JP2004501355A - Real-time evaluation of stress field and characteristics of line structure formed on substrate - Google Patents

Abstract

A method and system for evaluating the stress of a line structure formed on a substrate. The stress can be calculated from the information of the measured curvature based on a simple analytical function. The curvature information can be obtained optically by, for example, a coherent gradient sensing method capable of performing a full-field measurement of an irradiation area.

Description

【００３３】
前掲Ｗｉｋｓｔｒｏｍらの分析法に基づいて、各ライン構造４０２の容積平均応力は、基板４００のｘ_１方向（すなわち縦方向）に沿った曲率ｋ_１、ｘ_２方向（すなわち横方向）に沿った曲率ｋ_２によって下記式で表すことができる。
【００３４】
【数２】

【００３５】
上記式中、σ_αβは応力テンソル成分（α、β＝１、２）を表し、そしてＥ_Ｓとν_Ｓはそれぞれ、基板４００のヤング率とポアソン比である。剪断応力σ_１２の容積平均値はこの場合ゼロである。式（１）の負の符号「−」は、選ばれた符号規約を実行するために使用する。すなわち、正の値は一方向の曲率を表し、一方、負の値は逆方向の曲率を表す。とりわけ、各応力成分は、ｆ_１（Ｅ_Ｓ、ν_Ｓ、ｈ、ｔ、ｄ、ｂ）・ｋ_１＋ｆ_２（Ｅ_Ｓ、ν_Ｓ、ｈ、ｔ、ｄ、ｂ）・ｋ_２で表される線形合計（ｌｉｎｅａｒ ｓｕｍ）である。なお式中の係数ｆ_１とｆ_２はＥ_Ｓ、ν_Ｓ、ｈ、ｔ、ｄ及びｂの関数である。したがって、各ライン構造の応力は、基板の弾性特性及びライン構造の形態に基づいて計算することができる。
【００３６】
したがって、基板４００の各ライン構造４０２における曲率の測定値は、基板４００と各ライン構造４０２の寸法パラメータ、基板４００の弾性特性（例えばヤング率とポアソン比）に基づいて、簡単な解析関数で、容積平均弾性応力を求めることができるようにする。この方法の一つの特徴は、式（１）による応力計算が、ライン構造自体の材料組成、機械的特性などの特性に関する詳細な情報を必要としないことである。ライン構造のこれらの特性は、ライン構造の応力挙動を決定する主要な要因であるが、これら特性の効果は、ライン構造に沿った曲率ｋ_１とライン構造を横切る曲率ｋ_２の測定値に含まれている。
【００３７】
この方法のもう一つの特徴は、式（１）が単純な分析式であるので、測定された曲率ｋ_１とｋ_２に基づいた応力の計算を、プロセッサによって、短時間で行えることである。例えば、マイクロプロセッサを使用してコンピュータルーチンを行い、式（１）に示す計算を実施することができる。したがって、複雑で時間がかかる数値計算は事実上回避される。その上に、式（１）で表される単純な分析式は、無限要素分析法（前掲Ｗｉｋｓｔｒｏｍの文献）に基づいた複雑な数値計算と比べて正確であることが分かった。データ処理モジュールの、ＣＧＳ光学的検出モジュールの全界並行処理と組み合わせたときのこの特徴によって、図１に示す応力測定システム１００は、比較的高い速度で、ある位置の曲率を測定してそれぞれの応力を生成することができる。したがって、システム１００を使用して、ライン構造の曲率及び関連する応力の時間的変化を、半導体製造の多数の工程についてリアルタイムで測定することができる。
【００３８】
式（１）に関する上記応力計算方法は、ライン構造が形成されている薄膜の情報を利用できない場合に、基板上のライン構造の応力データを得る方法を提供する。この状況の例は、完成したＩＣ回路などの、ライン構造が薄膜で製造された後の装置の応力を確認する場合である。
【００３９】
図５は、式（１）に基づいた上記応力測定法のフローチャートである。この応力測定は、基板の製造が完了した後又は製造中に、系内監視機構として実施できる。
【００４０】
基板及び薄膜の曲率がパターン化の前に測定できるならば、本願の別法を利用して、基板上の薄膜からパターン化されたライン構造の応力を、ライン構造が形成される前でも確認することができる。この状況の一例は、図１に示す曲率測定システム１００を使用することによる、製造中の系内測定である。
【００４１】
第一に、層が基板上に形成される前に、裸の基板の曲率マップを測定する（したがって関連する応力のマップが測定される）。基板及びそののち基板上に堆積された連続薄膜が事実上等方性である場合、いずれの位置の曲率もあらゆる方向に沿って同一であるはずである。次に、薄膜が基板上に堆積された後、その連続膜の曲率マップが測定される。対象の位置のパターン化されていない連続膜の応力は下記Ｓｔｏｎｅｙの式で求めることができる。
【００４２】
【数３】

【００４３】
上記式中、ｋ_ｆｉｌｍとｋ_Ｓはそれぞれ、同じ対象位置の、堆積された膜と裸の基板の曲率の測定値である。ここで、膜が堆積される基板表面が凸面である場合、曲率が正の値であり、該表面が凹面の場合負の値であるように符号規約が選ばれる。
【００４４】
反復ライン構造（ｐｅｒｉｏｄｉｃ ｌｉｎｅ ｆｅａｔｕｒｅ）がこの膜上に形成された場合、各ライン構造を横切る曲率ｋ_１と各ライン構造に沿った曲率ｋ_２は、その膜と基板の弾性特性及びライン構造の形態から、下記分析式によって求めることができる。
【００４５】
【数４】

【００４６】
上記式中、ν_ｆｉｌｍは該薄膜のポアソン比であり、χは下記式で表される。
【００４７】
【数５】

【００４８】
そして係数ｄ_ｊは下記表１に示す。ｔ／ｂ→０の場合χ→０であり、そしてｔ／ｂ→∞の場合χ→１であることに留意せよ（前掲のＷｉｋｓｔｒｏｍらの文献参照）。ここでｋ_ｆｉｌｍからｋ_１及びｋ_２への曲率の変化は、単に、膜のライン構造へのパターン化による形態の変化から起こると仮定する。また、ライン構造の弾性特性は膜とほとんど同じであると仮定する。
【００４９】
【表１】

【００５０】
したがって、各ライン構造の容積平均弾性応力は下記式から得ることができる。
【００５１】
【数６】

【００５２】
この方法は、先に述べた方法と同様に、式（２）、（３）及び（４）の単純な分析式を利用して、各ライン構造の応力を計算する。しかし、先に述べた方法と異なり、式（２）に必要な基板の曲率は該膜が堆積される前に測定され、一方、式（１）に必要な基板の曲率ｋ_１とｋ_２はライン構造が基板上に形成された後に測定される。したがって、この方法は、形成されるライン構造の応力を予測するのに利用できる。図６は、式（４）に基づいて行う応力測定のフローチャートを示す。
【００５３】
さらに、式（２）、（３）及び（４）の分析式は、基板上の１又は２以上の薄膜の上に形成されたラインに適用することもできる。この場合、式（２）のパラメータｋ_Ｓは、ライン形成膜が堆積される前の下側の膜と基板によって形成される構造体の総曲率である。この総曲率はＣＧＳ法を使用して直接測定することができる。一次近似として、前記総曲率は、個々の層各々がそれ自体によって基板上に堆積されるならば誘発されるであろう曲率の合計である。
【００５４】
上記応力測定法は、２以上の方向に例えば互いに直角の方向に配向されているライン構造を有する基板を測定するのに適用できる。基板上の対象の全領域は、基板上に形成されたパターンに応じて２以上のサブディビジョン領域に分割して、各サブディビジョン領域が単に、一方向に沿って互いに平行なライン構造を有するようにすることができる。したがって、図４Ａと４Ｂに示す一方向のライン構造のモデルは、個々のサブディビジョン領域に適用して、ＣＧＳによる測定由来の曲率データに基づいて対応する応力を計算することができる。したがって、非直線の単一導電ラインは、異なるサブディビジョン領域内に２以上の異なるセグメントを含んでいることがある。このラインの応力は、ＣＧＳの曲率データに基づいて、異なるセグメントの応力を計算することによって得られる。
【００５５】
図７は基板上に形成されたライン構造の一部分を示し、同部分は二つのサブディビジョン領域ＡとＢを含んでいる。各サブディビジョン領域のライン構造の方向は同じである。サブディビジョン領域ＡとＢは、各領域の端縁から、ラインが方向を変える最も近い鋭角のかどまでの距離が、各ライン構造の一ラインの幅ｂ又は厚さｔより少なくとも大きい値である方式で選択される。この条件は、図４Ａと４Ｂに示すモデルに基づいた応力計算の正確さを維持することができる。サブディビジョン領域ＡとＢは、光学的プローブビームが領域ＡとＢを同時に示すように導かれると、図１に示すシステム１００を使って同時に測定できる。
【００５６】
多くの実用装置において、基板上に形成されるライン構造は、異なる材料中に埋めこまれることが多い。例えば導電ラインは、酸化物などの絶縁性導電材料（ｉｎｓｕｌａｔｉｎｇ ｃｏｎｄｕｃｔｉｖｅ ｍａｔｅｒｉａｌ）中に埋めこまれることが多い。図４Ａと４Ｂに示すモデルは、このような構造体の曲率と応力の分析にもはや適用できない。事実、このような埋めこまれたライン構造の応力を、複雑な数値計算なしで計算することは困難である。しかし、新しいモデルを利用して、埋めこまれたライン構造の曲率を、構造設計、埋めこまれたライン構造の材料特性及びまわりの材料に基づいて計算できる。
【００５７】
図８Ａは、基板８００上に形成された層８２０のトレンチ内に埋めこまれたライン構造８１０の曲率を計算するためのモデルを示す。図４Ａと４Ｂに示すモデルと同様に、基板８００の横方向の寸法は、その厚さｈよりはるかに大きいと仮定する。ライン構造８１０は平行でかつ、基板８００上に間隔ｄの等間隔でｘ_２方向に沿って位置している。また、各ライン構造８１０の幅ｂと厚さｔも、ｘ_１方向に沿ったその縦方向の長さ及び基板８００の厚さｈよりはるかに小さいと仮定する（Ｐａｒｋ及びＳｕｒｅｓｈ、「Ｅｆｆｅｃｔｓ ｏｆ Ｌｉｎｅ ａｎｄ Ｐａｓｓｉｖａｔｉｏｎ Ｇｅｏｍｅｔｒｙ ｏｎ Ｃｕｒｖａｔｕｒｅ Ｅｖｏｌｕｔｉｏｎ ｄｕｒｉｎｇ Ｐｒｏｃｅｓｓｉｎｇ ａｎｄ Ｔｈｅｒｍａｌ Ｃｙｃｌｉｎｇ ｉｎ Ｃｏｐｐｅｒ Ｉｎｔｅｒｃｏｎｎｅｃｔ Ｌｉｎｅｓ」、Ａｃｔａ Ｍａｔｅｒｉａｌｉａ、２０００年４月参照）。
【００５８】
さらに、ライン構造８１０のアスペクト比：ｆ_０＝ｔ／ｂ及びまわりの層８２０に形成されたラインのアスペクト比：ｆ_１＝ｔ／（ｄ−ｂ）は、１に等しいか１より大きくそして、ライン構造８１０に沿った曲率とライン構造８１０を横切る曲率は互いに弾性変形に影響しないと仮定する。ＰａｒｋとＳｕｒｅｓｈの前掲文献によれば、ライン方向ｘ_１のライン構造８１０の曲率ｋ_１及び弾性領域内の温度変化ΔＴによって起こるライン方向ｘ_１に直角の方向の曲率ｋ_２は下記式で表すことができる。
【００５９】
【数７】

【００６０】
【数８】

【００６１】
上記式中次のとおりである。
【００６２】
【数９】

【００６３】
【数１０】

【００６４】
【数１１】

【００６５】
【数１２】

【００６６】
そしてＥ_１、ν_１及びα_１はそれぞれ、ライン構造８１０のヤング率、ポアソン比及び熱膨張係数であり、及びＥ_０、ν_０、α_０はそれぞれ層８２０のヤング率、ポアソン比及び熱膨張係数である。複合体であると類推して、ライン構造８１０（例えば銅ライン）とまわりの層８２０（二酸化ケイ素などの酸化物）を含む層は、ラインの方向のヤング率がＥ_１でラインの方向を横切る方向のヤング率がＥ_２でかつ、ラインの方向の熱膨張係数がα_１でラインの方向を横切る方向の熱膨張係数がα_２の異方性複合層として均質化される。
【００６７】
この簡単な分析結果の予測は、より綿密な無限要素シミュレーションの結果と適度に近いことを示し、偏差は約３〜約１７％であった。酸化物トレンチ内のＣｕラインのいくつかの実用的配置構成の場合、誤差は一般に１７％より小さい。
【００６８】
図８Ｂは、キャッピング不活性化層８３０が、ライン構造８１０と層８２０の上に形成されている別のモデルを示す。不活性化層８３０の厚さが基板８００の厚さよりはるかに薄いと仮定すると、不活性化されたライン構造８１０の、温度の変化ΔＴで起こる弾性変形による曲率は下記式で表すことができる。
【００６９】
【数１３】

【００７０】
【数１４】

【００７１】
上記式中、Ｅ_Ｐ、ν_Ｐ、α_Ｐはそれぞれ、不活性化層８３０のヤング率、ポアソン比及び熱膨張係数である。
【００７２】
図８Ａと８Ｂに示す上記モデルを利用し、基板ベース装置の特定の既知のパラメータに基づいて、基板上に埋めこまれたラインの曲率を計算することができる。上記埋めこまれたラインの応力は、式（５）〜（１２）から直接計算することはできないが、これらモジュールは、図１に示すシステム１００の処理モジュール１０５で実行させて、残留応力がこれら装置に残っているかどうかを確認することができる。
【００７３】
図９は、ＣＧＳ測定値を、図８Ａと８Ｂに示すモデルに基づいた曲率の推定と結びつけて、埋めこまれたラインの応力情報を確認する方法のフローチャートである。第一に、装置の埋めこまれたラインの曲率をＣＧＳ法で測定し次いで図８Ａと８Ｂに示すモデルに基づいて計算する。上記ＣＧＳ測定値はラインの実際の曲率を提供するが、上記曲率計算値は単に弾性変形によって起こる曲率だけである。次にその曲率計算値と曲率の実測値を比較する。これらの値の差は、上記計算値には含まれていない残留応力によって起こる曲率を示す。この残留応力は、装置の正常な作動と望ましい寿命を保証するため、許容レベルより低く保たねばならない。したがって、ラインに沿った方向又はラインを横切る方向の上記差が許容レベルを超えると、装置の信頼性又は性能は許容できないとみなされる。
【００７４】
ＣＧＳ法は現場で測定できるので、上記の方法を利用して、製造工程中の、埋めこまれたラインの応力を監視することができる。上記分析とＣＧＳ測定による曲率の差は、設計時には明らかでない、応力／曲率の発生について実際に進行していることの指標を提供する。したがって、これら装置の製造又は設計の１又は２以上の側面を検査し改変して、残留応力を許容範囲内に減らすことができる。さらに、その系内測定値を利用して、該残留応力が中間ステップにおいて許容レベルを超えた場合、全工程を完了する前に、製造を停止することができる。この監視機構によって、コストを下げかつ製造効率を上げることができる。
【００７５】
式（５）、（６）及び（１１）、（１２）を利用して曲率の測定データをあてはめ、基板又はライン構造のヤング率、熱膨張係数及びポアソン比などのライン構造又は基板の特性を確認することができる。例えば、不活性化層８３０を有する装置において、曲率のＣＧＳ測定値を利用し、式（１１）と（１２）に基づいて、不活性化層８３０の特性を確認することができる。不活性化層８３０の二軸モジュラス（ｂｉａｘｉａｌ ｍｏｄｕｌｕｓ）：Ｅ_{Ｐ ， Ｂ}＝Ｅ_Ｐ／（１−ν_Ｐ）は、不活性化層が堆積される前後の工程中に行ったＣＧＳ測定による測定値ｋ_１ ^ｐａｓｓとｋ_２ ^ｐａｓｓから計算することができる。
【００７６】
埋めこまれたラインを測定する上記方法は、酸化物のトレンチ中に銅の導電ラインをつくる新しい製造法「ダマシーン法（Ｄａｍａｓｃｅｎｅ ｐｒｏｃｅｓｓ）」に適用できる。この技法では、Ｓｉ基板上に形成される回路内の銅の相互接続ラインの形態に合致するように、トレンチが酸化物の層中にエッチングされる。そのエッチングはドライエッチング法を利用して実施される。次いで、これら酸化物のトレンチに、気相化学成長法（ＣＶＤ）又は電気メッキ法を利用してＣｕを充填する。次に、トレンチの上にはみだした余分の銅は、化学−機械研磨法（ＣＭＰ）によって除去し、次いで不活性化層すなわちキャッピング層を該相互接続構造体の最上面の上に堆積させる。
【００７７】
ダマシーン法は研磨による材料の除去を含んでいるので、研磨及びその後の処理を行っている間に曲率が生じたことを知ることは、各種の問題点に対して不可欠である。例えば、ＣＧＳ法を利用する曲率の系内監視は、層が堆積される研磨面の「平坦度」の情報を提供することができる。これは、品質管理に不可欠のステップである。また、曲率発生の知見は、製造中の内部応力の発生の指標も提供する。
【００７８】
さらに、非不活性化ライン及び不活性化ラインの上記分析値を利用して熱サイクリング中の弾性応力の発生をシミュレートすることができ、そしてＣＧＳ測定値とすぐに比較することができる。このような計算の例は、ＰａｒｋとＳｕｒｅｓｈの文献に記載されており、そして無限要素シミュレーション値と比較することによって確認される。
【００７９】
図１に示すシステム１００は、弾性変化によって起こる応力を測定することに加えて、図４Ａと４Ｂに示すモデルに基づいて配置構成し、基板上に形成されたライン構造のいくつかの塑性特性を確認することもできる。基板上に形成されたライン構造は、特定の熱機械的処理によって永久塑性変形を受けることがある。一般に、ライン構造と前記薄膜は、温度が、これらそれぞれのしきい降伏温度Ｔ_１ ^Ｙ及びＴ_ｆ ^Ｙより低い場合、弾性変形を受ける。弾性変形による曲率は温度によって直線的に変化する。しかし、温度がしきい降伏温度Ｔ_１ ^ＹとＴ_ｆ ^Ｙより高いと、塑性変形が起こり、そして曲率は、温度によって、非線形態様で変化する。例えば、塑性変型は、導電ラインに、不活性化中に降伏温度を超える温度で加熱されると起こる。このような塑性変形によって起こった応力を確認することが望ましい。
【００８０】
ライン構造及びそのライン構造が基板上にパターン化されている連続薄膜それぞれの初期の応力なし温度（ｉｎｉｔｉａｌ ｓｔｒｅｓｓ−ｆｒｅｅ ｔｅｍｐｅｒａｔｕｒｅ）をＴ_１ ^０とＴ_ｆ ^０と仮定する。ライン／基板系及び薄膜／基板系の応力なし温度範囲は、ＣＧＳ法を利用し曲率を温度の関数として測定して、実験で確認することができる。未処理の連続薄膜の曲率は上記式（２）に基づいて確認できる。ライン及び薄膜それぞれが、初期応力なし温度から塑性降伏を始める温度への温度変化は下記式で表すことができる。
【００８１】
【数１５】

【００８２】
【数１６】

【００８３】
上記式中Ｚ^ｅは下記式で表される。
【００８４】
【数１７】

【００８５】
上記式中、Ｔ_１ ^ＹとＴ_ｆ ^Ｙはそれぞれ、永久塑性変形が、ライン構造と連続薄膜に起こり始まる温度である。Ｔ_１ ^Ｙ及びＴ_ｆ ^Ｙを超える温度で、ラインと薄膜の曲率は、温度によって非線形で変化し始める。式（１３）〜（１５）は、Ｇｏｕｌｄｓｔｏｎｅ， Ｗｉｋｓｔｒｏｍ， Ｇｕｄｍｕｎｄｓｏｎ及びＳｕｒｅｓｈ、”Ｏｎｓｅｔ ｏｆ Ｐｌａｓｔｉｃ Ｙｉｅｌｄｉｎｇ ｉｎ Ｔｈｉｎ Ｍｅｔａｌ Ｌｉｎｅｓ Ｄｅｐｏｓｉｔｅｄ ｏｎ Ｓｕｂｓｔｒａｔｅｓ”、Ｓｃｒｉｐｔａ Ｍａｔｅｒｉａｌｉａ， ４１巻３号２９７〜３０４頁（１９９９年８月）による分析法に基づいて、図４Ａと４Ｂに示すモデルによって誘導することができる。
【００８６】
式（１３）と（１４）から下記式を得ることができる。
【００８７】
【数１８】

【００８８】
上記温度差の比率はＣＧＳ法を利用して測定することができ、かつパラメータＺ^ｅは式（４）に基づいて計算できるので、ライン構造と薄膜の降伏応力の比率は式（１６）から求めることができる。したがって、ＣＧＳ法は上記分析と共同して、パターン化されたラインの降伏開始を確認するのに役立つ手段を提供する。
【００８９】
上記方法とシステムを利用して、基板、ライン構造又はそれらの上に形成された薄膜の応力の履歴と空間変動（ｓｐａｔｉａｌ ｖａｒｉａｔｉｏｎ）をリアルタイムで測定することができる。特に、コヒーレント・グラジエント・センシング法で得た測定値は、分析計算によって、迅速に処理して、応力と塑性歪の空間変動と時間による変動を得ることができる。基板上のライン構造と膜の塑性変形に関する情報も測定できる。
【００９０】
本発明のいくつもの実施態様を説明してきた。しかし、各種の変型と改善を、本願の特許請求の範囲から逸脱することなく行えることは分かるであろう。
【図面の簡単な説明】
【図１】本発明の一実施態様の応力測定システムのブロック図である。
【図２】コヒーレント・グラジエント・センシング・システムの一実施態様を示す。
【図３】二つの独立した光学的アームを有し、二つの異なる方向の空間シャリング（ｓｐａｔｉａｌ ｓｈｅａｒｉｎｇ）を同時に得るコヒーレント・グラジエント・センシング・システムを示す。
【図４Ａ】本発明の一実施態様の熱弾性モデルの代表的構造体の上面図を示す。
【図４Ｂ】図４Ａに示す構造体の断面図を示す。
【図５】光学的全界表面曲率の測定値に基づいてライン構造の応力を測定する二つの方法を示すフローチャートである。
【図６】光学的全界表面曲率の測定値に基づいてライン構造の応力を測定する二つの方法を示すフローチャートである。
【図７】基板上のパターン化されたライン構造の二つの代表的サブディビジョン領域を示す。
【図８Ａ】基板上の層中に埋めこまれたライン構造のモデル及び基板上の層に埋めこまれて不活性化層でキャップされたライン構造のモデルを示す。
【図８Ｂ】基板上の層中に埋めこまれたライン構造のモデル及び基板上の層に埋めこまれて不活性化層でキャップされたライン構造のモデルを示す。
【図９】図１に示すシステムを用いて、基板上の層に埋めこまれたライン構造の曲率を測定する方法を示すフローチャートである。[0001]
This application claims the benefit of US Patent Application Serial No. 09 / 560,719, filed April 27, 2000.
[0002]
background
The present application relates to the evaluation of stress fields and characteristics of line features formed on a substrate.
[0003]
There are important uses for measuring various properties of a substrate and the structures formed on the substrate. For example, manufacturing a particular device requires manufacturing various structures and components on a substrate (eg, a semiconductor or glass substrate). Such substrate-based integrated devices include, inter alia, integrated electronic circuits in which microcircuit elements are formed on a semiconductor substrate; integrated optical devices in which microscopic optical elements are manufactured on the substrate; A micro electromechanical system in which mechanical elements such as small actuators are manufactured on a semiconductor substrate; a flat panel display system in which elements such as light emitting devices and thin film transistors are manufactured on a transparent substrate [for example, the device is transparent Manufactured on a substrate (eg, glass)]; or a combination of two or more of these devices.
[0004]
Different materials and different structures are typically formed on the substrate and in contact with each other. Also, some devices utilize complex multilayer configurations. Thus, when different materials and different structures are brought into contact, complex structures within each structure due to differences in material and structural characteristics at the interconnect under different manufacturing methods and environmental factors (eg, temperature fluctuations or fluctuations). Stress states can occur. When fabricating integrated circuits, for example, the stress state of interconnect conductive lines is affected by thin film deposition, short thermal etching, chemical-mechanical polishing, and passivation during the fabrication process.
[0005]
Measures stress on various structures formed on a substrate to improve device design, material selection, manufacturing processes, and other aspects of the device to improve device performance and reliability. It is desirable to do. These stress measurements can be used to assess or evaluate the reliability of materials that prevent failure based on phenomena such as electromigration, stress voiding, and hillock formation. These stress measurements can also be used to facilitate quality control of the mechanical integrity and electromechanical functions of circuit chip dies during large-scale production at wafer fabs. In addition, these stress measurements can be used to improve various heat treatments (eg, temperature excursion during passivation) and chemical-mechanical treatments (eg, polishing) to reduce the residual stress of the final product equipment. The contribution of processing can be reduced.
[0006]
Overview
The system according to an embodiment of the present invention includes an optical detection module for obtaining surface curvature information of a substrate base device having a line structure formed on a substrate, and stress information of the line structure based on the curvature information. Is provided. The optical detection module may include a coherent gradient sensing system that measures a surface gradient of the surface based on phase information in a wavefront of the reflected beam of the optical probe.
[0007]
One method of an embodiment is to first measure a first curvature of the substrate at a location along a longitudinal direction of a line structure formed at a location on the substrate, and then to measure a transverse direction perpendicular to said longitudinal direction. Measuring the second curvature of the substrate at the same location along. Next, a stress applied to the line structure is calculated based on the measured first and second curvatures using an analytical function.
[0008]
Alternatively, the stress of the line structure may be checked before the line structure is formed. In this method, the curvature of the substrate is measured before the thin film is deposited. In this case, the thin film is deposited on a substrate, and then its curvature is measured. Next, stress information of the deposited thin film is obtained, and using this, the stress applied to the line structure is confirmed, and the thin film is patterned based on an analytical function. This method can be extended to structures where the line structure is formed on two or more thin films located on the substrate.
[0009]
Another method confirms stress information of a line structure embedded in a trench of a layer formed on a substrate. The curvature of the embedded line structure is measured using an optical probe beam and a curvature map of the illuminated area is obtained based on the spatial gradient information in the reflected light beam. Next, the measured curvature is compared with the curvature of the line structure calculated from the analytical function. Next, the existence of the residual stress is confirmed using the deviation.
[0010]
Yet another method is to measure the curvature of the line structure and the thin film on which the line structure is formed as a function of temperature so that the line and the thin film can determine the dependence of their curvature on the temperature from a linear system to a non-linear method. Check the yield temperature to change to the linear method. Next, the ratio between the yield stress of the line structure and the yield stress of the thin film at each yield temperature can be confirmed from the analytical function.
[0011]
These and other features of the present invention, and the attendant advantages thereof, will be apparent from the description and drawings, and from the claims.
[0012]
Detailed description
The method and system of the present application provide at least one optical detection mechanism for measuring a parameter of a curvature of a line structure formed on a substrate and a process for deriving stress information of the line structure from the measured curvature parameter. It has a mechanism. The optical detection mechanism is a full-field measurement that simultaneously measures the curvature of one or more regions where the line structure is located, without performing conventional point-to-point scanning measurements. Can provide the ability. The processing mechanism can directly calculate the stress based on the analytical formula using only the curvature information, and can eliminate complicated numerical calculations. Therefore, the stress information can be obtained within a short processing time. By combining the whole-field optical detection with the process, a spatial map of the stress distribution in the area under measurement can be created in virtually real time as long as the change in stress is slower than the process time.
[0013]
FIG. 1 illustrates an embodiment of a stress measurement system 100 that includes an optical detection module 102 that performs the optical detection mechanism and a data processing module 105 that performs the processing mechanism. The optical detection module 102 generates an illumination light beam 103 on the surface of the sample substrate 130 and then detects the reflected beam 104. The illumination beam 103 is directed to illuminate a region including one or more regions having a line structure under measurement. Next, the reflected beam 104 from the sample substrate 130 is optically processed to generate an optical pattern having curvature information for the entire irradiated area. This optical pattern is converted into a curvature signal 106. This signal is sent to a processing module 105, which may include a processor, such as an electronic processor. The curvature signal 106 may be an electronic signal representing the optical pattern. This signal is then processed to generate curvature data for the entire illuminated area on substrate 130. The processing module 105 generates desired stress data for a line structure formed at one or more desired positions of an irradiation area on the substrate 130 based on the respective curvature data.
[0014]
FIG. 2 illustrates one embodiment of a coherent gradient sensing (“CGS”) system 200 as an example of an optical detection module 102 (see US Pat. No. 6,031,611 to Rosakis et al.). The CGS system 200 uses the collimated coherent light beam 112 from the light source 110 as an optical probe to obtain curvature information indicative of a specular surface 130 of virtually any material. Beam 112 can be directed to surface 130 using an optical element 120 such as a beam splitter. If the reflective surface 130 is curved, the wavefront of the reflected probe beam 132 will be distorted, so that the reflected probe beam 132 will acquire an optical distance difference or phase change related to the curvature of the surface 130 under measurement. . The system generates a "snapshot" of each point in the illuminated area on the surface 130, so that it can obtain curvature information for any point along any direction within the illuminated area. This eliminates the need to measure points one at a time in a sequential manner using a scanning system.
[0015]
Two spaced gratings 140 and 150 are positioned in the path of the reflected probe beam 132 to manipulate the distorted wavefront and measure curvature. The two diffraction components generated by the second grating 150 that diffract the two different diffraction components generated by the first grating 140 are combined using an optical element 160 such as a lens and interfere with each other. Diffraction by the two gratings 140 and 150 causes a relative spatial displacement or phase shift between the two selected diffraction components. This phase shift is a function of the spacing between the two gratings 140 and 150 when other grating parameters are fixed. A spatial filter 170 is positioned relative to the optical element 160 to transmit the interference pattern of the selected diffractive component and block other diffractive orders from the second grating 150.
[0016]
The transmitted interference pattern is then acquired by an imaging sensor 180, which may include an array of sensing pixels, such as a CCD array, to generate an electrical signal representative of the interference pattern. A signal processor 190, which is part of the processing module 105 shown in FIG. 1, processes the electrical signal to derive a spatial gradient of phase distortion caused by the curvature of the reflective surface 130. This spatial gradient can then be further processed to obtain curvature information, so that a curvature map of the illuminated area of surface 130 can be obtained. A single spatial differentiation is performed on the interference pattern to measure the surface gradient. This method corrects the curvature of the surface exactly when the variation of the curvature of the surface is a gradual variation, ie when the out-of-plane displacement is less than the thickness of the thin film, line or substrate. Can be measured. This method is less responsive to rigid body motion than some other interferometry. The details of this data processing operation are described in US Pat. No. 6,031,611 to Rosakis et al., Cited above.
[0017]
Generally, the two gratings 140 and 150 may be gratings having different grating periods and being oriented at an arbitrary angle with respect to each other. The two gratings are preferably oriented in the same direction as one another and have the same grating period to simplify data processing. In this case, the orientation of the grating is effectively set by the direction of the relative spatial displacement ("shearing") between the two selected diffraction components due to double diffraction by gratings 140 and 150.
[0018]
Certain applications may require two different directions of spatial shearing to make a two-dimensional curvature measurement across the world. This uses the CGS system 200 to make a first measurement when the sample surface 130 is oriented in a first orientation direction, and then to make the sample surface 130 in a second orientation direction (eg, with respect to the first orientation direction). (Right angle direction) by performing a second measurement. Alternatively, a two-arm CGS system as shown in FIG. 3 is provided, having two separate sets of double gratings in two different directions and simultaneously generating interference patterns in two different spatial shearing directions. Therefore, it is possible to obtain the effect of varying the curvature distribution in both the spatial shearing directions with time.
[0019]
The CGS system can be used to directly or indirectly measure the curvature of various structures and elements formed on a substrate. When measuring directly, the CGS probe beam can be sent directly to the top of these devices to obtain curvature information. To do this, it is usually necessary that the surface structures and elements and the area surrounding them are preferably smooth and reflective. In addition, it is desirable that the characteristics of the structure or element and the region surrounding them other than their curvature do not significantly contribute to the distortion of the wavefront. Therefore, the distortion of the wavefront can be used as an index of the curvature of the region irradiated by the optical probe beam. For example, some completed integrated circuits have a top passivation layer, typically of a non-conductive insulating material, over the circuit elements on the substrate to protect the underlying circuitry. The surface of the passivation layer is generally smooth and sufficiently reflective to perform CGS measurements.
[0020]
However, the above conditions are not compatible with some other substrate-based devices. For example, structures or elements formed on the front surface of the substrate or regions surrounding them may not be light reflective. These structures and elements on the front surface may distort the reflected wavefront due to factors other than curvature, such as different heights of the structures or elements from the area surrounding them. In such a case, the curvature of the structure or element can be measured indirectly by estimation from the curvature measurements at the corresponding position on the opposite side of the back side of the substrate. This is possible. This is because the stress of discontinuous structures and elements formed on the substrate will deform the substrate, and the thin film formed on the substrate will generally conform to the substrate surface.
[0021]
If the heights of the particular structures are different from their surroundings, the phase distortion of the wavefront of the reflected probe beam of each structure will include at least a portion resulting from the height difference and a portion resulting from the curvature. In addition to using the back surface of the substrate for measurement by CGS, measurement by CGS can be performed by illuminating the front surface. Therefore, the curvature information can be derived by removing the effect of the height difference when calculating the curvature, if the height information is known.
[0022]
In addition to measuring the curvature of the completed substrate-based device, the CGS method can also be used to perform curvature measurements within the system of the substrate and each layer or structure during each manufacturing step of the substrate base. it can. The CGS method achieves this by being able to simultaneously measure the curvature of all locations within the illuminated area over its entire field. Therefore, each measurement can be performed and completed in a short time without interrupting the continuous operation of the production. Since the CGS method uses the optical probe beam as a probe to obtain curvature information, the measurement is non-invasive, so that if the intensity of the optical probe beam is properly maintained below an acceptable level. Does not hinder the manufacturing process. In addition, the optical probe beam and the reflected beam of the beam from the substrate can be conveniently guided to and from the substrate in the processing chamber through one or more optical windows of the processing chamber. .
[0023]
Therefore, during fabrication of the thin film layers and various structures in each layer, the curvature and associated stress of each layer and each structure formed in each layer can be monitored by the CGS method. This on-site stress monitoring mechanism can be applied to various aspects of substrate manufacturing.
[0024]
For example, the in-situ stress monitoring mechanism can be used to exclude a defective batch of processed substrates at an intermediate stage during manufacturing before the entire manufacturing process is completed. It is known that the manufacturing process and associated thermal cycling can introduce stresses into the manufactured structure. For example, various metallization methods are performed at elevated temperatures. Also, these layers exhibit different mechanical, physical and thermal properties, which are high in the interconnect structure, for example, due to mismatches in the magnitude of thermal expansion and contraction between different materials. May cause stress. These stresses can contribute to electromigration, among other things, by causing undesirable voiding and interface cracking caused by the stress. In addition, these stresses can cause the substrate to crack. Voiding, electromigration, and substrate cracking are major failure factors for integrated circuits.
[0025]
Some of these defects are caused by stress after an intermediate step during manufacturing. The device becomes a defective device when the stress of various components exceeds a predetermined allowable value. The in-system stress monitoring described above can be used to measure stress during manufacturing, at selected stages, or continuously. The measured stress is compared to a tolerance. A defect is found if the stress measurement is greater than its tolerance. The manufacturing process is stopped because the device of the final product will be a defective device. Therefore, the remaining manufacturing steps need not be performed. In this way, the uneconomic and inefficient practice of some conventional manufacturing methods, in which defects in the manufactured devices are checked only after the entire manufacturing process has been completed, is avoided.
[0026]
Another typical application of this in-situ stress monitoring mechanism is to adjust and optimize processing conditions with manufacturing processing parameters to reduce substrate stress. Because the CGS method can be used to monitor stress in situ during manufacturing, the contribution of different processing steps to stress can be ascertained by monitoring the stress at each processing step. In addition, the processing parameters (eg, temperature, duration or duty cycle) of each processing step can be adjusted independently of or with reference to the processing parameters of other processing steps to reduce stress. The effect of each adjustment on stress can be measured by the CGS method, so that a relationship between the parameter and the stress can be established. Adjusting the processing parameters and then measuring the generated stress can be performed in an iterative manner until the generated stress falls to a satisfactory level. Therefore, the processing steps can be controlled to increase the total production yield.
[0027]
Yet another application of the CGS method is for monitoring large surface deformations where the out-of-plane displacement is greater than the line and substrate thickness. If the surface deformation is no longer small compared to the thickness of the line and the substrate, the accuracy of the CGS measurement will decrease, but the deviation of the CGS measurement from the expected curvature value will cause the CGS system to be used for on-site monitoring. If so, it can be used as an indicator that there is a uniform large surface deformation.
[0028]
Referring again to FIG. 1, after the curvature map is obtained, the processing module 105 processes the curvature map to create a corresponding stress map of the illuminated area on the sample surface. This is an important aspect of the system 100 shown in FIG. 1 and is accomplished by using simple analytical formulas to calculate the stress on the structure from the curvature data and the material parameters of the substrate and material of the structure. .
[0029]
In one embodiment, the process is based on a thermoelastic model of a thin periodic line feature formed on a thick substrate as described below. Specific aspects of the thermoelastic model, including in-depth computation steps, are described in Wikstrom, Gudmundson and Suresh, "Thermoelastic Analysis of Periodic Thin Thines Deposited on a Substantial Subsidiary of a Substantial Subsidiary." It was disclosed in May.
[0030]
4A and 4B schematically illustrate the structure of a thermoelastic model of one embodiment. A plurality of identical line structures 402 are formed on the surface of the substrate 400. Each of the line structures 402 has a width b and a thickness, that is, a height t, and is spaced equidistantly from each other to form a repetitive pattern. Assume that the dimensions (eg, diameter) of the substrate 400 are much larger than the thickness h of the substrate 400. For example, in some devices, it will be practically sufficient for the dimensions (eg, diameter) of the substrate to be at least 10 or preferably 50 times h. It is also assumed that the thickness t and width b of each line structure 402 are both much smaller than the length l and thickness h of the substrate 400 in the vertical direction, and are at least 1/10, for example, 1/25 or less. The accuracy of the model depends on these assumptions, i.e., generally it increases as these scaling and reduction factors increase. Based on these assumptions, the substrate 400 can be treated as a homogenized anisotropic plate.
[0031]
Cartesian coordinate system (x₁, X₂, X₃) Is shown in FIGS. 4A and 4B for the thermoelastic model. x₁And x₂The directions indicated by, respectively, are in the plane of the substrate 400, and represent the direction along and across the line structure. x₃The direction denoted by represents a direction perpendicular to the plane of the substrate 400. The volume average value of the volume amount A exceeding a certain volume V is defined by the following equation.
[0032]
(Equation 1)

[0033]
Based on the analysis method of Wikstrom et al., Supra, the volume average stress of each line structure 402 is calculated as x₁Curvature k along the direction (ie the longitudinal direction)₁, X₂Curvature k along the direction (ie, transverse)₂Can be represented by the following equation.
[0034]
(Equation 2)

[0035]
In the above equation, σ_αβRepresents the stress tensor components (α, β = 1, 2), and E_SAnd ν_SAre the Young's modulus and Poisson's ratio of the substrate 400, respectively. Shear stress σ₁₂Is zero in this case. The negative sign "-" in equation (1) is used to implement the chosen sign convention. That is, positive values represent curvature in one direction, while negative values represent curvature in the opposite direction. In particular, each stress component is f₁(E_S, Ν_S, H, t, d, b) · k₁+ F₂(E_S, Ν_S, H, t, d, b) · k₂Is the linear sum represented by Note that the coefficient f in the equation₁And f₂Is E_S, Ν_S, H, t, d and b. Therefore, the stress of each line structure can be calculated based on the elastic characteristics of the substrate and the form of the line structure.
[0036]
Therefore, the measured value of the curvature in each line structure 402 of the substrate 400 is a simple analytical function based on the dimensional parameters of the substrate 400 and each line structure 402, and the elastic properties (eg, Young's modulus and Poisson's ratio) of the substrate 400. The volume average elastic stress can be determined. One feature of this method is that the stress calculation according to equation (1) does not require detailed information on properties such as the material composition and mechanical properties of the line structure itself. While these properties of the line structure are key factors in determining the stress behavior of the line structure, the effect of these properties is the curvature k along the line structure.₁And the curvature k across the line structure₂Are included in the measured values.
[0037]
Another feature of this method is that, since equation (1) is a simple analytical equation, the measured curvature k₁And k₂The calculation of the stress based on can be performed in a short time by the processor. For example, a computer routine can be performed using a microprocessor to perform the calculations shown in equation (1). Thus, complicated and time-consuming numerical calculations are virtually avoided. In addition, it has been found that the simple analytical expression represented by the expression (1) is more accurate than a complicated numerical calculation based on the infinite element analysis method (Wikstrom, supra). This feature of the data processing module, when combined with the global parallel processing of the CGS optical detection module, allows the stress measurement system 100 shown in FIG. Stress can be generated. Thus, the system 100 can be used to measure, in real time, the time course of the curvature of the line structure and associated stresses for a number of steps in semiconductor manufacturing.
[0038]
The above-described stress calculation method relating to equation (1) provides a method for obtaining stress data of a line structure on a substrate when information on a thin film on which a line structure is formed cannot be used. An example of this situation is when checking the stress of a device, such as a completed IC circuit, after the line structure has been manufactured in thin film.
[0039]
FIG. 5 is a flowchart of the stress measurement method based on the equation (1). This stress measurement can be performed as an in-system monitoring mechanism after or during the manufacture of the substrate.
[0040]
If the curvature of the substrate and the thin film can be measured before patterning, another method of the present application is used to confirm the stress of the patterned line structure from the thin film on the substrate even before the line structure is formed. be able to. One example of this situation is in-system measurement during manufacturing by using the curvature measurement system 100 shown in FIG.
[0041]
First, before the layer is formed on the substrate, the curvature map of the bare substrate is measured (and therefore the associated stress map is measured). If the substrate and subsequently the continuous thin film deposited on the substrate are virtually isotropic, the curvature at any location should be the same along all directions. Next, after the thin film is deposited on the substrate, the curvature map of the continuous film is measured. The stress of the unpatterned continuous film at the target position can be obtained by the following Stoney equation.
[0042]
(Equation 3)

[0043]
In the above formula, k_filmAnd k_SAre the measurements of the curvature of the deposited film and the bare substrate at the same target location, respectively. Here, the code rule is selected such that the curvature is a positive value when the surface of the substrate on which the film is deposited is convex, and a negative value when the surface is concave.
[0044]
If a periodic line feature is formed on this film, the curvature k across each line structure₁And the curvature k along each line structure₂Can be determined from the elastic properties of the film and the substrate and the form of the line structure by the following analytical formula.
[0045]
(Equation 4)

[0046]
In the above formula, ν_filmIs the Poisson's ratio of the thin film, and χ is represented by the following equation.
[0047]
(Equation 5)

[0048]
And the coefficient d_jIs shown in Table 1 below. Note that χ → 0 for t / b → 0 and χ → 1 for t / b → ∞ (see Wikstrom et al., supra). Where k_filmTo k₁And k₂It is assumed that the change in curvature to 起 こ る simply results from a change in morphology due to patterning of the film into a line structure. It is also assumed that the elastic properties of the line structure are almost the same as the membrane.
[0049]
[Table 1]

[0050]
Therefore, the volume average elastic stress of each line structure can be obtained from the following equation.
[0051]
(Equation 6)

[0052]
In this method, the stress of each line structure is calculated using the simple analytical formulas of Expressions (2), (3) and (4), similarly to the method described above. However, unlike the previously described method, the curvature of the substrate required for equation (2) is measured before the film is deposited, while the curvature k of the substrate required for equation (1) is measured.₁And k₂Is measured after the line structure is formed on the substrate. Therefore, this method can be used to predict the stress of the formed line structure. FIG. 6 shows a flowchart of the stress measurement performed based on the equation (4).
[0053]
Further, the analytical equations of equations (2), (3) and (4) can also be applied to lines formed on one or more thin films on a substrate. In this case, the parameter k in equation (2)_SIs the total curvature of the structure formed by the lower film and the substrate before the line forming film is deposited. This total curvature can be measured directly using the CGS method. As a first approximation, the total curvature is the sum of the curvatures that would be induced if each individual layer were deposited on the substrate by itself.
[0054]
The stress measurement method described above can be applied to measure a substrate having a line structure oriented in two or more directions, for example, directions perpendicular to each other. The entire region of interest on the substrate is divided into two or more subdivision regions according to the pattern formed on the substrate, such that each subdivision region simply has a line structure parallel to one another along one direction. Can be Thus, the unidirectional line structure models shown in FIGS. 4A and 4B can be applied to individual subdivision regions to calculate corresponding stresses based on curvature data derived from CGS measurements. Thus, a non-linear single conductive line may include two or more different segments in different subdivision areas. The stress of this line is obtained by calculating the stress of different segments based on the CGS curvature data.
[0055]
FIG. 7 shows a part of a line structure formed on a substrate, and the part includes two subdivision areas A and B. The direction of the line structure in each subdivision area is the same. The subdivision areas A and B are such that the distance from the edge of each area to the nearest acute corner where the line changes direction is at least a value greater than the width b or thickness t of one line of each line structure. Is selected. This condition can maintain the accuracy of the stress calculation based on the model shown in FIGS. 4A and 4B. The subdivision areas A and B can be measured simultaneously using the system 100 shown in FIG. 1 when the optical probe beam is directed to indicate areas A and B simultaneously.
[0056]
In many practical devices, line structures formed on a substrate are often embedded in different materials. For example, conductive lines are often embedded in an insulating conductive material, such as an oxide. The models shown in FIGS. 4A and 4B can no longer be applied to the curvature and stress analysis of such structures. In fact, it is difficult to calculate the stress of such an embedded line structure without complicated numerical calculations. However, utilizing the new model, the curvature of the embedded line structure can be calculated based on the structural design, the material properties of the embedded line structure, and the surrounding materials.
[0057]
FIG. 8A shows a model for calculating the curvature of a line structure 810 embedded in a trench of a layer 820 formed on a substrate 800. Similar to the models shown in FIGS. 4A and 4B, assume that the lateral dimension of substrate 800 is much greater than its thickness h. The line structures 810 are parallel and at equal intervals d on the substrate 800,₂It is located along the direction. Also, the width b and the thickness t of each line structure 810 are x₁It is assumed that its longitudinal length along the direction is much less than the thickness h of the substrate 800 (Park and Suresh, "Effects of Line and Passivation Geometry on Curvature Evolution in the Terminating Promotion Cooperation and Terminating Terminating Procedure and Terminating Procedures and Termination Procedures and Termination Procedures and Terminating Procedures and Termination Procedures and Termination Procedures and Terminating Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Termination Procedures and Coding). Acta Materialia, April 2000).
[0058]
Further, the aspect ratio of the line structure 810: f₀= T / b and the aspect ratio of the line formed in the surrounding layer 820: f₁= T / (db) is equal to or greater than 1 and it is assumed that the curvature along the line structure 810 and the curvature across the line structure 810 do not affect each other elastically. According to Park and Suresh, supra, the line direction x₁The curvature k of the line structure 810 of₁And the line direction x caused by the temperature change ΔT in the elastic region₁Curvature k in the direction perpendicular to₂Can be represented by the following formula.
[0059]
(Equation 7)

[0060]
(Equation 8)

[0061]
In the above equation, it is as follows.
[0062]
(Equation 9)

[0063]
(Equation 10)

[0064]
(Equation 11)

[0065]
(Equation 12)

[0066]
And E₁, Ν₁And α₁Are the Young's modulus, Poisson's ratio and coefficient of thermal expansion of the line structure 810, respectively, and E₀, Ν₀, Α₀Are the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of layer 820, respectively. By analogy with a composite, a layer comprising a line structure 810 (eg, a copper line) and a surrounding layer 820 (an oxide such as silicon dioxide) has a Young's modulus in the line direction of E.₁And the Young's modulus in the direction crossing the line direction is E₂And the coefficient of thermal expansion in the direction of the line is α₁The coefficient of thermal expansion in the direction crossing the line direction is α₂As an anisotropic composite layer.
[0067]
The prediction of this simple analysis result was reasonably close to the result of a more infinite element simulation, with a deviation of about 3 to about 17%. For some practical arrangements of Cu lines in oxide trenches, the error is typically less than 17%.
[0068]
FIG. 8B shows another model in which a capping passivation layer 830 has been formed over the line structure 810 and the layer 820. Assuming that the thickness of the passivation layer 830 is much smaller than the thickness of the substrate 800, the curvature of the passivated line structure 810 due to the elastic deformation caused by the temperature change ΔT can be expressed by the following equation.
[0069]
(Equation 13)

[0070]
[Equation 14]

[0071]
In the above formula, E_P, Ν_P, Α_PAre the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the passivation layer 830, respectively.
[0072]
Using the above model shown in FIGS. 8A and 8B, the curvature of a line embedded on a substrate can be calculated based on certain known parameters of the substrate-based device. Although the stress of the embedded line cannot be calculated directly from equations (5)-(12), these modules are executed by the processing module 105 of the system 100 shown in FIG. You can check if it remains in the device.
[0073]
FIG. 9 is a flow chart of a method for combining CGS measurements with curvature estimates based on the models shown in FIGS. 8A and 8B to confirm stress information for embedded lines. First, the curvature of the embedded line of the device is measured by the CGS method and then calculated based on the model shown in FIGS. 8A and 8B. While the CGS measurement provides the actual curvature of the line, the calculated curvature is simply the curvature caused by elastic deformation. Next, the calculated curvature value is compared with the actually measured curvature value. The difference between these values indicates the curvature caused by residual stress not included in the above calculated values. This residual stress must be kept below an acceptable level to ensure proper operation and desired life of the device. Thus, if the difference along the line or across the line exceeds an acceptable level, the reliability or performance of the device is considered unacceptable.
[0074]
Since the CGS method can be measured in the field, the above method can be used to monitor the stress of the embedded line during the manufacturing process. The difference in curvature from the above analysis and the CGS measurement, which is not apparent at design time, provides an indication that stress / curvature development is actually in progress. Accordingly, one or more aspects of the manufacture or design of these devices may be inspected and modified to reduce residual stress to an acceptable level. Further, utilizing the in-system measurements, if the residual stress exceeds an acceptable level in an intermediate step, the production can be stopped before completing the entire process. This monitoring mechanism can reduce costs and increase manufacturing efficiency.
[0075]
Using the equations (5), (6) and (11) and (12), the curvature measurement data is fitted to determine the characteristics of the line structure or the substrate such as the Young's modulus, thermal expansion coefficient and Poisson's ratio of the substrate or the line structure. You can check. For example, in a device having the passivation layer 830, the characteristics of the passivation layer 830 can be confirmed based on the equations (11) and (12) using the CGS measurement value of the curvature. Biaxial modulus of passivation layer 830: E_{P , B}= E_P/ (1-ν_P) Indicates a measured value k obtained by CGS measurement performed before and after the passivation layer is deposited.₁ ^passAnd k₂ ^passCan be calculated from
[0076]
The above method of measuring buried lines is applicable to a new manufacturing method, the "Damascene process", which creates copper conductive lines in oxide trenches. In this technique, a trench is etched into a layer of oxide to match the morphology of the copper interconnect lines in the circuit formed on the Si substrate. The etching is performed using a dry etching method. Next, the trenches of these oxides are filled with Cu using a chemical vapor deposition (CVD) method or an electroplating method. Next, the excess copper that has run over the trenches is removed by chemical-mechanical polishing (CMP), and then a passivation or capping layer is deposited over the top surface of the interconnect structure.
[0077]
Since the damascene method involves removal of material by polishing, knowing that curvature has occurred during polishing and subsequent processing is essential for various problems. For example, in-system monitoring of curvature using the CGS method can provide information on the "flatness" of the polished surface on which the layer is deposited. This is an essential step in quality control. Knowledge of the occurrence of curvature also provides an indication of the occurrence of internal stress during manufacturing.
[0078]
In addition, the above analysis of the non-passivated and passivated lines can be used to simulate the generation of elastic stress during thermal cycling and can be readily compared to CGS measurements. Examples of such calculations are described in the Park and Suresh literature and are confirmed by comparison to infinite element simulation values.
[0079]
The system 100 shown in FIG. 1, in addition to measuring the stress caused by the change in elasticity, is configured based on the model shown in FIGS. 4A and 4B, and provides some plastic properties of the line structure formed on the substrate. You can also check. Line structures formed on a substrate may undergo permanent plastic deformation due to certain thermomechanical treatments. In general, the line structure and the thin film have a temperature at their respective threshold breakdown temperatures T.₁ ^YAnd T_f ^YIf it is lower, it undergoes elastic deformation. The curvature due to elastic deformation changes linearly with temperature. However, when the temperature reaches the threshold yield temperature T₁ ^YAnd T_f ^YAbove that, plastic deformation occurs, and the curvature changes with temperature in a non-linear manner. For example, plastic deformation occurs when a conductive line is heated above the breakdown temperature during passivation. It is desirable to confirm the stress caused by such plastic deformation.
[0080]
The initial stress-free temperature of each of the line structure and the continuous thin film in which the line structure is patterned on the substrate is T.₁ ⁰And T_f ⁰Assume that The stress-free temperature ranges of the line / substrate system and the thin film / substrate system can be confirmed experimentally by measuring the curvature as a function of temperature using the CGS method. The curvature of the untreated continuous thin film can be confirmed based on the above equation (2). The temperature change from the initial stress-free temperature to the temperature at which plastic yielding starts for each of the line and the thin film can be expressed by the following equation.
[0081]
(Equation 15)

[0082]
(Equation 16)

[0083]
Z in the above formula^eIs represented by the following equation.
[0084]
[Equation 17]

[0085]
In the above formula, T₁ ^YAnd T_f ^YIs the temperature at which permanent plastic deformation begins to occur in the line structure and continuous film, respectively. T₁ ^YAnd T_f ^YAt temperatures above, the curvatures of the lines and films begin to change non-linearly with temperature. Equations (13)-(15) are described by Gouldstone, Wikstrom, Gummundson and Suresh, "Onset of Plastic Yielding in Thin Metal Lines Deposited," Vol. Based on the analytical method, it can be derived by the model shown in FIGS. 4A and 4B.
[0086]
The following expression can be obtained from Expressions (13) and (14).
[0087]
(Equation 18)

[0088]
The temperature difference ratio can be measured using the CGS method, and the parameter Z^eCan be calculated based on equation (4), so that the ratio between the line structure and the yield stress of the thin film can be obtained from equation (16). Thus, the CGS method, in conjunction with the above analysis, provides a means to help identify the onset of breakdown of patterned lines.
[0089]
Using the above method and system, the stress history and spatial variation of a substrate, a line structure, or a thin film formed thereon can be measured in real time. In particular, measured values obtained by the coherent gradient sensing method can be processed quickly by analytical calculation to obtain spatial and temporal variations in stress and plastic strain. Information about the line structure on the substrate and the plastic deformation of the film can also be measured.
[0090]
A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications and improvements may be made without departing from the scope of the claims herein.
[Brief description of the drawings]
FIG. 1 is a block diagram of a stress measurement system according to one embodiment of the present invention.
FIG. 2 illustrates one embodiment of a coherent gradient sensing system.
FIG. 3 shows a coherent gradient sensing system having two independent optical arms and simultaneously obtaining spatial shearing in two different directions.
FIG. 4A shows a top view of a representative structure of a thermoelastic model of one embodiment of the present invention.
FIG. 4B shows a cross-sectional view of the structure shown in FIG. 4A.
FIG. 5 is a flow chart illustrating two methods for measuring the stress of a line structure based on a measurement of optical whole-surface curvature.
FIG. 6 is a flow chart illustrating two methods for measuring the stress of a line structure based on a measurement of optical whole-surface curvature.
FIG. 7 shows two representative subdivision regions of a patterned line structure on a substrate.
FIG. 8A shows a model of a line structure embedded in a layer on a substrate and a model of a line structure embedded in a layer on a substrate and capped with a passivation layer.
FIG. 8B shows a model of a line structure embedded in a layer on the substrate and a model of a line structure embedded in a layer on the substrate and capped with a passivation layer.
FIG. 9 is a flowchart showing a method for measuring a curvature of a line structure embedded in a layer on a substrate using the system shown in FIG. 1;

Claims (39)

An optical detection module for directing an optical probe beam to a reflection surface of a processed substrate having a line structure and generating a reflection probe beam, wherein the curvature signal having information on a curvature of a region of the reflection surface is provided. An optical detection module operative to generate based on the reflected probe beam;
A processing module for calculating the stress of each line structure on the substrate from an analytical function of the curvature of the substrate in two different directions corresponding to the position of the line structure. The optical detection module includes first and second gratings in the optical path of the reflected probe beam, and diffracts two different diffraction components from the first grating, thereby providing two diffractions from the second grating. The system of claim 1, wherein a phase shift occurs between the components. The system of claim 1, wherein the analytic function comprises a linear sum of the curvatures along the two different directions having a coefficient determined by a substrate thickness, Poisson's ratio and Young's modulus, and a dimension of a line structure. . A line structure is formed by patterning a continuous thin film deposited on a substrate, and the analytical function is the stress of the thin film before being patterned, the Poisson's ratio and thickness of the thin film, and the dimensions of the line structure. The system of claim 1, which is a function of The system of claim 1, wherein the optical detection module projects an optical probe beam onto a surface of the substrate on which the line structure is formed. The system of claim 1, wherein the optical detection module projects an optical probe beam onto a surface of the substrate that does not have a line structure. A line structure is formed on at least one thin film layer on the substrate, and the processing module is operative to calculate the stress from a total curvature of the thin film layer on the substrate before the line structure is formed. Item 2. The system according to Item 1. The system of claim 1, wherein the processing module is operative to calculate the stress from a total curvature of the substrate before a line structure is formed. Irradiating the substrate with an optical probe beam to generate a reflected probe beam acquiring information on the surface space gradient of the irradiated area on the substrate,
Processing the surface space gradient information in the reflected probe beam, the first curvature of the longitudinal substrate at that position of the line structure formed at one position on the substrate, and the lateral curvature perpendicular to the longitudinal direction. A method comprising simultaneously measuring a second curvature of a substrate at the same location, and then utilizing an analytical function to calculate a stress on the line structure based on the measured first and second curvatures. The method of claim 9, wherein the analytic function comprises a measured first and second linear sum. 11. The method of claim 10, wherein the linear sum has a factor determined by the thickness of the substrate, Poisson's ratio and Young's modulus, and the dimensions of the line structure. The line structure includes a first portion along the first line direction and a second portion along a second line direction different from the first line direction, and further, the line structure changes from the first line direction to the second line direction. 10. The method of claim 9 including measuring first and second curvatures of the substrate corresponding to locations on the line structure at least a selected distance from the location where the stress is the first portion. Method. 13. The method of claim 12, wherein the selected distance is greater than the line structure thickness and line width values. Measure the curvature along the line structure and the curvature across the line structure of the second portion at a position at least a selected distance from the position where the line structure changes from the first line direction to the second line direction, and then measure the curvature. The method of claim 12, further comprising determining a two-part stress based on the analytical function. The method according to claim 9, wherein the optical probe beam is directed at a surface of the substrate on which the line structure is formed. The method according to claim 9, wherein the optical probe beam is directed at a surface opposite the surface of the substrate on which the line structure is formed. The line structure is embedded in a thin film layer deposited on the substrate,
Based on the elastic deformation model, calculate the curvature of the line structure along and across the line direction due to elastic deformation caused by a change in temperature,
10. The method of claim 9, comprising comparing the calculated curvature with the measured curvature to determine a difference in curvature, and then extracting information about the line structure based on the difference in curvature. The method according to claim 17, wherein the calculation is performed using an analytic function. The method of claim 17, wherein the information about the line structure includes information about a residual stress. The method according to claim 17, wherein the information about the line structure includes characteristics of the substrate or the line structure. 21. The method of claim 20, wherein the property is an elastic property. The substrate before the thin film is deposited is irradiated with an optical probe beam, and the curvature of the irradiated area of the substrate is simultaneously measured based on the spatial gradient information in the reflected probe beam,
Deposit a thin film on the substrate,
Irradiating the thin film with an optical probe beam, simultaneously measuring the curvature of the irradiated area of the thin film based on spatial gradient information in the reflected probe beam,
A method comprising determining stress information of a deposited thin film based on measured curvatures of the thin film and the substrate, and then utilizing an analytical function to determine stress on a line structure patterned from the thin film. Compare the measured stress on the line structure to the maximum allowable stress and then stop further processing of the substrate when the measured stress on the line structure exceeds the maximum allowable stress 23. The method of claim 22, further comprising: 23. The method of claim 22, wherein the analytic function is a function of stress information and Poisson's ratio of the unpatterned film, and a ratio of thickness to line width of the line structure. 23. The method of claim 22, wherein measuring the curvature of the substrate and the thin film comprises obtaining a spatial gradient map of the illuminated area from phase information in a reflected probe beam from the area. By using first and second gratings spaced in the optical path of the reflected probe beam and diffracting two different diffraction components from the first grating, the two diffraction components from the second grating can be diffracted. 23. The method of claim 22, further comprising causing a phase shift to occur. The method according to claim 26, wherein the grating directions of the first grating and the second grating are parallel to each other along the first direction. Generating a second reflected probe beam by dividing a portion of the reflected probe beam,
Using the third and fourth gratings spaced apart in the optical path of the second reflected probe beam, where the grating direction is parallel along the second direction different from the first direction, a phase shift occurs. 27. The method of claim 26, further comprising processing the phase shifts in the reflected probe beam and the second reflected probe beam to produce substrate and thin film curvature. Under a certain range of temperature, irradiate a light beam and simultaneously measure the curvature of the thin film deposited on the substrate,
Controlling the temperature so that the curvature of the thin film changes from linear to non-linear with respect to temperature;
Find the yield temperature of the thin film where the linear dependence changes to a nonlinear dependence,
Pattern the thin film to form a line structure,
Under a certain range of temperature, irradiate a light beam and simultaneously measure the curvature of the line structure,
Controlling the temperature so that the curvature of the line structure changes from linear to non-linear dependence on temperature;
Find the yield temperature of the line where the linear dependence changes to a nonlinear dependence,
Determine the first temperature difference between the yield temperature of the thin film and the temperature of the thin film lower than the yield temperature of the thin film,
Find the second temperature difference between the yield temperature of the line and the temperature of the line that is lower than the yield temperature of this line,
Calculating the ratio of the yield stress of the line structure to the yield stress of the thin film corresponding to the yield temperature of the line and the yield temperature of the thin film, respectively, according to the first temperature difference and the second temperature difference and the analysis function. Method. 30. The method of claim 29, wherein the analytic function is a function of the Poisson's ratio of the thin film and the dimensions of the line structure. 30. The method of claim 29, wherein the curvature is measured by obtaining spatial gradient information of the line structure and the thin film. A substrate having a line structure formed in a thin film trench is irradiated with an optical probe beam, and the curvature of the line structure is simultaneously measured based on spatial gradient information in the reflected probe beam,
The curvature of the line structure is calculated from the analytical function based on the elastic deformation,
A method comprising: comparing a calculated value of the curvature of a line structure to its measured value to obtain a difference in curvature, and then determining information about the residual stress of the line structure by the difference in curvature. 33. The method of claim 32, wherein a passivation capping layer is formed over the line structure and the thin film, and wherein the analytic function includes a passivation capping layer effect. 33. The method of claim 32, further comprising modifying aspects of the manufacturing process or structural design of the line structure and the thin film on the substrate according to the difference in curvature. 33. The method of claim 32, wherein the modification is made to reduce residual stress below an acceptable value. Irradiating the optical probe beam to the substrate on which the line structure is formed before the manufacturing is completed, and simultaneously measuring the curvature of the line structure based on the spatial gradient information in the reflected probe beam;
The stress of the line structure is evaluated based on the measured curvature,
Performing said one or more subsequent manufacturing steps when said stress is below an acceptable value, and then terminating production when said stress exceeds an acceptable value. 37. The method of claim 36, wherein the stress is estimated from an analytical function of curvature in two different directions of the substrate, corresponding to a position of a line structure. Irradiating the optical probe beam onto the substrate on which the line structure is formed in an intermediate step of manufacturing, and simultaneously measuring the curvature of the line structure based on the spatial gradient information in the reflected probe beam;
Evaluating the stress of the line structure based on the measured curvature, and then adjusting manufacturing parameters to reduce the stress below an acceptable value. 39. The method of claim 38, wherein the stress is estimated from an analytical function of curvature in two different directions of the substrate corresponding to the location of the line structure.

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