JP7193456B2 - ニューラルネットワークを使用する分光モニタリング - Google Patents
ニューラルネットワークを使用する分光モニタリング Download PDFInfo
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Description
CV=C1*tanh(0.5(N1・S)+0.5b1)+C2*tanh(0.5(N2・S)+0.5b2)+…+CL*tanh(0.5(NL・S)+0.5bL)
ここで、Sは測定スペクトルであり、Nk=(ak1V1・+ak2V2・+…+akLVL)であり、aki、bi、及びCiはニューラルネットワークによって設定される重みであり、かつ、Viは次元削減のための固有ベクトルである。
tanh(0.5*ak1(I1)+ak2(I2)+…+akM(IM)+bk) 方程式1
ここで、tanhは双曲線正接であり、akxはk番目の中間ノードと(M個の入力ノードのうちの)x番目の入力ノードとの間の接続の重みであり、かつ、IMはM番目の入力ノードの値である。しかし、tanhの代わりに他の非線形関数(例えば、正規化線形ユニット(ReLU)関数及びその変種)も使用されうる。
Hk=tanh(0.5*ak1(I1)+ak2(I2)+…+akL(IL)+bk)
Hk=tanh(0.5*ak1(V1・S)+ak2(V2・S)+…+akL(VL・S)+bk) 方程式2
ここで、Vxは、測定スペクトルを、削減後の次元数のデータの(L個の成分のうちの)x番目の成分の値へと変換させる、行行列(v1、v2、…,vn)である。例えば、Vxは、後述する行列W又はW’の(L個の列のうちの)x番目の列によって提供されうる。すなわち、VxはWTのx番目の行である。ゆえに、Wxは、次元削減行列のx番目の固有ベクトルを表わしうる。
CV=C1*H1+C2*H2+…+CL*HL
ここで、Ckはk番目の隠れノードの出力の重みである。
R=(i1,i2,…,in)
ここで、ijは、全部でn個の波長のうちのj番目の波長における光強度を表わす。スペクトルは、例えば、200~500の強度測定値を含みうる(nは200~500でありうる)。
ここで、ijkは、j番目の参照スペクトルのk番目の波長における光強度を表わす。行列Aの各行は、参照スペクトル(例えば基板上のある1つの場所における測定値)を表わす。
tki=Ai・wkである。
T=AW
ここで、Wはn×p行列であり、その列はATAの固有ベクトルである。
CV=C1*tanh(0.5(N1・S)+0.5b1)+C2*tanh(0.5(N2・S)+0.5b2)+…+CL*tanh(0.5(NL・S)+0.5bL)
ここで、Nk=(ak1V1・+ak2V2・+…+akLVL)であり、重みakiは、ニューラルネットワーク120によって設定された重みであり、ベクトルViは次元削減モジュール110によって決定された固有ベクトルである。
Claims (16)
- 基板の処理を制御するためのコンピュータプログラム製品であって、プロセッサに、
基板の研磨中に、インシトゥの光学モニタシステムから、研磨が行われている前記基板からの反射光の測定スペクトルを受信することと、
複数の成分値を生成するために、前記測定スペクトルの次元数を削減することと、
人工ニューラルネットワークを使用して、研磨プロセスを経る前記基板の進捗を表現する特性値を生成することであって、前記人工ニューラルネットワークが、前記複数の成分値を受信するための複数の入力ノードと、研磨プロセスを経る前記基板の進捗を表現する前記特性値を出力するための1つの出力ノードと、前記入力ノードと前記出力ノードとを接続する複数の隠れノードとを有する、特性値を生成することと、
前記特性値に基づいて、前記基板の処理を停止するか否かと処理パラメータの調整との少なくとも一方を決定することとを、
実行させるための命令を備え、
前記測定スペクトルはN個の波長に対してN個の強度値を含み、前記次元数を削減する前記命令は、N列中に前記N個の強度値を有する1行N列の行列にN行L列(L<N)の行列を乗算して、L個の成分値を生成する命令を含むコンピュータプログラム製品。 - 複数の成分を生成するために複数の参照スペクトルについて特徴抽出を実施するための命令を備える、請求項1に記載のコンピュータプログラム製品。
- 特徴抽出を実施するための前記命令が、主成分解析、特異値分解、独立成分解析、又は自己符号化を実施するための命令を含む、請求項2に記載のコンピュータプログラム製品。
- トレーニングデータを生成するために、既知の特性値を有する前記複数の参照スペクトルのうちの2つ以上のものについて次元削減を実施するための命令を備える、請求項2に記載のコンピュータプログラム製品。
- 前記トレーニングデータ及び前記既知の特性値を使用して、逆伝搬法によって前記人工ニューラルネットワークをトレーニングするための命令を備える、請求項4に記載のコンピュータプログラム製品。
- 前記2つ以上のスペクトルは複数のスペクトルの全数よりも少ない数である、請求項5に記載のコンピュータプログラム製品。
- トレーニングデータを生成するために、既知の特性値を有する複数の参照スペクトルについて次元削減を実施するための命令を備える、請求項5に記載のコンピュータプログラム製品。
- 前記人工ニューラルネットワークが、前記基板の事前測定値、直前の基板の測定値、処理システム内の別のセンサからの測定値、前記処理システムの外部のセンサからの測定値、コントローラが記憶している処理レシピからの値、前記コントローラが追跡する変数の値のうちの、少なくとも1つを受信するよう設定された、少なくとも1つの入力ノードを備える、請求項1に記載のコンピュータプログラム製品。
- 基板を処理する方法であって、
基板に、研磨を行うことと、
前記研磨中に、研磨が行われている前記基板からの反射光の測定スペクトルを、インシトゥの光学モニタシステムを用いて測定することと、
複数の成分値を生成するために、前記測定スペクトルの次元数を削減することと、
人工ニューラルネットワークを使用して、研磨プロセスを経る前記基板の進捗を表現する特性値を生成することであって、前記人工ニューラルネットワークが、前記複数の成分値を受信するための複数の入力ノードと、研磨プロセスを経る前記基板の進捗を表現する前記特性値を出力するための1つの出力ノードと、前記入力ノードと前記出力ノードとを接続する複数の隠れノードとを有する、特性値を生成することと、
前記特性値に基づいて、前記基板の処理を停止するか否かと処理パラメータの調整との少なくとも一方を決定することとを含み、
前記測定スペクトルはN個の波長に対してN個の強度値を含み、前記次元数を削減することは、N列中に前記N個の強度値を有する1行N列の行列にN行L列(L<N)の行列を乗算して、L個の成分値を生成することを含む、
方法。 - 前記処理が化学機械研磨を含む、請求項9に記載の方法。
- 複数の成分を生成するために複数の参照スペクトルについて特徴抽出を実施することを含む、請求項9に記載の方法。
- トレーニングデータを生成するために、既知の特性値を有する前記複数の参照スペクトルのうちの2つ以上のものについて次元削減を実施することを含む、請求項11に記載の方法。
- 研磨パッドを保持するための支持体と、
前記研磨パッドと接触するように基板を保持するためのキャリアヘッドと、
前記支持体と前記キャリアヘッドとの間に相対運動を発生させるためのモータと、
研磨中に前記基板からの反射光のスペクトルを測定するためのインシトゥの光学モニタシステムとを備える、研磨システムであって、更に、
前記基板の前記研磨中に、前記インシトゥの光学モニタシステムから、研磨が行われている前記基板からの反射光の測定スペクトルを受信することと、
複数の成分値を生成するために、前記測定スペクトルの次元数を削減することと、
人工ニューラルネットワークを使用して、研磨プロセスを経る前記基板の進捗を表現する特性値を生成することであって、前記人工ニューラルネットワークが、前記複数の成分値を受信するための複数の入力ノードと、研磨プロセスを経る前記基板の進捗を表現する前記特性値を出力するための1つの出力ノードと、前記入力ノードと前記出力ノードとを接続する複数の隠れノードとを有する、特性値を生成することと、
前記特性値に基づいて、前記基板の処理を停止するか否かと処理パラメータの調整との少なくとも一方を決定することとを、
行うよう設定されたコントローラを備え、
前記測定スペクトルはN個の波長に対してN個の強度値を含み、前記コントローラは前記次元数を削減するため、N列中に前記N個の強度値を有する1行N列の行列にN行L列(L<N)の行列を乗算して、L個の成分値を生成するように構成された、研磨システム。 - 前記コントローラが、複数の成分を生成するために複数の参照スペクトルについて特徴抽出を実施するよう設定されている、請求項13に記載のシステム。
- 前記コントローラが、トレーニングデータを生成するために、既知の特性値を有する前記複数の参照スペクトルのうちの2つ以上のものについて次元削減を実施するよう設定されている、請求項14に記載のシステム。
- 前記次元数を削減する命令及び前記特性値を生成する命令は、つぎの式:
CV=C1*tanh(0.5(N1・S)+0.5b1)+C2*tanh(0.5(N2・S)+0.5b2)+…+CL*tanh(0.5(NL・S)+0.5bL)
に従って、前記特性値(CV)を計算する命令を含み、
ここで、Sは測定された前記測定スペクトルであり、Nk=(ak1V1・+ak2V2・+…+akLVL)であり、aki、bi及びCiは、前記人工ニューラルネットワークによって設定された重みであり、Viは次元削減のための固有ベクトルである、請求項1に記載のコンピュータプログラム製品。
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