JP3928714B2 - Analytical method of thin film multilayer structure using spectroscopic ellipsometer - Google Patents

Description

ここで、Ｐは、パラメータの数である。χ² が小さいということは測定結果とモデルの一致度が大きいということに他ならないから、複数のモデルについて比較するときに、χ² の最も低いものがベストモデルということになる。
【０００６】
前述した測定試料が基板上に膜が１層ついているサンプルの場合、偏光変化量は、位相角（β）×ビーム径の面積に比例する。位相角（β）は次の式で表される。
β＝２π（ｄ／λ）（Ｎ² −Ｎ_A ² ｓｉｎ² φ）^1/2
ビーム径が一定とすると偏光変化量は次のようになる。
偏光変化量∝膜厚（ｄ）×複素屈折率（Ｎ）×ｆ（φ）
ここでＮ_A は周囲（Ambient）の複素屈折率、Ｎは膜の複素屈折率、φは入射角である。膜厚（ｄ）が薄く、複素屈折率（Ｎ）が低ければ、位相角（β）の変化が小さくなり、測定が困難になる可能性が出てくる。明確に言うと、ｄとＮの間に相関関係が強くなる。
【０００７】
前述した問題は、極薄膜多層構造の場合、上記にさらに各層の間に相関関係が発生する可能性があり、偏光変化量を表している測定結果（Ψ_E ( λ_i ) ，Δ_E ( λ_i ) ）から、各層のｄ，ｎ，ｋを求めることが困難となる。
【０００８】
また、前述した式のとおり、入射角の正しさによって、偏光変化量の値も変わる。したがって、何らかの方法で、入射角を正しく求める必要がある。正しい入射角度が決定できることにより偏光変化量の値も正しく求めることが可能となる。
【０００９】
本発明では、様々な理由により１つの分散式では膜の誘電率の波長依存性を特定できないかまたは困難な場合についても問題にして、有効媒質論（Effective Medium Theory)を利用して、有効誘電率(Effective Dielectric Function) を計算する。
一般的に、例えばホスト材料中に様々な誘電率を持つＮ個の物質（ゲスト）が混ざり合っている場合、有効誘電率（ε）は、下記の様に表される。

この時ε_h はホストの誘電率を、ε_j はｊ個目の誘電率を、ｋはスクリーニングファクターを示している。ここで、ホストの材料と、中に入っている材料がほぼ同じ量で混ざり合っているか、またはどちらがホストかゲストか分からない場合、ホストの材料自身が有効媒質材料と同じε＝ε_h になる。この条件の有効媒質論をブラッグマンの有効媒質近似（Bruggeman Effective Medium Approximation以下本願において単にＥＭＡ）と呼ばれている。３つの球状物質ａ，ｂ，ｃが対照的に混在しているときの誘電率εは次の式で与えられる。

ここで、
ε : 求めようとする有効誘電率
ε_a , ε_b , ε_c : 球状物質ａ，ｂ，ｃの誘電率
ｆ_a , ｆ_b , ｆ_c : 各物質の混合比（Volume Fraction 以下Vf）で、
ｆ_a ＋ｆ_b ＋ｆ_c ＝1
基板上の膜が不均一または不連続や、いくつかの材料が混ざり合っている場合、波長オーダーより十分小さく、物理的に混合している複数の物質から成る媒質については、有効媒質近似（ＥＭＡ）を利用してモデルをたてる。
物質ａと物質ｂと物質ｃが混合している場合について説明する。このときの有効媒質近似（ＥＭＡ）は、物質ａの混合比、物質ｂの混合比、物質ｃの混合比、ａとｂとｃの混合層の膜厚、誘電率には分散式やリファレンスデータなどを推定してフィッティングを行い、評価する。
【００１０】
本発明では、ＢＬＭＣ（ Best Local Minimum Calculation ）とＥＢＬＭＣ（Extended Best Local Minimum Calculation ）と言う計算方法を多用するから、これを簡単に定義してＢＬＭＣとＥＢＬＭＣという略語を直接用いることにする。
ＢＬＭＣとは、一つの層に対して行う方法である。任意のパラメータの初期値を一定の範囲内で変えながら、決まった手順でフィッティングを行い、最良な結果を決定する。
ＥＢＬＭＣとは、複数の層に対して行う方法である。ＢＬＭＣを行う以外の層の、任意のパラメータをその中心値および付近の複数点にわたり選択して各点についてＢＬＭＣを行い、最良な結果を決定する。
【００１１】
本発明の目的は、膜厚や複素屈折率などの組み合わせモデルを設定し、そのシミュレーションスペクトルを算出して、そのシミュレーションスペクトルと測定スペクトルとのフィッティングを広範囲最極小値計算法（ＥＢＬＭＣ）を使用して行うことにより、薄膜多層（複数）層構造を決定する、分光エリプソメータを用いた薄膜複数層構造の解析方法を提供することにある。
【００１２】
【課題を解決するための手段】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記薄膜複数層構造の層数は３層であり、分光エリプソメータを用いて測定データを得る分光測定フェーズと、薄膜３層構造の解析初期段階モデルを決定する解析フェーズ１と、前記解析初期段階モデルについて、３層構造中の注目層以外の層の定数をその中心点及び付近の複数点にわたり変えながら前記注目層の未知の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する第１段階、および決定された定数の中心点及び付近の複数点にわたり変えながら、他の層の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する第２段階を含む解析フェーズ２と
から構成されている。
【００１３】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記薄膜複数層構造の層数は３層であり、分光エリプソメータを用いて測定データを得る分光測定フェーズと、薄膜３層構造の解析初期段階モデルを決定する解析フェーズ１と、前記解析初期段階モデルについて、３層構造中の注目層以外の層の定数をその中心点及び付近の複数点にわたり変えながら前記注目層の未知の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する第１段階、および決定された定数の中心点及び付近の複数点にわたり変えながら、他の層の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する第２段階を含む解析フェーズ２と、前記解析フェーズ２で各定数が決定されたモデルの所定の定数を固定しそれ以外の定数についてフィッティングを行う解析フェーズ３とから構成されている。
【００１４】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、分光エリプソメータを用いて測定データを得る分光測定フェーズと、薄膜複数層構造の解析初期段階モデルを決定する解析フェーズ１と、薄膜複数層構造の解析初期段階モデルについて、複数層構造中の注目層以外の層の定数をその中心点及び付近の複数点にわたり変えながら前記注目層の未知の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する解析フェーズ２とから構成されている。
【００１５】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、分光エリプソメータを用いて測定データを得る分光測定フェーズと、薄膜複数層構造の解析初期段階モデルを決定する解析フェーズ１と、薄膜複数層構造の解析初期段階モデルについて、複数層構造中の注目層以外の層の定数をその中心点及び付近の複数点にわたり変えながら前記注目層の未知の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する解析フェーズ２と、前記解析フェーズ２で未知の定数が決定されたモデルの所定の定数を固定しそれ以外の定数についてフィッティングを行う解析フェーズ３とから構成されている。本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記未知の定数は、各層の膜厚、未知材料の光学定数、または混合比とする。
【００１６】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記分光測定フェーズは、
入射光の波長を変えて各波長λ_i ごとの入射光と反射光の偏光の変化を表わしている測定スペクトルΨ_E （λ_i ）とΔ_E （λ_i ）を得るΨ_E ，Δ_E スペクトル測定ステップと、
前記測定で得たデータを保存する保存ステップと
を含む。
【００１７】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記解析フェーズ１では、複数種類のモデルから選択した１つの最良近似モデル（Best First Approximation Model 以下ＢＦＡＭと称す）を解析初期段階モデルとして決定する場合、前記解析フェーズ１は、
考えられるモデルを複数種類たてる第１ステップと、
前記複数種類のモデルについて少なくとも膜厚、および入射角度についてフィッティングを行う第２ステップと、
前記第２ステップの結果から平均二乗誤差（χ² ）の値の最も低いモデルまたは、あらかじめ設定した膜厚、入射角度の最大値と最小値の間に入っている最低平均二乗誤差（χ² ）の値のモデルをＢＦＡＭとして選択する第３ステップと
から成る分光エリプソメータを用いた薄膜複数層構造の解析方法。
また、本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記解析フェーズ１は、複数のモデルからフィッティングにより選択した１つの最良近似モデル（ＢＦＡＭ）、または既知のデータから仮定した初期モデルを解析初期段階モデルとして決定する。
【００１８】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記解析フェーズ２の第１段階は、前記解析フェーズ１で決定した解析初期段階モデルにおいて、複数層構造中の最も未知な材料層である注目層の光学定数を１つの分散式におきかえる第１ステップと、注目層以外の層の膜厚を、その中心点及び付近の複数点にわたり変えながら各点について注目層の最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）を行う第２ステップと、前記第２ステップの最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）の結果から平均二乗誤差（χ² ）の値の最も良い結果を選択する第３ステップとを含んで構成されている。
【００１９】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記解析フェーズ２の第２段階は、前記第１段階で決定された注目層の光学定数を既知とし、それ以外の層の中から最も未知な材料層を新たな注目層にして、その新たな注目層の光学定数を１つの分散式におきかえる第１ステップと、新たな注目層以外の層の膜厚を、その中心点及び付近の複数点にわたり変えながら各点について新たな注目層の最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）を行う第２ステップと、前記第２ステップの最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）の結果から平均二乗誤差（χ² ）の値の最も良い結果を選択する第３ステップとを含んで構成されている。
【００２０】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記解析フェーズ２は、３層構造中の注目層以外の層の定数をその中心点及び付近の複数点にわたり変えながら前記注目層の未知の定数を最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）により決定する段階を３つ以上有し、各段階を順次行うようにしており、前記解析フェーズ２の１番目になる第１段階は、前記解析フェーズ１で決定した解析初期段階モデルにおいて、複数層構造中の最も未知な材料層である注目層の光学定数を１つの分散式におきかえる第１ステップと、注目層以外の層の少なくとも膜厚を、その中心点及び付近の複数点にわたり変えながら各点について注目層の最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）を行う第２ステップと、前記第２ステップの最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）の結果から平均二乗誤差（χ² ）の値の最も良い結果を選択する第３ステップとを含み、前記解析フェーズ２の２番目以降の各段階は、前の段階で得られた注目層の光学定数を既知とし、それ以外の層の中から最も未知な材料層を新たな注目層として、新たな注目層の光学定数を１つの分散式におきかえる第１ステップと、新たな注目層以外の層の少なくとも膜厚を、その中心点及び付近の複数点にわたり変えながら各点について新たな注目層の最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）を行う第２ステップと、前記第２ステップの最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）の結果から平均二乗誤差（χ² ）の値の最も良い結果を選択する第３ステップとを含むよう構成されている。
【００２１】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記解析フェーズ２の最終段階で選択された平均二乗誤差（χ² ）の値の最も良い結果が、あらかじめ設定した各層の膜厚、分散式パラメータ、混合比、入射角度のそれぞれの最大・最小値の範囲内にない場合には、前記解析フェーズ２の第１段階の第２ステップに戻り、注目層以外の層の少なくとも膜厚を変えることを特徴とする。
【００２２】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記解析フェーズ３は、前記解析フェーズ２で平均二乗誤差（χ ² ）の最も良い結果をもつモデルに係る任意のパラメータについてフィッティングを行い、フィッティングの結果を確認して保存するフェーズとして構成されている。
【００２３】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、
前記解析フェーズ３のフィッティングの結果があらかじめ設定した最大値と最小値の範囲内にない場合、新たな解析初期段階モデルを決定する前記解析フェーズ１に戻るように構成されている。
【００２４】
本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法は、前記解析フェーズ１は、注目層に有効媒質近似を用いて解析初期段階モデルを決定しており、前記解析フェーズ２の第１段階の第１ステップで、注目層にいくつかの材料が混ざり合っているとして、有効媒質近似を用いて注目層中のいくつかの材料のうち少なくとも１つを分散式で表し、前記解析フェーズ２の第１段階の第２ステップで、前記注目層以外の層の膜厚、混合比を複数点にわたり選択して、各点について注目層の混合比を変えながらこの層について最極小値計算法（ＢＬＭＣ:Best Local Minimum Calculation）を行うように構成されている。
【００２５】
なお、本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法では、
計測対象の基板上の薄膜複数層構造を、入射光の波長を変えて各波長λ_i ごとの入射光と反射光の偏光の変化を表わす測定スペクトルΨ_E （λ_i ）とΔ_E （λ_i ）を得るΨ_E ，Δ_E スペクトル分光測定フェーズと、
予想される範囲内にある複数の測定条件（Ｚｉ）ごとに解析フェーズ１の第３ステップ、または解析フェーズ２解析の最終段階の第３ステップまでを行い、各測定条件ごとに得られる結果の中から、最低の平均二乗誤差（χ² ）の値または分散式のパラメータや混合比、入射角度が、設定した最大、最小値の間に入っている組み合わせの中で、平均二乗誤差（χ² ）の値の最も良いものを選択する第４ステップとにより構成されるようにしてもよい。
【００２６】
また本発明による分光エリプソメータを用いた薄膜複数層構造の解析方法では、
前記解析フェーズ１，２，３における前記差の最も少ないものを選択するステップは、フィッティングしたものと、測定値の平均二乗誤差を求め、最も小さい平均二乗誤差のものまたは、あらかじめ設定した膜厚、分散式パラメータ、混合比、入射角の変量のそれぞれの最大・最小値の中に入っている最も小さい平均二乗誤差のものに決定するように構成されるようにしてもよい。
【００２７】
【発明の実施の形態】
以下図面等を参照して本発明による分光エリプソメータを用いた薄膜多層構造の解析方法を説明する。
図１は、本発明方法で使用するエリプソメータの構成を示す略図である。
本発明は、一般的に言って、２層以上の極薄膜または薄膜多層構造の解析方法に利用できるものである。理解を容易にするためにまず、極薄膜３層構造データの解析方法を例にして説明する。なお図１において、測定の対象の試料 (サンプル) ４の一部を拡大して示してある。
【００２８】
図１に示されている分光エリプソメータにより、後述する方法の分光測定データの獲得ステップ（測定フェーズ）が実行される。先ず、測定装置について簡単に説明する。Ｘｅランプ１は、多数の波長成分を含む、いわゆる白色光源である。このＸｅランプ１の発光は光ファイバ２を介して偏光子３に導かれる。偏光子３により偏光された光は、測定対象であるサンプル４の表面に特定の入射角（例えばφ＝７５．００°）で入射させられる。サンプル４は後述する基板表面に３層に薄膜を形成した測定試料である。
サンプル４からの反射は、光弾性変調器（ＰＥＭ）５を介して検光子６に導かれる。光弾性変調器（ＰＥＭ）５により５０ｋＨｚの周波数に位相変調されて、直線から楕円偏光までが作られる。そのため、数ｍ秒の分解能でΨ，Δを決定することができる。検光子６の出力は光ファイバ７を介して分光器８に接続される。分光器８の出力データがデータ取込部９に取り込まれ、分光測定データの獲得ステップを終了する。なお、ＰＥＭ５の位置は偏光子３の後か検光子６の前どちらでも可能とする。
【００２９】
図２は、極薄膜３層測定方法の流れ図、図８は本発明方法の一般形態である薄膜ｎ層構造の解析方法の流れ図である。
本発明方法における解析は、基本的には３つのフェーズに分けて考えることができる。解析フェーズ１は、解析フェーズ２以降で解析の対象となる実際のサンプルに最もよく合うと考えられる初期モデルを決定するフェーズである。
このフェーズ１は、後述するように、複数のモデルからフィッティングにより一つの最良近似モデル（Best First Approximation Model 以下ＢＦＡＭ）を選択（図３の３１，３２，３３、図８の８１Ａ）しても良いし、与えられるかまたは既知のデータから仮定した初期モデルの設定（図３の３４、図８の８１Ｂ）であっても良い。いずれにしてもここで選択されたモデルが解析フェーズ２以降の解析の対象となる。
【００３０】
解析フェーズ１で前記モデル（ＢＦＡＭ）を決定するためのモデルの数は、構造中の未知層数と利用できるデータの数に依存する。ここで未知層とは正確な光学定数を決定しなければならない層等のことである。
解析フェーズ２では多層構造中の未知材料、特に最も未知な材料から解析第１、解析第２段階、の順番にＥＢＬＭＣ手順を順次実行する。
例えば、解析第１段階では後述するようにＭａｔ2 について、ＥＢＬＭＣ手順を実行し、解析第２段階で第１段階の結果を利用してＭａｔ3 について、ＥＢＬＭＣ手順を実行するのである。解析フェーズ３は、解析フェーズ２の結果について、最終フィッティングを行い結果の確認をしてデータとして出力または保存を行うのである。
【００３１】
以下本発明で用いる記号を一括して示す。
（記号の定義）
Ｓｕｂ： 基板（光学定数は既知，バルクとして取り扱い可能）
Ｍａｔ： 薄膜材料（物質の光学定数）
ｄ_i : ｉ層目の膜厚
ｄ_i(best) : フィッティングによって得られたｉ層目の膜厚
ｄ_ij： j 番目のモデルのｉ層目の膜厚
ｄ_ij(best)： フィッティングで得たj 番目のモデルのｉ層目の膜厚
X2 : 平均二乗誤差（χ²)値
X2_(j) : j番目のモデルにおける平均二乗誤差（χ²)値
Void : ｎ＝１，ｋ＝０の物質
Vf_(ij) : j 番目のモデルのｉ層目の混合比(Volume fraction)
Vf_(ij)(best) : フィッティングで得られた j番目のモデルのｉ層目の混合比
【００３２】
以下の実施例では、各層は次の材料から構成されている。
第３層 ＴａＯ_x （Ｍａｔ₃ ） ｄ₃
第２層 Ｓi Ｎ （Ｍａｔ₂ ） ｄ₂
第１層 Ｓi Ｏ₂ （Ｍａｔ₁ ） ｄ₁
基板（Ｓｕｂ） Ｓi バルク
【００３３】
測定フェーズ（測定ステップ）図２の２０Ａの測定は、図１に示す装置で測定を行う。計測対象４の基板上の極薄膜３層構造（図中の拡大図を参照されたい）を、入射光の波長を変えて各波長λ_i ごとの入射光と反射光の偏光の変化を表わす測定スペクトルΨ_E （λ_i ）とΔ_E （λ_i ）に係るΨ_E ，Δ_E スペクトルを測定する。測定フェーズデータ保存ステップ２０Ｂは、前のステップで測定したデータを保存して比較の対象データとする（図２参照）。
【００３４】
極薄膜３層膜フィッティング過程
この実施例では、物質１（Ｍａｔ1 ）は略既知、２，３層目の物質（Ｍａｔ2 ，Ｍａｔ3 ）および１，２，３層目の膜厚（ｄ_1,ｄ_2,ｄ₃ ）は未知とする。
なおこの例では２層目の物質（Ｍａｔ2 ）の光学定数がもっとも分からないものとして説明する。
【００３５】
解析フェーズ１でＢＦＡＭの設定３１〜３３を行う。または、初期モデルの仮定３４を行う。
（解析フェーズ１ステップ１）
図３の３１に示すように、考えられるモデル複数種類をたてる。そして最も合う構造および初期膜厚を決定する。
このステップで、基板の（Ｎ₀ （ｎ₀ ，ｋ₀ ））および各薄膜の材料（Ｍａｔ1，Ｍａｔ2，Ｍａｔ3）の考えられる複素屈折率（Ｎ ₁ （ｎ₁ ，ｋ₁ ）），（Ｎ ₂ （ｎ₂ ，ｋ₂ ）），（Ｎ ₃ （ｎ₃ ，ｋ₃ ）），各層の膜厚（ｄ₁ ，ｄ₂ ，ｄ₃ ）を利用し、いくつかのモデルをたてる。
この実施例では、下記各モデル（1）〜（4）を設定したものとする。
図３の３１が示す部分に前記各モデルを略図示してある。
モデル（1）は、基板（Ｓｕｂ）の上に第１層（Ｍａｔ1の光学定数，膜厚ｄ₁₁）、第２層（Ｍａｔ2の光学定数，膜厚ｄ₂₁）、第３層（Ｍａｔ3の光学定数，膜厚ｄ₃₁）を形成したものである。
モデル（2）は、基板（Ｓｕｂ）の上に第１層（Ｍａｔ1の光学定数，膜厚ｄ₁₂）、第２層（Ｍａｔ2の光学定数＋Ｖｏｉｄ、膜厚ｄ₂₂）と第３層（Ｍａｔ3の光学定数＋Ｖｏｉｄ、膜厚ｄ₃₂）を形成したものである。なおＶｏｉｄとは屈折率１の空間である。
モデル（3）は、基板（Ｓｕｂ）の上に第１層（Ｍａｔ1の光学定数，膜厚ｄ₁₃）、第２層（Ｍａｔ2の指定光学定数＋Ｖｏｉｄ、膜厚ｄ₂₃）、第３層（Ｍａｔ3の指定光学定数＋Ｖｏｉｄ、膜厚ｄ₃₃）を形成したものである。
なお、指定光学定数とは光学定数の基準にする量（Special reference）を意味し、基準にする量とは似たような試料を用いて得られた光学定数である。第３層についても同様である。
モデル（4）は、基板（Ｓｕｂ）の上に第１層（Ｍａｔ1の光学定数、膜厚ｄ₁₄）第２層（Ｍａｔ2＋Ｍａｔ2’、膜厚ｄ₂₄）、第３層（Ｍａｔ3＋Ｍａｔ3’、膜厚ｄ₃₄）を形成したものである。
ここで、モデル（2）〜（4）の２，３層目で設定されている混合比からは、有効媒質近似論を用いて、均質膜としての光学定数を求めることができる。なお前記各モデルは、基板Ｓｕｂの材料の光学定数は既知、第１層の光学定数は、ほぼ既知で、第２層、第３層の光学定数および、第１層の膜厚ｄ_{1 ，}第２層の膜厚ｄ_{2 ，}第３層の膜厚ｄ₃ は、未知（不確か）であることを前提にして前述の４個のモデルをたててある。
【００３６】
（解析フェーズ１ステップ２）
前記ステップ１で選定した４個のモデル(1) 〜(4) のそれぞれについて、前記測定スペクトルより得られた測定データΨ_E ，Δ_E とのフィッティングを行う。図３の３２の示す部分に各モデルのフィッティングの対象とフィッティングの結果得られたデータのχ² 値を示してある。
モデル(1) では、第１層目の膜厚ｄ₁₁、第２層目の膜厚ｄ₂₁，第３層目の膜厚ｄ₃₁および入射角φ₁ をフィッティングして、その結果ｄ_11(best)，ｄ_21(best), ｄ_31(best)，φ_{1 (best)}およびχ² 値 X2 ₍₁₎ を得る。
モデル(2) では、第１層目の膜厚ｄ₁₂，第２層目の膜厚ｄ_22, 第３層目の膜厚ｄ_32, 第２層目の混合比Vf_22, 第３層目の混合比Vf₃₂および入射角φ₂ のフィッティングをして、その結果ｄ_12(best)，ｄ_22(best)，ｄ_32(best)，Vf_22(best)，Vf_32(best)，φ_{2 (best)}およびχ² 値 X2 ₍₂₎ を得る。
モデル(3) では、第１層目の膜厚ｄ₁₃，第２層目の膜厚ｄ₂₃，第３層目の膜厚ｄ_33, 第２層目の混合比Vf_23, 第３層目の混合比Vf₃₃および入射角φ₃ のフィッティングをして、その結果ｄ_13(best)，ｄ_23(best)，ｄ_33(best)，Vf_23(best)，Vf_33(best)，φ_{3 (best)}およびχ² 値 X2 ₍₃₎ を得る。
モデル(4) では、第１層目の膜厚ｄ₁₄，第２層目の膜厚ｄ₂₄，第３層目の膜厚ｄ₃₄，第２層目の混合比Vf₂₄，第３層目の混合比Vf₃₄および入射角φ₄ のフィッティングをして、その結果ｄ_14(best)，ｄ_24(best)，ｄ_34(best)，Vf_24(best)，Vf_34(best)，φ_{4 (best)}およびχ² 値 X2 ₍₄₎ を得る。
【００３７】
（解析フェーズ１ステップ３）
前記複数組のフィッティングの結果から、最低χ² 値またはあらかじめ設定した膜厚や混合比、入射角度の最大値と最小値の間に入っている最低χ² 値のモデルの結果を選択するステップであり、これを図３の３３に示す。
【００３８】
解析フェーズ２は、最も未知な材料から順序立ててＥＢＬＭＣを行う。
（解析フェーズ２解析第１段階ステップ１）
図４の４１に解析第２段階で使用するモデルであるＢＦＡＭが示されている。この例では、解析フェーズ１のフィッティング結果でモデル(4) のχ² 値が最も低かったものとする。２層目の光学定数を１つの分散式でおきかえる。このとき全層の膜厚（ｄ_1,ｄ_2,ｄ₃ ）および１，３層目の光学定数，３層目の混合比は解析フェーズ１のフィッティング結果の値で設定する。
【００３９】
（解析フェーズ２解析第１段階ステップ２）
この例では、図４に示すように、１層目の膜厚を下記の値で固定し、さらに３層目の膜厚を±１０％程度、混合比を±１０％程度変えながらそれぞれ２層目についてＢＬＭＣを行う。４２−１はｄ₁ ＝ｄ_{1 (best)}−１０％に固定して、ｄ₃ ＝ｄ_{3 (best)}±１０％の範囲，Vf₁ ＝Vf_{1 (best)}±１０％の範囲でそれぞれ動かしながら、２層目のＭａｔ2 （ＤＳＰ）についてＢＬＭＣを行うものである。
４２−１（ｄ₁ ＝ｄ_{1 (best)}−１０％に固定）の詳細を図７に示してある。
図７の例では４２−１−２−ｆに示すように、まず、Vf₁ ＝Vf_{1 (best)}に固定し、ｄ₃ ＝ｄ_{3 (best)}を中心値とし、±１０％変えながら、２層目についてＢＬＭＣを行い、それぞれについての厚さ，光学定数およびχ² を求め、そのうちχ² 値の最も良い結果（４２−１−２−ｓ）を選択する。これと、さらに、Vf₁ を変化させながら同様の手順を行った（４２−１−１−ｓ）や（４２−１−３−ｓ）などと比較してχ² 値の最も良い結果（図４および図７の（４２−１−１））を選択する。
【００４０】
なお、図４に示す４２−２では、ｄ₁ ＝ｄ_{1 (best)}に固定して前記同様にＢＬＭＣを行う。４２−３はｄ₁ ＝ｄ_{1 (best)}＋１０％に固定して前記同様にＢＬＭＣを行う。それぞれから得られたχ² 値の最も良い結果（４２−２−１），（４２−３−１）と前述の（４２−１−１）とを比較してχ² 値の最も良い結果を選択する（４３）。
【００４１】
解析フェーズ２解析第２段階は、図５に示すように３層目の光学定数を１つの分散式におきかえる（ステップ１）。そして全層の膜厚（ｄ_1,ｄ_2,ｄ₃ ）および１，２層目の光学定数は解析フェーズ２解析第１段階のフィッティング結果の値で決定する。
（解析フェーズ２解析第２段階ステップ２）
ステップ１で設定したモデルについて、ＥＢＬＭＣを行う。
１層目の膜厚をｄ_{1 (best)}±１０％程度変えながら、さらに２層目の膜厚をｄ₂ ＝ｄ_2(best) ±１０％変えながらそれぞれ３層目についてＢＬＭＣを行う。
（解析フェーズ２解析第２段階ステップ３）図５の５３では前述した結果からχ² 値の最も良い結果を選択する。なおこの際最も良い結果として選択されたものが、あらかじめ設定した各層の膜厚や、分散式パラメータ、混合比、入射角度のそれぞれの最大・最小値の範囲内に入っていないときは解析フェーズ２の解析第１段階のステップ２に戻る。なお、この繰り返しは必要な回数行われる。
【００４２】
図６に示す解析フェーズ３の最終段階ステップ１では、前述したχ² 値の最も良い結果をもつモデルについて以下のフィッティングを行う。
全層の光学定数を固定し、全層の膜厚のフィッティングを行う。または
１，３層の光学定数を固定し、全層の膜厚，および２層目の光学定数のフィッティングを行う。または
１，２層の光学定数を固定し、全層の膜厚，および３層目の光学定数のフィッティングを行う。または
１層目の光学定数を固定して、全層の膜厚，および２，３層目の光学定数のフィッティングを行う。
【００４３】
解析フェーズ３のステップ２図６の６２では、ステップ１のフィッティングの結果を確認する。たとえばフィッティングの結果があらかじめ定めた範囲内に入るか否かの確認を行う。この確認の結果が設定範囲から外れた場合には解析フェーズ１に戻る。解析フェーズ３のステップ３図６の６３では、確認された結果を保存する。
【００４４】
【発明の効果】
本発明によれば、
１．相関関係が強い多層膜構造（特に極薄膜）でも、信頼できる膜厚（全ての層）および光学定数（少なくとも構造中の２層）を得ることができる。
２．ＢＦＡＭ決定ステップでは、考えられる必要な未知変数を最小限にすることができる。
３．ＥＢＬＭＣを順序立てて行うことにより、別のローカルミニマムに落ちてしまうことは劇的に減り、結果の信頼性があがる。
４．未知材料が多く含まれた多層膜構造でも、この方法により、膜厚や光学定数を決定することができる。
【００４５】
以上詳しく説明した実施例について、本発明の範囲内で種々の変形を施すことができる。理解を容易にするために、データの取得、モデルの設定に関連して、一貫してΨ，Δを用いて説明した。当業者には良く知られている以下のデータ対を用いても同様な、測定およびフィッティングが可能であり、本発明の技術的範囲に含まれるものである。
（ｎ，ｋ）、（ε_i ，ε_r ）、( tan Ψ，cos Δ) 、 (Ｉ_s,Ｉ_c ）
【００４６】
また、基板上にＳｉＯ₂ 層，ＳｉＮ_x 層，ＴａＯ_x 層を３層形成する例を示したが、様々な材料の単層・多層構造の測定や広い範囲の膜厚の測定にも同様に利用できる。
【００４７】
光学定数には、既知の数値（リファレンス）を用いたが、物質の誘電率の波長依存性を示す分散式なども使用可能であり、本発明の技術的範囲に含まれるものとする。また、分散式を使用する例では、既知の数値を光学定数に使用する場合もあり、これも本発明の技術的範囲に含まれるものとする。
【００４８】
実施例として光弾性変調器（ＰＥＭ）の例を示したが、ＰＥＭ使用以外のエリプソメータを使用することもできる。
【００４９】
基板もSiの他、ガラスや石英、その他透明基板や化合物半導体なども同様に利用できる。また、基板の種類によらず、どんな平坦な基板でも、あれている基板でも使用することができる。
【００５０】
分散式には、古典力学理論から作成された式や量子力学理論から作成された式、経験式の他、様々な式・パラメータも使用可能であり、これも本発明の技術的範囲に含まれるものとする。
【００５１】
例では、ＥＭＡを使用すると説明したが、他の有効媒質近似論の使用も可能であり、これも本発明の技術的範囲に含まれるものとする。
【００５２】
全ての例の１部または全部は、手動や自動（コンピュータやロボットなど）で行うことができ、これも本発明の技術的範囲に含まれるものとする。
【００５３】
例では入射角度を７５度として説明したが、これ以外の角度でも使用可能であり、これも本発明の技術的範囲に含まれるものとする。
【００５４】
公称入射角度（７５度）近傍で動かしながら解析すると説明したが、その他、物理的に決定した入射角度の近傍で変化させながら解析する場合もあり、これも本発明の技術的範囲に含まれるものとする。
【００５５】
入射角度を自動でいくつか変化させながら測定（Variable Angle Measurement）を行い、これら全体のデータ、またはこの中の特定角度のデータを用いて解析する場合もあり、これらも本発明の技術的範囲に含まれるものとする。さらに、前記測定で得られた全体のデータ、またはこの中の特定角度のデータ解析において、各入射角度近傍を変化させながらフィッティングする場合もあり、これも本発明の技術的範囲に含まれるものとする。
【００５６】
例では基板上の３層構造の極薄膜（Ｍａｔ1 ，Ｍａｔ2 ，Ｍａｔ3 ）としたが、Ｍａｔ1 ，Ｍａｔ2 ，Ｍａｔ3 には、極薄膜誘電体材料だけでなく、様々な厚さや材料など、幅広いアプリケーションにも使用することができる。
【００５７】
上記手段の全部または１部を行う場合もあり、これも本発明の技術的範囲に含まれるものである。
【００５８】
あらゆる任意のパラメータを同時にフィッティングすると説明したが、別々にフィッティングする場合もあり、これも本発明の技術的範囲に含まれるものとする。
【００５９】
ＥＢＬＭＣの一部であるＢＬＭＣでは、前述したとおり、入射角度をフィッティングする場合がある。また、手順では入射角度と様々なパラメータを同時にフィッティングするとしたが、別々にフィッティングする場合や、入射角度を固定する場合もあり、これらも全て本発明の技術的範囲に含まれるものとする。
【００６０】
入射角度はＢＬＭＣ以外でも、一般的なパラメータとしてフィッティングすることがあり、これも本発明の技術的範囲に含まれるものとする。
【００６１】
例では、ＢＬＭＣやＥＢＬＭＣを行う際に、中心値および付近の複数点にわたり選択する時に±１０％、ステップ数５％として説明したが、さらに広い範囲や様々なステップ数も設定可能である。また、％として表したが、「最小値」、「最大値」、「ステップ数」として設定する場合もあり、これも本発明の技術的範囲に含まれるものとする。
【００６２】
例で示した様に、ＥＢＬＭＣは最も未知な材料から始めることが効果的だが、別の順序でも同じ手順を行うことができ、これも本発明の技術的範囲に含まれるものとする。
【００６３】
例では、測定段階のステップの１つとしてデータ保存としたが、これは「この全解析過程が終了した後にも、再度データとして使用できるような永久保存する場合」や「全解析過程が終了するまでの一時保存とする場合」があり、これらも技術的範囲に含まれるものとする。
【００６４】
例では、モデル準備過程において様々な材料を混ぜ合わせた１〜４つのモデルを使用したが、製造プロセスや未知総数によってモデルの種類・数が変わる場合があり、これも本発明の技術的範囲に含まれるものとする。
【００６５】
例では、フィッティングは入射角と膜厚の組み合わせで書いたが、ソフトによっては入射角を分散式と同時にフィッティングすることもあり、これも本発明の技術的範囲に含まれるものとする。
【００６６】
平均二乗誤差の計算式として１例をあげたが、これ以外の式でも同様の手順が可能であり、これも本発明の技術的範囲に含まれるものとする。
【００６７】
例では２種類の材料の混ぜ合わせで説明したが、３種類以上混ぜ合わせる場合もあり、これも本発明の技術的範囲に含まれるものとする。
【図面の簡単な説明】
【図１】本発明方法の実施例である極薄膜３層構造の解析方法で使用するエリプソメータの構成を示す略図であり、測定の対象の試料 (サンプル) ４の一部を拡大して示してある。
【図２】本発明方法の実施例である極薄膜３層構造の解析方法の流れ図である。
【図３】前記実施例における解析フェーズ１を示す詳細説明図である。
【図４】前記実施例における解析フェーズ２の解析第１段階を示す詳細説明図である。
【図５】前記実施例における解析フェーズ２の解析第２段階を示す詳細説明図である。
【図６】前記実施例における解析フェーズ３の詳細説明図である。
【図７】前記実施例における解析フェーズ２の解析第１段階のステップ２の一部の詳細説明図である。
【図８】本発明方法の一般形態である薄膜ｎ層構造の解析方法の流れ図である。
【符号の説明】
１ Ｘｅランプ
２ 光ファイバ
３ 偏光子
４ サンプル
５ 光弾性変調器（ＰＥＭ）
６ 検光子
７ 光ファイバ
８ 分光器
９ データ取込部
２０ 測定フェーズ
３０ 解析フェーズ１
４０ 解析フェーズ２の第１段階
５０ 解析フェーズ２の第２段階
６０ 解析フェーズ３
８１ 解析フェーズ１（ｎ層モデル）
８２ 解析フェーズ２
８３ 解析フェーズ３[0001]
BACKGROUND OF THE INVENTION
  The present invention relates to a method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer.
More specifically, the method of the present invention is a widespread means of analysis.MostThe present invention relates to a method for analyzing a thin film multi-layer structure using a spectroscopic ellipsometer that processes data of a multilayer film made from an unknown material using an extended best local minimum calculation (EBLMC).
[0002]
[Prior art]
A spectroscopic ellipsometer is an apparatus that applies polarized light to a sample and measures the amount of change in polarization of light returned from the sample. The amount of change in polarization of incident light and reflected light is measured using a spectroscopic ellipsometer, and the film thickness (d) and complex refractive index (N = n−ik) can be calculated from the results. The amount of change in polarization (ρ) is expressed by ρ = tanψexp (iΔ) and depends on parameters such as wavelength (λ), incident angle (φ), film thickness, complex refractive index, and the relationship is as follows. .
(D, n, k) = F (Ψ, Δ, λ, φ)
[0003]
When the incident angle is fixed, the single wavelength ellipsometer can measure only two independent variables for the three unknowns (d, n, k), so one of d, n, k is known. Need to be fixed as. Even with a single wavelength, the measurement variable increases when the incident angle is changed. However, due to the difference in incident angle (φ) (Ψφ_i , Δφ_i ) Since there is a strong correlation in the pair, it is difficult to accurately obtain d, n, and k.
[0004]
[Problems to be solved by the invention]
A measurement spectrum (Ψ representing the change in polarization of single and multilayer thin films formed on a substrate measured using a spectroscopic ellipsometer._E (λ_i ) And Δ_E (λ_i )) Includes all of the n, k information of the substrate and d, n, k information of each layer. From now on, the n, k information of the substrate, the d, n, k information of each layer are the only ones. Cannot be calculated (except for the case of only the substrate). This method of searching for the only combination is called spectroscopic ellipsometer data analysis. When the analysis is performed, a model is created by using the n, k information of the substrate and the d, n, k information of each layer. For the n and k information of the substrate and each layer, a reference (known table data), a dispersion formula, or an optical constant of a single layer thin film of a similar material is used.
The dispersion formula is a formula showing the wavelength dependence of the dielectric constant of a substance. In the near infrared to ultraviolet range, this dielectric constant ε (λ) is determined from the bonding mode of the constituent atoms of the material. As a dispersion formula, a calculation formula based on a harmonic oscillator, a calculation formula based on quantum mechanics, an empirical formula, and the like are known, and usually includes two or more parameters. While changing all the unknowns (thickness of each layer, dispersion parameters, mixing ratio, etc.) included in the above-mentioned model, it is adjusted to the measurement data. This is called fitting, and as a result of this fitting, the film thickness and mixing ratio of each layer are obtained, and the complex dielectric constant ε (λ) of the material can be calculated from the dispersion equation parameters. The complex dielectric constant and complex refractive index of the material have the following relationship.
ε (λ) = N² (Λ)
[0005]
Here, the fitting frequently used in the method of the present invention will be briefly described.
(Χ of fitting result² Meaning of)
N measured data pairs, Exp (i = 1, 2,..., N) and corresponding N model calculated data pairs, Mod (i = 1, 2..., N), The measurement error is normally distributed, and the standard deviation is σ_i Then the mean square error (χ² ) Is given as follows.

Here, P is the number of parameters. χ² Is small, it means that the agreement between the measurement results and the model is large, so when comparing multiple models, χ² The lowest is the best model.
[0006]
When the above-described measurement sample is a sample having one film on the substrate, the amount of change in polarization is proportional to the area of phase angle (β) × beam diameter. The phase angle (β) is expressed by the following equation.
β = 2π (d / λ) (N² -N_A ² sin² φ)^1/2
If the beam diameter is constant, the amount of change in polarization is as follows.
Polarization change amount film thickness (d) × complex refractive index (N) × f (φ)
Where N_A Is the complex refractive index of the ambient, N is the complex refractive index of the film, and φ is the incident angle. If the film thickness (d) is thin and the complex refractive index (N) is low, the change in the phase angle (β) becomes small, and the measurement may become difficult. To be clear, the correlation between d and N increases.
[0007]
The above-described problem is that, in the case of an ultra-thin film multilayer structure, there is a possibility that a correlation may occur between the above layers, and the measurement result (Ψ_E (λ_i ), Δ_E (λ_i )), It becomes difficult to obtain d, n, and k of each layer.
[0008]
Further, as described above, the value of the amount of change in polarization also changes depending on the correctness of the incident angle. Therefore, it is necessary to correctly determine the incident angle by some method. Since the correct incident angle can be determined, the value of the amount of change in polarization can be determined correctly.
[0009]
In the present invention, the wavelength dependence of the dielectric constant of the film cannot be specified or difficult by one dispersion formula for various reasons, and the effective medium theory is used to determine the effective dielectric. Calculate the Effective Dielectric Function.
In general, when N substances (guests) having various dielectric constants are mixed in the host material, for example, the effective dielectric constant (ε) is expressed as follows.

At this time ε_h Is the dielectric constant of the host, ε_j Represents the j-th dielectric constant, and k represents the screening factor. Here, if the host material and the contained material are mixed in approximately the same amount, or if it is not known which is the host or guest, the host material itself is the same as the effective medium material ε = ε_h become. The effective medium theory under this condition is called Braggman Effective Medium Approximation (hereinafter simply referred to as EMA). The dielectric constant ε when the three spherical substances a, b, and c are mixed is given by the following equation.

here,
ε: Effective dielectric constant to be obtained
ε_a , ε_b , ε_c   : Dielectric constant of spherical materials a, b, c
f_a , f_b , f_c   : Mixing ratio of each substance (Volume Fraction)
f_a + F_b + F_c = 1
When the film on the substrate is non-uniform or discontinuous, or some materials are mixed, the effective medium approximation (EMA) is used for a medium composed of a plurality of substances that are sufficiently smaller than the wavelength order and physically mixed. ) To build a model.
The case where the substance a, the substance b, and the substance c are mixed will be described. The effective medium approximation (EMA) at this time is a dispersion formula or reference data for the mixing ratio of the substance a, the mixing ratio of the substance b, the mixing ratio of the substance c, the film thickness of the mixed layer of a, b, and c and the dielectric constant. Etc. are estimated and fitted and evaluated.
[0010]
In the present invention, calculation methods called BLMC (Best Local Minimum Calculation) and EBLMC (Extended Best Local Minimum Calculation) are frequently used. Therefore, the abbreviations BLMC and EBLMC are directly used by simply defining them.
BLMC is a method performed for one layer. While changing the initial value of an arbitrary parameter within a certain range, fitting is performed according to a predetermined procedure to determine the best result.
EBLMC is a method performed on a plurality of layers. Arbitrary parameters of the layers other than the BLMC are selected over the central value and a plurality of nearby points, and the BLMC is performed for each point to determine the best result.
[0011]
  The object of the present invention is to set a combined model such as film thickness and complex refractive index, calculate the simulation spectrum, and fit a wide range of the simulation spectrum and measurement spectrum.MostAn object of the present invention is to provide a method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer that determines a thin film multilayer (plurality) layer structure by using a local minimum calculation method (EBLMC).
[0012]
[Means for Solving the Problems]
  The method for analyzing a thin film multi-layer structure using a spectroscopic ellipsometer according to the present invention includes three layers of the thin film multi-layer structure, a spectroscopic phase for obtaining measurement data using the spectroscopic ellipsometer, An analysis phase 1 for determining an analysis initial stage model, and an unknown constant of the target layer while changing constants of layers other than the target layer in the three-layer structure over a plurality of points near the center point in the analysis initial stage model TheMostThe first stage determined by the local minimum calculation (BLMC), and the constants of the other layers are changed while changing over the central point of the determined constant and a plurality of nearby points.MostAnalysis phase 2 including the second stage determined by the local minimum calculation (BLMC)
  It is composed of
[0013]
  The method for analyzing a thin film multi-layer structure using a spectroscopic ellipsometer according to the present invention is such that the thin film multi-layer structure has three layers, a spectroscopic measurement phase for obtaining measurement data using the spectroscopic ellipsometer, and a thin film three-layer structure. An analysis phase 1 for determining an analysis initial stage model, and an unknown constant of the target layer while changing constants of layers other than the target layer in the three-layer structure over a plurality of points near the center point in the analysis initial stage model TheMostThe first stage determined by the local minimum calculation (BLMC), and the constants of the other layers are changed while changing over the central point of the determined constant and a plurality of nearby points.MostAnalysis phase 2 including a second stage determined by a local minimum calculation (BLMC) method, and fixing a predetermined constant of the model in which each constant is determined in the analysis phase 2 and fitting for other constants The analysis phase 3 is performed.
[0014]
  The method of analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention includes a spectroscopic measurement phase for obtaining measurement data using the spectroscopic ellipsometer, an analysis phase 1 for determining an analysis initial stage model of the thin film multilayer structure, For the initial stage model of layer structure analysis, the constants of layers other than the target layer in the multi-layer structure are changed over the central point and a plurality of nearby points, and the unknown constant of the target layer is changed.MostIt comprises an analysis phase 2 determined by a local minimum calculation (BLMC).
[0015]
  The method of analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention includes a spectroscopic measurement phase for obtaining measurement data using the spectroscopic ellipsometer, an analysis phase 1 for determining an analysis initial stage model of the thin film multilayer structure, For the initial stage model of layer structure analysis, the constants of layers other than the target layer in the multi-layer structure are changed over the central point and a plurality of nearby points, and the unknown constant of the target layer is changed.MostAnalysis phase 2 determined by the local minimum calculation (BLMC) method, and analysis phase in which a predetermined constant of the model whose unknown constant is determined in the analysis phase 2 is fixed and fitting is performed for other constants. 3. In the method for analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention, the unknown constant is a film thickness of each layer, an optical constant of an unknown material, or a mixing ratio.
[0016]
  According to the present inventionMinuteThin film using optical ellipsometerMultipleHow to analyze the layer structure,
  in frontThe spectroscopic measurement phase,
  EnterEach wavelength λ by changing the wavelength of incident light_iMeasured spectrum Ψ representing the change in polarization of incident and reflected light for each_E(Λ_i) And Δ_E(Λ_i) To get)_E, Δ_EA spectral measurement step;
  A storage step for storing data obtained by the measurementWhen
TheIncluding.
[0017]
  The method for analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention is as follows:
  In the analysis phase 1, one best approximation model (hereinafter referred to as BFAM) selected from a plurality of types of models is determined as an analysis initial stage model.PlaceIn the analysis phase 1,
  The first step of creating multiple possible models,
  A second step of fitting at least the film thickness and the incident angle for the plurality of types of models;
  From the result of the second step, the mean square error (χ² ) Model with the lowest value, or the minimum mean square error (χ² ) The third step of selecting the value model as BFAM;
  A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer comprising:
  Moreover, the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to the present invention is as follows:
  In the analysis phase 1, one best approximate model (BFAM) selected by fitting from a plurality of models, or an initial model assumed from known data is determined as an analysis initial stage model.
[0018]
  According to the analysis method of a thin film multilayer structure using a spectroscopic ellipsometer according to the present invention, the first stage of the analysis phase 2 is the most unknown material layer in the multilayer structure in the analysis initial stage model determined in the analysis phase 1 The first step of changing the optical constant of the target layer to one dispersion formula, and changing the film thickness of the layers other than the target layer over a plurality of points near and at the center point,MostA second step of performing a local minimum calculation (BLMC), and the second stepMostFrom the result of the local minimum calculation (BLMC), the mean square error (χ² And the third step of selecting the best result of the value of).
[0019]
  In the analysis method of a thin film multi-layer structure using the spectroscopic ellipsometer according to the present invention, the second stage of the analysis phase 2 is such that the optical constant of the target layer determined in the first stage is known, and The first unknown step is to change the optical constant of the new layer of interest into a single dispersion equation, and the film thicknesses of the layers other than the new layer of interest from the center point and New points of interest for each point while changing over multiple nearby pointsMostA second step of performing a local minimum calculation (BLMC), and the second stepMostFrom the result of the local minimum calculation (BLMC), the mean square error (χ² And the third step of selecting the best result of the value of).
[0020]
  In the analysis method of a thin film multi-layer structure using a spectroscopic ellipsometer according to the present invention, the analysis phase 2 is performed by changing the constants of layers other than the target layer in the three-layer structure over a plurality of points near and at the center point. Unknown constants ofMostThere are three or more stages determined by a local minimum calculation (BLMC), and each stage is sequentially performed. The first stage of the analysis phase 2 is the analysis phase. In the analysis initial stage model determined in 1, the first step of changing the optical constant of the target layer, which is the most unknown material layer in the multi-layer structure, into one dispersion formula, and at least the film thickness of the layers other than the target layer, While changing the center point and multiple nearby points,MostA second step of performing a local minimum calculation (BLMC), and the second stepMostFrom the result of the local minimum calculation (BLMC), the mean square error (χ² And the third step of selecting the best result of the value of the analysis phase 2 in each of the second and subsequent stages of the analysis phase 2 in which the optical constant of the target layer obtained in the previous stage is known, and the other layers The first step to change the optical constant of the new layer of interest into a single dispersion formula with the most unknown material layer as the new layer of attention, and at least the film thickness of layers other than the new layer of interest And a new layer of attention for each pointMostA second step of performing a local minimum calculation (BLMC), and the second stepMostFrom the result of the local minimum calculation (BLMC), the mean square error (χ² ) To select the best result of the value of).
[0021]
  The method for analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention is as follows:
  Final stage of analysis phase 2Selected bySelected mean square error (χ²) Value is not within the range of the maximum and minimum values of each layer thickness, dispersion parameter, mixing ratio, and incident angle set in advance, the first stage of the analysis phase 2 Return to the second stepCharacterized by changing at least the film thickness of layers other than the target layer.
[0022]
  The method for analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention is as follows:
  The analysis phase 3 is the analysis phase 2Mean square error (χ ² ) Model with the best resultsIt is configured as a phase in which fitting is performed for such an arbitrary parameter, and the result of the fitting is confirmed and stored.
[0023]
  The method for analyzing a thin film multilayer structure using the spectroscopic ellipsometer according to the present invention is as follows:
  If the result of the analysis phase 3 fitting is not within the range of the maximum and minimum values set in advance,Determine a new initial analysis modelIt is configured to return to the analysis phase 1.
[0024]
  In the analysis method of a thin film multi-layer structure using a spectroscopic ellipsometer according to the present invention, the analysis phase 1 uses an effective medium approximation for the target layer to determine an analysis initial stage model, and the first phase of the analysis phase 2 In the first step, assuming that several materials are mixed in the target layer, at least one of the several materials in the target layer is expressed by a dispersion formula using the effective medium approximation, and the analysis phase 2 In the second step of the first stage, the film thickness and mixing ratio of the layers other than the target layer are selected over a plurality of points, and this layer is changed while changing the mixing ratio of the target layer for each pointMostIt is configured to perform a local minimum calculation (BLMC).
[0025]
  In addition,According to the present inventionMinuteThin film using optical ellipsometerMultipleLayer structure analysis methodsoIs,
  TotalOn the board to be measuredMultiple thin filmsLayer structure, each wavelength λ by changing the wavelength of incident light_iMeasurement spectrum representing the change in polarization of incident and reflected light for each_E(Λ_i) And Δ_E(Λ_i) To get)_E, Δ_ESpectral spectroscopy phase;
  Analysis phase 1 for each of multiple measurement conditions (Zi) within the expected rangeofThird step or analysis phase 2 analysisLast ofStageofPerform up to the third step, and select the lowest result from the results obtained for each measurement condition.Mean square error of (χ² )ofAmong the combinations in which the value or dispersion parameter, mixing ratio, and incident angle are between the set maximum and minimum values,Mean square error (χ² )ofAnd the fourth step of selecting the best valueYou may make it.
[0026]
  AlsoAccording to the present inventionMinuteThin film using optical ellipsometerMultipleLayer structure analysis methodsoIs,
  in frontThe step of selecting the smallest difference in the analysis phases 1, 2 and 3 is to obtain the mean square error of the measured value and the fitted one, and the smallest mean square error or the preset film thickness, It is configured to determine the one with the smallest mean square error that is contained in the maximum and minimum values of the dispersion parameter, mixing ratio, and incident angle variable.You may make it.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer according to the present invention will be described with reference to the drawings.
FIG. 1 is a schematic diagram showing the configuration of an ellipsometer used in the method of the present invention.
Generally speaking, the present invention can be used for an analysis method of an ultra-thin film or thin-film multilayer structure having two or more layers. In order to facilitate understanding, first, an analysis method of ultrathin film three-layer structure data will be described as an example. In FIG. 1, a part of the sample 4 to be measured is shown in an enlarged manner.
[0028]
The spectroscopic ellipsometer shown in FIG. 1 executes a spectroscopic measurement data acquisition step (measurement phase) of a method described later. First, the measurement apparatus will be briefly described. The Xe lamp 1 is a so-called white light source including a large number of wavelength components. The light emitted from the Xe lamp 1 is guided to the polarizer 3 through the optical fiber 2. The light polarized by the polarizer 3 is incident on the surface of the sample 4 to be measured at a specific incident angle (for example, φ = 75.00 °). Sample 4 is a measurement sample in which a thin film is formed in three layers on the substrate surface described later.
The reflection from the sample 4 is guided to the analyzer 6 through a photoelastic modulator (PEM) 5. Phase modulation is performed at a frequency of 50 kHz by a photoelastic modulator (PEM) 5 to produce linear to elliptically polarized light. Therefore, Ψ and Δ can be determined with a resolution of several milliseconds. The output of the analyzer 6 is connected to the spectroscope 8 via the optical fiber 7. The output data of the spectroscope 8 is taken into the data take-in unit 9 and the spectroscopic measurement data acquisition step is completed. The position of the PEM 5 can be either after the polarizer 3 or before the analyzer 6.
[0029]
FIG. 2 is a flowchart of an ultrathin film three-layer measurement method, and FIG. 8 is a flowchart of an analysis method of a thin film n-layer structure, which is a general form of the method of the present invention.
The analysis in the method of the present invention can be basically divided into three phases. The analysis phase 1 is a phase in which an initial model that is considered to best suit an actual sample to be analyzed in the analysis phase 2 and later is determined.
In this phase 1, as will be described later, one best approximation model (BFAM) may be selected from a plurality of models by fitting (31, 32, 33 in FIG. 3, 81A in FIG. 8). Alternatively, it may be an initial model setting (34 in FIG. 3, 81B in FIG. 8) given or assumed from known data. In any case, the model selected here becomes the object of analysis in the analysis phase 2 or later.
[0030]
The number of models for determining the model (BFAM) in analysis phase 1 depends on the number of unknown layers in the structure and the number of available data. Here, the unknown layer is a layer or the like for which an accurate optical constant must be determined.
In the analysis phase 2, the EBLMC procedure is sequentially executed in the order of the analysis first and second analysis steps from the unknown material in the multilayer structure, particularly the most unknown material.
For example, as described later, the EBLMC procedure is executed for Mat2 in the first analysis stage, and the EBLMC procedure is executed for Mat3 using the result of the first stage in the second analysis stage. In the analysis phase 3, the result of the analysis phase 2 is subjected to final fitting, the result is confirmed, and output or saved as data.
[0031]
The symbols used in the present invention are collectively shown below.
(Definition of symbols)
Sub: Substrate (optical constants are known, can be handled as bulk)
Mat: Thin film material (optical constant of matter)
d_i : i-th layer thickness
d_{i (best)} : Film thickness of the i-th layer obtained by fitting
d_ij: The film thickness of the i-th layer of the jth model
d_{ij (best)}: Film thickness of the i-th layer of the j-th model obtained by fitting
X2: Mean square error (χ²)value
X2_(j) : Mean square error (χ²)value
Void: n = 1, k = 0
Vf_(ij) : Volume fraction of the i-th layer of the jth model
Vf_{(ij) (best)} : Mixing ratio of the i-th layer of the j-th model obtained by fitting
[0032]
In the following examples, each layer is composed of the following materials.
3rd layer TaO_x (Mat_Three D)_Three
Second layer Si N (Mat₂ D)₂
1st layer SiO₂ (Mat₁ D)₁
Substrate (Sub) Si Bulk
[0033]
  Measurement Phase (Measurement Step) 20A in FIG. 2 is measured by the apparatus shown in FIG. The ultrathin film three-layer structure on the substrate of the measurement object 4 (see the enlarged view in the figure) is changed to each wavelength λ by changing the wavelength of the incident light._iMeasurement spectrum representing the change in polarization of incident and reflected light for each_E(Λ_i) And Δ_E(Λ_i)In chargeΨ_E, Δ_EMeasure the spectrum. In the measurement phase data storage step 20B, the data measured in the previous step is stored as comparison target data (see FIG. 2).
[0034]
Ultra-thin three-layer film fitting process
In this embodiment, the substance 1 (Mat1) is substantially known, the second and third layer substances (Mat2, Mat3) and the first, second and third layer thicknesses (d_1,d_2,d_Three ) Is unknown.
In this example, it is assumed that the optical constant of the second layer substance (Mat2) is least known.
[0035]
  In analysis phase 1, BFAM settings 31 to 33 are performed. Alternatively, the initial model assumption 34 is made.
(Analysis Phase 1 Step 1)
  As shown at 31 in FIG. 3, a plurality of possible models are created. The most suitable structure and initial film thickness are determined.
  In this step, the (N₀(N₀, K₀)) And the possible complex refractive index (N of each thin film material (Mat1, Mat2, Mat3)) ₁ (n₁, K₁)), (N ₂ (n₂, K₂)), (N _Three (n_Three, K_Three)), Film thickness of each layer (d₁, D₂, D_Three) And make several models.
  In this embodiment, the following models (1) to (4) are set.
  Each of the models is schematically shown in a portion indicated by 31 in FIG.
  In the model (1), the first layer (Mat1 optical constant, film thickness d) is formed on the substrate (Sub).₁₁), Second layer (Mat2 optical constant, film thickness d)_{twenty one}), Third layer (Mat3 optical constant, film thickness d)₃₁).
  In the model (2), the first layer (Mat1 optical constant, film thickness d) is formed on the substrate (Sub).₁₂), Second layer (Mat2 optical constant + Void, film thickness d)_{twenty two}) And the third layer (Mat3 optical constant + Void, film thickness d)₃₂). Note that “Void” is a space having a refractive index of 1.
  Model (3) is a first layer (Mat1 optical constant, film thickness d) on a substrate (Sub).₁₃), Second layer (specified optical constant of Mat 2 + Void, film thickness d)_{twenty three}), Third layer (specified optical constant of Mat3 + Void, film thickness d)₃₃).
  The designated optical constant means an amount used as a reference for the optical constant (Special reference), and the amount used as the reference is an optical constant obtained using a sample similar to the reference. The same applies to the third layer.
  In the model (4), the first layer (Mat1 optical constant, film thickness d) is formed on the substrate (Sub).₁₄) Second layer (Mat2 + Mat2 ', film thickness d_{twenty four}), Third layer (Mat3 + Mat3 ', film thickness d)₃₄).
  Here, from the mixing ratios set in the second and third layers of the models (2) to (4), the optical constant as a homogeneous film can be obtained using the effective medium approximation theory. In each model, the optical constant of the material of the substrate Sub is known, the optical constant of the first layer is almost known, the optical constants of the second layer and the third layer, and the film thickness d of the first layer._{1 ,}Second layer thickness d_{2 ,}Film thickness d of the third layer_ThreeIs based on the assumption that it is unknown (uncertain).
[0036]
(Analysis Phase 1 Step 2)
Measurement data Ψ obtained from the measurement spectrum for each of the four models (1) to (4) selected in step 1_E , Δ_E And fitting. In the part indicated by 32 in FIG. 3, the object of fitting of each model and the χ of the data obtained as a result of the fitting² Values are shown.
In model (1), the film thickness d of the first layer₁₁, Film thickness d of the second layer_{twenty one}, Film thickness d of the third layer₃₁And incident angle φ₁ And the result d_{11 (best)}, D_{21 (best),} d_{31 (best)}, Φ_1 (best)And χ² Value X2₍₁₎ Get.
In model (2), film thickness d of the first layer₁₂, Film thickness d of the second layer_{twenty two,} Film thickness d of the third layer_32, Second layer mixing ratio Vf_{twenty two,} 3rd layer mixing ratio Vf₃₂And incident angle φ₂ And fitting the result d_{12 (best)}, D_{22 (best)}, D_{32 (best)}, Vf_{22 (best)}, Vf_{32 (best)}, Φ_2 (best)And χ² Value X2₍₂₎ Get.
In model (3), film thickness d of the first layer₁₃, Film thickness d of the second layer_{twenty three}, Film thickness d of the third layer_33, Second layer mixing ratio Vf_{twenty three,} 3rd layer mixing ratio Vf₃₃And incident angle φ_Three And fitting the result d_{13 (best)}, D_{23 (best)}, D_{33 (best)}, Vf_{23 (best)}, Vf_{33 (best)}, Φ_{Three (best)}And χ² Value X2₍₃₎ Get.
In model (4), the film thickness d of the first layer₁₄, Film thickness d of the second layer_{twenty four}, Film thickness d of the third layer₃₄, Second layer mixing ratio Vf_{twenty four}, Third layer mixing ratio Vf₃₄And incident angle φ_Four And fitting the result d_{14 (best)}, D_{24 (best)}, D_{34 (best)}, Vf_{24 (best)}, Vf_{34 (best)}, Φ_Four (best)And χ² Value X2_(Four) Get.
[0037]
(Analysis Phase 1 Step 3)
From the results of the multiple sets of fittings, the minimum χ² Value or a preset film thickness, mixing ratio, and minimum χ that falls between the maximum and minimum values of the incident angle² This is the step of selecting the result of the value model, which is shown at 33 in FIG.
[0038]
In analysis phase 2, EBLMC is performed in order from the most unknown material.
(Analysis Phase 2 Analysis 1st Step 1)
BFAM which is a model used in the second stage of analysis is shown at 41 in FIG. In this example, the result of fitting in analysis phase 1² Assume that the value was the lowest. The optical constant of the second layer is replaced with one dispersion formula. At this time, the film thickness of all layers (d_1,d_2,d_Three ), The optical constants of the first and third layers, and the mixing ratio of the third layer are set by the values of the fitting results of analysis phase 1.
[0039]
(Analysis Phase 2 Analysis 1st Stage Step 2)
In this example, as shown in FIG. 4, the film thickness of the first layer is fixed at the following values, and further, the film thickness of the third layer is changed by about ± 10%, and the mixing ratio is changed by about ± 10%. Perform BLMC on the eyes. 42-1 is d₁ = D_1 (best)Fixed at -10%, d_Three = D_{Three (best)}± 10% range, Vf₁ = Vf_1 (best)BLMC is performed on Mat2 (DSP) of the second layer while moving each within a range of ± 10%.
42-1 (d₁ = D_1 (best)Details of (fixed to -10%) are shown in FIG.
In the example of FIG. 7, as shown in 42-1-2-f, first, Vf₁ = Vf_1 (best)Fixed to d_Three = D_{Three (best)}The center value is changed by ± 10%, BLMC is performed on the second layer, and the thickness, optical constant and χ² Of which χ² Select the result with the best value (42-1-2-s). And this, and Vf₁ Compared with (42-1-1-s), (42-1-3-s), etc., in which the same procedure was performed while changing² The result with the best value ((42-1-1) in FIGS. 4 and 7) is selected.
[0040]
In addition, in 42-2 shown in FIG.₁ = D_1 (best)The BLMC is performed in the same manner as described above. 42-3 is d₁ = D_1 (best)The BLMC is performed in the same manner as described above with + 10% fixed. Χ obtained from each² The best result (42-2-1), (42-3-1) and the above-mentioned (42-1-1)² The result with the best value is selected (43).
[0041]
Analysis Phase 2 In the second analysis stage, as shown in FIG. 5, the optical constant of the third layer is replaced with one dispersion equation (step 1). And the film thickness of all layers (d_1,d_2,d_Three ) And the optical constants of the first and second layers are determined by the value of the fitting result in the first stage of the analysis phase 2 analysis.
(Analysis Phase 2 Analysis 2nd Stage Step 2)
EBLMC is performed on the model set in step 1.
The film thickness of the first layer is d_1 (best)While changing about ± 10%, the thickness of the second layer is further changed to d₂ = D_{2 (best)} Perform BLMC on the third layer while changing ± 10%.
(Analysis Phase 2 Analysis Second Stage Step 3) In 53 of FIG.² Choose the result with the best value. In this case, the best result selected is analysis phase 2 when it is not within the maximum / minimum values of each layer thickness, dispersion parameter, mixing ratio, and incident angle set in advance. Return to Step 2 of the first analysis stage. This repetition is performed as many times as necessary.
[0042]
In the final step 1 of the analysis phase 3 shown in FIG.² Perform the following fitting on the model with the best results:
The optical constants of all layers are fixed and the film thicknesses of all layers are fitted. Or
The optical constants of the first and third layers are fixed, and the film thicknesses of all the layers and the optical constants of the second layer are fitted. Or
The optical constants of the first and second layers are fixed, and the film thickness of all layers and the optical constant of the third layer are fitted. Or
The optical constants of the first layer are fixed, and the film thicknesses of all the layers and the optical constants of the second and third layers are fitted.
[0043]
Step 2 of analysis phase 3 In 62 of FIG. 6, the result of fitting in step 1 is confirmed. For example, it is confirmed whether or not the fitting result falls within a predetermined range. If the result of this confirmation is outside the set range, the process returns to analysis phase 1. Step 3 of the analysis phase 3 In 63 of FIG. 6, the confirmed result is stored.
[0044]
【The invention's effect】
According to the present invention,
1. Even with a multilayer film structure (particularly an ultrathin film) having a strong correlation, a reliable film thickness (all layers) and optical constants (at least two layers in the structure) can be obtained.
2. In the BFAM determination step, possible necessary unknown variables can be minimized.
3. By performing EBLMC in sequence, falling to another local minimum is dramatically reduced and results are more reliable.
4). Even in a multilayer structure containing many unknown materials, the film thickness and optical constant can be determined by this method.
[0045]
Various modifications can be made to the embodiments described in detail within the scope of the present invention. In order to facilitate understanding, Ψ and Δ have been consistently described in relation to data acquisition and model setting. Similar measurements and fittings are possible using the following data pairs well known to those skilled in the art and are within the scope of the present invention.
(N, k), (ε_i , Ε_r ), (Tan Ψ, cos Δ), (I_s,I_c )
[0046]
In addition, SiO on the substrate₂ Layer, SiN_x Layer, TaO_x Although an example in which three layers are formed has been shown, the present invention can be similarly used for measurement of a single layer / multilayer structure of various materials and measurement of a wide range of film thicknesses.
[0047]
Although a known numerical value (reference) is used for the optical constant, a dispersion formula indicating the wavelength dependence of the dielectric constant of the substance can also be used, and is included in the technical scope of the present invention. In the example using the dispersion formula, a known numerical value may be used for the optical constant, and this is also included in the technical scope of the present invention.
[0048]
Although an example of a photoelastic modulator (PEM) has been shown as an example, an ellipsometer other than the use of PEM can also be used.
[0049]
In addition to Si, glass, quartz, other transparent substrates, compound semiconductors, and the like can be used as well. In addition, any flat substrate or any substrate can be used regardless of the type of substrate.
[0050]
In addition to formulas created from classical mechanics theory, formulas created from quantum mechanics theory, and empirical formulas, various formulas and parameters can be used as the dispersion formula, and these formulas are also included in the technical scope of the present invention. Shall.
[0051]
In the example, it has been described that EMA is used. However, other effective medium approximation theory can be used, which is also included in the technical scope of the present invention.
[0052]
Part or all of all examples can be performed manually or automatically (computer, robot, etc.), and this is also included in the technical scope of the present invention.
[0053]
In the example, the incident angle has been described as 75 degrees, but other angles can also be used, and this is also included in the technical scope of the present invention.
[0054]
Although it has been described that the analysis is performed while moving near the nominal incident angle (75 degrees), there are cases where the analysis is performed while changing near the incident angle that is physically determined, and this is also included in the technical scope of the present invention. And
[0055]
There are cases where the measurement is performed while automatically changing some incident angles (Variable Angle Measurement), and analysis is performed using the whole data or data of a specific angle in these, and these are also within the technical scope of the present invention. Shall be included. Further, in the data analysis of the whole data obtained by the measurement or the data analysis of a specific angle in this, fitting may be performed while changing the vicinity of each incident angle, which is also included in the technical scope of the present invention. To do.
[0056]
In the example, a three-layer ultrathin film (Mat1, Mat2, Mat3) on the substrate is used. Can be used.
[0057]
All or part of the above means may be performed, and this is also included in the technical scope of the present invention.
[0058]
Although it has been described that all arbitrary parameters are fitted at the same time, they may be fitted separately, and this is also included in the technical scope of the present invention.
[0059]
In the BLMC that is a part of the EBLMC, the incident angle may be fitted as described above. In the procedure, the incident angle and various parameters are fitted at the same time. However, the fitting may be performed separately or the incident angle may be fixed, all of which are included in the technical scope of the present invention.
[0060]
The incident angle may be fitted as a general parameter other than BLMC, and this is also included in the technical scope of the present invention.
[0061]
In the example, when performing BLMC or EBLMC, the center value and a plurality of neighboring points are selected as ± 10% and the number of steps is 5%. However, a wider range and various number of steps can be set. In addition, although expressed as%, there are cases where “minimum value”, “maximum value”, and “number of steps” are set, which are also included in the technical scope of the present invention.
[0062]
As shown in the examples, the EBLMC is effective to start with the most unknown material, but the same procedure can be performed in another order, which is also within the scope of the present invention.
[0063]
In the example, data was saved as one of the steps in the measurement stage, but this is “when the data is permanently stored so that it can be used again after this whole analysis process” or “the whole analysis process is finished. In some cases, these are also included in the technical scope.
[0064]
In the example, 1 to 4 models with various materials mixed in the model preparation process were used, but the type and number of models may vary depending on the manufacturing process and the unknown total number, and this is also within the technical scope of the present invention. Shall be included.
[0065]
In the example, the fitting is written with a combination of the incident angle and the film thickness, but depending on the software, the incident angle may be fitted simultaneously with the dispersion formula, and this is also included in the technical scope of the present invention.
[0066]
Although one example has been given as an equation for calculating the mean square error, the same procedure is possible with other equations, and this is also included in the technical scope of the present invention.
[0067]
In the example, two kinds of materials are mixed, but there are cases where three or more kinds are mixed, which are also included in the technical scope of the present invention.
[Brief description of the drawings]
FIG. 1 is a schematic diagram showing the configuration of an ellipsometer used in an analysis method of an ultrathin film three-layer structure which is an embodiment of the method of the present invention, and shows an enlarged part of a sample (sample) 4 to be measured. is there.
FIG. 2 is a flowchart of an analysis method of an ultrathin film three-layer structure which is an embodiment of the method of the present invention.
FIG. 3 is a detailed explanatory view showing an analysis phase 1 in the embodiment.
FIG. 4 is a detailed explanatory view showing an analysis first stage of an analysis phase 2 in the embodiment.
FIG. 5 is a detailed explanatory diagram showing a second analysis stage of analysis phase 2 in the embodiment.
FIG. 6 is a detailed explanatory diagram of an analysis phase 3 in the embodiment.
FIG. 7 is a detailed explanatory diagram of a part of Step 2 in the analysis first stage of the analysis phase 2 in the embodiment.
FIG. 8 is a flowchart of a method for analyzing a thin-film n-layer structure, which is a general form of the method of the present invention.
[Explanation of symbols]
1 Xe lamp
2 Optical fiber
3 Polarizer
4 samples
5 Photoelastic modulator (PEM)
6 Analyzer
7 Optical fiber
8 Spectrometer
9 Data acquisition part
20 Measurement phase
30 Analysis phase 1
40 Phase 1 of analysis phase 2
50 Second stage of analysis phase 2
60 Analysis Phase 3
81 Analysis phase 1 (n-layer model)
82 Analysis Phase 2
83 Analysis Phase 3

Claims (15)

A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer,
The number of layers of the thin film multilayer structure is three layers,
A spectroscopic phase for obtaining measurement data using a spectroscopic ellipsometer;
Analysis phase 1 for determining an analysis initial stage model of a thin film three-layer structure;
For the analysis initial stage model, the unknown constant of the target layer is changed to a minimum local value calculation method (BLMC: Best Local Minimum) while changing the constants of layers other than the target layer in the three-layer structure over the central point and a plurality of nearby points. The first step of determining by the calculation (Calculation), and the second step of determining the constants of the other layers by the minimum local value calculation method (BLMC) while changing over the central point of the determined constant and a plurality of nearby points. An analysis method of a thin film multilayer structure using a spectroscopic ellipsometer composed of an analysis phase 2 including steps. A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer,
The number of layers of the thin film multilayer structure is three layers,
A spectroscopic phase for obtaining measurement data using a spectroscopic ellipsometer;
Analysis phase 1 for determining an analysis initial stage model of a thin film three-layer structure;
For the analysis initial stage model, the unknown constant of the target layer is changed to a minimum local value calculation method (BLMC: Best Local Minimum) while changing the constants of layers other than the target layer in the three-layer structure over the central point and a plurality of nearby points. The first step of determining by the calculation (Calculation), and the second step of determining the constants of the other layers by the minimum local value calculation method (BLMC) while changing over the central point of the determined constant and a plurality of nearby points. Analysis phase 2 including stages;
An analysis method of a thin film multi-layer structure using a spectroscopic ellipsometer comprising: an analysis phase 3 in which predetermined constants of the model in which each constant is determined in the analysis phase 2 are fixed and fitting is performed for other constants. A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer,
A spectroscopic phase for obtaining measurement data using a spectroscopic ellipsometer;
Analysis phase 1 for determining an initial stage model of analysis of a thin film multilayer structure;
Regarding the initial stage model of analysis of a thin film multi-layer structure, the constants of layers other than the target layer in the multi-layer structure are changed over a plurality of points near and at the center point, and the unknown constants of the target layer are calculated using the minimum local value calculation method (BLMC : Best Local Minimum Calculation) Analysis method of thin film multi-layer structure using spectroscopic ellipsometer composed of analysis phase 2 determined by A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer,
A spectroscopic phase for obtaining measurement data using a spectroscopic ellipsometer;
Analysis phase 1 for determining an initial stage model of analysis of a thin film multilayer structure;
Regarding the initial stage model of analysis of a thin film multi-layer structure, the constants of layers other than the target layer in the multi-layer structure are changed over a plurality of points near and at the center point, and the unknown constants of the target layer are calculated using the minimum local value calculation method (BLMC : Analysis phase 2 determined by Best Local Minimum Calculation)
An analysis method of a thin film multi-layer structure using a spectroscopic ellipsometer comprising: an analysis phase 3 in which a predetermined constant of a model for which an unknown constant has been determined in the analysis phase 2 is fixed and fitting is performed for other constants. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 1 to 4,
The unknown constant is a method of analyzing a thin film multi-layer structure using a spectroscopic ellipsometer, wherein the unknown constant is a film thickness of each layer, an optical constant of an unknown material, or a mixing ratio. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 1 to 5,
The spectroscopic measurement phase includes:
Ψ _E , Δ _E spectrum measurement to obtain measurement spectra Ψ _E (λ _i ) and Δ _E (λ _i ) representing the change in polarization of incident light and reflected light for each wavelength λ _i by changing the wavelength of incident light Steps,
A method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer, comprising: storing a data obtained by the measurement. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 1 to 6,
In the analysis phase 1, when one best approximation model (BestFirst Approximation Model, hereinafter referred to as BFAM) selected from a plurality of types of models is determined as an analysis initial stage model, the analysis phase 1 includes:
The first step of creating multiple possible models,
A second step of fitting at least the film thickness and the incident angle for the plurality of types of models;
The model with the lowest mean square error (χ ² ) value from the result of the second step, or the minimum mean square error (χ ² ) that falls between the preset film thickness and the maximum and minimum values of the incident angle A third step of selecting a model of the value of γ as a BFAM, and a method for analyzing a thin film multilayer structure using a spectroscopic ellipsometer. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to claim 7,
The analysis phase 1 includes a thin film multilayer structure using a spectroscopic ellipsometer that determines one best approximate model (BFAM) selected from a plurality of models by fitting, or an initial model assumed from known data as an analysis initial stage model. analysis method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to claim 1 or 2,
The first stage of the analysis phase 2 is:
In the analysis initial stage model determined in the analysis phase 1, the first step of replacing the optical constant of the layer of interest, which is the most unknown material layer in the multilayer structure, into one dispersion formula;
The thickness of the layers other than the target layer, the center point and the outermost local minimum value calculation method of the target layer for each point while changing over a plurality of points near: a second step of performing (BLMC Best Local Minimum Calculation),
The highest minimum value calculation method of the second step (BLMC: Best Local Minimum Calculation) of the thin film more using spectroscopic ellipsometer results and a third step of selecting the best results in the value of the mean square error (chi ²⁾ Layer structure analysis method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to claim 9,
The second stage of the analysis phase 2 includes
The optical constant of the target layer determined in the first step is made known, the most unknown material layer among the other layers is made a new target layer, and the optical constant of the new target layer is set to one dispersion formula. The first step to replace
The thickness of the new target layer other layers, the outermost local minimum value calculation method of the new target layer for each point while changing over a plurality of points of the center point and the vicinity of: a second step of performing (BLMC Best Local Minimum Calculation) ,
The highest minimum value calculation method of the second step (BLMC: Best Local Minimum Calculation) of the thin film more using spectroscopic ellipsometer results and a third step of selecting the best results in the value of the mean square error (chi ²⁾ Layer structure analysis method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 3 to 8,
The analysis phase 2, the outermost local minimum value calculation method an unknown constants of the target layer while changing a constant of the layer other than the target layer over a plurality of points of the center point and the vicinity of the 3-layer structure (BLMC: Best Local Minimum Calculation ) Have three or more stages determined, and each stage is performed sequentially.
The first stage of the first analysis phase 2 is:
In the analysis initial stage model determined in the analysis phase 1, the first step of replacing the optical constant of the layer of interest, which is the most unknown material layer in the multilayer structure, into one dispersion formula;
At least the thickness of the layers other than the target layer, the center point and the outermost local minimum value calculation method of the target layer for each point while changing over a plurality of points near: a second step of performing (BLMC Best Local Minimum Calculation),
And a third step of selecting the best results of the values of: (Best Local Minimum Calculation BLMC) of the mean square error from the results (chi ^2), the outermost local minimum value calculation method of the second step
The second and subsequent stages of the analysis phase 2 are:
The optical constant of the target layer obtained in the previous step is made known, the most unknown material layer among the other layers is used as the new target layer, and the optical constant of the new target layer is replaced with one dispersion formula. One step,
At least the thickness of the new target layer other layers, the outermost local minimum value calculation method of the new target layer for each point while changing over a plurality of points of the center point and the vicinity (BLMC: Best Local Minimum Calculation) second step of performing When,
The highest minimum value calculation method of the second step (BLMC: Best Local Minimum Calculation) of the thin film more using spectroscopic ellipsometer results and a third step of selecting the best results in the value of the mean square error (chi ²⁾ Layer structure analysis method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 9 to 11,
The best result of the mean square error (χ ² ) value selected in the final stage of the analysis phase 2 shows the maximum and minimum values of the thickness, dispersion parameter, mixing ratio, and incident angle of each layer set in advance. If it is not within the range, the process returns to the second step of the first stage of the analysis phase 2, and at least the film thickness of the layer other than the target layer is changed, and the thin film multi-layer structure using the spectroscopic ellipsometer is characterized. analysis method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to claim 2 or 4,
The analysis phase 3 includes a spectroscopic ellipsometer which is a phase in which an arbitrary parameter related to the model having the best result of the mean square error (χ ² ) in the analysis phase 2 is performed, and the result of the fitting is confirmed and stored. Analysis method of thin film multilayer structure used. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 2, 4 to 13,
When the result of the fitting in the analysis phase 3 is not within the range between the maximum value and the minimum value set in advance, the analysis returns to the analysis phase 1 for determining a new analysis initial stage model. Analysis of the thin film multilayer structure using the spectroscopic ellipsometer Method. In the analysis method of the thin film multilayer structure using the spectroscopic ellipsometer according to any one of claims 1 to 4,
In the analysis phase 1, an analysis initial stage model is determined using an effective medium approximation for the target layer,
In the first step of the first stage of the analysis phase 2, assuming that several materials are mixed in the target layer, at least one of the several materials in the target layer is distributed using the effective medium approximation. Represented by
In the second step of the first stage of the analysis phase 2, the film thickness and the mixing ratio of the layer other than the target layer are selected over a plurality of points, and the minimum of the layer is selected while changing the mixing ratio of the target layer for each point. An analysis method of a thin film multi-layer structure using a spectroscopic ellipsometer that performs a best local minimum calculation (BLMC).

Images