基於全局敏感度分析之次微米高深寬結構關鍵尺寸光學量測系統設計最佳化研究

Abstract

隨著電晶體的微型化和先進封裝技術的發展，三維封裝技術已成為異質整合中的關鍵架構。然而，隨著製程中結構類型的改變以及關鍵尺寸(Critical Dimension, CD)的縮小，傳統光學關鍵尺寸量測技術面臨嚴峻挑戰。這些挑戰包括結構的深寬比增加以及結構的複雜化，導致反向解析關鍵尺寸的難度大增，對產品良率的維持產生了重大影響。因此，如何有效量測這些複雜結構尺寸並實際應用於線上關鍵尺寸量測技術，成為推進先進封裝製程發展的關鍵。 本篇碩士論文旨在開發一套最佳化光學關鍵尺寸量測系統的演算法，透過該演算法制定光學系統照明條件參數及量測策略，以提升次微米級高深寬結構關鍵尺寸量測的準確性。針對此目標，我們在研究過程中深入探討了光學響應的物理背景，並藉由有限時域差分法建立相應的物理和電磁模擬模型，從而理解真實情境中電磁波與結構幾何的交互作用及其響應特性。隨後，我們設計了基於全局敏感度分析（Global sensitivity analysis）和實驗設計（Experimental design）的最佳化演算法，利用該演算法揭示光學系統在何種條件下能達到最高的關鍵尺寸量測能力。同時，我們也通過全局敏感度分析方法揭示了關鍵尺寸間的交互作用對光學響應的影響程度，從而制定出合理且有效的量測策略。 研究結果顯示，將本研究開發的敏感度分析和量測能力最佳化演算法應用於光譜式反射儀時，我們能夠量化量測條件的差異對光學系統量測能力的影響，並推斷出光譜式反射儀的最佳量測條件。實際量測結果驗證了這些最佳條件對提升量測準確度的有效性，並且在最佳量測條件下與掃描式電子顯微鏡相比，光譜式反射儀對次微米級高深寬比結構之深度、線寬、側壁倾角量測誤差皆小於2%。此外，本研究還將自行開發的演算法應用於高光譜散射儀上，展示其對多種量測條件最佳化分析的能力。最佳化分析結果揭示了量測條件對量測能力的影響趨勢，為次微米級高深寬結構的關鍵尺寸量測提供了實用的策略建議。這些策略不僅可以提高光學量測技術的準確性，也為未來技術的發展提供了可操作的指導。

With the miniaturization of transistors and the development of advanced packaging technologies, three-dimensional (3D) packaging has become a critical architecture in heterogeneous integration. However, as the types of structures in the manufacturing process change and the critical dimensions (CD) shrink, traditional optical critical dimension (OCD) measurement techniques face severe challenges. These challenges include increased structure aspect ratios and complexity, making it significantly more difficult to reverse-engineer the CDs and maintain product yield. Therefore, effectively measuring these complex structure dimensions and applying them in online CD measurement techniques is crucial for advancing the development of advanced packaging processes. This master's thesis aims to develop an algorithm to optimize the measurement capabilities of an OCD measurement system. Through this innovative algorithm, we establish illumination conditions and measurement strategies for the optical system to enhance the accuracy of measuring CDs of submicron high aspect ratio structures. To achieve this goal, we deeply explore the physical background of optical responses and utilize finite-difference time-domain to build corresponding physical and electromagnetic simulation models to understand electromagnetic waves' interactions and response characteristics with structural geometries in real-world scenarios. Subsequently, we develop an optimization algorithm based on global sensitivity analysis (GSA) and experimental design to reveal under which conditions the system achieves the highest CD measurement capabilities. Additionally, we use GSA to reveal the impact of interactions between CDs on optical responses, thereby formulating effective measurement strategies. The research results show that applying the sensitivity analysis and measurement capability optimization algorithm developed in this study to a spectral reflectometry allows us to quantify the impact of different measurement conditions on the measurement capabilities of the optical system and deduce the optimal measurement conditions for the reflectometry. Actual measurement results validate the effectiveness of these optimal conditions in improving measurement accuracy. Under the optimal conditions, compared with scanning electron microscopes, the depth, spacing, and side wall angle measurement bias of the spectral reflectometry are less than 2 %. Furthermore, this study also applies the self-developed algorithm to a hyperspectral scatterometry, demonstrating its ability to optimize analysis under various measurement conditions. The optimization analysis results reveal trends in the impact of measurement conditions on measurement capabilities, providing practical strategies for measuring the CDs of submicron high aspect ratio structures. These strategies not only improve the accuracy of optical measurement technology but also provide actionable guidance for the development of future technologies.