以廣義高斯常數使用於深紫外光學微影之成像與照明系統設計

Abstract

此研究的主要目的為開發及系統化極紫外光波段之光刻機之成像及照明系統的設計。光刻為一系列頗複雜的流程的組合。其中，最為關鍵的部分之一為曝光這一步驟。曝光機的成像品質，於其成品的製程密度與解析度甚至於此製成的生產效率中間，存在直接的影響與關係。然而，曝光機之光學系統特性，及其參數之間，存在著許多複雜且繁瑣之關係，導致於此光學系統不易分系，也不易設計。因此，此研究最為核心的目的，為研究及開發某一系統化之分析方法，以達到簡化此光學系統之設計之目的。此研究核心之關鍵，為將廣義高斯常數應用於光刻機之分析及設計上。通過廣義高斯常數，眾多複雜且繁瑣之光學特性及光學系統之間之聯繫能以之表達及簡化，而將所有關係結合並簡化後，從中所導出之數學關係式可用於與商用光學設計軟體之結合，以達到幫助分析及設計簡化。 原理上，廣義高斯常數與光學分析中常用之 ABCD 矩陣極為相似，唯一最大不同為當以 ABCD 矩陣進行光學系統分析時，計算其矩陣及將其展開時，其難度及複雜性與其光學系統中光學元件之數量呈指數增長，因此，不適用於較為複雜之光學系統分析。而相較於 ABCD 矩陣，廣義高斯常數適用於表達及分析由多數光學系統組合所形成之相對複雜之光學系統，而其又可將之分解成更小之光學系統看待。此廣義高斯常數之特性，可隨心將多數光學系統視為一總光學系統，或是將一光學系統拆開以多數小光學系統看待，可適用於分析或推導個別光學元件之參數及整體光學系統特性之關係。 廣義高斯常數之最初用途為變焦光學系統之分析及設計，其中通常有複數多件光學元件所組成之組合，及其為配合不同使用狀況而改變位置及光學特性。而將之強大分析能力應用於極紫外光刻機之分析及設計為此研究之重要關鍵之一。此研究之成果之一為某一 0.4 數值孔徑之極紫外光刻機之反射式成像光學系統之分析與設計，以及其照明光學系統之分析與設計。設計過程中所用之光學設計軟體中包含市售光學設計軟體，及一簡單 Monte Carlo 優化演算法將廣義高斯常數與市售光學設計程式結合使用以達成協助光學設計之目的。

This study aims to develop a systematic design procedure for the EUV lithography (EUVL) tools, for both the projection part and the illumination part. The optical lithography is a complex process encompasses many stages. Wafer preparation, resist coating, pre-exposure bake, exposure, post-exposure bake, etching, and metrology. Through analysis using generalized Gaussian constants (GGC), relationships between optical properties and requirements can be obtained, and can be used to help ensuring that optical system properties required for the tool are upheld during the design process. The GGC is closely related to the ABCD matrix method, however over and above, it is also useful in analyzing the whole system as a combination of smaller subsystems, which can then again be broken down into even smaller subsystems to any degree desired. This abstraction of raw lens data into optical properties of the sub-systems at arbitrary level of abstraction is a great help in analyzing the inter-subsystem relations, which are easily lost in the raw expansion of the ABCD matrix of even a slightly larger optical system. In fact, the development of GGC was initially intended for purpose of zoom lens design and analysis, where inside the complex optical system the optical elements are constantly moving in relation to one another. This analytic power lends itself well to optics design of other applications, such as this case of EUVL projection systems. As verification of the design method, this study demonstrates an eight mirror 0.4 NA projector, and its illuminator. In addition to the use of commercial design software, a simple Monte Carlo random walk algorithm is also deviced for the purpose of integrating the use of GGC into existing design software.