應用最佳化辦法於反向式光罩修正以提升光學微影製程容忍度

Abstract

後光學微影時代，使用 193 nm 光源曝出次波長最小線寬已經遠遠超過古典光學繞射極限，解析度增益技術不斷的被開發出來以滿足光學微影需求。近幾年，光學鄰近修正術結合次解析輔助特徵廣泛應用半導體工程以增加圖形保真度與降低製程變異，使得光學微影得以延續許多世代，延續摩爾定律。不幸的，隨著最小線寬不斷的微縮，光的繞射現象以及空間同調性的影響越來越顯著，圖形保真度對於製程變異也越來越敏感，此現象尤以 k1 不斷的縮小而更加顯著，上述兩種解析度增益技術已經遇到了瓶頸。為了解決微影製程的瓶頸，反向式光罩修正為一有希望的新興解析度增益技術，使用像素化光罩搭配演算法搜尋更大的解空間來曝出更小的最小線寬以及更大的製程容忍度。 在本篇論文中，我提出了與製程參數相關的梯度演算法，像素化光罩最佳化不僅僅只是在理想的製程條件下，製程偏差實際存在於真實的微影製程中，所以將可能發生的製程偏差同時考慮進去。我們的目標是將製程窗口變大，以利於量產。使用此方法輸出的像素化光罩，其顯影影像在理想的製程條件下雖然增加失真，然而此權衡是因為同時將不同製程偏差的顯影影像考慮進去，而使得真實的微影製程得以降低影像失真，我們將可能發生的製程偏差考慮進去，以降低量產後的顯影失真。目標函數的梯度將會被推導，在不同製程偏差下的梯度都能有解析的形式，而且均被使用於更新像素化光罩。更新後的像素化光罩將會自動產生類似光學鄰近修正術的主要圖形以及自動產生和擺放不規則的次解析輔助特徵。結果顯示我們的演算法的確能增加製程窗口。

In post-optical lithography, printing sub-wavelength features is way beyond the Rayleigh diffraction limit and increasing the need of Resolution Enhancement techniques (RETs). In the near past, optical proximity correction (OPC) incorporating sub-resolution assist features (SRAFs) are extensively used in the semiconductor industry to improve the pattern fidelity and reduce the process variations, which pushes the limits of optical lithography for many generations in order to stay on the pace of Moore’s Law. Unfortunately, the diffraction effects and spatial coherence of light become more and more influential as critical dimension still shrinking. Thus pattern fidelity becomes highly sensitive to the process variations in the low k1 regimes. Therefore, such two techniques are of no avail. To overcome the two problems, Inverse lithography (IL) becomes a promising candidate which uses pixelated mask to obtain the more degrees of freedom than previous techniques in solution space. IL calculates the optimal masks by minimizing the designed cost functions incorporating the forward and backward algorithms. Various lithography conditions and requirements can be joined into the cost functions with adequately mathematically modeling. Hence the optimal mask can ensure the most important dual goal of optical lithographers. Recent researches propose many kinds of optimization algorithms, cost function designs, and hardware verifications. In this work, we present a process condition-aware gradient-based optimization approach which optimizes the pixelated mask not only at the perfect process condition but also other process conditions simultaneously. Our goal is to maximize the exposure-defocus (E-D) process window (PW). The images of the optimal masks at the perfect process condition will lose some pattern fidelity as other process conditions are jointly considered. However such tradeoff is in the realities of the situation. Thus balancing the pattern fidelity through the whole working range is the name of the game in our work. The gradients of the cost functions under different process conditions are derived. The gradients will be updated once process condition changing during computer practice. Hence the corrected patterns will be generated and placed automatically. The results show that the process windows are enlarged by our proposed algorithm. The images formed by final optimal masks are degraded at the perfect process condition, but hold acceptable pattern fidelity over the broad working range.