本研究探討穿透式電子顯微鏡在相位影像回復以及空間分辨率改善的問題，論文從電鏡的相位問題著手，文中包含現今幾種相位回復方法的介紹與不同方法間優缺點的比較。本研究利用最大熵解捲法(maximum entropy de-convolution method)來解強度傳遞方程(transport of intensity equation)二次微分方程式，求得TIE方程式解即可回復電子波相位的訊息。我們將這種相位回復的方法應用在半導體製程中多孔隙的低介電材料與pn接面(junction) 二維型態分析。 我們以相位回復的技術為基礎，進一步解決透鏡系統像差修正與試片出口波(exit wave)重構的問題，由於經過像差修正後的出口波非常接近試片實際的結構，因此出口波重建的技術可以視為是一種實空間的直接法。這種實空間的直接法包含了在影像平面利用最大熵解捲法解強度傳遞方程(TIE/MEM)及出口波重構，由於出口波是從影像平面的複數電子波完整的訊息直接重建，從影像到出口波的演算過程中沒有以前的舊方法所存在一些限制性的基本假設性問題。重建的試片出口波在某種程度上去除像差影響，影像可以回復較細微的結構訊息，但是分辨率仍在電鏡訊息極限之下。我們藉由相位外推的方法將分辨率外推，使得影像分辨率超越信息極限的，利用複數形式的最大熵法並結合Gerchberg-Saxton演算法的概念，將相位訊息外推到較高的頻率空間，可得到更佳的分辨率。

This thesis examines problems in phase retrieval and resolution improvement in transmission electron microscopy. It begins with the study of phase and the phase problems in microscopy. In this context a number of methods of phase retrieval are introduced and evaluated. The maximum entropy de-convolution method (MEM) is employed to solve the transport of intensity equation (TIE) for phase retrieval problems. . The theoretical basis of this method is presented along with its potential applications in the quantitative phase analysis of porous low-k dielectric materials and of p-n junction profiles in advanced IC devices using a transmission electron microscope. Using the phase retrieval method as an essential tool, the thesis continues with a study of aberration corrected and exit wave reconstructed problems. As the aberration corrected exit wave is closely related to the structure of object this technique of exit wave reconstruction can be referred as a “direct method” in real space. The direct method in real space involves the use of a novel method to retrieve the phase in the image plane using Transport of Intensity Equation/Maximum Entropy Method (TIE/MEM) and exit wave reconstruction by self-consistent propagation. Since the exit wave is restored from the complex signal in the image planes, no image model between the exit wave and image is assumed. Finally the structural information in the reconstructed exit wave is then further extended by a “complex” maximum entropy method as a direct method in reciprocal space to extrapolate the phase to higher frequencies.

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