TW407291B - The simulation of the post-exposure bake process of the chemically amplified resist - Google Patents
The simulation of the post-exposure bake process of the chemically amplified resist Download PDFInfo
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407291 a7 ΙΓ 五、發明説明() 發明領域: 本發明與一種半導體製程之光阻烘焙程序有關,特 别是在深次微米元件的微影製程中,野化學倍增式光阻 (Chemically amplified resists)其曝光後烘烤(Post-Exposure Bake Process) 製程之模擬。 發明背景: 訂 隨著半導體製程發展至超大型積體電路(VLSI),爲 了滿足積體電路高積隼度之要求,所形成元件之尺寸已降 低至深次微米元件。因此在製造極精細圖案(pattern)的 微影製程中,所使用的光阻材料便具有與傳統技術相異的 操作原理。一般而言,爲了降低具有深紫外線(Deep Ultra-Violet, DUV)波長之光源其功率,業界發展出應用 化學放大效應原理之光阻材料,亦即所謂的化學倍增式光 阻(Chemically amplified resists, CAR)。 4 經濟部中央標準局員工消f合作社印製 當上述化學倍增式光阻薄膜曝光於深紫外線中,光 罩上的圖案會轉移至該光阻材料上,並形成潛在影像 (Latent Image)。在進行曝光製程後,該光阻薄膜可在高 溫環境下進行烘烤程序,用以驅使光阻材料中之保護高分 子(Protection P〇lymers)與光酸物質(ph〇t〇acids)發生 反應,此製程即一般所稱的曝光後烘烤製程(P〇st_ 2 本紙張尺度適用中國國家標隼(〔‘〜、)六4規格(21〇/29"?公犛) 經满部中央標準局員工消费合作社印奴 Λ 7 ----ζ---- 五、發明説明()407291 a7 ΙΓ 5. Description of the invention Field of the invention: The present invention relates to a photoresist baking process for a semiconductor process, especially in the lithography process of deep sub-micron devices. Chemically amplified resists Simulation of Post-Exposure Bake Process. Background of the Invention: With the development of semiconductor processes to very large scale integrated circuits (VLSI), in order to meet the requirements of high integration of integrated circuits, the size of the formed components has been reduced to deep sub-micron components. Therefore, the photoresist material used in the lithography process for manufacturing extremely fine patterns has a different operating principle than the traditional technology. In general, in order to reduce the power of light sources with deep ultra-violet (DUV) wavelengths, the industry has developed photoresist materials that use the principle of chemical amplification effects, so-called chemically amplified resists (Chemically amplified resists, CAR). 4 Printed by a staff member of the Central Bureau of Standards, Ministry of Economic Affairs. When the above chemically multiplied photoresist film is exposed to deep ultraviolet light, the pattern on the photomask will be transferred to the photoresist material and form a latent image. After the exposure process is performed, the photoresist film can be subjected to a baking process under a high temperature environment to drive the protective polymers (Protection Polymers) in the photoresist material to react with the photoacids (ph0acids). This process is generally called the post-exposure baking process (P〇st_ 2 This paper size applies to the Chinese national standard (['~,) 6 4 specifications (21〇 / 29 "? 公 牦)) Bureau Consumer Consumption Cooperative Innu Λ 7 ---- ζ ---- 5. Description of Invention ()
Exposure Bake, ?EB)。 一般而言,對於正化學倍增式光阻(p〇sitive chemically amplified resists)進行曝光後烘烤製程 (PEB)時,位於光阻材料中之保護高分子會與光酸物質產 生催化反應(catalytic reaction)而減少。因此在該曝光 後烘烤程序完成後,位於曝光區域之光阻材料將失去保護 高分子之保護作用’且相對於其它未曝光的區域而言,將 具有較大的蝕刻速率。亦即在曝光後烘烤程序結束後,該 光阻薄膜中曝光的部份將具有可溶性,且可輕易的被顯像 溶液所移除。 在高溫環境中進行的烘烤程序往往具有兩種不同的 機制’其一爲保護高分子與光酸物質彼此所發生之反應 (reaction);其二則爲光酸物質之擴散(diffusion)作用。 請參照專利文件 U.S, Patent 5J17,612,或參見 L. Capodieci, A. Krasnoperova,F. Cerrina,C. Lyons, C. Spence, and K. Early,Exposure Bake,? EB). Generally speaking, during the post-exposure baking process (PEB) for positive chemically amplified resists, the protective polymer located in the photoresist material will have a catalytic reaction with the photoacid substance. ) While decreasing. Therefore, after the post-exposure baking process is completed, the photoresist material located in the exposed area will lose the protective effect of the polymer and will have a larger etch rate compared to other unexposed areas. That is, after the post-exposure baking process is completed, the exposed portion of the photoresist film will be soluble and can be easily removed by the developing solution. A baking process performed in a high-temperature environment often has two different mechanisms. One is to protect the reaction between the polymer and the photoacid material; the other is the diffusion effect of the photoacid material. Please refer to U.S. Patent 5J17,612, or see L. Capodieci, A. Krasnoperova, F. Cerrina, C. Lyons, C. Spence, and K. Early,
Novel post-exposure bake simulator: first results," J. Vac. Sci. Technol., vol. B13, no. 6, pp. 2963-2967, 1995。其中 該文獻所提出之曝光後烘烤模型(PEB model)便包括了上 述兩種機制。然而在該文獻中,上述之反應機制以及擴散 機制均使用固定的反應常數與擴散係數來建立其曝光後烘 烤模型。 然而由於該反應常數(reaction constants)可滿足 3 本紙伕尺度適用中國國家標準(CNS ) A4规格(210X297公趁) (讀洗閱讀背,6之;1<5事項存填寫本茛) ir 涑 經濟部中央標隼局只工消费合作社印¾ 4〇柳1 a 1Γ 五、發明説明() 阿爾尼斯關係式(Arrhenius relations),是以該反應之 速率會與製程中溫度產生極大的關聯性。並且對於該曝光 後烘烤製程而言,其溫度-時間歷程(temperature-time history)往往會隨著烘烤機台(bake apparatus)的設定 (configurations)而產生不同的結果。因此上述的反應常 數可視爲以時間爲囡子之變數。 更者,對於光酸物質之擴散作用而言,其擴散係數 (diffusion coefficient)亦與溫度以及保護單元胞 (Protection-site)濃度,具有極大的關聯性。因此在建主 曝光後烘烤製程之模型時,應該將溫度因子與保護單元胞 濃度因子加入反應常數與擴散係數中,且需考慮該烘烤機 台之溫度-時間歷程。 發明目的及概述: 本發明之目的在提供一種模擬化學倍增式光阻其曝 光後烘烤製程(PEB)之方法。 本發明之再一目的在提供一種模擬化學倍增式光阻 其曝光後烘烤製程(PEB)之模型。 本發明所提供用以模擬化學倍增式光阻其曝光後烘 烤製程之模型可使用下列步驟來加以建立: (a)將保護高分子與光酸物質之反應機制、以及光物 4 本紙張尺度適用中國國家標準(CNS ) Λ4規格(2丨0X297公筇) ---------裝------訂j-------線 (;ι.·'ίι先聞讀;背而之;'1念?項再填巧太1) . . Λ: W: 經濟部中央標麥局負工消费合作社印製 407291 五、發明説明() 質之擴散機制致置於曝光後烘烤制程> 1+ j征 <,其型中,並以一組 包含反應及擴散的微分方程式 、(Reaction-diffusior equation)力口以顯示; (b) 將保護高分子與光酸物質之后斑+缸 * <反應常數以阿爾尼斯 方程式(Arrhenius expression)類示. (c) 使用以阿爾尼斯方程式顯示之反應常數來建立該 光酸物質損失機制; (d) 顯示該擴散係數爲溫度因子部份與保護單元胞濃 度囡子部份之乘積,其中該溫度因子部份亦可以阿爾尼斯 方程式表示;該保護單元胞濃度因子部份則可以指數函數 來表示; (e) 使用指數函數表示製程之溫度-時間歷程,以眞 實顯示該烘烤機台之加熱狀態與冷卻狀態· (f) 上述曝光後烘烤製程模型之反應常數與擴散係數 亦包含時間因子。 至於本發明所提供用以模擬化學倍增式光阻其曝光 後烘烤製程之數値方法則如下列步驟所示: (g) 劃分該光阻材料進行模擬之區域爲複數個具有相 同大小之格子; (h) 區分該製程時間爲複數個相等之時段,其中每個 時段之大小可藉著模擬所需精確度來決定; (i) 計算下一時段之保護單元胞濃度,其中該計算程 序是使用保護單元胞濃度、以及目前時段與下—時段之光 酸物質濃度來進行演算; 本紙乐尺度適用中國國家標準(CNS ) Λ4規怙(2丨0X297公筇) 先閲續 •背而之注f項再填碎本頁)Novel post-exposure bake simulator: first results, " J. Vac. Sci. Technol., Vol. B13, no. 6, pp. 2963-2967, 1995. Among them, the post-exposure baking model (PEB model) proposed in this document includes the above two mechanisms. However, in this document, the above-mentioned reaction mechanism and diffusion mechanism both use fixed reaction constants and diffusion coefficients to establish their post-exposure baking models. However, since the reaction constants can meet 3 paper scales, the Chinese National Standard (CNS) A4 specification (210X297) is available (reading and reading back, 6 of 1; 5 items are filled in this buttercup) ir 涑 economy The Ministry of Standards and Technology Bureau of the People's Republic of China only prints consumer cooperatives. 40 柳 1 a 1Γ 5. Description of the invention () Arrhenius relations (Arrhenius relations), the rate of this reaction will have a great correlation with the temperature in the process. And for the post-exposure baking process, its temperature-time history will often produce different results with the configuration of the bake apparatus. Therefore, the above-mentioned reaction constant can be regarded as a variable that takes time as a lame. Furthermore, the diffusion coefficient of the photoacid material has a great correlation with the temperature and the protection-site concentration. Therefore, when building a model of the main post-exposure baking process, the temperature factor and the protection unit cell concentration factor should be added to the reaction constant and diffusion coefficient, and the temperature-time history of the baking machine should be considered. OBJECTS AND SUMMARY OF THE INVENTION The object of the present invention is to provide a method for simulating a chemical multiplication type photoresistor and its post-exposure baking process (PEB). Another object of the present invention is to provide a model that simulates a chemical multiplication type photoresist and its post-exposure baking process (PEB). The model provided by the present invention to simulate the chemical multiplication type photoresistor and its post-exposure baking process can be established using the following steps: (a) the reaction mechanism of the protective polymer and the photoacid material, and the photo paper size Applicable to China National Standard (CNS) Λ4 specification (2 丨 0X297) 筇 --------- install -------- order j ------- line (; ι. · 'Ίι 先I read it; the other way around; '1 read? The item is filled in too much 1).. Λ: W: Printed by the Central Standards and Wheat Bureau of the Ministry of Economic Affairs and printed by the Consumers Cooperative 407291 5. Description of the invention () The nature of the diffusion mechanism Post-exposure baking process > 1+ jsign <, in its model, is displayed with a set of differential equations including reaction and diffusion, and (Reaction-diffusior equation) forces; (b) Protecting polymers and light Spot after acid substance + cylinder * < Reaction constant is shown by Arrhenius expression. (C) Use the reaction constant shown by Arnis equation to establish the photoacid substance loss mechanism; (d) Display the diffusion coefficient It is the product of the temperature factor part and the cell concentration part of the protection unit. The temperature factor part can also be The Ernes equation is expressed; the cell concentration factor part of the protection unit can be expressed by an exponential function; (e) The exponential function is used to represent the temperature-time history of the process, and the heating and cooling states of the baking machine are displayed in a solid display. f) The reaction constant and diffusion coefficient of the above post-exposure baking process model also include a time factor. As for the numerical method provided by the present invention to simulate the chemical multiplication type photoresistor and its post-exposure baking process, the following steps are shown: (g) Dividing the area where the photoresistive material is simulated into a plurality of grids with the same size (H) Distinguish the process time into multiple equal time periods, where the size of each time period can be determined by the accuracy required for the simulation; (i) Calculate the cell concentration of the protection unit for the next period, where the calculation procedure is Use the cell concentration of the protection unit and the concentration of the photoacid substance in the current period and the next period to perform calculations. The paper scale is applicable to the Chinese National Standard (CNS) Λ4 Regulations (2 丨 0X297). f)
五、發明説明 407391 ⑴計算沿著第-方向、中介晗段之光酸物質濃度, 其中該中介時段位於目前時段與下一時段之間 ㈤計算沿著第二方向之光酸物質淚度,其中第二方 向垂直於第一方向; ⑴重覆步驟⑴至(k) ’直到所獲得之光酸物質濃度 滿足收叙條件; (m)進展至下一時段且重覆步驟⑻到⑴,直到該烘 烤製程結束爲止; 圖式簡單説明: 藉由以下詳細之描述結合所附圖示 解上述内容及此項發明之諸多優點,其中 將可輕易的了 第一圖爲烘烤機台之溫度_時間歷程,用以顯示本 發明之曝光後烘烤製程; 第一圖爲演算方法流程圖,顯示根據本發明建立曝 光後烘烤製程模型之演算方法流程圖;以及 第三圖爲光阻材料之截面圖,顯示根據本發明將光 阻截面上進行模擬之區域,劃分爲複數個網狀格子。 發明詳細説明: (-先閱绩背而之'-H事項再填袴^反 裝V. Description of the invention 407391 ⑴ Calculate the concentration of photoacid material along the-direction and the intermediary segment, where the intermediary period is located between the current period and the next period. Calculate the photoacid material tear along the second direction, of which the second The direction is perpendicular to the first direction; ⑴Repeat steps ⑴ to (k) 'until the obtained photoacid material concentration meets the conditions of the description; (m) progress to the next period and repeat steps ⑻ to ⑴ until the baking By the end of the manufacturing process, the drawings are simply explained: The above-mentioned content and the many advantages of this invention will be explained by the following detailed description combined with the attached drawings. Among them, the first picture is the temperature and time history of the baking machine. To show the post-exposure baking process of the present invention; the first figure is a flow chart of a calculation method, which shows a flowchart of a calculation method for establishing a post-exposure baking process model according to the present invention; and the third picture is a cross-sectional view of a photoresist material Shows that the area where the simulation is performed on the photoresist section is divided into a plurality of mesh grids according to the present invention. Detailed description of the invention: (-first read the results and then the '-H matters and then fill in ^ reverse
、1T 泉 經濟部中央標象局員工消费合作社印聚 一般而言化學倍增式光阻(chemical amplified resists)具有四個主要的組成部份,分别爲製造光酸物質 (Photo-Acid generat〇rs,pag}、保護高分子(pr〇tecti〇n 本紙張尺度適用中國國家標準(CNS ) A4i^i~(17〇x 297.i>^ ) 五、發明説明() polymers)、樹脂(resins)、以及溶劑(solvei^-S)。從製 程模擬的觀點而言,製造光酸物質(PAG)與保護高分子在 曝光後烘烤製程(PEB)的模型中扮演主要的角色。 在深紫外光的照射之下,上述製造光酸物質(PAG) 會分解爲光酸物質(Photoacids)以及附屬產物(by_ products)。該光酸物質接者會與保護高分子之反應單元 胞(reaction sites)發生反應,並在高溫環境中產生其它 酸性物質。對於正光阻而言,所發生之反應會使得保護高 分子減少,是以光阻材料中之樹脂將不再受到保護高分子 的保護。因此該反應亦可稱爲解除保護反應(deprotection reaction),且其中保護高分子亦可視爲一種抗化劑 (inhibitors),至於該抗化劑的反應單元胞亦即所稱之保 護單元胞(protection-site)。 經濟部中央標準局員工消费合作社印製 更者’隨著者溫度的上升,該光酸物質的擴散作用 會更加顯著。囡此光酸物質的擴散作用也應該包含在曝光 後烘烤製程(PEB)的模型中。其中對該光阻材料而言,光 酸物質必須擴散到適當的位置,以便與保護高分子其反應 單元孢發生作用。在擴散的過程中,該光酸物質可視爲陷 落(trapped)於保護高分子中,且從製程模型的觀點而言, 可視島光酸物質之損失。 因此對於一個曝光後烘烤製程的模型而言,該解除 保護反應(deprotection reaction)、光酸物質擴散作用、 7 CNS ) Λ4^ ( 210X29^7 407291 A < B7 五、發明説明( 以及光酸物質損失之機剞眭曲* k杜士 丄 $應包括其中。由此可獲得下列 之反應-擴散方程組,以海_ , ώ X頌不製程中反應與擴散之機制: ΘΜ ~di 5H ~dt', 1T Quanquan Ministry of Economic Affairs, Central Bureau of Standards, Employees' Consumer Cooperatives, Printing Concentration Generally speaking, chemically amplified photoresist (chemical amplified resists) has four main components, which are Photo-Acid generators, pag}, protective polymer (pr〇tecti〇n This paper size applies to the Chinese National Standard (CNS) A4i ^ i ~ (17〇x 297.i > ^) 5. Description of the invention () polymers), resin (resins), And solvent (solvei ^ -S). From the viewpoint of process simulation, the manufacture of photoacids (PAG) and protective polymers play a major role in the model of the post-exposure baking process (PEB). Under irradiation, the above-mentioned photoacid substance (PAG) will be decomposed into photoacids and by-products. The photoacid substance will then react with the reaction site that protects the polymer , And produce other acidic materials in high temperature environment. For positive photoresist, the reaction that occurs will reduce the protective polymer, so the resin in the photoresist material will no longer be protected by the protective polymer. Therefore The reaction can also be called a deprotection reaction, and the protective polymer can also be regarded as an inhibitor, and the reaction unit of the inhibitor is also called a protection-site. ). Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs' As the author's temperature rises, the diffusion effect of the photoacid material will become more significant. Therefore, the diffusion effect of the photoacid material should also be included in the baking process after exposure ( PEB) model. Among the photoresist materials, the photoacid material must diffuse to an appropriate position in order to interact with the protective polymer and its reaction unit spores. During the diffusion process, the photoacid material can be regarded as a sink. (Trapped) in the protective polymer, and from the viewpoint of the process model, the loss of the photoacid material is visible. Therefore, for a model of the post-exposure baking process, the deprotection reaction, photoacid Matter diffusion effect, 7 CNS) Λ4 ^ (210X29 ^ 7 407291 A < B7 V. Description of the invention (and the mechanism of loss of photoacid substance * k Du Shi丄 $ should be included. From this, the following reaction-diffusion equations can be obtained. The mechanism of reaction and diffusion in the process is described as follows: ΘΜ ~ di 5H ~ dt '
-k〇MH :V(DHVH)+La (1)(2) 且光酸物質彳員^份可以下式表示-k〇MH: V (DHVH) + La (1) (2), and the photoacid member can be expressed by the following formula
La = —kaH2 (3) 其中Μ與Η分别代表保護單元胞濃度以及光酸物 濃度,且兩者皆可以時間⑴與空間(χ)的函數來加以表示 如方%式(1)所顯不,該解除保護反應可使用保護單元 滚度與光酸物質濃度之—階反應(first_〇rder reacti〇 ,加以描述。至於方程式(2)則顯示該光酸物質濃度包 了一擴散係數D H以及光酸物質損失機制之函數。其中 光酸物質損失機制可使用光酸物質濃度的二階反 (second-order reaction)來加以描述,如方程式(3)所 示 〇 ---------|装------訂------:果 (請先閱讀'"面之注"事項再填寫本頁) , . 經濟部中央標準局貝工消費合作社印" 根據本發明之最佳實施例,可將烘烤機台其加熱程 序與冷卻程序所產生之效應,皆併入該曝光後烘烤製程模 型中。藉著使用該烘烤機台的溫度-時間歷程,可獲得解 除保護反應常數(kD)、光酸物質損失常數(ka)、與擴散係 數(dh),其中上述三者皆可表示爲時間之函數。由此可實 本紙張尺度適用中國國家標準(CNS ) A4規格(2丨0X 297公筇) 40^291 五、發明説明 現本济明所提供之最佳實施例。値得注意的是上述常狖與 係數其溫度囡子,皆可藉著阿爾尼斯關係式(Arrhenius expressions)來描述 ° 在方程式(1)與(3)中之反應常數可顯示爲: kD= kD(T)= Ad exp(-ED/kT) (4) 以及 ka= ka(T)= Aa exp(-Ea/kT) (5) 其中AD以及Aa分爲代表指數前常數(preexponential constants), 且該ED與已3爲活化能 (activation energies),至於k則爲波斯曼常數 (Boltzmann constant) »而T則代表製程溫度。 至於在方程式(2)中之擴散係數則可表示爲溫度以及 保護單元胞濃度之函數:La = —kaH2 (3) where M and 代表 respectively represent the cell concentration of the protection unit and the photoacid concentration, and both can be expressed as a function of time ⑴ and space (χ) as shown in Equation (1). The deprotection reaction can be described using the first-order reaction of the roll of the protection unit and the concentration of the photoacid material (first_〇rder reacti0). As for the equation (2), the concentration of the photoacid material includes a diffusion coefficient DH and A function of the photoacid material loss mechanism. The photoacid material loss mechanism can be described using a second-order reaction of the photoacid material concentration, as shown in equation (3). | Install ------ Order ------: Fruits (please read '" Matter's Note " Matters before filling this page),. In the preferred embodiment of the present invention, the effects of the heating process and the cooling process of the baking machine can be incorporated into the post-exposure baking process model. By using the temperature-time history of the baking machine , Can obtain deprotection reaction constant (kD), photoacid substance loss constant (ka) And diffusion coefficient (dh), of which the above three can be expressed as a function of time. From this, it can be realized that the paper size is applicable to the Chinese National Standard (CNS) A4 specification (2 丨 0X 297 cm) 40 ^ 291 5. Description of the invention The best embodiment provided by Benjiming. It should be noted that the above-mentioned constants, coefficients, and temperature variables can be described by Arrhenius expressions. In equations (1) and (3 The reaction constant in) can be shown as: kD = kD (T) = Ad exp (-ED / kT) (4) and ka = ka (T) = Aa exp (-Ea / kT) (5) where AD and Aa Divided into representative exponential constants, and the ED and 3 are activation energies, as k is Boltzmann constant »and T represents the process temperature. As for equation (2) The diffusion coefficient in can be expressed as a function of temperature and cell concentration of the protection unit:
Dh = Dh(M, Mo, T) = Doexp ⑹ (請先閱讀嘴而之注"事項洱填寫木頁 .裝—— 訂 經滴部中央標隼局員工消费合作社印製Dh = Dh (M, Mo, T) = Doexp ⑹ (please read the note first " matter 洱 fill in the wooden page. Packing-order printed by the employee consumer cooperative of the Central Bureau of Standards, Didi Bureau
其中 x= 1-M/MC (7) 且 本紙張尺度適用中國國家標準(CNS ) Λ4規格(210X297公筇) 五、發明説明 407291 Λ 7 Β7 D〇~ D〇(T)= A〇 exp (-E〇/kT) (8) 其中該擴散係數DH包含溫度因子之部份、以及濃度 因子部份。其中溫度因子部份亦即方程式(6)中所顯示之 D。,而濃度因子部份則爲方程式(6)中之指數部份。至於 Μ。則代表該保護單元胞之初始濃度,而A。與E。則分别代 表該擴散係數DHt,溫度因子部份之指數前常數、以及 光酸物質之活化能。α與β則代表該擴散係數〇{1其與濃度 因子部份之模型參數(model parameters)。 請參照第一圖,該圖所顯示爲烘烤機台之製程溫度 範圍。其中製程溫度的分佈近似於時間之指數函數。至於 該製程之溫度-時間歷程(temperature-time history)包 括一自烘烤開始至烘烤時間tb之加熱狀態、以及自烘烤時 間tb到終止時間tf之冷卻狀態。其中該終止時間%之選擇, 在於確認該製程之溫度T(tf)已夠趨近於室温。因此該溫度 模型可以下列方程式表示: T = T(t) |AT(l-e't/Th) + To △re+H)〜+T〇 if 0<t<tb if tk <t (9) ---------Λ------訂—--.---涑 (訪洗閱讀背面之:;5-"事項再填寫本頁) . 』 經"部中央標"-局员工消費合作社印^ 其中 AT = Tf-T〇 且 ΔΤ'=Τί'-Το 10 本紙張尺度適用中國國家標準(CNS ) Λ4規格(210Χ297公牮) (10) (11) 407291 Λ — __________ΙΓ _ 五、發明説明() 其中 '與Tf分别代表室溫與烘烤溫度,'與\则分别 代表加熱狀態與冷卻狀態之時間常數,且烘烤時間以“來 表示。爲了確認在時間tb處的溫度爲連續溫度,T/可以下 式來表示 T'f = AT(l-e-,k/^) + T〇 (12) 综合上述’根據本發明所形成之製程模型,將保護 單元胞濃度因子加入擴散係數(如方程式(6)所示),可使 違化學倍增式光阻其曝光後烘烤製程之模擬更加眞實。 接著請參照第二圖,該圖所顯示爲使用上述曝光後 烘烤製程模型進行模擬演算之流程圖。至於第三圖則爲光 阻截面圖’所顯示爲根據本發明在光阻截面上進行模擬之 區域。其中如第三圖所示該光阻位於由實線段2〇〇、210、 22Q、以及230所構成之區域中。該實線段2〇〇以及“ο 分别代表該光阻與空氣接觸之上表面、以及該光阻與底材 相接觸之下表面。因此χ_軸24〇是沿著底材表面水平延伸; 而Υ-軸2 50則沿著該光阻薄膜之厚度向上延伸。至於圖中 所示之整個模擬區域20則被劃分爲複數個相二 W Η尺寸之烟 狀格子。 垌 其中該模擬區域2 0之邊界條件,可以获# a 、 知者使用中心 差分法(central difference method)而求 士 甘义, ★丹迎似解。 例如,位於邊界230之光酸物質濃度其一階微八 刀J表不爲 11 本纸張尺度適用中國國家標窣(CNS ) Λ4現格(210X 297公势) •t先閲#背面之注意事項#填艿本茛 裝. 訂 經滅部中央標準局貝工消合作社印裂 407291 經嫡部中央標苹局員工消费合作社印^ AT B7五、發明説明() 下式 dx (0 7) 2Δχ (13) 其中j = 〇至Ν ’且厶又爲χ_軸方向網狀格子之尺寸。 因此爲了獲得該模擬區域2 0之邊界條件,位於模擬區域2 〇 之網狀格子必須延伸至由虚線26〇、27〇、280以及290 所包圍之方塊區域,如第三圖中所顯示。 其中對於方程式(1)〜(3)中之反應方程式與擴散方程 式’可使用叠代式的交又方向内含法(Iterative Alternating Direction Implicit,IADI)來進行計算。其 演算流程圖如第二囷中所顯示。至於該演算流程之詳細説 明則如下所述。 首先進行步驟1〇〇,輸入參數以模擬該烘烤機台之 溫度-時間歷程。其中所輸入之參數包含室内溫度丁0與烘 烤溫度Tf、烘烤時間tb、以及時間常數、與、,如同方程式 (9)~(12)所示。 工 接著進行步驟110,輸入該化學倍增式光阻之物理 性參數。其中該物理性參數包含指數前常數、A與A ’活化能E〇、己0與Ea、以及如同方程式(4卜(8 D_ a 與β-參數。 W所ucc- 12 本紙張尺賴财關家料-_ (請先閱讀.背面之注意事項再填巧水頁) (裝— J----媒 407291 五、發明説明 進行步驟1 2 0,對製程時間進行劃分,而得到複數 個時段《其中每一個時段At Ξ tn+i -、其大小,可藉著控 (讀先閱讀背而之注念f項洱填穹本莨) 制第二圖中每一網格&(n〇dai p〇ints)之相對誤差平均値 來加以決定。 進行步骤130 ’使用上述内含法scheme) 計算下一時段n+l (亦即時間t +At)之保護單元胞濃度。其 中對方格(i,j)而言’下一時段n+l之保護單元胞濃度可藉 著使用位於方格(i,j)處目前時段η、以及下一時段n+ 1之 保護單元胞濃度來加以計算。因此需要使用令心差分法 (iteration)以便推斷出下一時段之濃度。 經濟部中央標率局員工消費合作社印製 “、、後’進行步驟140,位於X -軸方向上且時段爲中 間時段n+l/2(亦即時間t + At/2)之光酸物質濃度,可使用 一内含法(Implicit scheme)來加以計算。其十在計算位 在方格(1,j)處’且時間爲中間時段n + 1 / 2之光酸物質濃度 Η時,需要下述兩項資料(a)、(b)。其中資料(a)爲位在三 相鄰方格(i,j - 1)、(i,j)與(i,j + q且時間同爲目前時段之光 酸物質濃度Η;至於資料(b)則分别爲目前時段與十間時段 之擴散係數DH。因爲對於下一個時段而言,保護單元胞 濃度M(n+1)在步驟130中已被計算出來,因此時間爲中 介時段之擴散係數DH(n+l/2)可藉著使用保護單元胞滚度 M(n+l/2)加以計算求得。其中該保護單元胞激度 M(n+l/2)爲目前時段之濃度M(n)以及下一時段濃度 M(n+1)之平均値。 13 本紙張尺度適用中國國家棉準(CNS ) Λ4規格(210X 29?公筇) Α7 Β7 五、發明説明() (请先閱讀背而之:;i"事項再填,"本页 然後進行步驟150,使用一内含法(Implicit schemt) 計算沿著γ-軸方向、且時間爲下一時段n+i(即t+At)之光 酸物質濃度。對於位在方格(i,j)且時間爲下一時段n+1之 光酸物質濃度而言,可藉著下列資科⑷與(d)來加以計 算。其中資料(c)爲位於三相鄰方格(i_ i ,』)、(U)與(i + i,』)、 且時間爲中介時段n + i / 2之光酸物質濃度;而資料⑷爲時 間是十介時段之擴散係數D H (η + 1 / 2 )、以及時間爲下一時 段之擴散係數DH(n+1)。其中時間爲中介時段之擴散係數 可藉著使用上述保護單元胞平均値Μ (n+1/2)來加以計 算。 如同在第二圖中虛線方塊160所顯示,藉著結合步 裸140與150可計算出下一時段n+1之光酸物質濃度,亦 即 Η (η + 1)。 -濟部中央標牟局貝工消費合作社印製 對於下一時段而言,步驟130~150構成一中心差分 法之運算。接著進行步驟170以檢查上述結果是否符合收 敛條件(convergence condition)。如果所計算之結果並 未滿足收斂條件,則使用所計算出來之保護單元胞濃度與 光酸物質濃度重覆進行中心差分法演算,直到所獲得答案 滿足收斂條件爲止。然後該計算裎序會自目前時段前進至 下一時段並繼續進行。 當所計算下一時段之結果滿足收斂條件時,則進行 14 本紙張尺度適用中國國家標準(CNS ) Λ4規格(21〇ί^97_公^ ) 五、發明説明() 步驟1 80,檢査該計算程序是否滿足該烘烤程沣之結 件。如果計算程序已到達該烘烤製程之結束條件,則=條 該曝光後烘烤製程之模擬。否則進行步祿丨9 〇繼續針束 一時段進行計算程序,亦即控制演算流程回覆至2下 120,以計算下一個新的時段。 ’裸 本發明所提供之模擬方法(如第二圖中所顯示 算流程圖)具有諸多優點: @ (1) 在整個曝光後烘烤製程模擬當中,對於每一個各 别時段、及中介時段而言,所有反應常數(]^與让」以及光 酸物質擴散係數(DH)皆可經計算而獲得。因此將可獲得包 含了溫度-時間歷程之曝光後烘烤(p E B)模擬。 、—·5 (2) 在整個曝光後烘烤製程模擬當中,對於每一個方 格而言,該光酸物質擴散係數(Dh)皆可經計算程序而獲 得。如此一來使得該曝光後烘烤製程之模擬具有以保護單 元胞濃度爲因子之光酸物質擴散係數(Dj。 (3) 根據本發明所提供之演算流程,下一時段之保護 單元胞濃度將先於光酸物質濃度計算獲得。因此所獲得之 保護單元胞濃度可使用於後績計算光酸物質濃度之程序 中。其中該擴散係數爲光酸物質擴散方程式之係數。藉著 使用上述方法可加速該演算程序到達收斂條件。 經濟部中央標準局員工消費合作社印 本發明雖以一較佳實例闡明如上,然其並非用以限 定本發明精神與發明實體,僅止於此一實施例爾。對熟悉 此領域技藝者,在不脱離本發明之精神與範圍内所作之修 改’均應包含在下述之申請專利範園内。 15 本紙張尺度適用中國國泰標草(CNS〉Λ4規格(2!〇x2W公筇〉Where x = 1-M / MC (7) and this paper size applies the Chinese National Standard (CNS) Λ4 specification (210X297) 筇 5. Description of the invention 407291 Λ 7 Β7 D〇 ~ D〇 (T) = A〇exp ( -E〇 / kT) (8) wherein the diffusion coefficient DH includes a temperature factor portion and a concentration factor portion. The temperature factor part is the D shown in equation (6). And the concentration factor part is the exponential part in equation (6). As for M. Represents the initial concentration of the protection unit cell, and A. With E. They respectively represent the diffusion coefficient DHt, the pre-exponential constant of the temperature factor part, and the activation energy of the photoacid material. α and β represent model parameters of the diffusion coefficient θ {1 and its concentration factor. Please refer to the first figure, which shows the process temperature range of the baking machine. The process temperature distribution is approximately an exponential function of time. The temperature-time history of the process includes a heating state from the start of baking to the baking time tb, and a cooling state from the baking time tb to the end time tf. The choice of the termination time% is to confirm that the temperature T (tf) of the process is close to room temperature. Therefore, the temperature model can be expressed by the following equation: T = T (t) | AT (l-e't / Th) + To △ re + H) ~ + T〇if 0 < t < tb if tk < t (9 ) --------- Λ ------ Order -----.--- 涑 (Visit and read the back of the book:; 5- " Matters and then fill out this page).》 经 " Central Standard " -Printed by the Bureau ’s Consumer Cooperatives ^ where AT = Tf-T〇 and ΔΤ '= Τί'-Το 10 This paper size applies to the Chinese National Standard (CNS) Λ4 specification (210 × 297 meters) (10) (11) 407291 Λ — __________ ΙΓ _ 5. Description of the invention () where 'and Tf respectively represent room temperature and baking temperature, and' and \ represent the time constants of the heating and cooling states, respectively, and the baking time is expressed by ". To confirm The temperature at time tb is a continuous temperature, and T / can be expressed by the following formula: T'f = AT (le-, k / ^) + T0 (12) Based on the above-mentioned process model formed according to the present invention, it will protect Adding the diffusion coefficient of the unit cell concentration factor (as shown in equation (6)) can make the simulation of the baking process after exposure to the chemical multiplication type photoresist more realistic. Then please refer to the second figure, which is shown as using The flow chart of the simulation calculation of the above post-exposure baking process model. As for the third figure, the photoresistive cross-section is shown as the area simulated on the photoresistive cross-section according to the present invention. The light is shown in the third figure. The resistor is located in the area formed by the solid line segments 200, 210, 22Q, and 230. The solid line segments 200 and "ο represent the upper surface of the photoresist in contact with air, and the phase between the photoresist and the substrate, respectively. Touch the surface below. Therefore, the χ-axis 24o extends horizontally along the surface of the substrate; and the Υ-axis 2 50 extends upwardly along the thickness of the photoresist film. As for the entire simulation area 20 shown in the figure, it is divided into a plurality of smoke-like lattices of two W 相 dimensions.垌 Among them, the boundary condition of the simulation area 20 can be obtained by using a central difference method to obtain the righteousness. ★ Dan Ying like solution. For example, the concentration of the photoacid substance at the boundary 230 is the first-order micro-eight-blade J, which is not 11 This paper size is applicable to the Chinese national standard (CNS) Λ4 is present (210X 297 public power) • t 先 读 # Note on the back Matter #fill in this buttercup. Ordered by the Central Standards Bureau of the Ministry of Economic Affairs and Industry, printed by the Cooperative Consumer Cooperative 407291. Printed by the Consumer Standards of the Central Bureau of Standards, Employees of the Ministry of Economic Affairs ^ AT B7 V. Description of the invention () The following formula dx (0 7) 2Δχ (13) where j = 0 to N ′ and 厶 is the size of the grid in the x-axis direction. Therefore, in order to obtain the boundary condition of the simulation area 20, the mesh grid located in the simulation area 20 must extend to the square area surrounded by the dotted lines 260, 270, 280, and 290, as shown in the third figure. For the reaction equations and diffusion equations in equations (1) to (3), the iterative alternating direction implicit method (IADI) can be used for calculation. The calculation flow chart is shown in Figure 2. The detailed description of the calculation process is as follows. First proceed to step 100, input parameters to simulate the temperature-time history of the baking machine. The parameters entered include room temperature D0 and baking temperature Tf, baking time tb, and time constants, and, as shown in equations (9) ~ (12). The process then proceeds to step 110, where the physical parameters of the chemically multiplied photoresist are entered. The physical parameters include pre-exponential constants, A and A 'activation energies E0, 0 and Ea, and parameters such as the equation (4 D (8 D_ a and β-parameters). Home materials-_ (Please read first. Note on the back and then fill in the water page) (Packing — J ---- Media 407291 V. Description of the invention Perform step 1 2 0 to divide the process time and get multiple time periods "Each of these periods At Ξ tn + i-, its size, can be controlled by (read first read the back and note the f item 穹 fill in the text) to make each grid in the second graph & (n〇 dai p〇ints) to determine the relative error average 値. Go to step 130 'use the above-mentioned inclusive scheme) to calculate the protection cell concentration of the next period n + l (that is, time t + At). In terms of i, j), the protection cell concentration of n + 1 in the next period can be calculated by using the protection cell concentration in the current period n at the square (i, j) and the protection cell n + 1 in the next period. It is therefore necessary to use the iteration method in order to infer the concentration in the next period. Make ",, after" to proceed to step 140, the concentration of the photoacid substance located in the X-axis direction and the time interval is an intermediate time period n + l / 2 (that is, time t + At / 2). An implicit method can be used. scheme) to calculate it. The tenth is to calculate the photoacid substance concentration Η at the square (1, j) 'and the time period is n + 1/2. The following two items of data (a), ( b). The data (a) is the photoacid substance concentration in the three adjacent squares (i, j-1), (i, j) and (i, j + q), and the time is the current time period; as for Data (b) are the diffusion coefficients DH of the current period and ten periods respectively. Because for the next period, the cell concentration M (n + 1) of the protection unit has been calculated in step 130, so the time is the intermediate period. The diffusion coefficient DH (n + l / 2) can be calculated by using the protection unit cell roll M (n + l / 2), where the protection unit cell excitability M (n + l / 2) is the current The average concentration of the concentration M (n) during the period and the concentration M (n + 1) of the next period. 13 This paper size is applicable to the Chinese National Cotton Standard (CNS) Λ4 specification (210X 29? Male) Α7 Β7 V. Description of the invention ( ) (please First read the reverse: "i" and fill in the items again, and then go to step 150, use an implicit method (Implicit scheme) to calculate along the γ-axis direction, and the time is the next period n + i (ie t + At) concentration of photoacid substance. For the concentration of photoacid substance in the square (i, j) and the time is n + 1 in the next period, it can be added by the following resources: (d) Calculation. The data (c) is the concentration of the photoacid substance in the three adjacent squares (i_i, "), (U) and (i + i,"), and the time is the intermediate period n + i / 2; and the data is The diffusion coefficient DH (η + 1/2) where time is the ten-second period, and the diffusion coefficient DH (n + 1) where time is the next period. The diffusion coefficient in which the time is an intermediate period can be calculated by using the above-mentioned average unit cell protection (M + n). As shown by the dashed box 160 in the second figure, by combining steps 140 and 150, the concentration of the photoacid substance in the next period n + 1 can be calculated, that is, + (η + 1). -Printed by the Central Ministry of Economic Affairs of the Ministry of Economic Affairs, Shellfish Consumer Cooperative. For the next period, steps 130 to 150 constitute a central difference method. Step 170 is then performed to check whether the above results meet the convergence condition. If the calculated results do not satisfy the convergence conditions, the calculated difference between the cell concentration of the protection unit and the concentration of the photoacid substance is used to perform the central difference method until the obtained answer satisfies the convergence conditions. The calculation sequence then advances from the current period to the next period and continues. When the calculated result for the next period meets the convergence conditions, 14 paper sizes are applied to the Chinese National Standard (CNS) Λ4 specification (21〇ί ^ 97_ 公 ^) 5. Description of the invention () Step 1 80, check the Calculate whether the program satisfies the conclusion of the baking process. If the calculation program has reached the end condition of the baking process, then = simulation of the baking process after the exposure. Otherwise, proceed to Lulu 丨 〇 Continue to perform calculation procedures for a period of time, that is, control the calculation process to return to 2 times 120 to calculate the next new period. 'The simulation method provided by the present invention (such as the calculation flowchart shown in the second figure) has many advantages: @ (1) In the entire post-exposure baking process simulation, for each individual time period and intermediary time period, In other words, all the reaction constants (] ^ and let ”and the photoacid material diffusion coefficient (DH) can be obtained by calculation. Therefore, a post-exposure baking (p EB) simulation including temperature-time history will be obtained. · 5 (2) In the simulation of the entire post-exposure baking process, for each square, the diffusion coefficient (Dh) of the photoacid material can be obtained through a calculation program. This makes the post-exposure baking process The simulation has a photoacid material diffusion coefficient (Dj.) Based on the protection unit cell concentration as a factor. (3) According to the calculation process provided by the present invention, the protection unit cell concentration in the next period will be calculated before the photoacid concentration. Therefore, The obtained concentration of the protection unit cell can be used in the subsequent calculation of the concentration of the photoacid material. The diffusion coefficient is the coefficient of the diffusion equation of the photoacid material. The above method can be used to accelerate the The calculation procedure has reached a convergence condition. Although printed by the Consumer Standards Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs, the present invention is illustrated above with a better example, but it is not intended to limit the spirit and the inventive entity of the present invention, only to this embodiment. Those skilled in the art should make modifications within the scope and spirit of the present invention that are to be included in the following patent application parks. 15 This paper size is applicable to China Cathay Standard (CNS> Λ4 specification (2.0 × 2W) species of bamboo>
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US6801297B2 (en) | 2002-07-12 | 2004-10-05 | Renesas Technology Corp. | Exposure condition determination system |
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US6801297B2 (en) | 2002-07-12 | 2004-10-05 | Renesas Technology Corp. | Exposure condition determination system |
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