反向式光罩與光源合成於光學微影解析度之提升

Abstract

隨著互補式金屬氧化物半導體(CMOS)朝著20奈米的節點推進，許多已被提出的解析度增益技術(Resolution Enhancement Technique，RET)有著不同程度的成功應用，其中包括光學鄰近修正術(Optical Proximity Correction，OPC)、浸潤式微影術(Immersion Lithography)、兩次圖案技術(Double Patterning) 、反向式微影術(Inverse Lithography，IL)以及光源光罩最佳化(Source and Mask Optimization，SMO)，然而在眾多RET技術中如何做選擇乃須審慎考量成本與圖形保真度(Pattern Fidelity)之間的平衡，因此本論文將目標著眼於利用反向式微影技術最佳化光罩(第三章與第四章)、光源最佳化用於自由型式光源之設計(第五章)以及產業接受度高的光源與光罩最佳化(第六章)於深次波長解析度增益之提升。 本論文的第一章概括介紹了現今微影技術的相關發展，其中包含目前主流技術與下一世代的候選技術，根據文中所引用文獻的調查結果使用反向式微影技術所優化的光罩以及光源與光罩最佳化設計在大量生產製造(High Value Manufacturing，HVM)上較其他下一世代微影技術更具成本優勢，第二章主要為探討以及分析在光學微影技術之影像形成的原理機制，並同時推導與歸納本論文所需的公式與數值方法，本文以波動光學的角度再次推導了 Abbe 與 Hopkins 兩種部分同調成像的影像公式。 在本論文的第三章提出了以波前為主像素翻轉(Wavefront-Based Pixel Inversion) 的反向式演算法在標準OPC流程之前快速計算出以模型為主的次解析輔助特徵(Model-Based Sub-Resolution Assist Features，MB-SRAFs)，另外藉由搭配圖形簡化的技術可使得經由反向式計算所產生的初步光罩圖形順利銜接後的OPC流程，結果顯示搭配所提出之反向式光罩修正流程可改善22.34%的邊緣配置誤差(Edge Placement Error，EPE)，而反應影像對比好壞的參數 – 常態化的影像指數斜率(Normalized Image Log Slop，NILS)僅變差了1.93%，然而使用反向式微影技術成敗與否乃取決於其價值方程式(Cost Function)的設計優劣，但是如何設計價值方程式以及其中的訣竅仍鮮少被討論，因此在第四章調查了兩個廣泛被使用的價值方程式其為光學影像以及光阻影像，另外亦設計了影像對比度的價值方程式並進行研究，最後發現同時搭配使用多個價值方程式情況下，設定較大係數於光阻影像價值方程式並搭配較小係數之光學影像或影像對比度的價值方程式可得到較好的修正光罩與成像結果。 在光源修正的部分，一般用來描述光阻化學反應的Sigmoid函數轉換使得光阻影像為一光學影像之非線性函數形式，如此便使得光阻影像在光源最佳化與光源光罩最佳化的使用受限，因此在第五章提出了一個利用結合兩個評估等高曲線影像優劣之二次價值方程式的方法近似Sigmoid函數轉換所模擬之光阻影像價值方程式進而可達到快速收斂之目的，此外本章使用了共軛方向梯度演算法使得疊帶次數在少於光源變數個數的情況下即可收斂，其結果與利用Sigmoid函數所得之最佳化光源極為相似，而使用本論文所提之方法可提升100倍以上的速度且改善了部分光罩圖形的製程窗口(Process Window)。 此外由於近來自由型式光源的問世，除了圖形解析度更進一步被提升外亦降低了光罩的複雜性進而減少了製程失敗的風險，因此接續第五章的研究，第六章提出了利用事先所儲存之不同光罩圖形結構的最佳化光源進行線性疊加以求得整體最佳化之光源的辦法，文中證明了用於線性疊加之光源所需係數可由Hopkins公式以及二次方程求得其解析解，相較於使用最佳調整的環形光源所修正之光罩，利用本文提出之方法所合成的光源搭配以模型為主的OPC修正可改善40%以上的邊緣配置誤差、提升50%以上的聚焦深度以及80%以上的製程窗口面積。

As CMOS manufacturing processes push towards the 20 nm node, many resolution enhancement techniques (RET) have been proposed and sometimes applied with varying degrees of success. These include the optical proximity correction (OPC), the immersion lithography, double patterning techniques, inverse lithography (IL) methods, and source and mask optimization (SMO) approaches. The selection among available RET options depends on a careful balance between manufacturing costs and pattern fidelity. As a result, this dissertation targets on the mask optimization (MO) using IL algorithms (Chapters 3 and 4), source optimization (SO) in the free form source design (Chapter 5), and industry friendly SMO (Chapter 6) for deep sub-wavelength resolution enhancement. The overall background of lithography is introduced in Chapter 1. The literatures show that IL-based masks and SMO have more benefit for saving the cost in the high volume manufacturing (HVM) than other RETs for the next generation lithography. Subsequently, the foundation of lithography image formations and numerical methods are derived and studied in Chapter 2. The partially coherent image formulas including the Abbe method and Hopkins approach are re-derived by applying wave optics. In Chapter 3, model-based sub-resolution assist features (SRAFs) can be quickly generated by using a wavefront-based pixel inversion IL algorithm in the pre-OPC flow and simplified to Manhattan shapes for flexibly applied to the succeeding OPC. It shows that average edge placement error (EPE) improvements of the poly and contact masks are about 22.34% with a 1.93% decrease in NILS. However, the success of IL relies highly on customized cost functions whose design and know-how have rarely been discussed. Chapter 4 investigates the IL patterning impacts of most commonly used objective functions, which are the resist and aerial images, and also presents a derivation for the aerial image contrast. The results show that a cost function composed of a dominant resist-image component and a minor aerial-image or image-contrast component can achieve a good mask correction and contour targets when using IL patterning. In terms of SO, the conventional approach for the resist imagewhich involves a sigmoid transformation of the aerial image results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous SMO is therefore limited. In Chapter 5, a linear combination of two quadratic line-contour objectives is presented to approximate the resist image effect for fast convergence. A conjugate gradient method is employed to assure the convergence within the number of iterations less than that of source variables. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the four cases studied. Furthermore, the availability of freeform sources permits the increase of pattern fidelity and relaxes mask complexities with minimal insertion risks to the current manufacturing flow. Therefore, as an extended work of Chapter 5, Chapter 6 presents a rigorous source synthesis algorithm via linear superposition of optimal sources for pre-selected patterns. The analytical solutions are made possible by using Hopkins formulation and quadratic programming. Comparing to that using an optimal annular source in MO, a synthesized source with the model-based OPC shows more than 40%, 50%, and 80% improvements in EPEs, depth of focuses (DoFs), and process windows, respectively.