JP4234945B2 - Surface inspection method and surface inspection apparatus - Google Patents

Description

散乱光強度Ｉξは散乱電場の絶対値の２乗と定義することで、次式のように表すことができる。
【００３６】
【数２】

Ｍｉｅ公式中の総和（Σ）の各項はそれぞれ、様々な分布の極を持つ電気・磁気多重極による輻射を表す。同一波長では、粒子が大きいほど総和をとるｎの値も大きくなる。また、粒子から十分に遠方で、粒径が波長に比べて十分に大きい場合にはいわゆる回折の式が導かれ、十分に小さい場合には電気双極子輻射の式が導かれる。
【００３７】
つぎに、Ｍｉｅ公式中の関数の定義と、数値計算に必要な漸化式について説明する。
【００３８】
Ｒｉｃｃａｔｉ−Ｂｅｓｓｅｌ関数
Ｂｅｓｓｅｌ関数から定義される次の関数をＲｉｃｃａｔｉ−Ｂｅｓｓｅｌ関数と呼ぶ。
【００３９】
【数３】

この漸化式は次式のように表すことができる。
【００４０】
【数４】

ここで、ｎ＝０、又は１の場合は
【数５】

となる。
【００４１】
散乱係数
Ｍｉｅ公式中の係数ａ_n、ｂ_n（散乱係数）はＲｉｃｃａｔｉ−Ｂｅｓｓｅｌ関数を用いて、次のように表される。
【００４２】
【数６】

ここでα及びβは以下の式となる。
【００４３】
【数７】

ここでｄは粒子の直径、ｍは粒子の屈折率（一般に複素数）、λは波長を表す。このパラメータαは粒径（正確には粒子の中心を含む断面の円周）と波長の比である。
【００４４】
ａ_n、ｂ_nの計算には次のアルゴリズムを用いる。
【００４５】
【数８】

として、散乱係数の表式を書き換えると、次のとおりである。
【００４６】
【数９】

Ｌｅｇｅｎｄｒｅ関数
前述の式（１）における、Ｌｅｇｅｎｄｒｅ関数の求め方を説明する。
【００４７】
【数１０】

π_n（ｃｏｓθ）、τ_n（ｃｏｓθ）は以下のように定義する。
【００４８】
【数１１】

計算に用いる漸化式は以下のようになる。
【００４９】
【数１２】

遠方での近似式と光散乱に関する物理量
実用的なＭｉｅ公式は、先に示した厳密解よりも、散乱体（球形粒子）から十分に遠い（ｒ>>λ）領域での表式である。
【００５０】
Ｒｉｃｃａｔｉ−Ｂｅｓｓｅｌ関数ξ_n（ｋｒ）の遠方での近似式は、次のと おりである。
【００５１】
【数１３】

これをＭｉｅ公式に代入すると、
【数１４】

が得られる。
【００５２】
ここで振幅関数を導入する。
【００５３】
【数１５】

これらを用いてＭｉｅ公式を書き換えると、
【数１６】

となり、更にこれを行列の積の形で表わすと次のようになる。
【００５４】
【数１７】

入射光の進行方向と散乱の方向で作る面を散乱面という。振幅関数はそれらを結び付ける役割を持ち、Ｍｉｅ公式を用いた計算の中心部分である。
【００５５】
この式を一般化した、任意の形状の散乱体による電場の散乱を記述する式は、次のとおりである。
【００５６】
【数１８】

この式は、散乱体が球形のときには対称性からＳ（θ，φ）はφに依存せず、またＳ２＝Ｓ３＝０となってＭｉｅ公式に一致する。
【００５７】
ここで、ウエハ表面検査装置であることを考慮し、散乱光強度（または散乱光量）を、散乱電場の絶対値の２乗をもって定義する。
【００５８】
本願発明の好ましい容態においては、散乱電場の絶対値の２乗を散乱光強度とすることで「散乱光」と「散乱電場」とを特に区別せずに用いることができる。これにより前述の式（１）〜（４）を基本として相対的な散乱光強度を演算により求めることが可能となり、装置の較正に係る負担を低減することができる。
【００５９】
【実施例】
以下、本発明の実施例を説明する。
【００６０】
ウエハ上粒子の散乱モデル
粒子がウエハ上にある場合の散乱光強度の計算は、光学的条件が複雑ということもあり、これまで行われていなかった。本発明では理論的考察を元に散乱モデルの基礎を組立て、付加的要素を補正項として適用することで、上記条件における散乱光強度をも演算可能とする。（なお、補正項の決定には実測値を参考とすることも可能である）
この補正項は、具体的には、予め計算値が実測値に合うように補正係数又は補正関数を掛けて、光学的条件を変えて実験検証を行い、さらなる修正を加えることで精度を上げることが可能となる。
【００６１】
図１は、ウエハ上粒子の散乱モデルの出発点として、入射光が粒子に散乱され、それが受光されるまでの過程を単純化した０次モデルを示す。
【００６２】
まず入射光が粒子に到達するまでの光路は、
ａ１：粒子に直接入射するもの
ａ２：ウエハで反射してから粒子に入射するもの
を考え、一方、散乱光が検出器に受光されるまでの光路として、
ｂ１：検出器に直接受光されるもの
ｂ２：ウエハで反射してから受光されるもの
を考慮する。つまりａ１−ｂ１、ａ１−ｂ２、ａ２−ｂ１、ａ２−ｂ２という４種類の光路を通った散乱光が同時に受光されるとし、それらの電場ベクトルを受光面上でベクトル的に加算し、その結果の絶対値の２乗を散乱光強度とする。
【００６３】
ここで上記散乱モデルはＭｉｅの公式に基づく。
【００６４】
このＭｉｅ公式は、浮遊粒子に対する入射光として無限に広がる平面波を仮定するものであり、以下の計算もその仮定下に成り立つ。表面検査装置の入射レーザー光がウエハ面上に集光するものの場合、厳密には平面波ではないが、ビームスポット径は測定（計算）対象となる粒子に比べて充分に大きく、さらに散乱はほぼビームウエストで発生することから、ほぼ平面波として扱っても実質的に問題はない。
【００６５】
さらにＭｉｅ公式での仮定の通り、入射光は単波長かつ直線偏光であり、粒子は均質かつ等方的な球で、１つのビームスポット内に複数の粒子は存在しないとし、またウエハも等方的で、表面粗さは無視する。
【００６６】
ウエハの分類と散乱モデル
膜付ウエハは、大きく２つのタイプに分けられる。１つは膜表面の反射のみを考慮すればよいもので、表面を透過する光量が小さく、かつ透過しても膜中で吸収されるアルミなどの金属膜で、ベアシリコンもこの分類に含まれる。それに対して膜表面を透過する光量が大きく、ウエハ表面とシリコン表面の、少なくとも２つの反射面を考慮しなければならないものがある。それらは酸化膜や窒化膜等の透過膜と、膜厚の極めて薄い（材料物質によるが、概ね入射光の波長以下）金属膜である。
【００６７】
ベアウエハと金属膜付ウエハ
ベアウエハについては、上記の０次モデルに補正係数を掛けることで実測値に対して精度の高い計算値が得られる。この補正係数は、入射光と反射光のクロスする領域で起こる定在波（明暗の縞）の考察から、粒子に入射するパワーの加減の効果を、粒径や入射角に応じて算出される。この係数によってベアウエハ及び金属膜については、表面材質の光学定数を置き換えるだけで同様の計算を行うことが可能となる。
【００６８】
透過膜付ウエハ
酸化膜や窒素膜等の透過膜付ウエハでは膜内における反射により反射面が２つ以上存在する。
【００６９】
そこで、本発明では、透過膜モデルへのアプローチとして、個々の光路を追跡するために０次モデルを拡張する手法を用いる。
【００７０】
ここでは単層膜のみを想定する。
【００７１】
透過膜モデルにおける０次モデルとの相違点は、図２に示すように、ウエハに向かう散乱光を‘膜表面で反射して検出器に向かうもの’と‘膜中でｎ回の反射を繰り返してから検出器に向かうもの’とに分ける点である。
【００７２】
なお多重散乱の効果を考慮する場合は、さらに‘シリコン表面で反射して再度粒子に入射して散乱を起こすもの’に関しても考慮が必要となる。
【００７３】
入射光の反射には、膜表面の反射率ではなく、膜とシリコン基板を一体化した合成反射率を用いる。
【００７４】
透過膜付ウエハモデルの補正
酸化膜により実測を行うと、直径０．２０８μｍのＰＳＬ粒子の散乱光が膜厚の変化に応じて周期的に変化する。
【００７５】
それに対して上述の透過膜モデルによる計算値の変化の位相は実測値に対して、位相が所定値だけスライドした状態の周期の強度変化を示す。そこで計算式中の強度変化の位相に寄与する要素部分にスライド分を補正可能とする補正項を適用することで、実測値と極めて近い透過膜付きウエハモデルの散乱光強度をシミュレートすることが出来る。
【００７６】
散乱モデル計算
次に（数式を交えながら）透過膜付ウエハ上粒子の散乱光量計算の手順を示す。この計算は図３に図示したフローに沿って行われる。
【００７７】
なお、ここでは単層膜に限定しているが、多層膜への拡張や、膜厚を０と置いてベアシリコンや金属膜付ウエハへの適用も可能である。
【００７８】
パラメータ設定
計算に用いる光学的パラメータを設定する。与えるパラメータは、
（ａ） 入射光の波長、シリコンの屈折率、膜の屈折率、ＰＳＬの屈折率
（ｂ） 入射角、検出角（仰角、方位角）、入射偏光（ｓまたはｐ）、粒径、膜厚である。ここで長さの単位は全てμｍとする。入射強度は１とする。次に与えたパラメータを用いて合成反射率と、Ｍｉｅ公式で使用する各係数を計算する。
【００７９】
ウエハ上座標
ウエハ表面上の所定位置における点を原点とし、ウエハ面に鉛直に上向きを正としてz軸をとり、入射面とウエハ面の光線をx軸として入射光の進む向きを正とし、その両者に垂直に右手系でｙ軸をとる。そして散乱光の検出位置（表面検査装置の受光光学素子のおける受光面の中心）を、仰角・方位角・原点からの距離（任意に設定：例えば１０⁴）から計算し、粒子の中心を原点として極座標で表 す。
【００８０】
さらに検出ＮＡの範囲で積分する場合には、この位置を中心に円を描き、適当に分割してそれぞれの位置を極座標で表して以下の計算を繰り返す。
【００８１】
Ｍｉｅ公式用の座標に変換
Ｍｉｅ公式による計算のプログラムを利用するために、ウエハ上の座標からＭｉｅ公式用の座標に変換する。
【００８２】
Ｍｉｅ公式用の座標とは、粒子の中心を原点として、入射光の進行方向にｚ′軸、入射光の電場の偏光方向にｘ′軸、その両者に垂直にｙ′軸をとり、それに対応した極座標---すなわち、原点から観測点までの距離をｒ′，ｚ′軸と散乱 光の観測方向との成す角をθ′，ｚ′軸と観測方向とで作る面（散乱面）と入射電場の偏光方向との成す角をφ′とする---を意味し、散乱計算にはその（ｒ′ ，θ′，φ′）を与える。
【００８３】
散乱モデルで考慮する散乱光は、入射光軸が２通り（直接入射、反射後入射）、散乱直後に進む方向が３通り（直接検出、反射後検出、粒子に再入射）であるから、次の６通りの光路を経て観測点に到達する（図２参照）。
【００８４】
ａ１：粒子に直接入射するもの
ａ１−ｂ１ 検出器に向かうもの
ａ１−ｂ２ ウエハで反射して検出器に向かうもの（膜内部での反射を含む）
ａ１−ｂ３ シリコンで反射して再び粒子に入射するもの
ａ２：ウエハで反射してから粒子に入射するもの
ａ２−ｂ１ 検出器に向かうもの
ａ２−ｂ２ ウエハで反射して検出器に向かうもの（膜内部での反射を含む）
ａ２−ｂ３ シリコンで反射して再び粒子に入射するもの
したがって、６つの（ｒ′，θ′，φ′）の組合せが得られる。ここでａ１−ｂ２、ａ２−ｂ２については、ウエハで反射する光と、膜中をＮ回往復してから検出器に向かう光との干渉を考慮に入れる。膜中の往復回数は、計算値が概ね収束するＮ＝５とする。
【００８５】
なお、ここで行う座標変換は入射光の偏光方向（ｓ偏光またはｐ偏光）によって、変換式が異なる。
【００８６】
光路ごとの散乱光の計算
座標変換によって散乱電場の計算が可能となるが、ａ１−ｂ１以外の計算では、Ｍｉｅ公式を利用した計算以外の補正を要する。まずａ２では入射光（電場）にウエハの合成反射率（振幅反射率）を掛ける。次にａ１−ｂ２、ａ２−ｂ２は計算後に膜中での往復回数に応じて膜表面やシリコン表面の振幅反射率、振幅透過率、光路差による位相差の項を掛ける。ａ１−ｂ３、ａ２−ｂ３はそれ自体を入射光として、再度Ｍｉｅ公式用の座標変換を行って散乱電場を計算する。ここで３度目の散乱は考慮せず、それぞれｂ１とｂ２のみを考える。
【００８７】
散乱光の座標統一と散乱光のベクトル和
計算した散乱電場をベクトル的に加算するために、同一の座標に変換する。ここでは、表面検査装置の検出光学系に偏光フィルタが存在する場合は、その効果を計算に取り入れるために、ウエハ上の座標に統一する。
【００８８】
補正項
補正項について述べる。
【００８９】
この補正項の追加によって計算値と実測値の溝が埋まり、表面検査装置における実験則が確立できた。
【００９０】
酸化膜実験の結果によると、散乱光強度は膜厚に対して周期的に変化するが、位相がずれる可能性も考慮するため、強度変化の位相に関する補正項を追加した。具体的には入射光の反射光や散乱光の反射光に対して任意の位相差を与える。
入射光の反射光
入射光がウエハで反射した後に粒子に入射するとき、その強度は元の入射光が１に対してウエハの合成反射率となる。計算の性質上、この部分は複素電場で表現しており、入射電場と合成振幅反射率との積がその後の計算の入射電場となる。ここではこの合成振幅反射率にさらに位相項を乗じる。
【００９１】
散乱電場の干渉
散乱光がウエハで反射して検出器に向かう場合、膜中を１〜Ｎ往復した後に検出器に向かう光との干渉を考慮する。各膜中反射光の光路差にしたがってそれぞれ位相差を乗じてそれらの総和をとり、粒子から直接検出器に向かう光とのベクトル和をとる。ここではさらに、その両者の間に位相差を与える。
【００９２】
散乱モデルの表式
これまでの計算を数式にまとめる。上述の２つの補正項については最後に記述する。
【００９３】
まず、ウエハ上の極座標で観測点の位置をＰ（ｒ，θ，φ）として、原点を粒子の中心に移し、所定の光路にしたがってＭｉｅ公式用の座標に変換して散乱光を計算する。
【００９４】
（１）ａ１−ｂ１：粒子に直接入射→検出器
Ｍｉｅ公式にＡを与えて計算される散乱電場の、散乱面（入射光軸と散乱の方向とで作る面）に垂直な成分と平行な成分を次のようにおく。
【００９５】
【数１９】

Ｍｉｅ公式用の座標で表した観測点の位置は（ｒ₁’，θ₁’，φ₁’）となる 。これは、入射光がウエハに対してｓ偏光かｐ偏光かに依存する。
【００９６】
【数２０】

（２）ａ１−ｂ２ ：粒子に直接入射→反射後に検出器
観測点の位置をＭｉｅ公式用の座標に変換したものを（ｒ₂’，θ₂’，φ₂’ ）とすると、
【数２１】

となる。
【００９７】
これを以後の計算のため、散乱の方向とウエハの法線で作る面に対して垂直な成分と平行な成分に分け直して、
観測点の位置をＭｉｅ公式用の座標に変換したものを（ｒ₂’，θ₂’，φ₂’ ）とすると、
【数２２】

となる。
【００９８】
これを用いて膜中を回往復する成分との干渉を考慮すると、下記式となる。
【００９９】
【数２３】

光路差に起因する位相差δは下記式となる。
【０１００】
【数２４】

（３）ａ１−ｂ３ ：粒子に直接入射→反射後粒子に入射
これまでと同様に観測点の位置をＭｉｅ公式用の座標に変換したものを（ｒ₃ ’，θ₃’，φ₃’）とすると、散乱電場は、
【数２５】

となる。
【０１０１】
この場合は散乱光が粒子の真下に向かうので、入射面と散乱面が一致している。従って、新たな入射光は、
【数２６】

である。この入射光は２つに分けて計算するが、両者は共通の散乱面に関して記述されるので１つの式で表すと、
【数２７】

となる。ここで
（ｒ₄’，θ₄’，φ₄’）、（ｒ₅’，θ₅’，φ₅’）は、２つの入射光について、観測点の位置をＭｉｅ公式用の座標に変換したもの、および
【数２８】

である。
【０１０２】
（４）ａ２−ｂ１ ：反射後に粒子に入射→検出器
ｓ偏光、ｐ偏光を選択すると下記式となる。
【０１０３】
【数２９】

（５）ａ２−ｂ２ ：反射後に粒子に入射→反射後に検出器
Ｍｉｅ公式用の座標に変換した観測点の位置を(ｒ７’，θ７’，φ７’)として散乱電場は下記式となる。
【０１０４】
【数３０】

ａ１−ｂ２と同様に、散乱の方向とウエハの法線で作る面に対して垂直な成分と平行な成分に分けて、
【数３１】

とする。これを用いて膜中をｎ回往復する成分との干渉を考慮すると、下記式となる。
【０１０５】
【数３２】

（６）ａ２−ｂ３ ：反射後に粒子に入射→反射後粒子に入射
Ｍｉｅ公式用の座標に変換した観測点の位置を（ｒ₈’，θ₈’，φ₈’）とし て散乱電場は下記式となる。
【０１０６】
【数３３】

ａ１−ｂ３と同様に考えると、下記式となる。
【０１０７】
【数３４】

ここで、
（ｒ₉’，θ₉’，φ₉’）、（ｒ₁₀’，θ₁₀’，φ₁₀’）：観測点の位置をＭ ｉｅ公式用の座標に変換したもの、および
【数３５】

である。
【０１０８】
以上の各散乱電場のベクトル和が観測点での散乱電場であるから、
【数３６】

となり、ここに補正項を加える。
【０１０９】
ここで下記２つの要素を補正項として加える。
【０１１０】
▲１▼入射光の反射の際に与える任意の位相差
入射光に合成反射率及び位相差を乗じて下記式となる。
【０１１１】
【数３７】

この補正の影響を受けることを表すために、以下のように書き換えを行う。
【０１１２】
【数３８】

▲２▼ａ１−ｂ２とａ２−ｂ２における、膜表面での反射光と膜中をＮ往復した反射光との間の任意の位相差
散乱光側の補正項で、ａ１−ｂ２とａ２−ｂ２において、膜表面での反射光と膜中をＮ往復した反射光との間に、任意の位相差を与える。この位相差は成分ごとに与え、散乱面に垂直な成分にexp(-iΔ_2S)を、平行な成分にexp(-iΔ_2p)を乗じる。ただしａ１−ｂ２、ａ２−ｂ２の散乱光側の光路は共通であるから、両方に同じΔ_2S，Δ_2pを与えるものとし、
【数３９】

の書き換えを行って、
【数４０】

となる。
【０１１３】
数式３６の（１３）式は次のように書き換えられて、下記式となる。
【０１１４】
【数４１】

この式が観測点での散乱電場の最終形となる。
【０１１５】
ただし、実際の計算ではウエハ上の座標に再変換し、次のように、ｚ軸と観測方向とで作る面について垂直な成分及び平行な成分に分けて加算する。
【０１１６】
【数４２】

従って、散乱強度Iscaは、
【数４３】

となり、偏光フィルタが存在する場合は、フィルタの偏光軸からのずれをΘ（反時計回りを正）とすると、
【数４４】

となる。
【０１１７】
標準粒子の粒径
好ましくは、表面検査装置が計測する粒径の値は、絶対値を示すものではなく、等価の散乱光を生じるＰＳＬ粒子の直径に相当する相対値を示すものとする。このため、ＰＳＬ粒子塗布ウェーハを用い、検出部に使用しているフォトマルの初期感度設定（適正感度の設定及びフォトマル出力と粒径との値付け）を行う。そして、フォトマルは経時変化に伴う劣化を生じるため、定期的な感度補正を行う。
【０１１８】
これらのフォトマルの感度設定および補正をキャリブレーション（較正）という。
【０１１９】
実験例
前述の実験則を加味した数学散乱モデルによる計算値と、表面検査装置を用いた実測値とを比較する。実験条件を表１に示す。
【０１２０】
【表１】

まず直径０．２０８μｍのＰＳＬ粒子を塗布した、膜厚の異なる酸化膜ウエハを順次測定し、膜厚に応じた特性曲線（膜厚ｖｓ散乱光強度；特性曲線（粒径ｖｓ散乱光強度）との区別のために、このように記す）を得る。
【０１２１】
次に膜厚２００、２５０、３５０、５００ｎｍの各ウエハに、それぞれ粒径０．２０８、０．３０９、０．５０６、１．００１μｍのＰＳＬ粒子を塗布して、特性曲線を得た。
【０１２２】
それぞれの実験では、入射偏光と検出方向の組み合わせにより、４通りのモード（ｓ偏光・側方検出、ｓ偏光・前方検出、ｐ偏光・側方検出、ｐ偏光・前方検出）で測定を行った。
【０１２３】
なお、側方とは入射面に垂直な方向を含む領域であり、前方とは入射面に垂直な面から正反射光に近い方向に４０°の領域とする。
【０１２４】
これらの実験結果に対し、適切な補正項のΔ₁、Δ_2S、Δ_2Pを決定した結果は 、図４及び図５に示す。
【０１２５】
なお、実測値には、ＰＳＬ粒子の散乱光強度に応じた電気信号のヒストグラムから算出される、重心位置の電圧値を採用した。
【０１２６】
図４は、散乱光強度の膜厚特性曲線の実測値と、補正項により修正された計算値を示す。補正項は比較的膜厚の小さなウエハのデータに基づいている。
【０１２７】
図６は、実験に使用した、表面に酸化膜を形成したウエハの平均値で規格化した膜厚分布を示す。それによると、膜ムラの程度は、そのウエハの膜厚によらず、ほぼ一定であることがわかる。即ち膜厚が大きい（数百ｎｍ以上）ほど、膜厚の平均値からのずれが大きくなる。従って、膜厚の大きなウエハの場合、膜ムラに関する補正を考慮する必要がある。
【０１２８】
図５は、計算した特性曲線と、実測値とを比較して示したものであり、粒径に関するシミュレートの精度を示す。
【０１２９】
本グラフは両軸とも対数表示であるため、ｓ偏光データ、特に膜厚３５０ｎｍウエハにおける計算値と実測値との差は、ヒストグラム上での散乱光強度の差としては特に大きなものではない。
【０１３０】
なお、これら相対散乱光強度の計算値は、縦軸方向に平行移動する補正項を付加している。
【０１３１】
その他、検出器（ＰＭＴ）の個体差などの機差要因も補正項とすることができる。
【０１３２】
また、同手法にて補正項を適用することで、酸化膜以外の膜付ウエハへの応用が可能であり、さらに膜厚を０として金属膜付ウエハやベアシリコンへの応用も可能となる。
【０１３３】
また、このようにして求められた数学散乱モデルによって計算した特性曲線を基にして、粒子弁別のための閾値（スライスレベル）を自動的に決定することが可能である。
【０１３４】
較正用ウエハとしては、Ｄ−ＴＥＯＳ他の酸化膜付ウエハ、酸化膜以外の透過膜・金属膜付ウエハも採用可能である。
【０１３５】
一方、本実施例では、透過膜モデルへのアプローチとして０次モデルを拡張して個々の光路を追跡した方法を述べたが、膜が単層、多層にかかわらず合成反射率を予め計算することで、その反射面を有する一つの反射面として扱う方法も選択することができる。
【０１３６】
【発明の効果】
本発明によれば、検出した散乱光出力とウエハ上の異物の粒径との相関関係を規定するための較正作業において、多数の種々の較正用ウエハを実測することなく、異なる粒径による散乱光強度も求めることができる。それゆえ、較正作業の手間、時間、人員コストの劇的な軽減と作業の高速化が実現できる。
【０１３７】
本発明は、ベアウエハだけでなく、表面に透過膜等が形成されているウエハについても対応可能である。
【０１３８】
較正作業を自動化するシステムが実現しやすい。
【０１３９】
また、“粒径”、“膜の種類”、“膜厚”のそれぞれに対応した較正用ウエハを揃える必要がない。そのため、較正用ウエハの作成コスト、収納スペースの占有、等の負担が大幅に軽減される。
【０１４０】
また、必要な較正ウエハの枚数分必要であった測定作業自体が不要となり、較正に要する時間が短縮され、捜査員の負担も軽減される。
【０１４１】
これにより、被検物表面の状態をパラメータとして、その反射特性をシミュレーションすることができる。
【０１４２】
較正用ウエハの枚数を大幅に減らすことができる。
【０１４３】
また、ウエハの光学的性質の他に装置自身の光学系の情報、及び装置の応答も、計算により正確に予測可能である。
【図面の簡単な説明】
【図１】基礎散乱モデルを示す概念図。
【図２】透過膜散乱モデルを示す概念図。
【図３】透過膜付ウエハ上粒子の散乱光量計算の手順を示す。
【図４】散乱光強度の膜厚特性曲線の実測値と、補正項により修正された計算値を示す図。
【図５】計算した特性曲線と、実測値との比較を示す図。
【図６】Ｄ−ＴＥＯＳウエハの平均値で規格化した膜厚分布を示す図。[0001]
BACKGROUND OF THE INVENTION
The present invention irradiates inspection light onto the surface of a wafer to be inspected, and detects the reflected light and scattered light generated when a foreign substance is present, thereby detecting the foreign substance present on the wafer surface. It relates to an inspection device.
[0002]
[Prior art]
Conventionally, when performing a calibration operation, standard particles selected in advance have been applied onto the wafer, a plurality of calibration wafers having different conditions were created, and the calibration operation was performed using these calibration wafers. That is, the calibration work is performed using a wafer coated with standard particles of a desired size for each film material and film thickness of the film-coated wafer. For example, when it is desired to detect the particle size in 10 stages, ten calibration wafers having different particle sizes are prepared, and the measurement operation is performed for each wafer. At this time, the wafer used for calibration is stored by the user.
[0003]
In addition, if the surface condition (existence of film, film type, film thickness, etc.) of the wafer to be inspected changes, the optical characteristics of the surface also change. Therefore, standard particles with different particle sizes were applied to each surface condition. Calibration wafers must be prepared and measurement operations must be performed.
[0004]
In particular, when the film type formed on the surface is a permeable film such as an oxide film or a nitride film, the scattering characteristics greatly change depending on the film thickness.
[0005]
Note that the standard particles made of PSL may be referred to as PSL particles.
[0006]
[Problems to be solved by the invention]
As described above, many calibration wafers corresponding to each of “particle size”, “film type”, and “film thickness” must be prepared in order to perform calibration work. As a result, it was necessary to carry out the measurement work, and the following large burden was generated.
[0007]
-The labor, time and personnel cost of calibration work are large.
[0008]
・ Cost of creating calibration wafer and large storage space.
[0009]
The number of calibration wafers is generally “number of film types × number of film thickness × number of particle diameters”, so that the number of wafers may be excessive depending on the user, and the wafer size will shift from 200 mm to 300 mm. Therefore, the burden has become greater not only in labor and time including the transfer of the calibration wafer, but also in terms of cost and occupied space for storage.
[0010]
The present invention aims to reduce the calibration work.
[0011]
[Means for lightly resolving issues]
Examples of the solving means of the present invention are as follows.
[0012]
  (1) In a surface inspection apparatus for detecting foreign matter existing on a wafer surface by irradiating inspection light onto the surface of a wafer to be inspected and detecting scattered light generated when the foreign matter is present,By calculating a scattered electric field for each optical path until the foreign object is irradiated with the inspection light and the scattered light is detected, and a mathematical model for obtaining the output intensity of the scattered light based on the sum of the scattered electric fields,Scattered light outputStrengthThe correlation between particle size and particle size on the waferShi,Calibration means for calibrating the surface inspection apparatus based on the correlationA surface inspection apparatus characterized by that.
[0013]
  (2) In a surface inspection apparatus for detecting foreign matter existing on a wafer surface by irradiating inspection light on the surface of the wafer to be inspected and detecting scattered light generated when the foreign matter is present,Calculate the scattered electric field for each optical path from the time when the foreign object is irradiated with the inspection light and the scattered light is detected, and determine the output intensity of the scattered light based on the sum of the scattered electric field. Has the function to calculate the theoretical intensity of scattered light with respect to the diameterA surface inspection apparatus characterized by that.
[0014]
  (3)The mathematical model obtains the output intensity of scattered light using the Mie formula, as described in (2) aboveSurface inspection device.
[0015]
  (4)By applying a correction term for the wafer film type, the output intensity of scattered light for the wafer film type can be calculated.Characterized by seekingThe aforementioned surface inspection device.
[0016]
  (5)By applying a correction term related to the film thickness of the wafer, the output intensity of scattered light with respect to the film thickness of the wafer is calculated.A surface inspection apparatus as described above.
[0019]
DETAILED DESCRIPTION OF THE INVENTION
The present invention is an apparatus and method for inspecting foreign matter on a wafer using a mathematical model of scattered light.
[0020]
A correlation between the output of scattered light from the wafer surface and the particle size of foreign matter on the wafer is obtained in advance as a mathematical model.
[0021]
For example, an equation based on the “Mie scattering formula” in a scattered electric field is applied to the intensity of scattered light from a foreign substance. This makes it possible to obtain relative scattered light intensities according to various particle sizes by calculation.
[0022]
In addition, by applying the correction term in the above equation, the scattered light intensity can be obtained by calculation even when the film type, film thickness, etc. on the wafer surface are different.
[0023]
That is, the scattered light intensity under a predetermined condition is obtained by calculation based on the optical properties of the measurement target wafer.
[0024]
In this way, it is possible to inspect foreign matter on the wafer by performing desired calibration without actually measuring the calibration wafer. For example, a threshold value can be set for each particle size corresponding to the foreign substance size.
[0025]
That is, the scattered light intensity with respect to the particle diameter, which has been obtained only by actual measurement of the foreign matter on the calibration wafer so far, can be obtained by calculation without actual measurement. Specifically, in the distribution on the histogram, the peak position of the scattered light intensity with respect to the particle diameter can be obtained by calculation based on the peak position corresponding to the particle diameter obtained as the gravity center position.
[0026]
Preferably, the scattered light intensity with respect to the particle diameter can be obtained by calculation by applying the scattered light formula to the scattered light intensity.
[0027]
Further, by applying the correction term, not only the particle diameter but also the film type and film thickness can be obtained as an element for theoretically obtaining the scattered light intensity.
[0028]
According to the present invention, the labor of calibration work can be dramatically reduced, and the work speed can be increased.
[0029]
The present invention can be applied not only to bare wafers but also to other wafers. In particular, a wafer having a permeable film or the like formed on the surface can also be handled.
[0030]
In the present invention, the theoretical calculation is preferably performed using a mathematical model, that is, a mathematical model of the scattered light, for the amount of light scattered by the particles on the wafer and the electrical signal output by detecting the scattered light. In particular, by adding a correction term that includes everything from the scattering phenomenon to the instrument function, the relative scattered light intensity based on the characteristic curve of the wafer (the change in the scattered light intensity due to the change in particle size, which becomes the standard for calibration). Is calculated. Since the characteristic curve of this wafer is unique to the wafer to be measured, it can be obtained by applying a value obtained in advance as a template or by actually measuring it. For example, a characteristic curve obtained by measuring at least one calibration wafer in which standard particles of a certain particle size are applied to a measurement target wafer with respect to a predetermined film type and film thickness, and calculating the measured value. Apply.
[0031]
When scattered light detection is performed in two directions (two PMTs), a wide dynamic range can be secured. In this case, since one wafer measurement is required for each detection channel, at least two wafers are used.
[0032]
In addition, the well-known Mie formula can be used for the mathematical model used as the basis of scattered light intensity calculation.
[0033]
The Mie formula is an exact solution that describes light scattering when a linearly polarized plane wave enters a spherical particle in a uniform medium. In this formula, if wavelength >> particle diameter, Rayleigh scattering, and if wavelength << particle diameter, this corresponds to the expression derived from geometric optics. Detailed solutions that derive the Mie formula starting from the Maxwell equation, and assumptions to avoid losing strictness (particle uniformity / isotropy / nonmagnetism, wavelength invariance, scattering isolation, etc.) are detailed here. Do not mention.
[0034]
Now, let the direction of incident light travel on the z axis, the direction of linearly polarized light of the incident light be the x axis, the zenith angle measured from the z axis be θ, and the azimuth angle measured from the x axis to the y axis be φ, According to the Mie formula, the scattered electric field Es is expressed as follows with respect to polar coordinates.
[0035]
[Expression 1]

By defining the scattered light intensity Iξ as the square of the absolute value of the scattered electric field, it can be expressed as the following equation.
[0036]
[Expression 2]

Each term of the summation (Σ) in the Mie formula represents radiation by electric / magnetic multipoles having poles with various distributions. At the same wavelength, the larger the particle, the larger the value of n taking the sum. When the particle size is sufficiently far from the particle and the particle size is sufficiently larger than the wavelength, a so-called diffraction equation is derived, and when the particle size is sufficiently small, an electric dipole radiation equation is derived.
[0037]
Next, the definition of the function in the Mie formula and the recurrence formula necessary for numerical calculation will be described.
[0038]
Riccati-Bessel function
The next function defined from the Bessel function is called a Riccati-Bessel function.
[0039]
[Equation 3]

This recurrence formula can be expressed as:
[0040]
[Expression 4]

Here, when n = 0 or 1,
[Equation 5]

It becomes.
[0041]
Scattering coefficient
Coefficient a in Mie formula_n, B_nThe (scattering coefficient) is expressed as follows using the Riccati-Bessel function.
[0042]
[Formula 6]

Here, α and β are as follows.
[0043]
[Expression 7]

Here, d is the diameter of the particle, m is the refractive index of the particle (generally a complex number), and λ is the wavelength. This parameter α is the ratio of the particle size (more precisely, the circumference of the cross section including the center of the particle) to the wavelength.
[0044]
a_n, B_nThe following algorithm is used to calculate.
[0045]
[Equation 8]

As a result, the expression of the scattering coefficient is rewritten as follows.
[0046]
[Equation 9]

Legendre function
A method for obtaining the Legendre function in the above equation (1) will be described.
[0047]
[Expression 10]

π_n(Cos θ), τ_n(Cos θ) is defined as follows.
[0048]
## EQU11 ##

The recurrence formula used for the calculation is as follows.
[0049]
[Expression 12]

Approximate equations in the distance and physical quantities related to light scattering
The practical Mie formula is an expression in a region far enough (r >> λ) from the scatterer (spherical particle) than the exact solution shown above.
[0050]
Riccati-Bessel function ξ_nThe approximate expression of (kr) in the distance is as follows.
[0051]
[Formula 13]

Substituting this into the Mie formula,
[Expression 14]

Is obtained.
[0052]
Here, an amplitude function is introduced.
[0053]
[Expression 15]

Using these to rewrite the Mie formula,
[Expression 16]

This can be expressed in the form of a matrix product as follows.
[0054]
[Expression 17]

A surface formed by the traveling direction of incident light and the direction of scattering is called a scattering surface. The amplitude function has a role of connecting them, and is the central part of the calculation using the Mie formula.
[0055]
An equation that generalizes this equation and describes the scattering of an electric field by a scatterer having an arbitrary shape is as follows.
[0056]
[Formula 18]

In this equation, when the scatterer is spherical, S (θ, φ) does not depend on φ due to symmetry, and S2 = S3 = 0, which is in agreement with the Mie formula.
[0057]
Here, in consideration of the wafer surface inspection apparatus, the scattered light intensity (or scattered light amount) is defined as the square of the absolute value of the scattered electric field.
[0058]
In a preferable condition of the present invention, “scattered light” and “scattered electric field” can be used without distinction by making the square of the absolute value of the scattered electric field the scattered light intensity. As a result, the relative scattered light intensity can be obtained by calculation based on the above-mentioned formulas (1) to (4), and the burden on the calibration of the apparatus can be reduced.
[0059]
【Example】
Examples of the present invention will be described below.
[0060]
Particle scattering model on wafer
The calculation of the scattered light intensity when the particles are on the wafer has not been performed so far due to the complicated optical conditions. In the present invention, the basis of a scattering model is assembled based on theoretical considerations, and an additional element is applied as a correction term, so that the scattered light intensity under the above conditions can also be calculated. (Note that actual values can be used as a reference for determining correction terms.)
Specifically, this correction term is multiplied by a correction coefficient or correction function so that the calculated value matches the actual measurement value, and the experiment is verified by changing the optical conditions, and the accuracy is improved by making further modifications. Is possible.
[0061]
FIG. 1 shows a zeroth-order model that simplifies the process until incident light is scattered by particles and received as a starting point of the particle scattering model on the wafer.
[0062]
First, the optical path until the incident light reaches the particle is
a1: Directly incident on the particle
a2: Reflected on the wafer and then incident on the particle
On the other hand, as an optical path until the scattered light is received by the detector,
b1: Directly received by the detector
b2: Received after being reflected by the wafer
Consider. In other words, it is assumed that scattered light passing through four types of optical paths, a1-b1, a1-b2, a2-b1, and a2-b2, are received simultaneously, and their electric field vectors are added in a vector form on the light-receiving surface. The square of the absolute value of is the scattered light intensity.
[0063]
Here, the scattering model is based on the Mie formula.
[0064]
This Mie formula assumes a plane wave that spreads infinitely as incident light on suspended particles, and the following calculation is also based on that assumption. In the case where the incident laser light of the surface inspection device is focused on the wafer surface, although it is not strictly a plane wave, the beam spot diameter is sufficiently larger than the particle to be measured (calculated), and the scattering is almost the beam. Since it occurs at the waist, there is virtually no problem even if it is treated as a plane wave.
[0065]
Furthermore, as assumed by the Mie formula, the incident light is single-wavelength and linearly polarized, the particles are homogeneous and isotropic spheres, and there are no multiple particles in one beam spot, and the wafer is isotropic The surface roughness is ignored.
[0066]
Wafer classification and scattering model
Film-coated wafers are roughly divided into two types. One is the one that only needs to consider the reflection on the surface of the film, and the amount of light transmitted through the surface is small and is a metal film such as aluminum that is absorbed in the film even though it is transmitted. Bare silicon is also included in this category. . In contrast, there is a large amount of light transmitted through the film surface, and at least two reflecting surfaces of the wafer surface and the silicon surface must be considered. They are a transmission film such as an oxide film or a nitride film, and a metal film having a very thin film thickness (depending on the material, but generally less than the wavelength of incident light).
[0067]
Bare wafer and wafer with metal film
For a bare wafer, a highly accurate calculated value can be obtained with respect to the actually measured value by multiplying the above zero-order model by a correction coefficient. This correction coefficient is calculated based on the standing wave (bright and dark stripes) that occurs in the region where incident light and reflected light cross, and the effect of adjusting the power incident on the particles is calculated according to the particle size and incident angle. . With this coefficient, the same calculation can be performed for the bare wafer and the metal film only by replacing the optical constant of the surface material.
[0068]
Wafer with permeable membrane
A wafer with a permeable film such as an oxide film or a nitrogen film has two or more reflecting surfaces due to reflection within the film.
[0069]
Therefore, in the present invention, as an approach to the permeable membrane model, a method of extending the 0th-order model to track individual optical paths is used.
[0070]
Here, only a single layer film is assumed.
[0071]
As shown in FIG. 2, the difference between the transmission film model and the zeroth-order model is that the scattered light traveling toward the wafer is reflected at the film surface and directed toward the detector, and is repeatedly reflected n times in the film. It is a point to divide it into 'what goes to the detector afterwards.
[0072]
When considering the effect of multiple scattering, it is also necessary to consider “what is reflected on the silicon surface and incident again on the particles to cause scattering”.
[0073]
For reflection of incident light, not the reflectance of the film surface but the combined reflectance obtained by integrating the film and the silicon substrate is used.
[0074]
Correction of wafer model with permeable membrane
When actual measurement is performed using an oxide film, the scattered light of PSL particles having a diameter of 0.208 μm changes periodically according to the change in the film thickness.
[0075]
On the other hand, the phase of the change of the calculated value by the above-mentioned permeable membrane model shows the intensity change of the period when the phase is slid by a predetermined value with respect to the actually measured value. Therefore, it is possible to simulate the scattered light intensity of a wafer model with a permeable membrane that is very close to the actual measurement value by applying a correction term that enables correction of the slide to the element part that contributes to the phase of intensity change in the calculation formula. I can do it.
[0076]
Scattering model calculation
Next, a procedure for calculating the amount of scattered light of the particles on the wafer with a permeable membrane (with a mathematical formula) will be described. This calculation is performed along the flow shown in FIG.
[0077]
Note that although it is limited to a single-layer film here, it can be applied to a wafer with bare silicon or a metal film by setting it to a multilayer film or setting the film thickness to zero.
[0078]
parameter settings
Set optical parameters for calculation. The parameters given are
(A) Incident light wavelength, silicon refractive index, film refractive index, PSL refractive index
(B) Incident angle, detection angle (elevation angle, azimuth angle), incident polarization (s or p), particle size, and film thickness. Here, the unit of length is all μm. The incident intensity is 1. Next, the composite reflectance and each coefficient used in the Mie formula are calculated using the given parameters.
[0079]
Wafer coordinates
A point at a predetermined position on the wafer surface is the origin, the z-axis is taken vertically upward on the wafer surface, and the light traveling on the incident surface and the wafer surface is taken as the x-axis. Take the y-axis with the right hand system. Then, the detection position of the scattered light (the center of the light receiving surface of the light receiving optical element of the surface inspection apparatus) is set to an elevation angle, an azimuth angle, and a distance from the origin (arbitrary setting: for example, 10^Four) And expressed in polar coordinates with the particle center as the origin.
[0080]
Further, when integrating within the range of the detected NA, a circle is drawn around this position, divided appropriately, each position is represented by polar coordinates, and the following calculation is repeated.
[0081]
Convert to Mie formula coordinates
In order to use a calculation program based on the Mie formula, the coordinates on the wafer are converted into coordinates for the Mie formula.
[0082]
The Mie formula coordinates are based on the center of the particle, the z 'axis in the traveling direction of the incident light, the x' axis in the polarization direction of the electric field of the incident light, and the y 'axis perpendicular to both. Polar coordinates --- The surface (scattering plane) that makes the distance between the origin and the observation point r ', z' axis and the observation direction of the scattered light the θ ', z' axis and the observation direction This means that the angle formed by the polarization direction of the incident electric field is φ ′, and (r ′, θ ′, φ ′) is given to the scattering calculation.
[0083]
The scattered light considered in the scattering model has two incident optical axes (direct incident and incident after reflection), and three traveling directions immediately after scattering (direct detection, detection after reflection, and re-incident on particles). The observation point is reached through the six optical paths (see FIG. 2).
[0084]
a1: Directly incident on the particle
to the a1-b1 detector
a1-b2 Reflected by the wafer and directed to the detector (including reflection inside the film)
a1-b3 Reflected by silicon and incident on the particles again
a2: Reflected on the wafer and then incident on the particle
to the a2-b1 detector
a2-b2 Reflected on the wafer and directed to the detector (including reflection inside the film)
a2-b3 Reflected by silicon and incident on the particles again
Therefore, six (r ′, θ ′, φ ′) combinations are obtained. Here, for a1-b2 and a2-b2, the interference between the light reflected from the wafer and the light traveling to the detector after reciprocating N times in the film is taken into consideration. The number of reciprocations in the film is N = 5, where the calculated value converges approximately.
[0085]
The coordinate conversion performed here has different conversion formulas depending on the polarization direction of incident light (s-polarized light or p-polarized light).
[0086]
Calculation of scattered light for each optical path
Although the scattered electric field can be calculated by coordinate conversion, corrections other than the calculation using the Mie formula are required for calculations other than a1-b1. First, in a2, the incident light (electric field) is multiplied by the combined reflectance (amplitude reflectance) of the wafer. Next, a1-b2 and a2-b2 are multiplied by the term of phase difference due to the amplitude reflectance, amplitude transmittance, and optical path difference of the film surface and silicon surface according to the number of round trips in the film after the calculation. a1-b3 and a2-b3 use the light itself as incident light to perform coordinate conversion for the Mie formula again to calculate the scattered electric field. Here, the third scattering is not considered, and only b1 and b2 are considered.
[0087]
Unification of scattered light coordinates and vector sum of scattered light
In order to add the calculated scattered electric field in a vector manner, it is converted into the same coordinates. Here, when a polarizing filter is present in the detection optical system of the surface inspection apparatus, in order to incorporate the effect into the calculation, the coordinates on the wafer are unified.
[0088]
Correction term
The correction term will be described.
[0089]
By adding this correction term, the groove between the calculated value and the actually measured value was filled, and an experimental rule for the surface inspection apparatus could be established.
[0090]
According to the results of the oxide film experiment, although the scattered light intensity periodically changes with respect to the film thickness, a correction term related to the phase of the intensity change was added in order to consider the possibility of phase shift. Specifically, an arbitrary phase difference is given to reflected light of incident light or reflected light of scattered light.
Incident light reflection
When the incident light is incident on the particle after being reflected by the wafer, its intensity is the combined reflectance of the wafer with respect to the original incident light of 1. Due to the nature of the calculation, this part is represented by a complex electric field, and the product of the incident electric field and the combined amplitude reflectance becomes the incident electric field for the subsequent calculation. Here, this combined amplitude reflectance is further multiplied by a phase term.
[0091]
Scattered electric field interference
When the scattered light is reflected by the wafer and travels toward the detector, interference with the light that travels 1 to N times through the film and then travels toward the detector is considered. According to the optical path difference of the reflected light in each film, the phase difference is multiplied to obtain the total sum, and the vector sum with the light directed from the particle directly toward the detector is obtained. Here, a phase difference is further given between the two.
[0092]
Scatter model expression
Summarize the previous calculations into mathematical formulas. The above two correction terms will be described last.
[0093]
First, the position of the observation point is set to P (r, θ, φ) in polar coordinates on the wafer, the origin is moved to the center of the particle, and converted into Mie formula coordinates according to a predetermined optical path to calculate scattered light.
[0094]
(1) a1-b1: Direct incidence on particle → detector
The component perpendicular to the scattering surface (the surface formed by the incident optical axis and the scattering direction) of the scattered electric field calculated by giving A to the Mie formula is set as follows.
[0095]
[Equation 19]

The position of the observation point expressed in the coordinates for Mie formula is (r₁′, Θ₁′, Φ₁’). This depends on whether the incident light is s-polarized or p-polarized with respect to the wafer.
[0096]
[Expression 20]

(2) a1-b2: Directly incident on particles → detector after reflection
What converted the position of the observation point into coordinates for Mie formula (r₂′, Θ₂′, Φ₂’)
[Expression 21]

It becomes.
[0097]
This is divided into a component perpendicular to the plane made by the direction of scattering and the normal of the wafer, and a component parallel to the plane for subsequent calculations.
What converted the position of the observation point into coordinates for Mie formula (r₂′, Θ₂′, Φ₂’)
[Expression 22]

It becomes.
[0098]
Considering interference with a component that reciprocates in the film using this, the following equation is obtained.
[0099]
[Expression 23]

The phase difference δ caused by the optical path difference is expressed by the following formula.
[0100]
[Expression 24]

(3) a1-b3: Directly incident on the particle → incident on the particle after reflection
As in the past, the position of the observation point is converted to the coordinates for Mie formula (r_Three ′, Θ_Three′, Φ_Three′), The scattered electric field is
[Expression 25]

It becomes.
[0101]
In this case, since the scattered light travels directly below the particles, the incident surface and the scattering surface are coincident. Therefore, the new incident light is
[Equation 26]

It is. This incident light is calculated in two parts, but since both are described with respect to a common scattering surface,
[Expression 27]

It becomes. here
(R_Four′, Θ_Four′, Φ_Four’), (R_Five′, Θ_Five′, Φ_Five′) Is obtained by converting the position of the observation point into coordinates for the Mie formula for two incident lights, and
[Expression 28]

It is.
[0102]
(4) a2-b1: incident on particle after reflection → detector
When s-polarized light and p-polarized light are selected, the following formula is obtained.
[0103]
[Expression 29]

(5) a2-b2: incident on particles after reflection → detector after reflection
The scattered electric field is represented by the following equation where the position of the observation point converted to the Mie formula coordinates is (r7 ', θ7', φ7 ').
[0104]
[30]

Similarly to a1-b2, the component is divided into a component perpendicular to the plane made by the scattering direction and the normal of the wafer, and a component parallel to the surface.
[31]

And Considering interference with a component that reciprocates n times in the film using this, the following equation is obtained.
[0105]
[Expression 32]

(6) a2-b3: incident on the particle after reflection → incident on the particle after reflection
The position of the observation point converted to the coordinates for Mie formula is (r₈′, Θ₈′, Φ₈′), The scattered electric field is expressed by the following equation.
[0106]
[Expression 33]

When considered similarly to a1-b3, the following equation is obtained.
[0107]
[Expression 34]

here,
(R₉′, Θ₉′, Φ₉’), (R_Ten′, Θ_Ten′, Φ_Ten′): The position of the observation point converted into coordinates for the Mie formula, and
[Expression 35]

It is.
[0108]
Since the vector sum of the above scattered electric fields is the scattered electric field at the observation point,
[Expression 36]

The correction term is added here.
[0109]
Here, the following two elements are added as correction terms.
[0110]
(1) Arbitrary phase difference given when incident light is reflected
Multiply the incident light by the composite reflectance and the phase difference to obtain the following formula.
[0111]
[Expression 37]

In order to express the influence of this correction, rewriting is performed as follows.
[0112]
[Formula 38]

(2) Arbitrary phase difference between the reflected light on the film surface and the reflected light that has reciprocated N times in the film at a1-b2 and a2-b2.
As a correction term on the scattered light side, at a1-b2 and a2-b2, an arbitrary phase difference is given between the reflected light on the film surface and the reflected light that has reciprocated N times in the film. This phase difference is given for each component, and exp (-iΔ_2S) To exp (-iΔ_2p). However, since the light paths on the scattered light side of a1-b2 and a2-b2 are common, both have the same Δ_2S, Δ_2pAnd
[39]

Rewrite
[Formula 40]

It becomes.
[0113]
The expression (13) in Expression 36 is rewritten as follows and becomes the following expression.
[0114]
[Expression 41]

This formula is the final form of the scattered electric field at the observation point.
[0115]
However, in actual calculation, the coordinates are reconverted into coordinates on the wafer, and the planes formed by the z-axis and the observation direction are divided into vertical components and parallel components and added as follows.
[0116]
[Expression 42]

Therefore, the scattering intensity Isca is
[Expression 43]

When there is a polarizing filter, if the deviation from the polarization axis of the filter is Θ (counterclockwise is positive)
(44)

It becomes.
[0117]
Standard particle size
Preferably, the value of the particle size measured by the surface inspection apparatus does not indicate an absolute value, but indicates a relative value corresponding to the diameter of the PSL particle that generates equivalent scattered light. For this reason, the initial sensitivity setting (setting of appropriate sensitivity and pricing of the photomal output and the particle size) used for the detection unit is performed using the PSL particle-coated wafer. Since the photomultiplier deteriorates with time, periodic sensitivity correction is performed.
[0118]
These photomultiplier sensitivity settings and corrections are referred to as calibration.
[0119]
Experimental example
The calculated value based on the mathematical scattering model considering the above experimental rule is compared with the actually measured value using the surface inspection apparatus. Table 1 shows the experimental conditions.
[0120]
[Table 1]

First, oxide film wafers having different film thicknesses coated with 0.208 μm diameter PSL particles were sequentially measured, and a characteristic curve corresponding to the film thickness (film thickness vs. scattered light intensity; characteristic curve (particle diameter vs. scattered light intensity) and For the distinction of
[0121]
Next, PSL particles having particle diameters of 0.208, 0.309, 0.506, and 1.001 μm were applied to wafers having film thicknesses of 200, 250, 350, and 500 nm, respectively, to obtain characteristic curves.
[0122]
In each experiment, measurement was performed in four modes (s-polarization / side detection, s-polarization / front detection, p-polarization / side detection, p-polarization / front detection) depending on the combination of incident polarization and detection direction. .
[0123]
The side is a region including a direction perpendicular to the incident surface, and the front is a region of 40 ° from the surface perpendicular to the incident surface to a direction close to regular reflection light.
[0124]
For these experimental results, an appropriate correction term Δ₁, Δ_2S, Δ_2PThe results of determining are shown in FIG. 4 and FIG.
[0125]
In addition, the voltage value of the gravity center position calculated from the histogram of the electric signal according to the scattered light intensity of PSL particles was adopted as the actual measurement value.
[0126]
FIG. 4 shows the measured value of the film thickness characteristic curve of the scattered light intensity and the calculated value corrected by the correction term. The correction term is based on data of a wafer having a relatively small film thickness.
[0127]
FIG. 6 shows the film thickness distribution normalized by the average value of the wafer having an oxide film formed on the surface used in the experiment. According to this, it can be seen that the degree of film unevenness is substantially constant regardless of the film thickness of the wafer. That is, the deviation from the average value of the film thickness increases as the film thickness increases (several hundred nm or more). Therefore, in the case of a wafer having a large film thickness, it is necessary to consider correction for film unevenness.
[0128]
FIG. 5 shows a comparison between the calculated characteristic curve and the actually measured value, and shows the accuracy of simulation regarding the particle diameter.
[0129]
Since this graph is logarithmic on both axes, the difference between the s-polarized data, particularly the calculated value and the actually measured value for a 350 nm-thickness wafer is not particularly large as the difference in scattered light intensity on the histogram.
[0130]
These calculated values of the relative scattered light intensity are added with a correction term that translates in the direction of the vertical axis.
[0131]
In addition, machine difference factors such as individual differences in the detector (PMT) can also be used as correction terms.
[0132]
Further, by applying the correction term by this method, application to a wafer with a film other than an oxide film is possible, and further, application to a wafer with metal film or bare silicon is possible with a film thickness of zero.
[0133]
Further, it is possible to automatically determine a threshold value (slice level) for particle discrimination based on the characteristic curve calculated by the mathematical scattering model thus obtained.
[0134]
As a calibration wafer, a wafer with an oxide film other than D-TEOS, and a wafer with a permeable film / metal film other than the oxide film can also be employed.
[0135]
On the other hand, in this embodiment, the method of extending the 0th-order model and tracking each optical path as an approach to the transmissive film model has been described. However, the composite reflectance is calculated in advance regardless of whether the film is a single layer or a multilayer. Thus, it is possible to select a method of handling the reflection surface as one reflection surface.
[0136]
【The invention's effect】
According to the present invention, in the calibration operation for defining the correlation between the detected scattered light output and the particle size of the foreign matter on the wafer, the scattering due to different particle sizes can be performed without actually measuring a large number of various calibration wafers. The light intensity can also be obtained. Therefore, it is possible to dramatically reduce the labor, time and personnel cost of the calibration work and to speed up the work.
[0137]
The present invention can be applied not only to a bare wafer but also to a wafer having a permeable film or the like formed on the surface.
[0138]
It is easy to realize a system that automates calibration work.
[0139]
Further, it is not necessary to prepare calibration wafers corresponding to each of “particle size”, “film type”, and “film thickness”. As a result, the burden of creating a calibration wafer, occupying a storage space, and the like are greatly reduced.
[0140]
Further, the measurement work itself required for the required number of calibration wafers becomes unnecessary, the time required for calibration is shortened, and the burden on the investigator is also reduced.
[0141]
Thereby, the reflection characteristic can be simulated using the state of the surface of the test object as a parameter.
[0142]
The number of calibration wafers can be greatly reduced.
[0143]
In addition to the optical properties of the wafer, information on the optical system of the apparatus itself and the response of the apparatus can be accurately predicted by calculation.
[Brief description of the drawings]
FIG. 1 is a conceptual diagram showing a basic scattering model.
FIG. 2 is a conceptual diagram showing a permeable membrane scattering model.
FIG. 3 shows a procedure for calculating a scattered light amount of particles on a wafer with a permeable membrane.
FIG. 4 is a diagram showing an actual measurement value of a film thickness characteristic curve of scattered light intensity and a calculated value corrected by a correction term.
FIG. 5 is a diagram showing a comparison between a calculated characteristic curve and an actual measurement value.
FIG. 6 is a diagram showing a film thickness distribution normalized by an average value of a D-TEOS wafer.

Claims (7)

In the surface inspection method for detecting the foreign matter existing on the wafer surface by irradiating the inspection light on the surface of the wafer to be inspected and detecting the scattered light generated when the foreign matter is present,
The scattered light output intensity and the wafer are calculated by a mathematical model that calculates the scattered electric field for each optical path from the time when the foreign object is irradiated with the inspection light and the scattered light is detected, and obtains the scattered light output intensity based on the sum of the scattered electric fields. A surface inspection method characterized by defining a correlation with the particle size of the foreign matter on the top and calibrating the surface inspection apparatus based on the correlation. In the surface inspection method for detecting the foreign matter existing on the wafer surface by irradiating the inspection light on the surface of the wafer to be inspected and detecting the scattered light generated when the foreign matter is present,
Calculate the scattered electric field for each optical path from the time when the foreign object is irradiated with the inspection light and the scattered light is detected, and calculate the output intensity of the scattered light based on the sum of the scattered electric field. A surface inspection method characterized in that a theoretical intensity of scattered light with respect to a diameter is obtained by calculation. The surface inspection method according to claim 1, wherein the mathematical model obtains an output intensity of scattered light using a Mie formula. The surface inspection method according to claim 1, wherein an output intensity of scattered light with respect to the film type of the wafer is obtained by calculation by applying a correction term relating to the film type of the wafer. 5. The surface inspection method according to claim 1, wherein an output intensity of scattered light with respect to the film thickness of the wafer is obtained by calculation by applying a correction term relating to the film thickness of the wafer. Irradiating means for irradiating inspection light onto the surface of the wafer to be inspected;
Detecting means for detecting scattered light generated when foreign matter is present by irradiation of inspection light by the irradiation means;
A scattered electric field is calculated for each optical path from the irradiating means for irradiating the inspection light to the foreign matter to the detecting means for detecting scattered light, and the scattered light is scattered by a mathematical model for determining the output intensity of the scattered light based on the sum of the scattered electric fields. Computation means for defining the correlation between the output intensity of light and the particle size of foreign matter on the wafer, the computation means has calibration means for calibrating the surface inspection apparatus based on the correlation,
A surface inspection apparatus for detecting foreign matter existing on a wafer surface. Irradiating means for irradiating inspection light onto the surface of the wafer to be inspected;
Detecting means for detecting scattered light generated when foreign matter is present by irradiation of inspection light by the irradiation means;
By calculating a scattered electric field for each optical path from the irradiating unit that irradiates the inspection light to the foreign substance to the detecting unit that detects scattered light, and calculating a scattered light output intensity based on the sum of the scattered electric fields, the wafer Having calculation means for calculating the theoretical intensity of scattered light with respect to the particle size of the foreign matter on the surface,
A surface inspection apparatus for detecting foreign matter existing on a wafer surface .

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