JP4237729B2 - 空間光変調器アレイの空間像を計算する方法およびシステム - Google Patents
空間光変調器アレイの空間像を計算する方法およびシステム Download PDFInfo
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- 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
- G03F7/70425—Imaging strategies, e.g. for increasing throughput or resolution, printing product fields larger than the image field or compensating lithography- or non-lithography errors, e.g. proximity correction, mix-and-match, stitching or double patterning
- G03F7/70433—Layout for increasing efficiency or for compensating imaging errors, e.g. layout of exposure fields for reducing focus errors; Use of mask features for increasing efficiency or for compensating imaging errors
- G03F7/70441—Optical proximity correction [OPC]
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- 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
- G03F7/20—Exposure; Apparatus therefor
- G03F7/2051—Exposure without an original mask, e.g. using a programmed deflection of a point source, by scanning, by drawing with a light beam, using an addressed light or corpuscular source
-
- 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
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- G03F7/70283—Mask effects on the imaging process
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- 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
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- 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
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- 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
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- 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
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- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
- Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)
- Mechanical Light Control Or Optical Switches (AREA)
Description
U(i)(x,α,f s) = F(U(p)(f p,α,f s)) (式1)
であり、ここでxは、画像面における2次元の位置ベクトル、すなわち(x,y)である。ベクトルα = [α1,…,αN]は、上記のように、SLMアレイの全ピクセルのパラメタのすべての変調の集合である。「小開口数、スカラモデル」ではFは、f p(すなわち、ひとみ面における位置)に依存しない変数からx(画像面における位置)へのフーリエ変換である。ここでf p = [fp (x),fp (y)]はひとみ位置座標であり、
Uj (i) = Uj (i) (x−xj,αj,fs) (式2)
によって得られる。
Uj (i) (x−x j,α j,f s) = g(αj)U(i)(x−x j,f s) (式4)
で与えられ、ここでg(αj)(|g(αj)| <= 1)は、ピクセルの有効な振幅グレイトーンであり、αjは、変調パラメタである(グレイトーン形SLMの場合、透過値)。変調パラメタαに対する振幅グレイトーンの依存関係を導き出すためにいくつかアプローチが可能である。例えば、傾斜形ミラーピクセルに対して、比較的正確なモデルはg(α) = sinc(α/α0),α0 = λ/(2*Lpixel)である。ピクセルツーピクセルの変化は、式4において無視されることにも注意されたい(すなわちU(i) jの代わりにU(i))。
U(k)(x,f s) = F(Pk(f p,f s)) (式9)
であり、nは基底関数の数である。結果的に得られる空間像は、
Uj (i) (x−x j,α j,f s) = g(αj)U(i)(x−x j,f s) (式4)
であり、ここでUj (i) (x−x j,f s)は、ピクセルの画像フィールドであり、g(αj)はグレイトーンである。傾斜形ミラーピクセルに対して、この近似によって、変調されたピクセル画像の振幅の変化が捕捉されるが、変調されたピクセル画像の位相の変化は捕捉されない。Pk(f p, f s)が、ひとみフィールドU(p)の変化を表す既知の基底関数であるとする。上記の近似は、n=1に相応し、また(緩慢に変化する偶関数上で)f pに関してP1(f p, f s)が一定であることに相応する。
n = 2 P1(f p, f s) = P1(f s)−ひとみ変化における定数項
P2(f p, f s) = fp (x)・P1(f s)−ひとみ変化における1次の項
である。
上では本発明のさまざまな実施形態を説明したが、これらは制限のためではなく、例として示しただけであることを理解されたい。本発明の精神および範囲から逸脱することなく、形態および詳細に種々の変更を行えることは当業者には明らかであろう。したがって本発明の範囲は、上記の例示的な実施形態のいずれによっても制限されるべきでなく、特許請求の範囲またとこれと同等のものにしたがってのみ定められるべきである。
102 照明システム、
104 空間光変調器、
106 ビームスプリッタ、
108 SLM光学系、
110 投影光学系、
112 対象体、
114,116 コントローラ、
200 マスクレスリソグラフィシステム、
202 照明源、
204 SLM、
210 投影光学系、
212 対象体、
214, 216 コントローラ、
300 アクティブエリア、
302 アクティブデバイス(ピクセル)、
400 イナクティブなパッケージング、
402 メインコントローラ、
500 アセンブリ、
502 サポートデバイス、
504 温度制御エリア
Claims (16)
- 空間光変調器アレイの空間像を計算する方法において、
該空間光変調器アレイのピクセル間で、2ピクセル1組みの干渉を表すピクセル干渉マトリクスを計算するステップと、
該ピクセルの変調状態に相応する有効グレイトーンを計算するステップと、
前記のピクセル干渉マトリクスおよび有効グレイトーンに基づいて空間像を計算するステップとを有することを特徴とする、
空間光変調器アレイの空間像を計算する方法。 - 前記の有効グレイトーンは、前記のピクセルの変調状態だけに依存する、
請求項1に記載の方法。 - 前記ピクセル干渉マトリクスは位置変数だけに依存する、
請求項1に記載の方法。 - 前記位置変数は、画像面における位置および電磁放射源の面における位置である、
請求項3に記載の方法。 - 前記ピクセル干渉マトリクスは、関数のマトリクスである、
請求項1に記載の方法。 - 前記ピクセル干渉マトリクスは4次元マトリクスである、
請求項1に記載の方法。 - sinc関数を使用して前記有効グレイトーンを近似する、
請求項1に記載の方法。 - 多項式関数を使用して前記有効グレイトーンを近似する、
請求項1に記載の方法。 - 空間光変調器アレイの空間像を計算する装置において、
該空間光変調器アレイのピクセル間で、2ピクセル1組みの干渉を表すピクセル干渉マトリクスを計算する手段と、
該ピクセルの変調状態に相応する有効グレイトーンを計算する手段と、
前記のピクセル干渉マトリクスおよび有効グレイトーンに基づいて空間像を計算する手段とを有することを特徴とする、
空間光変調器アレイの空間像を計算する装置。 - 前記の有効グレイトーンは、前記のピクセルの変調状態だけに依存する、
請求項9に記載の装置。 - 前記ピクセル干渉マトリクスは位置変数だけに依存する、
請求項9に記載の装置。 - 前記位置変数は、画像面における位置および電磁放射源の面における位置である、
請求項11に記載の装置。 - 前記ピクセル干渉マトリクスは、関数のマトリクスである、
請求項9に記載の装置。 - 前記ピクセル干渉マトリクスは4次元マトリクスである、
請求項9に記載の装置。 - 前記有効グレイトーンは、sinc関数を使用して近似される、
請求項9に記載の装置。 - 前記有効グレイトーンは、多項式関数を使用して近似される、
請求項9に記載の装置。
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US10/835,403 US6963434B1 (en) | 2004-04-30 | 2004-04-30 | System and method for calculating aerial image of a spatial light modulator |
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-
2004
- 2004-04-30 US US10/835,403 patent/US6963434B1/en not_active Expired - Lifetime
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2005
- 2005-04-27 TW TW094113474A patent/TWI278730B/zh not_active IP Right Cessation
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US20080219562A1 (en) | 2008-09-11 |
CN100470372C (zh) | 2009-03-18 |
KR20060047613A (ko) | 2006-05-18 |
US7889411B2 (en) | 2011-02-15 |
US6963434B1 (en) | 2005-11-08 |
KR100636039B1 (ko) | 2006-10-19 |
JP2005322924A (ja) | 2005-11-17 |
CN1700097A (zh) | 2005-11-23 |
US20050243398A1 (en) | 2005-11-03 |
US20050243397A1 (en) | 2005-11-03 |
TWI278730B (en) | 2007-04-11 |
US7394584B2 (en) | 2008-07-01 |
TW200535587A (en) | 2005-11-01 |
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