature control unit. And a control unit 58.
[0025]
The arithmetic unit 51 corresponds to an arithmetic unit in the present invention, and is realized using, for example, a CPU (Central Processing Unit) of a workstation.
The arithmetic unit 51 calculates an exposure amount of the electron beam Bi for irradiating the resist film 230 of the blank 200 based on the input mask pattern data 60. The method of calculating the exposure amount will be described later in detail.
[0026]
The control command section 52 corresponds to the control means in the present invention. The control command unit 52 is also realized using, for example, a CPU of a workstation.
The control command unit 52 receives the data of the exposure amount calculated by the calculation unit 51, and controls the electron gun control unit 53 and the blanking unit so that the exposure amount of each shot that differs depending on the irradiation position becomes the calculated exposure amount. A command signal is given to the electron gun 120 via the controller 120 to control the irradiation amount of the electron beam Bi from the electron gun 120.
[0027]
The electron optical system control unit 54 receives a command signal from the control command unit 52, adjusts the state such as the focal position of the electron optical system constituted by the lenses 24a to 24d, and transmits the electron beam by the electron beam Bi to the resist film 230. Image.
[0028]
The pattern data 60 input to the arithmetic unit 51 is stored in a pattern memory 59. The calculation unit 51 and the control command unit 52 can extract the pattern data 60 from the pattern memory 59 via the memory control unit 55.
The memory control unit 55 also transmits the pattern data 60 to the deflection control unit 56 and the stage control unit 57. Based on the pattern data 60, the deflection controller 56 and the stage controller 57 cooperate to control the deflectors 25a and 25b and the stage 23, respectively, so that a predetermined position of the resist film 230 is irradiated with the electron beam Bi. So that
[0029]
The temperature control unit 58 manages the temperature of the loader 22 so as to prevent an error in the exposure position for each blank due to expansion and contraction of the blanks 200 caused by a temperature change.
The operator inputs commands to the calculation unit 51 and the control command unit 52 via the console 61 to control the control device 50 and the entire EB drawing device 10.
[0030]
Hereinafter, calculation of the exposure amount for each shot by the calculation unit 51 will be described.
First, the relationship between the energy for exposing the resist film 230 to light and the amount of exposure will be described.
When a fixed point represented by the coordinates (0, 0) of the resist film 230 as a two-dimensional plane is irradiated with the electron beam Bi of the unit exposure amount, the resist film at a position represented by the coordinates (x, y) around the same. The energy distribution G (x, y) stored in 230 is represented by the following equation as the sum of the photosensitive phenomena including the influence of the proximity effect and the influence of the fog exposure.
[0031]
[Equation 11]

[0032]
Where E_f(X, y) is a forward scattering function representing an energy distribution due to forward scattering of the electron beam in the resist film 230;_b(X, y) is a backscattering function representing the energy distribution due to the reflection of the electron beam from the light-shielding film 220. When both are normalized, the symbol η represents the ratio of forward scattering to backscattering as a backscattering coefficient. Express. Fog (x, y) is a fog exposure function representing the energy distribution due to fog exposure.
Function E_f(X, y), E_bVarious specific shapes of (x, y) and Fog (x, y) have been proposed according to the type of blanks 200 and the drawing method, and Ef (x, y) and Eb (x, y) Although a Gaussian distribution function is mainly used, an arbitrary creation function is often used for Fog (x, y).
[0033]
When the accelerating voltage of the electron beam is increased, the forward scattering decreases and the back scattering increases. The range of the backscattering depends on conditions such as the type of the resist, but as an example, when the acceleration voltage is 50 kV, the backscattering radius R from the center position of the irradiation of the electron beam is R._BIs within a circle of about 25 μm.
On the other hand, the range over which the fogging exposure extends is, for example, a case where the acceleration voltage is 50 kV and the radius R_AIs within a circle of about 50 mm, which is much wider than the range that backscattering can reach.
[0034]
It is assumed that the photosensitivity phenomenon with respect to the electron beam incident at the unit exposure amount is invariably reproduced in the plane of the resist film 230, and the superposition of the photosensitivity is established. At this time, when a drawing area in which a pattern is formed by exposure is drawn with an exposure amount distribution D (x, y), an energy distribution E () representing the energy stored in the resist film 230 at arbitrary coordinates (x, y). x, y) can be expressed by the following equation using convolution integral.
[0035]
(Equation 12)

[0036]
The area of integration in equation (12) is a drawing area.
The thickening and thinning of the pattern are remarkable at the pattern edge points. Therefore, it is desired to calculate the exposure distribution D (x, y) such that the stored energy E (x, y) accurately matches the resist sensitivity Eth at the pattern edge point.
[0037]
When calculating the exposure amount distribution D (x, y), in the first embodiment, first, the entire drawing area is divided into a first area sufficiently smaller than the fog exposure radius. The area of the first region Cl (xl, yl) is set to Sl, but is, for example, about 1 mm square. Hereinafter, the first region is referred to as a large cell. In the following, since the calculation is performed using such a rectangle as a unit, for example, the symbols xl and yl in the symbol (記号) of the symbol Cl represent not the coordinates but the number of each large cell.
[0038]
Next, a fog exposure energy component FE representing the contribution of energy storage by fog exposure to each large cell Cl (xl, yl).₀(Xl, yl) is obtained. When the fog exposure energy to a certain large cell is approximated by convolving the pattern area ratio within the range of the fog exposure, the fog exposure energy component FE₀(Xl, yl) can be represented by the following equation.
[0039]
(Equation 13)

[0040]
In equation (3), the unit of calculation is each large cell Cl (xl, yl), so convolution is calculated not by integration but by sum using the symbol Σ. The range of the sum in the expression (3) is a fog exposure range FG which is a range over which fog exposure is performed with a certain large cell Cl (xl, yl) as a center. Symbols p and q are variables used in calculations for large cells.
Hereafter, similarly, in the calculation using the rectangular area as a unit, the sum is used instead of the integration.
The symbol Pl (xl, yl) in the equation (13) is the pattern area ratio in the large cell with the number (xl, yl).
[0041]
Next, the entire drawing area is covered by the large cell and the backscattering radius R shown in FIG._BInto a second region that is sufficiently smaller than the second region. The area of the second region Cs (xs, ys) is Ss, for example, about 1 μm square. Hereinafter, the second area is referred to as a small cell. Symbols xs and ys in () of the symbol Cs representing the small cell also represent the number of each small cell instead of the coordinates.
For each of the small cells Cs (xs, ys), the backscattering energy component BE for the exposure amount distribution D (x, y)₀(Xs, ys) is obtained.
Backscatter energy component BE₀(Xs, ys) is given by the following equation using the pattern area ratio Ps (xs, ys) in the small cell with the number (xs, ys).
[0042]
[Equation 14]

[0043]
Equation (14) also takes into account the effect of backscattering due to shots in small cells in the periphery of the target small cell Cs (xs, ys), and convolution uses small cell Cs (xs, ys). The calculation is performed in the backscattering range BS, which is the center and is the range to which the backscattering reaches. Symbols r and s are variables used in calculations for small cells.
[0044]
As described above, the exposure amount for the sample needs to be corrected in consideration of the influence of backscattering and the influence of fogging exposure.
In the present embodiment, the fog exposure energy component FE₀(Xl, yl) and the backscattered energy component BE₀Using (xs, ys), the correction exposure amount is calculated for each small cell. In this case, as the fog exposure energy component for each small cell Cs (xs, ys), the fog exposure energy component FE for the large cell Cl (xl, yl) including the small cell Cs (xs, ys).₀(Xl, yl) shall be used.
Corrected exposure amount D in the first embodiment_conv.(Xs, ys) can be calculated as follows using Expressions (13) and (14).
[0045]
[Equation 15]

[0046]
Where the symbol D₀Is a fixed exposure amount set in advance. Further, Cs (xs, ys) ⊂Cl (xl, yl) in Equation (15) includes each small cell Cs (xs, ys) when performing an operation on each small cell Cs (xs, ys). Means that the target is within the area of each large cell Cl (xl, yl).
Note that the symbol C in Expression (16) is an arbitrary constant.
This corrected exposure amount D_conv.(Xs, ys) corresponds to the exposure distribution D (x, y).
When actual exposure is performed using the EB lithography apparatus 10, the correction exposure amount D is calculated as shown in Expression (15)._conv.(Xs, ys) is changed to the set exposure₀And this set exposure amount D₀As the product of the exposure amount modulation rates m (xs, ys) that change the magnitude of Since the exposure amount modulation rate m (xs, ys) changes for each small cell, the exposure amount of each shot that exposes each small cell is corrected as a result.
[0047]
However, in the first embodiment, the fog exposure energy component FE of Expression (13) is used.₀(Xl, yl) and the backscattered energy component BE in equation (14)₀When each of (xs, ys) is obtained, a sum based on the area ratio of each cell is used. However, the resulting corrected exposure dose D_conv.Since (xs, ys) is different for each small cell, the actual fog exposure energy from the peripheral pattern is an amount different from the product of the equation (13) and the constant C as seen in the equation (16). In the first embodiment, since the difference is not taken into account, the obtained corrected exposure amount D_conv.The correction accuracy of the exposure amount by (xs, ys) decreases.
[0048]
For example, when patterning both the logic region and the memory region on one resist film, the exposure amount per shot differs between the shot in the logic region and the shot in the memory region. The exposure amount per shot is large in a logic region where patterns are formed at a low density, and is small in a memory region where patterns are formed at a high density.
Therefore, especially when exposing a pattern in which a logic area and a memory area are mixed, the exposure amount is corrected with high accuracy unless a correction exposure amount is calculated in consideration of a difference in the exposure amount depending on such an area. I can't.
Also, the backscatter energy component BE₀Since the coefficient for multiplying the pattern area ratio Ps (xs, ys) in (xs, ys) is set to the constant 2, it is possible to sufficiently correct the dimensional variation that occurs in a post-drawing process such as development or etching. Can not.
In the following embodiment, a correction exposure amount calculation method in which correction accuracy is improved by using a provisional exposure amount modulation rate instead of an area ratio distribution of each cell when obtaining a fog exposure energy component and a backscattering energy component Is described.
[0049]
Second embodiment
An exposure method according to the second embodiment of the present invention will be described along each step of the flowchart shown in FIG. In the following, the symbols appearing in the first embodiment have the same meaning as in the first embodiment, and will not be described.
Step ST1: In the second embodiment, the correction exposure amount is recalculated by repeated calculation, and the correction accuracy of the exposure amount is improved. In this step, the number n of repetitive calculations is set by an integer from 0 to infinity.
Step ST2: Here, an initial value of a counter i for counting the number n of repetitive calculations set in step ST1 is set to i = 0.
[0050]
Step ST3: The provisional exposure amount modulation rate is calculated here before the repetitive calculation. In the second embodiment, the fog exposure energy component and the backscattering energy component are both calculated in small cell units. Therefore, the entire drawing area is divided into small cells.
Assuming that the photosensitive phenomenon with respect to the unit exposure amount is represented by Expression (11) as in the first embodiment, the backscatter energy component BE₀(Xs, ys) and fog exposure energy component FE₀(Xs, ys) is calculated by the following equation by taking the sum of each small cell.
[0051]
(Equation 16)

[0052]
The following provisional exposure amount modulation rate m defined as a variable whose value differs for each small cell using Expressions (17) and (18)._p0(Xs, ys) is calculated.
[0053]
[Equation 17]

[0054]
The symbol A (xs, ys) is a variable that takes into account the pattern dimension variation that occurs in a post-drawing process such as development or etching. Normally, it may be replaced by the constant 2. It is effective to set a value larger than 2 for a point where the dimension is reduced due to development or etching, and conversely, a value smaller than 2 for a point where the dimension is increased.
Equation (19) is an equation for the provisional exposure amount modulation rate obtained as a result of calculation in units of small cells. When Equation (19) is generalized using an (x, y) coordinate system centered on a fixed point represented by coordinates (0, 0), Equations (2), (4), (7), and (9) are obtained. Is obtained. Until the final drawing exposure amount is obtained, the provisional exposure amount modulation rate m_p0(Xs, ys) is assumed to mean the provisional exposure amount.
[0055]
Step ST4: It is determined whether or not the counter i matches the number of repetitions n. If the counter i matches the number of repetitions n and the repetition calculation is not performed, the process proceeds to step ST9.
[0056]
If the counter i does not match the number of repetitions n and the repetition calculation is to be performed, the process proceeds to step ST5 to enter a repetition calculation routine.
[0057]
Step ST5: Increase the number of the counter i by one.
[0058]
Step ST6: If i = 1, provisional exposure amount modulation rate m_P0(Xs, ys), when i ≧ 2, the corrected exposure amount modulation rate m_{P (i-1)}Using (xs, ys), the fog exposure energy component FE_Pi(Xs, ys) is calculated.
[0059]
(Equation 18)

[0060]
Step ST7: Next, similarly, the backscattering energy component BE is calculated by the following equation._Pi(Xs, ys) is calculated.
[0061]
[Equation 19]

[0062]
Step ST8: Fog exposure energy component FE_Pi(Xs, ys) and backscatter energy component BE_Pi(Xs, ys) and the i-th (i ≧ 1) corrected exposure amount modulation rate m_Pi(Xs, ys) is calculated.
[0063]
(Equation 20)

[0064]
It returns to step ST4.
[0065]
Step ST9: Drawing exposure amount D according to the value of the number of repetitions n_E2n(Xs, ys) is D_E2n(Xs, ys) = D₀× m_pn(Xs, ys). When the number of repetitions n = 0, the drawing exposure amount D_E20(Xs, ys) is D_E20(Xs, ys) = D₀× m_P0(Xs, ys).
[0066]
Step ST10: Drawing exposure amount D_E2nExposure is actually performed using (xs, ys).
[0067]
In the successive substitution calculation used in the present embodiment, the sum of the backscattering coefficient η and the fog exposure energy component is calculated by calculating the forward scattering function E accumulated at the pattern edge point._fIf it is larger than the forward scattering energy according to (x, y), convergence is not necessarily guaranteed. However, if the calculation is repeated 5 to 6 times, it is considered that sufficient accuracy can be obtained as a semiconductor process.
[0068]
Third embodiment
In addition to the general sequential substitution calculation described in the second embodiment, a repetition calculation for correcting the proximity effect is known. The present embodiment is a method for simultaneously correcting the fog exposure and the proximity effect using such a repetitive calculation formula.
[0069]
In the present embodiment, instead of steps ST6 to ST8 of the second embodiment, an error of the backscattering energy component and an error of the fog exposure energy component, which occur when the exposure is performed with the correction exposure amount during each iteration during the repetition. The step of calculating a new corrected exposure amount by paying attention to the minute is used.
Steps ST1 to ST5 are the same as those in the second embodiment and are omitted (however, the provisional exposure amount modulation rate in step ST3 is m₀(Xs, ys). ), Steps ST16 to ST21 instead of Steps ST6 to ST10 are described below.
[0070]
Step ST16: The error of the fog exposure energy component is calculated by the following equation (23).
[0071]
(Equation 21)

[0072]
Step ST17: The error of the backscattering energy component is calculated by the following equation (24).
[0073]
(Equation 22)

[0074]
Step ST18: Backscatter energy component error DBE_i(Xs, ys) and error DFE of fog exposure energy component_iUsing (xs, ys), the i-th (i ≧ 1) exposure amount modulation rate error m_i(Xs, ys) is calculated.
[0075]
[Equation 23]

[0076]
It returns to step ST4.
[0077]
Step ST19: Corrected exposure amount modulation rate m_pn(Xs, ys) is represented by the following equation as the sum of the modulation rate errors calculated in each repetition step.
[0078]
(Equation 24)

[0079]
Step ST20: The drawing exposure amount D according to the value of the number of repetitions n_E3n(Xs, ys) is D_{E 3n}(Xs, ys) = D₀× m_pn(Xs, ys). When the number of repetitions n = 0, the drawing exposure amount D_E30(Xs, ys) is D_E30(Xs, ys) = D₀× m_P0(Xs, ys).
[0080]
Step ST21: Drawing exposure amount D_E3nExposure is actually performed using (xs, ys).
[0081]
In the present embodiment, it is considered that a practical exposure amount correction accuracy can be obtained with a smaller number of calculations than in the second embodiment. Further, since the fog exposure and the proximity effect are simultaneously corrected, highly accurate correction is possible.
The method of obtaining the provisional exposure amount modulation rate calculated in step ST3 of the second and third embodiments is arbitrary.
[0082]
As described above, in the second and third embodiments, the exposure area is divided into cells, and the fog exposure energy is calculated in consideration of the difference in the shot exposure amount at each position. Further, the difference in the exposure amount of each shot is repeatedly corrected by repeated calculation. Therefore, in the first stage, the correction exposure amount of each shot can be calculated with higher accuracy than in the first embodiment in which the difference in the exposure amount of each shot is not taken into account and the repeated calculation is not performed. Calculating the corrected exposure in consideration of the difference in the exposure of each shot is particularly effective when exposing a device that has a mixture of areas with large pattern area ratios, such as a logic area and a memory area. It is a target.
In the second and third embodiments, the fog exposure energy component is also calculated in units of small cells Cs (xs, ys) like FE (xs, ys). Therefore, also from this point, the exposure amount can be corrected with higher accuracy than in the first embodiment. Since the coefficient to be multiplied by the pattern area ratio is also made variable by the symbol A (x, y)> 0, it is possible to cope with dimensional variations that occur in the process after drawing.
It is conceivable that the variation in the resist dimensions is reduced to 1 nm or less in the second and third embodiments. In addition, it is considered that the dimensional variation occurring in the post-drawing process can be reduced to within 3 nm in the second and third embodiments.
[0083]
However, as described above, the range over which the fogging exposure extends is as wide as a radius of about 50 mm from the exposure point as an example. Therefore, for example, when the blanks 200 of 10 cm □ are divided into small cells of 1 μm □ and the influence of fogging exposure is corrected for each small cell, the number of cells to be corrected is 10 billion, which is practical. It is difficult to perform the correction calculation in time.
In the fourth and subsequent embodiments, a method of calculating a corrected exposure amount that can eliminate the disadvantage and obtain sufficient correction accuracy will be described.
[0084]
Fourth embodiment
An exposure method according to the fourth embodiment of the present invention will be described along with each step of the flowchart shown in FIG. In FIG. 4, FIG. 4A shows a state in which the drawing area is divided into large cells, and FIG. 4B shows a state in which, in one large cell, a region to which backscattering is further divided into small cells.
The calculation method of the correction exposure amount according to the fourth embodiment is, first, to calculate the fog exposure energy component in units of large cells, and to use this fog exposure energy component to reduce the influence of backscattering in small cell units. The correction is performed by repeated calculation.
[0085]
Step ST31: First, as shown in FIG. 4A, the entire drawing area is divided into, for example, 1 mm square large cells. In the following, any one large cell will be represented by the symbol Cl (xl, yl). First provisional exposure amount D for each large cell Cl (xl, yl)_prov(Xl, yl) is defined. In the fourth embodiment, as an example, when exposing the center point of each large cell Cl (xl, yl), the shot exposure amount corrected so as not to cause the proximity effect due to the back scattering is used as the first provisional exposure amount. D_provUsed as (xl, yl).
[0086]
To this end, as shown in FIG. 4B, the area where the back scattering reaches in the center of the small cell Cs (xlc, ylc) and the periphery of the large cell Cl (xl, yl) is, for example, 1 μm. Divide into small cells of □. The range BS to which the backscatter reaches is, as described above, the radius R in FIG._A, For example, within a circle of 25 μm.
In FIG. 4B, the scales of the large cells Cl (xl, yl) and the small cells Cs (xs, ys) are not actual.
[0087]
As shown in FIG. 4B, in each of the large cell Cl (xl, yl) and the small cell Cs (xs, ys), there is a pattern area Pa in which a pattern is to be formed by exposure. The ratio occupied by the pattern area Pa in each of the large cells Cl (xl, yl) and the small cells Cs (xs, ys) is determined by the pattern area ratio Pl (xl, yl) and the small cell Cs (in the large cell Cl (xl, yl), respectively. Let xs, ys) be the pattern area ratio Ps (xs, ys). At this time, the first provisional exposure amount modulation rate m for correcting the proximity effect_prov(Xl, yl) represents the set exposure amount as D₀, And the backscattering energy component can be given by equation (28) as is well known.
[0088]
(Equation 25)

[0089]
Here, the symbol Ps (xlc + r, ylc + s) represents the pattern area ratio of the r-th small cell in the x-axis direction and the s-th small cell in the y-axis direction from the small cell Cs (xlc, ylc). The variable A (xl, yl) may be usually set to 2.
Equation (28) is an equation of a provisional exposure amount modulation rate obtained as a result of calculation in units of small cells. When Equation (28) is generalized using an (x, y) coordinate system centered on a fixed point represented by coordinates (0, 0), Equations (1), (3), (6), and (8) are obtained. Is obtained. Until the final drawing exposure amount is obtained, the provisional exposure amount modulation rate can be regarded as meaning the exposure amount._prov(Xl, yl) is converted to the first provisional exposure amount D_prov(Xl, yl).
[0090]
Step ST32: Calculated first provisional exposure amount modulation rate m_provUsing (xl, yl), a fog exposure energy component is calculated for each large cell Cl (xl, yl) in the same manner as in the first to third embodiments. In the fourth embodiment, the fog exposure energy component is called a provisional fog exposure energy component.
The calculated provisional fog exposure energy component FE_prov(Xl, yl) is represented by the following equation.
[0091]
(Equation 26)

[0092]
Step ST33: The calculated provisional fog exposure energy component FE_prov(Xl, yl), resist threshold sensitivity Eth, set exposure amount D₀, The provisional beam scattering energy E for each first region_prov(Xl, yl) is determined by the following equation.
[0093]
[Equation 27]

[0094]
Step ST34: Hereinafter, iterative calculation for correcting the proximity effect is performed. First, the number n of repeated calculations is set by an integer from 0 to infinity.
[0095]
Step ST35: Here, an initial value of a counter i for counting the number of repetition calculations n set in step ST34 is set to i = 0.
[0096]
Step ST36: The entire drawing area is divided into small cells, and the backscattered energy component BE is used as in the past.₀(Xs, ys) is calculated by the following equation.
[0097]
[Equation 28]

[0098]
Step ST37: Using the provisional beam scattering energy of the equation (30) and the backscattering energy component of the equation (31), a second provisional exposure amount modulation rate m represented by the following equation:_p0(Xs, ys) is calculated. This second provisional exposure amount modulation rate m_p0(Xs, ys), the resist threshold sensitivity of the second embodiment is set to the provisional electron scattering energy E set for each large cell containing a small cell._provIt is calculated by replacing (xl, yl) with a term relating to fog exposure from the calculation formula.
[0099]
(Equation 29)

[0100]
The symbol A (xs, ys) is a variable that takes into account the pattern dimensional variation that occurs in a post-drawing process such as development or etching, and may be replaced by a constant 2 in general.
[0101]
Step ST38: It is determined whether or not the counter i matches the number of repetitions n. If the counter i matches the number of repetitions n and the repetition calculation is not performed, the process proceeds to step ST42.
[0102]
If the counter i does not match the number of repetitions n, and the repetition calculation is to be performed, the process proceeds to step ST39 to enter a repetition calculation routine.
[0103]
Step ST39: The number of the counter i is increased by one.
[0104]
Step ST40: If i = 1, the second provisional exposure amount modulation rate m_P0(Xs, ys), when i ≧ 2, the corrected exposure amount modulation rate m_{p (i-1)}Using (xs, ys), the backscattered energy component BE_pi(Xs, ys) is calculated.
[0105]
[Equation 30]

[0106]
Step ST41: provisional beam scattering energy E_prov(Xl, yl) and backscatter energy component BE_pi(Xs, ys) and the i-th (i ≧ 1) corrected exposure amount modulation rate m_pi(Xs, ys) is calculated.
[0107]
(Equation 31)

[0108]
It returns to step ST38.
[0109]
Step ST42: A drawing exposure amount D according to the value of the number of repetitions n_E4n(Xs, ys) is D_{E 4n}(Xs, ys) = D₀× m_pn(Xs, ys). When the number of repetitions n = 0, the drawing exposure amount D_E40(Xs, ys) is D_E40(Xs, ys) = D₀× m_P0(Xs, ys).
[0110]
Step ST43: Drawing exposure amount D_E4nExposure is actually performed using (xs, ys).
According to the fourth embodiment, the provisional fog exposure energy component FE_provSince (xl, yl) is calculated in units of large cells Cl (xl, yl), the number of cells for fog exposure correction is significantly reduced as compared with the second and third embodiments, and the calculation time is also reduced. Become.
In detail, for example, when a 10 cm square drawing area is divided into 1 mm square large cells, the number of large cells to be corrected for fogging exposure is 10,000, which is 100 in the second and third embodiments. Significantly less than 100 million.
[0111]
Fifth embodiment
In this embodiment, the provisional beam scattering energy E is exactly the same as in the fourth embodiment._provAfter calculating (xl, yl), the proximity effect correction is calculated for each small cell by the same iterative calculation as in the third embodiment.
The calculation procedure in the fifth embodiment will be described according to the flowchart shown in FIG. 6, but steps ST31 to ST39 in FIG. 6 are the same as those in the fourth embodiment, and a description thereof will be omitted.
[0112]
Step ST50: An error of the backscattering energy component is obtained by the following equation.
[0113]
(Equation 32)

[0114]
Step ST51: Backscattering energy error DBE of equation (35)_iUsing (xs, ys), the i-th (i ≧ 1) corrected exposure amount modulation rate m_i(Xs, ys) is calculated from the following equation.
[0115]
[Equation 33]

[0116]
It returns to step ST38.
[0117]
Step ST52: Correction exposure amount modulation rate m_pn(Xs, ys) is expressed by the following equation as the total sum of the exposure amount modulation rate errors calculated in each repetition step.
[0118]
(Equation 34)

[0119]
Step ST53: According to the value of the number of repetitions n, the drawing exposure amount D_E5n(Xs, ys) is D_E5n(Xs, ys) = D₀× m_pn(Xs, ys). When the number of repetitions n = 0, the drawing exposure amount D_E50(Xs, ys) is D_E50(Xs, ys) = D₀× m_P0(Xs, ys).
[0120]
Step ST54: Drawing exposure amount D_E5nExposure is actually performed using (xs, ys).
[0121]
Also in the fifth embodiment, the provisional fog exposure energy component FE_provSince (xl, yl) is calculated in units of the large cell Cl (xl, yl), the calculation time is shortened as in the case of the fourth embodiment.
Further, since the fog exposure and the proximity effect are simultaneously corrected, highly accurate correction is possible.
[0122]
The correction accuracy of the fourth and fifth embodiments is the first provisional exposure amount D set for each large cell._provFirst provisional exposure amount modulation rate m relating to (x, y)_prov(Xl, yl) is the final corrected exposure amount modulation rate m calculated for each small cell._Pn(Xs, ys) depending on whether or not the following equation is satisfied.
Note that the first provisional exposure amount modulation rate m_prov(Xl, yl) and the first provisional exposure amount D_prov(X, y) and the final corrected exposure amount modulation rate m_Pn(Xs, ys) and the final corrected exposure amount are D_corThere is a direct correlation with (xs, ys). Therefore, the following equation (38) can be regarded as meaning equations (5) and (10).
[0123]
(Equation 35)

[0124]
In each large cell, the first provisional exposure amount modulation rate only needs to be the average value of the final corrected exposure amount modulation rate. However, the first provisional exposure amount modulation rate given in step ST31 of the fourth and fifth embodiments may be used. Whether or not the exposure amount modulation ratio satisfies the relationship of Expression (38) depends on the pattern distribution. Therefore, if the method of giving the first provisional exposure amount modulation rate in step ST31 and the method of repeated calculation after step ST40 or step ST50 are combined, many variations of the fourth and fifth embodiments can be considered. .
In the sixth embodiment, an example will be described in which the fog exposure energy component is also taken into account when giving the first provisional exposure amount.
[0125]
Sixth embodiment
The present embodiment uses the fog exposure energy calculated for each large cell and the backscattering energy component calculated for each central point of the large cell in order to more accurately satisfy the relationship of Expression (38). And the provisional exposure amount modulation rate m similar to that of the third embodiment._provIn this embodiment, (xl, yl) is calculated for each large cell.
Since the basic flow is the same as that of the fifth embodiment, the flow chart shown in FIG. 6 will be described below.
[0126]
Step ST31: In step ST31 of the sixth embodiment, the entire drawing area is divided into large cells Cl (xl, yl), and the periphery of the central point of the large cell is divided into small cells. The small cell at the central point is defined as Cs (xlc, ylc), and the backscattered energy component BE for each large cell including the central point.₀(Xlc, ylc) and fog exposure energy component FE₀(Xl, yl) is calculated by the following equation.
[0127]
[Equation 36]

[0128]
Using the equations (39) and (40), the first provisional exposure amount modulation rate m for each large cell is calculated._prov(Xl, yl) is calculated by the following equation.
[0129]
(37)

[0130]
Hereinafter, since the steps after step ST32 are the same as those in the fourth or fifth embodiment by selecting the method of the repetitive calculation, the description is omitted.
[0131]
Exposure amount modulation factor m for correcting fog exposure for each large cell in order to suppress increase in calculation time_provAfter calculating (xl, yl), the proximity effect correction may be performed for each small cell after removing the influence of the fog exposure energy component. Temporary fog exposure energy component FE assumed before calculation of proximity effect correction_provIf (xl, yl) is the same as the actual fogging exposure energy component when the exposure is performed with the final corrected exposure amount, it may be considered that the accuracy of the correction calculation is increased.
[0132]
In the fourth to sixth embodiments, it is considered that the variation in the resist dimension can be made within 3 nm. In addition, it is possible to cope with dimensional variations that occur in a process after drawing such as etching, and it is considered that the dimensional variations in the subsequent processes can be made within 5 nm in the fourth to sixth embodiments. Further, according to the fourth to sixth embodiments, it is possible to calculate the exposure amount within the same time as the conventional case.
[0133]
As described above, the contents of the present invention have been described with reference to various embodiments, but the present invention is not limited to the above embodiments and the matters described in the drawings.
For example, the order of each step such as the step of calculating each energy component in each flowchart, the step of defining the number of repetitions n, and the step of increasing the counter can realize the contents of the present invention described in the claims. If so, it is optional. Also, the flow of the repetitive calculation may be any flow as long as the intended drawing exposure amount is finally obtained.
It is obvious that the description of the function in the claims and the embodiments can be changed by appropriately changing the changeable portion such as the coefficient of the photosensitive function with respect to the unit exposure irradiation shown in the equation (11).
In addition, the present invention can be applied to a device other than a photomask such as a silicon substrate as long as a pattern can be drawn by an exposure beam.
[0134]
【The invention's effect】
As described above, according to the present invention, in addition to the influence of the proximity effect, the influence of the fog exposure can be corrected with high accuracy by calculating the exposure amount of each shot in consideration of the influence of the fog exposure. Thus, it is possible to provide an exposure method whose correction calculation time is equivalent to that of the conventional case.
Further, according to the present invention, it is possible to highly accurately correct not only the effect of the proximity effect but also the effect of fog exposure, and it is also possible to provide an exposure apparatus whose correction calculation time is equivalent to that of the conventional case.
[Brief description of the drawings]
FIG. 1 is a schematic configuration diagram of a main part of an EB lithography apparatus according to a first embodiment of the present invention.
FIG. 2 is a flowchart for describing an exposure method according to a second embodiment of the present invention.
FIG. 3 is a flowchart for describing an exposure method according to a third embodiment of the present invention.
FIG. 4 is a view showing a state where a drawing area is divided, FIG. 4 (a) shows a state where the drawing area is divided into large cells, and FIG. 4 (b) is a view showing FIG. In a large cell among the large cells shown in FIG. 5, a region in which backscattering is exerted is further divided into small cells.
FIG. 5 is a flowchart for describing an exposure method according to a fourth embodiment of the present invention.
FIG. 6 is a flowchart for describing an exposure method according to a fifth embodiment of the present invention.
FIG. 7 is a diagram showing a state of fog exposure that occurs in exposure of a resist using an EB lithography apparatus.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 10 ... EB drawing apparatus, 20 ... EB drawing apparatus main body, 50 ... Control device, 100 ... Barrel, 120 ... Electron gun, 200 ... Blanks, 210 ... Substrate, 220 ... Light shielding film, 230 ... Resist film

Claims (20)

For each position of the sample on which the resist is applied, using a provisional exposure amount having a different value according to each position, including the influence from the peripheral portion of each position to each position, a backscattered energy component and A first step of calculating a fog exposure energy component;
A second step of calculating a correction exposure amount for each position based on the fog exposure energy component and the backscatter energy component;
The first step and the second step are repeated a predetermined number of times using the corrected exposure amount at each position as the provisional exposure amount, and a final corrected exposure amount is calculated for each position. Exposing the resist at each of the positions using an exposure beam having a typical correction exposure amount. A first step of dividing the resist-coated sample into a plurality of first regions that are sufficiently smaller than a fog exposure radius, and defining a first provisional exposure amount having a different value for each of the first regions; ,
A second calculating unit that calculates a provisional fog exposure energy component by using the first provisional exposure amount for each of the first regions, including an influence from the first region around the first region; Steps and
A third step of calculating a provisional beam scattering energy for each of the first regions based on the provisional fog exposure energy component;
The entire surface of the sample is divided into the first region and a plurality of second regions that are sufficiently smaller than the backscattering diameter, and the provisional beam scattering energy in the first region including the second region is calculated. A fourth step of calculating a second provisional exposure amount for each of the second regions based on the second step;
Fifth, for each of the second regions, a backscattering energy component including an influence from the second region around the second region is calculated using the calculated second provisional exposure amount. Steps and
A correction exposure amount is calculated for each of the second regions based on the provisional beam scattered energy in the first region including the second region and the backscattered energy component for each of the second regions. The sixth step,
The fifth and sixth steps are repeated a predetermined number of times using the corrected exposure amount as the second provisional exposure amount, and a final corrected exposure amount is calculated for each of the second areas, and the final correction amount is calculated. Exposing the resist for each of the second regions using an exposure beam of an exposure amount. The provisional exposure amount D _prov (x, y) at each of the positions is
A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a normalized backscattering function Eb (x, y) representing an energy distribution due to backscattering of the exposure beam, and a backscattering coefficient η, a function P (x, y) = {1 pattern area / 0 non-pattern area} representing a drawing pattern distribution of the sample, an arbitrary variable A (x, y)> 0, and a resist sensitivity Eth. The exposure method according to claim 1, which is given by the following equation.

The provisional exposure amount D _prov (x, y) at each of the positions is
A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a range FG covered by the fog exposure energy component, and a normalized backscattering function representing an energy distribution due to backscattering of the exposure beam. Eb (x, y), the backscattering coefficient η, the fog exposure function Fog (x, y) representing the distribution of the fog exposure energy component, and the function P (x, y) representing the drawing pattern distribution of the sample = The exposure method according to claim 1, wherein the value is given by the following equation using {1 pattern area / 0 non-pattern area}, arbitrary variable A (x, y)> 0, and resist sensitivity Eth.

A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a normalized backscattering function Eb (x, y) representing an energy distribution due to backscattering of the exposure beam, and a backscattering coefficient η, a function P (x, y) = {1 pattern area / 0 non-pattern area} representing a drawing pattern distribution of the sample, an arbitrary variable A (x, y)> 0, and a resist sensitivity Eth,
Dividing a range BS of the backscattered energy component around a specific point defined in advance in the first area into cell units representing the second area,
3. The method according to claim 2, wherein the first provisional exposure amount defined for each of the first areas is given as a value D _prov (x, y) obtained by calculating the integral of the following equation and adding the integral by the cell representing the second area. Exposure method according to 1.

6. The exposure method according to claim 5, wherein the arbitrary variable A (x, y) is given by being arbitrarily set for each of the second regions. A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a range FG covered by the provisional fogging exposure energy component, and a normalized backscattering representing an energy distribution due to backscattering of the exposure beam. A function Eb (x, y), a backscattering coefficient η, a fog exposure function Fog (x, y) representing the distribution of the provisional fog exposure energy component, and a function P (x, y) representing the drawing pattern distribution of the sample ) = {1 pattern area / 0 non-pattern area}, arbitrary variable A (x, y)> 0, and resist sensitivity Eth,
Dividing a range BS of the backscattered energy component around a specific point defined in advance in the first area into cell units representing the second area,
The first provisional exposure amount defined for each of the first regions is calculated by summing the integral of the backscattering function Eb (x, y) in the following equation by a cell unit representing the second region, 3. The exposure method according to claim 2, wherein the integral relating to the fog exposure function Fog (x, y) is given as a value D _prov (x, y) calculated by summation in units of cells representing the first area.

The exposure method according to claim 7, wherein the arbitrary variable A (x, y) is given by being arbitrarily set for each of the second regions. The cell unit representing the first area is Cl (xl, yl), the cell unit representing the second area is Cs (xs, ys), and the final corrected exposure amount calculated for each of the second areas Is D _cor (xs, ys), the drawing pattern area ratio of the first region is P (xl, yl), the drawing pattern area ratio of the second region is P (xs, ys), and the first region is Is the area of S1, and the area of the second region is Ss,
3. The exposure method according to claim 2, wherein the first provisional exposure amount D _prov (xl, yl) defined for the first area is provided so as to satisfy the following expression. 4.

The provisional beam scattering energy calculated for each of the first regions is set in advance by setting the sensitivity of the resist and the provisional fog exposure energy component calculated for each of the first regions including the second region. The exposure method according to claim 2, wherein the difference is given as a difference between the product of the exposure amount and the product. Exposure means for irradiating the resist-coated sample with an exposure beam,
For each position of the sample, computing means for calculating the amount of exposure by the exposure beam,
Control means for giving to the exposure means a command signal for irradiating the exposure beam at which the exposure amount at each position is the calculated exposure amount,
The calculating means includes:
Using a provisional exposure amount having a different value according to each position, including the influence from the peripheral portion of each position to each position, a backscattering energy component, and calculating a fog exposure energy component,
Based on the fog exposure energy component and the backscatter energy component, calculate a correction exposure amount for each position,
Calculation of a new correction exposure amount by using the correction exposure amount of each position as the provisional exposure amount is repeated a predetermined number of times to calculate a final correction exposure amount for each position, and the final correction An exposure apparatus for setting an exposure amount to the exposure amount. Exposure means for irradiating the resist-coated sample with an exposure beam,
For each position of the sample, computing means for calculating the amount of exposure by the exposure beam,
Control means for giving to the exposure means a command signal for irradiating the exposure beam at which the exposure amount at each position is the calculated exposure amount,
The calculating means includes:
The sample is divided into a plurality of first regions that are sufficiently smaller than a fog exposure radius, and a first provisional exposure amount having a different value for each first region is defined;
For each of the first regions, using the first temporary exposure amount, including the influence from the first region around the first region, calculate a temporary fog exposure energy component,
Calculating a provisional beam scattering energy for each of the first regions based on the provisional fog exposure energy component;
The entire surface of the sample is divided into the first region and a plurality of second regions that are sufficiently smaller than the backscattering diameter, and the provisional beam scattering energy in the first region including the second region is calculated. Calculating a second provisional exposure amount for each of the second regions,
Using the calculated second provisional exposure amount, for each of the second regions, calculate the backscattering energy component including the influence from the second region around the second region,
Calculating a corrected exposure amount for each of the second regions based on the provisional beam scattered energy in the first region including the second region and the backscattered energy component for each of the second regions; ,
The calculation of a new corrected exposure amount by using the corrected exposure amount as the second provisional exposure amount is repeated a predetermined number of times to calculate a final corrected exposure amount for each of the second regions, and the final correction amount is calculated. An exposure apparatus for setting an exposure amount to the exposure amount. The provisional exposure amount D _prov (x, y) at each of the positions is
A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a normalized backscattering function Eb (x, y) representing an energy distribution due to backscattering of the exposure beam, and a backscattering coefficient η, a function P (x, y) = {1 pattern area / 0 non-pattern area} representing a drawing pattern distribution of the sample, an arbitrary variable A (x, y)> 0, and a resist sensitivity Eth. The exposure apparatus according to claim 11, which is given by the following equation.

The provisional exposure amount D _prov (x, y) at each of the positions is
A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a range FG covered by the fog exposure energy component, and a normalized backscattering function representing an energy distribution due to backscattering of the exposure beam. Eb (x, y), the backscattering coefficient η, the fog exposure function Fog (x, y) representing the distribution of the fog exposure energy component, and the function P (x, y) representing the drawing pattern distribution of the sample = The exposure apparatus according to claim 11, wherein the following equation is given using {1 pattern area / 0 non-pattern area}, arbitrary variable A (x, y)> 0, and resist sensitivity Eth.

A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a normalized backscattering function Eb (x, y) representing an energy distribution due to backscattering of the exposure beam, and a backscattering coefficient η, a function P (x, y) = {1 pattern area / 0 non-pattern area} representing a drawing pattern distribution of the sample, an arbitrary variable A (x, y)> 0, and a resist sensitivity Eth,
Dividing a range BS of the backscattered energy component around a specific point defined in advance in the first area into cell units representing the second area,
13. The first provisional exposure amount defined for each of the first areas is given as a value D _prov (x, y) obtained by calculating the integral of the following equation by summation in units of cells representing the second area. Exposure apparatus according to 1.

16. The exposure apparatus according to claim 15, wherein the arbitrary variable A (x, y) is given by being arbitrarily set for each of the second areas. A predetermined set exposure amount D ₀ , a range BS covered by the backscattering energy component, a range FG covered by the provisional fogging exposure energy component, and a normalized backscattering representing an energy distribution due to backscattering of the exposure beam. A function Eb (x, y), a backscattering coefficient η, a fog exposure function Fog (x, y) representing the distribution of the provisional fog exposure energy component, and a function P (x, y) representing the drawing pattern distribution of the sample ) = {1 pattern area / 0 non-pattern area}, arbitrary variable A (x, y)> 0, and resist sensitivity Eth,
Dividing a range BS of the backscattered energy component around a specific point defined in advance in the first area into cell units representing the second area,
The first provisional exposure amount defined for each of the first regions is calculated by summing the integral of the backscattering function Eb (x, y) in the following equation by a cell unit representing the second region, 13. The exposure apparatus according to claim 12, wherein the integral relating to the fog exposure function Fog (x, y) is given as a value D _prov (x, y) calculated by summation in units of cells representing the first area.

18. The exposure apparatus according to claim 17, wherein the arbitrary variable A (x, y) is given by being arbitrarily set for each of the second regions. The cell unit representing the first area is Cl (xl, yl), the cell unit representing the second area is Cs (xs, ys), and the final corrected exposure amount calculated for each of the second areas Is D _cor (xs, ys), the drawing pattern area ratio of the first region is P (xl, yl), the drawing pattern area ratio of the second region is P (xs, ys), and the first region is Is the area of S1, and the area of the second region is Ss,
13. The exposure apparatus according to claim 12, wherein the first provisional exposure amount _Dprov (xl, yl) defined for the first area is provided so as to satisfy the following expression.

The provisional beam scattering energy calculated for each of the first regions is set in advance by setting the sensitivity of the resist and the provisional fog exposure energy component calculated for each of the first regions including the second region. 13. The exposure apparatus according to claim 12, wherein the difference is given as a difference between the product of the exposure amount and the product.

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