Process Variation Aware Inverse Mask Optimization in Photolithography
|摘要:||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。
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.
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