雷射光干涉微影技術之建立及應用於光子能隙結構

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簡政尉(Cheng-Wei Chien) 查詢紙本館藏

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機械工程學系

論文名稱

雷射光干涉微影技術之建立及應用於光子能隙結構
(The study of laser interferometric lithography technique and its application on the fabrication and analysis of the photonic band gap structures)

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摘要(中)

近年來，雷射光干涉技術已漸漸展露出頭角，不論是在光電與半導體產業中的光子能隙 (Photonic band gap, PBG)結構之製作及光阻的直寫亦或材料方面之薄膜上的熱處理與磁性材料上網格點的磁化等，皆有亮眼的表現，也因此雷射光干涉技術在未來應可被廣泛使用。本論文將利用干涉的原理建構出一套雷射光干涉微影系統(Laser interferometric lithography system)。此系統之優點在於不需透過光罩、可輕易透過調變干涉角度得到不同週期之一維干涉條紋。透過搭配旋轉平台於曝光基板處，便能夠透過此系統直接於光阻上建構出二維甚至三維小週期的週期性結構。
由於一般干涉微影數學模型大多不考慮雷射光高斯強度的分佈以及不同干涉角度下所造成曝光能量的衰減對結構尺寸的影響。本論文透過Beer-Lambert定律與干涉光學的相互搭配，並考慮雷射光強度的高斯分佈以及Fresnel反射建立一套干涉微影曝光過程之數學模式，透過此數學模式預測出曝光後光活性化合物濃度的分佈進而推測不同曝光與製程參數的改變對結構特徵尺寸與其外型輪廓之影響。研究結果顯示在靜態曝光的情況下，在整個曝光區域內所得到均勻的結構尺寸大小是不均勻的，而當干涉角大於15度時，雷射光束因不同干涉角度所造成光點變形的效應則不能忽略。當光阻內部會與光線產生反應的物質其吸收係數發生變化時，發現當吸收係數A下降時對光阻的穿透率與顯影後結構線寬有較大的影響。此外當干涉光的對比度不佳時，顯影後，不僅僅造成整體曝光區域內結構尺寸的不均勻，更會使得結構的高寬比(Aspect ratio)下降。
除了研究干涉技術的微影製程外，本論文亦透過干涉配合基板旋轉的曝光方式建構與分析二維週期性結構的幾何形狀與排列方式，發現除了旋轉基板可以變化結構的尺寸與外型外，亦可利用顯影條件的控制達到結構幾何尺寸的改變。此外，透過等強度面的分析，詳細的探討結構排列之晶格(Lattice)、晶格常數(Lattice constant)以及晶軸夾角(axial angle)與基板旋轉角度之間的關係，發現透過此系統可以得到正方形、長方形、圓形與橢圓形的二維週期性結構排列在平行四邊(Parallelogram)、三角(Triangular)與正方(Square)晶格內。不僅如此，本論文亦研究上述結構於不同晶格排列、不同晶格常數以及不同尺寸與形狀之散射體(Scatterers)光子能隙的大小。發現當基板旋轉角度與填充率(Filling factor)固定時，其光子能隙結構的禁止頻率將不隨著干涉角度的改變而發生變化，並討論在不同狀況下其光子能隙與禁帶效率隨基板旋轉角度變動的情形。上述結果將有助於透過干涉微影技術設計特定禁止頻率之光子能隙元件。

摘要(英)

Recently, laser interferometic lithography technique shows its potentials on the fabrication of photonic band gap structures in photoelectric industry, direct writing the interference patterns into photoresist, heat treatment of thin films and magnetization of the dot arrays on the magnetic materials. Therefore, laser interferometric lithography technique has been widely used and investigated. In this study, the principle of interference optics is utilized to build up a laser interferomeric lithography system. The advantages of this system are without using the mask when the exposure process is proceeded and the period of the interference patterns can be easily change by altering the interference angles. The two or three dimensional periodic structures can be constructed in photoresist by the assistance of the rotational stage to expose the photoresist for multi-times.
We utilize a modified interferometric exposure model, enhanced with Beer-Lambert law, to study how some process parameters influence the structural dimensions within the whole exposure area. An experimental apparatus is built to verify the accuracy of this model. The simulation results indicate that when the incident angle is larger than 15°, the effect of the beam deformation can not be neglected. One can not readily obtain periodic structures with the same dimension during static exposure because of the Gaussian distribution of the light intensity. The theoretical results match the experimental ones quite well. The variation of the Dill’s parameter A has a greater influence on the transmittance and the line width when A is decreasing. If a poor contrast fringe is exposed in the photoresist, it will not only cause greater non-uniformity of the structural dimensions, but also a decreased aspect ratio in the structure after the development process.
Besides, an interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular and elliptical scatterers which are arranged in parallelogram, triangular and square lattices (with different lattice constants) can be obtained. The photonic band gaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency of photonic band gap structures with an equal filling factor are very similar regardless of the interference angle. Furthermore, the gap-midgap ratios and the forbidden frequencies vary with the substrate rotational angles are also discussed. The results are very helpful in designing the forbidden frequency when the lattice constant and scatterer shape can be controlled by the interferometric lithographic technique.

關鍵字(中)

★ 干涉微影
★ 光子晶體
★ 光活性化合物

關鍵字(英)

★ photoactive compound
★ photonic crystal
★ interferometric lithography

論文目次

摘要……..…………..……………………………………………………...…...I
Abstract............................................................................................................III
致謝……..…………..…………………………...………………………….....V目錄……..…………..…………………………...…………………………....VI表目錄……..…………..…………………………………………………....VIII圖目錄………………………………………………………………..…….…IX
第一章緒論..………..…………..………………………………………….…1
1.1 研究背景……..……………………………………….……………….…..2
1.2 相關研究………………………………….…………….…………………4
1.2.1 干涉系統於週期性結構的建立與材料加工之應用………………...4
1.2.2 干涉系統穩定性研究……………………………..…….……………6
1.2.3 微影製程曝光與顯影之研究…………………………………………...7
1.3 研究動機與目的……….………………………..………………………...9
1.4 研究方法……………….………………………………………………...10
圖………………………………………………….…………………………..12
第二章理論基礎…………………………………………………………….14
2.1 干涉光學…………………………….…….….…………………..........14
2.2 干涉微影曝光數學模型……………………...…………..……...…….18
2.3 辛普森積分法………...…………………...………………………….. 23
2.4 光子晶體特性計算…………………………..……………………..….26
圖………………………………………………….…………………………..33
第三章系統設備與實驗方法……………………………………………….36
3.1 干涉系統的評估…………………………………………………………36
3.2 干涉系統的架設…………………………………………………………37
3.2.1 防震設備…………………………………………………………….38
3.2.2 雷射光源…………………………………………………………….38
3.2.3 光學元件…………………………………………………………….38
3.2.3.1 擴束器……...………………………………………………….39
3.2.3.2 分光鏡……...………………………………………………….39
3.2.3.3 極化片……...………………………………………………….39
3.2.3.4 衰減片…...…………………………………………………….39
3.2.3.5 空間濾波器……...…………………………………………….40
3.2.3.6 干涉實驗流程…...…………………………………………….41
3.2.4 量測設備…………………………………………………………….41
3.3 試片的準備……………………………………………………………....41
3.3.1 光阻………………………………………………………………….42
3.3.2 去水烘烤…………………………………………………………….44
3.3.3 光阻塗佈…………………………………………………………….44
3.3.4 軟烤………………………………………………………………….45
3.4 曝光顯影與硬烤…………………………………………………………46
3.4.1 曝光顯影……………………………….……………………………46
3.4.2 硬烤……………….…………………………………………………47
3.5 試片結構的觀察…………………………………………………………47
3.5.1 掃瞄式電子顯微鏡…………………….……………………………47
3.5.2 原子力顯微鏡………………………….……………………………47
圖……………………………………………………………………………...51
第四章干涉微影模型與製程參數對結構線寬的影響...…………….…….57
4.1 干涉曝光數學模型…..…………………..……...……………………….57
4.2 實驗與模擬的連結.…………………………...………………...……….60
4.3 雷射光點變形效應……………….……………………...………...…….61
4.4 透過曝光時間的改變來控制結構線寬.……………….……….....…….62
4.5 曝光區域內不同位置穿透率與結構尺寸之研究….…………......…….63
4.6 Dill參數變動所引起結構尺寸的改變..…………………………………64
4.7 對比度對結構的影響..…………………………………...…..………….65
4.8 二維週期性結構受曝光與製程參數之影響………….…..…..…..…….66
4.9 本章結論……………..……..………...………………………………….70
圖表…………………………………………………………………………...71
第五章利用干涉微影技術建構與分析二維光子晶體結構.…………...….98
5.1 散射體外型與尺寸的控制…...………....………...……………………..99
5.2 基板旋轉角度與結構晶格常數之關係.....……...…………......………102
5.3 雷射光干涉微影技術所建構之光子晶體特性分析.……...……..……105
5.3.1 光子晶體特性分析在不同干涉角度與固定散射體大小……...…106
5.3.2 光子晶體能隙與禁帶效率分析……………………….………..…108
5.4 本章結論……………..……….…………………………………...……113
圖表…..……………………………………………………………………...115
第六章總結論…………………………………….………………………..145
參考文獻…………………………………………………………………….148

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2007-7-19

推文