- 學位論文
靜電透鏡模擬與分析並應用於次世代電子束微影
Simulation and Analysis of Electrostatic Lens and Application to Next Generation Electron Beam Direct-write Lithography
摘要
對於22奈米世代之IC製造技術，多重電子束微影術被公認為極具潛力的發展中技術之一，利用多束電子束同時運作可大量增加系統之產能；在此類系統中，微型靜電場透鏡常被大量使用，系統之成像品質則受透鏡系統設計優劣所影響，然而目前市售之電子光學系統設計軟體不僅量少且相當昂貴。此論文旨在開發一適用二維與三維靜電透鏡模擬與分析之環境，並將之應用於次世代之多電子束微影系統設計上。此模擬軟體中之靜電場計算使用COMSOL Multiphysics所提供之有限元素分析法來完成，而電子路徑與成像分析則在MATLAB環境下建構。電子路徑部分可模擬分為基於高斯方程式之理想路徑與基於勞倫茲方程式之真實路徑，成像分析部分則可計算幾何相差與色散相差。除了上述傳統透鏡分析功能外，針對聚焦系統所作之最小聚焦點的找尋與分析功能也被成功建置；並藉由MATLAB強大之內建功能程式，此模擬軟體之分析功能將有高度之擴充性與彈性。論文末尾章節介紹發展中之多電子束直寫微影系統——MPML2，並將此軟體應用於其初代靜電透鏡系統之設計上。
並列摘要
Multiple Electron beam lithography is one of the promising technologies for 22nm-node integrated circuit (IC) fabrications. For the purpose of improving system throughput, large amount of beams should be driven at one time, and miniature electrostatic elements are widely utilized in these systems. Electrostatic lens governs the imaging properties of the electron optical systems (EOS), while tools for EOS design or analysis are rare and expensive. In this thesis, a simulator capable of 2D and 3D electrostatic lens simulation is implemented for the application to the next generation e-beam direct-write system design. In this simulator, lens field is evaluated via finite element method (FEM) with the core of COMSOL Multiphysics, while the other parts are developed under MATLAB environment. Electron trajectories governed by Lorentz’s equation can be calculated. Some problems rising from the numerical computation are dealt with and solved, so that acceptable accuracy is obtained. The primary geometrical and chromatic aberrations are evaluated for rotationally symmetrical lenses. Besides the conventional aberration analysis of e-beam systems, minimum spot size evaluation is also implemented. With the plentiful and powerful functions provided by MATLAB, this simulator becomes highly flexible and expandable. Finally, this simulator is applied to e-beam direct-write system design and analysis for preliminary lens design of MPML2.