JP2006505876A - 電気的製造制御に対する確率制約最適化 - Google Patents
電気的製造制御に対する確率制約最適化 Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
- G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
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- H—ELECTRICITY
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- H01L22/00—Testing or measuring during manufacture or treatment; Reliability measurements, i.e. testing of parts without further processing to modify the parts as such; Structural arrangements therefor
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
Description
Y=XC+V (1)
で表される線形相関(linearly related)を持つ、と仮定すると、
入力X行列と出力Y行列とをまず、直交する一連の潜在変数に投影することによって、PLS回帰が線形モデルを形成し、
u=thbh+rh (4)
により、関連づけられ、
bhが通常の部分最小二乗回帰により決定される。その後、次の因子に関して、残りのものに対するプロセスが繰り返され、因子の数が相互検証を通じて決定される。
制約条件は、
ここでPは制約が満たされる確率を表し、また、ρは確率のしきい値を表す。
Claims (10)
- デバイスを製造するための複数のステップを含むプロセスのモデルを定義する処理と、
前記プロセスのステップの少なくとも一つのサブセットに対して、複数のインラインプロセスターゲットを定義する処理であって、前記モデルは前記インラインプロセスターゲットを、複数のプロセス出力パラメータに関係づけるものである処理と、
前記インラインプロセスターゲットに対する確率制約の第1セットを定義する処理と、
前記プロセス出力パラメータに対する確率制約の第2セットを定義する処理と、
前記モデルと、前記複数のプロセス出力パラメータに基づき、目的関数を定義する処理と、
プロセスの各ステップにおいて、前記インラインプロセスターゲットに対する値を決定するために、プロセスの各ステップに対し、確率制約の第1および第2セットを条件として、目的関数を最適化することにより、プロセス出力パラメータのトラジェクトリを決定する処理であって、プロセスの残りのステップのために、各ステップ完了後に最適化を繰り返す処理とを含む方法。 - 前記目的関数を最適化する処理が更に、個々の確率制約技術、及び、共有の確率制約技術の一つを用いて、前記制約の第1及び第2セットを条件として、前記目的関数を最適化する処理を含む、請求項1記載の方法。
- 前記確率制約の第1セットを定義する処理が更に、前記インラインプロセスターゲットの値域に対して、確率制約を定義する処理を含み、かつ、前記確率制約の第2セットを定義する処理が更に、前記プロセス出力パラメータに対する値域に対して確率制約を定義する処理を含む、請求項1記載の方法。
- 前記確率制約の第1セットを定義する処理が更に、前記インラインプロセスターゲットにおける変更に対するステップサイズの値域に対して、確率制約を定義する処理を更に含む、請求項1記載の方法。
- 前記確率制約の第1及び第2セットのうちの一つが満たされえないことを決定する処理と、
前記確率制約の第1及び第2セットの少なくとも一つを変更する処理と、
前記変更された前記確率制約の第1及び第2セットの一つに基づき、トラジェクトリを決定する処理とを更に含む、請求項1記載の方法。 - 複数のステップを経てデバイスを製造するための複数のツール(30−80)と、
前記ツール(30−80)の少なくとも一つのサブセットに関連する複数のプロセスコントローラ(160)を含み、各プロセスコントローラは(160)、インラインプロセスターゲットに基づき、少なくとも一つの関連ツール(30−80)のプロセスを制御するように構成されており、
デバイスを製造するために、前記プロセスステップのモデルを採用するように構成されており、前記モデルは、前記インラインプロセスターゲットを複数のプロセス出力パラメータに関係づけるものであって、前記インラインプロセスターゲットに対する確率制約の第1セットを定義し、前記プロセス出力パラメータに対する確率制約の第2セットを定義し、前記モデル、及び、前記複数のプロセス出力パラメータに基づく目的関数を定義し、かつ、関連のプロセスコントローラを持つ、各プロセスステップにおけるインラインプロセスターゲットに対する値を決定するために、各プロセスステップに対する、確率制約の第1及び第2セットを条件として、目的関数を最適化することにより、プロセス出力パラメータのトラジェクトリを決定し、前記最適化が残りのプロセスステップのために、各プロセスステップの完了後に繰り返されるように構成される監視コントローラ(140)とを含む、システム(10)。 - 前記監視コントローラ(140)が更に、個々の確率制約技術、および、共有の確率制約技術の一つを用いて、前記制約の第1及び第2セットを条件として、目的関数を最適化するように構成されている、請求項6記載のシステム(10)。
- 前記監視コントローラ(140)が更に、前記インラインプロセスターゲットの値域に対して、前記確率制約の第1セットを定義し、かつ、前記プロセス出力パラメータに対する値域に対して、前記確率制約の第2セットを定義するように構成されている、請求項6記載のシステム(10)。
- 前記監視コントローラ(140)が更に、前記インラインプロセスターゲットにおける変更に対するステップサイズの値域に対して、確率制約を定義するように構成されている、請求項6記載のシステム(10)。
- 前記監視コントローラ(140)が更に、前記確率制約の第1及び第2セットのうちの一つが満たされえないことを決定し、前記確率制約の第1及び第2セットの少なくとも一つを変更し、かつ、前記変更された前記確率制約の第1及び第2セットの一つに基づき、前記トラジェクトリを決定するように構成されている、請求項6記載のシステム(10)。
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US42494402P | 2002-11-08 | 2002-11-08 | |
US10/335,748 US6959224B2 (en) | 2002-11-08 | 2003-01-02 | Probability constrained optimization for electrical fabrication control |
PCT/US2003/034848 WO2004044660A2 (en) | 2002-11-08 | 2003-10-29 | Probability constrained optimization for electrical fabrication control |
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JP2006505876A true JP2006505876A (ja) | 2006-02-16 |
JP2006505876A5 JP2006505876A5 (ja) | 2009-01-29 |
JP4472637B2 JP4472637B2 (ja) | 2010-06-02 |
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JP2005507067A Expired - Lifetime JP4472637B2 (ja) | 2002-11-08 | 2003-10-29 | 電気的製造制御に対する確率制約最適化 |
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US (1) | US6959224B2 (ja) |
EP (1) | EP1558977B1 (ja) |
JP (1) | JP4472637B2 (ja) |
KR (1) | KR101003558B1 (ja) |
AU (1) | AU2003290570A1 (ja) |
DE (1) | DE60307310T2 (ja) |
TW (1) | TWI308703B (ja) |
WO (1) | WO2004044660A2 (ja) |
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EP3869271A1 (en) * | 2020-02-20 | 2021-08-25 | ASML Netherlands B.V. | Method for controlling a manufacturing process and associated apparatuses |
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JPH0616475B2 (ja) * | 1987-04-03 | 1994-03-02 | 三菱電機株式会社 | 物品の製造システム及び物品の製造方法 |
US6041270A (en) * | 1997-12-05 | 2000-03-21 | Advanced Micro Devices, Inc. | Automatic recipe adjust and download based on process control window |
US6434441B1 (en) * | 1998-04-30 | 2002-08-13 | General Electric Company | Designing and making an article of manufacture |
EP1045304A1 (fr) * | 1999-04-16 | 2000-10-18 | Martine Naillon | Procédé de pilotage d'un processus décisionnel lors de la poursuite d'un but dans un domaine d'application déterminé, tel qu'économique, technique organisationnel ou analogue et système pour la mise en oeuvre du procédé |
US6470230B1 (en) | 2000-01-04 | 2002-10-22 | Advanced Micro Devices, Inc. | Supervisory method for determining optimal process targets based on product performance in microelectronic fabrication |
DE10047381A1 (de) * | 2000-09-25 | 2002-04-18 | Siemens Ag | Verfahren und Vorrichtung zum Betreiben einer Anlage der Grundstoffindustrie |
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AU2003290570A8 (en) | 2004-06-03 |
DE60307310T2 (de) | 2007-10-18 |
DE60307310D1 (de) | 2006-09-14 |
TW200415497A (en) | 2004-08-16 |
US20040093107A1 (en) | 2004-05-13 |
JP4472637B2 (ja) | 2010-06-02 |
US6959224B2 (en) | 2005-10-25 |
WO2004044660A3 (en) | 2004-07-29 |
KR20050074561A (ko) | 2005-07-18 |
TWI308703B (en) | 2009-04-11 |
EP1558977B1 (en) | 2006-08-02 |
AU2003290570A1 (en) | 2004-06-03 |
WO2004044660A2 (en) | 2004-05-27 |
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