本論文對數位微反射鏡 (Digital Micro-mirror Device, DMD) 的成像式無光罩曝光系統提出了三種光學鄰近效應修正方法 (Optical Proximity Correction, OPC)，分別為：輪廓片段擾動法、基因演算修正法、與梯度式修正法。研究方法是先建立曝光系統的數值模擬，並優化曝光時DMD的光罩圖形，以消除製作出的光阻圖形與原先設計的誤差。
光阻圖形的誤差通常存在於轉角部分，輪廓片段擾動法與基因演算修正法是針對轉角圖形進行優化，並將優化後的光罩圖形取代原本的轉角圖形。輪廓片段擾動法將轉角圖型的輪廓切割分段，這些輪廓片段往內側或往外側的移動使轉角圖形產生額外凸出或凹陷。計算片段移動後的光阻圖形並計算誤差，反覆測試直到獲得具有最小誤差的光罩圖形。
基因演算法根據模擬光阻圖形與原始目標之間的誤差作為適性方程式，並模擬生物在演化的過程中篩選較佳的個體。在演算過程中每個世代的光罩圖形不斷進行繁衍，越新世代所得到的適性質會越小，及光阻圖形誤差越小，最終產出優化後的光罩圖形。
梯度式修正法將曝光系統與光阻圖形誤差建立成為可微分的數學方程式，光罩圖形中的所有像素皆為方程式中的未知數。使用梯度下降法計算此數學式中光阻圖形誤差最小的解，做優化後的光罩圖形。
本論文對所提出的OPC方法分別作數值計算模擬與實驗操作，成功在數位微反射鏡之無光罩曝光系統下，製作出更加符合原始目標的光阻圖形，提升光阻製程的圖形準確度。

This paper proposes three optical proximity correction (OPC) methods for an imaging maskless lithography system based on Digital Micro-mirror Device (DMD). They are contour-segment perturbation method, genetic-algorithms correction method, and gradient-based correction method. The research involves establishing a numerical simulation of the exposure system and optimizing the DMD mask pattern layout to eliminate discrepancies between the fabricated photoresist patterns and the original design.
Errors in the photoresist patterns typically occur at the corners of the patterns. The Contour-Fragment Perturbation method and the Genetic-Algorithms correction method are aimed at optimizing corner patterns by replacing the original corner patterns with optimized corner patterns. The Contour-Fragment Perturbation method cuts the corner shape’s outline into fragments, and by moving these fragments inward or outward, additional protrusions or recessions are introduced to the corner shape. After calculating the photoresist patterns resulting from the fragment movements and the patterns errors, the process is iterated until the mask pattern with the minimal error is achieved.
The Genetic-Algorithms correction method uses the error between the simulated photoresist patterns and the original target as the fitness function, simulating the selection of better individuals during the evolutionary process. In the algorithm, each generation of mask patterns continuously evolves, with the fitness value decreasing and the error in the photoresist pattern diminishing in newer generations. This process ultimately yields an optimized mask pattern.
The Gradient-Based correction method models the exposure system and the errors in the photoresist pattern as differentiable mathematical equations, with all pixels in the mask pattern being the unknown variables in these equations. The gradient descent method is used to compute the solution that minimizes the photoresist pattern error in this equation, resulting in an optimized mask pattern.
This paper conducts numerical simulations and experimental operations on the proposed OPC methods, successfully fabricating photoresist patterns more closely aligned with the original target in a DMD maskless lithography system, thereby improving the pattern accuracy in the photoresist process.

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