JPS62117321A - Controller for thickness of coating film by karman-filter - Google Patents
Controller for thickness of coating film by karman-filterInfo
- Publication number
- JPS62117321A JPS62117321A JP60256563A JP25656385A JPS62117321A JP S62117321 A JPS62117321 A JP S62117321A JP 60256563 A JP60256563 A JP 60256563A JP 25656385 A JP25656385 A JP 25656385A JP S62117321 A JPS62117321 A JP S62117321A
- Authority
- JP
- Japan
- Prior art keywords
- film thickness
- coating film
- coating
- controller
- rotation speed
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Preparing Plates And Mask In Photomechanical Process (AREA)
- Coating Apparatus (AREA)
- Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)
Abstract
Description
【発明の詳細な説明】
〔発明の利用分野〕
本発明は、半導体製造プロセスの塗布工程において、塗
布膜厚をばらつきなく常に設計等で定められた値に制御
する塗布膜厚制御装置に関する。DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to a coating film thickness control device that constantly controls the coating film thickness to a value determined by design or the like without variation in a coating process of a semiconductor manufacturing process.
従来、処理毎にばらつく塗布膜厚を自動制御する試みは
なく、ノウハウによって塗布装置を運転していた。この
ため、塗布膜厚に大きなばらつきを生じさせ、最終的に
は半導体製品の歩留りを低下させるという大きな問題が
あった。たとえば、電子材料別冊、超ＬＳＩ製造・試験
装置（１９８４年度版）の第９２頁「ホトレジスト処理
装置」 （遠藤）の第３図に示されているように、処理
ウェハ毎にかなりのばらつきを生じていた。Until now, there has been no attempt to automatically control the coating film thickness, which varies from process to process, and coating equipment has been operated based on know-how. For this reason, there is a major problem in that the coating film thickness varies greatly and ultimately the yield of semiconductor products is reduced. For example, as shown in Figure 3 of "Photoresist Processing Equipment" (Endo) on page 92 of the Electronic Materials Special Edition, VLSI Manufacturing and Testing Equipment (1984 edition), considerable variation occurs between processed wafers. was.
本発明の目的は所望の値で、ばらつきなく塗布膜厚を形
成するために上述のような問題を解決し。An object of the present invention is to solve the above-mentioned problems in order to form a coating film with a desired thickness without variation.
塗布装置環境温度などの変化に応じて、カルマン・フィ
ルターを適用することにより最適なスピナー回転数を決
定するカルマン・フィルターによる塗布膜厚制御装置を
提供することにある。An object of the present invention is to provide a coating film thickness control device using a Kalman filter that determines the optimum spinner rotation speed by applying a Kalman filter in accordance with changes in the environmental temperature of the coating device.
」１記の目的を達成させるために、過去の時点に処理さ
れた塗布膜厚の検査データに基づいて、カルマン・フィ
ルターを適用することにより塗布膜厚モデルのモデル係
数を逐次求め、上記のモデルに目標塗布膜厚を入力する
ことにより最適なスピナー回転数を決定する。塗布膜厚
とスピナー回転数との関係のみに注目していた従来法で
は、塗布装置の設置された環境、特に雰囲気温度などの
変動を吸収できず、塗布膜厚に大きなばらつきを生じさ
せ、最終的には半導体製品の歩留りを低下させる結果と
なる。In order to achieve the purpose stated in item 1, model coefficients of the coating film thickness model are sequentially determined by applying a Kalman filter based on the coating film thickness inspection data processed at past points in time, and the model coefficients of the coating film thickness model are sequentially calculated. Determine the optimal spinner rotation speed by inputting the target coating film thickness. Conventional methods that focused only on the relationship between coating film thickness and spinner rotation speed were unable to absorb fluctuations in the environment in which the coating equipment was installed, especially the ambient temperature, resulting in large variations in coating film thickness and poor final performance. This ultimately results in a decrease in the yield of semiconductor products.
以下ではカルマン・フィルターによる塗布膜厚制御のア
ルゴリズムを詳細に説明する。塗布膜厚のスピナー回転
数依存性は、一般に、次のように表わせることが知られ
ている。The algorithm for controlling the coating film thickness using the Kalman filter will be explained in detail below. It is known that the spinner rotation speed dependence of coating film thickness can generally be expressed as follows.
Ｊ
Ｔ ＝ ａΩ２ （１）ここに
、Ｔは塗布膜厚、Ωはスピナー回転数。J T = aΩ2 (1) Here, T is the coating film thickness and Ω is the spinner rotation speed.
ａはモデル係数を表わす。モデル係数ａは塗布環境が同
じであれば定数であるが、クリーンルーム内においても
人の出入り等の原因により塗布環境、特に雰囲気温度な
どの変動によりモデル係数ａは変動しているものと思わ
れる。処理順のウェハに番号ｊを付すと、モデル係数ａ
もＤＩと書ける。a represents a model coefficient. The model coefficient a is a constant if the coating environment is the same, but it is thought that even in a clean room, the model coefficient a fluctuates due to changes in the coating environment, especially the ambient temperature, due to factors such as people entering and leaving the room. If a number j is assigned to a wafer in the processing order, the model coefficient a
can also be written as DI.
このモデル係数の変動を表わす式を次のように仮定する
。The equation representing the variation of this model coefficient is assumed as follows.
ａ ｉ ＝８ ＋−１＋ζＩ−１（２）ここで、ζ＋−
１は塗布装置環境温度などの要因による雑音を表わし、
次のような性質を有するものとする。a i =8 +-1+ζI-1 (2) Here, ζ+-
1 represents noise caused by factors such as the coating equipment environmental temperature;
It shall have the following properties.
Ｅ［ζ＋］＝０．（ζ吸ζａ）＝ｊＪδＩＪ Ｃ
５）Ｅは平均を意味する。E[ζ+]=0. (ζ absorptionζa)=jJδIJ C
5) E means average.
次に式（１）を次のように書き改める。Next, equation (1) is rewritten as follows.
上
ＴｉΩｌ” ＝ ａ＋＋ １７＋ （
４）ここで付加したη噛は言わば観１１＋１１に伴う誤
差を表わすもので、次のような条件を満たすものとする
。Upper TiΩl” = a++ 17+ (
4) The η bit added here represents the error associated with the equation 11+11, and it is assumed that the following conditions are satisfied.
Ｅ〔η１）＝Ｏ，Ｅ（η１ η−）＝Ｗ δ ＊ａ
（５）式（２）および式（４）は、現代制御輪にお
けるシステム方程式および観測方程式に相当する。E[η1)=O, E(η1 η−)=W δ *a
(5) Equations (2) and (4) correspond to the system equation and observation equation in modern control wheels.
観測雑音η１は必ず存在するものであり、モデル係数８
１は直接観測できない。このため、カルマン・フィルタ
ーを用いてモデル係数８１の推定領置１を求める。Observation noise η1 always exists, and the model coefficient 8
1 cannot be observed directly. Therefore, the estimated region 1 of the model coefficient 81 is determined using a Kalman filter.
ａ １＝ ａ ｔ−ｔ ＋ Ｐ １’ Ｗ−ニー（Ｔｌ
Ω＊２ａｔ−１） （５）Ｐｉ−１＝（（Ｐ １−２
＋ Ｕ ）−１＋ Ｗ−１）−工 （６）式（６）
の定常解を求めると、
−Ｕ＋ｆ戸イー「ゴＷ
ｐｔ＝ （７）とな
る。今Ｕ＝αＷとおくと、
式（８）を式（５）に代入すると、
得る。第１番目のウェハはすでに処理されたものである
ので、これから処理しようとするウェハ番号はｉ＋１と
なる。このウェハに対して、’ｊ；ｔ＋１＝當ｒ
（１１）を求めると、所定の目標
塗布膜厚Ｔ”を得るための最適なスピナー回転数は次の
ようになる。a 1 = a t-t + P 1' W-knee (Tl
Ω*2at-1) (5) Pi-1=((P 1-2
+ U)-1+W-1)-Equation (6)
When we find the steady-state solution of -U+fWpt= (7).If we now set U=αW, then by substituting equation (8) into equation (5), we get:The first wafer has already been processed, so the wafer number to be processed is i+1.
When (11) is determined, the optimum spinner rotation speed to obtain a predetermined target coating film thickness T'' is as follows.
Ω１＋１＝（令ｔ＋ｔ／ Ｔ ”）” （
１２）結果はαの値にあまり依存しないので、以下では
α＝１とする。Ω1+1=(order t+t/T ”)” (
12) Since the result does not depend much on the value of α, α=1 in the following.
第１図は本発明による一実施例を示すカルマン・フィル
ターによる塗布膜厚制御装置の全体構成図である。第１
図において、１は回転塗布装置を示し、コントローラー
２でＰ、１．Ｄ、（比例＋積分十微分）制御によりフィ
ードバック制御される。FIG. 1 is an overall configuration diagram of a coating film thickness control device using a Kalman filter, showing one embodiment of the present invention. 1st
In the figure, 1 indicates a spin coating device, and a controller 2 controls P, 1. D, feedback control is performed by (proportional+integral-sufficient differential) control.
コントローラー２へ与える操作量は以下に述べるように
、目標塗布膜厚５が与えられた時に最適スピナー回転数
を決定するスピナー回転数決定装置３で計算される。The amount of operation given to the controller 2 is calculated by the spinner rotation speed determination device 3 which determines the optimum spinner rotation speed when the target coating film thickness 5 is given, as described below.
スピナー回転数決定装置３では１式（ＪＯ）により逐次
モデル係数の推定値、％量 を求め、式（１２）に従っ
て最適スピナー回転数を決定する。The spinner rotation speed determining device 3 sequentially obtains the estimated value and percentage of the model coefficient using equation 1 (JO), and determines the optimum spinner rotation speed according to equation (12).
第２図はカルマン・フィルターを用いて塗布膜厚を目標
の値に制御するための具体的なアルゴリズムを示す。係
数推定装置３１では１番ウェハの膜厚測定値３０１を受
信すると、式（１０）。FIG. 2 shows a specific algorithm for controlling the coating film thickness to a target value using a Kalman filter. When the coefficient estimating device 31 receives the film thickness measurement value 301 of the No. 1 wafer, the coefficient estimating device 31 calculates Equation (10).
（１１）に従って、推定係数ａ 羞＋ｔ を算出する。According to (11), estimate coefficient a+t is calculated.
この値３０２をスピナー回転数計算装置３２にわたす。This value 302 is passed to the spinner rotation speed calculation device 32.
ここで計算した回転数３０：３をこれから処理しようと
するスピナーにわたして、ウェハの塗布処理を実行する
。The rotation speed calculated here, 30:3, is passed to the spinner to be processed, and the coating process on the wafer is executed.
第３図は、推定係数雀象＋１を具体的に求めるためのフ
ローを示す。まず、３１１ですでに求められている古い
係数８１−１をワークエリアに保存し、同様に３１−２
で−・つ前のウェハに対して設定した回転数Ω、を保存
する。次に１番［１ウエハに対して行った１換厚検査よ
り出力された膜厚ＴＩを取り込む。式（１０）に従いコ
３１４〜：３１７で倉オ を求め、最後に式（１１）に
従い７日８でＲ１（１を計算する。この値を３１９でス
ピナー回転数ｎ１算装置３２にわたす。FIG. 3 shows a flow for concretely determining the estimated coefficient 1+1. First, save the old coefficient 81-1 already found in 311 in the work area, and similarly
- Save the rotation speed Ω set for the previous wafer. Next, the film thickness TI outputted from the 1st equivalent thickness inspection performed on the 1st wafer is taken in. According to formula (10), calculate Kurao at 314 to 317, and finally calculate R1 (1) at 7 days and 8 according to formula (11). This value is passed to the spinner rotation speed n1 calculating device 32 at 319.
第４図は、第；）図の最後で計算した１日＋１ｔｖ−３
２１で受けとる。次にコ３２２でこれから処理しようと
する１番目ウェハの目標１摸厚Ｔ”を設定する。３２３
では式（１２）に従って、スピナー回転数Ω、÷ヱを計
算し、３コ化４でスピナー回転装置にわたす。Figure 4 is 1 day + 1tv-3 calculated at the end of Figure ;)
Pick up at 21. Next, in step 322, set the target thickness T'' of the first wafer to be processed. 323
Now, according to equation (12), calculate the spinner rotation speed Ω, ÷ヱ, and send it to the spinner rotation device by converting it into 3 pieces 4.
第５図では、本発明によるカルマン・フィルターによる
塗布膜厚制御の効果を示すために、実測した塗布膜厚（
実線）と式（１０）、（１１）により推定した膜厚（破
線）を比較した。その差は、平均０．２ ％であり２本
制御方式の有効性を示した。つまり、塗布膜厚の目標値
をいかに設定したとしても、わずか０，２ ％以内で必
ず所望の塗布膜厚が得られることを示している。In FIG. 5, the actually measured coating film thickness (
The film thickness (solid line) estimated by equations (10) and (11) (broken line) was compared. The difference was 0.2% on average, demonstrating the effectiveness of the two-line control system. In other words, no matter how the target value of the coating film thickness is set, the desired coating film thickness can always be obtained within just 0.2%.
本発明によれば、塗布膜厚をばらつきなく定めることが
できるという効果を有する。According to the present invention, there is an effect that the coating film thickness can be determined without variation.
第１図は、塗布膜厚制御装置の全体構成図、第２図は制
御方式の具体化、第３，４図は制御アル第 １ 口
第 Ｚ 図
εｔｉ、ｊ＃−目 −一く１乏「乙〕〉−竿 ３ 図Fig. 1 is an overall configuration diagram of the coating film thickness control device, Fig. 2 is a concrete example of the control method, and Figs. 3 and 4 are the control system. ``Otsu〉〉-rod 3 diagram
Claims (1)
られた値で再現性よくウェハ面上に塗布膜厚を形成する
ために、塗布膜厚のスピナー回転数および塗布装置環境
温度依存性などを表わす塗布膜厚モデルを構成し、塗布
膜厚モデルに含まれるモデル係数はカルマン・フィルタ
ーにより、逐次、処理済のウェハに対する塗布膜厚、ス
ピナー回転数環境温度の測定データから推定し、これか
ら処理を行うウェハに対して塗布膜厚モデルから目標の
値で塗布膜厚を形成するための最適なスピナー回転数を
算出できることを特徴とするカルマン・フィルターによ
る塗布膜厚制御装置。In the coating process of the semiconductor manufacturing process, in order to form a coating film thickness on the wafer surface with good reproducibility at a value determined by design, etc., coating is used to express the dependence of the coating film thickness on the spinner rotation speed and coating equipment environmental temperature. The model coefficients that constitute the film thickness model and are included in the coating film thickness model are estimated sequentially using a Kalman filter from the measured data of coating film thickness, spinner rotation speed, and environmental temperature for processed wafers. A coating film thickness control device using a Kalman filter, which is capable of calculating the optimum spinner rotation speed for forming a coating film thickness at a target value from a coating film thickness model.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP60256563A JPS62117321A (en) | 1985-11-18 | 1985-11-18 | Controller for thickness of coating film by karman-filter |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP60256563A JPS62117321A (en) | 1985-11-18 | 1985-11-18 | Controller for thickness of coating film by karman-filter |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPS62117321A true JPS62117321A (en) | 1987-05-28 |
Family
ID=17294376
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP60256563A Pending JPS62117321A (en) | 1985-11-18 | 1985-11-18 | Controller for thickness of coating film by karman-filter |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS62117321A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0307076A2 (en) * | 1987-07-17 | 1989-03-15 | Toray Industries, Inc. | Method for controlling the thickness of a sheet material |
| US6033728A (en) * | 1993-05-13 | 2000-03-07 | Fujitsu Limited | Apparatus for spin coating, a method for spin coating and a method for manufacturing semiconductor device |
| CN117089817A (en) * | 2023-06-29 | 2023-11-21 | 同济大学 | Optical film hybrid monitoring method based on Kalman filtering data fusion |
-
1985
- 1985-11-18 JP JP60256563A patent/JPS62117321A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0307076A2 (en) * | 1987-07-17 | 1989-03-15 | Toray Industries, Inc. | Method for controlling the thickness of a sheet material |
| US4931982A (en) * | 1987-07-17 | 1990-06-05 | Toray Industries, Inc. | Method for controlling the thickness of a sheet material and method for monitoring a correspondence relationship between the thickness distribution across a sheet material and means for adjusting the thickness |
| US6033728A (en) * | 1993-05-13 | 2000-03-07 | Fujitsu Limited | Apparatus for spin coating, a method for spin coating and a method for manufacturing semiconductor device |
| CN117089817A (en) * | 2023-06-29 | 2023-11-21 | 同济大学 | Optical film hybrid monitoring method based on Kalman filtering data fusion |
| CN117089817B (en) * | 2023-06-29 | 2024-02-13 | 同济大学 | Optical film hybrid monitoring method based on Kalman filtering data fusion |
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