二維完美匹配層應用於多重解析法之光學微影模擬

Abstract

隨著光微影技術向極限推進時，極化效應正變得更加明顯[20]。由於橫向電波和橫向磁波之間結合的不同造成在圖罩(photomask)表面的散射及在晶圓的極化使得成像品質降低[16]。因此我們需要以馬克斯威爾方程式快速且精確的計算晶圓裡的成像。

著眼此點，我們企圖將完美匹配層(PML)應用在多重解析法。於是我們先找出一對Battle-Lemarie系的尺度和小波函數。在文獻中[1][2]，使用這個可以當作完整基底函數的集合被稱為多重解析度分析。因此我們表明，將多重解析法應用於離散馬克斯威爾方程式的新計畫稱為MRTD。在此篇論文中，為了簡化我們將只使用尺度函數來開發模擬程式(S-MRTD)。除此之外我們將使用此程式搭配完美吸收邊界層(PML)來模擬開放的二維相移圖罩結構的繞射電磁分析。

Polarization effects are becoming more pronounced [20] as optical lithography technique is pushed towards its limit. Photomask topography scattering, and wafer polarization effects caused by differences in coupling between transverse electric and transverse magnetic waves degrade image quality.[16] Therefore we need to fast and rigorous calculation Latent images in wafer by Maxwell’s equations.

To solve this problem,we attempt to apply’’ Perectly Matched Layer’’ (PML) to ‘’Multiresolution Time-Domain Method’’. Thus we find a pair of cubic spline Battle-Lemarie scaling and wavelet functions. In literature[1][2],the use of these functions as a complete set of basis functions is called multiresolution analysis. Thus we show that the application of multiresolution analysis in the method of moments for the discretization of Maxwell’s equations leads to new multiresolution time-domain (MRTD) schemes. In this paper, for simplicity, we will use the scaling function scheme(S-MRTD) only to develop simulation program. In addition, this program is applied to the rigorous simulation of diffraction from two-dimension open phase-shifting mask structure. Open boundaries are simulated by the use of a novel formulation of the perfect matching layer(PML) absorber.